Proceedings ofISROMAC 2016

Honolulu, Hawaii,USA,April 10-15,2016ISROMAC-2016-44042

A Combined Numerical and Experimental Studyof Heat Transfer in a Cooling Channel

Roughened with 90◦ Ramped Ribs

M.E. Taslim and B. Ren

Mechanical and Industrial Engineering Department

Northeastern University

Boston, MA, USA

Abstract

Varieties of cooling methods have been used to protect

the hot sections in modern gas turbine engines so as to allow

a higher inlet temperature for increasing turbine efficiency.

One such method is to route the cooling air through passages

roughened with ribs within the airfoils in order to enhance

the convective heat transfer coefficients in those passages.

Much work is reported in open literature dealing with a va-

riety of rib geometries and flow arrangements. This study’s

focus, however, is on the ramped-ribs. Both upstream- and

downstream-ramped ribs are investigated. The presence of

these ramps could be by design, or due to casting imperfec-

tions, or by the accumulation of micron-size sand particles

that find their way from the engine inlet to the cooling pas-

sages when the engine is operated in harsh environments.

The ramp can be formed on both sides of the ribs in the

flow direction. A square channel roughened with 90◦ ribs

of three geometries was tested. Square as well as ramped

(with decreasing or increasing slopes in the flow direction i.e.

ramping up or down) ribs in a staggered arrangement were

studied. Square ribs of the same height as the ramped-ribs

were tested first to which the ramped-rib results were com-

pared. The numerical models contained all the features of the

tested geometries. The applied thermal boundary conditions

to the CFD models matched the test boundary conditions.

Numerical results were obtained from a three-dimensional

unstructured computational fluid dynamics model with over

13 million hexahedral elements. For turbulence modeling,

the realizable k − ε was employed in combination with the

standard wall functions. In the experimental part, all these

geometries were built and tested for heat transfer coefficients

at a Reynolds numbers range from 10,000 to 60,000, using

steady state liquid crystal thermography. Comparisons were

made between the test and numerically-obtained results in

order to evaluate the employed turbulence models and vali-

date the numerically obtained results. The test and numer-

ically evaluated results showed reasonable agreements be-

tween the two for all rib geometries. Friction factors were

also measured, and both heat transfer and friction factor re-

sults for the three rib geometries were compared. The re-

sults showed that there is a considerable penalty, up to about

28%, in heat transfer coefficients for the ramped ribs. Pas-

sage pressure drop (friction factor) could decrease by up to

43%. However, the deficit in heat transfer coefficients could

have significant impact on the airfoil life.

Nomenclature

A channel area, 25.81cm2

Dh hydraulic diameter of test section, 5.08 cm

e rib height, 0.5715 cm

P rib pitch, 5.715 cm

w rib width, 0.5715 cm

f Darcy friction factor=∆P(Dh/L)

12 ρU2

m

fs smooth wall friction factor

h heat transfer coefficient, W/(m2K)L rib-roughened length of the channel, 28.575 cm

1

i current through the surface foil heater, amps

k air thermal conductivity, W/(mK)m air mass flow rate, Kg/s

N̄u area-averaged Nusselt number based on the channel hy-

draulic diameter,hDh/k

Nus all smooth channel Nusselt number from Dittus-

Boelter correlation

Pamb ambient (lab) pressure, Pa

P channel perimeter, 20.32 cm

Pr Prandtl number

q′′

total heat flux generated by the foil heater (= vi/Aheater)

q′′

b total heat loss through the polyurethane back wall to the

ambient

q′′

r total radiational losses from the heated measurement

wall to the surrounding unheated walls

rrib rib top corner radii, 0.127 cm

Re Reynolds number based on the channel hydraulic diam-

eter, 4m/Pµ)Tf film temperature where the heat transfer coefficient is

measured, (Tm +Ts)/2

Tm Air mixed mean temperature where the heat transfer co-

efficient is measured

Ts surface temperature where the heat transfer coefficient

is measured

Um air average velocity

v voltage across the surface foil heater, volts

α rib angle with the flow direction, 90◦

∆P pressure drop across the rib-roughened length of the

channel, L

ρ air density, Kg/m3

1 Introduction

Various methods have been developed over the years to

keep turbine airfoil temperatures below critical levels. The

main purpose in turbine airfoil cooling is achieving maxi-

mum heat transfer coefficients while minimizing the coolant

air flow rate. One such method is to route the air through

rib-roughened serpentine passages within the airfoil and re-

move heat from the airfoil by convection. The coolant is

then ejected either at the tip of the airfoil, through the cool-

ing slots along the trailing edge or cooling holes along the

airfoil surface. Shed vortices from the rib tip and formation

of secondary flows give rise to the level of mixing of the

coolant air in the cavity core with the warmer near-wall air

thus increase the heat transfer from the airfoil walls. Addi-

tional heat transfer gain is accomplished due to the increased

extended surface area. However, roughening the walls in-

creases the friction factors in the cooling cavities which re-

sults in higher pressure drop penalties. Figure 1 shows a typ-

ical internal cooling arrangement for a multi-pass turbine air-

foil (Ligrani[1]).

Geometric parameters such as rib height to passage hy-

draulic diameter or blockage ratio e/Dh, rib angle with the

flow direction(α), the manner in which the ribs are posi-

tioned relative to one another (in-line, staggered, crisscross,

etc.), rib pitch-to-height ratio P/e, and rib corners (round vs

sharp corners, fillets, skewness towards the flow direction)

have pronounced effects on both local and overall heat trans-

fer coefficients. Some of these effects were studied by dif-

ferent investigators such as Burggraf [2], Webb et al. [3],

Han et al. [4], Metzger et al. [5], Han [6], Han et al. [7],

Metzger et al. [8], Metzger and Vedula [9], Chandra [10],

Chandra and Han [11], Han et al. [12], Zhang et al. [13],

Dutta and Han [14], Taslim and Spring [15], Taslim et al.

[16], Taslim et al. [17]. Numerous experimental and numeri-

cal studies have been performed in rectangular rib-roughened

cooling channels. Arts et al. [18] compared the computa-

tional results from a three-dimensional Navier-Stokes solver

for heat transfer of a steady viscous compressible flow in a

square channel with one rib-roughened wall with detailed ex-

periments. The three-dimensional computations captured the

correct position of the reattachment point using the k− l tur-

bulence model. Gupta et al. [19] measured the local heat

transfer distributions in a double wall ribbed square chan-

nel with 90◦ continuous, 90◦ saw tooth profiled and 60◦ V-

broken ribs. Taslim and Spring [20] used liquid crystals to

study the effects of rib profile and spacing on heat transfer

coefficient. They concluded that low aspect ratio ribs, es-

pecially with round corners, produced lower heat transfer

coefficients. They also found an optimum pitch-to-height

ratio for 90◦ square ribs was around 8. Gao and Sunden

[21] investigated the thermal and hydraulic performance of

three rib-roughened rectangular ducts. The ribs were ar-

ranged staggered on the two wide walls. They employed

liquid crystal thermography in the heat transfer experiment

to demonstrate detailed temperature distribution between a

pair of ribs on the ribbed surfaces. They found that the sec-

ondary flows caused by the inclined ribs created a significant

spanwise variation of the heat transfer coefficients on the rib-

roughened wall with high heat transfer coefficient at one end

of the rib and low value at the other. In the streamwise di-

rection between two consecutive ribs, the temperature dis-

tribution showed a sawtooth variation because of flow reat-

tachment. Lu and Jiang [22] experimentally and numerically

investigated forced convection heat transfer of air in a rectan-

gular channel with 45◦ ribs on one wall. They compared the

experimental and numerical results and showed that the SST

k−ω turbulence model was more suitable for the convection

heat transfer in such channels than the RNG k−ε turbulence

model. They found that the average heat transfer coefficients

increased with increasing mass flow rates and decreasing

spacings. Peng et al. [23] experimentally and numerically

studied convection heat transfer in a channel with 90◦ ribs

and V-shaped ribs. They found that both the 90◦ ribs and

V-shaped ribs enhanced the convection heat transfer com-

pared with a flat wall without ribs, but the pressure drop also

increased. They also compared continuous ribs and inter-

rupted ribs and concluded that the heat transfer with the 90◦

interrupted ribs is more than with the 90◦ continuous ribs.

Promvonge and Thianpong [24] conducted experiments to

assess turbulent forced convection heat transfer and friction

loss behaviors for air flow through a constant heat flux chan-

nel fitted with different shaped ribs. The rib cross-sections

used in this study were triangular (isosceles), wedge (right-

2

triangular) and rectangular shapes. They introduced two rib

arrangements, namely, in-line and staggered arrays. The ex-

perimental results showed a significant effect of the presence

of the ribs on the heat transfer rate and friction loss over the

smooth wall channel. They found that the in-line rib arrange-

ment provided higher heat transfer and friction loss than the

staggered one for a similar mass flow rate. Kamali and Bi-

nesh [25] developed a computer code to study the turbulent

heat transfer and friction in a square duct with various shaped

ribs, mounted on one wall. The simulations were performed

for four rib shapes, i.e., square, triangular, trapezoidal with

decreasing height in the flow direction, and trapezoidal with

increasing height in the flow direction. The prepared algo-

rithm and the computer code were applied to demonstrate

distribution of the heat transfer coefficient between a pair of

ribs. The results showed that features of the inter-rib distri-

bution of the heat transfer coefficient are strongly affected by

the rib shape and trapezoidal ribs with decreasing height in

the flow direction provide higher heat transfer enhancement

and pressure drop than other shapes. Taslim and Liu [26]

showed that CFD could be considered as a viable tool for the

prediction of heat transfer coefficients in a rib-roughened test

section. In the numerical part, a square channel roughened

with 45◦ ribs of four blockage ratios (e/Dh) of 0.10, 0.15,

0.20, and 0.25, each for a fixed pitch-to-height ratio (P/e)

of 10, was modeled. Sharp as well as round-corner ribs (r/e

= 0 and 0.25) in a staggered arrangement were studied. In

the experimental part, a selected number of these geometries

were built and tested for heat transfer coefficients at elevated

Reynolds numbers up to 150000, using a liquid crystal tech-

nique.

As for the heat transfer coefficient data on the sur-

faces of the rib (in contrast to the heat transfer coeffi-

cient on the area between the adjacent ribs), several stud-

ies are reported. The reported work of Metzger et al.

[27], Taslim and Wadsworth [28], Korotky and Taslim [29],

Taslim and Lengkong [30],Taslim and Korotky [31], Taslim

and Lengkong [32] cover a wide range of pertinent parame-

ters affecting the on-rib heat transfer coefficients.

When gas turbines are operated in harsh environments

such as sand storms or particle-laden winds, extremely fine

particles,(below 10 microns in diameter) are ingested into

the turbomachinery, compromise engine performance and

significantly reduce the normal life expectancy of the en-

gine. These particles could find their way into the airfoils

cooling cavities and block the cooling features such as film

holes, tip holes, crossover holes and the trailing-edge slots.

Compounded by high gas temperatures, the particles may go

through chemical reactions and conglomerate to make de-

posits at the turbulators’ roots, 180-degree turns in the ser-

pentine cooling cavities, around the base of the pins in the

pin banks and in the trailing-edge holes and slots, to name a

few. Similar behavior is observed around the airfoils outer

peripheries especially on their platform. Deposition of these

particles on different cooling features often has severe unde-

sirable effects on their thermal performance. The severity of

these effects is different for different cooling features and it

has to be studied one by one. Hot and harsh environment is

Fig. 1. Typical internal cooling arrangement for a multipass turbine

blade [1].

not the only cause of altering the cooling features effective-

ness. Casting imperfections and wear and tear of the core

dies could also be other causes.

In this study, downstream- and upstream-ramped ribs,

simulating the changes in rib shape due to the accumulation

of foreign particles such as sand in front or on the back side

of the ribs, are studied for their effects on the heat transfer

coefficient as well as the friction factor in the cooling cavities

of a gas turbine airfoil.

2 Test Section

Figure ?? shows schematically the test section and rib

geometries. Steady state liquid crystal thermography tech-

nique is used for the measurement of heat transfer coeffi-

cient. In this technique, the most temperature-sensitive color

displayed by the liquid crystals is chosen as the reference

color corresponding to a known temperature. By proper ad-

justment of the Ohmic power to a very thin foil heater im-

mediately underneath the liquid crystals, the reference color

is moved from one location to another so that the entire area

of interest is eventually covered with the reference color at

one time or another. This process results in a series of pho-

tographs which correspond to a certain location of the refer-

ence color. Among the advantages of liquid crystal thermog-

raphy is to depict the flow ”footprints” and local values of

heat transfer coefficient on the surface under investigation.

This simultaneous flow visualization enhances the under-

standing of the underlying physics and helps the investiga-

tor in interpretation of the results. Furthermore, unexpected

asymmetries in flow are revealed as well as the slightest heat

and flow leaks, nonuniformities in surface heat flux, imper-

fections associated with the attachment of the heater to the

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Fig. 2. schematics of the test section and the ribs.

test section surface and nonuniformities in wall material ther-

mal conductivity. The test section was a 5.08cm× 5.08cm

square channel with a length of 91.44cm, three walls of

which were made of 1.27cm−thick clear acrylic plastic. The

fourth wall, on which a sheet of encapsulated liquid crystals

was attached and all measurements were taken, was made

of a 10.16cm-thick machinable polyurethane board with a

thermal conductivity of 0.0576W/mK in order to mitigate

heat losses from the heaters to the ambient. Three 5.08cm

x 28.2cm custom-made etched foil heaters were glued onto

the polyurethane wall where measurements were taken. The

heaters covered the entire polyurethane wall including the

smooth entry and exit lengths. The 0.15-mm-thick etched

foil heaters were made of a 0.0127mm-thick inconel heat-

ing element and a 0.0127mm-thick electrically inactive in-

conel foil to further spread the heat uniformly over the

polyurethane surface. These two inconel foils were sand-

wiched and glued between three layers of Kapton. It is noted

that in a stationary channel, the heat transfer coefficient is

not sensitive to the number of heated walls [33]. The test

section was covered on all sides, except for a small win-

dow at the location where the pictures were taken, with a

5-cm-thick styrofoam slab to minimize heat losses to the en-

vironment. The radiational heat loss from the heated wall

to the unheated walls as well as losses to ambient air were

taken into consideration when heat transfer coefficients were

calculated. A digital camera, in conjunction with proper fil-

ters and background lighting to simulate daylight conditions,

was used to take pictures of isochrome patterns formed on

the liquid crystal sheet. A centrifugal compressor supplied

compressed air to a 0.76m3 storage tank. A combination of

an air dryer and two air filters dried and cleaned the air. A

pressure regulator was used to set the air mass flow rate for

a desired jet Reynolds number. A critical venturi, choked for

all mass flow rates, was then used to measure the air mass

flow rate before it entered a 50.8cm × 50.8cm × 53.34cm

plenum equipped with a honeycomb flow straightener, and

to the the test section at about ambient temperature. To-

tal mass flow rate entering the supply channel varied from

0.0093 to 0.056Kg/s. Heat was induced to the air in the

test section via the heaters through a custom-designed power

supply unit. Each heater was individually controlled by a

variable transformer to assure a constant heat flux over the

entire heated wall. Two thermocouples at the channel inlet

measured the air inlet temperature. Their measurements did

not differ by more than a fraction of a degree. A typical air

temperature at the channel inlet was 21oC. A pressure tap

measured the static pressure in the plenum and four pres-

sure tap readings, one on each wall at the test section inlet

were averaged for the test section inlet pressure. Five ribs,

also machined out of clear acrylic plastic, were mounted on

the liquid crystal wall using a double-sided tape with min-

imum deformation, and five ribs on the opposite clear wall

in a staggered arrangement. Ribs were normal to the flow

direction. All Ribs had a height of 0.572cm, corresponding

to a blockage ratio, e/Dh, of 0.125 and they were 5.72cm

apart, corresponding to a pitch to height ratio, P/e, of 10.

Measurements for all three cases were performed on the area

between the third and fourth ribs in the flow direction on the

liquid crystal side. This area is shown in Fig. 2 as the mea-

surement area and the reported heat transfer coefficient is the

area-weighted heat transfer coefficient for the area between

the third and fourth ribs on the liquid crystal side. The rib-

roughened length in all cases was 28.58cm, so approximately

62.87cm of the channel length at the inlet and the exit was

smooth. The smooth inlet section simulates the cooling cav-

ity in the dovetail region of an airfoil. Heat flux on the heated

wall was provided by the foil heaters through a custom de-

signed power supply unit. Before testing, the liquid crystal

sheet was calibrated as follows. A water bath was used to

attain uniform isochromes on a small sample piece of the

liquid crystal sheet used throughout this investigation. The

temperature corresponding to each color was measured using

a precision thermocouple and photographs were taken at lab-

oratory conditions simultaneously so as to simulate closely

the actual testing environment. A reference color along with

its measured temperature of 34.6oC was then chosen to be

used throughout the experiments. It should be noted that all

possible shades of the selected reference color showed a tem-

perature difference of no more than 0.3oC. A contact micro-

manometer with an accuracy of about 0.0254 millimeter of

water column measured the pressure drop across the channel

for the calculation of friction factor.

For a typical test run, the Reynolds number was set by

precisely fixing the mass flow rate. The heat flux was then

induced by turning on the main power supply and adjust-

ing heater power until the first band of reference color was

observed on the liquid crystal sheet in the area of interest.

Enough time was allowed so that the system came to thermal

equilibrium when a photograph was taken and data recorded.

The power to the heaters was then increased so that the ref-

4

erence color was moved to a location next to the previous

one and another picture was taken. This procedure was con-

tinued until the entire surface of interest on was covered by

the reference color at one time or another. The process was

repeated for all Reynolds numbers. Each photograph was

digitized in order to measure the area covered by the refer-

ence color. This was done by using a commercial software

package installed on a PC. Once the areas (pixels) were mea-

sured, the area-weighted average heat transfer coefficient for

the surface area between the third and fourth ribs was calcu-

lated. Experimental uncertainties in friction factor and heat

transfer coefficients, following the method of Kline and Mc-

Clintock [34], were ±5% and ±6%, respectively.

3 Computational Model

The computational model was constructed for the en-

tire rib-roughened channel. Figure 3 shows the mesh for

the test section and square ribs while Fig. 4 shows the de-

tails of the mesh distribution around the rib-roughened sec-

tion of the channel with ramped ribs. The CFD analyses

were performed using Fluent/UNS solver by Ansys, Inc., a

pressure-correction based, multi-block, multi-grid, unstruc-

tured/adaptive solver. Incompressible fluid with a turbulent

Prandtl number of unity is assumed. Boundary conditions for

the numerical models were identical to those of the experi-

ments. At the inlet, a total mass flow rate exactly the same

as what was measured was specified at the same temperature

(18−25 ◦C range) and pressure (101.35−105.4 KPa range)

of the air entering the rig. The turbulence intensity at the inlet

was set to 5%. The heat fluxes on the heated walls were also

identical to those of experiment (2500−4000 W/m2 range).

Channel exit had a pressure boundary condition identical to

that of the lab. The realizable k − ε turbulence model was

employed in combination with the standard wall functions.

The average y+ for the first layer of cells was calculated to

be below 5 for all cases. Other available turbulence models in

this commercial code including the k−ω with Shear Stress

Transport (SST) option and the realizable k− ε turbulence

model in combination with enhanced wall treatment were

also tested and the corresponding results are compared. Cells

in all models were entirely hexagonal, a preferred choice for

CFD analyses, and were varied in size bi-geometrically from

the boundaries to the center of the computational domain in

order to have finer mesh close to the boundaries. Mesh inde-

pendence was achieved at about 12 million cells for a typical

model. For a representative geometry, the heat transfer re-

sults of a series of meshed models with different number of

elements were compared. As the mesh became more and

more refined, the heat transfer results came closer and closer

to each other. When a difference of a fraction of a percent

between two consecutive meshes was observed, no further

refinement was done. We reached that situation when the

total number of elements was about 13 million. We started

at 8M and increased the element numbers by about 2M at a

time first, and 1M at the end. Residual sums for all variables

in all models were less than 1x10−7. Convergence, for most

Fig. 3. A typical CFD model representing the entire square-rib test

section.

cases, was achieved at around 25,000 iterations.

4 Results and Discussion

As was mentioned earlier, three turbulence models were

tested for our numerical models. The CFD results of these

three turbulence models - realizable k− ε with standard wall

functions, realizable k− ε with enhanced wall treatment and

5

Fig. 4. Details of the mesh around the ramped ribs.

k−ω with Shear Stress Transport (SST) are compared for

the square rib geometry in Fig. 5. These cases were run un-

der otherwise identical conditions i.e. same mesh size and

arrangement and same boundary conditions. Only the turbu-

lence model was changed. Measured values are also shown.

It was concluded that the realizable k− ε turbulence model

with standard wall functions produced the closest results to

the measure values, thus in all reported CFD results, this tur-

bulence model was employed.

The first test for each rib geometry was a cold test for the

measurement of the pressure drop across the rib-roughened

channel and calculation of the Darcy friction factor for a

range of Reynolds numbers. The surface heaters were off

so that the air properties could be evaluated accurately at the

measured channel inlet temperature. Figure 6 compares the

test as well as the numerically-obtained friction factor re-

sults for the three rib geometries. It should be noted that,

in these and ensuing figures, the symbols represent the mea-

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

50

100

150

200

250

300

350

400

450

z/Dh

Nu

Re

Area 1

Top

Back

Test

600005000040000300002000010000

kωSST

Real. kε,Std.Wall Funcs.

Front

Real. kε withWall Treat.

Floor

Area 4Area 3Area 2 Area 5

Fig. 5. Comparison of the laterally-averaged local CFD Nusselt

number variation along the rib-roughened section of the channel us-

ing three turbulence models and the measured area-averaged Nus-

selt numbers.

0 10000 20000 30000 40000 50000 600000

0.05

0.1

0.15

0.2

0.25

0.3

Re

f

Square Ribs, TESTDownstream­Ramped Ribs, TESTUpstream­Ramped Ribs, TESTSquare Ribs, CFDDownstream­Ramped Ribs, CFDUpstream­Ramped Ribs, CFD

Fig. 6. Darcy friction factor variation with Reynolds number for the

three rib geometries - a comparison between the measured and

numerically-obtained results.

sured data while the lines represent the numerically-obtained

results. Square ribs, as expected, produce a much higher

pressure drop across the channel, compared with the ramped

ribs. This is explained by the fact that the square ribs intro-

duce a rather abrupt blockage to the flow while the ramped

6

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

Vmag

m/s

Square Ribs

Downstream­Ramped Ribs

Upstream­Ramped Ribs

Fig. 7. CFD contours of velocity magnitudes around the ribs for the

three rib geometries at Re=40,000.

ribs introduce a gradual blockage to the flow. CFD con-

tours of velocity magnitudes for the three rib geometries,

shown in Fig. 7, show wider areas of high velocity mag-

nitudes for the ramped rib cases indicating less resistance to

the flow. Test results do not show a difference in pressure

drop between the two ramped rib geometries beyond the ex-

perimental uncertainties while the numerical results show an

average of about 4.5% decrease in the friction factor for the

upstream-ramped ribs compared to the friction factor for the

downstream-ramped ribs.

The heat transfer coefficient corresponding to each

recorded picture of liquid crystals display on the measure-

ment area, shown in Fig. 2, was calculated from:

h =q′′−q

′′

b −q′′

r

(Ts−Tm)

where Ts and Tm are the surface and air mixed mean temper-

atures, respectively. q′′

is the total heat flux generated by the

foil heater, q′′

b is the total heat loss from the heaters to am-

bient through the back polyurethane wall and q′′

r is the total

radiational losses from the heated measurement wall to the

surrounding unheated walls. Air properties were evaluated

at the film temperature, Tf . Heat transfer results were gath-

ered for Reynolds numbers from about 10,000 to 60,000.

Figure 8 compares the tested and numerically-obtained

area-averaged Nusselt numbers for the three rib geometries.

The error bars on the symbols represent the experimental un-

certainties. Square ribs, as expected, produce higher Nusselt

numbers, compared with the ramped ribs. This behavior is in

agreement with Colburn Analogy of higher heat transfer co-

efficients corresponding to higher friction factors. It has been

established both experimentally and analytically that, given

10000 20000 30000 40000 50000 600000

50

100

150

200

250

300

350

Re

Nu

Square Ribs, TESTDownstream­Ramped Ribs, TESTUpstream­Ramped Ribs, TESTSquare Ribs, CFDDownstream­Ramped Ribs,CFDUpstream­Ramped Ribs, CFD

Fig. 8. Nusselt number variation with Reynolds number on the mea-

surement area for the three rib geometries - a comparison between

the measured and numerically-obtained results.

enough space between a pair of adjacent ribs in the flow di-

rection (P/e≥ 5), for the flow to re-attach after tripping over

the rib, the heat transfer coefficient reaches its maximum

value in the re-attachment zone and decreases monotonically

in the flow direction until it approaches the next rib where it

starts to increase again due to a stagnation point type of flow.

Streamlines of Fig. 9 and CFD contours of the Nusselt num-

bers, shown in Fig. 10, support this argument as well. There-

fore, air trips over the square ribs and re-attaches around the

middle of the area between the adjacent ribs. The shed vor-

tices from the rib top edges promote the mixing of the cooler

core air with the near-wall warm air thus increase the heat

transfer coefficient. This phenomenon occurs on the ramped

ribs to a lesser degree as the air climbs up or down the ramps

gradually thus the enhancement in heat transfer coefficient

is not as high as of that for the square ribs. The square and

upstream-ramped rib results are in agreement with the test

results. The downstream-ramped numerical results, however,

show a slight increase in heat transfer coefficients compared

with the square ribs. This behavior was observed regard-

less of the turbulence model employed in our CFD analyses.

Given that the pressure drop along the channel for the ramped

ribs were in agreement with the test results, it is speculated

that numerical analyses for the downstream-ramped ribs did

not capture all viscous effects. As the air Reynolds num-

ber increases, there is stronger interaction between the flow

and the ribs. These interactions increase the heat transfer

coefficients on the area in between the two ribs where the

measurement were performed.

Figure 11 shows the variation of the numerical Nusselt

numbers along the channel on the rib-roughened surface for

the square ribs. In general, the Nusselt number on the roof of

7

Fig. 9. CFD contours of streamlines around the ribs for the three rib

geometries at Re=40,000.

Fig. 10. CFD contours of the Nusselt numbers for the three rib ge-

ometries at Re=40,000.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

50

100

150

200

250

300

350

400

450

500

550

60000

50000

40000

30000

20000

10000

z/Dh

Nu

Re FLOW

z/Dh

Front

Top

Back

Floor

TopFloor

Back

Front

Area 1

Area 5Area 4Area 3Area 2

Area 1 Area 2 Area 3 Area 4 Area 5

Fig. 11. Laterally-averaged numerically-obtained Nusselt number

variation along the rib-roughened section for the square ribs.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

50

100

150

200

250

300

350

400

450

500

550

z/Dh

Nu

Re CFD Test

Area­WeightedAverage

FLOW

z/Dh

Front

Top

Back

Floor

TopFloor

Back

Front

600005000040000300002000010000

Area 1 Area 5Area 4Area 3Area 2

Area 1

Area 2 Area 3 Area 4 Area 5

Fig. 12. Numerical (laterally-averaged and area-averaged) and

measured (area-averaged)Nusselt number variation along the rib-

roughened section for the square ribs.

a rib is much higher than that on the other surfaces. The first

rib for all geometries does not benefit from the presence of

any upstream rib on the opposite wall. The second and other

ribs, however, receive the diverted air from the opposite rib-

roughened surface and produce a higher heat transfer coeffi-

cient as seen in Fig. 10. The back surface of the rib has the

lowest heat transfer coefficient due to the formation of a re-

circulating zone behind the rib (Fig. 9). The points indicated

by front, top, back and floor represent the area-averaged Nus-

selt numbers on those areas. A consistent pattern of Nusselt

number variation at different Reynolds numbers is what is

8

Z/Dh

FLOW Front RampTop Floor

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

50

100

150

200

250

300

350

400

450

500

550

z/Dh

Nu

Re CFD Test

Area­WeightedAverage

Front

Top

Floor

Area 1

Ramp

Area 3Area 2 Area 5Area 4

Area 1

Area 4Area 3Area 2 Area 5600005000040000300002000010000

Fig. 13. Numerical (laterally-averaged and area-averaged) and

measured (area-averaged)Nusselt number variation along the rib-

roughened section for the downstream-ramped ribs.

Z/Dh

FLOWBackRamp

TopFloor

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 60

50

100

150

200

250

300

350

400

450

500

550

z/Dh

Nu

Re CFD Test

Area­WeightedAverage

Back

TopFloor

Ramp

Area 1

Area 5Area 3Area 1 Area 4Area 4

Area 5Area 4Area 3Area 2

600005000040000300002000010000

Area 2

Fig. 14. laterally-averaged and area-averaged) and measured

(area-averaged)Nusselt number variation along the rib-roughened

section for the upstream-ramped ribs.

expected.

Figure 12 shows the same numerical results as in Fig.

11 with some new features. The parallel, almost horizontal

lines, are the ”area-weighted average” Nusselt number vari-

ations on the rib-roughed section at different Reynolds num-

bers. The symbols are the measured values corresponding to

the measurement area where the camera is located (Fig. 2).

There is an about 15% difference between the measured and

numerically-obtained Nusselt numbers. The CFD results for

the ramped ribs are depicted in Figs. 13 and 14. Figures

12, 13 and 14 have the same scales so the three rib geome-

tries can be compared. The downstream-ramped ribs show a

higher level of heat transfer coefficients which is not what ex-

pected. Since this rib geometry produced much lower pres-

sure drop, evidenced by Fig. 6, one would expect that the

heat transfer coefficients be lower than those for the square

ribs. Furthermore, the measured values for the downstream-

ramped ribs are lower than those of the square ribs. There-

fore, it is speculated that the CFD model does not capture the

negative effects of the recirculating zone in front of each rib.

The upstream-ramped rib results (Fig. 14), however, are in

line with the measured values as well as confirming the Col-

burn analogy of lower pressure drops corresponding to lower

heat transfer coefficients.

5 Conclusions

Downstream- and upstream-ramped ribs, simulating the

changes in rib shape due to the accumulation of foreign par-

ticles such as sand in front or on the back side of the ribs,

are studied both experimentally and numerically and results

are compared with the square rib results in the presence of

no foreign particles. Major conclusions of this study were:

1) There is a substantial decrease of about 43% in pres-

sure drop (friction factor) for the ramped ribs. The gradual

change of rib-roughened surface geometry, compared to the

square ribs, is responsible for this decrease.

2) Along with the decrease in pressure drop, there is

a deficit of about 28% in heat transfer coefficients for the

ramped ribs.

3) Numerically-obtained results using the realizable k−

ε turbulence model with standard wall functions are in rea-

sonable agreement with the measured results.

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