CHT/CFD Predictions of Impingement Cooling with Four Sided Flow Exit

CHT/CFD Predictions of Impingement Cooling with Four Sided Flow Exit

Abubakar M. El-Jummah, Gordon E. Andrews and John E.J. Staggs

Energy Research Institute School of Chemical and Process Engineering

University of Leeds Leeds LS2 9JT, UK

ABSTRACT Impingement/effusion cooling has no cross-flow in the

impingement gap if all the coolant flow through the

impingement wall passes through the effusion wall. In this

investigation, the impingement part of the

impingement/effusion cooling was investigated by

minimising the cross-flow using a four sided exit

impingement cooling geometry. The impingement

geometry investigated was a square array of 10 by 10

impingement holes with a pitch to diameter, X/D, of 11,

hole density, n, of 4306m-2

, and gap to diameter ratio, Z/D,

of 7.25 for coolant mass flux G of 0.2 - 1.1 kg/sm2bar. The

impingement target and jet walls were modelled as

Nimonic-75 as used in the experimental work used for

validation of the computational methods. Conjugate heat

transfer (CHT) computational fluid dynamics (CFD) was

used with ANSYS Fluent code. The measured impingement

target wall pressure loss ∆P/P% and target wall surface

averaged heat transfer coefficient together with the heat

transfer to the impingement jet wall were all predicted in

agreement with the measurements, within the measured

error bars. The predicted surface distributions of Nu and

turbulent kinetic energy (TKE) were compared with

predictions for impingement single sided exit flow and the

impingement/effusion approach (target) walls. This showed

that the reduced crossflow with the four sided exit gave

higher surface averaged heat transfer. However, comparison

with the impingement/effusion wall heat transfer, for the

same impingement wall geometry, showed that the removal

of coolant through the effusion wall reduced the

recirculating flow in the impingement gap and this reduced

the heat transfer to the impingement jet wall, but increased it

to the target effusion wall.

INTRODUCTION Impingement/effusion heat transfer is used in both gas

turbine (GT) combustor and turbine blade cooling

applications[1-6]. In combustor impingement/effusion wall

cooling the minimum mass flux, G kg/sm2bar, is desired that

will adequately cool the combustor wall. This is because

this effusion cooling air is not availabe for lean combustion

and this means that the lean combustion zone operates richer

at higher temperature and this increases NOx emissions [7].

For turbine blades, effusion film cooling air mass flux needs

to be minimised from a cycle thermal efficiency viewpoint.

Thus for both combustor and turbine blade wall cooling the

use of effusion and impingement/effusion cooling requires

low coolant mass flow rates, G. This is the application of the

present work and the overall surface impingement cooling

was investigated at low G, which was varied from 0.2 – 1.1

kg/sm2bar. Although the present work only investigated

impingement cooling, the aim was to determine the

impingement cooling under the low G circumstances that

apply in impingement/effusion cooling. In this application,

the impingement jet wall has the bulk of the combustor

pressure loss, which combined with the low G requires a

high impingement X/D such as the 11/1 used in the present

work.

In previous CHT/CFD work on impingement cooling

with a single sided exit the authors [2-4] have investigated

high G of about 2 kg/sm2bar, which is representative of all

the combustion air being used for regenerative impingement

combustor wall cooling, which enables film cooling air to be

reduced to zero, as first suggested by Abdul Hussain and

Andrews [5] and Andrews et al. [8]. The outlet from the

impingement gap flows into the low NOx flame stabiliser.

This single sided exit geometry gives the maximum cross-

flow in the impingement gap. This high G impingement

combustor wall cooling application has to occur with a low

pressure loss and most of the available pressure loss has to

be retained for flame stabilisation and fuel and air mixing. A

high G low pressure loss application requires a low X/D

impingement geometry [2]. The first application of high G

low ∆P/P regenerative cooling for low NOx combustors

was that of Huitenga and Norster [9].

Impingement/effusion cooling has no impingement air

cross-flow in the gap, as all the impingement air flows out of

the effusion holes. The nearest impingement geometry to

this, without the effusion jets present, is for the impingement

gap to have four sided exits [6, 10-14], so that cross-flow is

minimised. From the centre hole to the gap exit edge, the

number of upstream rows of holes N in the present work

was 5, compared with 10 for the equivalent single sided exit

case. This automatically reduces the influence of cross-flow

in the impingement gap. Figure 1 was the geometry

investigated in the present work using flat surface heat

transfer, which approximates to a large diameter combustor

surface with low curvature [14-18]. This flat surface

approximation is also often used in turbine blade cooling for

the mid-chord region [18, 19].

The minimum cross-flow effect for the four sided

impingement jet flow exit geometry shown in Figure 1 [6,

11, 13, 20-22] has been shown experimentally to be

1 Copyright © 2015 by ASME

Proceedings of ASME Turbo Expo 2015: Turbine Technical Conference and Exposition GT2015

June 15 – 19, 2015, Montréal, Canada

GT2015-42256

Downloaded From: http://turbomachinery.asmedigitalcollection.asme.org/ on 08/21/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-use

(a) Impingement jet wall (b) Target wall

Figure 3 Experimental test walls with range of thermocouples location [2, 11]

compatable with the impingement heat transfer in

impingement/effusion cooling [8, 22, 23]. Abdul Husain et

al. [24] have reported overall cooling effectiveness

experimental results for impingement/effusion cooling using

a hot wall test rig.

Electrically heated metal wall impingement experimental

rigs [13, 25-27], as shown in Figure 2 [1-5, 11] have been

used to determine the surface averaged heat transfer

coefficient using the lumped capacitance experimental

method with a transient cooling technique. These

measurements are used to validate the present CHT/CFD

predictions. Similar work has been carried out with

adiabatic walls [28-30].

The present CHT CFD investigates the influence of mass

flux G for a fixed X/D and Z/D of four sided impingement

jet exit flow that has been investigated experimentally [10,

11, 22] using Figure 2 test rig and flat test walls of Figure 3.

For single sided impingement flow exit, the optimum

number of impingement holes was shown to be n of

4306/m2, which is 10 rows of square array holes. For

impingement/effusion cooling a low coolant mass flux is

required, as explained above and the optimum geometry will

have the main pressure loss at the impingement jet wall, as

this gives the highest impingement jet velocities. The

effusion wall will have a low pressure loss with low jet

velocities or low blowing ratio M. This requires, for the

same n or pitch X, larger diameter effusion holes than

impingement holes or large X/D for the impingement jet

wall and low X/D for the effusion wall.

The impingement wall X/D was 11.04 in the present

work and for a design G of 0.4 kg/sm2bar, this gives a 3%

pressure loss, which is typical of combustor wall pressure

loss. The authors [2] have previously predicted the effect of

the impingement X/D for single sided exit for a high G of

1.9 kg/sm2bar. This showed the large increase in

impingement heat transfer that occurred as X/D was

increased for the same G. The range of G in the present

work was varied from 0.2 - 1.1 kg/sm2bar, which also varied

Figure 1 Four sided impingement jet flow exit geometry [6]

Figure 2 Four sided impingement gap Z exit flow

experimental test rig [10, 11]



the jet hole Reynolds number Re from 2.1 × 103 - 13.1 ×

103, this corresponds to the range of G in the experimental

data best used for comparison [6, 11-13].

A constant impingement gap Z of 10 mm was used as

this is a practical Z for combustor wall impingement

cooling. At the X/D of 11.04 this gives a Z/D of 7.25.

Andrews et al. [6] have shown that for an X/D of 11 the

influence of Z/D on the surface averaged heat transfer was

small over the Z/D range of 2 - 8. A feature of impingement

heat transfer that is rarely investigated is that the

impingement jet on a hot wall is heated by the surface heat

transfer and this heated jet reflects in the gap and the reverse

flow [26] impinges on the impingement jet surface and heats

it. However, the convected heat transfer to the impingement

jet surface has had few measurements, apart from that of

Andrews et al. [11, 13, 24, 31]. This work expressed the

temperature of the impingement jet surface as a dimensional

ratio to the impingement jet wall to coolant temperature

difference and this was predicted in the present work. This

impingement jet wall heat transfer was predicted for a single

sided exit flow [2-5], but the experimental results used for

comparison did not report this heat transfer, although good

agreement with the target wall surface average heat transfer

was achieved. The present work gives the first comparison

of measured and predicted normalized temperature showing

the effect of the reverse flow impingement jet wall surface

heat transfer.

EXPERIMENTAL GEOMETRIES MODELLED

The impingement wall porosity A (hole area/X2), is

related to X/D by Equation 1. The impingement jet array

coolant mass flux G and the impingement jet wall pressure

loss are related to the impingement X/D by Equation 2 [22,

23] and the impingement jet Re is given by Equation 3 and

the impingement jet velocity by Equation 4 [11]. The

crossflow velocity, Uc, for single sided impingement gap

exit flow is given by Equation 5 and its ratio to the

impingement jet velocity in Equation 6. Experimentally, the

measured pressure loss was the difference in the air plenum

static pressure from the ambient pressure. This was

corrected for the duct exit static pressure loss to give the

static pressure from the plenum to the wall static pressure of

the impingement gap discharge duct, which was the

predicted pressure loss.

)1(4

5.0

AD

X

)2(2

5.0

P

P

RTAC

RT

AVG d

j

)3(4

Re

5.0

An

G

)4(24

5.02

P

PRTC

D

XG

A

GV dj

The crossflow velocity at the impingement gap exit for

single sided exit, Uc, is fixed by G and Z, as shown in Eq. 5.

However, as the impingement jet velocity increases with

X/D then the ratio of this jet velocity to the crossflow

velocity, Vj/Uc, increases as shown by Equation 6, which

assumes that the two flow densities are the same.

ZXnGU c (5)

NAX

Z

X

Z

D

X

NU

V

c

j

241

(6)

The specific impingement geometries modelled for all G

values in the present work, are the same as that used

experimentally [10, 31] and is given in Table 1. This

geometry is a practical actual size combustor cooling

geometry and is not a scaled up model of the geometry as is

often used. The holes were manufactured using spark

erosion and thus had a practical internal surface roughness.

The flow conditions modelled were also the same as those

used experimentally, but with no specific surface roughness

procedure other than the use of wall functions.

Table 1 Geometrical Parameters

Table 2 Computational Flow Conditions

G

kg/sm2bar

Vj

(m/s)

Reh

(ρVjD/μ)

Predicted

∆P/P (%)

Measured

ΔP/P %

0.20 25.34 2380 0.74 0.63 0.30 38.02 3570 1.62 1.42 0.50 63.32 5940 4.30 3.94

0.63 79.77 7490 6.58 6.23

0.77 97.61 9160 11.71 9.35

1.10 139.36 13080 17.62 19.08

The flow conditions are summarised in Table 2, which also

gives the experimentally measured pressure loss. The range

of jets Re are all higher than the critical Re for turbulent

flow limit of > 2300. However, the jet turbulence in the

impingement jet hole that is controlled by the hole Re, is

largely irrelevant in the heat transfer as it is the impingement

on the target surface that creates the intense turbulence that

controls the heat transfer [17, 32].

The use of realistic GT combustor jet hole sizes [22] in

the present work ensures that the length scale of turbulence

is correctly modelled, as this is set by the hole diameter.

The common practice of investigating impingement heat

transfer is of the order of 10 times the jet hole size, so that

spatial resolution of the heat transfer can be achieved. This

has a problem of increased turbulence length scale, which

may influence the heat transfer. In engines impingement Re

are higher than in the present work due to the high pressure

which increases the flow density, but does not change the jet

velocity. The turbulence on the impingement target wall is

considered to be more realistically generated using actual

scale impingement geometries than in scaled up geometries.

Cd 0.80 [11, 32]

D (mm) 1.38

X (mm)

Z (mm)

15.24

10.00

L (mm)

L/D

6.35

4.60

X/D 11.04

Z/D

X/Z

7.25

1.52

A% 0.64

n ( m-2

) 4306

Array 10 × 10



However, it does mean that experimental spatial resolution

of heat transfer is lost and for metal surfaces gives only the

locally surface average heat transfer, which was the data

used to validate the computations.

The experimental results for four sided exit impingement

heat transfer that are modelled here used the lumped

capacity method [1-5] in determining the surface averaged

heat transfer coefficient. The target wall was 6.3 mm thick

and was heated to about 353 K. The heat was removed and

the impingement flow established. There was an array of

imbedded thermocouples 25.4 mm apart in the test walls as

Figure 3 shows, where transient cooling of the target wall by

the impingement jet flow was recorded [10-12, 22, 31]. The

time constant of the cooling was determined and from this

the local surface average HTC h was determined for each

thermocouple location using Equation 7, hence the Nu in

Equation 8 could be determined. An additional experimental

technique that was used was to operate the test rig of Figure

2 at steady state with an insulated heated target wall. A

steady state heat balance then determined the locally average

target surface temperature from which h could be

determined. Overall the maximum error for h was 10% and

1% for the test wall diameter [22], which gives an 11% Nu

uncertainty. This was the technique used to measure the

surface average temperature of the impingement jet wall and

these measurements are directly predicted in this work.

)7(

TT

qh

s

Not to scale and all dimensions are in mm as shown in Table 1

Figure 4 Symmetrical elements of the model geometry

Figure 5 Model geometry computational grids

)8(fk

hDNu

)9(2X

hDLhX



Table 3 Grid Size for Wall First Cell Layer y+ of ~ 35

The CHT CFD predictions of these results used the

steady state approach to determine the heat transfer and

imposed a constant temperature of 353 K on the hot side of

the Nimonic-75 wall of 11.7 W/m K thermal conductivity.

The technique for determining h and Nu has been previously

shown to agree with experimental data for single sided exit

impingement heat transfer [2-4]. The hole surface HTC hx

given by Equation 9, was also predicted as there are

established short hole heat transfer data that this can be

compared with [33]. This gives a precise average h in the

hole cross sectional area over X2 region, as the h in Equation

4 is for the entire test walls area inputs in the CFD.

Xing and Weigand [21] used the liquid crystals

techniques to measure the surface distribution of h. Obot

and Trabold [6] used a segmented copper target plate to

determine the locally averaged h. Hollworth and Berry [13]

used a continuous copper plate, similar to the experiments

that are modelled in the present work, apart from the

difference in the thermal conductivity of the walls.

COMPUTATIONAL METHODS

Grid Model Geometry

Application of symmetry at the jet to jet centre line fixed

at 76.2mm (L/2) or quarter geometry of 5 × 5 jet holes for

the 152.4 square arrays of 10 × 10 holes was used to model

the present grid geometry. Figure 4 show the computational

domain that was used and the grid geometry used is shown

in Figure 5 that was generated from ANSYS ICEM meshing

tool. El-Jummah et al. [2-4] applied similar symmetrical

procedures fixed at the centreline of the holes and between

row of holes that gives only one row of 10 half holes for the

single sided exit impingement heat transfer predictions,

which was computationally simpler than the present larger

cell size used for the four sided exit case. This CHT CFD

geometry had to be modelled for 25 complete holes, as

Figure 4 shows, which was based on the four sided exit flow

used.

The computational domain and grid model geometry,

shown in Figure 4 and 5 respectively are designed using

representative parameters shown in Table 1. The cell size 'ξ'

of each hole and for the range of all the G values modelled,

was kept constant with 21 planes/hole (~ 120 cells/plane),

with similar number of planes for the test walls. But the cell

size per plane for each impingement gap varies, as the

Reynolds number Re changes with G, which helps in fixing

the average y+ (= ξUτ/ν) values on the target wall. The grid

cells in the plenum were fixed at 55 planes with boundary

layer cells growth at the approach surface of the

impingement jet wall, which was based on the accelerated

airflow into the impingement holes from the plenum inlet.

The total cell size and the percentage of grids in all the

parts modelled in Figure 5 are shown in Table 3. The total

number of cells in all the grid geometries for the ranged of G

(0.2 - 1.1 kg/sm2bar) geometry modelled, varied from 3.64 -

3.94 million cells. Previous work by the authors [25, 27] for

a sensitivity test, showed that this number of cells were

adequate to resolve any influences in the aerodynamics and

heat transfer in the impingement jet holes and gap, as they

have equal cell height, width and planes at these regions

hence the grid is reliable. These gave a fixed maximum grid

aspect ratio and orthogonal quality of the cells for all the

geometries to be equal to 53.3 and 0.72, respectively.

CFD Simulation

Table 2 shows the computational flow conditions for the

coolant air jet temperature T∞ of 288 K for an air density ρ

of 1.225 kg/m3 with the target hot wall side temperature Tw

of 353 K, whereby the two temperatures were interfaced at

the target surface. The boundary conditions used at the

plenum inlet, impingement gap exit, side walls (plenum, gap

and test walls) and inside test wall surfaces are: the velocity

inlet (= G/ρ), outflow, adiabatic walls (q" = 0) and coupled

thermal conditions, respectively. These CHT CFD

investigations used the standard k - ɛ turbulence model with

the standard wall functions. This computational procedures

have been previously validated [2-4] for the single sided exit

impingement heat transfer.

The first cell size near the target wall was maintained at

a y+ value of ~ 35 as Table 3 shows for all G, which was the

criteria employed in reducing the total number of cells close

to 4.0 × 106 and therefore reducing the computational time

and cost [2, 35]. This computed y+ value is within the

required range (30 < y+ < 300) for the near wall law of the

wall. The convergence criteria were set at 10-4

for

continuity, 10-8

for energy and 10-6

for k, ɛ and momentum

(x, y and z velocities) respectively, as the flow in each flow

direction is completely symmetrical. Transient state

solution was also carried out in order to stabilize the

converged steady state cases for all G, which was for a

calculated flow time ~ 0.04. The initial number of time step

and size used are 3 × 103 and 10

-3 respectively, by using

adaptive method 10-5

time step size was then reached for the

simulated flow time.

COMPUTATIONAL RESULTS

Influence of G on Aerodynamics

The key predicted aerodynamic data for comparison with

experiments was the percentage pressure loss ∆P/P%. Also

predicted, but with no direct experimental validation was the

impingement hole and gap velocity profiles and the

distribution of turbulent kinetic energy TKE [2-4, 27].

However, the latter two parameters were assumed to be

correct if the pressure loss was correctly predicted, as the

origin of the kinetic energy of turbulence is the pressure loss

energy. The predicted and measured influence of G on ∆P/P

are shown in Table 2 and these results are shown as a

function of G in Figure 6(a) and as a function of Re in

Figure 6(b).

Figure 6 (b) also shows a comparison of the pressure loss

for single sided flow exit [2] for the same impingement wall

geometry. This shows that the change from four sided exit

to single sided exit has little effect on the pressure loss. This

is because the main pressure loss is due to the flow through

the holes and there is not a major pressure loss along the

Parts Size

Total cells

Total nodes

3.94 × 106

3.73 × 106

Plenum chamber

Test walls

38.2%

15.7%

Impingement gap 37.2%

Impingement jet holes 8.9%



(a) Four sided exit flow

(b) Comparison with El-jummah et al. [2] CFD predictions

Figure 6 Comparison of predicted and measured ∆P/P

impingement gap caused by the cross-flow. Also shown in

Figure 6 (b) are the ∆P/P predictions [2] at very high G,

where the Re is varied by varying the hole diameter at

constant coolant flow rate. The same computational

procedures as in the present work were used and good

agreement with the experimental results are shown. The

present work has reasonable agreement with the

experimental pressure loss results as shown in Table 2 and

Figure 6 (a). The difference between predicted and

measured ∆P/P varied between 5 and 27%, with the best

agreement was for G = 0.6 - 1.

The measurements in Table 1 are based on the

assumption of constant Cd in Equation 2. However, the

actual experimental results [11, 32] show a dependence of

Cd on Re and at low Re of 4000 was 0.77 and at 2000 was

0.76. For high mass flux at Re > 10,000 compressibility

effects are significant and the Cd falls to 0.76. These changes

in Cd account for most of the differences in the predications

and measurement for low and high G in Figure 6 (a) as a Cd

difference of 0.76 from 0.80 is a 10% difference in pressure

loss. When this is taken into account the agreement between

measurement and predictions is all better than 10%. This

shows that the predictions of the aerodynamics were

reasonable.

Figure 7 (a and b) shows the CFD three-dimensional

(3D) predicted and two-dimensional (2D) experimental [27]

(a) CFD predictions: 3D for G of 0.5kg/sm2bar

(b) Experiment [27]: 2D

Figure 7 Impingement gap jet flow pathlines velocity

velocity pathlines. The interactions of the jets on the target

wall that creates a flow reversal jet flow, on the centreline

between the impingement holes is shown in Figure 7. This

reverse flow takes away heat from the target wall [2] and

recirculates it to heat up the impingement jet wall.

The surface distribution of turbulent kinetic energy

(TKE) for the square arrays of 100 holes and for a G of 0.5

kg/sm2bar is shown in Figure 8. The peak TKE distribution

is centred around the impingement point with low

turbulence elsewhere on the surface. Figure 8 (a) shows that

as the flow moves to the outer regions there is some

evidence of convection of the turbulence in the cross-flow

direction, but this is much lower than for single exit cross-

flow, as Figure 8 (b) shows. The central region is

unaffected by the cross-flow for the central 16 holes, which

is two rows of holes in the cross-flow direction.

The central four holes are compared with the leading

edge four holes for single sided exits in Figure 9, for the

same G of 0.5 kg/sm2bar at the same X/D and Z/D. Figure 9

(a) for the present four sided exits has lower TKE between

the impingement points. This indicates that with single sided

exit the flow for the first row of holes is affected in a way

that increased the turbulence between the impingement

points as the flow has to turn in one direction. This will be

shown later to result in better heat transfer for the single

sided exit.

Figure 9 (c) compares the impingement only predictions

of Figure 9 (a and b) with the equivalent turbulence for

impingement/effusion cooling. This prediction shows that

the surface distribution of turbulence in the inter



Figure 8 Target surface distribution of TKE for G of 0.5

kg/sm2bar at fixed X/D of 11.04 and Z/D of 7.25

Figure 9 Comparison of target surface distribution of TKE

for G of 0.5 kg/sm2bar at X/D of 11.04 and Z/D of 7.25

impingement jet region is enhanced with very little of the

surface having the lowest turbulence level. With

impingement only flow there is a reverse jet flow, as shown

in Figure 7, but this flow is reduced with

impingement/effusion cooling due to the extraction of the

effusion flow at the location of the reverse flow jet. Thus it

forces the impingement flow to remain attached to the

surface with a consequence in the better surface distribution

of turbulence, relative to the impingement only cases.

Surface Distribution of Nusselt Number

The pattern of the predicted surface TKE distribution in

Figure 8 is shown in Figure 10 to be similar for the target

surface distribution of Nusselt number for 0.5 kg/sm2bar.

Figure 10 (a) shows for the four sided exit a minimum

downstream cross-flow influence and Figure 10 (b) shows

that the single sided exit impingement configuration

maximizes the cross-flow influence. Similar predicted

comparisons of TKE and Nu are made in Figures 9 and 11.

Figure 10 Contour of Nusselt number on target surface for

G of 0.5 kg/sm2bar at fixed X/D of 11.04 and Z/D of 7.25

Figure 11 Comparison of target surface distribution of Nu

for G of 0.5 kg/sm2bar, X/D of 11.04 and Z/D of 7.25

Figure 10 shows that the impact of the cross-flow for the

four sided exit is relatively small and is only apparent in the

outer regions. For the central region Figure 11(a) shows that

there is still some distortion of the Nu profiles in the outflow

direction, which is similar to that for the TKE profiles in

Figure 9(a). For single sided exit the Nu profiles for the

second row of holes in Figure 11(b), show a more uniform

distribution and a reduced area of the lowest Nu. For the

impingement/effusion flow, Figure 11(c) shows a much

better surface coverage of high Nu, which was due to the

flow acceleration into the effusion holes, this locally

enhances the cooling in the hole entry region. In all three

cases of Figure 11, the peak impingement Nusselt number is

the same.

The comparison of the predicted surface average NuPr1/3

with surface average experimentally measured NuPr1/3

of

Andrews and Hussain [11] is shown in Figure 12, for the

same geometry that was modelled with an X/D of 11.04.

The ± 11% error for the Nusselt number based on Equation

5 is shown for each data point in Figure 12, which shows



Figure 12 Predicted and measured variation of surface

averaged Nusselt number v. Re for four sided exit

impingement heat transfer

good agreement between the predictions and measurements

mainly within the error bars. There was exact agreement

between prediction and measurement for Re = 2500 and

7500. There was an under prediction of the measurements

by 17% at Re = 3500, 14% at Re = 6000 and 12% at a Re of

9000, 4% over prediction at the highest Re. On average the

predictions were 6.5% lower than the measurements.

Figure 12 also compares the present predictions for four

sided exit impingement heat transfer with other

measurements for similar X/D. The differences are

significant and mainly due to the differences in X/D.

However, the results of Andrews and Hussain [11] showed a

decrease in Nu with increase in X/D. But for the same X/D

with smaller Z/D, the results of Andrews and Hussain [11]

fall in the measured error bars, except for Re of 3600 and

6500 that were slightly below the measurements. Hollworth

and Berry’s [13] results for an X/D of 15 were similar to the

present for a Re of 6500, but their Re exponent was higher.

Obot and Trabold [6] for an X/D of 9 had a similar Nu for

Re = 5000 but a larger increase in Nu with increase in Re.

Influence of G on the Impingement Jet Wall and Target

Surface Average Heat Transfer

Figure 13 shows the surface distribution of h on the

target and inside impingement jet walls for three G values.

This is the first time that heat transfer coefficient to the

impingement jet wall has been predicted and measured.

Figure 13 (ia) shows that at low G there was little surface

coverage of the enhanced impingement heat transfer and

Figure 13 (iia) shows that there were no reflected jets on the

centreline between the holes, giving heat transfer to the

impingement jet wall. However, at higher G the high heat

transfer due to the reflected jets in Figure 13 (iib and c) were

predicted to occur at the midpoint of the four jet holes. This

heat transfer was convected in the direction of the exit flow

as the flow moved to the exit and a cross-flow was

established. Figure 13 (ii) shows that the action of the

crossflow was to deflect the reflected impingement jets on

the jet wall surface diagonally at 45o

to the line of the

impingement holes. This was a feature of the four sided exit

with the flow to the two edges leading to a flow direction of

45o. It was unexpected that this flow direction would be so

(i) Target wall

(ii) Inside impingement jet wall

Figure 13 Impingement jet wall surface distribution of

HTC h for varied G at fixed X/D of 11.04 and Z/D of 7.25

Figure 14 Comparison of predicted target surface average

HTC versus G at X/D of 11.04 and Z/D of 7.25

clearly seen approaching each impingement hole but absent

after the hole. This implies that with four sided exits the

diagonal flow on the jet surfaces was entrained by the jet as

none of this flow appears on the surface after the jet, where

there is a gap of low heat transfer before the next reverse

flow impingement point occurs. Thus interaction of the

reflected flow with the impingement jet flow does not occur

with single sided exits as the crossflow is between the rows

of impingement holes [2-4].

Figure 14 show the predicted surface average h as a

function of G, with three components of the heat transfer

predicted: firstly, the impingement target wall heat transfer;

secondly, the heat transfer due to the reverse flow jets to the

impingement jet wall; thirdly, the heat transfer to the coolant

as it passes through the heated impingement jet wall. The

increase in the heat transfer coefficients with G was



Figure 15 Comparison of the present predictions with

impingement single flow exit and impingement/effusion

predicted target surface average and X2 average HTC h.

predicted to be much greater for the target wall. The reverse

jet heat transfer to the impingement wall was 53% of the

impingement target wall heat transfer at the lowest G and

31% at the highest G. The heating of this surface by the

reverse jet was predicted to be recycled as heat transfer to

the impingement air as it flows through the walls. This

occurred on the hole approach surface and inside the holes

and there was a close balance between the reverse jet heat

transfer and the impingement jet flow heating.

Comparison of Impingement Surface Averaged h for

Different Impingement Cross-flow Configurations

Figure 15 compares the predicted surface averaged h for

different impingement wall configurations. The present

predictions for the four side exit are compared with those for

a single sided exit and for the first two holes, where

crossflow is at a minimum. Finally these three geometries

are compared with predictions for impingement/effusion

cooling for a very similar geometry. Figure 15 shows that

highest h was for impingement/effusion cooling and the

lowest, was the present predictions for four sided exit

impingement heat transfer. The difference in these two was

due to the suction effect of the effusion hole flow on the

impingement jet wall flow. This leads to more surface TKE

and higher surface heat transfer. In between these two was

the surface average heat transfer for the second row of

impingement holes, where the cross-flow effect was not

significant.

The surprising result of the predictions was the higher

surface averaged heat transfer for the single sided flow exit

compared with the four sided exit, where the crossflow

velocities were lower. This should have led to a lower effect

of the crossflow in reducing the heat transfer with distance

along the gap due to the deflection of the reverse flow jets

and convection of surface turbulence by the cross-flow [24,

26, 30]. The crossflow effect of the reverse flow jets was

shown in Figure 13 (ii) to be diagonal and not along the gap

between the rows of jets as for single sided exits. The

impingement jet surface heat transfer was due to the flow of

the reverse flow jet diagonally towards the next

impingement jet where it was entrained, leaving no cooling

downstream of the jet. This mixing of the reverse flow hot

gases with the incoming cold impingement jets did not

Figure 16 Comparison of surface Tz on impingement jet

walls for varied G at fixed X/D of 11.04 and Z/D of 7.25

)10(

TT

TTT

m

IZ

)11(*

TT

TTT

w

happen for single sided exit and the result was reduced heat

transfer due to the impingement jets being hotter at the

surface after entrainment of the hot reverse flow jets.

Heating of the Impingement Jet Wall

Andrews et al. [9], experimentally measured the

impingement jet wall heating using the dimensionless

temperature TZ of Equation 10. In the present work the

dimensionless temperature T* in Equation 11 was also

predicted, which allows the surface distribution of the

impingement jet wall metal temperature to be shown in a

dimensionless form.

The predicted values of TZ for the mean impingement jet

wall temperature are shown in Figure 16 where they are

compared with the experimental measurements [10]. The

results for lower G of 0.2 and 0.45 kg/sm2bar show good

agreement with the experiments, but for G of 0.77 and 1.1

kg/sm2bar the prediction disagrees with the measurement.

For impingement/effusion cooling it is the lower G that is of

interest. It is possible that the experimental test rig was not

as adiabatic as intended, but this would influence all the

measurements. The aerodynamics should be correct as the

predicted and measured pressure loss agree at all G. The

implication of these results is that the peak heat transfer on

the impingement jet wall in Figure 13 (iic) is over predicted.

It is also possible that the disagreement could be due to the

five thermocouples in the impingement jet wall that are not

representative of the mean surface average heat transfer

coefficient. However, the agreement with low G values

would suggest that this is not the problem. Thus there is no

clear explanation for this lack of agreement at high G.

Figure 17 shows the equivalent predictions for the

impingement jet wall as were given in Figure 15 for the

target wall. This shows the predictions for the mean heat

transfer coefficient to the impingement jet wall for the four

sided exit compared with those for a single sided exit. The

single sided exit predictions for the first two rows of holes,



Figure 17 Comparison of the present work with

impingement single flow exit and impingement/effusion

predicted surface average and X2 average HTC h on

impingement jet plate.

where cross-flow is at a minimum, is also shown in

Figure 17. Finally these three geometries are compared with

predictions for impingement/effusion cooling for a very

similar geometry. Figure 17 shows that the predicted

surface average HTC h for the impingement jet wall was

significantly lower for the four sided exit predictions. The

reason for this is as discussed above, the diagonal flow of

the impingement jet wall resulted in entrainment into the

impingement jets of the heated reverse flow jets with a

consequence of reduced cooling of the target surface.

The big difference for the four sided exit was that the

cross-flow number of holes was reduced by a half, but also

the cross-flow area was increased by a factor of 4.

However, as crossflow deteriorates the heat transfer for

single sided exit an increase in the heat transfer with four

sided exit was expected. The authors [27] have shown that

for the single sided exit, the aerodynamics of the cross-flow

displaced the flow towards the impingement jet wall and

increased the heat transfer there [2, 3, 27]. For the four

sided exit these reverse flow jets are displaced by the

crossflow in the diagonal direction on the impingement jet

surface, as shown in Fig. 13 (ii). This leads to the

impingement of this surface flow onto the impingement jets

and entrainment into those jets. The subsequent heating of

these jets reduced the impingement cooling temperature

difference and so reduce the heat transfer.

Figure 17 shows that the highest heat transfer was for the

impingement/effusion geometry, where there is no cross-

flow. With no cross-flow to deflect the impingement jet

reverse flow the greatest impingement heat transfer occurs.

In addition to the impingement cooling there is the enhanced

cooling of the flow acceleration into the effusion holes and

the internal cooling inside the holes.

Figure 18 shows for three values of G the predicted

surface distributions of the dimensionless temperature T* for

the target wall. In Equation 11 for T*, the hot wall side

temperature Tw is 353K and T is the predicted temperature

on either the cooled target wall or the impingement jet wall.

On the target wall of Figure 18 (i) the lower T* is a

consequence of the higher h. These dimensionless

temperature plots in Figure 18 include the uncooled flange

(i) Target surface

(ii) Impingement plate Figure 18 Surface distribution of normalised temperature

T* for varied G at fixed X/D of 11.04 and Z/D of 7.25

Figure 19 Comparison of jet hole centre line contours of

normalised temperature T* for G of 0.5 kg/sm

2bar with

impingement and impingement/effusion cooling geometries.

of the test section, which can be ignored. Figure 18 (i)

shows that the target wall temperature gradients were

significant at high G, but at low G the wall was a fairly

uniform temperature. The extra cooling as G was increased

causes increased thermal gradients. In contrast, the thermal

gradients predicted on the impingement jet wall are shown

in Figure 18 (ii) to be much more uniform for all G. The

cross-flow effect in the exit region can be seen with cooler

walls, especially at low G.

Equation 11 was also used to show the heating of the air

jets and the thermal gradients in the metal walls, as shown in

Figure 19. This clearly shows the heated reversed flow jets

that causes the heat transfer to the impingement jet wall.

The deflection of the reversed flow jets by the cross-flow is

also clear. Better cooling of the target (or effusion) wall in

Figure 19c occurs for the impingement/effusion geometry,



as there was no cross-flow to increase the wall heating, the

mean temperature was lower. Figure 19c shows an absence

of the reverse flow jets with the addition of effusion cooling.

The effusion holes are located where the reverse flow jet

originates and the heated flow is simply an outflow through

the effusion holes rather than reversing and impinging on

the impingement jet wall. This also means that the heated

coolant now flows into the effusion holes and this hotter

effusion film cooling flow will reduce the effusion film

cooling compared with no effusion air heating. The

additional heat transfer in the acceleration of the coolant

flow into the effusion holes plus the heat transfer inside the

holes is the reason that the impingement/effusion

configuration has the highest overall wall heat transfer, as

shown in Figure 17.

Figure 17 also shows the predicted thermal gradients

through the thickness of the wall. These are considerably

increased by the additional heat transfer in this surface in the

impingement/effusion configuration. These thermal

gradients are 10% of the temperature difference through the

6.35mm wall thickness. For a 700K coolant and 1300K gas

side metal temperature the thermal gradient would be 130K

or 20K/mm.

CONCLUSIONS The CHT CFD predictions for four sided exit

impingement heat transfer for G from 0.2 to 1.1 kg/sm2bar at

X/D of 11.04 and Z/D of 7.25 showed good agreement with

the measured surface average Nusselt number. The average

difference of the predictions from the measurements was

6.5% low.

The predictions of the pressure loss also showed good

agreement with the measurements, indicating that the

aerodynamics were correctly predicted.

The predictions showed that there was a reverse flow jet

from the target wall to the impingement jet wall that resulted

in heating of the wall. The predictions of this heating

showed good agreement with measured TZ at lower G, but

not at higher G.

The predictions of the impingement jet wall heat transfer

coefficient showed that it was a significant feature of the

overall impingement heat transfer process.

ACKNOWLEDGEMENTS Abubakar M. El-jummah wishes to acknowledge the

financial support from University of Maiduguri and the

Government of Nigeria. The computational work was

supported by part of an ERSRC grant.

NOMENCLATURE A Impingement hole porosity = (π D

2/4)/X

2

D Impingement air hole diameter, m

Cd Discharge coefficient

G Coolant mass flux, kg/sm2bar

h Heat transfer coefficient (HTC), W/m2K

k Thermal conductivity of fluid, W/mK

L Target wall metal thickness, m

n Number of impingement hole/unit surface area, m-2

N Number of upstream rows of impingement holes

Nu Nusselt Number

ρ Density of air, kg/m3

ΔP Impingement wall pressure loss, Pa

P Coolant supply static pressure (approx. 1bar)

Pr Prandtl number

R Gas constant for air, 287 J/kg.K

Re Impingement hole Reynolds number

T∞ Coolant temperature, 288K

T* Normalized mean temperature

T Metal wall temperature, K

TZ Impingement plate dimensionless temperature

U Velocity along the wall in y+

Uc Velocity in the impingement gap at the single exit

μ Dynamic viscosity, kg/ms

Vj Impingement jet mean velocity (or Vm), m/s

ν Kinematic viscosity, m2/s

X Impingement hole square array pitch, m

y+ Inner variable wall normal coordinate (ξUτ/ν)

Z Impingement gap, m

ξ Grid cell size, m

Subscripts

h Hole

d Discharge

j Jet

w Wall

s Surface

∞ Coolant

f fluid

I Impingement jet wall

m mean

Z gap height

REFERENCES [1] Andrews G. E., Abdul Husain R. A. A. and Mkpadi

M. C. 2006. "Enhanced Impingement Heat Transfer:

The Influence of Impingement X/D for Interrupted

Rib Obstacles (Rectangular Pin Fins)". Trans. ASME

J. Turbomachinery, 128, 321 - 331.

[2] El-jummah A. M., Abdul Hussain R. A. A., Andrews

G. E. and Staggs J. E. J. 2014. "Conjugate Heat

Transfer Computational Fluid Dynamic Predictions of

Impingement Heat Transfer: The Influence of Hole

Pitch to Diameter Ratio X/D at Constant Impingement

Gap Z". Trans. ASME J. Turbomachinery, 136 (12), 1

- 16.

[3] El-jummah A. M., Abdul Hussain R. A. A., Andrews


Transfer CFD Predictions of Impingement Heat

Transfer: Influence of the Number of Holes for a

Constant Pitch to Diameter Ratio X/D". Proc. ASME

Gas Turbine Conference, GT-25268, 1 - 14.

[4] El-jummah, A. M., Abdul Hussain R. A. A., Andrews


Transfer CFD Predictions of the Surface Averaged

Impingement Heat Transfer Coefficients for

Impingement Cooling with Backside Cross-flow".

Proc. ASME IMECE Conference, IMECE-63580, 1 -

14.

[5] Abdul Husain R. A. A. and Andrews G. E. 1990. "Full

Coverage Impingement Heat Transfer at High

Temperature". Proc. ASME Int. Gas Turbine &

Aeroengine Congress & Eposition, 90-GT-285, 1 - 12.

[6] Obot N. T. and Trabold T. A. 1987. "Impingement

Heat Transfer within Arrays of Circular Jets: Part 1-

Efects of Minimum, Intermediate and Complete



Cross-Flow for Small and Large Spacings". Trans.

ASME J. Heat Transfer, 109, 872 - 879.

[7] Andrews G. E. and Kim M. N. 2001. "The Influence

of Film Cooling on Emissions of a Low NOx Radial

Swirler Gas Turbine Combustor". ASME Int. Gas

Turbine & Aeroengine Congress & Exhibition, GT-

71, 1 - 11.

[8] Andrews G. E., Alkabie H. S., Abdul Husain U. S.

and Abdul Aziz M. 1993. "Ultra Low NOx Ultra Lean

Gas Turbine Primary Zones With Liquid Fuels". Proc.

AGARD 81 Symposium of the Propulsion and

Energetics Panel of Fuels and Combustion

Technology for Advanced Aircraft Engines, 24.1 -

24.14.

[9] Huitenga H. and Norster E. R. 2014. "Development

Approach to the Dry Low Emission Combustion

System of MAN Diesel & Turbo Gas Turbines". Proc.

ASME Turbo Expo, GT-25164, 1 - 10.

[10] Andrews G. E., Asere A. A., Hussain C. I. and Mkpadi

M. C. 1985. "Transpiration and Impingement/Effusion

Cooling of Gas Turbine Combustion Chambers".

ISABE and AIAA 7th Propulsion Joint Specialist

Conference, ISABE 85-7095, 794 - 803.

[11] Andrews G. E. and Hussain C. I. 1984. "Impingement

Cooling of Gas Turbine Components". High

Temperature Technology, 2 (2), 99 - 106.

[12] Andrews G. E. and Hussain C. I. 1984. "Full

Coverage Impingement Heat Transfer: The Influence

of Impingement Jet Size". 1st UK National Heat

Transfer Conference, IChemE Symposium, Series

No.86, 1115 - 1124.

[13] Hollworth B. R. and Berry R. D. 1978. "Heat Transfer

from Arrays of Impinging Jets with Large Jet-to-Jet

Spacing". Trans. ASME J. Heat Transfer, 100, 352 -

357.

[14] Friedman S.J. and Mueller A.C. 1951. "Heat Transfer

to flat surfaces ". Proc. IMechE: General Discussions

on Heat Transfer, 138 - 142.

[158 Kercher D. M. and Tabakoff W. 1970. "Heat Transfer

by a Square Array of Round Air Jets Impinging

Perpendicular to a Flat Surface Including Effect of

Spent Air". Trans. ASME J. Eng. Power, 73 - 82.

[16] Chance J. L. 1974. "Experimental Investigation of Air

Impingement Heat Transfer Under an Array of Round

Jets". Tappi, 57 (6), 108 - 112.

[17] Huang L. and El-Genk M. 1994. "Heat Transfer of an

Impinging Jet on a Flat Surface". Elsevier Science Int.

J. Heat Mass Transfer, 37 (13), 1915 - 1923.

[18] Van Treuren K. W., Wang Z., Ireland P. T., Jones T.

V. and Kohler S. T. 1994. "Local Heat Transfer

Coefficient and Adiabatic Wall Temperature

Measurement Beneath Arrays of Staggered and Inline

Impinging Jets". Proc. ASME Int. Gas Turbine &

Aeroengine Congress & Eposition, 94-GT-181, 1 - 10.

[19] Consonni S. 1995. "Cooling Flow Prediction for Fully

Impingement Cooled Gas Turbine Blades". Proc.

ASME Int. Gas Turbine & Aeroengine Congress and

Exposition, 95-GT-22, 1 - 12.

[20] kanokjaruvijit K. and Martinez-Botas R. F. 2005. "Jet

Impingement on a Dimpled Surface With Different

Cross-Flow Schemes". Elsevier Int. J. Heat and Mass

Transfer, 48, 161 - 170.

[21] Xing Y. and Weigand B. 2013. "Optimum Jet-to-Plate

Spacing of Inline Impingement Heat Transfer for

Different Cross-Flow Schemes". Trans. ASME J. Heat

Transfer, 135 1 - 8.

[22] Andrews G. E., Durance J., Hussain C. I. and Ojobor

S. N. 1987. "Full Coverage Impingement Heat

Transfer: Influence of the Number of Holes". Trans.

ASME J. Turbomachinery, 109, 557 - 563.

[23] Al Dabagh A. M., Andrews G. E., Abdul Husain R. A.

A., Husain C. I., Nazari A. and Wu J. 1990.

"Impingement/ Effusion Cooling: The Influence of

Number of Impingement Holes and Pressure Loss on

the Heat Transfer Coefficient". Trans. ASME J.

Turbomachinery, 112, 467 - 476.

[24] Abdul Husain R. A. A., Andrews G. E., Asere A. A.

and Ndiema C. K. W. 1988. "Full Coverage

Impingement Heat Transfer: Cooling Effectiveness".

Proc. ASME Int. Gas Turbine & Aeroengine

Congress, 88-GT-270, 1 - 9.

[25] El-jummah, A. M., Andrews, G. E. and Staggs, J. E. J.

2013. "Conjugate Heat Transfer CFD Predictions of

the Influence of the Impingement Gap on the Effect of

Cross-Flow". Proc. ASME Heat Transfer Conference,

HT-17180, 1 - 12.

[26] Hollworth, B. R., Lehmann, G. and Rosiczkowski, J.

1983. "Arrays of Impinging Jets with Spent Fluid

Removal Through Vent Holes on the Target Surface,

Part 2: Local Heat transfer". Trans. ASME J. Eng.

Power, 105, 393 - 402.

[27] El-jummah, A. M., Andrews, G. E. and Staggs, J. E. J.

2013. "Conjugate Heat Transfer CFD Predictions of

Impingement Jet Array Flat Wall Cooling

Aerodynamics with Single Sided Flow Exit". Proc.

ASME Turbo Expo Conference, GT-95343, 1 - 12.

[28] Ireland P. T., Neely A. J., Gillespie D. R. H. and

Robertson A. J. 1999. "Turbulent Heat Transfer

Measurements using Liquid Crystals". Elsevier. Int. J.

Heat and Fluid Flow, 20, 355 - 367.

[29] Goldstein R. J. and Timmers J. F. 1982.

"Visualization of Heat Transfer from Arrays of

Impinging Jets". Pergamon Int. J. Heat Mass

Transfer, 25 (12), 1857 - 1868.

[30] Goldstein R. J., Behbahani A. I. and Heppelmann K.

1986. "Streamwise Distribution of the Recovery

Factor and the Local Heat Transfer Coefficient to an

Impinging Circular Airjet". Pergamon Int. J. Heat

Mass Transfer, 29 (8), 1227 - 1235.

[31] Andrews G. E., Asere A. A., Hussain C. I. and

Mkpadi M. C. 1985. "Full Coverage Impingement

Heat Transfer: The Variation in Pitch to Diameter

Ratio at a Constant Gap". Proportion and Energetics

Panel of AGARD, 65th

Symposium, 'Heat Transfer and

Cooling in Gas Turbines', Paper 26, 1 - 12.

[32] Andrews G. E. and Mpadi M. C. 1984. "Full-

Coverage Discrete Hole Wall Cooling: Discharge

Coefficients". Trans. ASME J. Eng. Gas Turbines and

Power, 106 183 - 192.

[33] Andrews G. E., Asere A. A., Hussain C. I., Mkpadi

M. C. and Nazari A. 1988. "Impingement/Effusion

Cooling: Overall Wall Heat Transfer". Proc. ASME

Int. Gas Turbine and Aeroengine Congress, 88-GT-

290, 1 - 9.

[34] Bailey J. C. and Bunker R. S. 2002. "Local Heat

Transfer and Flow Distributions for Impinging Jet

Arrays of Dence and Sparse Extent.". Proc. ASME

Turbo Expo, GT-30473, 1 - 10.



CHT/CFD Predictions of Impingement Cooling with Four Sided Flow Exit

Documents

Transcript of CHT/CFD Predictions of Impingement Cooling with Four Sided Flow Exit