Proceedings of GPPS Forum 18 Global Power and Propulsion Society

Montreal, 7th-9th May 2018 www.gpps.global

1 *Corresponding author

GPPS-2018-0159

EFFECT OF UNIFORM AND STEPPED PIN-FIN PROFILES ON HEAT TRANSFER AND FRICTIONAL LOSSES IN A NARROW CHANNEL WITH AR 4:1

Kishore Ranganath Ramakrishnan*

Department of Mechanical and Aerospace Engineering North Carolina State University

kramakr4@ncsu.edu Raleigh, NC, USA

Prashant Singh Department of Mechanical and Aerospace Engineering

North Carolina State University psingh23@ncsu.edu

Raleigh, NC, USA

Srinath V Ekkad Department of Mechanical and Aerospace Engineering

North Carolina State University sekkad@ncsu.edu Raleigh, NC, USA

ABSTRACT

Heat transfer and flow characteristics of different

staggered pin-fin array configurations in a channel of aspect

ratio 4:1(W:H) have been numerically studied. Three different

pin-fin shapes, viz. cylinder, diamond and triangle were

modelled. The spanwise and streamwise separation between

consecutive pins was 2.5 times the pin diameter across all

configurations. Stepped cases had three coaxial cylinders,

where the ones on either ends had same cross-sectional area and

height, and the cylinder in middle had a reduced cross-sectional

area and variable height. The ratio of pin diameter of inner part

of stepped geometry to outer part was kept at 0.7. Ratio of

height of stepped part to overall pin height was varied from 0.25

to 0.75. Reynolds number based on channel hydraulic diameter

was varied from 10000 to 50000. Heat transfer results of

uniform pin-fin cases have been compared with stepped cases

using row averaged and array averaged normalized Nusselt

number ratio. Overall, the stepped pin-fins have shown promise

in terms of pumping power recovery compared to uniform pins,

although at a cost of reduction in global heat transfer levels. An

overall increase in the thermal hydraulic performance

improvement of 5-60% was observed across different

investigated configurations.

INTRODUCTION

Department of Energy (USA) roadmap indicates a target of

achieving 65% combined cycle efficiency of power cycles [1].

Turbines which are used in power generation, aircrafts, etc.

have their efficiency limited by the maximum temperature that

the material of the blades and vanes can reach. To

accommodate higher inlet air temperature, sophisticated

internal and external cooling concepts are typically employed

in turbine airfoils. Internal cooling concepts include, rib

turbulators [2-5], dimples, pin-fins [6] and jet impingement [7-

9] etc. Recent studies on rib turbulators were carried out by

Singh et al. [2-5] where the authors investigated different rib

turbulator shapes along with combinations of cylindrical

dimples. The authors demonstrated through experimental and

numerical investigation that rib turbulators and dimples

combined together can provide high thermal hydraulic

performance configurations. Heat load on the external blade

surface depends upon fluid flow over the blade, blade profile,

turbulence levels, passage aerodynamics etc. Typically, the

leading edge regions are equipped with jet impingement, mid-

chord region is equipped with serpentine passages featuring rib

turbulators on two opposite walls, and trailing edge is equipped

with cylindrical pin fins. Present study is focused towards pin-

fin channels, where attempts have been made to increase the

thermal hydraulic performance of the cooling channels by

reducing the cross-sectional area of pins in the central region.

In the past, many researchers have worked on

understanding the effects of varying pin aspect ratio (H/D),

spanwise separation (X/D), streamwise separation (S/D) and

pin shape with varying Reynolds number on heat transfer

enhancement [10-11]. VanFossen [11], Brigham and

VanFossen [12], Metzger et al. [13], Zukauskas [14] have

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reported that pins with lower aspect-ratio have relatively lower

heat transfer enhancement compared to high aspect ratio

channels. Chyu et al. [15] studied heat transfer enhancement on

pin fin wall and endwall. The authors reported that heat transfer

coefficient of pins were 10 to 20% higher than that of endwall.

Chyu studied effects of pin-fin with endwall fillet on heat

transfer enhancement [16] and concluded that pins with

endwall fillet had lower Nusselt number and higher pressure

drop compared to uniform pins. Siw et al. [17] carried out

numerical study by varying spanwise and streamwise distance

between consecutive pins. They observed an increasing trend

in heat transfer enhancement with increasing streamwise

distance for the staggered configuration, whereas the heat

transfer levels were found to be periodic for the inline case.

Most probable reason behind such trend is simply insufficient

channel length for the staggered case to allow for periodicity in

heat transfer. Ostanek and Thole [18] varied aspect ratio,

spanwise and streamwise distance between pins. The aspect

ratio of pin had minimal effect on the overall heat transfer

enhancement. With increasing spanwise distance between pins,

Nusselt number ratio was found to increase. Simoneau and

VanFossen [19] studied the effect of adding rows of pins in

inline and staggered array of pins. One row of pins was

considered as the baseline case, and addition of up to five rows

upstream were studied experimentally. Authors have observed

that adding rows upstream in inline configuration increases the

heat transfer, but the number of rows added had no significant

effect. However, in case of staggered grid there was a

significant effect of additional upstream rows and also the

number of rows added on heat transfer enhancement.

Metzger et al. [20] experimentally investigated the effect

of relative orientation of cylindrical and oblong pin fins with

respect to the mean flow direction. Cylindrical pin orientation

with respect to the mean flow direction did not show noticeable

effect on heat transfer and pressure drop. Oblong pins were

found to have 20% higher heat transfer than corresponding

cylindrical pins. However, their pressure drop was about 100%

more than that of corresponding cylindrical pins. Chyu et al.

[21] studied the effect of pin-fin clearance. They used an inline

cubic pin fin array with ratio of clearance to pin height varying

from 0 to 2. Heat transfer from endwall and smooth wall above

the clearance were found to reduce with increase in clearance.

However, heat transfer from the pins was observed to increase

marginally when the clearance to pin height ratio was 0.25 and

0.5 and then reduce for gaps greater than 1. Wang et al. [22]

compared results from cylindrical, elliptical and tear drop

shaped pins. They found that more streamlined teardrop shaped

pins have lower pressure penalty than circular pins. However,

the heat transfer levels for the teardrop shape was lower than

cylindrical pins by about 25%. Chyu et al. [23] compared the

heat transfer enhancement levels of cubic, circular, and

diamond cross section pins in a staggered array. Diamond pin

array was observed to have the highest heat transfer

enhancement. However, the thermal performance of cylindrical

pins was highest and that of diamond pins was lowest.

Goldstein et al. [24] studied the effect of varying height of

the stepped part in a stepped circular cross section pin fin array.

They observed that stepped pin fins have higher heat transfer

rate and lower pressure loss than the uniform pins of same

dimensions. The longer the stepped portion of the pin, lower

the pressure loss due to reduced flow blockage. Kim and Moon

[25] varied the ratio of height of stepped portion to overall pin

height and ratio of diameter of stepped portion to overall height

of the pin. They used Kriging method to find the objective

function values at optimum design parameters. Numerical

simulation results were evaluated against the results produced

by the optimization technique. The stepped pin fins were

observed to produce multiple strong vortices which move

downstream to enhance turbulent heat transfer, thus yielding

higher thermal performance compared to uniform pins.

In this current work, an attempt is made to numerically

study the heat transfer enhancement by varying the ratio of

height of the stepped part of the pin fin to its overall height as

0.25, 0.5, and 0.75, whilst keeping the ratio of characteristic

length of stepped part to uniform part a constant 0.7. Three

different pin-fin shapes, viz. cylinder, diamond and triangle,

have been modeled. Detailed flow physics has been analyzed to

understand the heat and fluid flow characteristics in the novel

configurations proposed in this study.

NUMERICAL SETUP

This section describes the geometry of fluid domain

simulated, boundary conditions, solver setup and mesh.

Description of fluid domain

Figure 1 shows the top view of baseline uniform case for

14 row staggered array of cylinder, diamond and triangular

pins. The height of the channel and each pin are 9.525 mm.

Characteristic length on the uniform portion of pin fin was 7.62

mm. Spanwise (S) and streamwise (X) spacing are 2.5 times the

pin characteristic length across all configurations. Figure 2

shows the cross sectional view of uniform pin fin and stepped

pin fin geometries. Characteristic length of a given pin fin was

calculated using equation 1. Across all stepped pin fin cases,

the characteristic length of the reduced portion was kept

constant at 0.7 times that of uniform pin fin. The ratio of height

of the stepped part to the total pin height was varied as 0.25,

0.5, and 0.75.

𝐷 =𝐴𝑝

𝑃 (1)

Boundary conditions and solver settings

Boundary nomenclature for the fluid domain is shown in

Fig. 3. Velocity flow inlet was specified using velocity

calculated based on Reynolds number (𝑅𝑒 = 𝑢𝑖𝑛𝐷ℎ 𝜈⁄ ), and

inlet temperature of air was kept constant at 275K. Outlet was

set to zero gauge pressure. At the channel inlet, turbulence

intensity was set to 5% and length scale as 10% of channel

3

hydraulic diameter. To reduce computational cost, only one-

half of the fluid domain was simulated with a symmetry

boundary condition. Constant heat flux 3000 𝑊/𝑚2 boundary

condition was provided on the bottom wall, top wall and pin-

fin walls. All other surfaces were set to adiabatic and no-slip

boundary condition was provided for fluid flow. An entry

length of 20 times channel hydraulic diameter was provided for

flow development and an exit length was provided to avoid

back pressure effects (reversed flow) on heat transfer.

Figure 1: Base case pin array geometry

Steady state simulations were carried out using ANSYS

Fluent solver. Reynolds-Averaged Navier-Stokes (RANS)

equations were solved using realizable k-ε model with

enhanced wall treatment to resolve the near-wall flow. The

convergence criteria for continuity, momentum and turbulence

equation parameters was set at 10-4, and 10-6 for energy

equation.

Figure 2: Uniform and stepped pin-fin geometry of (a) cylindrical pins, (b) diamond pins and (c)

triangular pins Meshing and Grid independence

Meshing was done using the ANSYS Workbench’s inbuilt

meshing module for Fluent. The fluid domain was discretized

using unstructured mesh, which is a hybrid of tetrahedrons,

hexahedrons, and prism layers. It was ensured that the wall y+

was less than 1, which was one of the requirements for proper

implementation of the realizable k-epsilon turbulence model.

For grid independence studies, three different mesh schemes

were simulated for uniform cylinder pin array, which resulted

in a total of 7M, 12M and 14M elements. The value of

normalized Nusselt number from coarse to fine mesh varied by

about 2.5%. In order to maintain a balance between accuracy

and computational cost, the mesh with 12M elements has been

chosen for other numerical simulations.

Figure 3: Fluid domain boundary nomenclature

Data Reduction

Heat transfer coefficient at endwall was calculated using

Eq. 2. The endwall temperature was computed through

numerical calculations. Since a constant heat flux was provided

on the endwalls and on the pins, the bulk fluid temperature

increased in the streamwise direction. In order to account for

streamwise variation in bulk fluid temperature, a total of 11

planes were drawn orthogonal to bulk flow, at equal spacing.

Mass-weighted average temperature (bulk fluid temperature)

was calculated at each plane and local variation of bulk fluid

temperature was then determined from the established

relationship. In this paper, heat transfer coefficient was

normalized with Dittus-Boelter correlation for developed

turbulent flow in circular duct. The normalized Nusselt number

has been shown in Eq. 3.

ℎ(𝑥, 𝑦) = 𝑞"

(𝑇𝑏𝑜𝑡𝑡𝑜𝑚(𝑥,𝑦)− 𝑇𝑏𝑢𝑙𝑘(𝑥)) (2)

𝑁𝑢(𝑥,𝑦)

𝑁𝑢𝑜=

1

0.023𝑅𝑒0.8𝑃𝑟0.4

ℎ(𝑥,𝑦)𝐷ℎ

𝑘 (3)

�̇� =𝜇𝑅𝑒𝐴∆𝑃

𝜌𝐷ℎ (4)

Further, the pumping power was calculated from Eq. 4.

RESULTS AND DISCUSSION

Numerically obtained heat transfer results were validated

against results of Goldstein et al. [24]. Goldstein et al. used a

10 row pin fin array with a pin diameter of 13.34mm, aspect

ratio of 2, and streamwise and spanwise distance of 2.5 times

the pin diameter. Fig. 4 shows the comparison of the

experimental and present numerical results for Re = 10000. It

is observed that the numerically predicted row-averaged

Nusselt numbers were about 8% lower than experimental

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results obtained by Goldstein et al. [24], which is an acceptable

deviation considering the limitations of chosen turbulence

model, which cannot capture fine details pertaining to fluid

dynamics which is not isotropic in nature.

Detailed normalized Nusselt number contours of all three

uniform pin fin shapes for Reynolds number of 10000 is shown

in Fig. 5.

Figure 4: Validation of numerically predicted heat transfer

Figure 5: Normalized Nusselt number contours for Re = 10000 (a) Cylinder, (b) Diamond and (c) Triangle

pin fins.

The basic heat transfer enhancement mechanism of

circular pin-fins is by flow stagnation at the leading edge and

the increase in near-wall turbulent kinetic energy leading to

enhancement in near wall-shear stress around the leading edge

of the cylindrical pin. Further, post-interaction with the leading

edge, the vortex-shedding happens which is also transported

towards the north-east (N-E) and south-east (S-E) directions

(flow oriented along west-to-east). The trailing edge region of

circular pin-fins has low levels of heat transfer due to flow

separation leading to counter rotating vortex pair. This

recirculating fluid leads to reduction in cooling potential and

reduction in near-wall turbulent kinetic energy.

For the diamond pins also, the dominant mechanism of

heat transfer is due to flow stagnation and transport in thus-

induced vortices due to flow stagnation and sharp corners of

pins, along the N-E and S-E directions. The vorticity strength

of diamond pins is expected to be higher compared to

cylindrical pins, simply because of the sharp profiles. However,

this phenomenon will have a direct effect on increase in

pumping power for diamond pins (discussed and presented

later). The diamond pins, owing to their shape, resulted in a

wider spread of low heat transfer region downstream of the

pins. A pair of counter-rotating vortex in a plane parallel to bulk

flow has been observed, which gains a more defined shape as it

gets transported with the bulk flow after its origin around the

north sharp end where it separates from the pin. The separated

flow eventually joins at a further downstream location,

resulting in enhancement in convective heat transfer coefficient

due to increase in local coolant velocity. This merged coolant

stream further interacts with a downstream pin, and this process

continues and repeats itself as the flow becomes periodic.

Figure 6: Velocity vectors in plane perpendicular

to bulk fluid flow at Re = 25000 (a) 0.5 times pin

characteristic length upstream of cylindrical pin, (b)

pin centre and (c) 0.5 times pin characteristic length

downstream of cylindrical pin

The heat transfer enhancement mechanism at the leading

edge of the triangular pin is also similar to that of the diamond

pin. The reduced heat transfer region in triangle pin case occurs

immediate downstream of the pin. However, the separation

region in the triangle pin case was relatively smaller compared

to the diamond pins. The stepped case detailed Nusselt number

ratios have not been shown for brevity, however, the reader is

informed that the trends were very similar to the uniform cases.

The heat transfer mechanism of different pin-shapes in

stepped and uniform cases is further analysed through Figs. 6,

7 and 8. Figures 6 through 8 show the velocity magnitude

5

contour superimposed by velocity vectors at three orthogonal

planes encompassing a total streamwise length of one pin

diameter. The precursor effects of the downstream pin were

realized in the orthogonal plane 0.5D upstream of the pin,

where the velocity vectors were found to travel outwards

towards the blocked wall and the neighbouring pin. As the flow

reaches the pin centreline, the velocity magnitudes increase due

to reduced flow area and the vectors still travelling away from

the pin – this is the juncture where flow separation takes place.

The flow after passing the pin, results in velocity vectors

traveling from outwards to inwards and a separation region is

identified by low velocity regions.

Figure 7: Velocity vectors in plane perpendicular to bulk fluid flow at Re = 25000 (a) 0.5 times pin

characteristic length upstream of diamond pin, (b) pin centre and (c) 0.5 times pin characteristic length

downstream of diamond pin.

Consider Fig. 6(b), for different stepped cylindrical pin

cases, where the topmost figure is for the uniform pin case. The

flow blockage reduced from top to bottom. Hence, the velocity

magnitudes reduce from top to bottom case. Further, at the

downstream plane (Fig. 6c), the separation region was affected

with the blockage ratio, and hence the heat transfer

characteristics of different h/H configurations were different.

For the diamond (Fig. 7) and triangle (Fig. 8) cases, the

trends of planes (a) and (b) were similar to that of cylinder case,

however, for the downstream plane, the coolant still travels

outwards towards the blocked wall and symmetric end, owing

to larger separation region compared to the cylindrical cases.

This large separation region is also reflected in planes in Figs.

6 and 7 (c). Compared to cylindrical case, the turbulent

transport mechanism in the diamond and triangle case was

found to be stronger due to presence of counter-rotating

vortices in the orthogonal planes.

One other mechanism of heat transfer enhancement is due

to enhancement in near-wall turbulent kinetic energy (TKE)

due to turbulence generation because of eddies shed in the wake

region of the pins. This flow phenomenon is captured in a plane

drawn parallel to the bulk flow and very close to the endwall

where heat transfer coefficient was calculated. Figure 9 shows

the normalized TKE superimposed with streamlines for all the

configurations.

Figure 8: Velocity vectors in plane perpendicular to bulk fluid flow at Re = 25000 (a) 0.5 times pin

characteristic length upstream of triangular pin, (b) pin centre and (c) 0.5 times pin characteristic length

downstream of triangular pin.

For the cylindrical case, the separation region downstream

of the pin resulted in reduction in near-wall TKE and hence

lower heat transfer. However, for the h/H = 0.25 case, this

recirculation region was reduced and immediate merging of

two fluid streams was observed, as a result of which, the heat

transfer levels of h/H = 0.25 case had higher heat transfer

compared to the uniform case. Compared to the cylinder pin,

the near wall TKE for the diamond and triangle pins was

significantly higher, owing to higher heat transfer levels on

both local (upstream of pins) and global scale. However, the

separation region for diamond and triangle cases was larger

compared to a smoother cylindrical profile.

Row-wise averaged and globally averaged Nusselt number ratio (𝑵𝒖 𝑵𝒖𝟎⁄ )

The row wise averaged normalized Nusselt numbers in

Fig. 10 was obtained by averaging the value over a surface

extending 0.5 times the pin characteristic length upstream and

downstream of each row of pins. As seen in the literature, row

averaged normalized Nusselt number reaches a maximum and

then is periodic for the remaining rows in case of cylindrical

pins.

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Figure 9: Normalized Turbulent Kinect Energy (TKE) in plane parallel to bulk fluid flow at Re = 25000 (a) uniform cylindrical pin and all three stepped cases, (b) uniform diamond pin and all

three stepped cases, and (c) uniform triangular pin and all three stepped cases

A similar trend was observed for the other two pin

geometries and for all their stepped cases as well. The row

averaged normalized Nusselt number decreased with increasing

Reynolds number – a trend seen in many other similar studies

on turbulent heat transfer. Fig. 10 (a) shows the trend

comparing uniform and stepped cylinders for all Reynolds

numbers. It can be observed that stepped cylinder h/H = 0.25

exhibits better heat transfer enhancement than the baseline

uniform cylinder case. With increasing Reynolds number, the

h/H = 0.25 showed increased benefits over the uniform

cylindrical pin. Stepped cylinder h/H = 0.50 is observed to have

a higher heat transfer enhancement than uniform cylinder at Re

= 50000. Whereas, stepped cylinder h/H = 0.75 approached the

value of uniform cylinder with increasing Reynolds number.

Stepped diamond h/H = 0.25 had higher heat transfer

enhancement compared to uniform diamond pins at Re =

25000, however for h/H = 0.5 and 0.75 cases, the uniform pin

was better than the stepped cases. Stepped diamond h/H = 0.50

and h/H = 0.75 was observed to reach similar level of heat

transfer enhancement as h/H = 0.25 case at higher Reynolds

numbers.

All the stepped triangle cases had lower heat transfer

enhancement compared to uniform triangular pin fin case for

investigated range of Reynolds numbers studied. Stepped

triangle h/H = 0.25 had the best heat transfer among the three

stepped triangle cases studied.

Pumping power requirements

Since the pin fins create an obstruction to the flow of fluid

through the channel, there is a pressure drop across each row of

pin fins.

Fig. 11 and Fig. 12 show the variation of globally averaged

Nusselt number ratio with pumping power. The pumping power

was calculated using Eq. 4. Pressure drop and array averaged

normalized Nusselt numbers were calculated across the rows

where heat transfer was observed to be periodic in nature. All

the stepped cases had lower pressure drop in comparison to

respective uniform pin fin case. This can be attributed to the

fact that area for obstruction to flow reduces for stepped pin

fins. The development of high performance cooling concepts is

aimed towards achieving higher heat transfer enhancement at

relatively lower enhancement in pumping power requirements.

Hence, the concepts which have high thermal hydraulic

performance, should lie in top-left region of the plots presented

in Fig. 11. It should be noted that the stepped cases lie on the

left side of their respective uniform cases, which is indicative

of higher thermal-hydraulic performance given the fact that the

loss in globally averaged heat transfer levels (if applicable) was

not substantial and the reduction in pumping power for stepped

cases was significant.

For more clarity, Fig. 12 shows the variation of relative

increase or decrease in Nusselt number ratio with relative

change in pumping power. Heat transfer levels for the h/H =

0.25 case for cylindrical pin-fins was slightly higher than the

corresponding uniform case. Moreover, the pumping power for

the h/H = 0.25 case was lower than the uniform case. These two

facts combined together results in increased thermal hydraulic

performance of the h/H = 0.25 case of cylindrical pins.

7

Figure 10: Row averaged normalized Nusselt number (a) uniform and stepped cylinder, (b) uniform and

stepped diamond and (c) uniform and stepped triangle.

The stepped cylinder cases had a maximum of 61%

reduction in pumping power requirement than uniform cylinder

case. Stepped diamond and stepped triangle pin fins had a

maximum reduction of 55% and 87% in pumping power,

respectively. Comparing uniform and stepped diamond and

triangle cases at Re = 10000, only stepped triangle h/H = 0.75

case had lower pumping power required to push the fluid

through it than all diamond pin fin cases. For higher Reynolds

numbers, more stepped triangle cases had lower pumping

power required compared to all diamond cases. The array

averaged normalized Nusselt number reduces with increasing

Reynolds number for cylindrical pins as seen in Fig. 13.

Figure 14 shows the variation of normalized Thermal

hydraulic performance (Eq. 5) with Reynolds number.

Stepped triangular pin fin h/H = 0.25 case at Reynolds

number of 50000 showed reduction in overall performance

compared to uniform triangle pin fin case at the same Reynolds

number. All other stepped cases had higher normalized

Thermal Hydraulic performance. Stepped triangular pin h/H =

0.75 case at Reynolds number 10000 showed an increase of

62% in overall performance over baseline case and is observed

to be the highest.

CONCLUSIONS Present study reports novel configurations of stepped and

uniform pin fins. Three different pin-fin shapes viz. cylinder,

diamond and triangle, have been studied. The pin fins were

arranged in staggered form in a channel of AR 4:1, which is

typical of the cooling channels in the trailing edge region of gas

8

Figure 11: Array averaged normalized Nusselt number versus pumping power for (a) Re = 10000, (b) Re =

25000 and (c) Re = 50000

Figure 12: Fractional improvement of heat

transfer enhancement and pumping power over baseline case

turbine blades. Three stepped cases with h/H ratios varying

from 0.25 to 0.75 have been simulated for Reynolds number

ranging from 10000 to 50000. The baseline cases for respective

pin-fin shapes was their corresponding uniform pin shapes.

Figure 13: Array averaged normalized Nusselt number at various Reynolds numbers

(𝑇𝐻𝑃)𝑆

(𝑇𝐻𝑃)𝑈=

𝑁𝑢𝑆𝑡𝑒𝑝𝑝𝑒𝑑

𝑁𝑢𝑈𝑛𝑖𝑓𝑜𝑟𝑚

(�̇�𝑠𝑡𝑒𝑝𝑝𝑒𝑑

�̇�𝑢𝑛𝑖𝑓𝑜𝑟𝑚)

1 3⁄ (5)

Figure 14: Comparison of fractional increase in overall performance of stepped pin fins over

baseline cases For the cylindrical pins, it was observed that h/H = 0.25

case resulted in both enhancement in heat transfer and reduction

in pumping power compared to the corresponding uniform pin.

However, for most of the cases, it was found that the heat

transfer levels were slightly lower than the baseline cases of

uniform pins. Due to reduction in blockage area in the stepped

cases, the pumping power requirements were significantly

lower. Above two facts combined together yielded in overall

higher thermal hydraulic performance of the stepped pin cases.

This is first study of its kind to look into the effects of reduced

flow blockage on heat transfer and pumping power for different

pin shapes. Future study will be focused on evaluation of the

new configurations in conjugate heat transfer studies.

NOMENCLATURE A inlet cross section area (m2)

𝐴𝑝 pin cross section area (m2)

9

D pin characteristic length (m)

𝐷ℎ channel hydraulic diameter (m)

h heat transfer coefficient (W/m2K)

ℎ̃ height of stepped portion of pin-fin (m)

H height of the channel (m)

K conductivity of coolant fluid (W/m-K)

Nu array averaged Nusselt number

𝑁𝑢0 Nusselt number from Dittus-Boelter equation

𝑁𝑢′ ((𝑁𝑢 𝑁𝑢0⁄ )𝑆 − (𝑁𝑢 𝑁𝑢0⁄ )𝑈) (𝑁𝑢 𝑁𝑢0⁄ )𝑈⁄ P perimeter of pin cross section (m)

Pr Prandtl number of coolant fluid

ΔP pressure drop (Pa)

𝑞" Heat flux (W/m2)

Re Reynolds number, 𝑢𝑖𝑛𝐷ℎ 𝜈⁄

S spanwise spacing (m)

THP Thermal hydraulic performance

𝑇𝑏𝑜𝑡𝑡𝑜𝑚 Temperature of endwall (K)

𝑇𝑏𝑢𝑙𝑘 Temperature of bulk fluid (K)

𝑢𝑖𝑛 Bulk flow velocity of coolant fluid (m/s)

W Width of the channel (m)

�̇� Pumping power (W)

W′ (�̇�𝑆 − �̇�𝑈) �̇�𝑈⁄

x streamwise coordinate (m)

X streamwise spacing (m)

y spanwise coordinate (m)

Subscripts

S stepped

U uniform

Greek symbols

ν Kinematic viscosity of coolant fluid (m2/s)

ρ Density of coolant fluid (kg/m3)

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