ghajar hefat 2004 keynote

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HEFAT2004

3rd

International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics

21 – 24 June 2004, Cape Town, South Africa

Paper number: K2

TWO-PHASE HEAT TRANSFER IN GAS-LIQUID NON-BOILING PIPE FLOWS

Afshin J. Ghajar, Ph.D., P.E., ASME Fellow

Regents Professor and Director of Graduate Studies

School of Mechanical and Aerospace Engineering,

Oklahoma State University,

Stillwater, OK 74078,

USA,

E-mail: [email protected]

ABSTRACTThis paper presents an overview of the research that has

been conducted at Oklahoma State University’s heat transfer

laboratory on non-boiling, two-phase, air-water flow in vertical,

horizontal, and inclined pipes for a variety of flow patterns.

INTRODUCTIONIn many industrial applications, such as the flow of natural

gas and oil in flow lines and wellbores, the knowledge of non-

boiling two-phase, two-component (liquid and permanent gas)

heat transfer is required. When a gas–liquid flows in a pipe, a

variety of flow patterns may occur, depending primarily on

flow rates, the physical properties of the fluids, and the pipe

inclination angle. The main flow patterns that generally exist invertical upward flow of a gas and liquid in tubes can be

classified as bubbly flow, slug flow, froth flow, and annular

flow. The main flow patterns that might exist in two-phase gas-

liquid flow in horizontal tubes can be classified as stratified

flow, slug flow, annular flow, and bubbly flow. The variety of

flow patterns reflects the different ways that the gas and liquid

phases are distributed in a pipe. This causes the heat transfer

mechanism to be different in the different flow patterns.

In this paper, an overview of our ongoing research on this

topic that has been conducted at our heat transfer laboratory

over the past several years will be presented. Our extensive

literature search revealed that numerous heat transfer

coefficient correlations have been published over the past 50years. We also found several experimental data sets for forced

convective heat transfer during gas-liquid two-phase flow in

vertical pipes, very limited data for horizontal pipes, and no

data for inclined pipes. However, the available correlations for

two-phase convective heat transfer were developed based on

limited experimental data and are only applicable to certain

flow patterns and fluid combinations.

The overall objective of our research has been to develop a

heat transfer correlation that is robust enough to span all or

most of the fluid combinations, flow patterns, flow regimesand pipe orientations (vertical, inclined, and horizontal). To this

end, we have constructed a state-of-the-art experimental facility

for systematic heat transfer data collection in horizontal and

inclined positions (up to 7°). The experimental setup is also

capable of producing a variety of flow patterns and is equipped

with two transparent sections at the inlet and exit of the tes

section for in-depth flow visualization. In this paper we present

the results of our extensive literature search, a detailed

development of our proposed heat transfer correlation and its

application to experimental data in vertical and horizonta

pipes, a detailed description of our experimental setup, flow

visualization results for different flow patterns, experimenta

results for slug and annular flows in horizontal and inclinedtubes, and our proposed heat transfer correlation for these flow

patterns and pipe orientations.

NOMENCLATUREA cross sectional area, m2

C constant value of the leading coefficient in Eqs. (11)

and (15), dimensionless

c specific heat at constant pressure, kJ/kg⋅K

D inside diameter of the tube, m

Gt mass velocity of total flow (=ρV), kg/s⋅m2

h heat transfer coefficient, W/m2⋅K

i index of thermocouple station, Eq.(14), dimensionless

j index of thermocouple in a station, Eq.(14),dimensionless

k thermal conductivity, W/m⋅K

L length, m

M number of thermocouples in a station, Eq.(14),

dimensionless

m constant exponent value on the quality ratio term in

Eqs. (11) and (15), dimensionless

m mass flow rate, kg/s or kg/min



N number of thermocouple stations, Eq.(14),

dimensionless

Nu Nesselt number, (=hD/k), dimensionless

n constant exponent value on the void fraction ratio term

in Eqs. (11) and (15), dimensionless

P mean system pressure, Pa

Pa atmospheric pressure, Pa

∆P pressure drop, Pa

∆P/∆L total pressure drop per unit length, Pa/m

p constant exponent value on the Prandtl number ratio

term in Eqs. (11) and (15), dimensionless

Pr Prandtl number, cµ/k, dimensionless

Q volumetric flow rate, m3/s

q constant exponent value on the viscosity ratio term in

Eqs. (11) and (15), dimensionless

q′′ heat flux, W/m2

r constant exponent value on the inclination factor in Eq.

(15), dimensionless

Re Reynolds number, 4 m /πDµ, dimensionless

ReL liquid in-situ Reynolds number, 4 Lm /π 1 α − µL D,dimensionless

ReM mixture Reynolds number in [32], dimensionless

ReTP two-phase flow Reynolds number, dimensionless

= ReSL/(1-α) in [2]

= GFD/µF where GF = mass flow rate of froth and µF =

(µWATER +µAIR )/2 in [25]= ReSL + ReSG in [26] and [28]

R L liquid holdup, (=1-α), dimensionlessT temperature, K

V mean velocity, m/s

XTT Martinelli parameter [=((1-x)/x)0.9(ρG/ρL)0.5(µL/µG)0.1],dimensionless

x flow quality, G G Lm /(m +m ) , dimensionless

Greek Letters

α void fraction, AG/(AG+AL), dimensionless

µ dynamic viscosity, Pa-s

ρ density, kg/m3

θ inclination angle, rad

Subscripts

B bulk

CAL calculated

EXP experimental

G gasi index of thermocouple station, Eq.(14)

j index of thermocouple in a station, Eq.(14)L liquid

M momentum

SG superficial gasSL superficial liquid

TP two-phaseTPF two-phase frictional

W wall

COMPARISON OF TWENTY TWO-PHASE HEATTRANSFER CORRELATIONS WITH SEVEN SETS OFEXPERIMENTAL DATA [1]

Numerous heat transfer correlations and experimental data

for forced convective heat transfer during gas-liquid two-phase

flow in vertical and horizontal pipes have been published over

the past 50 years. In a study published in 1999 by Kim et al

[1], a comprehensive literature search was carried out and atotal of 38 two-phase flow heat transfer correlations wereidentified. The validity of these correlations and their ranges o

applicability have been documented by the original authors. In

most cases, the identified heat transfer correlations were based

on a small set of experimental data with a limited range of

variables and liquid-gas combinations. In order to assess the

validity of those correlations, they were compared againsseven extensive sets of two-phase flow heat transfer

experimental data available from the literature, for vertical and

horizontal tubes and different flow patterns and fluids. Fo

consistency, the validity of the identified heat transfer

correlations were based on the comparison between the

predicted and experimental two-phase heat transfer coefficientmeeting the ±30% criterion. A total of 524 data points from thefive available experimental studies (see Table 1) were used for

these comparisons. The experimental data included fivedifferent liquid-gas combinations (water-air, glycerin-air

silicone-air, water-helium, water-Freon 12), and covered a wide

range of variables, including liquid and gas flow rates and

properties, flow patterns, pipe sizes, and pipe inclination. Fiveof these experimental data sets are concerned with a wide

variety of flow patterns in vertical pipes and the other two data

sets are for limited flow patterns (slug and annular) within

horizontal pipes.

Table 2 shows 20 of the 38 heat transfer correlations that

were identified in the reported study [1]. The rest of the two- phase flow heat transfer correlations were not tested, since therequired information for the correlations was not available

through the identified experimental studies. In assessing the

ability of the 20 identified heat transfer correlations, their

predictions were compared with the seven sets of experimentadata, both with and without considering the restrictions on ReSL

and VSG/VSL accompanying the correlations. The results

comparing those heat transfer correlations and the seven sets o

experimental data are summarized in Table 3 for major flow

patterns in vertical and horizontal pipes and Table 4 fo

transitional flow patterns in vertical pipes. The shaded cells ofTables 3 and 4 indicate the correlations that best satisfied the

±30% two-phase heat transfer coefficient criterion that was setThere were no remarkable differences for the recommendations

of the heat transfer correlations based on the results with and

without the restrictions on ReSL and VSG/VSL, except for thecorrelations of Chu and Jones [2] and Ravipudi and Godbold

[3], as applied to the water-air experimental data of Vijay [4]Based on the results without the authors' restrictions, the

correlation of Chu and Jones [2] was recommended for only

annular, bubbly-froth, slug-annular, and froth-annular flow

patterns; and the correlation of Ravipudi and Godbold [3] wa



recommended for only annular, slug-annular, and froth-annular

flow patterns of the vertical tube water-air experimental data.

However, considering the ReSL and VSG/VSL, restrictions, thecorrelation of Chu and Jones [2] was recommended for all

vertical tube water-air flow patterns including transitional flow

patterns except the annular-mist flow pattern; and the

correlation of Ravipudi and Godbold [3] was recommended for

slug, froth, and annular flow patterns and for all of thetransitional flow patterns of the vertical water-air experimentaldata of Vijay [4]. With regard to air-water flow in horizontal

pipes, Kim et al. [1] recommended use of Shah [5] correlation

for annular flow, and use of the Chu and Jones [2], Kudirka et

al. [6], and Ravipudi and Godbold [3] correlations for slug flow

(see Table 3).

The above-recommended correlations all have the following

important parameters in common: ReSL, Pr L, µB/µW and either

void fraction (α) or superficial velocity ratio (VSG/VSL). It

appears that void fraction and superficial velocity ratio,although not directly related, may serve the same function in

two-phase heat transfer correlations. However, since there is no

single correlation capable of predicting the flow for all fluidcombinations in vertical pipes, there appears to be at least one

parameter [ratio], which is related to fluid combinations, that ismissing from these correlations. In addition, since, for the

limited horizontal data available, the recommended correlations

differ in most cases from those of vertical pipes, there appears

to be at least one additional parameter [ratio], related to pipeorientation, that is missing from the correlations. In the next

section we report on the results of our efforts in thedevelopment of a heat transfer correlation that is robust enough

to span all or most of the fluid combinations, flow patterns,

flow regimes, and pipe orientations.

DEVELOPMENT OF THE NEW HEAT TRANSFERCORRELATION [7]

In order to improve the prediction of heat transfer rate inturbulent two-phase flow, regardless of fluid combination and

flow pattern, a new correlation was developed by Kim et al. [7].

The improved correlation uses a carefully derived heat transfer

model which takes into account the appropriate contributions of

both the liquid and gas phases using the respective cross-

sectional areas occupied by the two phases.

The void fraction α is defined as the ratio of the gas-flowcross-sectional area AG to the total cross-sectional area A (=

AG+AL),

G

G L

Aα=A +A

(1)

The actual gas velocity VG can be calculated from

G G

G

G G G G

Q m mxV = = =

A ρ A ρ αA

(2)

Similarly, for the liquid VL is defined as:

L LL

L L L L

Q m m(1-x)V = = =

A ρ A ρ (1-α)A

(3)

The total gas-liquid two-phase heat transfer is assumed to

be the sum of the individual single-phase heat transfers of thegas and liquid, weighted by the volume of each phase present:

G

TP L G L

L

hαh =(1-α)h +αh =(1-α)h 1+

1-α h

⎡ ⎤⎛ ⎞⎛ ⎞⎢ ⎥⎜ ⎟⎜ ⎟

⎝ ⎠⎢ ⎥⎝ ⎠⎣ ⎦(4)

There are several well-known single-phase heat transfer

correlations in the literature. In this study the Sieder and Tate

[8] equation was chosen as the fundamental single-phase heat

transfer correlation because of its practical simplicity and proven applicability (see Table 2). Based upon this correlationthe single-phase heat transfer coefficients in Eq. (4) hL and hG

can be modeled as functions of Reynolds number, Prandtlnumber and the ratio of bulk to wall viscosities. Thus, Eq. (4)

can be expressed as:

B W GTP L

B W L

fctn(Re,Pr, µ µ )αh =(1-α)h 1+

1-α fctn(Re,Pr, µ µ )

⎡ ⎤⎢ ⎥⎣ ⎦

(5)

( )

( )B WG G G

TP L

L L B W L

µ µRe Pr αh =(1-α)h 1+ fctn , ,

1-α Re Pr µ µ

⎡ ⎤⎧ ⎫⎛ ⎞⎛ ⎞ ⎛ ⎞⎪ ⎪⎢ ⎥⎜ ⎟⎨ ⎬⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎪ ⎪⎝ ⎠⎩ ⎭⎣ ⎦(6)

Substituting the definition of Reynolds number (Re = ρVD/µB)

for the gas (ReG) and liquid (ReL) yields

( )

( )

( )

( )

( )

( )B WBTP GG GL

L B L B WL G L

ρVD µ µµh α Pr = 1+ fctn , ,

(1-α)h 1-α ρVD µ Pr µ µ

⎡ ⎤⎧ ⎫⎛ ⎞ ⎛ ⎞⎛ ⎞⎪ ⎪⎢ ⎜ ⎟ ⎜ ⎟⎨ ⎬⎜ ⎟ ⎜ ⎟⎜ ⎟⎢ ⎝ ⎠⎪ ⎪⎝ ⎠⎝ ⎠⎩ ⎭⎣ ⎦(7)

Rearranging yields

( )

( )WTP G G G G L

L L L L L W G

µh α ρ V D Pr = 1+ fctn , ,

(1-α)h 1-α ρ V D Pr µ

⎡ ⎤⎧ ⎫⎛ ⎞⎛ ⎞⎛ ⎞⎛ ⎞⎛ ⎞ ⎛ ⎞⎪ ⎪⎢ ⎥⎜ ⎟⎜ ⎟⎨ ⎬⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠⎝ ⎠⎝ ⎠ ⎝ ⎠⎪ ⎪⎝ ⎠ ⎝ ⎠⎩ ⎭⎣ ⎦

(8)

where the assumption has been made that the bulk viscosityratio in the Reynolds number term of Eq. (7) is exactlycancelled by the last term in Eq. (7), which includes bulk

viscosity ratio. Substituting Eq. (1) for the ratio of gas-to-liquid

diameters (DG/DL) in Eq.(8) and based upon practica

considerations assuming that the ratio of liquid-to-gas

viscosities evaluated at the wall temperature [(µW)L/(µW)G] iscomparable to the ratio of those viscosities evaluated at the

bulk temperature (µL/µG), Eq. (8) reduces to



G G GTP L

L L L L G

ρ V Pr h µα α= 1+ fctn , ,

(1-α)h 1-α ρ V Pr µ1-α

⎡ ⎤⎧ ⎫⎛ ⎞⎛ ⎞ ⎛ ⎞⎛ ⎞⎛ ⎞ ⎛ ⎞⎪ ⎪⎢ ⎥⎜ ⎟⎜ ⎟⎨ ⎬⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎪ ⎝ ⎠ ⎪⎝ ⎠⎩ ⎭⎣ ⎦

(9)

For use in further simplifying Eq. (9), combine Eqs. (2) and (3)for VG (gas velocity) and VL (liquid velocity) to get the ratio of

VG/VL and substitute into Eq. (9) to get

G LTP L

L G

Pr µx αh =(1-α)h 1+fctn , , ,

1-x 1-α Pr µ

⎡ ⎤⎧ ⎫⎛ ⎞⎛ ⎞⎪ ⎪⎛ ⎞ ⎛ ⎞⎢ ⎥⎨ ⎬⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠⎪ ⎪⎢ ⎥⎝ ⎠ ⎝ ⎠⎩ ⎭⎣ ⎦(10)

Assuming that two-phase heat transfer coefficient can be

expressed using a power-law relationship on the individual

parameters that appear in Eq. (10), then Eq. (10) can be

expressed as:

p qm n

G GTP L

L L

Pr µx αh =(1-α)h 1+C

1-x 1-α Pr µ⎡ ⎤⎧ ⎫⎛ ⎞ ⎛ ⎞⎪ ⎪⎛ ⎞ ⎛ ⎞⎢ ⎥⎨ ⎬⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎪ ⎪⎩ ⎭⎣ ⎦

(11)

where hL comes from the Sieder and Tate [8] equation as

mentioned earlier (see Table 2). For the Reynolds number

needed in that single-phase correlation, the following

relationship is used to evaluate the in-situ Reynolds number

(liquid phase) rather than the superficial Reynolds number (ReSL) as commonly used in the correlations of the available

literature (see Kim et al. [1]):

L

LL L

4mρVDRe = =

µ π 1-αµ D

⎛ ⎞

⎜ ⎟⎝ ⎠

(12)

Any other well-known single-phase turbulent heat transfer

correlation could have been used in place of the Sieder and Tate

[8] correlation. The difference resulting from the use of a

different single-phase heat transfer correlation will be absorbed

during the determination of the values of the leading coefficient

and exponents on the different parameters in Eq. (11).

In the next section the proposed heat transfer correlation,

Eq. (11), will be tested with four extensive sets of vertical flow

two-phase heat transfer data available from the literature (see

Table 1) and a new set of horizontal flow two-phase heat

transfer data obtained by Kim and Ghajar [10]. The values of

the void fraction (α) used in Eq. (11) were either directly takenfrom the original experimental data sets (if available) or were

calculated based on the equation provided by Chisholm [9],

which can be expressed as

-1

G G

L L

V ρ1-xα= 1+

V x ρ

⎡ ⎤⎛ ⎞⎛ ⎞⎢ ⎥⎜ ⎟⎜ ⎟

⎝ ⎠⎢ ⎥⎝ ⎠⎣ ⎦(13)

ROBUST HEAT TRANSFER CORRELATION FORTURBULENT GAS-LIQUID FLOW IN VERTICAL ANDHORIZONTAL PIPES

Correlation For Vertical Flow [7]

To determine the values of leading coefficient and the

exponents in Eq. (11), four sets of experimental data (see the

first column in Table 5) for vertical pipe flow were used. The

ranges of these four sets of experimental data can be found in

Kim et al. [1]. The experimental data (a total of 255 data

points) included four different liquid-gas combinations (water-

air, silicone-air, water-helium, water-Freon 12), and covered a

wide range of variables, including liquid and gas flow rates

properties, and flow patterns. The selected experimental data

were only for turbulent two-phase heat transfer data in which

the superficial Reynolds numbers of the liquid (ReSL) were al

greater than 4000. Table 5 and Fig. 1 provide the details of the

correlation and how well the proposed correlation predicted the

experimental data. The proposed general correlation predicted

the heat transfer coefficients for the 255 experimental data

points of vertical flow with an overall mean deviation of about2.5%, an rms deviation of about 12.8%, and a deviation range

of –65% to 40%. About 83% of the data (212 data points) were

predicted with less than ±15% deviation, and about 96% of the

data (245 data points) were predicted with less than ±30%

deviation. The results clearly show that the proposed heat

transfer correlation is robust and can be applied to turbulent

gas-liquid flow in vertical pipes with different fluid flow

patterns and fluid combinations.

Correlation for Horizontal Flow [10]

To continue the validation of the proposed heat transfer

correlation, Eq. (11), and apply it to two-phase heat transfer

data in horizontal pipes, Kim and Ghajar under took the studyreported in [10]. As mentioned before, there is very limited

horizontal pipe flow two-phase heat transfer data available

from the open literature. In order to achieve the validation

process successfully, a reliable two-phase heat transfer

experimental setup was built, and experimental horizontal hea

transfer two-phase flow data for different flow patterns were

obtained. Details of the experimental setup and the data

reduction procedure will be presented in the next section. For

additional details on the experiments performed and the data

collected for this segment of the paper, refer to Kim and Ghajar

[10].

To determine the values of leading coefficient and the

exponents in Eq. (11), the horizontal pipe flow experimentadata of Kim and Ghajar [10] were used. Table 6 and Fig. 2

provide the details of the correlation and how well the proposed

correlation predicted the experimental data. The proposed

general correlation predicted the heat transfer coefficients for

the 150 experimental data points of horizontal flow with an

overall mean deviation of about 1%, an rms deviation of abou

12%, and a deviation range of –25% to 34%. About 93% o

data (139 data points) were predicted with less than ±20%

deviation. The results clearly show that the proposed heat



transfer correlation is robust and can be applied to gas-liquid

flow in horizontal pipes with different fluid flow patterns.

EXPERIMENTAL SETUP AND DATA REDUCTION FORHORIZONTAL AND SLIGHTLY UPWARD INCLINEDPIPE FLOWS

A schematic diagram of the overall experimental setup for

heat transfer and pressure drop measurements and flow

visualizations in two-phase air-water pipe flow in horizontal

and inclined positions is shown in Fig. 3. The test section is a

25.4 mm straight standard stainless steel schedule 10S pipe

with a length to diameter ratio of a 100. The setup rests atop an

aluminum I-beam that is supported by a pivoting foot and a

stationary foot that incorporates a small electric screw jack. The

I-beam is approximately 9 m in length and can be inclined to an

angle of approximately 8° above horizontal. Inclination angles

of the test cradle are measured with a contractor’s angle-

measuring tool and with a digital x-y axis accelerometer to

determine the angle to within 0.5°.

In order to apply uniform wall heat flux boundary

conditions to the test section, copper plates were silver solderedto the inlet and exit of the test section. The uniform wall heat

flux boundary condition was maintained by a Lincoln SA-750

welder. The entire length of the test section was wrapped using

fiberglass pipe wrap insulation, followed by a thin polymer

vapor seal to prevent moisture penetration.

In order to develop various two-phase flow patterns (by

controlling the flow rates of gas and liquid), a two-phase gas

and liquid flow mixer was used. The mixer consisted of a

perforated stainless steel tube (6.35 mm I.D.) inserted into the

liquid stream by means of a tee and a compression fitting. The

end of the copper tube was silver-soldered. Four holes (3 rows

of 1.59 mm, 4 rows of 3.18 mm, and 8 rows of 3.97 mm) were

positioned at 90° intervals around the perimeter of the tube andthis pattern was repeated at fifteen equally spaced axial

locations along the length of the stainless steel tube (refer to

Fig. 4). The two-phase flow leaving mixer entered the

transparent calming section.

The calming section [clear polycarbonate pipe with 25.4

mm I.D. and L/D = 88] served as a flow developing and

turbulence reduction device, and flow pattern observation

section. One end of the calming section is connected to the test

section with an acrylic flange and the other end of the calming

section is connected to the gas-liquid mixer. For the horizontal

flow measurements, the test section and the observation section

(refer to Fig. 3) were carefully leveled to eliminate the effect of

inclination on these measurements.Holes for eleven pressure taps were drilled along the test

section (refer to Fig. 5). The diameters of the holes were 1.73

mm, and were equally spaced at 254 mm intervals along the

test section. The holes were located at the bottom of the

stainless steel tube in order to ensure that only water could get

into the pressure measuring system. The pressure taps were

standard saddle type self-tapping valves with the tapping core

removed. The first pressure tap in the flow direction was used

as a reference pressure tap for comparison with the other

pressure taps; and the system pressure was measured by an

OMEGA PX242-060G pressure transducer which had a 0 to 60

psig operation range. The reference pressure tap was also

directly connected to a VALIDYNE DP15 wet-wet differentia

pressure transducer with CD15 carrier demodulator. The

pressure tap desired to measure the differential pressure among

the other 10 pressure taps was connected to the differential

pressure transducer in isothermal condition. Note that the

pressure measurements are not reported in this paper.

T-type thermocouple wires were cemented with

Omegabond 101, an epoxy adhesive with high thermal

conductivity and electrical resistivity, to the outside wall of the

stainless steel test section (refer to Fig. 5). Omega

EXPP-T-20-TWSH extension wires were used for relay to the

data acquisition system. Thermocouples were placed on the

outer surface of the tube wall at uniform intervals of 254 mm

from the entrance to the exit of the test section. There were 10

thermocouple stations in the test section. All stations had four

thermocouples, and they were labeled looking at the tail of the

fluid flow with peripheral location “A” being at the top of the

tube, “B” being 90° in the clockwise direction, “C” at the bottom of the tube, and “D” being 90° from the bottom in the

clockwise sense (refer to Fig. 5). All the thermocouples were

monitored with a National Instruments data acquisition system

The experimental data were averaged over a user chosen length

of time (typically 20 samples/channel with a sampling rate o

400 scans/sec) before the heat transfer measurements were

actually recorded. The average system stabilization time period

was from 30 to 60 min after the system attained steady state

The inlet liquid and gas temperatures and the exit bulk

temperature were measured by Omega TMQSS-125U-6

thermocouple probes. The thermocouple probe for the exit bulk

temperature was placed after the mixing well. Calibration o

thermocouples and thermocouple probes showed that they wereaccurate within ±0.5°C. The operating pressures inside the

experimental setup were monitored with a pressure transducer.

To ensure a uniform fluid bulk temperature at the inlet and

exit of the test section, a mixing well was utilized. An

alternating polypropylene baffle type static mixer for both gas

and liquid phases was used. This mixer provided an

overlapping baffled passage forcing the fluid to encounter flow

reversal and swirling regions. The mixing well at the exit of the

test section was placed below the clear polycarbonate

observation section (after the test section), and before the liquid

storage tank (refer to Fig. 3). Since the cross-sectional flow

passage of the mixing section was substantially smaller than the

test section, it had the potential of increasing the system back- pressure. Thus, in order to reduce the potential back-pressure

problem, which might affect the flow pattern inside of the tes

section, the mixing well was placed below and after the test

section and the clear observation sections. The outlet bulk

temperature was measured immediately after the mixing well.

The fluids used in the test loop are air and water. The water

is distilled and stored in a 55-gallon cylindrical polyethylene

tank. A Bell & Gosset series 1535 coupled centrifugal pump

was used to pump the water through an Aqua-Pure AP12T



water filter. An ITT Standard model BCF 4063 one shell and

two-tube pass heat exchanger removes the pump heat and the

heat added during the test to maintain a constant inlet water

temperature. From the heat exchanger, the water passes through

a Micro Motion Coriolis flow meter (model CMF125)

connected to a digital Field-Mount Transmitter (model

RFT9739) that conditions the flow information for the data

acquisition system. Once the water passes through the Coriolis

flow meter it then passes through a 25.4 mm, twelve-turn gate

valve that regulates the amount of flow that entered the test

section. From this point, the water travels through a 25.4 mm

flexible hose, through a one-way check valve, and into the test

section. Air is supplied via an Ingersoll-Rand T30 (model

2545) industrial air compressor mounted outside the laboratory

and isolated to reduce vibration onto the laboratory floor. The

air passes through a copper coil submerged in a vessel of water

to lower the temperature of the air to room temperature. The air

is then filtered and condensate removed in a coalescing filter.

The air flow is measured by a Micro Motion Coriolis flow

meter (model CMF100) connected to a digital Field-Mount

Transmitter (model RFT9739) and regulated by a needle valve.Air is delivered to the test section by flexible tubing. The water

and air mixture is returned to the reservoir where it is separated

and the water recycled.

The heat transfer measurements at uniform wall heat flux

boundary condition were carried out by measuring the local

outside wall temperatures at 10 stations along the axis of the

tube and the inlet and outlet bulk temperatures in addition to

other measurements such as the flow rates of gas and liquid,

room temperature, voltage drop across the test section, and

current carried by the test section. The peripheral heat transfer

coefficient (local average) were calculated based on the

knowledge of the pipe inside wall surface temperature and

inside wall heat flux obtained from a data reduction programdeveloped exclusively for this type of experiments [11]. The

local average peripheral values for inside wall temperature,

inside wall heat flux, and heat transfer coefficient were then

obtained by averaging all the appropriate individual local

peripheral values at each axial location. The large variation in

the circumferential wall temperature distribution, which is

typical for two-phase gas-liquid flow in horizontal and slightly

inclined tubes, leads to different heat transfer coefficients

depending on which circumferential wall temperature was

selected for the calculations. In two-phase heat transfer

experiments, in order to overcome the unbalanced

circumferential heat transfer coefficients, Eq. (14) was used to

calculate an overall mean two-phase heat transfer coefficient(EXPTPh ) for each test run.

( ) ( )EXP

M

i,j N j

TP Mi

W Bi,j i j

1q

M1h =

1 NT - T

M

⎡ ⎤′′⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

∑∑

∑

(14)

The data reduction program used a finite-difference

formulation to determine the inside wall temperature and the

inside wall heat flux from measurements of the outside waltemperature, the heat generation within the pipe wall, and the

thermophysical properties of the pipe material (electrica

resistivity and thermal conductivity). In these calculations, axia

conduction was assumed negligible, but peripheral and radia

conduction of heat in the tube wall were included. In addition

the bulk fluid temperature was assumed to increase linearlyfrom the inlet to outlet.

A National Instruments data acquisition system was used to

record and store the data measured during these experiments

The acquisition system is housed in an AC powered four-slo

SCXI 1000 Chassis that serves as a low noise environment for

signal conditioning. Three NI SCXI control modules are housedinside the chassis. There are two SCXI 1102/B/C modules and

one SCXI 1125 module. From these three modules, input

signals for all 40 thermocouples, the two thermocouple probes

voltmeter, and flow meters are gathered and recorded. The

computer interface used to record the data is a LabVIEW

Virtual Instrument (VI) program written for this specificapplication.

The reliability of the flow circulation system and of the

experimental procedures was checked by making severa

single-phase calibration runs with distilled water. The single-

phase heat transfer experimental data were checked against thewell established single-phase heat transfer correlations [10] in

the Reynolds number range from 3000 to 30,000. In most

instances, the majority of the experimental results were wel

within ±10% of the predicted results [10, 12]. In addition to the

single-phase calibration runs, a series of two-phase, air-water

slug flow tests were also performed for comparison against thetwo-phase experimental slug flow data of [12, 13]. The results

of these comparisons, for majority of the cases were also wellwithin the ±10% deviation range.

The uncertainty analyses of the overall experimenta

procedures using the method of Kline and McClintock [14

showed that there is a maximum of 11.5% uncertainty for heattransfer coefficient calculations. Experiments under the same

conditions were conducted periodically to ensure the

repeatability of the results. The maximum difference between

the duplicated experimental runs was within ±10%. Moredetails of experimental setup and data reduction procedures can

be found from Durant [12].

The heat transfer data obtained with the presenexperimental setup were measured under a uniform wall heat

flux boundary condition that ranged from 2606 to 10,787 W/mand the resulting mean two-phase heat transfer coefficients

(hTP) ranged from 545 to 4907 W/m2⋅K. For these experiments

the liquid superficial Reynolds numbers (ReSL) ranged from836 to 26,043 (water mass flow rates from about 1.18 to 42.5

kg/min) and the gas superficial Reynolds numbers (ReSG)ranged from 560 to 47,718 (gas mass flow rates from abou

0.013 to 1.13 kg/min).



FLOW PATTERNSDue to the multitude of flow patterns and the various

interpretations accorded to them by different investigators, nouniform procedure exists at present for describing and

classifying them. In our reported studies the flow pattern

identification for the experimental data was based on the

procedures suggested by Kim and Ghajar [10] and visual

observations deemed appropriate. All observations for the flow

pattern judgments were made at two locations, just before thetest section (about L/D = 93 in the calming section) and rightafter the test section. Leaving the liquid flow rate fixed, flow

patterns were observed for various air flow rates. The liquid

flow rate was then adjusted and the process was repeated. If the

observed flow patterns differed at the two locations of before

and after the test section, experimental data was not taken andthe flow rates of gas and liquid were readjusted for consistent

flow pattern observations. Flow pattern data were obtained with

the pipe at horizontal position and at 2°, 5°, and 7° upwardinclined positions. These experimental data were plotted and

compared using their corresponding values of mass flow rates

of air and water and the flow patterns. The digital images of each flow pattern at each inclination angle were also comparedwith each other in order to identify the inclination effect on the

flow pattern.The different flow patterns depicted on Fig. 6 illustrate the

capability of our experimental setup in producing multitude of

flow patterns. The shaded regions represent the boundaries of

these flow patterns. Also shown on Fig. 6 with symbols is thedistribution of the heat transfer data that were obtained

systematically in our experimental setup with the pipe in the

horizontal position. As can be seen from Fig. 6, we did not

collect heat transfer data at low air and water flow rate

combinations (water flow rates of less than about 5 kg/min and

air flow rates of less than about 0.5 kg/min). At these low water and air flow rates and heating there is a strong possibility of

either dry-out or local boiling which could damage the testsection. Figure 7 shows photographs of the representative flow

patterns that were observed in our experimental setup with the

pipe in the horizontal position and no heating (isothermal runs).

SYSTEMATIC INVESTIGATION ON TWO-PHASE GAS-LIQUID HEAT TRANSFER IN HORIZONTAL ANDSLIGHTLY UPWARD INCLINED PIPE FLOWS

In this section we present an overview of the different

trends that we have observed in the heat transfer behavior of the

two-phase air-water flow in horizontal and inclined pipes for a

variety of flow patterns. The two-phase heat transfer data wereobtained by systematically varying the air or water flow rates

and the pipe inclination angle.

Figure 8 provides an overview of the pronounced influence

of the flow pattern, superficial liquid Reynolds number (water

flow rate) and superficial gas Reynolds number (gas flow rate)on the two-phase mean heat transfer coefficient in horizontal

pipe flows. The results presented in Fig. 8 clearly show that thetwo-phase mean heat transfer coefficients are strongly

influenced by the liquid superficial Reynolds number (ReSL). In

addition, for a fixed ReSL, the two-phase mean heat transfer

coefficients are strongly influenced by the flow pattern and the

gas superficial Reynolds number (ReSG). Therefore, to fullyunderstand the two-phase heat transfer behavior in horizonta

pipes, further systematic research is required to unravel the

complicated relationship that exits amongst flow pattern, ReSL

and ReSG

. To complicate matters even further, we also studied the

effect of inclination angle on two-phase heat transfer in pipeflows for different flow patterns. To demonstrate the effect ofinclination we have selected three representative runs from the

results presented in Fig. 8 (ReSL = 5000, 12000, and 17000) and

varied the inclination angle of the pipe, going from the

horizontal position to 2°, 5°, and 7° upward inclined positionsFigure 9 shows the heat transfer results for these cases. The

results clearly show that a slight change in the inclination angle

(say 2°) has a significant positive effect on the two-phase heat

transfer and the effect decreases with increasing the inclinationangle. The figure also shows that the effect of inclination on the

two-phase heat transfer is very complicated and depends on the

ReSL and the flow pattern (ReSG). At low ReSL values the effecis significant and decreases with increasing ReSL. Also for a

fixed ReSL as the flow pattern changes (increasing ReSG), theenhancement in two-phase heat transfer due to inclination

decreases. Therefore, to fully understand the two-phase hea

transfer behavior in inclined pipes, further systematic research

is required to fully realize the complicated relationship thatexits between ReSL, ReSG, and flow pattern.

To address some of the issues raised in regard to the resultsof Figs. 8 and 9, we decided to focus on two popular flow

patterns in horizontal pipe flow, namely slug and annular flow

patterns. The comparison between horizontal and inclined two

phase mean heat transfer coefficients is given in Figs. 10 and

11, respectively. The presented results show that the effect ofinclination on the two-phase mean heat transfer coefficients ismore pronounced in slug flow in comparison to annular flow

The slug flow results (see Fig. 10) show a 48% maximum

increase from the horizontal to the 2° inclined position with a

27% average increase in the mean heat transfer coefficientComparison of the horizontal to the 5° inclined position showed

an 85% maximum increase with a 46% average increase in themean heat transfer coefficient. Comparison of the results from

2° to 5° inclined position showed a maximum increase of 32%

with an average increase of 15% for the mean heat transfer

coefficient. The findings indicate that there appears to be a

substantial increase in the slug flow heat transfer as the pipe is

inclined upward from the horizontal position and the amount oincrease in hTP is related to the combined condition of the

inclination angle, ReSL, and ReSG. Next, consider the annular

flow results shown in Fig. 11. Comparing the horizontal and the

5° incline data in annular flow, the mean heat transfercoefficient showed a maximum increase of about 33% and a

minimum increase of about 11%. The average percent increasewas about 19%. Comparison of the horizontal to the 7°inclined position showed a maximum increase of about 35%

and a minimum increase of about 18%. The average percent



increase was about 24%. The comparison of the results from 5°

to 7° inclined position showed a maximum increase of about

9% with an average increase of about 5% for the mean heattransfer coefficient.

The inclined heat transfer results presented in Figs. 10 and

11 for the two specific flow patterns shed some additional light

on the effect of inclination angle on the two-phase heat transfer

for a specific flow pattern, and at the time raises a few

additional questions. What is the relationship among theinclination angle, the flow pattern, and heat transfer? Howmuch enhancement for a specific flow pattern should one

expect due to inclination? What is optimum inclination angle

for enhancement? These questions require systematic heat

transfer measurements for a variety of flow patterns and

inclination angles.

HEAT TRANSFER CORRELATION FOR HORIZONTAL AND INCLINED ANNULAR FLOW [15]

In an earlier section of this paper we presented a two-phase

heat transfer correlation for horizontal flow in pipes (see Table

6). The correlation was developed based on our proposedgeneral correlation, Eq. (11). In this section we will continuethat effort by modifying the correlation to account for

inclination effect on two-phase heat transfer. For this purpose

we will use the heat transfer results presented in Fig. 11 for

horizontal and inclined annular flow. The modified form of our

general correlation, Eq. (11) with inclusion of an inclinationfactor is:

( ) p qm n

r θG G

TP L

L L

Pr µx αh =(1-α)h 1+C e

1-x 1-α Pr µ

⎡ ⎤⎧ ⎫⎛ ⎞ ⎛ ⎞⎪ ⎪⎛ ⎞ ⎛ ⎞⎢ ⎥⎨ ⎬⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎪ ⎪⎩ ⎭⎣ ⎦

(15)

where hL comes from the Sieder and Tate [8] heat transfer correlation (see Table 2).

To determine the values of the leading coefficient (C) and

constants (m, n, p, q, r) in Eq. (15), the horizontal and inclined

experimental data of Ghajar et al. [15] for annular flow were

used. They collected a total of 123 data points with 45 points in

the horizontal orientation, 49 points at 5° incline, and 29 points

in the 7° incline position. Table 7 and Fig. 12 provide thedetails of the correlation and how well the proposed correlation

predicted the experimental data. The correlation predicted the

experimental data with an overall mean deviation of –1.8%, an

rms deviation of 5.9%, and a deviation range of –15.1 to

14.6%. Only one of the 123 data points was predicted withslightly more than ±15% deviation. These results provide

additional validation on the robustness of our proposed two- phase heat transfer correlation. In addition, the modification

made to the general heat transfer correlation to account for the

effect of inclination appears to be correct. We will continue our

validation of the proposed modified general heat transfer

correlation, Eq. (15), by comparing it with additional two-phase

inclined heat transfer data for different flow patterns as the data

becomes available from our laboratory.

FUTURE PLANSAs it was pointed out in the introduction, the overal

objective of our research has been to develop a heat transfer

correlation that is robust enough to span all or most of the fluid

combinations, flow patterns, flow regimes, and pipe

orientations (vertical, inclined, and horizontal). As it was

presented in this paper, we have made a lot of progress towardthis goal. However, we still have a long ways to go. In order to

accomplish our research objective we need to have a much

better understanding of the heat transfer mechanism in each

flow pattern and perform systematic heat transfer

measurements to capture the effect of several parameters thatinfluence the heat transfer results. We will complement thesemeasurements with extensive flow visualizations.

We also plan to take systematic isothermal pressure drop

measurements in the same regions that we will obtain or have

obtained heat transfer data. We will then use the pressure drop

data through “modified Reynolds Analogy” to back out heatransfer data. By comparing the predicted heat transfer resultsagainst our experimental heat transfer results, we would be able

to establish the correct form of the “modified Reynolds

Analogy”. Once the correct relationship has been established, i

will be used to obtain two-phase heat transfer data for the

regions that due limitations of our experimental setup we didnot collect heat transfer data. The additional task at this stagewould be collection of isothermal pressure drop in these

regions.

The above-mentioned systematic measurements will allow

us to develop a complete database for the development of our

“general” two-phase heat transfer correlation.

ACKNOWLEDGMENTSThe assistance of Mr. Jae-yong Kim (Ph.D. candidate), Mr

Steve Trimble (Ph.D. candidate), and Mr. Kapil Malhorta (M.S

candidate) with this manuscript is greatly appreciated.

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K., 1999, "Comparison of 20 Two-Phase Heat Transfer

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Transfer during Two Component Gas-Liquid Flow in

Tubes and Other Channels," AIChE Symp. Series, Vol.

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[6] Kudiraka, A. A., Grosh, R. J., and McFadden, P. W.,

1965, "Heat Transfer in Two-Phase Flow of Gas-LiquidMixtures," I&EC Fundamentals, Vol. 4, No. 3, pp. 339-334.

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"Robust Heat Transfer Correlation for Turbulent Gas-

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[9] Chisholm, D., 1973, "Research Note: Void Fraction

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Experimental Thermal and Fluid Science, Vol. 25, No.8, pp. 659-676.

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[12] Durant, W. B., 2003, "Heat Transfer Measurement of Annular Two-Phase Flow in Horizontal and a Slightly

Upward Inclined Tube," M.S. Thesis, Oklahoma StateUniversity, Stillwater, OK.

[13] Trimble, S., Kim, J., and Ghajar, A. J., 2002,

"Experimental Heat Transfer Comparison in Air-Water

Slug Flow in Slightly Upward Inclined Tube," Proc.

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pp. 569-574.

[14] Kline, S. J. and McClintock, F. A., 1953, "Describing

Uncertainties in Single-Sample Experiments," Mech.

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A., 2004, "An Experimental Study of Heat Transfer inAnnular Two-Phase Flow in A Horizontal and Slightly

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a Vertical Tube." Ph.D. Thesis, University of Manitoba,

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[17] Aggour, M. A., 1978, "Hydrodynamics and Hea

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for an Air-Water Mixture Flowing in a 0.737inch I.DHorizontal Tube." M.S. Thesis, University of CaliforniaBerkeley, CA.

[20] Knott, R. F., Anderson, R. N., Acrivos, A., and Petersen

E. E., 1959, "An Experimental Study of Heat Transfer to

Nitrogen-Oil Mixtures," Industrial and Engineering

Chemistry, Vol. 51, No. 11, pp. 1369-1372.[21] Davis, E. J. and David, M. M., 1964, "Two-Phase Gas

Liquid Convection Heat Transfer," I&EC Fundamentals

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and Heat Transfer Gas-Liquid Slug Flow in Horizonta

Tubes," British Chemical Engineering, Vol. 9, No. 9, pp

590-596.

[25] Dusseau, W. T., 1968, "Overall Heat TransferCoefficient for Air-Water Froth in a Vertical Pipe," M.S

Thesis, Vanderbilt University, Nashville, TN.[26] Elamvaluthi, G. and Srinivas, N. S., 1984, "Two-Phase

Heat Transfer in Two Component Vertical Flows," Int. J

Multiphase Flow, Vol. 10, No. 2, pp. 237-242.

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Two-Phase and Two-Component Flow in Vertica

Tubes," AIChE Symp. Series, Vol. 83, pp. 109-114.

[28] Groothuis, H. and Hendal, W. P., 1959, "Heat Trasnfe

in Two-Phase Flow," Chemical Engineering Science

Vol. 11, pp. 212-220.

[29] Serizawa, A., Kataoka, I., and Michiyoshi, I., 1975"Turbulence Structure of Air-Water Bubbly Flow-III

Transport Properties," Int. J. Multiphase Flow, Vol. 2 pp. 247-259.

[30] Hughmark, G. A., 1965, "Holdup and Heat Transfer inHorizontal Slug Gas-Liquid Flow," Chemica

Engineering Scinece, Vol. 20, pp. 1007-1010.

[31] Khoze, A. N., Dunayev, S. V., and Sparin, V. A., 1976

"Heat and Mass Transfer in Rising Two-Phase Flows in

Rectangular Channels," Heat Transfer Soviet Research

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[32] Ueda, T. and Hanaoka, M., 1967, "On Upward Flow of

Gas-Liquid Mixtures in Vertical Tubes: 3rd. Report,

Heat Transfer Results and Analysis," Bull. JSME , Vol.10, pp. 1008-1015.

[33] Vijay, M. M., Aggour, M. A., and Sims, G. E., 1982, "A

Correlation of Mean Heat Transfer Coefficients for Two-

Phase Two-Component Flow in a Vertical Tube," Proc.

7th International Heat Transfer Coefficient , Vol. 5, pp.

367-372.

Table 1. Ranges of the Experimental Data Used in this Study.

Source Orientation Fluids No. of Data

Vijay [4] Vertical Water-Air 139

Vijay [4] Vertical Glycerin-Air 57

Rezkallah [16] Vertical Silicone-Air 162

Aggour [17] Vertical Water-Helium 53Aggour [17] Vertical Water-Freon 12 44

Pletcher [18] Horizontal Water-Air 48

King [19] Horizontal Water-Air 21

Table 2. Heat Transfer Correlations Chosen for this Study.

Source Heat Transfer Correlations Source Heat Transfer Correlations

Aggour [17]

-1/3

TP Lh /h = (1-α) Laminar (L)

1/3 0.14

L SL L B W Nu =1.615 (Re Pr D/L) (µ /µ ) (L)

-0.83

TP Lh /h = (1-α) Turbulent (T)

0.83 0.5 0.33

L SL L B W Nu =0.01 55 Re Pr (µ /µ ) (T)

Knott et al. [20]

1/3

SGTP

L SL

Vh= 1+

h V

⎛ ⎞⎜ ⎟⎝ ⎠

where hL is from Sieder & Tate [8]

Chu & Jones [2]

0.14 0.17

0.55 1/3 B

TP TP LW

µ Pa

Nu =0 .43 (Re ) (Pr ) µ P

⎛ ⎞ ⎛ ⎞

⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠

Kudirka et al. [6] ( ) ( )

1/8 0.140.6

1/4 1/3SG G B

TP SL LSL L W

V µ µ

Nu =12 5 Re Pr V µ µ

⎛ ⎞ ⎛ ⎞⎛ ⎞

⎜ ⎟ ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠ ⎝ ⎠

Davis & David[21]

( ) ( )0.28 0.87 0.4

TP L G t L L Nu =0.06 0 ρ ρ DG x µ Pr

Martin & Sims[22]

TP L SG SLh h =1+0.64 V V


Dorresteijn [23]

-1/3

TP Lh /h = (1-α) (L)

-0.8

TP Lh /h = (1-α) (T)

0.9 0.33 0.14

L SL L B W Nu =0.0123 Re Pr (µ /µ )

Oliver & Wright[24]

TP L 0.36

L L

1.2 0.2 N u =N u -

R R

⎛ ⎞⎜ ⎟⎝ ⎠

1/3

0.14G LL L B W

(Q +Q )ρD Nu =1.615 Pr D/L (µ /µ )

Aµ

⎡ ⎤⎢ ⎥⎣ ⎦

Dusseau [25]0.87 0.4

TP TP L Nu = 0.029 (Re ) (Pr )Ravipudi &Godbold [3]

( ) ( )0.3 0.140.2

0.6 1/3SG G BTP SL L

SL L W

V µ µ Nu =0.56 Re Pr

V µ µ

⎛ ⎞ ⎛ ⎞⎛ ⎞⎜ ⎟ ⎜ ⎟⎜ ⎟

⎝ ⎠⎝ ⎠ ⎝ ⎠

Elamvaluthi &

Srinivas [26]

( ) ( ) ( ) ( )1/4 0.7 1/3 0.14

TP G L TP L B W Nu =0.5 µ µ Re Pr µ µ Rezkallah & Sims

[27]

-0.9

TP Lh /h = (1-α)


Groothuis &Hendal [28]

0.87 1/3 0.14

TP TP L B W Nu = 0.029 (Re ) (Pr ) (µ /µ )

(for water-air)0.39 1/3 0.14

TP TP L B W Nu = 2.6 (Re ) (Pr ) (µ /µ )

(for (gas-oil)-air)

Serizawa et al.[29]

-1.27TPTT

L

h=1+462X

h


Hughmark [30] ( )0.141/3

-1/2 L L BTP L

L L W

m c µ Nu =1.75 R

R k L µ

⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟

⎝ ⎠ ⎝ ⎠

Shah [5]

( )1/4

TP L SG SLh h = 1+ V V

1/3 0.14

L SL L B W Nu =1.8 6 (R e Pr D/L) (µ /µ ) (L)

( )0.140.8 0.4

L SL L B W Nu =0 .023 Re Pr µ /µ (T)

Khoze et al. [31]0.2 0.55 0.4

TP SG SL L Nu =0.26 Re Re Pr Ueda & Hanaoka[32]

0.6 LTP M

L

Pr Nu =0.07 5(R e )

1+0.035(Pr -1)

King [19]

0.32-0.52

TP L0.5

TP LL SG

h R ∆P ∆P= /h 1+0.025Re ∆L ∆L⎡ ⎤⎛ ⎞ ⎛ ⎞⎢ ⎥⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎣ ⎦

0.8 0.4

L SL L Nu =0.0 23 Re Pr

Vijay et al. [33]

0.451

TP L TPF Lh /h =(∆P /∆P )

1/3 0.14

L SL L B W Nu =1.6 15 (Re Pr D/L) (µ /µ ) (L)0.83 0.5 0.33

L SL L B W Nu =0.0155 R e Pr (µ /µ ) (T)

Sieder & Tate [8]

1/3 0.14

L SL L B W Nu =1.8 6 (R e Pr D/L) (µ /µ ) (L)

0.8 0.33 0.14

L SL L B W Nu =0 .02 7 R e Pr (µ /µ ) (T)

Note: α and R L are taken from the original experimental data. ReSL < 2000 implies laminar flow, otherwise turbulent; and for Shah [5], replace 2000

by 170. With regard to the eqs. given for Shah [5] above, the laminar two-phase correlation was used along with the appropriate single phasecorrelation, since Shah [5] recommended a graphical turbulent two-phase correlation.



Table 3. Recommended Correlations from the General Comparisons with Regard to Pipe Orientation, Fluids, and Major F

Abbreviations).

Vertical Experimental Pipe

Water-Air Glycerin-Air Silicone-Air Water-Helium Correlations with Restrictions

on ReSL and VSG/VSL B S F A B S F A B S C A F B S F A B

Aggour [17] -V -V -V -V -V -V -

Chu & Jones [2] RV RV RV RV R R RV V RV R

Knott et al. [20] V V V R V V V V V

Kudirka et al. [6] RV V

Ravipudi & Godbold [3] RV RV RV V RV V R RV

Rezkallah & Sims [27] RV RV RV RV RV RV R

Shah [5] V V RV V V V V V

Water-Air Glycerin-Air Silicone-Air Water-Helium Correlations with No

Restrictions B S F A B S F A B S C A F B S F A B

Aggour [17] N N N N N N N

Chu & Jones [2] N N N

Knott et al. [20] N N N N N N N N

Kudirka et al. [6]

Martin & Sims [22] N N N

Ravipudi & Godbold [3] N N N

Rezkallah & Sims [27] N N N N N N

Shah [5] N N N N N N N N

Water-Air Glycerin-Air Silicone-Air Water-Helium Correlation RecommendationsBased on Comparisons Above B S F A B S F A B S C A F B S F A B

Aggour [17] √ √ √ √ √ √

Chu & Jones [2] √ √ √

Knott et al. [20] √ √ √ √ √

Kudirka et al. [6]

Martin & Sims [22] √ √

Ravipudi & Godbold [3] √ √ √

Rezkallah & Sims [27] √ √ √ √ √

Shah [5] √ √ √ √ √ √ √

Note: R = Recommended correlation with the range of ReSL. V = Recommended correlation with the range of

correlation with no restrictions. √ = Recommended correlation with and without restrictions. - = Correlation either ReSL or VSG/VSL. Correlation of Martin & Sims [22] did not provide ranges for ReSL and VSG/VSL.



Table 4. Recommended Correlations from the General Comparisons with Regard to Experimental Fluids and Transition F

Abbreviations).

Vertical Experimental Pipe

Water-Air Glycerin-Air Silicone-Air WateCorrelations with Restrictions

on ReSL and VSG/VSL B-F S-A F-A A-M B-S S-A B-S B-F S-C C-A F-A A-M B-S B-F

Aggour [17] -V -V

Chu & Jones [2] RV RV RV R V

Knott et al. [20] V V V

Kudirka et al. [6] RV R V RV

Ravipudi & Godbold [3] RV RV RV RV V V V RV R

Rezkallah & Sims [27] RV RV RV RV RV RV RV

Shah [5] V V V V R

Water-Air Glycerin-Air Silicone-Air WateCorrelations with NoRestrictions B-F S-A F-A A-M B-S S-A B-S B-F S-C C-A F-A A-M B-S B-F

Aggour [17] N N N N

Chu & Jones [2] N N N N

Knott et al. [20] N N N N

Kudirka et al. [6] N N

Martin & Sims [22] N N

Ravipudi & Godbold [3] N N N N N N N N

Rezkallah & Sims [27] N N N N N N N

Shah [5] N N N N N N

Water-Air Glycerin-Air Silicone-Air WateCorrelation Recommendations

Based on Comparisons Above B-F S-A F-A A-M B-S S-A B-S B-F S-C C-A F-A A-M B-S B-F

Aggour [17] √ √

Chu & Jones [2] √ √ √ √

Knott et al. [20] √ √ √

Kudirka et al. [6] √ √

Martin & Sims [22] √ √

Ravipudi & Godbold [3] √ √ √ √ √ √ √ √

Rezkallah & Sims [27] √ √ √ √ √ √ √ Shah [5] √ √ √ √

Note: R = Recommended correlation with the range of ReSL. V = Recommended correlation with the range of VSG/VSL

with no restrictions. √ = Recommended correlation with and without restrictions. - = Correlation that did not VSG/VSL. Correlation of Martin & Sims [22] did not provide ranges for ReSL and VSG/VSL.



Table 5. Results of the Predictions for Available Two-Phase Heat Transfer Experimental Data Using the General Correlation, Eq. (11)

Value of C and Exponents (m, n, p, q) Range of Parameter Fluids

(ReSL > 4000) C m n p q

mean

Dev.(%)

rms

Dev.(%)

No. of

Datawithin

±30%

Dev.

range(%) ReSL

1

x

x

⎛ ⎞⎜ ⎟−⎝ ⎠

1

α

α

⎛ ⎞⎜ ⎟−⎝ ⎠

Pr

Pr G

L

⎛ ⎞⎜ ⎟⎝ ⎠

G

L

µ

µ

⎛ ⎞⎜ ⎟⎝ ⎠

All

255 data points2.54 12.78 245

–64.71to

39.55

Water-Air 105 data points

Vijay [4]3.53 12.98 98

–34.97to

39.55

Silicone-Air

56 data pointsRezkallah [16]

5.25 7.77 56 –7.25

to12.13

Water-Helium

50 data pointsAggour [17]

–1.66 15.68 48 –64.71

to32.19

Water-Freon 1244 data points

Aggour [17]

0.27 –0.04 1.21 0.66 –0.72

1.51 13.74 43 –24.51

to

32.96

4000

to

1.26×105

8.4×10-6

to0.77

0.01

to18.61

1.18×10-3

to0.14

3.64×10-6

to0.02

Table 6. Summary of the Values of the Leading Coefficient and Exponents in the General Correlation, Eq. (11), the Results of

Prediction, and the Parameter Range of the Correlation.

Value of C and Exponents (m, n, p, q) Range of Parameter Experimental Data

[10] C m n p q

meanDev.(%)

rmsDev.(%)

No. of Data

within

±20%

Dev.range(%) ReSL

1

x

x

⎛ ⎞⎜ ⎟−⎝ ⎠

1

α

α

⎛ ⎞⎜ ⎟−⎝ ⎠

Pr

Pr G

L

⎛ ⎞⎜ ⎟⎝ ⎠

G

L

µ

µ

⎛ ⎞⎜ ⎟⎝ ⎠

Slug, Bubbly/Slug,

Bubbly/Slug/Annular

89 data points2.86 0.42 0.35 0.66 –0.72 0.36 12.29 82

–25.17

to31.31

2468

to35503

6.9x10-4

to0.03

0.36

to3.45

0.102

to0.137

0.015

to0.028

Wavy-Annular 41 data points 1.58 1.40 0.54 –1.93 –0.09 1.15 3.38 41

–12.77

to19.26

2163

to4985

0.05

to0.13

3.10

to4.55

0.10

to0.11

0.015

to0.018

Wavy20 data points

27.89 3.10 –4.44 –9.65 1.56 3.60 16.49 16 –19.79

to34.42

636to

1829

0.08to

0.25

4.87to

8.85

0.102to

0.107

0.016to

0.021

All 150 data pointsSee Above for the Values for

Each Flow Pattern1.01 12.08 139

–25.17to

34.42

636to

35503

6.9x10-4 to

0.25

0.36to

8.85

0.102to

0.137

0.015to

0.028

Table 7. Curve-Fitted Constants, Results of Predictions of the Horizontal and Inclined Annular Air-Water Flow Experimental Data

and the Parameter Range for Eq. (15).

Value of C and Exponents (m, n, p, q, r) Range of Parameter

Experimental Data[15]

C m n p q r

meanDev.

[%]

rmsDev.

[%]

No. of

Datawithin

±15%

Dev.Range

[%] ReSL ⎟ ⎠

⎞⎜⎝

⎛ − x1

x ⎟ ⎠

⎞⎜⎝

⎛ −α

α

1

⎟⎟

⎠

⎞⎜⎜⎝

⎛

L

G

Pr

Pr ⎟⎟ ⎠

⎞⎜⎜⎝

⎛

L

G

µ

µ θ [rad]

Annular 123 data points

65 0.25 0.25 0.33 0.14 1.4 –1.8 5.9 122 –15.1

to

14.6

2863to

8298

0.076to

0.237

8.25to

15.71

0.117to

0.121

0.021to

0.022

0 (0°)to

0.122 (7°)



h TPEXP

(Btu/hr-ft2-°F)

100 1000 10000

h T P C A L

( B t u / h r - f t 2 - ° F

)

100

1000

10000

Water-Airfrom Vijay [4]

Silicone-Airfrom Rezkallah [16]

Water-Heliumfrom Aggour [17]Water-Freon 12from Aggour [17]

+30 %

-30 %

Figure 1. Comparison of the Prediction by the General

Correlation, Eq. (11) with the Experimental Data for Vertical Flow (255 Data Points) in Table 5.

h TPEXP

(Btu/hr-ft2-°F)

100 1000

h T P C A L

( B t u / h r - f t 2 - ° F

)

100

1000

+30 %

-30 %

+20 %

-20 %

Figure 2. Comparison of the Predictions by Ganeta

Correlation, Eq. (11) with the Experimental Data forHorizontal Flow (150 data points).

Thermocouple ProbeLincoln SA-750

Welder

Aluminum I-Beam

Thermocouple Probe

Pump

CoriolisWater Flow Meter

Filter

Air Compressor

Air SideHeat Exchanger

CoriolisAir Flow Meter

Check Valves

Mixing Well

Mixing Well

Shell and TubeHeat ExchangerMain Control Valve

for Water Flow

Clear Poly CarbonateObservation

Section

Air Out

WaterStorage Tank

Regulator

Pivoting Foot Electric Screw J ack

Insulation

NI-DAQ CARD

Main Control Valvefor Air Flow

Transmitter

Transmitter

SCXI

NationalInstruments

SCXI-1000

SCXI 1102/B/C

modules

SCXI 1125

moduleCPU withLabVIEW Virtual Instument

Clear Poly CarbonateCalming & Observation Section Stainless Steel Test Section

Drain

Drain

Drain

Data Acquisition System:

Filter&

Separator

Figure 3. Schematic of Experimental Setup.



Figure 4. Air-Water Mixer.

Figure 5. Stainless Steel Test Section.

Figure 6. Flow Map for Horizontal Flow.

(a) Stratified

(b) Plug

(c) Slug

(d) Wavy

(e) Bubbly/Slug

(f) Annular/Bubbly/Slug

(g) Annular/Wavy

(h) Annular

Figure 7. Photographs of Representative Flow Pattern

(Horizontal Flow and Isothermal).

ReSG

X 103

0.6 0.8 2 4 6 8 20 40 601 10

h T P E X P

[ W / m 2 - K

]

0

1000

2000

3000

4000

5000

6000

2600022000

17000

15000

12000

9500

7000

5000

1500

850

ReSLFlow Pattern

PlugSlug & S lug/Bubbly

Slug/Wavy

Wavy/Annular

Slug/Bubbly/Annular

Annular

Figure 8. Variation of Overall Mean Heat Transfe

Coefficients of Horizontal Flow over ReSG with Fixed

ReSL.



ReSL

=5000

ReSG

1000 10000 100000

h T P E X P

[ W / m 2 - K

]

0

1000

2000

3000

4000

Horizontal

2 Degrees

5 Degrees

7 Degrees

(a) ReSL = 5000

ReSL

=12000

ReSG

1000 10000 100000

h T P E X P

[ W / m 2 - K

]

0

1000

2000

3000

4000

Horizontal

2 Degrees

5 Degrees

7 Degrees

(b) ReSL = 12000

ReSL

=17000

ReSG

1000 10000 100000

h T P E X P

[ W / m 2 - K

]

0

1000

2000

3000

4000

Horizontal

2 Degrees5 Degrees

7 Degrees

(c) ReSL = 17000

Figure 9. Inclination Effects on Overall Mean Heat Transfer Coefficients.

ReSL

4000 6000 8000 10000 12000 14000 16000 18000

h T P E X P

[ W / m 2 K ]

0

500

1000

1500

2000

2500

3000

3500

4000

Horizontal

2 Degrees Inclined5 Degrees Inclined

Figure 10. Variation of Mean Heat Transfer Coefficient withReSL for Horizontal and Inclined Slug Air-Water Flow.

ReSL

2000 4000 6000 8000 10000

h T P E X P

[ W / m 2 K ]

500

1000

1500

2000

2500

3000

3500

Horizontal

5 Degrees Inclined7 Degrees Inclined

Figure 11. Variation of Mean Heat Transfer Coefficient with

ReSL for Horizontal and Inclined Annular Air-WaterFlow.

h TPEXP

[W/m2K]

600 800 2000 40001000

h T P C A L

[ W / m 2 K ]

600

800

2000

4000

1000

Horizontal5 Degrees Inclined

7 Degrees Inclined

+15 %

-15 %

Figure 12. Comparison of the Predictions of the

Recommended Heat Transfer Correlation, Eq. (15)

with the Horizontal and Inclined Annular Air-WaterFlow Experimental Data (123 Data Points).

ghajar hefat 2004 keynote

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