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Numerical Study of Interrupted Impinging Jets for Cooling of Electronics

TL;DR: In this article, the authors present the results of a numerical investigation of the effect of flow pulsations on local, time-averaged Nusselt number of an impinging air jet.
Abstract: The objective of this paper is to present the results of a numerical investigation of the effect of flow pulsations on local, time-averaged Nusselt number of an impinging air jet. The problem was considered to provide inputs to augmenting heat transfer from electronic components. The solution is sought through the FLUENT (Version 6.0) platform. The standard k-epsiv model for turbulence equations and two-layer zonal model in wall function are used in the problem. Pressure-velocity coupling is handled using the SIMPLEC algorithm. The model is first validated against some experimental results available in the literature. A parametric study is carried out to quantify the effect of the pulsating jets. The parameters considered are (1) average jet Reynolds number (5130 < Re < 8560), (2) sine and square wave pulsations, (3) frequencies of pulsations (25 < / <400 Hz), and (4) height of impingement to jet diameter ratios (5 < H/d < 9). In the case of sine wave pulsations, the ratio of root mean square value of the amplitude to the average value (AN) was varied from 18% to 53%. The studies are restricted to a constant wall heat flux condition. Parametric conditions for which enhancement in the time-averaged heat transfer from the surface can be expected are identified.

Summary (2 min read)

Introduction

  • - model for turbulence equations and two-layer zonal model in wall function are used in the problem.
  • A further enhancement in the convective heat transfer coefficient is possible if the boundary layer can be disrupted.
  • Some lacuna of numerical investigations of the pulsated impinging jets sets the agenda for the present work.

II. MATHEMATICAL FORMULATION

  • The pulsated impinging jet heat transfer problem is numerically computed with the commercial finite-volume code FLUENT 6.0 using the time-averaged Navier-Stokes and energy equations with the standard turbulent model.
  • Hence, the geometric boundaries and physical conditions are symmetric about the axis of the jet; a 2-D axi-symmetric model is constructed.
  • The two-layer zonal model is used in the wall function for numerical computations [13].
  • In the viscosity-affected near-wall region (where 200), the (5) is only employed.
  • And instead of using (8), the turbulent viscosity is computed from (20).

III. NUMERICAL PROCEDURE

  • The finite-volume code FLUENT 6.0 is used to solve the thermal and flow fields using the standard turbulence model.
  • Successful computation of the turbulent model requires some consideration during the mesh generation, also known as Near-wall meshing.
  • Since turbulence plays a dominant role in the solving of transport equations, it must be ensured that turbulence quantities are properly resolved.
  • Convergence in inner iterations is declared only when the scaled residual is decreased to 10 for all equations except the energy equation, for which the criterion is 10 .
  • So is defined for all governing equations (except the continuity equation) as (27) where stands for each variable , , , and at grid point , is coefficient and are the neighbouring coefficients in the discretization equation.

IV. RESULTS AND DISCUSSION

  • The present model is validated using the results of Mladin and Zumbrunnen [5], who performed experiments with pulsating planar jets with nozzle dimensions 5 50 mm.
  • A common feature is that there is an increase in the time averaged Nusselt number in the stagnation region for Reynolds numbers up to 7000 at frequencies greater than about 200 Hz. Fig. 12(b) is for 7, which is about optimum height for a steady jet.
  • Comparison of square and sine wave jets: Fig. 16 shows an assessment of the percentage for increase in time-averaged Nusselt number (w.r.t. the steady value) along the wall for different waveforms of jet.
  • The initial steep rise can be attributed to instabilities caused by pulsing and reduction in average thickness of boundary layer.
  • Yet, the augmentation level seems to remain the same.

V. CONCLUSION

  • This paper is focused on the possible improvements to heat transfer with pulsated impinging jets.
  • A numerical model is developed for simulating heat transfer and fluid flow with turbulence model.
  • For the case of a square wave jet with 5130 and 7, the time-averaged Nusselt number increases by up to 12% in the stagnation zone and 35% in the wall jet zone in the frequency range (25 400 Hz) as compared to that of the steady jet.
  • The results of the parametric investigation reported here clearly exhibit that the pulsated impinging jet enhances the performance impinging jets.
  • Hence, these designs can be utilized to enhance heat transfer for cooling of electronic systems.

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IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES, VOL. 30, NO. 2, JUNE 2007 275
Numerical Study of Interrupted Impinging
Jets for Cooling of Electronics
Ramesh Chandra Behera, Pradip Dutta, and K. Srinivasan
Abstract—The objective of this paper is to present the results
of a numerical investigation of the effect of flow pulsations on
local, time-averaged Nusselt number of an impinging air jet.
The problem was considered to provide inputs to augmenting
heat transfer from electronic components. The solution is sought
through the FLUENT (Version 6.0) platform. The standard
- model for turbulence equations and two-layer zonal model
in wall function are used in the problem. Pressure-velocity cou-
pling is handled using the SIMPLEC algorithm. The model is
first validated against some experimental results available in the
literature. A parametric study is carried out to quantify the effect
of the pulsating jets. The parameters considered are 1) average jet
Reynolds number
(
5130 8560
)
, 2) sine and square wave
pulsations, 3) frequencies of pulsations (25
400 Hz), and
4) height of impingement to jet diameter ratios
(
5
9
)
.
In the case of sine wave pulsations, the ratio of root mean square
value of the amplitude to the average value
(
)
was varied from
18% to 53%. The studies are restricted to a constant wall heat
flux condition. Parametric conditions for which enhancement in
the time-averaged heat transfer from the surface can be expected
are identified.
Index Terms—Heat flux condition, impinging air jet, pulsating
jet.
NOMENCLATURE
Pulse amplitude ( 100).
Fluid specific heat (J kg K .
Diameter of circular nozzle (m).
Frequency of the pulsating jet (Hz).
Production of turbulent kinetic energy (m s ).
Convective heat transfer coefficient (W
m
K ).
Height of nozzle-to-wall spacing (m).
Turbulent kinetic energy (m s ).
Fluid thermal conductivity (W m K ).
Length of the wall (m).
Nusselt number based on nozzle diameter
.
Pressure (N m ).
Manuscript received May 20, 2004; revised March 21, 2005. This work was
supported by a Defence Research and Development Organization, Government
of India Grant-in-Aid. This work was recommended for publication by Asso-
ciate Editor P. Sathyamurthy upon evaluation of the reviewers comments.
The authors are with the Department of Mechanical Engineering, Indian
Institute of Science, Bangalore 560012, India (e-mail: mecks@mecheng.iisc.
ernet.in; mecks@hotmail.com).
Digital Object Identifier 10.1109/TCAPT.2007.898353
Fluid prandtl number.
Turbulent prandtl number 0.85 .
Wall heat flux (W m ).
Reynolds number based on nozzle diameter
.
Time (s).
T Time period (s).
Temperature (K).
,
Velocities in x, and r directions (m s ).
Time-averaged velocity component of a pulsating
jet (m s
).
Periodic velocity component of a sine wave jet
(m s
).
Jet velocity (m s ).
Maximum velocity component of a square wave
jet (m s
).
Root mean square value of the (m s ).
Turbulent velocity component (m s ).
, Coordinate axes.
Greek Symbols
Dissipation rate of kinetic energy (m s .
Von Karman’s constant 0.42 .
Fluid dynamic viscosity (kg m s ).
Turbulent viscosity (kg m s ).
Fluid density (kg m ).
Shear stress (N m ).
Hydrodynamic boundary layer thickness (m).
Subscripts
avg Time-averaged value.
amp Periodic value.
peak Maximum value.
rms Root mean square value.
s Stagnation point.
Radial.
Axial.
Wall value.
Superscripts
Turbulent value.
1521-3331/$25.00 © 2007 IEEE

276 IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES, VOL. 30, NO. 2, JUNE 2007
I. INTRODUCTION
I
MPINGING jets have been used extensively in thermal sys-
tems such as drying, manufacture of steel, turbine-blades,
etc for enhancement of heat transfer. More specically, in
the thermal management of electronic components, increased
power dissipation in chips with ever higher component-densi-
ties has propelled the use of impinging jets to augment cooling.
If the performance of impinging jets can be further enhanced,
there will be a potential for an increase in the electronic com-
ponents life span.
There is an excellent compilation of literature on enhancing
the convective heat transfer coefcient with steady impinging
jets [1], [2]. Parameters that inuence the magnitude of en-
hancement are the height and angle of impingement and turbu-
lence intensity. A steady impinging jet stabilizes the boundary
layer on the surface to be cooled. A further enhancement in the
convective heat transfer coefcient is possible if the boundary
layer can be disrupted. One method of achieving this is by pul-
sating the jet, i.e., making it unsteady. The speed of pulsation
should be such that the boundary layer can be disturbed and yet
adequate coolant is made available.
Some of the possible features that could cause the enhance-
ment due to pulsed jets are: a) higher turbulence promoted
by ow instabilities at the free surface, b) chaotic mixing
which promotes entrainment, and c) reduced resistance of
the boundary layer growth on the impingement surface. The
nonlinear dynamic response of the hydrodynamic and thermal
boundary layers to ow pulsations has been investigated re-
cently [3].
Zumbrunnen and Aziz [4] were, perhaps, the rst to study the
importance of pulsation frequency and amplitude. They inves-
tigated convective heat transfer with a planar impinging water
jet (50.8
5.08 mm) on a surface subjected to a constant heat
ux. Their experiments covered Reynolds numbers ranging
from 3300 to 19600 and frequencies up to 142 Hz. A two fold
enhancement of heat transfer was reported. They observed that,
to be effective, the pulsation frequency must be of the order of
100s of Hz. Experimental investigations were reported also
by Mladin and Zumbrunnen [5] who studied the effect of ow
pulsations on the local heat transfer coefcient of a planar jet
at Reynolds numbers of 1000, 5500, and 11000, frequencies up
to 82 Hz and with a nozzle outlet size of 50
5 mm. It was
observed that Nusselt number enhancement depends on pulse
frequency and amplitude in addition to Reynolds number and
the impingement height. The largest Nusselt was observed at
a
ratio between 7 and 8. Another investigation by them
[6] brings out that the forcing Strouhal number is an inuential
parameter that controlled the large-scale structure formation
and interaction, as well as downstream penetration distance,
and a high value of Strouhal number may enhance cooling
of electronic packages by surface renewal effects from large
incident ow structures.
Further contributions in the area of multiple jets came from
Sheriff and Zumbrunnen [7] by way of multiple orices and con-
vergent nozzle jets. They observed a greater heat transfer rate
and a better heat transfer distribution in the latter case. The dif-
ference was 34%38%. It was also brought out that the best re-
sults were obtained for a jet height to diameter ratio of 2. Flow
pulsations appear to increase the time averaged boundary layer
thickness and lead to reduction in heat transfer for pulsations in
the region of 1065 Hz frequency. They further concluded that
at high pulsation frequencies, a more abundant succession of
incident vortices was produced in the jet so that non-linear dy-
namical boundary layer effects became secondary to improved
mixing.
Sheriff and Zumbrunnen [8] expanded the study to pulsating
array of jets. An array of nine convergent jets in a square matrix
was used to cover a Reynolds number range of 2 50010 000, a
jet height to diameter ratio of 26, pulse frequency up to 65 Hz,
a Strouhal number of 0.028 and a ow pulsation magnitude up
to 60%. Their conclusions were: 1) increased jet interactions
at large magnitude of ow pulsations was found to reduce the
jet potential core length by up to 20%, 2) turbulence intensi-
ties were higher by 715% than in steady jets, and 3) despite
evidence of coherent ow structures and increased turbulence,
stagnation Nusselt numbers were lower by 18% for a 60% pulse
magnitude. The heat transfer rate was unchanged in the region
away from the stagnation point.
Studies on the waveform of pulsations by Sheriff and Zum-
brunnen [9] indicate that the time averaged stagnation Nusselt
numbers reduced by 17% for sinusoidal pulsations for large
pulse magnitudes and increased by 33% for square wave pulses.
The experiments were conducted with water as the cooling
medium. The frequency range covered was up to 280 Hz. The
range of Reynolds numbers covered was 315015800.
The importance of duty cycle (i.e., the ratio of pulse cycle
on-time to total cycle time) for a pulsated impinging jet was
investigated by Sailor
et al. [10]. They show that a duty cycle of
0.25 produces a better effect than at 0.33 or 0.50 for frequencies
up to 60 Hz in the Reynolds number range of 2100031000 and
jet-to wall spacing ratios of 48.
Mladin and Zumbrunnen [3], [11] developed a mathematical
model to study the nonlinear dynamics of the hydrodynamic
and thermal boundary layers within a planar stagnation region.
They conclude that high frequency, low amplitude uctuations
are better than low frequency, high amplitude uctuations.
The present study is complementary to the above efforts on
using pulsated jets in applications involving cooling of elec-
tronic systems. This paper focuses on axi-symmetric submerged
air jet. The physical model of an impinging jet is shown in Fig. 1.
Some lacuna of numerical investigations of the pulsated im-
pinging jets sets the agenda for the present work. A systematic
analysis of the inuence of waveform, frequency of pulsating,
height of impingement and Reynolds number is represented.
The solution is obtained through the use of FLUENT 6.0 [12]
as a solver for thermal and ow elds using the standard
turbulence model. The range covered is jet Reynolds number,
51308560, frequencies of interruptions from 0400 Hz, and
height to jet diameter ratios from 5 to 9. The studies are re-
stricted to constant wall heat ux condition as this is the most
common feature of cooling of electronic components.
II. M
ATHEMATICAL FORMULATION
The pulsated impinging jet heat transfer problem is nu-
merically computed with the commercial nite-volume code

BEHERA et al.: NUMERICAL STUDY OF INTERRUPTED IMPINGING JETS 277
Fig. 1. Schematic diagram of an impingement jet ow eld.
FLUENT 6.0 using the time-averaged Navier-Stokes and en-
ergy equations with the standard
turbulent model. The
model is chosen due to its simplicity, computational
economy and wide acceptability.
The circular air jet is assumed to have constant thermo-
physical physical properties such as density, specic heat and
thermal conductivity. Hence, the geometric boundaries and
physical conditions are symmetric about the axis of the jet;
a 2-D axi-symmetric model is constructed. It neglects grav-
itational effect during the impinging jet. The axi-symmetric
domain is shown in Fig. 2. The equations for 2-D incompress-
ible ow can be written as follows.
Conservation of mass
(1)
Conservation of linear momentum
For
-momentum
(2)
and for
-momentum
(3)
Fig. 2. Schematic illustration of the computational domain.
Energy conservation
(4)
The Standard
Turbulent Model
(5)
and
(6)
where the values for the empirical constants are
1.44, 1.92, 1.0 and 1.3.
The term
is the volumetric rate of generation of turbulent
kinetic energy and is dened as
(7)
The turbulent viscosity
term is dened as
(8)
where the value of empirical constant,
is 0.09.
Initial and Boundary Conditions: The boundary conditions
adopted for solution of the governing equations are:
a) Velocity boundary condition at the inlet of the domain:

278 IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES, VOL. 30, NO. 2, JUNE 2007
The jet velocity is assumed to be steady or pulsated with
respect to time. The type of the pulsation waveform of
the jet velocity is shown in Fig. 3 and is discussed subse-
quently.
A steady jet is dened as
(9)
A jet with sinusoidal waveform can be described as
(10)
where
.
A jet with a square waveform can be described as
for
for
(11)
where
2) and 0,1,2,3,4,5, .
The turbulent kinetic energy,
is calculated as
(12)
where the turbulent intensity
is dened as
(13)
where
and are the root-mean-square (rms) of
the velocity uctuations
and time-average of the ve-
locity component
respectively.
The dissipation rate,
, is calculated as
(14)
where
is the turbulence length scale which is a physical
quantity related to the size of the large eddies that contain
the energy in turbulent ows. An approximate relationship
between
and the physical size of the nozzle is dened as
(15)
where
is the relevant dimension and it is equal to hy-
draulic diameter of the nozzle
The jet inlet temperature is constant and is same as atmo-
spheric temperature (i.e.,
).
b) Pressure boundary condition:
The boundary condition is imposed with constant atmo-
spheric pressure and temperature:
(16)
c) Wall boundary condition:
No-slip condition with constant heat ux is imposed at the
wall boundaries.
d) Initial condition:
The initial conditions appropriate to the physical situa-
tions are as follows:
Fig. 3. Different waveforms of the impinging jet velocity.
at
(17)
Treatment near wall: The two-layer zonal model is used in
the wall function for numerical computations [13]. In two-layer
zonal model, the whole domain is subdivided into a viscosity
affected region and a fully turbulent region. The demarcation of
the two regions is determined by a wall-distance based, turbulent
Reynolds number
,isdened as
(18)
where
is the normal distance from the wall at the cell centers.
In the fully turbulent region (where
200), both and
equations are employed. In the viscosity-affected near-wall
region (where
200), the (5) is only employed. And
instead of using (6), the
is algebraically calculated as
(19)
And instead of using (8), the turbulent viscosity
is com-
puted from
(20)
The length scales (
and ) that appear in (19) and (20) are
dened as [14]
(21)
and
(22)
The constants (
, and ) are given by
(23)

BEHERA et al.: NUMERICAL STUDY OF INTERRUPTED IMPINGING JETS 279
Fig. 4. Comparison of steady Nusselt number with numerical and experimental
results [16], [17] for
Re
=
500,
H=w
=
1 and
q
=
500 wm
.
III. NUMERICAL
PROCEDURE
The nite-volume code FLUENT 6.0 is used to solve the
thermal and ow elds using the standard
turbulence
model. Diffusion terms of all the governing equations are dis-
cretized using the central difference scheme. Convective terms
of the momentum and energy equations are discretized using the
third order QUICK interpolation scheme and convective terms
of the turbulent kinetic energy and turbulent dissipation rate
equations are discretized using a second-order upwind differ-
encing scheme. Pressure-velocity coupling is handled using the
SIMPLEC algorithm [15].
Near-wall meshing: Successful computation of the turbulent
model requires some consideration during the mesh generation.
Since turbulence plays a dominant role in the solving of trans-
port equations, it must be ensured that turbulence quantities are
properly resolved. It is therefore proposed to use sufciently ne
meshes to resolve the near-wall region sufciently. Hence, the
following meshing requirements are adopted.
a) A two-layer zonal model is employed for resolving the
laminar sublayer,
value should be within 4 to 5 at the
cell adjacent to the wall.
is dened as:
(24)
where
is the friction velocity, and is dened as
(25)
b) There should be at least 10 cells within the viscosity-af-
fected near-wall region
200 to be able to resolve
the mean velocity and turbulent quantities in that region.
A comprehensive study was undertaken to determine the grid
sizes, time steps and iteration convergence criteria. As an out-
come of the grid independence study, a non-uniform grid size
was chosen as follow: 120
100 (for ), 120 140
(for
7) and 120 180 (for 9) in the axisym-
metric domain, thus satisfying the near-wall meshing condition
as discussed above. A ner grid is taken near the wall and the
air jet region of the domain, while a coarser grid system is used
far away from the boundary layer.
It is found that time step has a profound effect on the conver-
gence of the solution in this periodic problem. An appropriate
time step which ensured a converged solution without costing
excessive computational time was determined following a series
of studies, and the following time step was chosen accordingly:
(26)
where
is the time period of the waveform of the jet.
Convergence in inner iterations is declared only when the
scaled residual
is decreased to 10 for all equations ex-
cept the energy equation, for which the criterion is 10
.So
is dened for all governing equations (except the conti-
nuity equation) as
(27)
where
stands for each variable , , , and at grid point
, is coefcient and are the neighbouring coefcients
in the discretization equation.
The scaled residual for the continuity equation is dened as
and
rate of mass creation in cell (28)
The denominator is the largest absolute value of the continuity
residual in the rst ve iterations.
IV. R
ESULTS AND DISCUSSION
The present model is validated using the results of Mladin and
Zumbrunnen [5], who performed experiments with pulsating
planar jets with nozzle dimensions 5
50 mm. This was ap-
proximated as a 2-D planar jet for the purpose of model vali-
dation in the present work, as the high-aspect-ratio nozzle used
in [5] is expected to behave like a 2-D jet. Similar validation
exercise was also performed using numerical and experimental
results presented in Ichimiya and Hosaka [16], [17] for steady
jets. The results of validation are shown in Figs. 4 and 5, respec-
tively. The Nusselt number variation is taken as a measure of
compliance. The qualitative behavior is well replicated in both
the cases. The quantitative differences can be attributed to 3-D
effects in slot jets which are approximated by an equivalent 2-D
planar jet. Since a reasonable compliance is obtained, the model
is used to characterize the pulsating jets as means of enhancing
heat transfer. Subsequent simulations for round jets were carried
out with an axisymmetric nozzle for the present study. Inter alia,
a parametric study is carried out to quantify the effect of each
of them. The parameters considered are the Reynolds number
of the jet, nozzle-to-wall spacing, and frequency, amplitude and
wave form of the pulsations. All results presented here pertain
to steady periodic conditions.The properties of air used in this
study are enumerated in Table I.
Flow characterization of pulsated impinging jets: Fig. 6
shows the variation of maximum radial velocity with time
for different waveforms of the pulsated impinging jets over

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TL;DR: In this article, the effect of flow intermittency on convective heat transfer to a planar water jet impinging on a constant heat flux surface has been investigated by periodically restarting an impinging flow and thereby forcing renewal of the hydrodynamic and thermal boundary layers.
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Frequently Asked Questions (1)
Q1. What are the contributions mentioned in the paper "Numerical study of interrupted impinging jets for cooling of electronics" ?

The objective of this paper is to present the results of a numerical investigation of the effect of flow pulsations on local, time-averaged Nusselt number of an impinging air jet. The problem was considered to provide inputs to augmenting heat transfer from electronic components. A parametric study is carried out to quantify the effect of the pulsating jets.