aiaa 2002–2925web.engr.uky.edu/~acfd/aiaa01.pdf · 2006-01-03 · aiaa 2002–2925 experimental...

AIAA 2002–2925EXPERIMENTAL ANDCOMPUTATIONAL INVESTIGATIONOF FLOW IN GAS TURBINE BLADECOOLING PASSAGESHarald Roclawski, Jamey D. Jacob, Tiangliang Yang,& James M. McDonoughMechanical Engineering Dept.University of Kentucky

31st AIAA Fluid DynamicsConference and Exhibit

June 11-14, 2002/Anaheim, CAFor permission to copy or republish, contact the American Institute of Aeronautics and Astronautics1801 Alexander Bell Drive, Suite 500, Reston, VA 20191–4344

June 7, 2001

EXPERIMENTAL AND COMPUTATIONAL

INVESTIGATION OF FLOW IN GAS

TURBINE BLADE COOLING PASSAGES

Harald Roclawski,∗ Jamey D. Jacob,† Tiangliang Yang,‡ & James M. McDonough§

Mechanical Engineering Dept.

University of Kentucky

Results of experimental and numerical investigations into gas turbine cooling passage

flows are presented. EXPAND ONCE ENTIRE PAPER IS COMPLETE.

Nomenclature

b Bar height, 25.4mmcf Skin friction coefficientD Channel width, 406mmFFP Forward flow probabilityh Backward facing step height, 28.6mmH Channel height, 203mmRe Reynolds numberU∞ Freestream velocityν Viscosityρ Density, kg/m3

Introduction

Continuing requirements for ever increasingthrust/weight ratio in high-performance aircraft gasturbine engines necessitates increasing operating tem-peratures to gain improved thermodynamic efficiency.Even a fractional improvement in performance canoffer significant savings (see, for example, Mayle1).Currently available materials for turbine blades areunable to withstand long periods of exposure tothese high temperatures while maintaining structuralintegrity, even with thermal barrier coatings (TBC),implying need for active cooling strategies. Overthe past 30 years turbine temperatures have beencontinually increased, and continuing improvementsin cooling techniques have been a major contributionto this.

Several different approaches to cooling are usuallyemployed in cooling even a single turbine blade, as canbe inferred from a sample blade circuit shown in fig-ure 1. In general, high-performance turbine blades arecooled by a combination of exterior flow film coolingwhich limits the heat flux from the combustion gases tothe blade material and interior cooling air circuit flowswhich extract heat from the interior surfaces of the

∗M.S. student; member AIAA.†Assistant Professor; senior member AIAA.‡Post-doctoral Fellow; member AIAA.§Professor; senior member AIAA.

Copyright c© 2002 by the authors. Published by the AmericanInstitute of Aeronautics and Astronautics, Inc. with permission.

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Incoming Cooling Air

Tip Bleed Air

Turbulators

Trailing−Edge

Turbulators

Bleed HolesFilm−Cooling

Bleed HolesFilm−Cooling

Region

Fig. 1 Typical turbine blade cooling circuit (afterHan et al., 1986).

blade. A key factor in this interior heat removal pro-cess is maintaining turbulent flow. At the same timethis results in greater pressure losses, so there must al-ways be a tradeoff between cooling circuit heat transfereffectiveness and pressure loss in turbine blade designstudies. A significant portion of the design effort is de-voted to this problem, and it is especially difficult forboth experimental and computational fluid dynamics(CFD) because of the highly complex geometries ofinterior cooling air circuits, the turbulent flow, and inthe case of experiments, the need to account for highrates of blade rotation.

Past experiments on turbine blade cooling have fo-

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June 7, 2001

cused on the flows within simple or complex channelsand the effect of turbulence generating devices on theflow field and heat transfer rates. The effect of rota-tion, which is a requisite parameter in turbine flows,has generally been ignored due to the complexity ofthe experimental apparatus. This has proved to be amajor gap in in experimental testing. Also, the ma-jority of experimental measurements have been singlepoint measurements, not allowing a full field analysis.This point has proved particular difficulty when tryingto validate numerical simulations which benefit fromfull field data. The maturation of modern optical fieldmeasurements have allowed these hurdles to be over-come, though any experiments must require extremecare in their formulation.

In the case of numerical simulations, turbulencemodeling based on Reynolds-averaged Navier-Stokes(RANS) approaches has generally proven inadequatefor this problem, and typical Reynolds numbers (Re)encountered in internal cooling air flows (∼ O(105))preclude use of direct numerical simulation (DNS) inmost cases. But recent advances in computing powerand in numerical procedures associated with large-eddy simulation (LES) suggest that certain forms ofthis approach may be applicable. However, a signifi-cant amount of laboratory experimentation is neededfor their validation, and (probably) tuning. In thepresent paper we will focus on one particular aspectof constructing synthetic velocity models. We remarkthat there are many alternative approaches,15,16 andwe shall not attempt a thorough review of the sub-ject. Instead, we will concentrate on the Hylin andMcDonough17 formalism.

Previous Work

Previous experimental research in turbine bladecooling has been primarily focused on the externalcooling effects (e.g., Wang et. al2). This is due tothe relative ease of the external measurements as com-pared to the complex apparatus or gross simplifica-tions required for internal duct measurements, partic-ularly when it applies to measurements of the flowfield. Previous research efforts on internal coolinghave been limited in scope, typically focusing on a sin-gle aspect of the multivariant problem. Bunker andMetzger3 examined the local heat transfer from inter-nal impingement cooling using temperature sensitivepaint. General relations showed increased heat trans-fer with increased jet Reynolds number. Bohn et. al4

numerically and experimentally examined trailing edgecooling in turbine blades. The experiments were con-ducted in a scaled test rig and showed anisotropic tur-bulence profiles resulting in non-symmetrical coolantdistribution. The numerical predictions compared rea-sonably well with the experimental data. Johnson et.al5 examined the heat transfer within rotating serpen-tine passages. Geometry and orientation were found

to have large effects on the maximum local heat trans-fer. Specifically, the angle to which the passage wasinclinded respective to the axis of rotation was foundto vary the heat transer ratio up to 50%. Flanneryet. al6 examined the heat transfer properties of variousheat transfer enhancement devices within a cooling cir-cuit using napthalene sublimation. Dimensional anal-ysis and scale modeling showed improvement in heattransfer in vortex flow cavities and sand-dune shapedturbulators, though actual measurements in a chan-nel or rotating cavity were not performed. Morris andChang7 investigated the heat transfer properties of acircular cooling channel. Full field heat transfer datawere obtained through a combination of measurementsand solution of the channel wall heat conduction equa-tion. The resulting internal heat flux distribution overthe full inner surface was subsequently used to deter-mine the local variation of heat transfer coefficient.Effects of the Coriolis force and centripetal buoyancyon the forced convection mechanism were investigatedand found to be of sufficient order to warrent consid-eration in further experimental and numerical studies.

Cakan and Arts8 studied the flow in a straight, rect-angular, rib-roughened internal cooling channel. At aReynolds number of 6500 and 30000 and a rib blockageratio of 0.133, DPIV measurements were taken. Theyfound that the flow through the ribbed channel can becharacterized by a series of accelerations, decelerationswith separation, reattachment and redevelopment dueto the sudden changes in cross-section. The ribs inducea separation and recirculation bubble. The flow reat-taches at X/e = 4.5 (Re = 6500). Comparing bothstudies, they claim that the reattachment distance isnot strongly dependent on the Reynolds number. Up-stream of the ribs, the flow impinges on the rib, movesto the sidewalls of the channel and produces to vor-tices. Behind the rib a similar motion occurs due to therecirculation region. In the span wise flow direction;two counter rotating secondary flow cells are observed.

The flow in a straight, rectangular channel with ribson two opposite walls was investigated by Lio et. al9

by means of LDV. The Reynolds number based on thechannel hydraulic diameter was 33000. The ribs wereperforated and the effect of the rib open area ratio wasinvestigated. They also found a periodic acceleratingand decelerating flow behavior. In contrast to the pre-vious paper, only one secondary flow cell is observed inthe span wise flow direction. Furthermore, it was dis-covered that the reattachment length downstream of arib pair is shorter than in the case of a backward-facingstep. The maximum heat transfer rate was found tobe dependent upon a critical range of the open arearatio governed by whether the flow treated the ribs aspermeable or impermeable. A PIV Investigation of theflow in a rectangular channel with a 90◦ and 45◦ ribarrangement and a 180◦ bend was done by Schabackerand Bolcs10 at Re = 45700 and a rib height equal to

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0.1 hydraulic diameters. Two counter rotating vorticesin the span wise flow direction were observed. The de-velopment length to achieve a fully developed flow con-dition is longer for the case of a 45◦ rib arrangement.Furthermore, the 45◦ ribs prevent the development ofzones of recirculating flow in the upstream outer cor-ner of the bend and the curvature-induced secondaryflows a weakened in this section of the channel. Com-pared to a smooth channel, the flow recovers fasterfrom the bend effect. Results for the case of a station-ary and rotating, rectangular, ribbed channel with a180◦ bend were obtained by Servouze11 using LDV.The flow conditions were Re=5000, Ro=0.33 and arib aspect ratio of 10. In the stationary case a peri-odic accelerating and decelerating flow behavior wasfound. In contrast to other papers, secondary flowstructures (vortices) in the span wise flow directionwere not observed. Iacovides12 did an LDA studyon the flow in a ribbed channel with a 180◦ bend.He investigated a staionary case at a Re=100000 andtwo rotating cases at Ro=(+-)0.2. The rib-height toduct diameter ratio was 0.1 He also observes a peri-odic flow behavior. Because of the ribs, turbulenceincreases at the bend entry and an additional separa-tion bubble over the first rib interval downstream ofthe bend exit is formed. Nevertheless, in agreementwith Schabacker and Bolcs, it is claimed that the flowrecovers faster from the bend effect in a ribbed chan-nel. Especially the separation bubble along the innerwall is reduced. Lastly, Hwang and Lai14 examinedlaminar flow within a rotating multiple-pass channelwith bends from a computational standpoint. Rota-tion was found to have a large impact on the wallfriction factor. Validations were only made with sta-tionary experiments, however. Heat transfer rate orturbulators were not examined.

Previous Modeling Efforts

Put previous modeling in here.

Experimental Portion

Setup & Diagnostics

The wind tunnel arrangements for the backwardfacing step and turbulator experiments are shown infigure 11(a) and 11(c), respectively. Both test sectionswere installed in a low-turbulence open-circuit blow-down wind tunnel. A 7.5 hp motor powers a radialfan at the inlet. A vibration damper, flow straightener,and turbulence dampening screens precede the nozzlewhich has a contraction ratio of 6.7. The maximumtest section velocity is 35 m/s with an open exhaustand approximately 10 m/s when a filter is installedto capture seeding particles. The test sections havea channel height H of 0.2 m (203 mm) and width Dof 0.4 m (406 mm). The backward facing step has astep height h of 28.6 mm. The turbulator test sec-tion is arranged so that multiple square ribs of various

Geometry Scale Re RangeBFS h 2.0 · 103 − 1.7 · 104

H 1.4 · 104 − 1.2 · 105

Turbulator b 1.8 · 103 − 1.8 · 104

H 1.4 · 104 − 1.4 · 105

Table 1 Experimental Parameters

sizes can be placed in different locations in the chan-nel. The current paper presents results for ribs of equalsizes with sides b = 24.5 mm. Ribs arrangements of 1,2, 3, and 4 bars are examined with equal separationdistances of 152 mm in the multiple turbulator runs.Re based on channel height, step size, and rib size arereported in table 1.

In both the backward facing step and turbulatortest sections, PIV, HWA, and static pressure measure-ments were made along the tunnel centerline down-stream of the step and last rib, respectively. For PIV,the laser sheet was generated by a 25 mJ double-pulsedNd:YAG laser with a maximum repetition rate of 15Hz. Pulse separations varied from 100 µs to 1 msbased upon the tunnel velocity. A 10 bit CCD cam-era with a 1008×1018 pixel array was used to captureimages. Uniform seeding was accomplished using ei-ther zinc stearate or talc injected at the fan inlet; a 1micron filter at the tunnel exhaust was required to cap-ture the particles thus reducing the maximum tunnelvelocity during PIV. A predictor-corrector algorithmwith an interrogation area of 32×32 was used to gener-ate displacement vectors and velocity gradients.13 Forthe hot-wire measurements, which are required to ob-tain details of random fluctuations in velocity for themodeling efforts, a single-component boundary layerhot-wire probe was used capable of wall measurementswithin 0.3 mm of the surface. 40,000 points or greaterwere recored at a sampling rate 10 kHz. For the staticpressure measurements, pressure taps were placed 25.4mm apart downstream of the backward facing step andslightly upstream and downstream of the last turbu-lator. Pressure measurements were made up to 14.5 bdownstream of the turbulator in the results presentedhere.

Results

Backward Facing Step

insert discussion files

Turbulators

insert discussion files

Discussion

Modeling

In the present paper we will focus on one partic-ular aspect of constructing synthetic velocity mod-els. We remark that there are many alternative ap-proaches,15,16 and we shall not attempt a thorough

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review of the subject. Instead, we will concentrate onthe Hylin and McDonough17 formalism.

We begin by noting that synthetic velocity turbu-lence models offer the potential of a much closer con-nection to laboratory measurements than can be ob-tained with other modeling approaches because prim-itive variables (e.g., velocity components) are directlymodeled and used instead of attempting to model flowstatistics—Reynolds stresses.

Within the Hylin and McDonough framework, asubgrid-scale quantity is expressed as a product ofthree factors, e.g.,

u∗ = AuζuMu. (1)

Here u∗ is a SGS velocity component; Au is an ampli-tude factor; ζu is an anisotropy correction, and Mu isa temporal fluctuation. Each of the three factors onthe right-hand side of (1) varies across the spatial grid,and from one resolved-scale time step to the next.

Expressions for the first two factors have been de-rived from first principles employing the Kolmogorovtheory of homogeneous turbulence (see Frisch,18

for a good overview), as given in Hylin and Mc-Donough17,19,20) and Sagaut.21 The third factor re-ceived little specific attention in early investigations.Hylin22 associated this factor with Kolmogorov’s“stochastic variable,” and considered the logistic map,“absolute value” logistic map and tent map for real-izations. All appear to give similar results when thesame map is used for all velocity components.

Two-dimensional simulations of turbine blade cool-ing presented by McDonough et al.23 suggest thatusing the same map for all solution components is notcorrect (especially for passive scalars). McDonoughand Huang24 provide a derivation of appropriate mapsfor use in (1) for reduced-kinetics H2–O2 combustionand show that the maps (discrete dynamical systems,DDSs) arising from the Navier–Stokes equations arebasically logistic maps while those corresponding tothermal energy and species concentrations are not.Finally, McDonough and Huang25 present a detailedanalysis of the 2-D “poor man’s N.–S. equations” de-rived as in the previous reference. They show thatessentially every temporal behavior seen in actual N.–S. flows can be produced by this simple 2-D DDS:

a(n+1) = β1a(n)

(

1− a(n))

− γ1a(n)b(n),

b(n+1) = β2b(n)

(

1− b(n))

− γ2a(n)b(n),

where (a, b)T can be viewed as high-wavenumberFourier coefficients of the velocity field, U = (U, V )T .

This DDS contains four bifurcations parameters (β1,β2, γ1, γ2). The first two are directly related to theReynolds number, Re, or possibly the integral scale orTaylor microscale Re, depending on details of imple-mentation,17 and thus might reasonably be set equal as

in McDonough and Huang.24,25 The other two param-eters are most closely associated with shear stress: uy

and vx in 2D. As noted in McDonough and Huang,25

in order to construct reliable synthetic velocities byemploying nonlinear DDSs it is essential to find a map-ping between physical parameters, say Re and∇U andthe above bifurcation parameters of the map(s). Thepresent paper documents our initial attempts to ac-complish this for a specific flow geometry.

We begin by noting that in order to establish sucha mapping we must first be able to accurately expressany appropriate set of physical data in terms of bifur-cation parameters of the DDS. This is nothing morethan a curve-fitting problem, and McDonough et al.26

and Mukerji et al.27 provided an approach to solvingit. This consists of first recognizing that an “exact”polynomial fit is not appropriate (cf., Casdagli and Eu-bank,28 for examples where it is appropriate), and thata global least-squares fit is needed. The next step is todetermine a set of data characterizations by means ofwhich to compare the fit with the original data. Mc-Donough et al.26 provide a long list of these but makeno claims as to either the necessity of any single one,or sufficiency of the set as a whole.

Once such a set of characterizations is chosen, weconstruct the model in the form given in McDonoughet al.:26

M (n+1) = (1−θ)M (n)+θ

K∑

k=1

αkS(n+1)k (dk, ωk,mk(βk)) .

(2)Details of this expression can be found in the citedreferences, but we briefly note the following. The pa-rameters θ, αk, βk, ωk, dk and K must all be foundin the course of the curve-fitting process. The αk areamplitude factors and can be considered analogous toFourier coefficients (although they do not arise from aformal inner product). Sk is a nonlinear discontinuousfunction of the behavior of the map; its purpose is toallow existence of frequencies of oscillation not foundin the DDS, itself (i.e., lower frequencies) in additionto permitting modeling of very irregular intermitten-cies. The parameters ωk are the frequencies at whichiterations of the kth map will be initiated; dk is theduration of evaluation once initiated; βk is the bifur-cation parameter, and for purposes herein, the form ofthe kth map is

m(n+1)k = βkm

(n)k

(

1−m(n)k

)

, (3)

the basic logistic map (see, e.g., May, 1976, for aninteresting and detailed treatment).

We will use the scalar map (3) in the present study,rather than the 2-D map described above, because thetemporal resolution of the current 2-D PIV data isinsufficient for capturing details of subgrid-scale tur-bulent fluctuations. On the other hand, the single

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velocity component obtained from hot-wire measure-ments at 10 KHz is sufficient. Our goal is thus todetermine the variation of each of the parameters inEq. (2) at a specific location in the physical flow fieldas a function of Re.

For each value of Re considered we will constructtwo separate curve fits of the data. The first will bebased on the complete velocity signal and thus, up tosubtracting out the mean, corresponds to a Reynolds-averaged N.–S. (RANS) quantity:

u′(x, t) = U(x, t)− u(x),

where the overbar denotes time average. The secondwill be obtained from high-pass filtered data analogousto the SGS behavior in a LES formalism. In this case

u∗(x, t) = U(x, t)− u(x, t),

where tilde denotes (formally) a spatial filtering.Both cases are of interest because the ability to fit

both types of data shows that synthetic velocity fieldsare applicable to both LES and RANS models. Butin addition, with both fits available we will see thatthey are very different—as one should expect. Thisraises very serious questions regarding validity of cer-tain forms of “very” large-eddy simulation (VLES)in which “time-accurate” RANS equations are solved,and conversely to forms of LES in which RANS for-malisms are employed to construct the SGS models.At the fundamental mathematical level RANS andLES are quite different, and the results we present be-low provide a direct empirical demonstration of this.Thus, considrable care must be taken when attempt-ing to bridge the gap between these two modelingapproaches.

The cases we consider correspond to Re = 4 × 104

and Re = 1 × 105 for the turbulator flows discussedabove in the section on experiments. For both valuesof Re the measurement location was ?? mm upstreamof reattachment, and at a height of 3.5 mm, behind thefirst turbulator. The curve-fitting process was carriedout essentially as described in McDonough et al.26 andMukerji et al. ,27 and as in those references once theprocess is complete we compare three additional fea-tures: i) the “appearance” of the time series, ii) thepower spectral density, and iii) the delay map.

As emphasized in these references, we consider theappearance of the modeled time series to be essentialto a good fit of the data (just as would be the casein an exact fit), and the characterizations employedin the least-squares fit are selected to guarantee this.But appearance in this case is a nontrivial notion, firstbecause it is difficult to define precisely, and secondbecause the objective function for the least-squares fitis highly nonlinear, discontinuous, contains both realand integer variables, and thus generally has multiplelocal minima.

McDonough et al.26 discuss appearance of the timeseries in some detail, indicating that close examina-tion of most such data will lead to identification of afinite number of types of “structures.” The number ofthese is typically used as the initial guess for the valueof K, the number of terms in the model representa-tion, Eq. (2). In comparing the model with the datait is important to observe, as already noted, that thefit is not intended to be exact because an exact fit isintrinsically incompatible with the physics (and math-ematics) of a turbulent flow. Our rule of thumb forchecking that the model has preserved the appearanceof the data is that if the modeled time series and dataare juxtaposed, it should be impossible to determinewhere the data ends and the model begins.

Use of power spectra and delay maps as additionaltests of goodness of fit is recommended because ap-pearance is at best only semi-quantitative. On theother hand, neither of these characterizations alonewill guarantee a good fit. Many different time seriesexhibit very similar power spectra, and the delay mapprovides only basic topological information associatedwith the underlying attractor (if there is one). Never-theless, both of these can be of value in “fine tuning”a fit of data.

Results for Complete Velocity

Figure ? displays three complete velocity time se-ries in parts (a) through (c). The first corresponds toexperimental data for Re = 4× 104; the second repre-sents evaluation of the model, Eq. (2), with and initialguess of the parameters to be determined in the least-squares fit, and the third shows the final fit of data.We display part (b) of the figure to emphasize thatfinding the correct parameters is a nontrivial process(and one which requires considerable CPU time). Ta-ble ? displays the initial guess of the parameter valuesand the associated objective function value, as well asthe same data for the final fit, for both values of Reconsidered. Part (c) of the figure indicates a signifi-cant improvement over the initial guess, and in fact afairly good representation of the data.

Figures ?? and ??? display comparisons of powerspectra and delay maps, respectively, with part (a)corresponding to measured data and part (b) to mod-eled results in both cases.

Similar results are presented in Figs. ????, ?????and ?????? for the Re = 1 × 105 case, except thatwe have not shown the initial guess result in Fig. ????.[Give comparative discussion of these results,and indicate dependence on Re from Table ?.Discuss application to RANS modeling.]

Results for High-Pass Filtered Velocity

[Repeat above figures (no Fig. ?(b)); indicatesuitability for LES SGS models. Discuss Re de-pendence of data.][Compare model results in the two cases

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emphasizing differences between complete andhigh-pass filtered behaviors—e.g., variation ofparameters with Re.]

Discussion

Continuing Work

Acknowledgements

This work is supported by AFOSR grant F49620-00-1-0258 under the supervision of Dr. Tom Beutner.

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R. Temam (1996). J. Comput. Phys. 127, 309–315.

Y. Yang, J. M. McDonough (1992). In BifurcationPhenomena and Chaos in Thermal Convection. Bauet. al. (Eds.). ASME-HTD 214, ASME, NY, 85–92.

7 of 22


June 7, 2001

��

��

U

HWA region

PIV region 1PIV region 2

(H−h)

h

H

D

a) Backward facing step geometry.

��

��

Hs

b

U

HWA region

PIV region 2

PIV region 1

D

b) Turbulator geometry.

Fig. 2 Channel geometry for experimental studies.

8 of 22


June 7, 2001

1

1.5

2

2.5

3

3.5

4

4.5

5

−1 0 1 2 3 40

0.5

1

1.5

2

2.5

x/b

y/h

Velocity Magnitude

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

−1 0 1 2 3 40

0.5

1

1.5

2

2.5

x/b

y/h

RMS Turbulence


9 of 22


June 7, 2001

2

4

6

8

10

12

0 2 4 6 8 10 120

1

2

x/b

y/h

Velocity Magnitude

0.2

0.4

0.6

0.8

0 2 4 6 8 10 120

1

2

x/b

y/h

RMS Turbulence


10 of 22


June 7, 2001

−1 0 1 2 3 4 5 60

0.5

1

1.5

2

2.5

x/b

y/h

u/U


0 1 2 3 4 5 6 70

0.5

1

1.5

2

2.5

x/b

y/h

7 8 9 10 11 12 13 140

0.5

1

1.5

2

2.5

x/b

y/h

u/U



11 of 22


June 7, 2001

−1 0 1 2 3 4 5 6 70

0.5

1

1.5

2

2.5

x/b

y/h

7 8 9 10 11 12 13 14 150

0.5

1

1.5

2

2.5

x/b

y/h

u/U


12 of 22


June 7, 2001

−1 0 1 2 3 4 5 6 7 8 90

1

2

y/h

1 bar

−1 0 1 2 3 4 5 6 7 8 90

1

2

y/h

2 bars

−1 0 1 2 3 4 5 6 7 8 90

1

2

x/b

y/h

4 bars


13 of 22


June 7, 2001

0 2 4 6 8 10 120

1

2

y/h

1 bar

0 2 4 6 8 10 120

1

2

y/h

2 bars

0 2 4 6 8 10 120

1

2

x/b

y/h

4 bars


14 of 22


June 7, 2001

0 2 4 6 8 10 120

1

2

x/b

y/h

4 bars

0 2 4 6 8 10 120

1

2

y/h

2 bars

0 2 4 6 8 10 120

1

2

y/h

1 bar


15 of 22


June 7, 2001

−1 0 1 2 3 4 5 6 7 8 90

1

2

y/h

1 bar

−1 0 1 2 3 4 5 6 7 8 90

1

2

y/h

2 bars

−1 0 1 2 3 4 5 6 7 8 90

1

2

x/b

y/h

4 bars


16 of 22


June 7, 2001

−4 −2 0 2 4 6 8 10 12 14 16−1

0

1

2 bars

Cp

−4 −2 0 2 4 6 8 10 12 14 16−1

0

1

1 bar

Cp

−4 −2 0 2 4 6 8 10 12 14 16−1

0

1

3 bars

Cp

−4 −2 0 2 4 6 8 10 12 14 16−1

0

1

4 bars

Cp

4 bars

x/b


−4 −2 0 2 4 6 8 10 12 14 16−1

0

1

4 bars

x/b

Cp

−4 −2 0 2 4 6 8 10 12 14 16−1

0

1

3 bars

Cp

−4 −2 0 2 4 6 8 10 12 14 16−1

0

1

2 bars

Cp

2 bars

−4 −2 0 2 4 6 8 10 12 14 16−1

0

1

1 bar

Cp


−4 −2 0 2 4 6 8 10 12 14 16−1

0

1

1 bar

Cp

−4 −2 0 2 4 6 8 10 12 14 16−1

0

1

2 bars

Cp

−4 −2 0 2 4 6 8 10 12 14 16−1

0

1

3 bars

Cp

−4 −2 0 2 4 6 8 10 12 14 16−1

0

1

4 bars

Cp

c) Turbulator geometry.


17 of 22


June 7, 2001

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Velocity: BFS

m/s

a) Velocity.

−80

−60

−40

−20

0

20

40

60

Vorticity: BFS

s−1

b) Vorticity.

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

RMS Turbulence Intensity: BFS

c) RMS turbulence intensity.

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

FFP: BFS

d) Forward flow probability.

Fig. 12 Backward facing step PIV: U∞=0.89 m/s, Re =1,702.

18 of 22


June 7, 2001

0.5

1

1.5

2

2.5

Velocity: BFS

m/s

a) Velocity.

−200

−150

−100

−50

0

50

100

150

200

Vorticity: BFS

s−1

b) Vorticity.

0.05

0.1

0.15

0.2

0.25

0.3



0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

FFP: BFS



19 of 22


June 7, 2001

1

2

3

4

5

6

7

8

Velocity: BFS

m/s

a) Velocity.

−400

−200

0

200

400

600

Vorticity: BFS

s−1

b) Vorticity.

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4



0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

FFP: BFS



Fig. 15 Detail of reattachment for backward facing step: U∞=2.56 m/s, Re =4,880..

20 of 22


June 7, 2001

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Velocity: BFS

m/s

a) Velocity.

−60

−40

−20

0

20

40

Vorticity: BFS

s−1

b) Vorticity.

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

FFP: BFS


0.02

0.04

0.06

0.08

0.1

0.12



Fig. 16 Turbulator - single rub PIV: U∞=0.71 m/s, Re =1,350.

21 of 22


June 7, 2001

CFD figures to go here.

22 of 22


aiaa 2002–2925web.engr.uky.edu/~acfd/aiaa01.pdf · 2006-01-03 · aiaa 2002–2925 experimental...

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