v>EPA
United States
Environmental Protection
Agency
Environmental Sciences Research
Laboratory
Research Triangle Park NC 27711
Research and Development
EPA-600/S3-82-007 May 1982
Project Summary
Wake of a Block Vehicle in a
Shear-Free Boundary Flow—
An Experimental and
Theoretical Study
Robert E. Eskridge and Roger S. Thompson
The wake of a moving vehicle was
simulated using a specially-con-
structed wind tunnel with a moving
floor. A "block-shaped" model vehicle
was fixed in position over the test-
section floor, while the floor moved at
the f reestream air speed to produce a
uniform, shear-free, approach flow.
This simulates an automobile traveling
along a straight highway under calm
atmospheric conditions.
Vertical and lateral profiles of mean
and fluctuating velocities and Reyn-
olds stresses in the wake of the vehicle
were obtained using a hot-film ane-
mometer with an X-probe. Profiles
were taken at distances of 10 to 80
model heights downwind.
A momentum-type wake was ob-
served behind the block-shaped vehi-
cle. The wake does not have a simple
self-preserving form. However, it is
possible to collapse the velocity deficit
with one length and one velocity scale.
Two new theories for the velocity
deficit are compared to the theory of
Eskridge and Hunt. A theory that con-
sidered a height-dependent eddy vis-
cosity was found to fit the data best.
Length and velocity scales were
found for the longitudinal variations of
the turbulent kinetic energy. The lat-
eral variation is described by a two-
dimensional numerical fit of the cross-
wind variation of the data.
This Project Summary was devel-
oped by EPA's Environmental Sci-
ences Research Laboratory. Research
Triangle Park. NC. to announce key
findings of the research project that is
fully documented in a separate report
of the same title (see Project Report
ordering information at back).
Introduction
The dispersion of automobile exhaust
near highways is of much current
interest. Mathematical models are need-
ed that will accurately predict concentra-
tion fields. This study on the structure of
the wakes of vehicles was undertaken
at the U.S. Environmental Protection
Agency's Fluid Modeling Facility to
provide information to be used in numer-
ical models of automobile exhaust dis-
persion.
A wind tunnel with a test-section
floor that moves at the freestream air
speed was constructed to generate a
uniform (constant speed with height)
approach flow. Scale model vehicles
with rotating wheels were held in posi-
tion in the test section by guys attached
to the test-section walls. A vehicle fixed
in a uniform flow over a moving floor is
aerodynamically equivalent to a vehicle
moving down a straight highway
through a calm atmosphere.
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Automobiles and scale model vehicles
have wakes that can be characterized as
momentum wakes, which contain an
organized vortex pair aligned with the
axis of the wake. In this 'paper we are
interested in only the momentum wake,
and therefore, generally discuss only
those data and theories applicable to
momentum wakes. To create a "pure"
(no mean swirl) momentum wake, block-
shaped vehicles of appropriate heights
and widths have been used. It should be
noted that momentum wakes contain
vortices, but the vortices disappear
when the flow is time-averaged.
A momentum wake's character is
determined mainly by the flow field in
which it is embedded. Flows that are
free of limiting walls and flows that are
influenced by a boundary are important
cases. Free flows may be subdivided
further into shear flows and shear-free
flows. In addition, wakes in the flows
can be subdivided into laminar and tur-
bulent wakes. J. C. R. Hunt'stheoryand
work showed that the strength of the
wake for surface-mounted objects is
determined by the couple, rather than
by the drag.
Hunt's work was extended by other
researchers. They have described wakes
of two-dimensional objects in a turbu-
lent boundary layer and have shown
that Hunt's theory is inapplicable when
the wake height approaches that of the
boundary layer. However, the wakes of
very small two-dimensional objects did
not agree with Hunt's theory as well as
those behind large two-dimensional
blocks. Some investigators conclude
that a constant eddy viscosity model will
not likely describe the complex flow in
this type of wake.
Theories for wakes behind three-
dimensional objects in turbulent bound-
ary layers have been developed by
various workers recently. Eskridge and
Hunt have developed a model of a three-
dimensional wake near a moving sur-
face (no shear in the approach flow).
There is an additional complexity in
wake flows not yet mentioned. The
Townsend hypothesis states that a wake
flow becomes self-preserving (i.e., one
length and one velocity scale will be
adequate to describe the velocity,
stresses, and higher turbulence mo-
ments) because the turbulence attains
an equilibrium state which depends only
on the type of flow and momentum
integral, or, in the present case, the
couple.
However, other researchers have
shown that wake strength depends not
only on the drag (momentum integral)
but also on the structure of the dominant
eddies. The flow behind a block-shaped
vehicle will shed vortices into the wake
like a sphere. The resulting "memory"
effect implies that in a block vehicle
wake, the turbulent kinetic energy terms
(u'2, v'2, w'2) will not be self-preserving
in the Townsend sense.
Apparatus
A wind tunnel was constructed espe-
cially for this study. A commercially
available conveyor-belt assembly was
used for the test-section floor, and for
supporting framework for the entrance,
test, and exit sections of the wind tunnel.
The test section was 4.75 m long (4.15
m of which was moving floor), with a
cross-section 0.82 m wide x 0.71 m
high.
The entrance section had the same
cross-section dimensions as the test
section. A bellmouth (diameter of 0.22
m) around the perimeter of the entrance
directed room air into a section of.
Verticel™(Verticel Co., Englewood, CO;
a paper trrangular-cell honeycomb with
a cell length of 0.15 m and a hydraulic
diameter of 0.01 m). Two fiberglass
screens (16 x 18 mesh) were placed
downwind of the honeycomb to further
lower the freestream turbulence.
The moving portion of the test-section
floor was the rubber conveyor belt (0.75
m wide). A notched overlapped joint and
large end rollers produced a smoothly
running belt. Rails along the tops of the
walls were installed to support an
instrument-traversing mechanism. The
longitudinal position of a probe was set
manually; vertical and lateral positions
were remotely set and read from an
operator's desk.
The exit section contained a section of
Verticel and a lateral contraction to a
0.71 m wide x 0.71 m high cross-
section. A cast aluminum fan with three
blades (diameter of 0.61 m) was power-
ed by a two-speed (1140/1725 RPM)
250 W electric motor (115 V, 60 Hz). The
fan was mounted in a metal "venturi
panel" (i.e., shroud) for efficient opera-
tion. Baffle plates of different porosities
were inserted into a slot just upwind of
the fan to fine tune the air speed or to
obtain a variety of air speeds for velocity
probe calibrations. The maximum air
speed, obtained with no baffle plate and
with the fan motor on high speed, was
4.0 m/s.
The operating speed of the tunnel
during all experiments was 1.9 m/s; the
turbulence intensity (root mean square
of the velocity fluctuation divided by the
mean speed) was less than 1 %.
Two additional wind tunnels of a more
conventional nature were used to per-
form additional tests to determine pos-
sible Reynolds number effects and the
extent of the blockage effects resulting
from the size of the models; the Fluid
Modeling Facility's Meteorological Wind
Tunnel, and the Air Pollution Training
Wind Tunnel with test sections of 3.7 m
wide x 2.1 m high x 38 m long and 1 m
wide x1 m high x 3 m long, respectively.
Velocities were measured with
Thermo-Systems(St. Paul, MN) hot-film
anemometers. X-configured probes
(model 1243-20) were used to obtain
transverse velocity components as well
as the streamwise component. The
bridge outputs of the anemometers
(model 1054-A) were suppressed with
signal conditioners(model 1057), atten-
uated, and sent to the laboratory's
Digital Equipment Corporation POP
11/40 minicomputer. Software in the
computer controlled the analog to digital
conversion or sampling rate, linearized
the signal, and provided real-time dis-
plays of results. The probes were cali-
brated in position on the instrument-
traversing mechanism against a pilot
tube located nearby for determining
mean test section velocities obtained
with the various baffle plates. The X-
probe was oriented to measure either
the streamwise and lateral components
or the streamwise and vertical compo-
nents. Calculated values were mean
streamwise speed, fluctuating stream-
wise and transverse components, and
the associated Reynolds stress. Most
measurements were made at 100
samples/s for 30 s. A few ten-minute
samples at 500 samples/s were taken
at 30 heights downwind of the vehicle at
various vertical positions, to calculate
turbulence spectra. From these, an eddy
viscosity formulation was derived for
use in a theory presented below.
Simple block-shaped models were
constructed of wood, with the dimen-
sional proportions of a typical automo-
bile. Each model was mounted on a
baseplate with wheels and rubber tires.
Approximate scale ratios of 1/32 and
1/8 were used.
The 1 /32-scale block-shaped vehicle
was patterned on the dimensions of an
intermediate size American automobile:
height = .043 m, width = .055 m, length =
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.145 m, ground clearance = .009 m, and
wheel diameter = .024 m. The 1 /8-scale
vehicle was four times as large in all
respects.
Summary and Conclusions
An experimental study of the wake of
a moving vehicle was made using a
specially-constructed wind tunnel with
a moving floor. A block-shaped model
vehicle was fixed in position over the
test-section floor, while the floor moved
at the freestream air speed to produce a
uniform, shear-free, approach flow. This
simulates an automobile traveling along
a straight highway under calm atmos-
pheric conditions.
Vertical and lateral profiles of mean
and fluctuating velocities and Reynolds
stresses in the wake of the vehicle were
obtained, using a hot-film anemometer
with an X-probe. Profiles were taken at
distances of 10 to 80 model heights
downwind of the vehicle.
A momentum wake was observed for
the block-shaped vehicle. The wake does
not have a simple self-preserving form.
However, it is possible to collapse the
velocity deficit with one length growth
rate and one velocity scale, and the
turbulence with different length growth
rate and velocity scales.
The velocity deficit behind the vehicle
decayed as (x/h)~3/J4, and the length
scale grew as (x/h)1/4, confirming the
earlier predictions of Eskeridge and
Hunt. However, the turbulent kinetic
energy components decayed as (x/h)"1'2,
and the turbulent length scale grew as
(x/h)04, instead of the self-preserving
solutions of (x/h)'3'2 and (x/h)1/4 that
were predicted.
Velocity deficit solutions were found
for the equations of motion in three
cases: first, when scale-lengths differed
for the lateral and axial directions with
constant viscosity (two scale lengths);
second, when viscosity varied continu-
ously in the vertical; and finally, a
matched solution where viscosity varied
linearly near the surface and then was
held constant above a given height.
None of the above solutions matched
the data in all respects, but the two-
scale-length, variable-viscosity solution
was the best.
The turbulence decayed longitudinally
as (x/h)~1 2. To describe the behavior in
the lateral and vertical direction, a two-
dimensional fit of the data was found by
least-squares-fit, using "orthogonal" poly-
nominals. Appropriate constants were
determined from the data which allow a
complete description of the wake tur-
bulence.
Numerical models that predict pollu-
tant concentrations along roadways can
be enhanced by including the physical
properties of wakes found in this study.
The EPA authors Robert E. Eskridge (also the EPA Project Officer, see below)
and Roger S. Thompson are with the Environmental Sciences Research
Laboratory. Research Triangle Park, NC 27711.
The complete report, entitled "Wake of a Block Vehicle in a Shear-Free Boundary
Flow—An Experimental and Theoretical Study," (Order No. PB 82-196 528:
Cost: $12.00, subject to change) will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield. VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Environmental Sciences Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
U.S. GOVERNMENT PRINTING OFFICE: 1982 - 559-017/0732
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United States
Environmental Protection
Agency
Center for Environmental Research
Information
Cincinnati OH 45268
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Fees Paid
Environmental
Protection
Agency
EPA 335
Official Business
Penalty for Private Use $300
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