Jet Impingement Heat Transfer:
Physics, Correlations, and Numerical Modeling
N. ZUCKERMAN and N. LIOR
Department of Mechanical Engineering and Applied Mechanics, The University of Pennsylvania,
Philadelphia, PA, USA; E-mail: zuckermn@seas.upenn.edu; lior@seas.upenn.edu
I. Summary
The applications, physics of the flow and heat transfer phenomena,
available empirical correlations and values they predict, and numerical
simulation techniques and results of impinging jet devices for heat transfer
are described. The relative strengths and drawbacks of the k–e, k–o,
Reynolds stress model, algebraic stress models, shear stress transport, and
v
2
f turbulence models for impinging jet flow and heat transfer are compared.
Select model equations are provided as well as quantitative assessments of
model errors and judgments of model suitability.
II. Introduction
We seek to understand the flow field and mechanisms of impinging jets
with the goal of identifying preferred methods of predicting jet performance.
Impinging jets provide an effective and flexible way to transfer energy or
mass in industrial applications. A directed liquid or gaseous flow released
against a surface can efficiently transfer large amounts of thermal energy or
mass between the surface and the fluid. Heat transfer applications include
cooling of stock material during material forming pro cesses, heat treatment
[1], cooling of electronic components, heating of optical surfaces for
defogging, cooling of turbine components, cooling of critical machinery
structures, and many other industrial process es. Typical mass transfer
applications include drying and removal of small surface particulates.
Abrasion and heat transfer by impingement are also studied as side effects of
vertical/short take-off and landing jet devices, for example in the case of
direct lift propulsion systems in vertical/short take-off and landing aircraft.
Advances in Heat Transfer
Volume 39 ISSN 0065-2717
DOI: 10.1016/S0065-2717(06)39006-5
565 Copyright r 2006 Elsevier Inc.
All rights reserved
ADVANCES IN HEAT TRANSFER VOL. 39
General uses and performance of impinging jets have been discussed in a
number of reviews [2–5].
In the example of turbine cooling applications [6], impinging jet flows may
be used to cool several different sections of the engine such as the combustor
case (combustor can walls), turbine case/liner, and the critical high-
temperature turbine blades. The gas turbine compressor offers a steady flow
of pressurized air at temperatures lower than those of the turbine and of the
hot gases flowing around it. The blades are cooled using pressurized bleed
flow, typically available at 6001C. The bleed air must cool a turbine immersed
in gas of 14001C total temperature [7], which requires transfer coefficients in
the range of 1000–3000 W/m
2
K. This equates to a heat flux on the order of
1 MW/m
2
. The ability to cool these components in high-temperature regions
allows higher cycle temperature ratios and higher efficiency, improving fuel
economy, and raising turbine power output per unit weight. Modern turbines
have gas temperatures in the main turbine flow in excess of the temperature
limits of the materials used for the blades, meaning that the structural
strength and component life are dependent upon effective cooling flow.
Compressor bleed flow is commonly used to cool the turbine blades by
routing it through internal passages to keep the blades at an acceptably low
temperature. The same air can be routed to a perforated internal wall to form
impinging jets directed at the blade exterior wall. Upon exiting the blade, the
air may combine with the turbine core airflow. Variations on this design may
combine the impinging jet device with internal fins, smooth or roughened
cooling passages, and effusion holes for film cooling. The designer may alter
the spacing or locations of jet and effusion holes to concentrate the flow in
the regions requiring the greatest cooling. Though the use of bleed air carries
a performance penalty [8], the small amount of flow extracted has a small
influence on bleed air supply pressure and temperature. In addition to high-
pressure compressor air, turbofan engines provide cooler fan air at lower
pressure ratios, which can be routed directly to passages within the turbine
liner. A successful design uses the bleed air in an efficient fashion to minimize
the bleed flow required for maintaining a necessary cooling rate.
Compared to other heat or mass transfer arrangements that do not
employ phase change, the jet impingement device offers efficient use of the
fluid, and high transfer rates. For example, compared with conventional
convection cooling by confined flow parallel to (under) the cooled surface,
jet impingement produces heat transfer coefficients that are up to three times
higher at a given maximum flow speed, because the impingement boundary
layers are much thinner, and often the spent flow after the impingement
serves to turbulate the surrounding fluid. Given a required heat transfer
coefficient, the flow required from an impinging jet device may be two
orders of magnitude smaller than that required for a cooling approach using
566 N. ZUCKERMAN AND N. LIOR
a free wall-parallel flow. For more uniform coverage over larger surfaces
multiple jets may be used. The impingement cooling approach also offers a
compact hardware arrangement.
Some disadvantages of impingement cooling devices are: (1) For moving
targets with very uneven surfaces, the jet nozzles may have to be located too
far from the surface. For jets starting at a large height above the target (over
20 jet nozzle diameters) the decay in kinetic energy of the jet as it travels to
the surface may redu ce average Nu by 20% or more. (2) The hardware
changes necessary for implementing an impinging jet device may degrade
structural strength (one reason why impinging jet cooling is more easily
applied to turbine stator blades than to rotor blades). (3) In static
applications where very uniform surface heat or mass transfer is required,
the resulting high density of the jet array and corresponding small jet height
may be impractical to construct and implement, and at small spacings jet-to-
jet interaction may degrade efficiency.
Prior to the design of an impinging jet device, the heat transfer at the
target surface is typically characterized by a Nusselt number (Nu), and the
mass transfer from the surface with a Schmidt number (Sc). For design
efficiency studies and device performance assessment, these values are
tracked vs. jet flow per unit area (G) or vs. the power required to supply the
flow (incremental compressor power).
A. I
MPINGING JET REGIONS
The flow of a submerged impinging jet passes through several distinct
regions, as shown in Fig. 1. The jet emerges from a nozzle or opening with a
velocity and temperature profile and turbulence characteristics dependent
upon the upstream flow. For a pipe-shaped nozzle, also called a tube nozzle
or cylindrical nozzle, the flow develops into the parabolic velocity profile
common to pipe flow plus a moderate amount of turbulence developed
upstream. In contrast, a flow delivered by application of differential pressure
across a thin, flat orifice will create an initial flow with a fairly flat velocity
profile, less turbulence, and a downstream flow contraction (vena contracta).
Typical jet nozzles designs use either a round jet with an axisymmetric flow
profile or a slot jet, a long, thin jet with a two-dimensional flow profile.
After it exits the nozzle, the emerging jet may pass through a region where it
is sufficiently far from the impingement surface to behave as a free submerged
jet. Here, the velocity gradients in the jet create a shearing at the edges of the
jet which transfers momentum laterally outward, pulling additional fluid
along with the jet and raising the jet mass flow, as shown in Fig. 2. In the
process, the jet loses energy and the velocity profile is widened in spatial extent
and decreased in magnitude along the sides of the jet. Flow interior to the
567JET IMPINGEMENT HEAT TRANSFER
progressively widening shearing layer remains unaffected by this momentum
transfer and forms a core region with a higher total pressure, though it may
experience a drop in velocity and pressure decay resulting from velocity
gradients present at the nozzle exit. A free jet region may not exist if the nozzle
lies within a distance of two diameters (2D) from the target. In such cases, the
nozzle is close enough to the elevated static pressure in the stagnation region
for this pressure to influence the flow immediately at the nozzle exit.
If the shearing layer expands inward to the center of the jet prior to
reaching the target, a region of core decay forms. For purposes of distinct
identification, the end of the core region may be defined as the axial position
where the centerline flow dynamic pressure (proportional to speed squared)
reaches 95% of its original value. This decaying jet begins four to eight nozzle
diameters or slot-widths downstream of the nozzle exit. In the decaying jet,
the axial velocity component in the central part decreases, with the radial
FIG. 1. The flow regions of an impinging jet.
568 N. ZUCKERMAN AND N. LIOR
velocity profile resembling a Gaussian curve that becomes wider and shorter
with distance from the nozzle outlet. In this region, the axial velocity and jet
width vary linearly with axial position. Martin [2] provided a collection of
equations for predicting the velocity in the free jet and decaying jet regions
based on low Reynolds number flow. Viskanta [5] further subdivided this
region into two zones, the initial ‘‘developing zone,’’ and the ‘‘fully developed
zone’’ in which the decaying free jet reaches a Gaussian velocity profile.
As the flow approaches the wall, it loses axial velocity and turns. This
region is labeled the stagnation region or deceleration region. The flow
builds up a higher static pressure on and above the wall, transmitting the
effect of the wall upstream. The nonuniform turning flow experiences high
normal and shear stresses in the deceleration region, which greatly influence
local transport properties. The resulting flow pattern stretches vortices in the
flow and increases the turbulence. The stagnation region typically extends
1.2 nozzle diameters above the wall for round jets [2]. Experimental work by
Maurel and Solliec [9] found that this impinging zone was characterized or
delineated by a negative normal-parallel veloci ty correlation (
uvo0). For
their slot jet this region extended to 13% of the nozzle height H, and did not
vary with Re or H/D.
FIG. 2. The flow field of a free submerged jet.
569JET IMPINGEMENT HEAT TRANSFER
