Hindawi Publishing CorporationThe Scientific World JournalVolume 2013 Article ID 195763 11 pageshttpdxdoiorg1011552013195763

Research ArticlePressure Losses across Multiple Fittings in Ventilation Ducts

Z T Ai and C M Mak

Department of Building Services Engineering The Hong Kong Polytechnic University Hong Kong

Correspondence should be addressed to C M Mak becmmakpolyueduhk

Received 1 September 2013 Accepted 8 October 2013

Academic Editors J Niu and G M Tashtoush

Copyright copy 2013 Z T Ai and C M Mak This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The accurate prediction of pressure losses across in-duct fittings is of significance in relation to the accurate sizing and good energyefficiency of air-delivery systems Current design guides provide design methods and data for the prediction of pressure losses onlyfor a single and isolated fitting This study presents an investigation of pressure losses across multiple interactive in-duct fittingsin a ventilation duct A laboratory measurement of pressure losses across one fitting and multiple fittings in a ventilation duct iscarried out The pressure loss across multiple interactive fittings is lower than that across multiple similar individual fittings whilethe percentage decrease is dependent on the configuration and combination of the fittingsThis implies that the pressure loss acrossmultiple closely mounted fittings calculated by summing the pressure losses across individual fittings as provided in the ASHRAEhandbook and the CIBSE guide is overpredicted The numerical prediction of the pressure losses across multiple fittings using thelarge-eddy simulation (LES) model shows good agreement with the measured data suggesting that this model is a useful tool inductwork design and can help to save experimental resources and improve experimental accuracy and reliability

1 Introduction

In air-delivery ductworks of HVAC systems pressure lossesacross duct fittings such as dampers sensors bends transi-tion pieces duct corners branches and even splitter attenu-ators are important in counteracting the pressure differencecreated by fans Accurately predicting pressure losses acrossduct fittings at the design stage is thus crucially importantto proper duct sizing and fan selection which could finallyresult in great economic benefits in terms of both the initialinvestment cost and the operational cost of duct systems

The commonly adopted data of pressure losses acrossHVAC duct fittings are those provided in the well-knowndesign guides such as the ASHRAE handbook [1] the CIBSEguide [2] and the handbook by Idelchik [3] These datawere summarized from many experimental works most ofwhich were conducted based on ASHRAE Standard 120P[4] However in terms of scope the data are limited to thetypes of duct fittings the range of duct sizes and the rangeof mean duct velocities In addition the accuracy of theexperimentally obtained data available in these handbooksand guide has been questioned by a number of investigators[5ndash11] One possible reason for their inaccuracy is that the

measurements were conducted on single isolated duct fit-tings without consideration of the influence of the interactionof other fittings [7] In practice there are commonly multiplefittings in a HVAC ductwork and very frequently someof these are relatively close to each other Rahmeyer [12]experimentally studied the effect of the interaction betweenbends and found that the pressure loss across two closelycoupled bends is related to their distance This findingimplies that the traditional calculation method which sumspressure losses across each individual duct bend couldsometimes be inaccurate Later Atkin and Shao [7] appliedcomputational fluid dynamics (CFD) modeling to analyzethe effects of the separation and orientation of two closelyconnected bends on total pressure loss They found that ata separation distance of 8 to 10 hydraulic diameters thepressure drop across the two bends is highly dependenton their relative orientation Unfortunately it is not knownwhether these findings from bends can be applied to otherfittings especially in-duct fittings Thus more studies arerequired

Another concern is that obvious differences are foundin part of the pressure loss data between the ASHRAEhandbook and the CIBSE guide [6] One factor that may

2 The Scientific World Journal

possibly contribute to these discrepancies [6] is that due tothe lack of understanding on airflow patterns at duct fittingspressure sensors are occasionally located at inappropriatesections such as disturbance sections which could cause largemeasurement errors However since the in-duct airflow pat-tern is strongly associated with the duct configuration meanduct velocity and local aerodynamic configuration of fittingsit is difficult and time consuming to find the appropriatelocations for placing pressure sensors before every test Insuch a condition a numerical method should be helpfulin terms of saving experimental investment and time Evenin an experimental way it is more reliable and economicalto know the flow patterns before a real test is set up andconducted As a numericalmethod CFDhas been sufficientlyverified and validated as a method of predicting fluid flowShao and Riffat [6 8] studied the possibility and accuracyof using the CFD method to predict the pressure loss factorand in turn determine pressure losses across duct bendsTheyevaluated the effect of a set of computational parameters onthe accuracy of numerical results Their numerical resultsare supported by the experiments of Gan and Riffat [13]In addition the CFD method has been used to predict thepressure loss coefficient of many other duct fittings suchas damper orifice transition [9ndash11 14] and junction [15]fittings in HVAC ductworks as well as to conduct other duct-related studies (eg air leakage) [16] Without exceptionthese previous numerical simulations used the ReynoldsAveraged Navier-Stokes (RANS) method [17ndash21] specificallythe steady standard 119896-120576 turbulence model However thismodel may be not accurate and reliable enough to predictthe flow field inside a duct with multiple fittings wherethe airflow is more strained and swirling as well as highlyfluctuating As an alternative CFDmodel the advanced large-eddy simulation (LES) model is well known for its accuracyin predicting airflow in the building-related field [22 23]The LES model which resolves large turbulent eddies andmodels small eddies has the capacity to reproduce tran-sient turbulent fluctuations and handle flow intermittencyalthough it consumes more numerical cost In this studythe accuracy and reliability of the LES turbulence model inpredicting pressure losses across multiple in-duct fittings areevaluated

The specific problems that motivated this study arethe inaccuracy of the available data in the current guidesand the lack of a predictive method for pressure lossesacross multiple in-duct fittings The purposes of this studytherefore are to examine the pressure losses across multiplein-duct fittings and to evaluate the accuracy and reliabilityof a predictive method The effect of the interaction offittings on the total pressure loss across multiple fittingsis analyzed by experimental tests The predictive methodnamely LES modeling is then evaluated by comparing itwith tested data It is expected that this study will reveal thepressure losses across multiple in-duct fittings and providedesigners with a predictive method that can be used eitherindependently as a design tool or to assist experimentaltesting

2 Conceptual Models

There are two types of pressure loss in duct systems namelyfriction loss and dynamic loss These losses are derivedfrom different mechanisms and are therefore calculated bydifferent methods [1]

Friction loss is due to fluid viscosity and results fromthe momentum exchange between molecules or betweenadjacent fluid layers moving at different velocities It occursalong the entire length of a duct Friction losses in fluidductworks can be calculated by the Darcy equation

Δ119875119891 =119891119871

119863ℎ

times1205881198802

2 (1)

where Δ119875119891 is a friction loss 119891 a dimensionless frictionfactor 119871 duct length119863ℎ hydraulic diameter119880 area-averagedstreamwise velocity and 120588 fluid density Friction factor 119891 isdetermined by the Colebrook equation

1

radic119891= minus2 log(

119890

37119863ℎ

+251

Reradic119891) (2)

where 119890 is the absolute roughness factor of a material and Reis the Reynolds number computed from

Re =119863ℎ119880

] (3)

where ] is kinematic viscosity The hydraulic diameter 119863ℎis defined as 4119860119875 where 119860 is the duct area and 119875 is theperimeter of the cross-section

Dynamic losses in fittings result from flow disturbancescaused by duct fittings that change the airflow direction orflow path area and can be calculated by

Δ119875119889 = 119862 times1205881198802

2 (4)

where 119862 is the dimensionless local loss coefficient (alsocalled 119896 factor) which is determined by the local dynamiccharacteristics

3 Experimental Method and Simplification

This experiment was a part of our previous test on flow noisecaused by in-duct elements [24] The experimental system isshown in Figure 1 Air flow was provided by a centrifugal fandriven by a variable speed motor The fan was enclosed ina 122 times 122 times 122m3 enclosure The 01 times 01m2 test ductwas made of steel The total length of the duct was 575m inwhich counted from the air flow inlet the first fitting (p1) waslocated 175m from the duct inlet section and the third fitting(p3)was located 1m from the duct outletThese upstream anddownstream lengths [6] were generally sufficient to ensurethat the test of the first and third fittings were not affectedby the inlet and outlet of the duct respectively The inlet andoutlet of the experimental system were placed on the outsideso as to eliminate the effect of relative pressure difference

As shown in Figure 2 flat plates were used to generallyrepresent the in-duct fittings in HVAC ductworks Here

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Table 1 Fifteen fitting configurations tested in this study

Case Configuration of fitting(s) Mean flow velocities(ms)

1r

r = 0025m at p110 15 20 25 30

2r

r = 005m at p110 14 18 22 26

3 r

r = 0075m at p110 12 14 16 18

4

r = 0025m at p1r2r2 15 20 25 30 35

5r = 005m at p1

r2r210 15 20 25 30

6r = 0075m at p1

r2r210 12 14 16 18

7r = 0025m at p1

r

r = 0025m at p2r 10 15 20 25 30

8

r = 005m at p2r = 0025m at p1r r

10 14 18 22 26

9

r = 0075m at p2r = 0025m at p1r r

10 12 14 16 18

10r r

r = 005m at p2r = 005m at p1

10 13 16 19 22

11r = 0075m at p2

r rr = 005m at p1

10 12 14 16 18

12r = 0075m at p1 r = 0075m at p2

r r10 11 12 13 14

4 The Scientific World Journal

Table 1 Continued

Case Configuration of fitting(s) Mean flow velocities(ms)

13

r = 005m at p1 r = 005m at p2r2r2 r2r2

10 14 18 22 26

14r = 005m at p1

r2r2

r = 005m at p2r2r2

r = 005m at p3r2r2 10 13 16 19 22

15r = 005m at p1

r

r = 005m at p2r

r = 005m at p3r

10 12 14 16 18

the control variable was the obstructed ratio of the fittingarea to the cross-sectional area of the duct The plates weremade from 1mm thick steel plate and they were fixed tothe adjoining flanges of the test duct The gap was sealedwith compressed foam rubber As shown in Table 1 15configurations were tested In Cases 1ndash6 only a single fittingwas inserted into position p1 In Cases 7ndash13 two fittings wereinserted at two different positions (p1 and p2) and in Cases14-15 three fittings were inserted at three different positions(p1 p2 and p3)

The velocity profile in the empty test duct was measuredto make sure that the flow could be symmetrically developedinside the duct A pitot tube was used to sample the dynamicpressure at specified points in the duct cross-section Basedon the measurements obtained using this empty duct arelationship between the mean duct velocity (119910) and thevelocity measured at the center of the duct (119909) was developed(119910 = 09639119909 minus 03289 (119877

2= 09997)) and this was used

to calibrate the mean duct velocity in later tests using themeasured center velocity The mean airflow velocities testedfor each case are listed in Table 1

The static pressure losses across the fittings were mea-sured using two piezometric rings placed at positions p1 p2and p3 (Figure 1) Each ring consisted of four static pressuretappings one in each duct face The downstream ring wassufficiently far away (five times the duct dimensions) from thetest fitting to ensure that full static pressure recovery couldtake place in the wake of the flow obstructions under test

4 Numerical Modeling

This section briefly discusses the numerical method usedby LES modeling and introduces the test cases selected toevaluate it

41 Governing Equations of LES The governing equationsused for large eddies can be obtained by filtering the time-dependent Navier-Stokes equations Eddies whose scales aresmaller than the filtering width or grid spacing adopted in thecomputations are effectively removed by the filtering process

Inlet

Outlet

Pitot

125 m 1 m 2 m575 m

ΔPS3ΔPS2ΔPS1

05 m

02 m05 m02 m 02 m

05 m05 m

p1 p2 p3

Figure 1 A schematic diagram of the experimental system (p1 p2and p3 are the positions where the first second and third fittingsare inserted respectively Δ1198751198781 Δ1198751198782 and Δ1198751198783 represent the staticpressure loss across the first second and third fittings resp)

Then the resulting equations only govern the dynamics oflarge eddies

In this study the filtering operation provided by thefinite volume discretization method as described in [25] isemployed

120593 (119909) =1

119881int

119881

0120593 (1199091015840) 1198891199091015840 1199091015840isin 119881 (5)

where 120593 (119909) represents a filtered variable and119881 the volume ofa computational control cell The filter function 119866(119909 119909

1015840) is

119866(119909 1199091015840) =

1

119881 1199091015840isin 119881 or 119866(119909 119909

1015840) = 0 119909

1015840notin 119881

(6)

The Scientific World Journal 5

01 m

01 m

r

(a)

01 m

01 m

r2 r2

(b)

Figure 2 Cross-section of the duct with two types of flat-plate fittings (shaded area) (a) Centrally placed fittings 119903 = 0025m 005m0075m (b) The geometries consisted of plates protruding symmetrically from both sides of the duct leaving a central vertical strip of theduct open later called a centrally opened fitting 119903 = 0025m 005m 0075m

In this study the governing equations of LES for incom-pressible flows were obtained by filtering the Navier-Stokesequations

120597119906119894

120597119909119894

= 0

120597

120597119905(120588119906119894) +

120597

120597119909119895

(120588119906119894 119906119895) =120597

120597119909119895

(120590119894119895) minus120597119901

120597119909119894

minus120597120591119894119895

120597119909119895

(7)

where 120590119894119895 is the stress tensor due to molecular viscositydefined by

120590119894119895 equiv [120583(120597119906119894

120597119909119895

+120597119906119895

120597119909119894

)] minus2

3120583120597119906119894

120597119909119894

120575119894119895 (8)

and 120591119894119895 is the subgrid-scale (SS) stress defined by

120591119894119895 equiv 120588119906119894119906119895 minus 120588119906119894119906119895 (9)

Since the subgrid-scale stress term in the LES modelis unknown it requires modeling to close the governingequations Currently the most adopted subgrid-scale turbu-lence model which employs the Boussinesq hypothesis [26]computes subgrid-scale turbulent stresses by

120591119894119895 minus1

3120591119896119896120575119894119895 = minus2120583119905119878119894119895 (10)

where 120583119905 is subgrid-scale turbulent viscosity The isotropicpart 120591119896119896 which is not modeled is added to the filteredstatic pressure term 119878119894119895 is the rate-of-strain tensor under theresolved scale defined by

119878119894119895 =1

2(

120597119906119894

120597119909119895

+120597119906119895

120597119909119894

) (11)

In this study the subgrid-scale turbulent viscosity 120583119905was modeled by the Smagorinsky-Lilly model which wasinitially proposed by Smagorinsky [27] In the Smagorinsky-Lillymodel the turbulent viscosity coefficient is calculated by

120583119905 = 1205881198712119878

1003816100381610038161003816100381611987810038161003816100381610038161003816 (12)

where |119878| equiv radic2119878119894119895119878119894119895 119871119878 is the subgrid mixing lengthcalculated by

119871119878 = min (120581119889 11986211987811988113

) (13)

where 120581 is the von Kaman constant 119889 the distance to theclosest wall and 119862119878 the Smagorinsky constant empiricallygiven as 01

42 Mesh Work Boundary Conditions and NumericalScheme In this study a full straight square duct (01 times 01m2in section and 575m in length) was simulated (see Figure 3)The fluid air was assumed to be incompressible and thegravitational acceleration was not considered The Reynoldsnumber based on the mean duct velocity and square ductdimensions was 067ndash147 times 105 Mean duct velocity wasimposed on the inlet boundary and the flow turbulence ischaracterized by turbulence intensity (10) and hydraulicdiameter (01m) On the outlet boundary it is assumed thatthe flow is fully developed with zero normal gradients andzero background pressure There was no slip of fluid at thesurfaces of the duct and fitting(s) Structured grids were usedto discretize the computational domain in which the firstgrids are 25 times 10

minus5m away from the fitting(s) Then the 119910+

(119910+ = 120588119906120591119910119901120583) value for the first grid points was around05ndash2 depending on the mean duct velocity which indicatesthat the first grids arewithin the laminar sublayerThemeshesbecome coarser in the region far away from the fitting(s) but

6 The Scientific World Journal

Inlet Outlet

02 m

02 m

02 m05 m

05 m

05 m

575 m

175 m

p1 p2 p3

2 m1 m

ΔPS1 ΔPS2ΔPS2

Figure 3 A schematic diagram of the duct system in the numerical simulations

remain high density near the duct walls (119910+ lt 5) When themesh is fine enough to resolve the laminar sublayer the LESmodel applies the laminar stress-strain relationship to obtainthe wall shear stress

119906

119906120591

=120588119906120591119910

120583 (14)

The sensitivity of mesh number was systematically tested Foreach case three different mesh systems (a coarser a mediumand a finer) were constructed and the final numerical solu-tions based on these three meshes were compared Finallyin compromise between the numerical accuracy and costmeshes with around 20 times 106 25 times 106 and 30 times 106 gridswere selected for the cases with one fitting two fittings andthree fittings respectively The time step size used in the LESsimulations was 00002 s which ensures that the convergencecan be achieved within 5ndash10 iterative steps for each timestep

Based on the finite volumemethod (FVM) the governingequations are discretized to algebraic equations on the gridsystemThe convection term was discretized by the boundedcentral differencing scheme while the pressure staggeringoption scheme (PRESTO) was selected for pressure interpo-lation Finally the SIMPLEC algorithm was used to couplethe pressure and velocity equations

43 Cases Simulated In order to evaluate the accuracy andreliability of the LES model in predicting the pressure lossesacross multiple in-duct fittings two tested cases are selectedto be numerically reproduced Case 7 at a mean flow velocityof 20ms and Case 14 at 19ms The predicted pressure lossesare compared with those measured in the experiments

5 Results and Discussions

As shown in Table 1 five mean flow velocities were testedfor each case However due to the difficulty in accuratelycontrolling the mean velocity during the tests the testedvelocities were not necessarily the same for all casesThis doesnot influence the later analysis In this section the measuredor simulated pressure losses (Pa) across in-duct fittings aredirectly presented and analyzed If one is interested in the 119896

factors these can be obtained using (5) in Section 2

51 Effect of Reynolds Number (119877119890) In practice there arevarious types of HVAC ducts in terms of cross-sectionalshape and dimension and mean flow velocity Despite thiscomplexity the dimensionless Re can be used to representthese duct characteristics given that the same Re indicatesaerodynamic similarity In this section the effect of Re on thepressure losses across fittings is examined when the fittingconfiguration remains unchanged It is found that the pres-sure loss across a fitting almost has a linear relationship withthe duct Re (the example of Case 10 is shown in Figure 4)This implies that any factors increasing the duct Re such asan increase in velocity and cross-sectional dimensions canresult in an increase in pressure loss across an in-duct fittingIn other words pressure losses across the in-duct fitting(s) ofa larger duct with a higher velocity remain high

52 Effect of Fitting Configuration In order to study the effectof fitting configuration on the pressure losses this sectiondiscusses the cases with the same Re to exclude the influenceof Re on the comparison of different fitting configurations

The effect of fitting type on pressure losses across fittingsis studied when the obstruction ratio is kept constant Theobstruction ratio is defined as the area ratio of the fitting tothe duct cross-section namely the ratio of the shaded areato the whole duct section (see Figure 2) Table 2 summarizesthe comparison of pressure losses across the two types offittings namely the centrally placed fitting and the centrallyopened fitting (in Figure 2) From Table 2 it can be seenthat the pressure loss across a centrally placed fitting isremarkably larger than that across a centrally opened fittingThis can be explained by the fact that the velocity profile inthe cross-section of a duct follows a parabolic distributionnamely the largest in the center and the smallest on the ductsurfaces Thus centrally placed fittings obstruct the fastestcentral airflow and lead to the largest pressure losses whereascentrally opened fittings allow this strongest airflow to passthrough and offer much less resistance to the airflow It canalso be observed that the deviation ratio of pressure lossbetween these two types of fittings is not the same and isdependent on the obstruction ratio

The effect of the obstruction ratio on pressure lossesacross fittings is studied at a Re of 67 times 104 and the resultsare shown in Figure 5 For all cases an increase in the

The Scientific World Journal 7

Table 2 Effect of fitting type on pressure losses (Pa) across fitting(s)

Re (times104)

Case 1 versus 4(only p1)

Case 2 versus 5(only p1)

Case 3 versus 6(only p1)

Case 10 versus 13(p1 and p2)

Case 15 versus 14(p1 p2 and p3)

67 mdash 204 versus 150 944 versus 640 190 versus 144 at p1172 versus 150 at p2

208 versus 142 at p1198 versus 154 at p2180 versus 118 at p3

133 286 versus 144 mdash mdash mdash mdash

Table 3 Effect of downstream fitting(s) on pressure loss (Pa) across an upstream fitting

(a) Base case Case 1

Re = 667 times 104 Case 1 Case 7 Case 8 Case 9

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782

Pressure loss 72 66 66 64 185 54 588Percentage decrease 83 111 250

(b) Base case Case 2

Re = 667 times 104 Case 2 Case 10 Case 11 Case 15

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 204 190 172 184 774 208 198 180Percentage decrease 69 98 minus20 29

(c) Base case Case 3

Re = 667 times 104 Case 3 Case 12

Δ1198751198781 Δ1198751198781 Δ1198751198782

Pressure loss 944 1030 750Percentage decrease minus91

(d) Base case Case 5

Re = 667 times 104 Case 5 Case 13 Case 14

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 150 144 150 142 154 118Percentage decrease 40 53 minus27

fittingrsquos obstruction ratio significantly increases the pressureloss across it However the percentage increase in pressureloss is dependent on the obstruction ratio fitting type andthe interaction of neighboring fittings For a centrally placedsingle fitting (Cases 1ndash3) when the obstruction ratio increasesfrom 05 to 075 (from Case 2 to 3) the percentage increaseis approximately 363 which is almost one time higher thanthe increase (183)when the obstruction ratio increases from025 to 05 (from Case 1 to 2) It is also observed that thispercentage increase is relatively lower in the case with thecentrally opened fitting (Cases 5-6) and is also influenced bythe presence of neighboring fittings (Cases 7ndash9 and Cases 10ndash12) However regardless of the change in the obstruction ratioof a neighboring fitting the pressure loss across a fitting isonly changed slightly

53 Effect of Interaction of Multiple Fittings Table 3 sum-marizes the pressure loss across an upstream fitting and itspercentage decrease as a result of its downstream fittingsFrom Table 3(a) it can be seen that the presence of adownstream centrally placed fitting can reduce the pressureloss across its upstream fitting and the percentage decrease

increases remarkably with the increase in the obstructionratio of the downstream fitting However a comparison ofTable 3(a)ndash(c) shows that with the increase in the obstructionratio of the upstream fitting the decrease in pressure lossacross it is gradually decreased becoming minus91 when theobstruction ratio reaches 075 As tabulated in Table 3(d) forthe centrally opened fitting the presence of a downstreamfitting can reduce the pressure loss across it whereas twodownstream fittings complicate this situation

The effect of upstream fittings on the pressure loss acrossa downstream fitting is also evaluated and the results arepresented in Table 4 For the centrally placed fitting the pres-ence of upstream fittings significantly reduces the pressurelosses across its downstream fitting(s) (see Table 4(a)ndash(c))Contrarily for the centrally opened fitting this pressure lossis negligibly affected by the presence of an upstream fittingwhereas it is significantly decreased by the presence of twoupstream fittings (see Table 4(d))

The above results suggest that as a result of the effect ofdownstream and upstreamfittings the pressure loss across anin-duct fitting is changed substantially This can be explainedby the fact that the presence of a fitting changes the airflow

8 The Scientific World Journal

Table 4 Effect of upstream fitting(s) on pressure loss (Pa) across a downstream fitting

(a) Base case Case 1

Re = 667 times 104 Case 1 Case 7

Δ1198751198781 Δ1198751198781 Δ1198751198782

Pressure loss 72 66 66Percentage decrease 83

(b) Base case Case 2

Re = 667 times 104 Case 2 Case 8 Case 10 Case 15

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 204 64 185 190 172 208 198 180Percentage decrease 93 157 29 118

(c) Base case Case 3

Re = 667 times 104 Case 3 Case 9 Case 11 Case 12

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782

Pressure loss 944 54 588 184 774 1030 750Percentage decrease 377 180 206

(d) Base case Case 5

Re = 667 times 104 Case 5 Case 13 Case 14

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 150 144 150 142 154 118Percentage decrease 00 minus27 213

Table 5 Comparison of pressure losses (Pa) across multiple interactive and individual fittings

Re = 667 times 104 Case 7 Case 8 Case 9 Case 10 Case 11 Case 12 Case 13 Case 14 Case 15

Across interactivefittings 132 249 642 362 958 1780 294 414 586

Across individualfittings 144 276 1016 408 1148 1888 300 450 612

Percentage decrease 83 98 368 113 166 57 20 80 42

direction and turbulence around its neighboring fitting(s)and consequently modifies the 119896 factor (see (5) in Section 2)The results also demonstrate that the effect of a neighboringfitting is complex that is different fitting type location(upstream or downstream) obstruction ratio and duct Recan result in very distinctive pressure lossesThis implies thatthe 119896 factors for individual fittings provided in the ASHRAEhandbook and the CIBSE guide are inaccurate in a condi-tion when the interaction of neighboring fittings cannot beignored

The pressure losses across multiple interactive and indi-vidual in-duct fittings are compared (see Table 5) In Table 5the pressure losses across interactive fittings for Cases 7ndash15are directly measured in the tests In order to evaluate theeffect of the fittingsrsquo interaction on the total pressure lossfor each case the pressure losses across every individualfitting are summed for comparison Taking Case 8 as anexample the pressure losses across its individual fittings aresummed fromCase 1 andCase 2 Based on the summations ofindividual pressure loss the percentage decreases in pressurelosses across multiple fittings are calculated It can be seen

that the pressure losses across multiple interactive fittingsare lower than those across multiple individual fittings andthe percentage decrease is dependent on the configurationand combination of the fittings This finding is supportedby the previous study on two bends by Rahmeyer [12]Again this demonstrates that the calculation of pressurelosses across multiple closely mounted fittings via summingthose across individual fittings is inaccurate This methodoverpredicts the total pressure loss which may consequentlyresult in energy waste owing to the selection of larger fans Insuch a condition exploring an accurate reliable and high-efficiency predictive method such as a validated CFDmodelis crucially important

54 Validation of LES Modeling In order to validate the LESmodel in predicting pressure losses across multiple in-ductfittings the predicted values of the pressure losses acrossfittings in Case 7 at 20ms andCase 14 at 19ms are comparedwith corresponding datameasured in the testsThe results arepresented in Table 6 It can be seen that the predicted results

The Scientific World Journal 9

0

200

400

600

800

1000

60000 90000 120000 150000

Pres

sure

loss

(Pa)

ReCase 10-p1Case 10-p2

Figure 4 Effect of Reynolds number on pressure loss acrossfitting(s)

Pres

sure

loss

(Pa)

0

200

400

600

800

1000

1200

0 1 2 3 4 5 6 7 8 9 10 11 12Case number

At p1At p2

Figure 5 Effect of obstruction ratio on pressure losses acrossfitting(s)

agree well with the measured data with a relative deviationless than 3This indicates that the LESmodel can accuratelyresolve the flow field in a HVAC duct with multiple in-ductfittings

Compared to the experimental measurement numericalmodeling has an incomparable advantage in obtaining in-duct flow details such as velocity and pressure distributionsFigure 6 presents the pressure distribution along the ductcenterline in Case 7 at a mean flow velocity of 20ms Figures7 and 8 show the pressure and air speed contours on the centerplane of the duct respectively These kinds of pressure andair speed distribution are useful because it can not only beused independently for ductwork design (if the numericalmodel is validated before) but also to indicate the locationswhere pressure sensors should be placed in the tests for thelatter the involvement of numerical modeling can save manyexperimental resources and help to produce more reliableexperimental data Thus the successful use of numerical

0

200

400

600

800

1000

0 1 2 3 4 5 6

Pres

sure

(Pa)

Distance along streamwise direction (m)

minus800

minus600

minus400

minus200

p1 p2

Figure 6 Pressure distribution along centerline of the duct (Case 7at 20ms)

modeling is of great significance in optimizing ductworkdesign and improving the database for pressure losses acrossfittings

6 Conclusions

This study examines the pressure losses across multiple in-duct fittings of a ventilation duct using experimental testsTwo tested cases are reproduced by LESmodeling to evaluatethe accuracy and reliability of this numerical method inpredicting the pressure field inside a duct with multiplefittings The following conclusions can be drawn

The flow resistance of a centrally placed fitting is remark-ably larger than that of a centrally opened fitting basicallydue to the fact that the velocity profile of a cross-sectionof a duct follows a parabolic distribution For all cases anincrease in the obstruction ratio of a fitting significantlyincreases the pressure loss across it However this pressureloss does not linearly increase with the obstruction ratiothere is a substantial increase in pressure loss when theobstruction ratio increases from 05 to 075 Again this isbecause the velocity profile on a cross-section is not a uniformdistribution

Since the presence of a fitting changes the airflow direc-tion and turbulence around its close neighboring fitting(s)and consequently modifies the 119896 factor the pressure lossesacross the neighboring fitting(s) are changed substantiallyHowever the magnitude of this change is affected by manyfactors such as fitting type location (upstream or down-stream) obstruction ratio and Re In addition the pressurelosses across multiple interactive fittings are lower thanthose across multiple similar individual fittings althoughthe percentage decrease is dependent on the configurationand combination of the fittings These findings imply thatthe calculation of pressure losses across multiple closelymounted fittings via summing those across individual fittingsis inaccurateThismethod overpredicts the total pressure lossand could result in energy waste via the selection of largerfans Thus a more accurate reliable and high-efficiency

10 The Scientific World Journal

0

005

01Z

(m)

18 2 22 24 26 28 3X (m)

Pressure minus300 minus200 minus100 0 100 200 300 400 500 600

Figure 7 Pressure (Pa) contour around the in-duct fittings on the center plane of the duct (Case 7 at 20ms)

18 2 22 24 26 28 3

Velocity-magnitude 5 10 15 20 25 30

0

005

01

Z(m

)

X (m)

Figure 8 Air speed (ms) contour around the in-duct fittings on the center plane of the duct (Case 7 at 20ms)

Table 6 Comparison of predicted and measured pressure losses(Pa)

Case 7 (20ms) Case 14 (19ms)Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Measurement 256 260 486 528 410LES simulation 258 254 491 539 417

predictive method such as a validated CFD model shouldbe explored

The predicted results by LES modeling agree well withthe measured data in the tests which demonstrates thatthe LES model can accurately resolve the flow field in aHVAC duct with multiple in-duct fittings Compared tothe experimental measurement the numerical modeling canprovide the details of pressure distribution This predictedpressure distribution can be used not only independently in aductwork design (if the numerical model has been validatedbefore) but also to assist in tests to find correct locations toplace pressure sensors In the latter case the use of numericalmodeling can potentially save many experimental resourcesand help to produce more reliable experimental data

References

[1] ASHRAE HandbookmdashFundamentals SI Edition chapter 21-22 American Society of Heating Refrigerating and Air-Conditioning Engineers Atlanta Ga USA 2009

[2] CIBSEThe Chartered Institution of Building Services EngineersHeating Ventilating Air Conditioning and Refrigeration CIBSEGuide B Chartered Institution of Building Services EngineersLondon UK 3rd edition 2005

[3] I E Idelchik Handbook of Hydraulic Resistance 3rd edition1994

[4] ASHRAE Standard 120P ldquoMethods of testing to determine flowresistance of HVAC air ducts and fittingsrdquo American Society ofHeating Refrigerating andAir-conditioning Engineers AtlantaGa USA 1995

[5] B Abushakra I S Walker and M H Sherman ldquoA studyof pressure losses in residential air distribution systemsrdquo inProceedings of the American Council for an Energy EfficientEconomy (ACEEE rsquo02) Washington DC USA 2002 LBNLReport 49700 Lawrence Berkeley National Laboratory CalifUSA 2002

[6] L Shao and S B Riffat ldquoAccuracy of CFD for predictingpressure losses in HVAC duct fittingsrdquo Applied Energy vol 51no 3 pp 233ndash248 1995

[7] S M Atkin and L Shao ldquoEffect on pressure loss of separationand orientation of closely coupledHVACduct fittingsrdquoBuildingServices Engineering Research and Technology vol 21 no 3 pp175ndash178 2000

[8] L Shao and S B Riffat ldquoCFD for prediction of k-factors of ductfittingsrdquo International Journal of Energy Research vol 19 no 1pp 89ndash93 1995

[9] R R Rend E M Sparrow D W Bettenhausen and J PAbraham ldquoParasitic pressure losses in diffusers and in theirdownstream piping systems for fluid flow and heat transferrdquoInternational Journal of Heat and Mass Transfer vol 61 pp 56ndash61 2013

[10] J P Abraham E M Sparrow J C K Tong and D WBettenhausen ldquoInternal flows which transist from turbulentthrough intermittent to laminarrdquo International Journal of Ther-mal Sciences vol 49 no 2 pp 256ndash263 2010

[11] E M Sparrow J P Abraham and W J Minkowycz ldquoFlowseparation in a diverging conical duct effect of reynolds numberand divergence anglerdquo International Journal of Heat and MassTransfer vol 52 no 13ndash14 pp 3079ndash3083 2009

The Scientific World Journal 11

[12] W J Rahmeyer ldquoPressure loss coefficients for close-coupledpipe ellsrdquo ASHRAE Transactions vol 108 pp 390ndash406 2002

[13] G Gan and S B Riffat ldquok-factors for HVAC ducts numericaland experimental determinationrdquo Building Services EngineeringResearch and Technology vol 16 no 3 pp 133ndash139 1995

[14] S A Mumma T A Mahank and Y-P Ke ldquoAnalytical determi-nation of duct fitting loss-coefficientsrdquo Applied Energy vol 61no 4 pp 229ndash247 1998

[15] G Gan and S B Riffat ldquoNumerical determination of energylosses at duct junctionsrdquo Applied Energy vol 67 no 3 pp 331ndash340 2000

[16] S Moujaes and R Gundavelli ldquoCFD simulation of leak inresidential HVAC ductsrdquo Energy and Buildings vol 54 pp 534ndash539 2012

[17] J P Abraham J C K Tong and E M Sparrow ldquoBreakdownof laminar pipe flow into transitional intermittency and subse-quent attainment of fully developed intermittent or turbulentflowrdquo Numerical Heat Transfer Part B vol 54 no 2 pp 103ndash115 2008

[18] W J Minkowycz J P Abraham and EM Sparrow ldquoNumericalsimulation of laminar breakdown and subsequent intermittentand turbulent flow in parallel-plate channels effects of inletvelocity profile and turbulence intensityrdquo International Journalof Heat and Mass Transfer vol 52 no 17ndash18 pp 4040ndash40462009

[19] J P Abraham E M Sparrow and J C K Tong ldquoHeat transferin all pipe flow regimes laminar transitionalintermittent andturbulentrdquo International Journal of Heat and Mass Transfer vol52 no 3ndash4 pp 557ndash563 2009

[20] R D Lovik J P AbrahamW JMinkowycz and EM SparrowldquoLaminarization and turbulentization in a pulsatile pipe flowrdquoNumerical Heat Transfer Part A vol 56 no 11 pp 861ndash8792009

[21] J P Abraham E M Sparrow and W J Minkowycz ldquoInternal-flow nusselt numbers for the low-reynolds-number end of thelaminar-to-turbulent transition regimerdquo International Journalof Heat and Mass Transfer vol 54 no 1ndash3 pp 584ndash588 2011

[22] D A Kose and E Dick ldquoPrediction of the pressure distributionon a cubical building with implicit LESrdquo Journal of WindEngineering and Industrial Aerodynamics vol 98 no 10ndash11 pp628ndash649 2010

[23] C-H HuM Ohba and R Yoshie ldquoCFDmodelling of unsteadycross ventilation flows using LESrdquo Journal of Wind Engineeringand Industrial Aerodynamics vol 96 no 10ndash11 pp 1692ndash17062008

[24] C M Mak J Wu C Ye and J Yang ldquoFlow noise from spoilersin ductsrdquo Journal of the Acoustical Society of America vol 125no 6 pp 3756ndash3765 2009

[25] Fluent Ansys Fluent 130 Theory Guide Turbulence ANSYSCanonsburg Pa USA 2010

[26] J O Hinze Turbulence McGraw-Hill New York NY USA1975

[27] J Smagorinsky ldquoGeneral circulation experiments with theprimitive equations the basic experimentrdquo Monthly WeatherReview vol 91 pp 99ndash164 1963

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2 The Scientific World Journal

possibly contribute to these discrepancies [6] is that due tothe lack of understanding on airflow patterns at duct fittingspressure sensors are occasionally located at inappropriatesections such as disturbance sections which could cause largemeasurement errors However since the in-duct airflow pat-tern is strongly associated with the duct configuration meanduct velocity and local aerodynamic configuration of fittingsit is difficult and time consuming to find the appropriatelocations for placing pressure sensors before every test Insuch a condition a numerical method should be helpfulin terms of saving experimental investment and time Evenin an experimental way it is more reliable and economicalto know the flow patterns before a real test is set up andconducted As a numericalmethod CFDhas been sufficientlyverified and validated as a method of predicting fluid flowShao and Riffat [6 8] studied the possibility and accuracyof using the CFD method to predict the pressure loss factorand in turn determine pressure losses across duct bendsTheyevaluated the effect of a set of computational parameters onthe accuracy of numerical results Their numerical resultsare supported by the experiments of Gan and Riffat [13]In addition the CFD method has been used to predict thepressure loss coefficient of many other duct fittings suchas damper orifice transition [9ndash11 14] and junction [15]fittings in HVAC ductworks as well as to conduct other duct-related studies (eg air leakage) [16] Without exceptionthese previous numerical simulations used the ReynoldsAveraged Navier-Stokes (RANS) method [17ndash21] specificallythe steady standard 119896-120576 turbulence model However thismodel may be not accurate and reliable enough to predictthe flow field inside a duct with multiple fittings wherethe airflow is more strained and swirling as well as highlyfluctuating As an alternative CFDmodel the advanced large-eddy simulation (LES) model is well known for its accuracyin predicting airflow in the building-related field [22 23]The LES model which resolves large turbulent eddies andmodels small eddies has the capacity to reproduce tran-sient turbulent fluctuations and handle flow intermittencyalthough it consumes more numerical cost In this studythe accuracy and reliability of the LES turbulence model inpredicting pressure losses across multiple in-duct fittings areevaluated

The specific problems that motivated this study arethe inaccuracy of the available data in the current guidesand the lack of a predictive method for pressure lossesacross multiple in-duct fittings The purposes of this studytherefore are to examine the pressure losses across multiplein-duct fittings and to evaluate the accuracy and reliabilityof a predictive method The effect of the interaction offittings on the total pressure loss across multiple fittingsis analyzed by experimental tests The predictive methodnamely LES modeling is then evaluated by comparing itwith tested data It is expected that this study will reveal thepressure losses across multiple in-duct fittings and providedesigners with a predictive method that can be used eitherindependently as a design tool or to assist experimentaltesting

2 Conceptual Models

There are two types of pressure loss in duct systems namelyfriction loss and dynamic loss These losses are derivedfrom different mechanisms and are therefore calculated bydifferent methods [1]

Friction loss is due to fluid viscosity and results fromthe momentum exchange between molecules or betweenadjacent fluid layers moving at different velocities It occursalong the entire length of a duct Friction losses in fluidductworks can be calculated by the Darcy equation

Δ119875119891 =119891119871

119863ℎ

times1205881198802

2 (1)

where Δ119875119891 is a friction loss 119891 a dimensionless frictionfactor 119871 duct length119863ℎ hydraulic diameter119880 area-averagedstreamwise velocity and 120588 fluid density Friction factor 119891 isdetermined by the Colebrook equation

1

radic119891= minus2 log(

119890

37119863ℎ

+251

Reradic119891) (2)

where 119890 is the absolute roughness factor of a material and Reis the Reynolds number computed from

Re =119863ℎ119880

] (3)

where ] is kinematic viscosity The hydraulic diameter 119863ℎis defined as 4119860119875 where 119860 is the duct area and 119875 is theperimeter of the cross-section

Dynamic losses in fittings result from flow disturbancescaused by duct fittings that change the airflow direction orflow path area and can be calculated by

Δ119875119889 = 119862 times1205881198802

2 (4)

where 119862 is the dimensionless local loss coefficient (alsocalled 119896 factor) which is determined by the local dynamiccharacteristics

3 Experimental Method and Simplification

This experiment was a part of our previous test on flow noisecaused by in-duct elements [24] The experimental system isshown in Figure 1 Air flow was provided by a centrifugal fandriven by a variable speed motor The fan was enclosed ina 122 times 122 times 122m3 enclosure The 01 times 01m2 test ductwas made of steel The total length of the duct was 575m inwhich counted from the air flow inlet the first fitting (p1) waslocated 175m from the duct inlet section and the third fitting(p3)was located 1m from the duct outletThese upstream anddownstream lengths [6] were generally sufficient to ensurethat the test of the first and third fittings were not affectedby the inlet and outlet of the duct respectively The inlet andoutlet of the experimental system were placed on the outsideso as to eliminate the effect of relative pressure difference

As shown in Figure 2 flat plates were used to generallyrepresent the in-duct fittings in HVAC ductworks Here

The Scientific World Journal 3

Table 1 Fifteen fitting configurations tested in this study

Case Configuration of fitting(s) Mean flow velocities(ms)

1r

r = 0025m at p110 15 20 25 30

2r

r = 005m at p110 14 18 22 26

3 r

r = 0075m at p110 12 14 16 18

4

r = 0025m at p1r2r2 15 20 25 30 35

5r = 005m at p1

r2r210 15 20 25 30

6r = 0075m at p1

r2r210 12 14 16 18

7r = 0025m at p1

r

r = 0025m at p2r 10 15 20 25 30

8

r = 005m at p2r = 0025m at p1r r

10 14 18 22 26

9

r = 0075m at p2r = 0025m at p1r r

10 12 14 16 18

10r r

r = 005m at p2r = 005m at p1

10 13 16 19 22

11r = 0075m at p2

r rr = 005m at p1

10 12 14 16 18

12r = 0075m at p1 r = 0075m at p2

r r10 11 12 13 14

4 The Scientific World Journal

Table 1 Continued

Case Configuration of fitting(s) Mean flow velocities(ms)

13

r = 005m at p1 r = 005m at p2r2r2 r2r2

10 14 18 22 26

14r = 005m at p1

r2r2

r = 005m at p2r2r2

r = 005m at p3r2r2 10 13 16 19 22

15r = 005m at p1

r

r = 005m at p2r

r = 005m at p3r

10 12 14 16 18

the control variable was the obstructed ratio of the fittingarea to the cross-sectional area of the duct The plates weremade from 1mm thick steel plate and they were fixed tothe adjoining flanges of the test duct The gap was sealedwith compressed foam rubber As shown in Table 1 15configurations were tested In Cases 1ndash6 only a single fittingwas inserted into position p1 In Cases 7ndash13 two fittings wereinserted at two different positions (p1 and p2) and in Cases14-15 three fittings were inserted at three different positions(p1 p2 and p3)

The velocity profile in the empty test duct was measuredto make sure that the flow could be symmetrically developedinside the duct A pitot tube was used to sample the dynamicpressure at specified points in the duct cross-section Basedon the measurements obtained using this empty duct arelationship between the mean duct velocity (119910) and thevelocity measured at the center of the duct (119909) was developed(119910 = 09639119909 minus 03289 (119877

2= 09997)) and this was used

to calibrate the mean duct velocity in later tests using themeasured center velocity The mean airflow velocities testedfor each case are listed in Table 1

The static pressure losses across the fittings were mea-sured using two piezometric rings placed at positions p1 p2and p3 (Figure 1) Each ring consisted of four static pressuretappings one in each duct face The downstream ring wassufficiently far away (five times the duct dimensions) from thetest fitting to ensure that full static pressure recovery couldtake place in the wake of the flow obstructions under test

4 Numerical Modeling

This section briefly discusses the numerical method usedby LES modeling and introduces the test cases selected toevaluate it

41 Governing Equations of LES The governing equationsused for large eddies can be obtained by filtering the time-dependent Navier-Stokes equations Eddies whose scales aresmaller than the filtering width or grid spacing adopted in thecomputations are effectively removed by the filtering process

Inlet

Outlet

Pitot

125 m 1 m 2 m575 m

ΔPS3ΔPS2ΔPS1

05 m

02 m05 m02 m 02 m

05 m05 m

p1 p2 p3

Figure 1 A schematic diagram of the experimental system (p1 p2and p3 are the positions where the first second and third fittingsare inserted respectively Δ1198751198781 Δ1198751198782 and Δ1198751198783 represent the staticpressure loss across the first second and third fittings resp)

Then the resulting equations only govern the dynamics oflarge eddies

In this study the filtering operation provided by thefinite volume discretization method as described in [25] isemployed

120593 (119909) =1

119881int

119881

0120593 (1199091015840) 1198891199091015840 1199091015840isin 119881 (5)

where 120593 (119909) represents a filtered variable and119881 the volume ofa computational control cell The filter function 119866(119909 119909

1015840) is

119866(119909 1199091015840) =

1

119881 1199091015840isin 119881 or 119866(119909 119909

1015840) = 0 119909

1015840notin 119881

(6)

The Scientific World Journal 5

01 m

01 m

r

(a)

01 m

01 m

r2 r2

(b)

Figure 2 Cross-section of the duct with two types of flat-plate fittings (shaded area) (a) Centrally placed fittings 119903 = 0025m 005m0075m (b) The geometries consisted of plates protruding symmetrically from both sides of the duct leaving a central vertical strip of theduct open later called a centrally opened fitting 119903 = 0025m 005m 0075m

In this study the governing equations of LES for incom-pressible flows were obtained by filtering the Navier-Stokesequations

120597119906119894

120597119909119894

= 0

120597

120597119905(120588119906119894) +

120597

120597119909119895

(120588119906119894 119906119895) =120597

120597119909119895

(120590119894119895) minus120597119901

120597119909119894

minus120597120591119894119895

120597119909119895

(7)

where 120590119894119895 is the stress tensor due to molecular viscositydefined by

120590119894119895 equiv [120583(120597119906119894

120597119909119895

+120597119906119895

120597119909119894

)] minus2

3120583120597119906119894

120597119909119894

120575119894119895 (8)

and 120591119894119895 is the subgrid-scale (SS) stress defined by

120591119894119895 equiv 120588119906119894119906119895 minus 120588119906119894119906119895 (9)

Since the subgrid-scale stress term in the LES modelis unknown it requires modeling to close the governingequations Currently the most adopted subgrid-scale turbu-lence model which employs the Boussinesq hypothesis [26]computes subgrid-scale turbulent stresses by

120591119894119895 minus1

3120591119896119896120575119894119895 = minus2120583119905119878119894119895 (10)

where 120583119905 is subgrid-scale turbulent viscosity The isotropicpart 120591119896119896 which is not modeled is added to the filteredstatic pressure term 119878119894119895 is the rate-of-strain tensor under theresolved scale defined by

119878119894119895 =1

2(

120597119906119894

120597119909119895

+120597119906119895

120597119909119894

) (11)

In this study the subgrid-scale turbulent viscosity 120583119905was modeled by the Smagorinsky-Lilly model which wasinitially proposed by Smagorinsky [27] In the Smagorinsky-Lillymodel the turbulent viscosity coefficient is calculated by

120583119905 = 1205881198712119878

1003816100381610038161003816100381611987810038161003816100381610038161003816 (12)

where |119878| equiv radic2119878119894119895119878119894119895 119871119878 is the subgrid mixing lengthcalculated by

119871119878 = min (120581119889 11986211987811988113

) (13)

where 120581 is the von Kaman constant 119889 the distance to theclosest wall and 119862119878 the Smagorinsky constant empiricallygiven as 01

42 Mesh Work Boundary Conditions and NumericalScheme In this study a full straight square duct (01 times 01m2in section and 575m in length) was simulated (see Figure 3)The fluid air was assumed to be incompressible and thegravitational acceleration was not considered The Reynoldsnumber based on the mean duct velocity and square ductdimensions was 067ndash147 times 105 Mean duct velocity wasimposed on the inlet boundary and the flow turbulence ischaracterized by turbulence intensity (10) and hydraulicdiameter (01m) On the outlet boundary it is assumed thatthe flow is fully developed with zero normal gradients andzero background pressure There was no slip of fluid at thesurfaces of the duct and fitting(s) Structured grids were usedto discretize the computational domain in which the firstgrids are 25 times 10

minus5m away from the fitting(s) Then the 119910+

(119910+ = 120588119906120591119910119901120583) value for the first grid points was around05ndash2 depending on the mean duct velocity which indicatesthat the first grids arewithin the laminar sublayerThemeshesbecome coarser in the region far away from the fitting(s) but

6 The Scientific World Journal

Inlet Outlet

02 m

02 m

02 m05 m

05 m

05 m

575 m

175 m

p1 p2 p3

2 m1 m

ΔPS1 ΔPS2ΔPS2

Figure 3 A schematic diagram of the duct system in the numerical simulations

remain high density near the duct walls (119910+ lt 5) When themesh is fine enough to resolve the laminar sublayer the LESmodel applies the laminar stress-strain relationship to obtainthe wall shear stress

119906

119906120591

=120588119906120591119910

120583 (14)

The sensitivity of mesh number was systematically tested Foreach case three different mesh systems (a coarser a mediumand a finer) were constructed and the final numerical solu-tions based on these three meshes were compared Finallyin compromise between the numerical accuracy and costmeshes with around 20 times 106 25 times 106 and 30 times 106 gridswere selected for the cases with one fitting two fittings andthree fittings respectively The time step size used in the LESsimulations was 00002 s which ensures that the convergencecan be achieved within 5ndash10 iterative steps for each timestep

Based on the finite volumemethod (FVM) the governingequations are discretized to algebraic equations on the gridsystemThe convection term was discretized by the boundedcentral differencing scheme while the pressure staggeringoption scheme (PRESTO) was selected for pressure interpo-lation Finally the SIMPLEC algorithm was used to couplethe pressure and velocity equations

43 Cases Simulated In order to evaluate the accuracy andreliability of the LES model in predicting the pressure lossesacross multiple in-duct fittings two tested cases are selectedto be numerically reproduced Case 7 at a mean flow velocityof 20ms and Case 14 at 19ms The predicted pressure lossesare compared with those measured in the experiments

5 Results and Discussions

As shown in Table 1 five mean flow velocities were testedfor each case However due to the difficulty in accuratelycontrolling the mean velocity during the tests the testedvelocities were not necessarily the same for all casesThis doesnot influence the later analysis In this section the measuredor simulated pressure losses (Pa) across in-duct fittings aredirectly presented and analyzed If one is interested in the 119896

factors these can be obtained using (5) in Section 2

51 Effect of Reynolds Number (119877119890) In practice there arevarious types of HVAC ducts in terms of cross-sectionalshape and dimension and mean flow velocity Despite thiscomplexity the dimensionless Re can be used to representthese duct characteristics given that the same Re indicatesaerodynamic similarity In this section the effect of Re on thepressure losses across fittings is examined when the fittingconfiguration remains unchanged It is found that the pres-sure loss across a fitting almost has a linear relationship withthe duct Re (the example of Case 10 is shown in Figure 4)This implies that any factors increasing the duct Re such asan increase in velocity and cross-sectional dimensions canresult in an increase in pressure loss across an in-duct fittingIn other words pressure losses across the in-duct fitting(s) ofa larger duct with a higher velocity remain high

52 Effect of Fitting Configuration In order to study the effectof fitting configuration on the pressure losses this sectiondiscusses the cases with the same Re to exclude the influenceof Re on the comparison of different fitting configurations

The effect of fitting type on pressure losses across fittingsis studied when the obstruction ratio is kept constant Theobstruction ratio is defined as the area ratio of the fitting tothe duct cross-section namely the ratio of the shaded areato the whole duct section (see Figure 2) Table 2 summarizesthe comparison of pressure losses across the two types offittings namely the centrally placed fitting and the centrallyopened fitting (in Figure 2) From Table 2 it can be seenthat the pressure loss across a centrally placed fitting isremarkably larger than that across a centrally opened fittingThis can be explained by the fact that the velocity profile inthe cross-section of a duct follows a parabolic distributionnamely the largest in the center and the smallest on the ductsurfaces Thus centrally placed fittings obstruct the fastestcentral airflow and lead to the largest pressure losses whereascentrally opened fittings allow this strongest airflow to passthrough and offer much less resistance to the airflow It canalso be observed that the deviation ratio of pressure lossbetween these two types of fittings is not the same and isdependent on the obstruction ratio

The effect of the obstruction ratio on pressure lossesacross fittings is studied at a Re of 67 times 104 and the resultsare shown in Figure 5 For all cases an increase in the

The Scientific World Journal 7

Table 2 Effect of fitting type on pressure losses (Pa) across fitting(s)

Re (times104)

Case 1 versus 4(only p1)

Case 2 versus 5(only p1)

Case 3 versus 6(only p1)

Case 10 versus 13(p1 and p2)

Case 15 versus 14(p1 p2 and p3)

67 mdash 204 versus 150 944 versus 640 190 versus 144 at p1172 versus 150 at p2

208 versus 142 at p1198 versus 154 at p2180 versus 118 at p3

133 286 versus 144 mdash mdash mdash mdash

Table 3 Effect of downstream fitting(s) on pressure loss (Pa) across an upstream fitting

(a) Base case Case 1

Re = 667 times 104 Case 1 Case 7 Case 8 Case 9

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782

Pressure loss 72 66 66 64 185 54 588Percentage decrease 83 111 250

(b) Base case Case 2

Re = 667 times 104 Case 2 Case 10 Case 11 Case 15

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 204 190 172 184 774 208 198 180Percentage decrease 69 98 minus20 29

(c) Base case Case 3

Re = 667 times 104 Case 3 Case 12

Δ1198751198781 Δ1198751198781 Δ1198751198782

Pressure loss 944 1030 750Percentage decrease minus91

(d) Base case Case 5

Re = 667 times 104 Case 5 Case 13 Case 14

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 150 144 150 142 154 118Percentage decrease 40 53 minus27

fittingrsquos obstruction ratio significantly increases the pressureloss across it However the percentage increase in pressureloss is dependent on the obstruction ratio fitting type andthe interaction of neighboring fittings For a centrally placedsingle fitting (Cases 1ndash3) when the obstruction ratio increasesfrom 05 to 075 (from Case 2 to 3) the percentage increaseis approximately 363 which is almost one time higher thanthe increase (183)when the obstruction ratio increases from025 to 05 (from Case 1 to 2) It is also observed that thispercentage increase is relatively lower in the case with thecentrally opened fitting (Cases 5-6) and is also influenced bythe presence of neighboring fittings (Cases 7ndash9 and Cases 10ndash12) However regardless of the change in the obstruction ratioof a neighboring fitting the pressure loss across a fitting isonly changed slightly

53 Effect of Interaction of Multiple Fittings Table 3 sum-marizes the pressure loss across an upstream fitting and itspercentage decrease as a result of its downstream fittingsFrom Table 3(a) it can be seen that the presence of adownstream centrally placed fitting can reduce the pressureloss across its upstream fitting and the percentage decrease

increases remarkably with the increase in the obstructionratio of the downstream fitting However a comparison ofTable 3(a)ndash(c) shows that with the increase in the obstructionratio of the upstream fitting the decrease in pressure lossacross it is gradually decreased becoming minus91 when theobstruction ratio reaches 075 As tabulated in Table 3(d) forthe centrally opened fitting the presence of a downstreamfitting can reduce the pressure loss across it whereas twodownstream fittings complicate this situation

The effect of upstream fittings on the pressure loss acrossa downstream fitting is also evaluated and the results arepresented in Table 4 For the centrally placed fitting the pres-ence of upstream fittings significantly reduces the pressurelosses across its downstream fitting(s) (see Table 4(a)ndash(c))Contrarily for the centrally opened fitting this pressure lossis negligibly affected by the presence of an upstream fittingwhereas it is significantly decreased by the presence of twoupstream fittings (see Table 4(d))

The above results suggest that as a result of the effect ofdownstream and upstreamfittings the pressure loss across anin-duct fitting is changed substantially This can be explainedby the fact that the presence of a fitting changes the airflow

8 The Scientific World Journal

Table 4 Effect of upstream fitting(s) on pressure loss (Pa) across a downstream fitting

(a) Base case Case 1

Re = 667 times 104 Case 1 Case 7

Δ1198751198781 Δ1198751198781 Δ1198751198782

Pressure loss 72 66 66Percentage decrease 83

(b) Base case Case 2

Re = 667 times 104 Case 2 Case 8 Case 10 Case 15

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 204 64 185 190 172 208 198 180Percentage decrease 93 157 29 118

(c) Base case Case 3

Re = 667 times 104 Case 3 Case 9 Case 11 Case 12

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782

Pressure loss 944 54 588 184 774 1030 750Percentage decrease 377 180 206

(d) Base case Case 5

Re = 667 times 104 Case 5 Case 13 Case 14

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 150 144 150 142 154 118Percentage decrease 00 minus27 213

Table 5 Comparison of pressure losses (Pa) across multiple interactive and individual fittings

Re = 667 times 104 Case 7 Case 8 Case 9 Case 10 Case 11 Case 12 Case 13 Case 14 Case 15

Across interactivefittings 132 249 642 362 958 1780 294 414 586

Across individualfittings 144 276 1016 408 1148 1888 300 450 612

Percentage decrease 83 98 368 113 166 57 20 80 42

direction and turbulence around its neighboring fitting(s)and consequently modifies the 119896 factor (see (5) in Section 2)The results also demonstrate that the effect of a neighboringfitting is complex that is different fitting type location(upstream or downstream) obstruction ratio and duct Recan result in very distinctive pressure lossesThis implies thatthe 119896 factors for individual fittings provided in the ASHRAEhandbook and the CIBSE guide are inaccurate in a condi-tion when the interaction of neighboring fittings cannot beignored

The pressure losses across multiple interactive and indi-vidual in-duct fittings are compared (see Table 5) In Table 5the pressure losses across interactive fittings for Cases 7ndash15are directly measured in the tests In order to evaluate theeffect of the fittingsrsquo interaction on the total pressure lossfor each case the pressure losses across every individualfitting are summed for comparison Taking Case 8 as anexample the pressure losses across its individual fittings aresummed fromCase 1 andCase 2 Based on the summations ofindividual pressure loss the percentage decreases in pressurelosses across multiple fittings are calculated It can be seen

that the pressure losses across multiple interactive fittingsare lower than those across multiple individual fittings andthe percentage decrease is dependent on the configurationand combination of the fittings This finding is supportedby the previous study on two bends by Rahmeyer [12]Again this demonstrates that the calculation of pressurelosses across multiple closely mounted fittings via summingthose across individual fittings is inaccurate This methodoverpredicts the total pressure loss which may consequentlyresult in energy waste owing to the selection of larger fans Insuch a condition exploring an accurate reliable and high-efficiency predictive method such as a validated CFDmodelis crucially important

54 Validation of LES Modeling In order to validate the LESmodel in predicting pressure losses across multiple in-ductfittings the predicted values of the pressure losses acrossfittings in Case 7 at 20ms andCase 14 at 19ms are comparedwith corresponding datameasured in the testsThe results arepresented in Table 6 It can be seen that the predicted results

The Scientific World Journal 9

0

200

400

600

800

1000

60000 90000 120000 150000

Pres

sure

loss

(Pa)

ReCase 10-p1Case 10-p2

Figure 4 Effect of Reynolds number on pressure loss acrossfitting(s)

Pres

sure

loss

(Pa)

0

200

400

600

800

1000

1200

0 1 2 3 4 5 6 7 8 9 10 11 12Case number

At p1At p2

Figure 5 Effect of obstruction ratio on pressure losses acrossfitting(s)

agree well with the measured data with a relative deviationless than 3This indicates that the LESmodel can accuratelyresolve the flow field in a HVAC duct with multiple in-ductfittings

Compared to the experimental measurement numericalmodeling has an incomparable advantage in obtaining in-duct flow details such as velocity and pressure distributionsFigure 6 presents the pressure distribution along the ductcenterline in Case 7 at a mean flow velocity of 20ms Figures7 and 8 show the pressure and air speed contours on the centerplane of the duct respectively These kinds of pressure andair speed distribution are useful because it can not only beused independently for ductwork design (if the numericalmodel is validated before) but also to indicate the locationswhere pressure sensors should be placed in the tests for thelatter the involvement of numerical modeling can save manyexperimental resources and help to produce more reliableexperimental data Thus the successful use of numerical

0

200

400

600

800

1000

0 1 2 3 4 5 6

Pres

sure

(Pa)

Distance along streamwise direction (m)

minus800

minus600

minus400

minus200

p1 p2

Figure 6 Pressure distribution along centerline of the duct (Case 7at 20ms)

modeling is of great significance in optimizing ductworkdesign and improving the database for pressure losses acrossfittings

6 Conclusions

This study examines the pressure losses across multiple in-duct fittings of a ventilation duct using experimental testsTwo tested cases are reproduced by LESmodeling to evaluatethe accuracy and reliability of this numerical method inpredicting the pressure field inside a duct with multiplefittings The following conclusions can be drawn

The flow resistance of a centrally placed fitting is remark-ably larger than that of a centrally opened fitting basicallydue to the fact that the velocity profile of a cross-sectionof a duct follows a parabolic distribution For all cases anincrease in the obstruction ratio of a fitting significantlyincreases the pressure loss across it However this pressureloss does not linearly increase with the obstruction ratiothere is a substantial increase in pressure loss when theobstruction ratio increases from 05 to 075 Again this isbecause the velocity profile on a cross-section is not a uniformdistribution

Since the presence of a fitting changes the airflow direc-tion and turbulence around its close neighboring fitting(s)and consequently modifies the 119896 factor the pressure lossesacross the neighboring fitting(s) are changed substantiallyHowever the magnitude of this change is affected by manyfactors such as fitting type location (upstream or down-stream) obstruction ratio and Re In addition the pressurelosses across multiple interactive fittings are lower thanthose across multiple similar individual fittings althoughthe percentage decrease is dependent on the configurationand combination of the fittings These findings imply thatthe calculation of pressure losses across multiple closelymounted fittings via summing those across individual fittingsis inaccurateThismethod overpredicts the total pressure lossand could result in energy waste via the selection of largerfans Thus a more accurate reliable and high-efficiency

10 The Scientific World Journal

0

005

01Z

(m)

18 2 22 24 26 28 3X (m)

Pressure minus300 minus200 minus100 0 100 200 300 400 500 600

Figure 7 Pressure (Pa) contour around the in-duct fittings on the center plane of the duct (Case 7 at 20ms)

18 2 22 24 26 28 3

Velocity-magnitude 5 10 15 20 25 30

0

005

01

Z(m

)

X (m)

Figure 8 Air speed (ms) contour around the in-duct fittings on the center plane of the duct (Case 7 at 20ms)

Table 6 Comparison of predicted and measured pressure losses(Pa)

Case 7 (20ms) Case 14 (19ms)Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Measurement 256 260 486 528 410LES simulation 258 254 491 539 417

predictive method such as a validated CFD model shouldbe explored

The predicted results by LES modeling agree well withthe measured data in the tests which demonstrates thatthe LES model can accurately resolve the flow field in aHVAC duct with multiple in-duct fittings Compared tothe experimental measurement the numerical modeling canprovide the details of pressure distribution This predictedpressure distribution can be used not only independently in aductwork design (if the numerical model has been validatedbefore) but also to assist in tests to find correct locations toplace pressure sensors In the latter case the use of numericalmodeling can potentially save many experimental resourcesand help to produce more reliable experimental data

References

[1] ASHRAE HandbookmdashFundamentals SI Edition chapter 21-22 American Society of Heating Refrigerating and Air-Conditioning Engineers Atlanta Ga USA 2009

[2] CIBSEThe Chartered Institution of Building Services EngineersHeating Ventilating Air Conditioning and Refrigeration CIBSEGuide B Chartered Institution of Building Services EngineersLondon UK 3rd edition 2005

[3] I E Idelchik Handbook of Hydraulic Resistance 3rd edition1994

[4] ASHRAE Standard 120P ldquoMethods of testing to determine flowresistance of HVAC air ducts and fittingsrdquo American Society ofHeating Refrigerating andAir-conditioning Engineers AtlantaGa USA 1995

[5] B Abushakra I S Walker and M H Sherman ldquoA studyof pressure losses in residential air distribution systemsrdquo inProceedings of the American Council for an Energy EfficientEconomy (ACEEE rsquo02) Washington DC USA 2002 LBNLReport 49700 Lawrence Berkeley National Laboratory CalifUSA 2002

[6] L Shao and S B Riffat ldquoAccuracy of CFD for predictingpressure losses in HVAC duct fittingsrdquo Applied Energy vol 51no 3 pp 233ndash248 1995

[7] S M Atkin and L Shao ldquoEffect on pressure loss of separationand orientation of closely coupledHVACduct fittingsrdquoBuildingServices Engineering Research and Technology vol 21 no 3 pp175ndash178 2000

[8] L Shao and S B Riffat ldquoCFD for prediction of k-factors of ductfittingsrdquo International Journal of Energy Research vol 19 no 1pp 89ndash93 1995

[9] R R Rend E M Sparrow D W Bettenhausen and J PAbraham ldquoParasitic pressure losses in diffusers and in theirdownstream piping systems for fluid flow and heat transferrdquoInternational Journal of Heat and Mass Transfer vol 61 pp 56ndash61 2013

[10] J P Abraham E M Sparrow J C K Tong and D WBettenhausen ldquoInternal flows which transist from turbulentthrough intermittent to laminarrdquo International Journal of Ther-mal Sciences vol 49 no 2 pp 256ndash263 2010

[11] E M Sparrow J P Abraham and W J Minkowycz ldquoFlowseparation in a diverging conical duct effect of reynolds numberand divergence anglerdquo International Journal of Heat and MassTransfer vol 52 no 13ndash14 pp 3079ndash3083 2009

The Scientific World Journal 11

[12] W J Rahmeyer ldquoPressure loss coefficients for close-coupledpipe ellsrdquo ASHRAE Transactions vol 108 pp 390ndash406 2002

[13] G Gan and S B Riffat ldquok-factors for HVAC ducts numericaland experimental determinationrdquo Building Services EngineeringResearch and Technology vol 16 no 3 pp 133ndash139 1995

[14] S A Mumma T A Mahank and Y-P Ke ldquoAnalytical determi-nation of duct fitting loss-coefficientsrdquo Applied Energy vol 61no 4 pp 229ndash247 1998

[15] G Gan and S B Riffat ldquoNumerical determination of energylosses at duct junctionsrdquo Applied Energy vol 67 no 3 pp 331ndash340 2000

[16] S Moujaes and R Gundavelli ldquoCFD simulation of leak inresidential HVAC ductsrdquo Energy and Buildings vol 54 pp 534ndash539 2012

[17] J P Abraham J C K Tong and E M Sparrow ldquoBreakdownof laminar pipe flow into transitional intermittency and subse-quent attainment of fully developed intermittent or turbulentflowrdquo Numerical Heat Transfer Part B vol 54 no 2 pp 103ndash115 2008

[18] W J Minkowycz J P Abraham and EM Sparrow ldquoNumericalsimulation of laminar breakdown and subsequent intermittentand turbulent flow in parallel-plate channels effects of inletvelocity profile and turbulence intensityrdquo International Journalof Heat and Mass Transfer vol 52 no 17ndash18 pp 4040ndash40462009

[19] J P Abraham E M Sparrow and J C K Tong ldquoHeat transferin all pipe flow regimes laminar transitionalintermittent andturbulentrdquo International Journal of Heat and Mass Transfer vol52 no 3ndash4 pp 557ndash563 2009

[20] R D Lovik J P AbrahamW JMinkowycz and EM SparrowldquoLaminarization and turbulentization in a pulsatile pipe flowrdquoNumerical Heat Transfer Part A vol 56 no 11 pp 861ndash8792009

[21] J P Abraham E M Sparrow and W J Minkowycz ldquoInternal-flow nusselt numbers for the low-reynolds-number end of thelaminar-to-turbulent transition regimerdquo International Journalof Heat and Mass Transfer vol 54 no 1ndash3 pp 584ndash588 2011

[22] D A Kose and E Dick ldquoPrediction of the pressure distributionon a cubical building with implicit LESrdquo Journal of WindEngineering and Industrial Aerodynamics vol 98 no 10ndash11 pp628ndash649 2010

[23] C-H HuM Ohba and R Yoshie ldquoCFDmodelling of unsteadycross ventilation flows using LESrdquo Journal of Wind Engineeringand Industrial Aerodynamics vol 96 no 10ndash11 pp 1692ndash17062008

[24] C M Mak J Wu C Ye and J Yang ldquoFlow noise from spoilersin ductsrdquo Journal of the Acoustical Society of America vol 125no 6 pp 3756ndash3765 2009

[25] Fluent Ansys Fluent 130 Theory Guide Turbulence ANSYSCanonsburg Pa USA 2010

[26] J O Hinze Turbulence McGraw-Hill New York NY USA1975

[27] J Smagorinsky ldquoGeneral circulation experiments with theprimitive equations the basic experimentrdquo Monthly WeatherReview vol 91 pp 99ndash164 1963

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World Journal 3

Table 1 Fifteen fitting configurations tested in this study

Case Configuration of fitting(s) Mean flow velocities(ms)

1r

r = 0025m at p110 15 20 25 30

2r

r = 005m at p110 14 18 22 26

3 r

r = 0075m at p110 12 14 16 18

4

r = 0025m at p1r2r2 15 20 25 30 35

5r = 005m at p1

r2r210 15 20 25 30

6r = 0075m at p1

r2r210 12 14 16 18

7r = 0025m at p1

r

r = 0025m at p2r 10 15 20 25 30

8

r = 005m at p2r = 0025m at p1r r

10 14 18 22 26

9

r = 0075m at p2r = 0025m at p1r r

10 12 14 16 18

10r r

r = 005m at p2r = 005m at p1

10 13 16 19 22

11r = 0075m at p2

r rr = 005m at p1

10 12 14 16 18

12r = 0075m at p1 r = 0075m at p2

r r10 11 12 13 14

4 The Scientific World Journal

Table 1 Continued

Case Configuration of fitting(s) Mean flow velocities(ms)

13

r = 005m at p1 r = 005m at p2r2r2 r2r2

10 14 18 22 26

14r = 005m at p1

r2r2

r = 005m at p2r2r2

r = 005m at p3r2r2 10 13 16 19 22

15r = 005m at p1

r

r = 005m at p2r

r = 005m at p3r

10 12 14 16 18

the control variable was the obstructed ratio of the fittingarea to the cross-sectional area of the duct The plates weremade from 1mm thick steel plate and they were fixed tothe adjoining flanges of the test duct The gap was sealedwith compressed foam rubber As shown in Table 1 15configurations were tested In Cases 1ndash6 only a single fittingwas inserted into position p1 In Cases 7ndash13 two fittings wereinserted at two different positions (p1 and p2) and in Cases14-15 three fittings were inserted at three different positions(p1 p2 and p3)

The velocity profile in the empty test duct was measuredto make sure that the flow could be symmetrically developedinside the duct A pitot tube was used to sample the dynamicpressure at specified points in the duct cross-section Basedon the measurements obtained using this empty duct arelationship between the mean duct velocity (119910) and thevelocity measured at the center of the duct (119909) was developed(119910 = 09639119909 minus 03289 (119877

2= 09997)) and this was used

to calibrate the mean duct velocity in later tests using themeasured center velocity The mean airflow velocities testedfor each case are listed in Table 1

The static pressure losses across the fittings were mea-sured using two piezometric rings placed at positions p1 p2and p3 (Figure 1) Each ring consisted of four static pressuretappings one in each duct face The downstream ring wassufficiently far away (five times the duct dimensions) from thetest fitting to ensure that full static pressure recovery couldtake place in the wake of the flow obstructions under test

4 Numerical Modeling

This section briefly discusses the numerical method usedby LES modeling and introduces the test cases selected toevaluate it

41 Governing Equations of LES The governing equationsused for large eddies can be obtained by filtering the time-dependent Navier-Stokes equations Eddies whose scales aresmaller than the filtering width or grid spacing adopted in thecomputations are effectively removed by the filtering process

Inlet

Outlet

Pitot

125 m 1 m 2 m575 m

ΔPS3ΔPS2ΔPS1

05 m

02 m05 m02 m 02 m

05 m05 m

p1 p2 p3

Figure 1 A schematic diagram of the experimental system (p1 p2and p3 are the positions where the first second and third fittingsare inserted respectively Δ1198751198781 Δ1198751198782 and Δ1198751198783 represent the staticpressure loss across the first second and third fittings resp)

Then the resulting equations only govern the dynamics oflarge eddies

In this study the filtering operation provided by thefinite volume discretization method as described in [25] isemployed

120593 (119909) =1

119881int

119881

0120593 (1199091015840) 1198891199091015840 1199091015840isin 119881 (5)

where 120593 (119909) represents a filtered variable and119881 the volume ofa computational control cell The filter function 119866(119909 119909

1015840) is

119866(119909 1199091015840) =

1

119881 1199091015840isin 119881 or 119866(119909 119909

1015840) = 0 119909

1015840notin 119881

(6)

The Scientific World Journal 5

01 m

01 m

r

(a)

01 m

01 m

r2 r2

(b)

Figure 2 Cross-section of the duct with two types of flat-plate fittings (shaded area) (a) Centrally placed fittings 119903 = 0025m 005m0075m (b) The geometries consisted of plates protruding symmetrically from both sides of the duct leaving a central vertical strip of theduct open later called a centrally opened fitting 119903 = 0025m 005m 0075m

In this study the governing equations of LES for incom-pressible flows were obtained by filtering the Navier-Stokesequations

120597119906119894

120597119909119894

= 0

120597

120597119905(120588119906119894) +

120597

120597119909119895

(120588119906119894 119906119895) =120597

120597119909119895

(120590119894119895) minus120597119901

120597119909119894

minus120597120591119894119895

120597119909119895

(7)

where 120590119894119895 is the stress tensor due to molecular viscositydefined by

120590119894119895 equiv [120583(120597119906119894

120597119909119895

+120597119906119895

120597119909119894

)] minus2

3120583120597119906119894

120597119909119894

120575119894119895 (8)

and 120591119894119895 is the subgrid-scale (SS) stress defined by

120591119894119895 equiv 120588119906119894119906119895 minus 120588119906119894119906119895 (9)

Since the subgrid-scale stress term in the LES modelis unknown it requires modeling to close the governingequations Currently the most adopted subgrid-scale turbu-lence model which employs the Boussinesq hypothesis [26]computes subgrid-scale turbulent stresses by

120591119894119895 minus1

3120591119896119896120575119894119895 = minus2120583119905119878119894119895 (10)

where 120583119905 is subgrid-scale turbulent viscosity The isotropicpart 120591119896119896 which is not modeled is added to the filteredstatic pressure term 119878119894119895 is the rate-of-strain tensor under theresolved scale defined by

119878119894119895 =1

2(

120597119906119894

120597119909119895

+120597119906119895

120597119909119894

) (11)

In this study the subgrid-scale turbulent viscosity 120583119905was modeled by the Smagorinsky-Lilly model which wasinitially proposed by Smagorinsky [27] In the Smagorinsky-Lillymodel the turbulent viscosity coefficient is calculated by

120583119905 = 1205881198712119878

1003816100381610038161003816100381611987810038161003816100381610038161003816 (12)

where |119878| equiv radic2119878119894119895119878119894119895 119871119878 is the subgrid mixing lengthcalculated by

119871119878 = min (120581119889 11986211987811988113

) (13)

where 120581 is the von Kaman constant 119889 the distance to theclosest wall and 119862119878 the Smagorinsky constant empiricallygiven as 01

42 Mesh Work Boundary Conditions and NumericalScheme In this study a full straight square duct (01 times 01m2in section and 575m in length) was simulated (see Figure 3)The fluid air was assumed to be incompressible and thegravitational acceleration was not considered The Reynoldsnumber based on the mean duct velocity and square ductdimensions was 067ndash147 times 105 Mean duct velocity wasimposed on the inlet boundary and the flow turbulence ischaracterized by turbulence intensity (10) and hydraulicdiameter (01m) On the outlet boundary it is assumed thatthe flow is fully developed with zero normal gradients andzero background pressure There was no slip of fluid at thesurfaces of the duct and fitting(s) Structured grids were usedto discretize the computational domain in which the firstgrids are 25 times 10

minus5m away from the fitting(s) Then the 119910+

(119910+ = 120588119906120591119910119901120583) value for the first grid points was around05ndash2 depending on the mean duct velocity which indicatesthat the first grids arewithin the laminar sublayerThemeshesbecome coarser in the region far away from the fitting(s) but

6 The Scientific World Journal

Inlet Outlet

02 m

02 m

02 m05 m

05 m

05 m

575 m

175 m

p1 p2 p3

2 m1 m

ΔPS1 ΔPS2ΔPS2

Figure 3 A schematic diagram of the duct system in the numerical simulations

remain high density near the duct walls (119910+ lt 5) When themesh is fine enough to resolve the laminar sublayer the LESmodel applies the laminar stress-strain relationship to obtainthe wall shear stress

119906

119906120591

=120588119906120591119910

120583 (14)

The sensitivity of mesh number was systematically tested Foreach case three different mesh systems (a coarser a mediumand a finer) were constructed and the final numerical solu-tions based on these three meshes were compared Finallyin compromise between the numerical accuracy and costmeshes with around 20 times 106 25 times 106 and 30 times 106 gridswere selected for the cases with one fitting two fittings andthree fittings respectively The time step size used in the LESsimulations was 00002 s which ensures that the convergencecan be achieved within 5ndash10 iterative steps for each timestep

Based on the finite volumemethod (FVM) the governingequations are discretized to algebraic equations on the gridsystemThe convection term was discretized by the boundedcentral differencing scheme while the pressure staggeringoption scheme (PRESTO) was selected for pressure interpo-lation Finally the SIMPLEC algorithm was used to couplethe pressure and velocity equations

43 Cases Simulated In order to evaluate the accuracy andreliability of the LES model in predicting the pressure lossesacross multiple in-duct fittings two tested cases are selectedto be numerically reproduced Case 7 at a mean flow velocityof 20ms and Case 14 at 19ms The predicted pressure lossesare compared with those measured in the experiments

5 Results and Discussions

As shown in Table 1 five mean flow velocities were testedfor each case However due to the difficulty in accuratelycontrolling the mean velocity during the tests the testedvelocities were not necessarily the same for all casesThis doesnot influence the later analysis In this section the measuredor simulated pressure losses (Pa) across in-duct fittings aredirectly presented and analyzed If one is interested in the 119896

factors these can be obtained using (5) in Section 2

51 Effect of Reynolds Number (119877119890) In practice there arevarious types of HVAC ducts in terms of cross-sectionalshape and dimension and mean flow velocity Despite thiscomplexity the dimensionless Re can be used to representthese duct characteristics given that the same Re indicatesaerodynamic similarity In this section the effect of Re on thepressure losses across fittings is examined when the fittingconfiguration remains unchanged It is found that the pres-sure loss across a fitting almost has a linear relationship withthe duct Re (the example of Case 10 is shown in Figure 4)This implies that any factors increasing the duct Re such asan increase in velocity and cross-sectional dimensions canresult in an increase in pressure loss across an in-duct fittingIn other words pressure losses across the in-duct fitting(s) ofa larger duct with a higher velocity remain high

52 Effect of Fitting Configuration In order to study the effectof fitting configuration on the pressure losses this sectiondiscusses the cases with the same Re to exclude the influenceof Re on the comparison of different fitting configurations

The effect of fitting type on pressure losses across fittingsis studied when the obstruction ratio is kept constant Theobstruction ratio is defined as the area ratio of the fitting tothe duct cross-section namely the ratio of the shaded areato the whole duct section (see Figure 2) Table 2 summarizesthe comparison of pressure losses across the two types offittings namely the centrally placed fitting and the centrallyopened fitting (in Figure 2) From Table 2 it can be seenthat the pressure loss across a centrally placed fitting isremarkably larger than that across a centrally opened fittingThis can be explained by the fact that the velocity profile inthe cross-section of a duct follows a parabolic distributionnamely the largest in the center and the smallest on the ductsurfaces Thus centrally placed fittings obstruct the fastestcentral airflow and lead to the largest pressure losses whereascentrally opened fittings allow this strongest airflow to passthrough and offer much less resistance to the airflow It canalso be observed that the deviation ratio of pressure lossbetween these two types of fittings is not the same and isdependent on the obstruction ratio

The effect of the obstruction ratio on pressure lossesacross fittings is studied at a Re of 67 times 104 and the resultsare shown in Figure 5 For all cases an increase in the

The Scientific World Journal 7

Table 2 Effect of fitting type on pressure losses (Pa) across fitting(s)

Re (times104)

Case 1 versus 4(only p1)

Case 2 versus 5(only p1)

Case 3 versus 6(only p1)

Case 10 versus 13(p1 and p2)

Case 15 versus 14(p1 p2 and p3)

67 mdash 204 versus 150 944 versus 640 190 versus 144 at p1172 versus 150 at p2

208 versus 142 at p1198 versus 154 at p2180 versus 118 at p3

133 286 versus 144 mdash mdash mdash mdash

Table 3 Effect of downstream fitting(s) on pressure loss (Pa) across an upstream fitting

(a) Base case Case 1

Re = 667 times 104 Case 1 Case 7 Case 8 Case 9

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782

Pressure loss 72 66 66 64 185 54 588Percentage decrease 83 111 250

(b) Base case Case 2

Re = 667 times 104 Case 2 Case 10 Case 11 Case 15

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 204 190 172 184 774 208 198 180Percentage decrease 69 98 minus20 29

(c) Base case Case 3

Re = 667 times 104 Case 3 Case 12

Δ1198751198781 Δ1198751198781 Δ1198751198782

Pressure loss 944 1030 750Percentage decrease minus91

(d) Base case Case 5

Re = 667 times 104 Case 5 Case 13 Case 14

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 150 144 150 142 154 118Percentage decrease 40 53 minus27

fittingrsquos obstruction ratio significantly increases the pressureloss across it However the percentage increase in pressureloss is dependent on the obstruction ratio fitting type andthe interaction of neighboring fittings For a centrally placedsingle fitting (Cases 1ndash3) when the obstruction ratio increasesfrom 05 to 075 (from Case 2 to 3) the percentage increaseis approximately 363 which is almost one time higher thanthe increase (183)when the obstruction ratio increases from025 to 05 (from Case 1 to 2) It is also observed that thispercentage increase is relatively lower in the case with thecentrally opened fitting (Cases 5-6) and is also influenced bythe presence of neighboring fittings (Cases 7ndash9 and Cases 10ndash12) However regardless of the change in the obstruction ratioof a neighboring fitting the pressure loss across a fitting isonly changed slightly

53 Effect of Interaction of Multiple Fittings Table 3 sum-marizes the pressure loss across an upstream fitting and itspercentage decrease as a result of its downstream fittingsFrom Table 3(a) it can be seen that the presence of adownstream centrally placed fitting can reduce the pressureloss across its upstream fitting and the percentage decrease

increases remarkably with the increase in the obstructionratio of the downstream fitting However a comparison ofTable 3(a)ndash(c) shows that with the increase in the obstructionratio of the upstream fitting the decrease in pressure lossacross it is gradually decreased becoming minus91 when theobstruction ratio reaches 075 As tabulated in Table 3(d) forthe centrally opened fitting the presence of a downstreamfitting can reduce the pressure loss across it whereas twodownstream fittings complicate this situation

The effect of upstream fittings on the pressure loss acrossa downstream fitting is also evaluated and the results arepresented in Table 4 For the centrally placed fitting the pres-ence of upstream fittings significantly reduces the pressurelosses across its downstream fitting(s) (see Table 4(a)ndash(c))Contrarily for the centrally opened fitting this pressure lossis negligibly affected by the presence of an upstream fittingwhereas it is significantly decreased by the presence of twoupstream fittings (see Table 4(d))

The above results suggest that as a result of the effect ofdownstream and upstreamfittings the pressure loss across anin-duct fitting is changed substantially This can be explainedby the fact that the presence of a fitting changes the airflow

8 The Scientific World Journal

Table 4 Effect of upstream fitting(s) on pressure loss (Pa) across a downstream fitting

(a) Base case Case 1

Re = 667 times 104 Case 1 Case 7

Δ1198751198781 Δ1198751198781 Δ1198751198782

Pressure loss 72 66 66Percentage decrease 83

(b) Base case Case 2

Re = 667 times 104 Case 2 Case 8 Case 10 Case 15

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 204 64 185 190 172 208 198 180Percentage decrease 93 157 29 118

(c) Base case Case 3

Re = 667 times 104 Case 3 Case 9 Case 11 Case 12

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782

Pressure loss 944 54 588 184 774 1030 750Percentage decrease 377 180 206

(d) Base case Case 5

Re = 667 times 104 Case 5 Case 13 Case 14

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 150 144 150 142 154 118Percentage decrease 00 minus27 213

Table 5 Comparison of pressure losses (Pa) across multiple interactive and individual fittings

Re = 667 times 104 Case 7 Case 8 Case 9 Case 10 Case 11 Case 12 Case 13 Case 14 Case 15

Across interactivefittings 132 249 642 362 958 1780 294 414 586

Across individualfittings 144 276 1016 408 1148 1888 300 450 612

Percentage decrease 83 98 368 113 166 57 20 80 42

direction and turbulence around its neighboring fitting(s)and consequently modifies the 119896 factor (see (5) in Section 2)The results also demonstrate that the effect of a neighboringfitting is complex that is different fitting type location(upstream or downstream) obstruction ratio and duct Recan result in very distinctive pressure lossesThis implies thatthe 119896 factors for individual fittings provided in the ASHRAEhandbook and the CIBSE guide are inaccurate in a condi-tion when the interaction of neighboring fittings cannot beignored

The pressure losses across multiple interactive and indi-vidual in-duct fittings are compared (see Table 5) In Table 5the pressure losses across interactive fittings for Cases 7ndash15are directly measured in the tests In order to evaluate theeffect of the fittingsrsquo interaction on the total pressure lossfor each case the pressure losses across every individualfitting are summed for comparison Taking Case 8 as anexample the pressure losses across its individual fittings aresummed fromCase 1 andCase 2 Based on the summations ofindividual pressure loss the percentage decreases in pressurelosses across multiple fittings are calculated It can be seen

that the pressure losses across multiple interactive fittingsare lower than those across multiple individual fittings andthe percentage decrease is dependent on the configurationand combination of the fittings This finding is supportedby the previous study on two bends by Rahmeyer [12]Again this demonstrates that the calculation of pressurelosses across multiple closely mounted fittings via summingthose across individual fittings is inaccurate This methodoverpredicts the total pressure loss which may consequentlyresult in energy waste owing to the selection of larger fans Insuch a condition exploring an accurate reliable and high-efficiency predictive method such as a validated CFDmodelis crucially important

54 Validation of LES Modeling In order to validate the LESmodel in predicting pressure losses across multiple in-ductfittings the predicted values of the pressure losses acrossfittings in Case 7 at 20ms andCase 14 at 19ms are comparedwith corresponding datameasured in the testsThe results arepresented in Table 6 It can be seen that the predicted results

The Scientific World Journal 9

0

200

400

600

800

1000

60000 90000 120000 150000

Pres

sure

loss

(Pa)

ReCase 10-p1Case 10-p2

Figure 4 Effect of Reynolds number on pressure loss acrossfitting(s)

Pres

sure

loss

(Pa)

0

200

400

600

800

1000

1200

0 1 2 3 4 5 6 7 8 9 10 11 12Case number

At p1At p2

Figure 5 Effect of obstruction ratio on pressure losses acrossfitting(s)

agree well with the measured data with a relative deviationless than 3This indicates that the LESmodel can accuratelyresolve the flow field in a HVAC duct with multiple in-ductfittings

Compared to the experimental measurement numericalmodeling has an incomparable advantage in obtaining in-duct flow details such as velocity and pressure distributionsFigure 6 presents the pressure distribution along the ductcenterline in Case 7 at a mean flow velocity of 20ms Figures7 and 8 show the pressure and air speed contours on the centerplane of the duct respectively These kinds of pressure andair speed distribution are useful because it can not only beused independently for ductwork design (if the numericalmodel is validated before) but also to indicate the locationswhere pressure sensors should be placed in the tests for thelatter the involvement of numerical modeling can save manyexperimental resources and help to produce more reliableexperimental data Thus the successful use of numerical

0

200

400

600

800

1000

0 1 2 3 4 5 6

Pres

sure

(Pa)

Distance along streamwise direction (m)

minus800

minus600

minus400

minus200

p1 p2

Figure 6 Pressure distribution along centerline of the duct (Case 7at 20ms)

modeling is of great significance in optimizing ductworkdesign and improving the database for pressure losses acrossfittings

6 Conclusions

This study examines the pressure losses across multiple in-duct fittings of a ventilation duct using experimental testsTwo tested cases are reproduced by LESmodeling to evaluatethe accuracy and reliability of this numerical method inpredicting the pressure field inside a duct with multiplefittings The following conclusions can be drawn

The flow resistance of a centrally placed fitting is remark-ably larger than that of a centrally opened fitting basicallydue to the fact that the velocity profile of a cross-sectionof a duct follows a parabolic distribution For all cases anincrease in the obstruction ratio of a fitting significantlyincreases the pressure loss across it However this pressureloss does not linearly increase with the obstruction ratiothere is a substantial increase in pressure loss when theobstruction ratio increases from 05 to 075 Again this isbecause the velocity profile on a cross-section is not a uniformdistribution

Since the presence of a fitting changes the airflow direc-tion and turbulence around its close neighboring fitting(s)and consequently modifies the 119896 factor the pressure lossesacross the neighboring fitting(s) are changed substantiallyHowever the magnitude of this change is affected by manyfactors such as fitting type location (upstream or down-stream) obstruction ratio and Re In addition the pressurelosses across multiple interactive fittings are lower thanthose across multiple similar individual fittings althoughthe percentage decrease is dependent on the configurationand combination of the fittings These findings imply thatthe calculation of pressure losses across multiple closelymounted fittings via summing those across individual fittingsis inaccurateThismethod overpredicts the total pressure lossand could result in energy waste via the selection of largerfans Thus a more accurate reliable and high-efficiency

10 The Scientific World Journal

0

005

01Z

(m)

18 2 22 24 26 28 3X (m)

Pressure minus300 minus200 minus100 0 100 200 300 400 500 600

Figure 7 Pressure (Pa) contour around the in-duct fittings on the center plane of the duct (Case 7 at 20ms)

18 2 22 24 26 28 3

Velocity-magnitude 5 10 15 20 25 30

0

005

01

Z(m

)

X (m)

Figure 8 Air speed (ms) contour around the in-duct fittings on the center plane of the duct (Case 7 at 20ms)

Table 6 Comparison of predicted and measured pressure losses(Pa)

Case 7 (20ms) Case 14 (19ms)Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Measurement 256 260 486 528 410LES simulation 258 254 491 539 417

predictive method such as a validated CFD model shouldbe explored

The predicted results by LES modeling agree well withthe measured data in the tests which demonstrates thatthe LES model can accurately resolve the flow field in aHVAC duct with multiple in-duct fittings Compared tothe experimental measurement the numerical modeling canprovide the details of pressure distribution This predictedpressure distribution can be used not only independently in aductwork design (if the numerical model has been validatedbefore) but also to assist in tests to find correct locations toplace pressure sensors In the latter case the use of numericalmodeling can potentially save many experimental resourcesand help to produce more reliable experimental data

References

[1] ASHRAE HandbookmdashFundamentals SI Edition chapter 21-22 American Society of Heating Refrigerating and Air-Conditioning Engineers Atlanta Ga USA 2009

[2] CIBSEThe Chartered Institution of Building Services EngineersHeating Ventilating Air Conditioning and Refrigeration CIBSEGuide B Chartered Institution of Building Services EngineersLondon UK 3rd edition 2005

[3] I E Idelchik Handbook of Hydraulic Resistance 3rd edition1994

[4] ASHRAE Standard 120P ldquoMethods of testing to determine flowresistance of HVAC air ducts and fittingsrdquo American Society ofHeating Refrigerating andAir-conditioning Engineers AtlantaGa USA 1995

[5] B Abushakra I S Walker and M H Sherman ldquoA studyof pressure losses in residential air distribution systemsrdquo inProceedings of the American Council for an Energy EfficientEconomy (ACEEE rsquo02) Washington DC USA 2002 LBNLReport 49700 Lawrence Berkeley National Laboratory CalifUSA 2002

[6] L Shao and S B Riffat ldquoAccuracy of CFD for predictingpressure losses in HVAC duct fittingsrdquo Applied Energy vol 51no 3 pp 233ndash248 1995

[7] S M Atkin and L Shao ldquoEffect on pressure loss of separationand orientation of closely coupledHVACduct fittingsrdquoBuildingServices Engineering Research and Technology vol 21 no 3 pp175ndash178 2000

[8] L Shao and S B Riffat ldquoCFD for prediction of k-factors of ductfittingsrdquo International Journal of Energy Research vol 19 no 1pp 89ndash93 1995

[9] R R Rend E M Sparrow D W Bettenhausen and J PAbraham ldquoParasitic pressure losses in diffusers and in theirdownstream piping systems for fluid flow and heat transferrdquoInternational Journal of Heat and Mass Transfer vol 61 pp 56ndash61 2013

[10] J P Abraham E M Sparrow J C K Tong and D WBettenhausen ldquoInternal flows which transist from turbulentthrough intermittent to laminarrdquo International Journal of Ther-mal Sciences vol 49 no 2 pp 256ndash263 2010

[11] E M Sparrow J P Abraham and W J Minkowycz ldquoFlowseparation in a diverging conical duct effect of reynolds numberand divergence anglerdquo International Journal of Heat and MassTransfer vol 52 no 13ndash14 pp 3079ndash3083 2009

The Scientific World Journal 11

[12] W J Rahmeyer ldquoPressure loss coefficients for close-coupledpipe ellsrdquo ASHRAE Transactions vol 108 pp 390ndash406 2002

[13] G Gan and S B Riffat ldquok-factors for HVAC ducts numericaland experimental determinationrdquo Building Services EngineeringResearch and Technology vol 16 no 3 pp 133ndash139 1995

[14] S A Mumma T A Mahank and Y-P Ke ldquoAnalytical determi-nation of duct fitting loss-coefficientsrdquo Applied Energy vol 61no 4 pp 229ndash247 1998

[15] G Gan and S B Riffat ldquoNumerical determination of energylosses at duct junctionsrdquo Applied Energy vol 67 no 3 pp 331ndash340 2000

[16] S Moujaes and R Gundavelli ldquoCFD simulation of leak inresidential HVAC ductsrdquo Energy and Buildings vol 54 pp 534ndash539 2012

[17] J P Abraham J C K Tong and E M Sparrow ldquoBreakdownof laminar pipe flow into transitional intermittency and subse-quent attainment of fully developed intermittent or turbulentflowrdquo Numerical Heat Transfer Part B vol 54 no 2 pp 103ndash115 2008

[18] W J Minkowycz J P Abraham and EM Sparrow ldquoNumericalsimulation of laminar breakdown and subsequent intermittentand turbulent flow in parallel-plate channels effects of inletvelocity profile and turbulence intensityrdquo International Journalof Heat and Mass Transfer vol 52 no 17ndash18 pp 4040ndash40462009

[19] J P Abraham E M Sparrow and J C K Tong ldquoHeat transferin all pipe flow regimes laminar transitionalintermittent andturbulentrdquo International Journal of Heat and Mass Transfer vol52 no 3ndash4 pp 557ndash563 2009

[20] R D Lovik J P AbrahamW JMinkowycz and EM SparrowldquoLaminarization and turbulentization in a pulsatile pipe flowrdquoNumerical Heat Transfer Part A vol 56 no 11 pp 861ndash8792009

[21] J P Abraham E M Sparrow and W J Minkowycz ldquoInternal-flow nusselt numbers for the low-reynolds-number end of thelaminar-to-turbulent transition regimerdquo International Journalof Heat and Mass Transfer vol 54 no 1ndash3 pp 584ndash588 2011

[22] D A Kose and E Dick ldquoPrediction of the pressure distributionon a cubical building with implicit LESrdquo Journal of WindEngineering and Industrial Aerodynamics vol 98 no 10ndash11 pp628ndash649 2010

[23] C-H HuM Ohba and R Yoshie ldquoCFDmodelling of unsteadycross ventilation flows using LESrdquo Journal of Wind Engineeringand Industrial Aerodynamics vol 96 no 10ndash11 pp 1692ndash17062008

[24] C M Mak J Wu C Ye and J Yang ldquoFlow noise from spoilersin ductsrdquo Journal of the Acoustical Society of America vol 125no 6 pp 3756ndash3765 2009

[25] Fluent Ansys Fluent 130 Theory Guide Turbulence ANSYSCanonsburg Pa USA 2010

[26] J O Hinze Turbulence McGraw-Hill New York NY USA1975

[27] J Smagorinsky ldquoGeneral circulation experiments with theprimitive equations the basic experimentrdquo Monthly WeatherReview vol 91 pp 99ndash164 1963

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Journal ofEngineeringVolume 2014

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Wind EnergyJournal of

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Nuclear EnergyInternational Journal of

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High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

4 The Scientific World Journal

Table 1 Continued

Case Configuration of fitting(s) Mean flow velocities(ms)

13

r = 005m at p1 r = 005m at p2r2r2 r2r2

10 14 18 22 26

14r = 005m at p1

r2r2

r = 005m at p2r2r2

r = 005m at p3r2r2 10 13 16 19 22

15r = 005m at p1

r

r = 005m at p2r

r = 005m at p3r

10 12 14 16 18

the control variable was the obstructed ratio of the fittingarea to the cross-sectional area of the duct The plates weremade from 1mm thick steel plate and they were fixed tothe adjoining flanges of the test duct The gap was sealedwith compressed foam rubber As shown in Table 1 15configurations were tested In Cases 1ndash6 only a single fittingwas inserted into position p1 In Cases 7ndash13 two fittings wereinserted at two different positions (p1 and p2) and in Cases14-15 three fittings were inserted at three different positions(p1 p2 and p3)

The velocity profile in the empty test duct was measuredto make sure that the flow could be symmetrically developedinside the duct A pitot tube was used to sample the dynamicpressure at specified points in the duct cross-section Basedon the measurements obtained using this empty duct arelationship between the mean duct velocity (119910) and thevelocity measured at the center of the duct (119909) was developed(119910 = 09639119909 minus 03289 (119877

2= 09997)) and this was used

to calibrate the mean duct velocity in later tests using themeasured center velocity The mean airflow velocities testedfor each case are listed in Table 1

The static pressure losses across the fittings were mea-sured using two piezometric rings placed at positions p1 p2and p3 (Figure 1) Each ring consisted of four static pressuretappings one in each duct face The downstream ring wassufficiently far away (five times the duct dimensions) from thetest fitting to ensure that full static pressure recovery couldtake place in the wake of the flow obstructions under test

4 Numerical Modeling

This section briefly discusses the numerical method usedby LES modeling and introduces the test cases selected toevaluate it

41 Governing Equations of LES The governing equationsused for large eddies can be obtained by filtering the time-dependent Navier-Stokes equations Eddies whose scales aresmaller than the filtering width or grid spacing adopted in thecomputations are effectively removed by the filtering process

Inlet

Outlet

Pitot

125 m 1 m 2 m575 m

ΔPS3ΔPS2ΔPS1

05 m

02 m05 m02 m 02 m

05 m05 m

p1 p2 p3

Figure 1 A schematic diagram of the experimental system (p1 p2and p3 are the positions where the first second and third fittingsare inserted respectively Δ1198751198781 Δ1198751198782 and Δ1198751198783 represent the staticpressure loss across the first second and third fittings resp)

Then the resulting equations only govern the dynamics oflarge eddies

In this study the filtering operation provided by thefinite volume discretization method as described in [25] isemployed

120593 (119909) =1

119881int

119881

0120593 (1199091015840) 1198891199091015840 1199091015840isin 119881 (5)

where 120593 (119909) represents a filtered variable and119881 the volume ofa computational control cell The filter function 119866(119909 119909

1015840) is

119866(119909 1199091015840) =

1

119881 1199091015840isin 119881 or 119866(119909 119909

1015840) = 0 119909

1015840notin 119881

(6)

The Scientific World Journal 5

01 m

01 m

r

(a)

01 m

01 m

r2 r2

(b)

Figure 2 Cross-section of the duct with two types of flat-plate fittings (shaded area) (a) Centrally placed fittings 119903 = 0025m 005m0075m (b) The geometries consisted of plates protruding symmetrically from both sides of the duct leaving a central vertical strip of theduct open later called a centrally opened fitting 119903 = 0025m 005m 0075m

In this study the governing equations of LES for incom-pressible flows were obtained by filtering the Navier-Stokesequations

120597119906119894

120597119909119894

= 0

120597

120597119905(120588119906119894) +

120597

120597119909119895

(120588119906119894 119906119895) =120597

120597119909119895

(120590119894119895) minus120597119901

120597119909119894

minus120597120591119894119895

120597119909119895

(7)

where 120590119894119895 is the stress tensor due to molecular viscositydefined by

120590119894119895 equiv [120583(120597119906119894

120597119909119895

+120597119906119895

120597119909119894

)] minus2

3120583120597119906119894

120597119909119894

120575119894119895 (8)

and 120591119894119895 is the subgrid-scale (SS) stress defined by

120591119894119895 equiv 120588119906119894119906119895 minus 120588119906119894119906119895 (9)

Since the subgrid-scale stress term in the LES modelis unknown it requires modeling to close the governingequations Currently the most adopted subgrid-scale turbu-lence model which employs the Boussinesq hypothesis [26]computes subgrid-scale turbulent stresses by

120591119894119895 minus1

3120591119896119896120575119894119895 = minus2120583119905119878119894119895 (10)

where 120583119905 is subgrid-scale turbulent viscosity The isotropicpart 120591119896119896 which is not modeled is added to the filteredstatic pressure term 119878119894119895 is the rate-of-strain tensor under theresolved scale defined by

119878119894119895 =1

2(

120597119906119894

120597119909119895

+120597119906119895

120597119909119894

) (11)

In this study the subgrid-scale turbulent viscosity 120583119905was modeled by the Smagorinsky-Lilly model which wasinitially proposed by Smagorinsky [27] In the Smagorinsky-Lillymodel the turbulent viscosity coefficient is calculated by

120583119905 = 1205881198712119878

1003816100381610038161003816100381611987810038161003816100381610038161003816 (12)

where |119878| equiv radic2119878119894119895119878119894119895 119871119878 is the subgrid mixing lengthcalculated by

119871119878 = min (120581119889 11986211987811988113

) (13)

where 120581 is the von Kaman constant 119889 the distance to theclosest wall and 119862119878 the Smagorinsky constant empiricallygiven as 01

42 Mesh Work Boundary Conditions and NumericalScheme In this study a full straight square duct (01 times 01m2in section and 575m in length) was simulated (see Figure 3)The fluid air was assumed to be incompressible and thegravitational acceleration was not considered The Reynoldsnumber based on the mean duct velocity and square ductdimensions was 067ndash147 times 105 Mean duct velocity wasimposed on the inlet boundary and the flow turbulence ischaracterized by turbulence intensity (10) and hydraulicdiameter (01m) On the outlet boundary it is assumed thatthe flow is fully developed with zero normal gradients andzero background pressure There was no slip of fluid at thesurfaces of the duct and fitting(s) Structured grids were usedto discretize the computational domain in which the firstgrids are 25 times 10

minus5m away from the fitting(s) Then the 119910+

(119910+ = 120588119906120591119910119901120583) value for the first grid points was around05ndash2 depending on the mean duct velocity which indicatesthat the first grids arewithin the laminar sublayerThemeshesbecome coarser in the region far away from the fitting(s) but

6 The Scientific World Journal

Inlet Outlet

02 m

02 m

02 m05 m

05 m

05 m

575 m

175 m

p1 p2 p3

2 m1 m

ΔPS1 ΔPS2ΔPS2

Figure 3 A schematic diagram of the duct system in the numerical simulations

remain high density near the duct walls (119910+ lt 5) When themesh is fine enough to resolve the laminar sublayer the LESmodel applies the laminar stress-strain relationship to obtainthe wall shear stress

119906

119906120591

=120588119906120591119910

120583 (14)

The sensitivity of mesh number was systematically tested Foreach case three different mesh systems (a coarser a mediumand a finer) were constructed and the final numerical solu-tions based on these three meshes were compared Finallyin compromise between the numerical accuracy and costmeshes with around 20 times 106 25 times 106 and 30 times 106 gridswere selected for the cases with one fitting two fittings andthree fittings respectively The time step size used in the LESsimulations was 00002 s which ensures that the convergencecan be achieved within 5ndash10 iterative steps for each timestep

Based on the finite volumemethod (FVM) the governingequations are discretized to algebraic equations on the gridsystemThe convection term was discretized by the boundedcentral differencing scheme while the pressure staggeringoption scheme (PRESTO) was selected for pressure interpo-lation Finally the SIMPLEC algorithm was used to couplethe pressure and velocity equations

43 Cases Simulated In order to evaluate the accuracy andreliability of the LES model in predicting the pressure lossesacross multiple in-duct fittings two tested cases are selectedto be numerically reproduced Case 7 at a mean flow velocityof 20ms and Case 14 at 19ms The predicted pressure lossesare compared with those measured in the experiments

5 Results and Discussions

As shown in Table 1 five mean flow velocities were testedfor each case However due to the difficulty in accuratelycontrolling the mean velocity during the tests the testedvelocities were not necessarily the same for all casesThis doesnot influence the later analysis In this section the measuredor simulated pressure losses (Pa) across in-duct fittings aredirectly presented and analyzed If one is interested in the 119896

factors these can be obtained using (5) in Section 2

51 Effect of Reynolds Number (119877119890) In practice there arevarious types of HVAC ducts in terms of cross-sectionalshape and dimension and mean flow velocity Despite thiscomplexity the dimensionless Re can be used to representthese duct characteristics given that the same Re indicatesaerodynamic similarity In this section the effect of Re on thepressure losses across fittings is examined when the fittingconfiguration remains unchanged It is found that the pres-sure loss across a fitting almost has a linear relationship withthe duct Re (the example of Case 10 is shown in Figure 4)This implies that any factors increasing the duct Re such asan increase in velocity and cross-sectional dimensions canresult in an increase in pressure loss across an in-duct fittingIn other words pressure losses across the in-duct fitting(s) ofa larger duct with a higher velocity remain high

52 Effect of Fitting Configuration In order to study the effectof fitting configuration on the pressure losses this sectiondiscusses the cases with the same Re to exclude the influenceof Re on the comparison of different fitting configurations

The effect of fitting type on pressure losses across fittingsis studied when the obstruction ratio is kept constant Theobstruction ratio is defined as the area ratio of the fitting tothe duct cross-section namely the ratio of the shaded areato the whole duct section (see Figure 2) Table 2 summarizesthe comparison of pressure losses across the two types offittings namely the centrally placed fitting and the centrallyopened fitting (in Figure 2) From Table 2 it can be seenthat the pressure loss across a centrally placed fitting isremarkably larger than that across a centrally opened fittingThis can be explained by the fact that the velocity profile inthe cross-section of a duct follows a parabolic distributionnamely the largest in the center and the smallest on the ductsurfaces Thus centrally placed fittings obstruct the fastestcentral airflow and lead to the largest pressure losses whereascentrally opened fittings allow this strongest airflow to passthrough and offer much less resistance to the airflow It canalso be observed that the deviation ratio of pressure lossbetween these two types of fittings is not the same and isdependent on the obstruction ratio

The effect of the obstruction ratio on pressure lossesacross fittings is studied at a Re of 67 times 104 and the resultsare shown in Figure 5 For all cases an increase in the

The Scientific World Journal 7

Table 2 Effect of fitting type on pressure losses (Pa) across fitting(s)

Re (times104)

Case 1 versus 4(only p1)

Case 2 versus 5(only p1)

Case 3 versus 6(only p1)

Case 10 versus 13(p1 and p2)

Case 15 versus 14(p1 p2 and p3)

67 mdash 204 versus 150 944 versus 640 190 versus 144 at p1172 versus 150 at p2

208 versus 142 at p1198 versus 154 at p2180 versus 118 at p3

133 286 versus 144 mdash mdash mdash mdash

Table 3 Effect of downstream fitting(s) on pressure loss (Pa) across an upstream fitting

(a) Base case Case 1

Re = 667 times 104 Case 1 Case 7 Case 8 Case 9

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782

Pressure loss 72 66 66 64 185 54 588Percentage decrease 83 111 250

(b) Base case Case 2

Re = 667 times 104 Case 2 Case 10 Case 11 Case 15

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 204 190 172 184 774 208 198 180Percentage decrease 69 98 minus20 29

(c) Base case Case 3

Re = 667 times 104 Case 3 Case 12

Δ1198751198781 Δ1198751198781 Δ1198751198782

Pressure loss 944 1030 750Percentage decrease minus91

(d) Base case Case 5

Re = 667 times 104 Case 5 Case 13 Case 14

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 150 144 150 142 154 118Percentage decrease 40 53 minus27

fittingrsquos obstruction ratio significantly increases the pressureloss across it However the percentage increase in pressureloss is dependent on the obstruction ratio fitting type andthe interaction of neighboring fittings For a centrally placedsingle fitting (Cases 1ndash3) when the obstruction ratio increasesfrom 05 to 075 (from Case 2 to 3) the percentage increaseis approximately 363 which is almost one time higher thanthe increase (183)when the obstruction ratio increases from025 to 05 (from Case 1 to 2) It is also observed that thispercentage increase is relatively lower in the case with thecentrally opened fitting (Cases 5-6) and is also influenced bythe presence of neighboring fittings (Cases 7ndash9 and Cases 10ndash12) However regardless of the change in the obstruction ratioof a neighboring fitting the pressure loss across a fitting isonly changed slightly

53 Effect of Interaction of Multiple Fittings Table 3 sum-marizes the pressure loss across an upstream fitting and itspercentage decrease as a result of its downstream fittingsFrom Table 3(a) it can be seen that the presence of adownstream centrally placed fitting can reduce the pressureloss across its upstream fitting and the percentage decrease

increases remarkably with the increase in the obstructionratio of the downstream fitting However a comparison ofTable 3(a)ndash(c) shows that with the increase in the obstructionratio of the upstream fitting the decrease in pressure lossacross it is gradually decreased becoming minus91 when theobstruction ratio reaches 075 As tabulated in Table 3(d) forthe centrally opened fitting the presence of a downstreamfitting can reduce the pressure loss across it whereas twodownstream fittings complicate this situation

The effect of upstream fittings on the pressure loss acrossa downstream fitting is also evaluated and the results arepresented in Table 4 For the centrally placed fitting the pres-ence of upstream fittings significantly reduces the pressurelosses across its downstream fitting(s) (see Table 4(a)ndash(c))Contrarily for the centrally opened fitting this pressure lossis negligibly affected by the presence of an upstream fittingwhereas it is significantly decreased by the presence of twoupstream fittings (see Table 4(d))

The above results suggest that as a result of the effect ofdownstream and upstreamfittings the pressure loss across anin-duct fitting is changed substantially This can be explainedby the fact that the presence of a fitting changes the airflow

8 The Scientific World Journal

Table 4 Effect of upstream fitting(s) on pressure loss (Pa) across a downstream fitting

(a) Base case Case 1

Re = 667 times 104 Case 1 Case 7

Δ1198751198781 Δ1198751198781 Δ1198751198782

Pressure loss 72 66 66Percentage decrease 83

(b) Base case Case 2

Re = 667 times 104 Case 2 Case 8 Case 10 Case 15

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 204 64 185 190 172 208 198 180Percentage decrease 93 157 29 118

(c) Base case Case 3

Re = 667 times 104 Case 3 Case 9 Case 11 Case 12

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782

Pressure loss 944 54 588 184 774 1030 750Percentage decrease 377 180 206

(d) Base case Case 5

Re = 667 times 104 Case 5 Case 13 Case 14

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 150 144 150 142 154 118Percentage decrease 00 minus27 213

Table 5 Comparison of pressure losses (Pa) across multiple interactive and individual fittings

Re = 667 times 104 Case 7 Case 8 Case 9 Case 10 Case 11 Case 12 Case 13 Case 14 Case 15

Across interactivefittings 132 249 642 362 958 1780 294 414 586

Across individualfittings 144 276 1016 408 1148 1888 300 450 612

Percentage decrease 83 98 368 113 166 57 20 80 42

direction and turbulence around its neighboring fitting(s)and consequently modifies the 119896 factor (see (5) in Section 2)The results also demonstrate that the effect of a neighboringfitting is complex that is different fitting type location(upstream or downstream) obstruction ratio and duct Recan result in very distinctive pressure lossesThis implies thatthe 119896 factors for individual fittings provided in the ASHRAEhandbook and the CIBSE guide are inaccurate in a condi-tion when the interaction of neighboring fittings cannot beignored

The pressure losses across multiple interactive and indi-vidual in-duct fittings are compared (see Table 5) In Table 5the pressure losses across interactive fittings for Cases 7ndash15are directly measured in the tests In order to evaluate theeffect of the fittingsrsquo interaction on the total pressure lossfor each case the pressure losses across every individualfitting are summed for comparison Taking Case 8 as anexample the pressure losses across its individual fittings aresummed fromCase 1 andCase 2 Based on the summations ofindividual pressure loss the percentage decreases in pressurelosses across multiple fittings are calculated It can be seen

that the pressure losses across multiple interactive fittingsare lower than those across multiple individual fittings andthe percentage decrease is dependent on the configurationand combination of the fittings This finding is supportedby the previous study on two bends by Rahmeyer [12]Again this demonstrates that the calculation of pressurelosses across multiple closely mounted fittings via summingthose across individual fittings is inaccurate This methodoverpredicts the total pressure loss which may consequentlyresult in energy waste owing to the selection of larger fans Insuch a condition exploring an accurate reliable and high-efficiency predictive method such as a validated CFDmodelis crucially important

54 Validation of LES Modeling In order to validate the LESmodel in predicting pressure losses across multiple in-ductfittings the predicted values of the pressure losses acrossfittings in Case 7 at 20ms andCase 14 at 19ms are comparedwith corresponding datameasured in the testsThe results arepresented in Table 6 It can be seen that the predicted results

The Scientific World Journal 9

0

200

400

600

800

1000

60000 90000 120000 150000

Pres

sure

loss

(Pa)

ReCase 10-p1Case 10-p2

Figure 4 Effect of Reynolds number on pressure loss acrossfitting(s)

Pres

sure

loss

(Pa)

0

200

400

600

800

1000

1200

0 1 2 3 4 5 6 7 8 9 10 11 12Case number

At p1At p2

Figure 5 Effect of obstruction ratio on pressure losses acrossfitting(s)

agree well with the measured data with a relative deviationless than 3This indicates that the LESmodel can accuratelyresolve the flow field in a HVAC duct with multiple in-ductfittings

Compared to the experimental measurement numericalmodeling has an incomparable advantage in obtaining in-duct flow details such as velocity and pressure distributionsFigure 6 presents the pressure distribution along the ductcenterline in Case 7 at a mean flow velocity of 20ms Figures7 and 8 show the pressure and air speed contours on the centerplane of the duct respectively These kinds of pressure andair speed distribution are useful because it can not only beused independently for ductwork design (if the numericalmodel is validated before) but also to indicate the locationswhere pressure sensors should be placed in the tests for thelatter the involvement of numerical modeling can save manyexperimental resources and help to produce more reliableexperimental data Thus the successful use of numerical

0

200

400

600

800

1000

0 1 2 3 4 5 6

Pres

sure

(Pa)

Distance along streamwise direction (m)

minus800

minus600

minus400

minus200

p1 p2

Figure 6 Pressure distribution along centerline of the duct (Case 7at 20ms)

modeling is of great significance in optimizing ductworkdesign and improving the database for pressure losses acrossfittings

6 Conclusions

This study examines the pressure losses across multiple in-duct fittings of a ventilation duct using experimental testsTwo tested cases are reproduced by LESmodeling to evaluatethe accuracy and reliability of this numerical method inpredicting the pressure field inside a duct with multiplefittings The following conclusions can be drawn

The flow resistance of a centrally placed fitting is remark-ably larger than that of a centrally opened fitting basicallydue to the fact that the velocity profile of a cross-sectionof a duct follows a parabolic distribution For all cases anincrease in the obstruction ratio of a fitting significantlyincreases the pressure loss across it However this pressureloss does not linearly increase with the obstruction ratiothere is a substantial increase in pressure loss when theobstruction ratio increases from 05 to 075 Again this isbecause the velocity profile on a cross-section is not a uniformdistribution

Since the presence of a fitting changes the airflow direc-tion and turbulence around its close neighboring fitting(s)and consequently modifies the 119896 factor the pressure lossesacross the neighboring fitting(s) are changed substantiallyHowever the magnitude of this change is affected by manyfactors such as fitting type location (upstream or down-stream) obstruction ratio and Re In addition the pressurelosses across multiple interactive fittings are lower thanthose across multiple similar individual fittings althoughthe percentage decrease is dependent on the configurationand combination of the fittings These findings imply thatthe calculation of pressure losses across multiple closelymounted fittings via summing those across individual fittingsis inaccurateThismethod overpredicts the total pressure lossand could result in energy waste via the selection of largerfans Thus a more accurate reliable and high-efficiency

10 The Scientific World Journal

0

005

01Z

(m)

18 2 22 24 26 28 3X (m)

Pressure minus300 minus200 minus100 0 100 200 300 400 500 600

Figure 7 Pressure (Pa) contour around the in-duct fittings on the center plane of the duct (Case 7 at 20ms)

18 2 22 24 26 28 3

Velocity-magnitude 5 10 15 20 25 30

0

005

01

Z(m

)

X (m)

Figure 8 Air speed (ms) contour around the in-duct fittings on the center plane of the duct (Case 7 at 20ms)

Table 6 Comparison of predicted and measured pressure losses(Pa)

Case 7 (20ms) Case 14 (19ms)Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Measurement 256 260 486 528 410LES simulation 258 254 491 539 417

predictive method such as a validated CFD model shouldbe explored

The predicted results by LES modeling agree well withthe measured data in the tests which demonstrates thatthe LES model can accurately resolve the flow field in aHVAC duct with multiple in-duct fittings Compared tothe experimental measurement the numerical modeling canprovide the details of pressure distribution This predictedpressure distribution can be used not only independently in aductwork design (if the numerical model has been validatedbefore) but also to assist in tests to find correct locations toplace pressure sensors In the latter case the use of numericalmodeling can potentially save many experimental resourcesand help to produce more reliable experimental data

References

[1] ASHRAE HandbookmdashFundamentals SI Edition chapter 21-22 American Society of Heating Refrigerating and Air-Conditioning Engineers Atlanta Ga USA 2009

[2] CIBSEThe Chartered Institution of Building Services EngineersHeating Ventilating Air Conditioning and Refrigeration CIBSEGuide B Chartered Institution of Building Services EngineersLondon UK 3rd edition 2005

[3] I E Idelchik Handbook of Hydraulic Resistance 3rd edition1994

[4] ASHRAE Standard 120P ldquoMethods of testing to determine flowresistance of HVAC air ducts and fittingsrdquo American Society ofHeating Refrigerating andAir-conditioning Engineers AtlantaGa USA 1995

[5] B Abushakra I S Walker and M H Sherman ldquoA studyof pressure losses in residential air distribution systemsrdquo inProceedings of the American Council for an Energy EfficientEconomy (ACEEE rsquo02) Washington DC USA 2002 LBNLReport 49700 Lawrence Berkeley National Laboratory CalifUSA 2002

[6] L Shao and S B Riffat ldquoAccuracy of CFD for predictingpressure losses in HVAC duct fittingsrdquo Applied Energy vol 51no 3 pp 233ndash248 1995

[7] S M Atkin and L Shao ldquoEffect on pressure loss of separationand orientation of closely coupledHVACduct fittingsrdquoBuildingServices Engineering Research and Technology vol 21 no 3 pp175ndash178 2000

[8] L Shao and S B Riffat ldquoCFD for prediction of k-factors of ductfittingsrdquo International Journal of Energy Research vol 19 no 1pp 89ndash93 1995

[9] R R Rend E M Sparrow D W Bettenhausen and J PAbraham ldquoParasitic pressure losses in diffusers and in theirdownstream piping systems for fluid flow and heat transferrdquoInternational Journal of Heat and Mass Transfer vol 61 pp 56ndash61 2013

[10] J P Abraham E M Sparrow J C K Tong and D WBettenhausen ldquoInternal flows which transist from turbulentthrough intermittent to laminarrdquo International Journal of Ther-mal Sciences vol 49 no 2 pp 256ndash263 2010

[11] E M Sparrow J P Abraham and W J Minkowycz ldquoFlowseparation in a diverging conical duct effect of reynolds numberand divergence anglerdquo International Journal of Heat and MassTransfer vol 52 no 13ndash14 pp 3079ndash3083 2009

The Scientific World Journal 11

[12] W J Rahmeyer ldquoPressure loss coefficients for close-coupledpipe ellsrdquo ASHRAE Transactions vol 108 pp 390ndash406 2002

[13] G Gan and S B Riffat ldquok-factors for HVAC ducts numericaland experimental determinationrdquo Building Services EngineeringResearch and Technology vol 16 no 3 pp 133ndash139 1995

[14] S A Mumma T A Mahank and Y-P Ke ldquoAnalytical determi-nation of duct fitting loss-coefficientsrdquo Applied Energy vol 61no 4 pp 229ndash247 1998

[15] G Gan and S B Riffat ldquoNumerical determination of energylosses at duct junctionsrdquo Applied Energy vol 67 no 3 pp 331ndash340 2000

[16] S Moujaes and R Gundavelli ldquoCFD simulation of leak inresidential HVAC ductsrdquo Energy and Buildings vol 54 pp 534ndash539 2012

[17] J P Abraham J C K Tong and E M Sparrow ldquoBreakdownof laminar pipe flow into transitional intermittency and subse-quent attainment of fully developed intermittent or turbulentflowrdquo Numerical Heat Transfer Part B vol 54 no 2 pp 103ndash115 2008

[18] W J Minkowycz J P Abraham and EM Sparrow ldquoNumericalsimulation of laminar breakdown and subsequent intermittentand turbulent flow in parallel-plate channels effects of inletvelocity profile and turbulence intensityrdquo International Journalof Heat and Mass Transfer vol 52 no 17ndash18 pp 4040ndash40462009

[19] J P Abraham E M Sparrow and J C K Tong ldquoHeat transferin all pipe flow regimes laminar transitionalintermittent andturbulentrdquo International Journal of Heat and Mass Transfer vol52 no 3ndash4 pp 557ndash563 2009

[20] R D Lovik J P AbrahamW JMinkowycz and EM SparrowldquoLaminarization and turbulentization in a pulsatile pipe flowrdquoNumerical Heat Transfer Part A vol 56 no 11 pp 861ndash8792009

[21] J P Abraham E M Sparrow and W J Minkowycz ldquoInternal-flow nusselt numbers for the low-reynolds-number end of thelaminar-to-turbulent transition regimerdquo International Journalof Heat and Mass Transfer vol 54 no 1ndash3 pp 584ndash588 2011

[22] D A Kose and E Dick ldquoPrediction of the pressure distributionon a cubical building with implicit LESrdquo Journal of WindEngineering and Industrial Aerodynamics vol 98 no 10ndash11 pp628ndash649 2010

[23] C-H HuM Ohba and R Yoshie ldquoCFDmodelling of unsteadycross ventilation flows using LESrdquo Journal of Wind Engineeringand Industrial Aerodynamics vol 96 no 10ndash11 pp 1692ndash17062008

[24] C M Mak J Wu C Ye and J Yang ldquoFlow noise from spoilersin ductsrdquo Journal of the Acoustical Society of America vol 125no 6 pp 3756ndash3765 2009

[25] Fluent Ansys Fluent 130 Theory Guide Turbulence ANSYSCanonsburg Pa USA 2010

[26] J O Hinze Turbulence McGraw-Hill New York NY USA1975

[27] J Smagorinsky ldquoGeneral circulation experiments with theprimitive equations the basic experimentrdquo Monthly WeatherReview vol 91 pp 99ndash164 1963

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

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StructuresJournal of

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Wind EnergyJournal of

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Nuclear EnergyInternational Journal of

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High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World Journal 5

01 m

01 m

r

(a)

01 m

01 m

r2 r2

(b)

Figure 2 Cross-section of the duct with two types of flat-plate fittings (shaded area) (a) Centrally placed fittings 119903 = 0025m 005m0075m (b) The geometries consisted of plates protruding symmetrically from both sides of the duct leaving a central vertical strip of theduct open later called a centrally opened fitting 119903 = 0025m 005m 0075m

In this study the governing equations of LES for incom-pressible flows were obtained by filtering the Navier-Stokesequations

120597119906119894

120597119909119894

= 0

120597

120597119905(120588119906119894) +

120597

120597119909119895

(120588119906119894 119906119895) =120597

120597119909119895

(120590119894119895) minus120597119901

120597119909119894

minus120597120591119894119895

120597119909119895

(7)

where 120590119894119895 is the stress tensor due to molecular viscositydefined by

120590119894119895 equiv [120583(120597119906119894

120597119909119895

+120597119906119895

120597119909119894

)] minus2

3120583120597119906119894

120597119909119894

120575119894119895 (8)

and 120591119894119895 is the subgrid-scale (SS) stress defined by

120591119894119895 equiv 120588119906119894119906119895 minus 120588119906119894119906119895 (9)

Since the subgrid-scale stress term in the LES modelis unknown it requires modeling to close the governingequations Currently the most adopted subgrid-scale turbu-lence model which employs the Boussinesq hypothesis [26]computes subgrid-scale turbulent stresses by

120591119894119895 minus1

3120591119896119896120575119894119895 = minus2120583119905119878119894119895 (10)

where 120583119905 is subgrid-scale turbulent viscosity The isotropicpart 120591119896119896 which is not modeled is added to the filteredstatic pressure term 119878119894119895 is the rate-of-strain tensor under theresolved scale defined by

119878119894119895 =1

2(

120597119906119894

120597119909119895

+120597119906119895

120597119909119894

) (11)

In this study the subgrid-scale turbulent viscosity 120583119905was modeled by the Smagorinsky-Lilly model which wasinitially proposed by Smagorinsky [27] In the Smagorinsky-Lillymodel the turbulent viscosity coefficient is calculated by

120583119905 = 1205881198712119878

1003816100381610038161003816100381611987810038161003816100381610038161003816 (12)

where |119878| equiv radic2119878119894119895119878119894119895 119871119878 is the subgrid mixing lengthcalculated by

119871119878 = min (120581119889 11986211987811988113

) (13)

where 120581 is the von Kaman constant 119889 the distance to theclosest wall and 119862119878 the Smagorinsky constant empiricallygiven as 01

42 Mesh Work Boundary Conditions and NumericalScheme In this study a full straight square duct (01 times 01m2in section and 575m in length) was simulated (see Figure 3)The fluid air was assumed to be incompressible and thegravitational acceleration was not considered The Reynoldsnumber based on the mean duct velocity and square ductdimensions was 067ndash147 times 105 Mean duct velocity wasimposed on the inlet boundary and the flow turbulence ischaracterized by turbulence intensity (10) and hydraulicdiameter (01m) On the outlet boundary it is assumed thatthe flow is fully developed with zero normal gradients andzero background pressure There was no slip of fluid at thesurfaces of the duct and fitting(s) Structured grids were usedto discretize the computational domain in which the firstgrids are 25 times 10

minus5m away from the fitting(s) Then the 119910+

(119910+ = 120588119906120591119910119901120583) value for the first grid points was around05ndash2 depending on the mean duct velocity which indicatesthat the first grids arewithin the laminar sublayerThemeshesbecome coarser in the region far away from the fitting(s) but

6 The Scientific World Journal

Inlet Outlet

02 m

02 m

02 m05 m

05 m

05 m

575 m

175 m

p1 p2 p3

2 m1 m

ΔPS1 ΔPS2ΔPS2

Figure 3 A schematic diagram of the duct system in the numerical simulations

remain high density near the duct walls (119910+ lt 5) When themesh is fine enough to resolve the laminar sublayer the LESmodel applies the laminar stress-strain relationship to obtainthe wall shear stress

119906

119906120591

=120588119906120591119910

120583 (14)

The sensitivity of mesh number was systematically tested Foreach case three different mesh systems (a coarser a mediumand a finer) were constructed and the final numerical solu-tions based on these three meshes were compared Finallyin compromise between the numerical accuracy and costmeshes with around 20 times 106 25 times 106 and 30 times 106 gridswere selected for the cases with one fitting two fittings andthree fittings respectively The time step size used in the LESsimulations was 00002 s which ensures that the convergencecan be achieved within 5ndash10 iterative steps for each timestep

Based on the finite volumemethod (FVM) the governingequations are discretized to algebraic equations on the gridsystemThe convection term was discretized by the boundedcentral differencing scheme while the pressure staggeringoption scheme (PRESTO) was selected for pressure interpo-lation Finally the SIMPLEC algorithm was used to couplethe pressure and velocity equations

43 Cases Simulated In order to evaluate the accuracy andreliability of the LES model in predicting the pressure lossesacross multiple in-duct fittings two tested cases are selectedto be numerically reproduced Case 7 at a mean flow velocityof 20ms and Case 14 at 19ms The predicted pressure lossesare compared with those measured in the experiments

5 Results and Discussions

As shown in Table 1 five mean flow velocities were testedfor each case However due to the difficulty in accuratelycontrolling the mean velocity during the tests the testedvelocities were not necessarily the same for all casesThis doesnot influence the later analysis In this section the measuredor simulated pressure losses (Pa) across in-duct fittings aredirectly presented and analyzed If one is interested in the 119896

factors these can be obtained using (5) in Section 2

51 Effect of Reynolds Number (119877119890) In practice there arevarious types of HVAC ducts in terms of cross-sectionalshape and dimension and mean flow velocity Despite thiscomplexity the dimensionless Re can be used to representthese duct characteristics given that the same Re indicatesaerodynamic similarity In this section the effect of Re on thepressure losses across fittings is examined when the fittingconfiguration remains unchanged It is found that the pres-sure loss across a fitting almost has a linear relationship withthe duct Re (the example of Case 10 is shown in Figure 4)This implies that any factors increasing the duct Re such asan increase in velocity and cross-sectional dimensions canresult in an increase in pressure loss across an in-duct fittingIn other words pressure losses across the in-duct fitting(s) ofa larger duct with a higher velocity remain high

52 Effect of Fitting Configuration In order to study the effectof fitting configuration on the pressure losses this sectiondiscusses the cases with the same Re to exclude the influenceof Re on the comparison of different fitting configurations

The effect of fitting type on pressure losses across fittingsis studied when the obstruction ratio is kept constant Theobstruction ratio is defined as the area ratio of the fitting tothe duct cross-section namely the ratio of the shaded areato the whole duct section (see Figure 2) Table 2 summarizesthe comparison of pressure losses across the two types offittings namely the centrally placed fitting and the centrallyopened fitting (in Figure 2) From Table 2 it can be seenthat the pressure loss across a centrally placed fitting isremarkably larger than that across a centrally opened fittingThis can be explained by the fact that the velocity profile inthe cross-section of a duct follows a parabolic distributionnamely the largest in the center and the smallest on the ductsurfaces Thus centrally placed fittings obstruct the fastestcentral airflow and lead to the largest pressure losses whereascentrally opened fittings allow this strongest airflow to passthrough and offer much less resistance to the airflow It canalso be observed that the deviation ratio of pressure lossbetween these two types of fittings is not the same and isdependent on the obstruction ratio

The effect of the obstruction ratio on pressure lossesacross fittings is studied at a Re of 67 times 104 and the resultsare shown in Figure 5 For all cases an increase in the

The Scientific World Journal 7

Table 2 Effect of fitting type on pressure losses (Pa) across fitting(s)

Re (times104)

Case 1 versus 4(only p1)

Case 2 versus 5(only p1)

Case 3 versus 6(only p1)

Case 10 versus 13(p1 and p2)

Case 15 versus 14(p1 p2 and p3)

67 mdash 204 versus 150 944 versus 640 190 versus 144 at p1172 versus 150 at p2

208 versus 142 at p1198 versus 154 at p2180 versus 118 at p3

133 286 versus 144 mdash mdash mdash mdash

Table 3 Effect of downstream fitting(s) on pressure loss (Pa) across an upstream fitting

(a) Base case Case 1

Re = 667 times 104 Case 1 Case 7 Case 8 Case 9

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782

Pressure loss 72 66 66 64 185 54 588Percentage decrease 83 111 250

(b) Base case Case 2

Re = 667 times 104 Case 2 Case 10 Case 11 Case 15

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 204 190 172 184 774 208 198 180Percentage decrease 69 98 minus20 29

(c) Base case Case 3

Re = 667 times 104 Case 3 Case 12

Δ1198751198781 Δ1198751198781 Δ1198751198782

Pressure loss 944 1030 750Percentage decrease minus91

(d) Base case Case 5

Re = 667 times 104 Case 5 Case 13 Case 14

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 150 144 150 142 154 118Percentage decrease 40 53 minus27

fittingrsquos obstruction ratio significantly increases the pressureloss across it However the percentage increase in pressureloss is dependent on the obstruction ratio fitting type andthe interaction of neighboring fittings For a centrally placedsingle fitting (Cases 1ndash3) when the obstruction ratio increasesfrom 05 to 075 (from Case 2 to 3) the percentage increaseis approximately 363 which is almost one time higher thanthe increase (183)when the obstruction ratio increases from025 to 05 (from Case 1 to 2) It is also observed that thispercentage increase is relatively lower in the case with thecentrally opened fitting (Cases 5-6) and is also influenced bythe presence of neighboring fittings (Cases 7ndash9 and Cases 10ndash12) However regardless of the change in the obstruction ratioof a neighboring fitting the pressure loss across a fitting isonly changed slightly

53 Effect of Interaction of Multiple Fittings Table 3 sum-marizes the pressure loss across an upstream fitting and itspercentage decrease as a result of its downstream fittingsFrom Table 3(a) it can be seen that the presence of adownstream centrally placed fitting can reduce the pressureloss across its upstream fitting and the percentage decrease

increases remarkably with the increase in the obstructionratio of the downstream fitting However a comparison ofTable 3(a)ndash(c) shows that with the increase in the obstructionratio of the upstream fitting the decrease in pressure lossacross it is gradually decreased becoming minus91 when theobstruction ratio reaches 075 As tabulated in Table 3(d) forthe centrally opened fitting the presence of a downstreamfitting can reduce the pressure loss across it whereas twodownstream fittings complicate this situation

The effect of upstream fittings on the pressure loss acrossa downstream fitting is also evaluated and the results arepresented in Table 4 For the centrally placed fitting the pres-ence of upstream fittings significantly reduces the pressurelosses across its downstream fitting(s) (see Table 4(a)ndash(c))Contrarily for the centrally opened fitting this pressure lossis negligibly affected by the presence of an upstream fittingwhereas it is significantly decreased by the presence of twoupstream fittings (see Table 4(d))

The above results suggest that as a result of the effect ofdownstream and upstreamfittings the pressure loss across anin-duct fitting is changed substantially This can be explainedby the fact that the presence of a fitting changes the airflow

8 The Scientific World Journal

Table 4 Effect of upstream fitting(s) on pressure loss (Pa) across a downstream fitting

(a) Base case Case 1

Re = 667 times 104 Case 1 Case 7

Δ1198751198781 Δ1198751198781 Δ1198751198782

Pressure loss 72 66 66Percentage decrease 83

(b) Base case Case 2

Re = 667 times 104 Case 2 Case 8 Case 10 Case 15

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 204 64 185 190 172 208 198 180Percentage decrease 93 157 29 118

(c) Base case Case 3

Re = 667 times 104 Case 3 Case 9 Case 11 Case 12

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782

Pressure loss 944 54 588 184 774 1030 750Percentage decrease 377 180 206

(d) Base case Case 5

Re = 667 times 104 Case 5 Case 13 Case 14

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 150 144 150 142 154 118Percentage decrease 00 minus27 213

Table 5 Comparison of pressure losses (Pa) across multiple interactive and individual fittings

Re = 667 times 104 Case 7 Case 8 Case 9 Case 10 Case 11 Case 12 Case 13 Case 14 Case 15

Across interactivefittings 132 249 642 362 958 1780 294 414 586

Across individualfittings 144 276 1016 408 1148 1888 300 450 612

Percentage decrease 83 98 368 113 166 57 20 80 42

direction and turbulence around its neighboring fitting(s)and consequently modifies the 119896 factor (see (5) in Section 2)The results also demonstrate that the effect of a neighboringfitting is complex that is different fitting type location(upstream or downstream) obstruction ratio and duct Recan result in very distinctive pressure lossesThis implies thatthe 119896 factors for individual fittings provided in the ASHRAEhandbook and the CIBSE guide are inaccurate in a condi-tion when the interaction of neighboring fittings cannot beignored

The pressure losses across multiple interactive and indi-vidual in-duct fittings are compared (see Table 5) In Table 5the pressure losses across interactive fittings for Cases 7ndash15are directly measured in the tests In order to evaluate theeffect of the fittingsrsquo interaction on the total pressure lossfor each case the pressure losses across every individualfitting are summed for comparison Taking Case 8 as anexample the pressure losses across its individual fittings aresummed fromCase 1 andCase 2 Based on the summations ofindividual pressure loss the percentage decreases in pressurelosses across multiple fittings are calculated It can be seen

that the pressure losses across multiple interactive fittingsare lower than those across multiple individual fittings andthe percentage decrease is dependent on the configurationand combination of the fittings This finding is supportedby the previous study on two bends by Rahmeyer [12]Again this demonstrates that the calculation of pressurelosses across multiple closely mounted fittings via summingthose across individual fittings is inaccurate This methodoverpredicts the total pressure loss which may consequentlyresult in energy waste owing to the selection of larger fans Insuch a condition exploring an accurate reliable and high-efficiency predictive method such as a validated CFDmodelis crucially important

54 Validation of LES Modeling In order to validate the LESmodel in predicting pressure losses across multiple in-ductfittings the predicted values of the pressure losses acrossfittings in Case 7 at 20ms andCase 14 at 19ms are comparedwith corresponding datameasured in the testsThe results arepresented in Table 6 It can be seen that the predicted results

The Scientific World Journal 9

0

200

400

600

800

1000

60000 90000 120000 150000

Pres

sure

loss

(Pa)

ReCase 10-p1Case 10-p2

Figure 4 Effect of Reynolds number on pressure loss acrossfitting(s)

Pres

sure

loss

(Pa)

0

200

400

600

800

1000

1200

0 1 2 3 4 5 6 7 8 9 10 11 12Case number

At p1At p2

Figure 5 Effect of obstruction ratio on pressure losses acrossfitting(s)

agree well with the measured data with a relative deviationless than 3This indicates that the LESmodel can accuratelyresolve the flow field in a HVAC duct with multiple in-ductfittings

Compared to the experimental measurement numericalmodeling has an incomparable advantage in obtaining in-duct flow details such as velocity and pressure distributionsFigure 6 presents the pressure distribution along the ductcenterline in Case 7 at a mean flow velocity of 20ms Figures7 and 8 show the pressure and air speed contours on the centerplane of the duct respectively These kinds of pressure andair speed distribution are useful because it can not only beused independently for ductwork design (if the numericalmodel is validated before) but also to indicate the locationswhere pressure sensors should be placed in the tests for thelatter the involvement of numerical modeling can save manyexperimental resources and help to produce more reliableexperimental data Thus the successful use of numerical

0

200

400

600

800

1000

0 1 2 3 4 5 6

Pres

sure

(Pa)

Distance along streamwise direction (m)

minus800

minus600

minus400

minus200

p1 p2

Figure 6 Pressure distribution along centerline of the duct (Case 7at 20ms)

modeling is of great significance in optimizing ductworkdesign and improving the database for pressure losses acrossfittings

6 Conclusions

This study examines the pressure losses across multiple in-duct fittings of a ventilation duct using experimental testsTwo tested cases are reproduced by LESmodeling to evaluatethe accuracy and reliability of this numerical method inpredicting the pressure field inside a duct with multiplefittings The following conclusions can be drawn

The flow resistance of a centrally placed fitting is remark-ably larger than that of a centrally opened fitting basicallydue to the fact that the velocity profile of a cross-sectionof a duct follows a parabolic distribution For all cases anincrease in the obstruction ratio of a fitting significantlyincreases the pressure loss across it However this pressureloss does not linearly increase with the obstruction ratiothere is a substantial increase in pressure loss when theobstruction ratio increases from 05 to 075 Again this isbecause the velocity profile on a cross-section is not a uniformdistribution

Since the presence of a fitting changes the airflow direc-tion and turbulence around its close neighboring fitting(s)and consequently modifies the 119896 factor the pressure lossesacross the neighboring fitting(s) are changed substantiallyHowever the magnitude of this change is affected by manyfactors such as fitting type location (upstream or down-stream) obstruction ratio and Re In addition the pressurelosses across multiple interactive fittings are lower thanthose across multiple similar individual fittings althoughthe percentage decrease is dependent on the configurationand combination of the fittings These findings imply thatthe calculation of pressure losses across multiple closelymounted fittings via summing those across individual fittingsis inaccurateThismethod overpredicts the total pressure lossand could result in energy waste via the selection of largerfans Thus a more accurate reliable and high-efficiency

10 The Scientific World Journal

0

005

01Z

(m)

18 2 22 24 26 28 3X (m)

Pressure minus300 minus200 minus100 0 100 200 300 400 500 600

Figure 7 Pressure (Pa) contour around the in-duct fittings on the center plane of the duct (Case 7 at 20ms)

18 2 22 24 26 28 3

Velocity-magnitude 5 10 15 20 25 30

0

005

01

Z(m

)

X (m)

Figure 8 Air speed (ms) contour around the in-duct fittings on the center plane of the duct (Case 7 at 20ms)

Table 6 Comparison of predicted and measured pressure losses(Pa)

Case 7 (20ms) Case 14 (19ms)Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Measurement 256 260 486 528 410LES simulation 258 254 491 539 417

predictive method such as a validated CFD model shouldbe explored

The predicted results by LES modeling agree well withthe measured data in the tests which demonstrates thatthe LES model can accurately resolve the flow field in aHVAC duct with multiple in-duct fittings Compared tothe experimental measurement the numerical modeling canprovide the details of pressure distribution This predictedpressure distribution can be used not only independently in aductwork design (if the numerical model has been validatedbefore) but also to assist in tests to find correct locations toplace pressure sensors In the latter case the use of numericalmodeling can potentially save many experimental resourcesand help to produce more reliable experimental data

References

[1] ASHRAE HandbookmdashFundamentals SI Edition chapter 21-22 American Society of Heating Refrigerating and Air-Conditioning Engineers Atlanta Ga USA 2009

[2] CIBSEThe Chartered Institution of Building Services EngineersHeating Ventilating Air Conditioning and Refrigeration CIBSEGuide B Chartered Institution of Building Services EngineersLondon UK 3rd edition 2005

[3] I E Idelchik Handbook of Hydraulic Resistance 3rd edition1994

[4] ASHRAE Standard 120P ldquoMethods of testing to determine flowresistance of HVAC air ducts and fittingsrdquo American Society ofHeating Refrigerating andAir-conditioning Engineers AtlantaGa USA 1995

[5] B Abushakra I S Walker and M H Sherman ldquoA studyof pressure losses in residential air distribution systemsrdquo inProceedings of the American Council for an Energy EfficientEconomy (ACEEE rsquo02) Washington DC USA 2002 LBNLReport 49700 Lawrence Berkeley National Laboratory CalifUSA 2002

[6] L Shao and S B Riffat ldquoAccuracy of CFD for predictingpressure losses in HVAC duct fittingsrdquo Applied Energy vol 51no 3 pp 233ndash248 1995

[7] S M Atkin and L Shao ldquoEffect on pressure loss of separationand orientation of closely coupledHVACduct fittingsrdquoBuildingServices Engineering Research and Technology vol 21 no 3 pp175ndash178 2000

[8] L Shao and S B Riffat ldquoCFD for prediction of k-factors of ductfittingsrdquo International Journal of Energy Research vol 19 no 1pp 89ndash93 1995

[9] R R Rend E M Sparrow D W Bettenhausen and J PAbraham ldquoParasitic pressure losses in diffusers and in theirdownstream piping systems for fluid flow and heat transferrdquoInternational Journal of Heat and Mass Transfer vol 61 pp 56ndash61 2013

[10] J P Abraham E M Sparrow J C K Tong and D WBettenhausen ldquoInternal flows which transist from turbulentthrough intermittent to laminarrdquo International Journal of Ther-mal Sciences vol 49 no 2 pp 256ndash263 2010

[11] E M Sparrow J P Abraham and W J Minkowycz ldquoFlowseparation in a diverging conical duct effect of reynolds numberand divergence anglerdquo International Journal of Heat and MassTransfer vol 52 no 13ndash14 pp 3079ndash3083 2009

The Scientific World Journal 11

[12] W J Rahmeyer ldquoPressure loss coefficients for close-coupledpipe ellsrdquo ASHRAE Transactions vol 108 pp 390ndash406 2002

[13] G Gan and S B Riffat ldquok-factors for HVAC ducts numericaland experimental determinationrdquo Building Services EngineeringResearch and Technology vol 16 no 3 pp 133ndash139 1995

[14] S A Mumma T A Mahank and Y-P Ke ldquoAnalytical determi-nation of duct fitting loss-coefficientsrdquo Applied Energy vol 61no 4 pp 229ndash247 1998

[15] G Gan and S B Riffat ldquoNumerical determination of energylosses at duct junctionsrdquo Applied Energy vol 67 no 3 pp 331ndash340 2000

[16] S Moujaes and R Gundavelli ldquoCFD simulation of leak inresidential HVAC ductsrdquo Energy and Buildings vol 54 pp 534ndash539 2012

[17] J P Abraham J C K Tong and E M Sparrow ldquoBreakdownof laminar pipe flow into transitional intermittency and subse-quent attainment of fully developed intermittent or turbulentflowrdquo Numerical Heat Transfer Part B vol 54 no 2 pp 103ndash115 2008

[18] W J Minkowycz J P Abraham and EM Sparrow ldquoNumericalsimulation of laminar breakdown and subsequent intermittentand turbulent flow in parallel-plate channels effects of inletvelocity profile and turbulence intensityrdquo International Journalof Heat and Mass Transfer vol 52 no 17ndash18 pp 4040ndash40462009

[19] J P Abraham E M Sparrow and J C K Tong ldquoHeat transferin all pipe flow regimes laminar transitionalintermittent andturbulentrdquo International Journal of Heat and Mass Transfer vol52 no 3ndash4 pp 557ndash563 2009

[20] R D Lovik J P AbrahamW JMinkowycz and EM SparrowldquoLaminarization and turbulentization in a pulsatile pipe flowrdquoNumerical Heat Transfer Part A vol 56 no 11 pp 861ndash8792009

[21] J P Abraham E M Sparrow and W J Minkowycz ldquoInternal-flow nusselt numbers for the low-reynolds-number end of thelaminar-to-turbulent transition regimerdquo International Journalof Heat and Mass Transfer vol 54 no 1ndash3 pp 584ndash588 2011

[22] D A Kose and E Dick ldquoPrediction of the pressure distributionon a cubical building with implicit LESrdquo Journal of WindEngineering and Industrial Aerodynamics vol 98 no 10ndash11 pp628ndash649 2010

[23] C-H HuM Ohba and R Yoshie ldquoCFDmodelling of unsteadycross ventilation flows using LESrdquo Journal of Wind Engineeringand Industrial Aerodynamics vol 96 no 10ndash11 pp 1692ndash17062008

[24] C M Mak J Wu C Ye and J Yang ldquoFlow noise from spoilersin ductsrdquo Journal of the Acoustical Society of America vol 125no 6 pp 3756ndash3765 2009

[25] Fluent Ansys Fluent 130 Theory Guide Turbulence ANSYSCanonsburg Pa USA 2010

[26] J O Hinze Turbulence McGraw-Hill New York NY USA1975

[27] J Smagorinsky ldquoGeneral circulation experiments with theprimitive equations the basic experimentrdquo Monthly WeatherReview vol 91 pp 99ndash164 1963

TribologyAdvances in

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International Journal of

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FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

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International Journal ofPhotoenergy

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Nuclear InstallationsScience and Technology of

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Solar EnergyJournal of

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Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

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High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

6 The Scientific World Journal

Inlet Outlet

02 m

02 m

02 m05 m

05 m

05 m

575 m

175 m

p1 p2 p3

2 m1 m

ΔPS1 ΔPS2ΔPS2

Figure 3 A schematic diagram of the duct system in the numerical simulations

remain high density near the duct walls (119910+ lt 5) When themesh is fine enough to resolve the laminar sublayer the LESmodel applies the laminar stress-strain relationship to obtainthe wall shear stress

119906

119906120591

=120588119906120591119910

120583 (14)

The sensitivity of mesh number was systematically tested Foreach case three different mesh systems (a coarser a mediumand a finer) were constructed and the final numerical solu-tions based on these three meshes were compared Finallyin compromise between the numerical accuracy and costmeshes with around 20 times 106 25 times 106 and 30 times 106 gridswere selected for the cases with one fitting two fittings andthree fittings respectively The time step size used in the LESsimulations was 00002 s which ensures that the convergencecan be achieved within 5ndash10 iterative steps for each timestep

Based on the finite volumemethod (FVM) the governingequations are discretized to algebraic equations on the gridsystemThe convection term was discretized by the boundedcentral differencing scheme while the pressure staggeringoption scheme (PRESTO) was selected for pressure interpo-lation Finally the SIMPLEC algorithm was used to couplethe pressure and velocity equations

43 Cases Simulated In order to evaluate the accuracy andreliability of the LES model in predicting the pressure lossesacross multiple in-duct fittings two tested cases are selectedto be numerically reproduced Case 7 at a mean flow velocityof 20ms and Case 14 at 19ms The predicted pressure lossesare compared with those measured in the experiments

5 Results and Discussions

As shown in Table 1 five mean flow velocities were testedfor each case However due to the difficulty in accuratelycontrolling the mean velocity during the tests the testedvelocities were not necessarily the same for all casesThis doesnot influence the later analysis In this section the measuredor simulated pressure losses (Pa) across in-duct fittings aredirectly presented and analyzed If one is interested in the 119896

factors these can be obtained using (5) in Section 2

51 Effect of Reynolds Number (119877119890) In practice there arevarious types of HVAC ducts in terms of cross-sectionalshape and dimension and mean flow velocity Despite thiscomplexity the dimensionless Re can be used to representthese duct characteristics given that the same Re indicatesaerodynamic similarity In this section the effect of Re on thepressure losses across fittings is examined when the fittingconfiguration remains unchanged It is found that the pres-sure loss across a fitting almost has a linear relationship withthe duct Re (the example of Case 10 is shown in Figure 4)This implies that any factors increasing the duct Re such asan increase in velocity and cross-sectional dimensions canresult in an increase in pressure loss across an in-duct fittingIn other words pressure losses across the in-duct fitting(s) ofa larger duct with a higher velocity remain high

52 Effect of Fitting Configuration In order to study the effectof fitting configuration on the pressure losses this sectiondiscusses the cases with the same Re to exclude the influenceof Re on the comparison of different fitting configurations

The effect of fitting type on pressure losses across fittingsis studied when the obstruction ratio is kept constant Theobstruction ratio is defined as the area ratio of the fitting tothe duct cross-section namely the ratio of the shaded areato the whole duct section (see Figure 2) Table 2 summarizesthe comparison of pressure losses across the two types offittings namely the centrally placed fitting and the centrallyopened fitting (in Figure 2) From Table 2 it can be seenthat the pressure loss across a centrally placed fitting isremarkably larger than that across a centrally opened fittingThis can be explained by the fact that the velocity profile inthe cross-section of a duct follows a parabolic distributionnamely the largest in the center and the smallest on the ductsurfaces Thus centrally placed fittings obstruct the fastestcentral airflow and lead to the largest pressure losses whereascentrally opened fittings allow this strongest airflow to passthrough and offer much less resistance to the airflow It canalso be observed that the deviation ratio of pressure lossbetween these two types of fittings is not the same and isdependent on the obstruction ratio

The effect of the obstruction ratio on pressure lossesacross fittings is studied at a Re of 67 times 104 and the resultsare shown in Figure 5 For all cases an increase in the

The Scientific World Journal 7

Table 2 Effect of fitting type on pressure losses (Pa) across fitting(s)

Re (times104)

Case 1 versus 4(only p1)

Case 2 versus 5(only p1)

Case 3 versus 6(only p1)

Case 10 versus 13(p1 and p2)

Case 15 versus 14(p1 p2 and p3)

67 mdash 204 versus 150 944 versus 640 190 versus 144 at p1172 versus 150 at p2

208 versus 142 at p1198 versus 154 at p2180 versus 118 at p3

133 286 versus 144 mdash mdash mdash mdash

Table 3 Effect of downstream fitting(s) on pressure loss (Pa) across an upstream fitting

(a) Base case Case 1

Re = 667 times 104 Case 1 Case 7 Case 8 Case 9

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782

Pressure loss 72 66 66 64 185 54 588Percentage decrease 83 111 250

(b) Base case Case 2

Re = 667 times 104 Case 2 Case 10 Case 11 Case 15

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 204 190 172 184 774 208 198 180Percentage decrease 69 98 minus20 29

(c) Base case Case 3

Re = 667 times 104 Case 3 Case 12

Δ1198751198781 Δ1198751198781 Δ1198751198782

Pressure loss 944 1030 750Percentage decrease minus91

(d) Base case Case 5

Re = 667 times 104 Case 5 Case 13 Case 14

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 150 144 150 142 154 118Percentage decrease 40 53 minus27

fittingrsquos obstruction ratio significantly increases the pressureloss across it However the percentage increase in pressureloss is dependent on the obstruction ratio fitting type andthe interaction of neighboring fittings For a centrally placedsingle fitting (Cases 1ndash3) when the obstruction ratio increasesfrom 05 to 075 (from Case 2 to 3) the percentage increaseis approximately 363 which is almost one time higher thanthe increase (183)when the obstruction ratio increases from025 to 05 (from Case 1 to 2) It is also observed that thispercentage increase is relatively lower in the case with thecentrally opened fitting (Cases 5-6) and is also influenced bythe presence of neighboring fittings (Cases 7ndash9 and Cases 10ndash12) However regardless of the change in the obstruction ratioof a neighboring fitting the pressure loss across a fitting isonly changed slightly

53 Effect of Interaction of Multiple Fittings Table 3 sum-marizes the pressure loss across an upstream fitting and itspercentage decrease as a result of its downstream fittingsFrom Table 3(a) it can be seen that the presence of adownstream centrally placed fitting can reduce the pressureloss across its upstream fitting and the percentage decrease

increases remarkably with the increase in the obstructionratio of the downstream fitting However a comparison ofTable 3(a)ndash(c) shows that with the increase in the obstructionratio of the upstream fitting the decrease in pressure lossacross it is gradually decreased becoming minus91 when theobstruction ratio reaches 075 As tabulated in Table 3(d) forthe centrally opened fitting the presence of a downstreamfitting can reduce the pressure loss across it whereas twodownstream fittings complicate this situation

The effect of upstream fittings on the pressure loss acrossa downstream fitting is also evaluated and the results arepresented in Table 4 For the centrally placed fitting the pres-ence of upstream fittings significantly reduces the pressurelosses across its downstream fitting(s) (see Table 4(a)ndash(c))Contrarily for the centrally opened fitting this pressure lossis negligibly affected by the presence of an upstream fittingwhereas it is significantly decreased by the presence of twoupstream fittings (see Table 4(d))

The above results suggest that as a result of the effect ofdownstream and upstreamfittings the pressure loss across anin-duct fitting is changed substantially This can be explainedby the fact that the presence of a fitting changes the airflow

8 The Scientific World Journal

Table 4 Effect of upstream fitting(s) on pressure loss (Pa) across a downstream fitting

(a) Base case Case 1

Re = 667 times 104 Case 1 Case 7

Δ1198751198781 Δ1198751198781 Δ1198751198782

Pressure loss 72 66 66Percentage decrease 83

(b) Base case Case 2

Re = 667 times 104 Case 2 Case 8 Case 10 Case 15

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 204 64 185 190 172 208 198 180Percentage decrease 93 157 29 118

(c) Base case Case 3

Re = 667 times 104 Case 3 Case 9 Case 11 Case 12

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782

Pressure loss 944 54 588 184 774 1030 750Percentage decrease 377 180 206

(d) Base case Case 5

Re = 667 times 104 Case 5 Case 13 Case 14

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 150 144 150 142 154 118Percentage decrease 00 minus27 213

Table 5 Comparison of pressure losses (Pa) across multiple interactive and individual fittings

Re = 667 times 104 Case 7 Case 8 Case 9 Case 10 Case 11 Case 12 Case 13 Case 14 Case 15

Across interactivefittings 132 249 642 362 958 1780 294 414 586

Across individualfittings 144 276 1016 408 1148 1888 300 450 612

Percentage decrease 83 98 368 113 166 57 20 80 42

direction and turbulence around its neighboring fitting(s)and consequently modifies the 119896 factor (see (5) in Section 2)The results also demonstrate that the effect of a neighboringfitting is complex that is different fitting type location(upstream or downstream) obstruction ratio and duct Recan result in very distinctive pressure lossesThis implies thatthe 119896 factors for individual fittings provided in the ASHRAEhandbook and the CIBSE guide are inaccurate in a condi-tion when the interaction of neighboring fittings cannot beignored

The pressure losses across multiple interactive and indi-vidual in-duct fittings are compared (see Table 5) In Table 5the pressure losses across interactive fittings for Cases 7ndash15are directly measured in the tests In order to evaluate theeffect of the fittingsrsquo interaction on the total pressure lossfor each case the pressure losses across every individualfitting are summed for comparison Taking Case 8 as anexample the pressure losses across its individual fittings aresummed fromCase 1 andCase 2 Based on the summations ofindividual pressure loss the percentage decreases in pressurelosses across multiple fittings are calculated It can be seen

that the pressure losses across multiple interactive fittingsare lower than those across multiple individual fittings andthe percentage decrease is dependent on the configurationand combination of the fittings This finding is supportedby the previous study on two bends by Rahmeyer [12]Again this demonstrates that the calculation of pressurelosses across multiple closely mounted fittings via summingthose across individual fittings is inaccurate This methodoverpredicts the total pressure loss which may consequentlyresult in energy waste owing to the selection of larger fans Insuch a condition exploring an accurate reliable and high-efficiency predictive method such as a validated CFDmodelis crucially important

54 Validation of LES Modeling In order to validate the LESmodel in predicting pressure losses across multiple in-ductfittings the predicted values of the pressure losses acrossfittings in Case 7 at 20ms andCase 14 at 19ms are comparedwith corresponding datameasured in the testsThe results arepresented in Table 6 It can be seen that the predicted results

The Scientific World Journal 9

0

200

400

600

800

1000

60000 90000 120000 150000

Pres

sure

loss

(Pa)

ReCase 10-p1Case 10-p2

Figure 4 Effect of Reynolds number on pressure loss acrossfitting(s)

Pres

sure

loss

(Pa)

0

200

400

600

800

1000

1200

0 1 2 3 4 5 6 7 8 9 10 11 12Case number

At p1At p2

Figure 5 Effect of obstruction ratio on pressure losses acrossfitting(s)

agree well with the measured data with a relative deviationless than 3This indicates that the LESmodel can accuratelyresolve the flow field in a HVAC duct with multiple in-ductfittings

Compared to the experimental measurement numericalmodeling has an incomparable advantage in obtaining in-duct flow details such as velocity and pressure distributionsFigure 6 presents the pressure distribution along the ductcenterline in Case 7 at a mean flow velocity of 20ms Figures7 and 8 show the pressure and air speed contours on the centerplane of the duct respectively These kinds of pressure andair speed distribution are useful because it can not only beused independently for ductwork design (if the numericalmodel is validated before) but also to indicate the locationswhere pressure sensors should be placed in the tests for thelatter the involvement of numerical modeling can save manyexperimental resources and help to produce more reliableexperimental data Thus the successful use of numerical

0

200

400

600

800

1000

0 1 2 3 4 5 6

Pres

sure

(Pa)

Distance along streamwise direction (m)

minus800

minus600

minus400

minus200

p1 p2

Figure 6 Pressure distribution along centerline of the duct (Case 7at 20ms)

modeling is of great significance in optimizing ductworkdesign and improving the database for pressure losses acrossfittings

6 Conclusions

This study examines the pressure losses across multiple in-duct fittings of a ventilation duct using experimental testsTwo tested cases are reproduced by LESmodeling to evaluatethe accuracy and reliability of this numerical method inpredicting the pressure field inside a duct with multiplefittings The following conclusions can be drawn

The flow resistance of a centrally placed fitting is remark-ably larger than that of a centrally opened fitting basicallydue to the fact that the velocity profile of a cross-sectionof a duct follows a parabolic distribution For all cases anincrease in the obstruction ratio of a fitting significantlyincreases the pressure loss across it However this pressureloss does not linearly increase with the obstruction ratiothere is a substantial increase in pressure loss when theobstruction ratio increases from 05 to 075 Again this isbecause the velocity profile on a cross-section is not a uniformdistribution

Since the presence of a fitting changes the airflow direc-tion and turbulence around its close neighboring fitting(s)and consequently modifies the 119896 factor the pressure lossesacross the neighboring fitting(s) are changed substantiallyHowever the magnitude of this change is affected by manyfactors such as fitting type location (upstream or down-stream) obstruction ratio and Re In addition the pressurelosses across multiple interactive fittings are lower thanthose across multiple similar individual fittings althoughthe percentage decrease is dependent on the configurationand combination of the fittings These findings imply thatthe calculation of pressure losses across multiple closelymounted fittings via summing those across individual fittingsis inaccurateThismethod overpredicts the total pressure lossand could result in energy waste via the selection of largerfans Thus a more accurate reliable and high-efficiency

10 The Scientific World Journal

0

005

01Z

(m)

18 2 22 24 26 28 3X (m)

Pressure minus300 minus200 minus100 0 100 200 300 400 500 600

Figure 7 Pressure (Pa) contour around the in-duct fittings on the center plane of the duct (Case 7 at 20ms)

18 2 22 24 26 28 3

Velocity-magnitude 5 10 15 20 25 30

0

005

01

Z(m

)

X (m)

Figure 8 Air speed (ms) contour around the in-duct fittings on the center plane of the duct (Case 7 at 20ms)

Table 6 Comparison of predicted and measured pressure losses(Pa)

Case 7 (20ms) Case 14 (19ms)Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Measurement 256 260 486 528 410LES simulation 258 254 491 539 417

predictive method such as a validated CFD model shouldbe explored

The predicted results by LES modeling agree well withthe measured data in the tests which demonstrates thatthe LES model can accurately resolve the flow field in aHVAC duct with multiple in-duct fittings Compared tothe experimental measurement the numerical modeling canprovide the details of pressure distribution This predictedpressure distribution can be used not only independently in aductwork design (if the numerical model has been validatedbefore) but also to assist in tests to find correct locations toplace pressure sensors In the latter case the use of numericalmodeling can potentially save many experimental resourcesand help to produce more reliable experimental data

References

[1] ASHRAE HandbookmdashFundamentals SI Edition chapter 21-22 American Society of Heating Refrigerating and Air-Conditioning Engineers Atlanta Ga USA 2009

[2] CIBSEThe Chartered Institution of Building Services EngineersHeating Ventilating Air Conditioning and Refrigeration CIBSEGuide B Chartered Institution of Building Services EngineersLondon UK 3rd edition 2005

[3] I E Idelchik Handbook of Hydraulic Resistance 3rd edition1994

[4] ASHRAE Standard 120P ldquoMethods of testing to determine flowresistance of HVAC air ducts and fittingsrdquo American Society ofHeating Refrigerating andAir-conditioning Engineers AtlantaGa USA 1995

[5] B Abushakra I S Walker and M H Sherman ldquoA studyof pressure losses in residential air distribution systemsrdquo inProceedings of the American Council for an Energy EfficientEconomy (ACEEE rsquo02) Washington DC USA 2002 LBNLReport 49700 Lawrence Berkeley National Laboratory CalifUSA 2002

[6] L Shao and S B Riffat ldquoAccuracy of CFD for predictingpressure losses in HVAC duct fittingsrdquo Applied Energy vol 51no 3 pp 233ndash248 1995

[7] S M Atkin and L Shao ldquoEffect on pressure loss of separationand orientation of closely coupledHVACduct fittingsrdquoBuildingServices Engineering Research and Technology vol 21 no 3 pp175ndash178 2000

[8] L Shao and S B Riffat ldquoCFD for prediction of k-factors of ductfittingsrdquo International Journal of Energy Research vol 19 no 1pp 89ndash93 1995

[9] R R Rend E M Sparrow D W Bettenhausen and J PAbraham ldquoParasitic pressure losses in diffusers and in theirdownstream piping systems for fluid flow and heat transferrdquoInternational Journal of Heat and Mass Transfer vol 61 pp 56ndash61 2013

[10] J P Abraham E M Sparrow J C K Tong and D WBettenhausen ldquoInternal flows which transist from turbulentthrough intermittent to laminarrdquo International Journal of Ther-mal Sciences vol 49 no 2 pp 256ndash263 2010

[11] E M Sparrow J P Abraham and W J Minkowycz ldquoFlowseparation in a diverging conical duct effect of reynolds numberand divergence anglerdquo International Journal of Heat and MassTransfer vol 52 no 13ndash14 pp 3079ndash3083 2009

The Scientific World Journal 11

[12] W J Rahmeyer ldquoPressure loss coefficients for close-coupledpipe ellsrdquo ASHRAE Transactions vol 108 pp 390ndash406 2002

[13] G Gan and S B Riffat ldquok-factors for HVAC ducts numericaland experimental determinationrdquo Building Services EngineeringResearch and Technology vol 16 no 3 pp 133ndash139 1995

[14] S A Mumma T A Mahank and Y-P Ke ldquoAnalytical determi-nation of duct fitting loss-coefficientsrdquo Applied Energy vol 61no 4 pp 229ndash247 1998

[15] G Gan and S B Riffat ldquoNumerical determination of energylosses at duct junctionsrdquo Applied Energy vol 67 no 3 pp 331ndash340 2000

[16] S Moujaes and R Gundavelli ldquoCFD simulation of leak inresidential HVAC ductsrdquo Energy and Buildings vol 54 pp 534ndash539 2012

[17] J P Abraham J C K Tong and E M Sparrow ldquoBreakdownof laminar pipe flow into transitional intermittency and subse-quent attainment of fully developed intermittent or turbulentflowrdquo Numerical Heat Transfer Part B vol 54 no 2 pp 103ndash115 2008

[18] W J Minkowycz J P Abraham and EM Sparrow ldquoNumericalsimulation of laminar breakdown and subsequent intermittentand turbulent flow in parallel-plate channels effects of inletvelocity profile and turbulence intensityrdquo International Journalof Heat and Mass Transfer vol 52 no 17ndash18 pp 4040ndash40462009

[19] J P Abraham E M Sparrow and J C K Tong ldquoHeat transferin all pipe flow regimes laminar transitionalintermittent andturbulentrdquo International Journal of Heat and Mass Transfer vol52 no 3ndash4 pp 557ndash563 2009

[20] R D Lovik J P AbrahamW JMinkowycz and EM SparrowldquoLaminarization and turbulentization in a pulsatile pipe flowrdquoNumerical Heat Transfer Part A vol 56 no 11 pp 861ndash8792009

[21] J P Abraham E M Sparrow and W J Minkowycz ldquoInternal-flow nusselt numbers for the low-reynolds-number end of thelaminar-to-turbulent transition regimerdquo International Journalof Heat and Mass Transfer vol 54 no 1ndash3 pp 584ndash588 2011

[22] D A Kose and E Dick ldquoPrediction of the pressure distributionon a cubical building with implicit LESrdquo Journal of WindEngineering and Industrial Aerodynamics vol 98 no 10ndash11 pp628ndash649 2010

[23] C-H HuM Ohba and R Yoshie ldquoCFDmodelling of unsteadycross ventilation flows using LESrdquo Journal of Wind Engineeringand Industrial Aerodynamics vol 96 no 10ndash11 pp 1692ndash17062008

[24] C M Mak J Wu C Ye and J Yang ldquoFlow noise from spoilersin ductsrdquo Journal of the Acoustical Society of America vol 125no 6 pp 3756ndash3765 2009

[25] Fluent Ansys Fluent 130 Theory Guide Turbulence ANSYSCanonsburg Pa USA 2010

[26] J O Hinze Turbulence McGraw-Hill New York NY USA1975

[27] J Smagorinsky ldquoGeneral circulation experiments with theprimitive equations the basic experimentrdquo Monthly WeatherReview vol 91 pp 99ndash164 1963

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World Journal 7

Table 2 Effect of fitting type on pressure losses (Pa) across fitting(s)

Re (times104)

Case 1 versus 4(only p1)

Case 2 versus 5(only p1)

Case 3 versus 6(only p1)

Case 10 versus 13(p1 and p2)

Case 15 versus 14(p1 p2 and p3)

67 mdash 204 versus 150 944 versus 640 190 versus 144 at p1172 versus 150 at p2

208 versus 142 at p1198 versus 154 at p2180 versus 118 at p3

133 286 versus 144 mdash mdash mdash mdash

Table 3 Effect of downstream fitting(s) on pressure loss (Pa) across an upstream fitting

(a) Base case Case 1

Re = 667 times 104 Case 1 Case 7 Case 8 Case 9

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782

Pressure loss 72 66 66 64 185 54 588Percentage decrease 83 111 250

(b) Base case Case 2

Re = 667 times 104 Case 2 Case 10 Case 11 Case 15

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 204 190 172 184 774 208 198 180Percentage decrease 69 98 minus20 29

(c) Base case Case 3

Re = 667 times 104 Case 3 Case 12

Δ1198751198781 Δ1198751198781 Δ1198751198782

Pressure loss 944 1030 750Percentage decrease minus91

(d) Base case Case 5

Re = 667 times 104 Case 5 Case 13 Case 14

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 150 144 150 142 154 118Percentage decrease 40 53 minus27

fittingrsquos obstruction ratio significantly increases the pressureloss across it However the percentage increase in pressureloss is dependent on the obstruction ratio fitting type andthe interaction of neighboring fittings For a centrally placedsingle fitting (Cases 1ndash3) when the obstruction ratio increasesfrom 05 to 075 (from Case 2 to 3) the percentage increaseis approximately 363 which is almost one time higher thanthe increase (183)when the obstruction ratio increases from025 to 05 (from Case 1 to 2) It is also observed that thispercentage increase is relatively lower in the case with thecentrally opened fitting (Cases 5-6) and is also influenced bythe presence of neighboring fittings (Cases 7ndash9 and Cases 10ndash12) However regardless of the change in the obstruction ratioof a neighboring fitting the pressure loss across a fitting isonly changed slightly

53 Effect of Interaction of Multiple Fittings Table 3 sum-marizes the pressure loss across an upstream fitting and itspercentage decrease as a result of its downstream fittingsFrom Table 3(a) it can be seen that the presence of adownstream centrally placed fitting can reduce the pressureloss across its upstream fitting and the percentage decrease

increases remarkably with the increase in the obstructionratio of the downstream fitting However a comparison ofTable 3(a)ndash(c) shows that with the increase in the obstructionratio of the upstream fitting the decrease in pressure lossacross it is gradually decreased becoming minus91 when theobstruction ratio reaches 075 As tabulated in Table 3(d) forthe centrally opened fitting the presence of a downstreamfitting can reduce the pressure loss across it whereas twodownstream fittings complicate this situation

The effect of upstream fittings on the pressure loss acrossa downstream fitting is also evaluated and the results arepresented in Table 4 For the centrally placed fitting the pres-ence of upstream fittings significantly reduces the pressurelosses across its downstream fitting(s) (see Table 4(a)ndash(c))Contrarily for the centrally opened fitting this pressure lossis negligibly affected by the presence of an upstream fittingwhereas it is significantly decreased by the presence of twoupstream fittings (see Table 4(d))

The above results suggest that as a result of the effect ofdownstream and upstreamfittings the pressure loss across anin-duct fitting is changed substantially This can be explainedby the fact that the presence of a fitting changes the airflow

8 The Scientific World Journal

Table 4 Effect of upstream fitting(s) on pressure loss (Pa) across a downstream fitting

(a) Base case Case 1

Re = 667 times 104 Case 1 Case 7

Δ1198751198781 Δ1198751198781 Δ1198751198782

Pressure loss 72 66 66Percentage decrease 83

(b) Base case Case 2

Re = 667 times 104 Case 2 Case 8 Case 10 Case 15

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 204 64 185 190 172 208 198 180Percentage decrease 93 157 29 118

(c) Base case Case 3

Re = 667 times 104 Case 3 Case 9 Case 11 Case 12

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782

Pressure loss 944 54 588 184 774 1030 750Percentage decrease 377 180 206

(d) Base case Case 5

Re = 667 times 104 Case 5 Case 13 Case 14

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 150 144 150 142 154 118Percentage decrease 00 minus27 213

Table 5 Comparison of pressure losses (Pa) across multiple interactive and individual fittings

Re = 667 times 104 Case 7 Case 8 Case 9 Case 10 Case 11 Case 12 Case 13 Case 14 Case 15

Across interactivefittings 132 249 642 362 958 1780 294 414 586

Across individualfittings 144 276 1016 408 1148 1888 300 450 612

Percentage decrease 83 98 368 113 166 57 20 80 42

direction and turbulence around its neighboring fitting(s)and consequently modifies the 119896 factor (see (5) in Section 2)The results also demonstrate that the effect of a neighboringfitting is complex that is different fitting type location(upstream or downstream) obstruction ratio and duct Recan result in very distinctive pressure lossesThis implies thatthe 119896 factors for individual fittings provided in the ASHRAEhandbook and the CIBSE guide are inaccurate in a condi-tion when the interaction of neighboring fittings cannot beignored

The pressure losses across multiple interactive and indi-vidual in-duct fittings are compared (see Table 5) In Table 5the pressure losses across interactive fittings for Cases 7ndash15are directly measured in the tests In order to evaluate theeffect of the fittingsrsquo interaction on the total pressure lossfor each case the pressure losses across every individualfitting are summed for comparison Taking Case 8 as anexample the pressure losses across its individual fittings aresummed fromCase 1 andCase 2 Based on the summations ofindividual pressure loss the percentage decreases in pressurelosses across multiple fittings are calculated It can be seen

that the pressure losses across multiple interactive fittingsare lower than those across multiple individual fittings andthe percentage decrease is dependent on the configurationand combination of the fittings This finding is supportedby the previous study on two bends by Rahmeyer [12]Again this demonstrates that the calculation of pressurelosses across multiple closely mounted fittings via summingthose across individual fittings is inaccurate This methodoverpredicts the total pressure loss which may consequentlyresult in energy waste owing to the selection of larger fans Insuch a condition exploring an accurate reliable and high-efficiency predictive method such as a validated CFDmodelis crucially important

54 Validation of LES Modeling In order to validate the LESmodel in predicting pressure losses across multiple in-ductfittings the predicted values of the pressure losses acrossfittings in Case 7 at 20ms andCase 14 at 19ms are comparedwith corresponding datameasured in the testsThe results arepresented in Table 6 It can be seen that the predicted results

The Scientific World Journal 9

0

200

400

600

800

1000

60000 90000 120000 150000

Pres

sure

loss

(Pa)

ReCase 10-p1Case 10-p2

Figure 4 Effect of Reynolds number on pressure loss acrossfitting(s)

Pres

sure

loss

(Pa)

0

200

400

600

800

1000

1200

0 1 2 3 4 5 6 7 8 9 10 11 12Case number

At p1At p2

Figure 5 Effect of obstruction ratio on pressure losses acrossfitting(s)

agree well with the measured data with a relative deviationless than 3This indicates that the LESmodel can accuratelyresolve the flow field in a HVAC duct with multiple in-ductfittings

Compared to the experimental measurement numericalmodeling has an incomparable advantage in obtaining in-duct flow details such as velocity and pressure distributionsFigure 6 presents the pressure distribution along the ductcenterline in Case 7 at a mean flow velocity of 20ms Figures7 and 8 show the pressure and air speed contours on the centerplane of the duct respectively These kinds of pressure andair speed distribution are useful because it can not only beused independently for ductwork design (if the numericalmodel is validated before) but also to indicate the locationswhere pressure sensors should be placed in the tests for thelatter the involvement of numerical modeling can save manyexperimental resources and help to produce more reliableexperimental data Thus the successful use of numerical

0

200

400

600

800

1000

0 1 2 3 4 5 6

Pres

sure

(Pa)

Distance along streamwise direction (m)

minus800

minus600

minus400

minus200

p1 p2

Figure 6 Pressure distribution along centerline of the duct (Case 7at 20ms)

modeling is of great significance in optimizing ductworkdesign and improving the database for pressure losses acrossfittings

6 Conclusions

This study examines the pressure losses across multiple in-duct fittings of a ventilation duct using experimental testsTwo tested cases are reproduced by LESmodeling to evaluatethe accuracy and reliability of this numerical method inpredicting the pressure field inside a duct with multiplefittings The following conclusions can be drawn

The flow resistance of a centrally placed fitting is remark-ably larger than that of a centrally opened fitting basicallydue to the fact that the velocity profile of a cross-sectionof a duct follows a parabolic distribution For all cases anincrease in the obstruction ratio of a fitting significantlyincreases the pressure loss across it However this pressureloss does not linearly increase with the obstruction ratiothere is a substantial increase in pressure loss when theobstruction ratio increases from 05 to 075 Again this isbecause the velocity profile on a cross-section is not a uniformdistribution

Since the presence of a fitting changes the airflow direc-tion and turbulence around its close neighboring fitting(s)and consequently modifies the 119896 factor the pressure lossesacross the neighboring fitting(s) are changed substantiallyHowever the magnitude of this change is affected by manyfactors such as fitting type location (upstream or down-stream) obstruction ratio and Re In addition the pressurelosses across multiple interactive fittings are lower thanthose across multiple similar individual fittings althoughthe percentage decrease is dependent on the configurationand combination of the fittings These findings imply thatthe calculation of pressure losses across multiple closelymounted fittings via summing those across individual fittingsis inaccurateThismethod overpredicts the total pressure lossand could result in energy waste via the selection of largerfans Thus a more accurate reliable and high-efficiency

10 The Scientific World Journal

0

005

01Z

(m)

18 2 22 24 26 28 3X (m)

Pressure minus300 minus200 minus100 0 100 200 300 400 500 600

Figure 7 Pressure (Pa) contour around the in-duct fittings on the center plane of the duct (Case 7 at 20ms)

18 2 22 24 26 28 3

Velocity-magnitude 5 10 15 20 25 30

0

005

01

Z(m

)

X (m)

Figure 8 Air speed (ms) contour around the in-duct fittings on the center plane of the duct (Case 7 at 20ms)

Table 6 Comparison of predicted and measured pressure losses(Pa)

Case 7 (20ms) Case 14 (19ms)Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Measurement 256 260 486 528 410LES simulation 258 254 491 539 417

predictive method such as a validated CFD model shouldbe explored

The predicted results by LES modeling agree well withthe measured data in the tests which demonstrates thatthe LES model can accurately resolve the flow field in aHVAC duct with multiple in-duct fittings Compared tothe experimental measurement the numerical modeling canprovide the details of pressure distribution This predictedpressure distribution can be used not only independently in aductwork design (if the numerical model has been validatedbefore) but also to assist in tests to find correct locations toplace pressure sensors In the latter case the use of numericalmodeling can potentially save many experimental resourcesand help to produce more reliable experimental data

References

[1] ASHRAE HandbookmdashFundamentals SI Edition chapter 21-22 American Society of Heating Refrigerating and Air-Conditioning Engineers Atlanta Ga USA 2009

[2] CIBSEThe Chartered Institution of Building Services EngineersHeating Ventilating Air Conditioning and Refrigeration CIBSEGuide B Chartered Institution of Building Services EngineersLondon UK 3rd edition 2005

[3] I E Idelchik Handbook of Hydraulic Resistance 3rd edition1994

[4] ASHRAE Standard 120P ldquoMethods of testing to determine flowresistance of HVAC air ducts and fittingsrdquo American Society ofHeating Refrigerating andAir-conditioning Engineers AtlantaGa USA 1995

[5] B Abushakra I S Walker and M H Sherman ldquoA studyof pressure losses in residential air distribution systemsrdquo inProceedings of the American Council for an Energy EfficientEconomy (ACEEE rsquo02) Washington DC USA 2002 LBNLReport 49700 Lawrence Berkeley National Laboratory CalifUSA 2002

[6] L Shao and S B Riffat ldquoAccuracy of CFD for predictingpressure losses in HVAC duct fittingsrdquo Applied Energy vol 51no 3 pp 233ndash248 1995

[7] S M Atkin and L Shao ldquoEffect on pressure loss of separationand orientation of closely coupledHVACduct fittingsrdquoBuildingServices Engineering Research and Technology vol 21 no 3 pp175ndash178 2000

[8] L Shao and S B Riffat ldquoCFD for prediction of k-factors of ductfittingsrdquo International Journal of Energy Research vol 19 no 1pp 89ndash93 1995

[9] R R Rend E M Sparrow D W Bettenhausen and J PAbraham ldquoParasitic pressure losses in diffusers and in theirdownstream piping systems for fluid flow and heat transferrdquoInternational Journal of Heat and Mass Transfer vol 61 pp 56ndash61 2013

[10] J P Abraham E M Sparrow J C K Tong and D WBettenhausen ldquoInternal flows which transist from turbulentthrough intermittent to laminarrdquo International Journal of Ther-mal Sciences vol 49 no 2 pp 256ndash263 2010

[11] E M Sparrow J P Abraham and W J Minkowycz ldquoFlowseparation in a diverging conical duct effect of reynolds numberand divergence anglerdquo International Journal of Heat and MassTransfer vol 52 no 13ndash14 pp 3079ndash3083 2009

The Scientific World Journal 11

[12] W J Rahmeyer ldquoPressure loss coefficients for close-coupledpipe ellsrdquo ASHRAE Transactions vol 108 pp 390ndash406 2002

[13] G Gan and S B Riffat ldquok-factors for HVAC ducts numericaland experimental determinationrdquo Building Services EngineeringResearch and Technology vol 16 no 3 pp 133ndash139 1995

[14] S A Mumma T A Mahank and Y-P Ke ldquoAnalytical determi-nation of duct fitting loss-coefficientsrdquo Applied Energy vol 61no 4 pp 229ndash247 1998

[15] G Gan and S B Riffat ldquoNumerical determination of energylosses at duct junctionsrdquo Applied Energy vol 67 no 3 pp 331ndash340 2000

[16] S Moujaes and R Gundavelli ldquoCFD simulation of leak inresidential HVAC ductsrdquo Energy and Buildings vol 54 pp 534ndash539 2012

[17] J P Abraham J C K Tong and E M Sparrow ldquoBreakdownof laminar pipe flow into transitional intermittency and subse-quent attainment of fully developed intermittent or turbulentflowrdquo Numerical Heat Transfer Part B vol 54 no 2 pp 103ndash115 2008

[18] W J Minkowycz J P Abraham and EM Sparrow ldquoNumericalsimulation of laminar breakdown and subsequent intermittentand turbulent flow in parallel-plate channels effects of inletvelocity profile and turbulence intensityrdquo International Journalof Heat and Mass Transfer vol 52 no 17ndash18 pp 4040ndash40462009

[19] J P Abraham E M Sparrow and J C K Tong ldquoHeat transferin all pipe flow regimes laminar transitionalintermittent andturbulentrdquo International Journal of Heat and Mass Transfer vol52 no 3ndash4 pp 557ndash563 2009

[20] R D Lovik J P AbrahamW JMinkowycz and EM SparrowldquoLaminarization and turbulentization in a pulsatile pipe flowrdquoNumerical Heat Transfer Part A vol 56 no 11 pp 861ndash8792009

[21] J P Abraham E M Sparrow and W J Minkowycz ldquoInternal-flow nusselt numbers for the low-reynolds-number end of thelaminar-to-turbulent transition regimerdquo International Journalof Heat and Mass Transfer vol 54 no 1ndash3 pp 584ndash588 2011

[22] D A Kose and E Dick ldquoPrediction of the pressure distributionon a cubical building with implicit LESrdquo Journal of WindEngineering and Industrial Aerodynamics vol 98 no 10ndash11 pp628ndash649 2010

[23] C-H HuM Ohba and R Yoshie ldquoCFDmodelling of unsteadycross ventilation flows using LESrdquo Journal of Wind Engineeringand Industrial Aerodynamics vol 96 no 10ndash11 pp 1692ndash17062008

[24] C M Mak J Wu C Ye and J Yang ldquoFlow noise from spoilersin ductsrdquo Journal of the Acoustical Society of America vol 125no 6 pp 3756ndash3765 2009

[25] Fluent Ansys Fluent 130 Theory Guide Turbulence ANSYSCanonsburg Pa USA 2010

[26] J O Hinze Turbulence McGraw-Hill New York NY USA1975

[27] J Smagorinsky ldquoGeneral circulation experiments with theprimitive equations the basic experimentrdquo Monthly WeatherReview vol 91 pp 99ndash164 1963

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

8 The Scientific World Journal

Table 4 Effect of upstream fitting(s) on pressure loss (Pa) across a downstream fitting

(a) Base case Case 1

Re = 667 times 104 Case 1 Case 7

Δ1198751198781 Δ1198751198781 Δ1198751198782

Pressure loss 72 66 66Percentage decrease 83

(b) Base case Case 2

Re = 667 times 104 Case 2 Case 8 Case 10 Case 15

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 204 64 185 190 172 208 198 180Percentage decrease 93 157 29 118

(c) Base case Case 3

Re = 667 times 104 Case 3 Case 9 Case 11 Case 12

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782

Pressure loss 944 54 588 184 774 1030 750Percentage decrease 377 180 206

(d) Base case Case 5

Re = 667 times 104 Case 5 Case 13 Case 14

Δ1198751198781 Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Pressure loss 150 144 150 142 154 118Percentage decrease 00 minus27 213

Table 5 Comparison of pressure losses (Pa) across multiple interactive and individual fittings

Re = 667 times 104 Case 7 Case 8 Case 9 Case 10 Case 11 Case 12 Case 13 Case 14 Case 15

Across interactivefittings 132 249 642 362 958 1780 294 414 586

Across individualfittings 144 276 1016 408 1148 1888 300 450 612

Percentage decrease 83 98 368 113 166 57 20 80 42

direction and turbulence around its neighboring fitting(s)and consequently modifies the 119896 factor (see (5) in Section 2)The results also demonstrate that the effect of a neighboringfitting is complex that is different fitting type location(upstream or downstream) obstruction ratio and duct Recan result in very distinctive pressure lossesThis implies thatthe 119896 factors for individual fittings provided in the ASHRAEhandbook and the CIBSE guide are inaccurate in a condi-tion when the interaction of neighboring fittings cannot beignored

The pressure losses across multiple interactive and indi-vidual in-duct fittings are compared (see Table 5) In Table 5the pressure losses across interactive fittings for Cases 7ndash15are directly measured in the tests In order to evaluate theeffect of the fittingsrsquo interaction on the total pressure lossfor each case the pressure losses across every individualfitting are summed for comparison Taking Case 8 as anexample the pressure losses across its individual fittings aresummed fromCase 1 andCase 2 Based on the summations ofindividual pressure loss the percentage decreases in pressurelosses across multiple fittings are calculated It can be seen

that the pressure losses across multiple interactive fittingsare lower than those across multiple individual fittings andthe percentage decrease is dependent on the configurationand combination of the fittings This finding is supportedby the previous study on two bends by Rahmeyer [12]Again this demonstrates that the calculation of pressurelosses across multiple closely mounted fittings via summingthose across individual fittings is inaccurate This methodoverpredicts the total pressure loss which may consequentlyresult in energy waste owing to the selection of larger fans Insuch a condition exploring an accurate reliable and high-efficiency predictive method such as a validated CFDmodelis crucially important

54 Validation of LES Modeling In order to validate the LESmodel in predicting pressure losses across multiple in-ductfittings the predicted values of the pressure losses acrossfittings in Case 7 at 20ms andCase 14 at 19ms are comparedwith corresponding datameasured in the testsThe results arepresented in Table 6 It can be seen that the predicted results

The Scientific World Journal 9

0

200

400

600

800

1000

60000 90000 120000 150000

Pres

sure

loss

(Pa)

ReCase 10-p1Case 10-p2

Figure 4 Effect of Reynolds number on pressure loss acrossfitting(s)

Pres

sure

loss

(Pa)

0

200

400

600

800

1000

1200

0 1 2 3 4 5 6 7 8 9 10 11 12Case number

At p1At p2

Figure 5 Effect of obstruction ratio on pressure losses acrossfitting(s)

agree well with the measured data with a relative deviationless than 3This indicates that the LESmodel can accuratelyresolve the flow field in a HVAC duct with multiple in-ductfittings

Compared to the experimental measurement numericalmodeling has an incomparable advantage in obtaining in-duct flow details such as velocity and pressure distributionsFigure 6 presents the pressure distribution along the ductcenterline in Case 7 at a mean flow velocity of 20ms Figures7 and 8 show the pressure and air speed contours on the centerplane of the duct respectively These kinds of pressure andair speed distribution are useful because it can not only beused independently for ductwork design (if the numericalmodel is validated before) but also to indicate the locationswhere pressure sensors should be placed in the tests for thelatter the involvement of numerical modeling can save manyexperimental resources and help to produce more reliableexperimental data Thus the successful use of numerical

0

200

400

600

800

1000

0 1 2 3 4 5 6

Pres

sure

(Pa)

Distance along streamwise direction (m)

minus800

minus600

minus400

minus200

p1 p2

Figure 6 Pressure distribution along centerline of the duct (Case 7at 20ms)

modeling is of great significance in optimizing ductworkdesign and improving the database for pressure losses acrossfittings

6 Conclusions

This study examines the pressure losses across multiple in-duct fittings of a ventilation duct using experimental testsTwo tested cases are reproduced by LESmodeling to evaluatethe accuracy and reliability of this numerical method inpredicting the pressure field inside a duct with multiplefittings The following conclusions can be drawn

The flow resistance of a centrally placed fitting is remark-ably larger than that of a centrally opened fitting basicallydue to the fact that the velocity profile of a cross-sectionof a duct follows a parabolic distribution For all cases anincrease in the obstruction ratio of a fitting significantlyincreases the pressure loss across it However this pressureloss does not linearly increase with the obstruction ratiothere is a substantial increase in pressure loss when theobstruction ratio increases from 05 to 075 Again this isbecause the velocity profile on a cross-section is not a uniformdistribution

Since the presence of a fitting changes the airflow direc-tion and turbulence around its close neighboring fitting(s)and consequently modifies the 119896 factor the pressure lossesacross the neighboring fitting(s) are changed substantiallyHowever the magnitude of this change is affected by manyfactors such as fitting type location (upstream or down-stream) obstruction ratio and Re In addition the pressurelosses across multiple interactive fittings are lower thanthose across multiple similar individual fittings althoughthe percentage decrease is dependent on the configurationand combination of the fittings These findings imply thatthe calculation of pressure losses across multiple closelymounted fittings via summing those across individual fittingsis inaccurateThismethod overpredicts the total pressure lossand could result in energy waste via the selection of largerfans Thus a more accurate reliable and high-efficiency

10 The Scientific World Journal

0

005

01Z

(m)

18 2 22 24 26 28 3X (m)

Pressure minus300 minus200 minus100 0 100 200 300 400 500 600

Figure 7 Pressure (Pa) contour around the in-duct fittings on the center plane of the duct (Case 7 at 20ms)

18 2 22 24 26 28 3

Velocity-magnitude 5 10 15 20 25 30

0

005

01

Z(m

)

X (m)

Figure 8 Air speed (ms) contour around the in-duct fittings on the center plane of the duct (Case 7 at 20ms)

Table 6 Comparison of predicted and measured pressure losses(Pa)

Case 7 (20ms) Case 14 (19ms)Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Measurement 256 260 486 528 410LES simulation 258 254 491 539 417

predictive method such as a validated CFD model shouldbe explored

The predicted results by LES modeling agree well withthe measured data in the tests which demonstrates thatthe LES model can accurately resolve the flow field in aHVAC duct with multiple in-duct fittings Compared tothe experimental measurement the numerical modeling canprovide the details of pressure distribution This predictedpressure distribution can be used not only independently in aductwork design (if the numerical model has been validatedbefore) but also to assist in tests to find correct locations toplace pressure sensors In the latter case the use of numericalmodeling can potentially save many experimental resourcesand help to produce more reliable experimental data

References

[1] ASHRAE HandbookmdashFundamentals SI Edition chapter 21-22 American Society of Heating Refrigerating and Air-Conditioning Engineers Atlanta Ga USA 2009

[2] CIBSEThe Chartered Institution of Building Services EngineersHeating Ventilating Air Conditioning and Refrigeration CIBSEGuide B Chartered Institution of Building Services EngineersLondon UK 3rd edition 2005

[3] I E Idelchik Handbook of Hydraulic Resistance 3rd edition1994

[4] ASHRAE Standard 120P ldquoMethods of testing to determine flowresistance of HVAC air ducts and fittingsrdquo American Society ofHeating Refrigerating andAir-conditioning Engineers AtlantaGa USA 1995

[5] B Abushakra I S Walker and M H Sherman ldquoA studyof pressure losses in residential air distribution systemsrdquo inProceedings of the American Council for an Energy EfficientEconomy (ACEEE rsquo02) Washington DC USA 2002 LBNLReport 49700 Lawrence Berkeley National Laboratory CalifUSA 2002

[6] L Shao and S B Riffat ldquoAccuracy of CFD for predictingpressure losses in HVAC duct fittingsrdquo Applied Energy vol 51no 3 pp 233ndash248 1995

[7] S M Atkin and L Shao ldquoEffect on pressure loss of separationand orientation of closely coupledHVACduct fittingsrdquoBuildingServices Engineering Research and Technology vol 21 no 3 pp175ndash178 2000

[8] L Shao and S B Riffat ldquoCFD for prediction of k-factors of ductfittingsrdquo International Journal of Energy Research vol 19 no 1pp 89ndash93 1995

[9] R R Rend E M Sparrow D W Bettenhausen and J PAbraham ldquoParasitic pressure losses in diffusers and in theirdownstream piping systems for fluid flow and heat transferrdquoInternational Journal of Heat and Mass Transfer vol 61 pp 56ndash61 2013

[10] J P Abraham E M Sparrow J C K Tong and D WBettenhausen ldquoInternal flows which transist from turbulentthrough intermittent to laminarrdquo International Journal of Ther-mal Sciences vol 49 no 2 pp 256ndash263 2010

[11] E M Sparrow J P Abraham and W J Minkowycz ldquoFlowseparation in a diverging conical duct effect of reynolds numberand divergence anglerdquo International Journal of Heat and MassTransfer vol 52 no 13ndash14 pp 3079ndash3083 2009

The Scientific World Journal 11

[12] W J Rahmeyer ldquoPressure loss coefficients for close-coupledpipe ellsrdquo ASHRAE Transactions vol 108 pp 390ndash406 2002

[13] G Gan and S B Riffat ldquok-factors for HVAC ducts numericaland experimental determinationrdquo Building Services EngineeringResearch and Technology vol 16 no 3 pp 133ndash139 1995

[14] S A Mumma T A Mahank and Y-P Ke ldquoAnalytical determi-nation of duct fitting loss-coefficientsrdquo Applied Energy vol 61no 4 pp 229ndash247 1998

[15] G Gan and S B Riffat ldquoNumerical determination of energylosses at duct junctionsrdquo Applied Energy vol 67 no 3 pp 331ndash340 2000

[16] S Moujaes and R Gundavelli ldquoCFD simulation of leak inresidential HVAC ductsrdquo Energy and Buildings vol 54 pp 534ndash539 2012

[17] J P Abraham J C K Tong and E M Sparrow ldquoBreakdownof laminar pipe flow into transitional intermittency and subse-quent attainment of fully developed intermittent or turbulentflowrdquo Numerical Heat Transfer Part B vol 54 no 2 pp 103ndash115 2008

[18] W J Minkowycz J P Abraham and EM Sparrow ldquoNumericalsimulation of laminar breakdown and subsequent intermittentand turbulent flow in parallel-plate channels effects of inletvelocity profile and turbulence intensityrdquo International Journalof Heat and Mass Transfer vol 52 no 17ndash18 pp 4040ndash40462009

[19] J P Abraham E M Sparrow and J C K Tong ldquoHeat transferin all pipe flow regimes laminar transitionalintermittent andturbulentrdquo International Journal of Heat and Mass Transfer vol52 no 3ndash4 pp 557ndash563 2009

[20] R D Lovik J P AbrahamW JMinkowycz and EM SparrowldquoLaminarization and turbulentization in a pulsatile pipe flowrdquoNumerical Heat Transfer Part A vol 56 no 11 pp 861ndash8792009

[21] J P Abraham E M Sparrow and W J Minkowycz ldquoInternal-flow nusselt numbers for the low-reynolds-number end of thelaminar-to-turbulent transition regimerdquo International Journalof Heat and Mass Transfer vol 54 no 1ndash3 pp 584ndash588 2011

[22] D A Kose and E Dick ldquoPrediction of the pressure distributionon a cubical building with implicit LESrdquo Journal of WindEngineering and Industrial Aerodynamics vol 98 no 10ndash11 pp628ndash649 2010

[23] C-H HuM Ohba and R Yoshie ldquoCFDmodelling of unsteadycross ventilation flows using LESrdquo Journal of Wind Engineeringand Industrial Aerodynamics vol 96 no 10ndash11 pp 1692ndash17062008

[24] C M Mak J Wu C Ye and J Yang ldquoFlow noise from spoilersin ductsrdquo Journal of the Acoustical Society of America vol 125no 6 pp 3756ndash3765 2009

[25] Fluent Ansys Fluent 130 Theory Guide Turbulence ANSYSCanonsburg Pa USA 2010

[26] J O Hinze Turbulence McGraw-Hill New York NY USA1975

[27] J Smagorinsky ldquoGeneral circulation experiments with theprimitive equations the basic experimentrdquo Monthly WeatherReview vol 91 pp 99ndash164 1963

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World Journal 9

0

200

400

600

800

1000

60000 90000 120000 150000

Pres

sure

loss

(Pa)

ReCase 10-p1Case 10-p2

Figure 4 Effect of Reynolds number on pressure loss acrossfitting(s)

Pres

sure

loss

(Pa)

0

200

400

600

800

1000

1200

0 1 2 3 4 5 6 7 8 9 10 11 12Case number

At p1At p2

Figure 5 Effect of obstruction ratio on pressure losses acrossfitting(s)

agree well with the measured data with a relative deviationless than 3This indicates that the LESmodel can accuratelyresolve the flow field in a HVAC duct with multiple in-ductfittings

Compared to the experimental measurement numericalmodeling has an incomparable advantage in obtaining in-duct flow details such as velocity and pressure distributionsFigure 6 presents the pressure distribution along the ductcenterline in Case 7 at a mean flow velocity of 20ms Figures7 and 8 show the pressure and air speed contours on the centerplane of the duct respectively These kinds of pressure andair speed distribution are useful because it can not only beused independently for ductwork design (if the numericalmodel is validated before) but also to indicate the locationswhere pressure sensors should be placed in the tests for thelatter the involvement of numerical modeling can save manyexperimental resources and help to produce more reliableexperimental data Thus the successful use of numerical

0

200

400

600

800

1000

0 1 2 3 4 5 6

Pres

sure

(Pa)

Distance along streamwise direction (m)

minus800

minus600

minus400

minus200

p1 p2

Figure 6 Pressure distribution along centerline of the duct (Case 7at 20ms)

modeling is of great significance in optimizing ductworkdesign and improving the database for pressure losses acrossfittings

6 Conclusions

This study examines the pressure losses across multiple in-duct fittings of a ventilation duct using experimental testsTwo tested cases are reproduced by LESmodeling to evaluatethe accuracy and reliability of this numerical method inpredicting the pressure field inside a duct with multiplefittings The following conclusions can be drawn

The flow resistance of a centrally placed fitting is remark-ably larger than that of a centrally opened fitting basicallydue to the fact that the velocity profile of a cross-sectionof a duct follows a parabolic distribution For all cases anincrease in the obstruction ratio of a fitting significantlyincreases the pressure loss across it However this pressureloss does not linearly increase with the obstruction ratiothere is a substantial increase in pressure loss when theobstruction ratio increases from 05 to 075 Again this isbecause the velocity profile on a cross-section is not a uniformdistribution

Since the presence of a fitting changes the airflow direc-tion and turbulence around its close neighboring fitting(s)and consequently modifies the 119896 factor the pressure lossesacross the neighboring fitting(s) are changed substantiallyHowever the magnitude of this change is affected by manyfactors such as fitting type location (upstream or down-stream) obstruction ratio and Re In addition the pressurelosses across multiple interactive fittings are lower thanthose across multiple similar individual fittings althoughthe percentage decrease is dependent on the configurationand combination of the fittings These findings imply thatthe calculation of pressure losses across multiple closelymounted fittings via summing those across individual fittingsis inaccurateThismethod overpredicts the total pressure lossand could result in energy waste via the selection of largerfans Thus a more accurate reliable and high-efficiency

10 The Scientific World Journal

0

005

01Z

(m)

18 2 22 24 26 28 3X (m)

Pressure minus300 minus200 minus100 0 100 200 300 400 500 600

Figure 7 Pressure (Pa) contour around the in-duct fittings on the center plane of the duct (Case 7 at 20ms)

18 2 22 24 26 28 3

Velocity-magnitude 5 10 15 20 25 30

0

005

01

Z(m

)

X (m)

Figure 8 Air speed (ms) contour around the in-duct fittings on the center plane of the duct (Case 7 at 20ms)

Table 6 Comparison of predicted and measured pressure losses(Pa)

Case 7 (20ms) Case 14 (19ms)Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Measurement 256 260 486 528 410LES simulation 258 254 491 539 417

predictive method such as a validated CFD model shouldbe explored

The predicted results by LES modeling agree well withthe measured data in the tests which demonstrates thatthe LES model can accurately resolve the flow field in aHVAC duct with multiple in-duct fittings Compared tothe experimental measurement the numerical modeling canprovide the details of pressure distribution This predictedpressure distribution can be used not only independently in aductwork design (if the numerical model has been validatedbefore) but also to assist in tests to find correct locations toplace pressure sensors In the latter case the use of numericalmodeling can potentially save many experimental resourcesand help to produce more reliable experimental data

References

[1] ASHRAE HandbookmdashFundamentals SI Edition chapter 21-22 American Society of Heating Refrigerating and Air-Conditioning Engineers Atlanta Ga USA 2009

[2] CIBSEThe Chartered Institution of Building Services EngineersHeating Ventilating Air Conditioning and Refrigeration CIBSEGuide B Chartered Institution of Building Services EngineersLondon UK 3rd edition 2005

[3] I E Idelchik Handbook of Hydraulic Resistance 3rd edition1994

[4] ASHRAE Standard 120P ldquoMethods of testing to determine flowresistance of HVAC air ducts and fittingsrdquo American Society ofHeating Refrigerating andAir-conditioning Engineers AtlantaGa USA 1995

[5] B Abushakra I S Walker and M H Sherman ldquoA studyof pressure losses in residential air distribution systemsrdquo inProceedings of the American Council for an Energy EfficientEconomy (ACEEE rsquo02) Washington DC USA 2002 LBNLReport 49700 Lawrence Berkeley National Laboratory CalifUSA 2002

[6] L Shao and S B Riffat ldquoAccuracy of CFD for predictingpressure losses in HVAC duct fittingsrdquo Applied Energy vol 51no 3 pp 233ndash248 1995

[7] S M Atkin and L Shao ldquoEffect on pressure loss of separationand orientation of closely coupledHVACduct fittingsrdquoBuildingServices Engineering Research and Technology vol 21 no 3 pp175ndash178 2000

[8] L Shao and S B Riffat ldquoCFD for prediction of k-factors of ductfittingsrdquo International Journal of Energy Research vol 19 no 1pp 89ndash93 1995

[9] R R Rend E M Sparrow D W Bettenhausen and J PAbraham ldquoParasitic pressure losses in diffusers and in theirdownstream piping systems for fluid flow and heat transferrdquoInternational Journal of Heat and Mass Transfer vol 61 pp 56ndash61 2013

[10] J P Abraham E M Sparrow J C K Tong and D WBettenhausen ldquoInternal flows which transist from turbulentthrough intermittent to laminarrdquo International Journal of Ther-mal Sciences vol 49 no 2 pp 256ndash263 2010

[11] E M Sparrow J P Abraham and W J Minkowycz ldquoFlowseparation in a diverging conical duct effect of reynolds numberand divergence anglerdquo International Journal of Heat and MassTransfer vol 52 no 13ndash14 pp 3079ndash3083 2009

The Scientific World Journal 11

[12] W J Rahmeyer ldquoPressure loss coefficients for close-coupledpipe ellsrdquo ASHRAE Transactions vol 108 pp 390ndash406 2002

[13] G Gan and S B Riffat ldquok-factors for HVAC ducts numericaland experimental determinationrdquo Building Services EngineeringResearch and Technology vol 16 no 3 pp 133ndash139 1995

[14] S A Mumma T A Mahank and Y-P Ke ldquoAnalytical determi-nation of duct fitting loss-coefficientsrdquo Applied Energy vol 61no 4 pp 229ndash247 1998

[15] G Gan and S B Riffat ldquoNumerical determination of energylosses at duct junctionsrdquo Applied Energy vol 67 no 3 pp 331ndash340 2000

[16] S Moujaes and R Gundavelli ldquoCFD simulation of leak inresidential HVAC ductsrdquo Energy and Buildings vol 54 pp 534ndash539 2012

[17] J P Abraham J C K Tong and E M Sparrow ldquoBreakdownof laminar pipe flow into transitional intermittency and subse-quent attainment of fully developed intermittent or turbulentflowrdquo Numerical Heat Transfer Part B vol 54 no 2 pp 103ndash115 2008

[18] W J Minkowycz J P Abraham and EM Sparrow ldquoNumericalsimulation of laminar breakdown and subsequent intermittentand turbulent flow in parallel-plate channels effects of inletvelocity profile and turbulence intensityrdquo International Journalof Heat and Mass Transfer vol 52 no 17ndash18 pp 4040ndash40462009

[19] J P Abraham E M Sparrow and J C K Tong ldquoHeat transferin all pipe flow regimes laminar transitionalintermittent andturbulentrdquo International Journal of Heat and Mass Transfer vol52 no 3ndash4 pp 557ndash563 2009

[20] R D Lovik J P AbrahamW JMinkowycz and EM SparrowldquoLaminarization and turbulentization in a pulsatile pipe flowrdquoNumerical Heat Transfer Part A vol 56 no 11 pp 861ndash8792009

[21] J P Abraham E M Sparrow and W J Minkowycz ldquoInternal-flow nusselt numbers for the low-reynolds-number end of thelaminar-to-turbulent transition regimerdquo International Journalof Heat and Mass Transfer vol 54 no 1ndash3 pp 584ndash588 2011

[22] D A Kose and E Dick ldquoPrediction of the pressure distributionon a cubical building with implicit LESrdquo Journal of WindEngineering and Industrial Aerodynamics vol 98 no 10ndash11 pp628ndash649 2010

[23] C-H HuM Ohba and R Yoshie ldquoCFDmodelling of unsteadycross ventilation flows using LESrdquo Journal of Wind Engineeringand Industrial Aerodynamics vol 96 no 10ndash11 pp 1692ndash17062008

[24] C M Mak J Wu C Ye and J Yang ldquoFlow noise from spoilersin ductsrdquo Journal of the Acoustical Society of America vol 125no 6 pp 3756ndash3765 2009

[25] Fluent Ansys Fluent 130 Theory Guide Turbulence ANSYSCanonsburg Pa USA 2010

[26] J O Hinze Turbulence McGraw-Hill New York NY USA1975

[27] J Smagorinsky ldquoGeneral circulation experiments with theprimitive equations the basic experimentrdquo Monthly WeatherReview vol 91 pp 99ndash164 1963

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

10 The Scientific World Journal

0

005

01Z

(m)

18 2 22 24 26 28 3X (m)

Pressure minus300 minus200 minus100 0 100 200 300 400 500 600

Figure 7 Pressure (Pa) contour around the in-duct fittings on the center plane of the duct (Case 7 at 20ms)

18 2 22 24 26 28 3

Velocity-magnitude 5 10 15 20 25 30

0

005

01

Z(m

)

X (m)

Figure 8 Air speed (ms) contour around the in-duct fittings on the center plane of the duct (Case 7 at 20ms)

Table 6 Comparison of predicted and measured pressure losses(Pa)

Case 7 (20ms) Case 14 (19ms)Δ1198751198781 Δ1198751198782 Δ1198751198781 Δ1198751198782 Δ1198751198783

Measurement 256 260 486 528 410LES simulation 258 254 491 539 417

predictive method such as a validated CFD model shouldbe explored

The predicted results by LES modeling agree well withthe measured data in the tests which demonstrates thatthe LES model can accurately resolve the flow field in aHVAC duct with multiple in-duct fittings Compared tothe experimental measurement the numerical modeling canprovide the details of pressure distribution This predictedpressure distribution can be used not only independently in aductwork design (if the numerical model has been validatedbefore) but also to assist in tests to find correct locations toplace pressure sensors In the latter case the use of numericalmodeling can potentially save many experimental resourcesand help to produce more reliable experimental data

References

[1] ASHRAE HandbookmdashFundamentals SI Edition chapter 21-22 American Society of Heating Refrigerating and Air-Conditioning Engineers Atlanta Ga USA 2009

[2] CIBSEThe Chartered Institution of Building Services EngineersHeating Ventilating Air Conditioning and Refrigeration CIBSEGuide B Chartered Institution of Building Services EngineersLondon UK 3rd edition 2005

[3] I E Idelchik Handbook of Hydraulic Resistance 3rd edition1994

[4] ASHRAE Standard 120P ldquoMethods of testing to determine flowresistance of HVAC air ducts and fittingsrdquo American Society ofHeating Refrigerating andAir-conditioning Engineers AtlantaGa USA 1995

[5] B Abushakra I S Walker and M H Sherman ldquoA studyof pressure losses in residential air distribution systemsrdquo inProceedings of the American Council for an Energy EfficientEconomy (ACEEE rsquo02) Washington DC USA 2002 LBNLReport 49700 Lawrence Berkeley National Laboratory CalifUSA 2002

[6] L Shao and S B Riffat ldquoAccuracy of CFD for predictingpressure losses in HVAC duct fittingsrdquo Applied Energy vol 51no 3 pp 233ndash248 1995

[7] S M Atkin and L Shao ldquoEffect on pressure loss of separationand orientation of closely coupledHVACduct fittingsrdquoBuildingServices Engineering Research and Technology vol 21 no 3 pp175ndash178 2000

[8] L Shao and S B Riffat ldquoCFD for prediction of k-factors of ductfittingsrdquo International Journal of Energy Research vol 19 no 1pp 89ndash93 1995

[9] R R Rend E M Sparrow D W Bettenhausen and J PAbraham ldquoParasitic pressure losses in diffusers and in theirdownstream piping systems for fluid flow and heat transferrdquoInternational Journal of Heat and Mass Transfer vol 61 pp 56ndash61 2013

[10] J P Abraham E M Sparrow J C K Tong and D WBettenhausen ldquoInternal flows which transist from turbulentthrough intermittent to laminarrdquo International Journal of Ther-mal Sciences vol 49 no 2 pp 256ndash263 2010

[11] E M Sparrow J P Abraham and W J Minkowycz ldquoFlowseparation in a diverging conical duct effect of reynolds numberand divergence anglerdquo International Journal of Heat and MassTransfer vol 52 no 13ndash14 pp 3079ndash3083 2009

The Scientific World Journal 11

[12] W J Rahmeyer ldquoPressure loss coefficients for close-coupledpipe ellsrdquo ASHRAE Transactions vol 108 pp 390ndash406 2002

[13] G Gan and S B Riffat ldquok-factors for HVAC ducts numericaland experimental determinationrdquo Building Services EngineeringResearch and Technology vol 16 no 3 pp 133ndash139 1995

[14] S A Mumma T A Mahank and Y-P Ke ldquoAnalytical determi-nation of duct fitting loss-coefficientsrdquo Applied Energy vol 61no 4 pp 229ndash247 1998

[15] G Gan and S B Riffat ldquoNumerical determination of energylosses at duct junctionsrdquo Applied Energy vol 67 no 3 pp 331ndash340 2000

[16] S Moujaes and R Gundavelli ldquoCFD simulation of leak inresidential HVAC ductsrdquo Energy and Buildings vol 54 pp 534ndash539 2012

[17] J P Abraham J C K Tong and E M Sparrow ldquoBreakdownof laminar pipe flow into transitional intermittency and subse-quent attainment of fully developed intermittent or turbulentflowrdquo Numerical Heat Transfer Part B vol 54 no 2 pp 103ndash115 2008

[18] W J Minkowycz J P Abraham and EM Sparrow ldquoNumericalsimulation of laminar breakdown and subsequent intermittentand turbulent flow in parallel-plate channels effects of inletvelocity profile and turbulence intensityrdquo International Journalof Heat and Mass Transfer vol 52 no 17ndash18 pp 4040ndash40462009

[19] J P Abraham E M Sparrow and J C K Tong ldquoHeat transferin all pipe flow regimes laminar transitionalintermittent andturbulentrdquo International Journal of Heat and Mass Transfer vol52 no 3ndash4 pp 557ndash563 2009

[20] R D Lovik J P AbrahamW JMinkowycz and EM SparrowldquoLaminarization and turbulentization in a pulsatile pipe flowrdquoNumerical Heat Transfer Part A vol 56 no 11 pp 861ndash8792009

[21] J P Abraham E M Sparrow and W J Minkowycz ldquoInternal-flow nusselt numbers for the low-reynolds-number end of thelaminar-to-turbulent transition regimerdquo International Journalof Heat and Mass Transfer vol 54 no 1ndash3 pp 584ndash588 2011

[22] D A Kose and E Dick ldquoPrediction of the pressure distributionon a cubical building with implicit LESrdquo Journal of WindEngineering and Industrial Aerodynamics vol 98 no 10ndash11 pp628ndash649 2010

[23] C-H HuM Ohba and R Yoshie ldquoCFDmodelling of unsteadycross ventilation flows using LESrdquo Journal of Wind Engineeringand Industrial Aerodynamics vol 96 no 10ndash11 pp 1692ndash17062008

[24] C M Mak J Wu C Ye and J Yang ldquoFlow noise from spoilersin ductsrdquo Journal of the Acoustical Society of America vol 125no 6 pp 3756ndash3765 2009

[25] Fluent Ansys Fluent 130 Theory Guide Turbulence ANSYSCanonsburg Pa USA 2010

[26] J O Hinze Turbulence McGraw-Hill New York NY USA1975

[27] J Smagorinsky ldquoGeneral circulation experiments with theprimitive equations the basic experimentrdquo Monthly WeatherReview vol 91 pp 99ndash164 1963

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World Journal 11

[12] W J Rahmeyer ldquoPressure loss coefficients for close-coupledpipe ellsrdquo ASHRAE Transactions vol 108 pp 390ndash406 2002

[13] G Gan and S B Riffat ldquok-factors for HVAC ducts numericaland experimental determinationrdquo Building Services EngineeringResearch and Technology vol 16 no 3 pp 133ndash139 1995

[14] S A Mumma T A Mahank and Y-P Ke ldquoAnalytical determi-nation of duct fitting loss-coefficientsrdquo Applied Energy vol 61no 4 pp 229ndash247 1998

[15] G Gan and S B Riffat ldquoNumerical determination of energylosses at duct junctionsrdquo Applied Energy vol 67 no 3 pp 331ndash340 2000

[16] S Moujaes and R Gundavelli ldquoCFD simulation of leak inresidential HVAC ductsrdquo Energy and Buildings vol 54 pp 534ndash539 2012

[17] J P Abraham J C K Tong and E M Sparrow ldquoBreakdownof laminar pipe flow into transitional intermittency and subse-quent attainment of fully developed intermittent or turbulentflowrdquo Numerical Heat Transfer Part B vol 54 no 2 pp 103ndash115 2008

[18] W J Minkowycz J P Abraham and EM Sparrow ldquoNumericalsimulation of laminar breakdown and subsequent intermittentand turbulent flow in parallel-plate channels effects of inletvelocity profile and turbulence intensityrdquo International Journalof Heat and Mass Transfer vol 52 no 17ndash18 pp 4040ndash40462009

[19] J P Abraham E M Sparrow and J C K Tong ldquoHeat transferin all pipe flow regimes laminar transitionalintermittent andturbulentrdquo International Journal of Heat and Mass Transfer vol52 no 3ndash4 pp 557ndash563 2009

[20] R D Lovik J P AbrahamW JMinkowycz and EM SparrowldquoLaminarization and turbulentization in a pulsatile pipe flowrdquoNumerical Heat Transfer Part A vol 56 no 11 pp 861ndash8792009

[21] J P Abraham E M Sparrow and W J Minkowycz ldquoInternal-flow nusselt numbers for the low-reynolds-number end of thelaminar-to-turbulent transition regimerdquo International Journalof Heat and Mass Transfer vol 54 no 1ndash3 pp 584ndash588 2011

[22] D A Kose and E Dick ldquoPrediction of the pressure distributionon a cubical building with implicit LESrdquo Journal of WindEngineering and Industrial Aerodynamics vol 98 no 10ndash11 pp628ndash649 2010

[23] C-H HuM Ohba and R Yoshie ldquoCFDmodelling of unsteadycross ventilation flows using LESrdquo Journal of Wind Engineeringand Industrial Aerodynamics vol 96 no 10ndash11 pp 1692ndash17062008

[24] C M Mak J Wu C Ye and J Yang ldquoFlow noise from spoilersin ductsrdquo Journal of the Acoustical Society of America vol 125no 6 pp 3756ndash3765 2009

[25] Fluent Ansys Fluent 130 Theory Guide Turbulence ANSYSCanonsburg Pa USA 2010

[26] J O Hinze Turbulence McGraw-Hill New York NY USA1975

[27] J Smagorinsky ldquoGeneral circulation experiments with theprimitive equations the basic experimentrdquo Monthly WeatherReview vol 91 pp 99ndash164 1963

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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