-------
Townsend (1976) hypothesized 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 moments) 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, Bevilaqua and Lykoudis (1978) 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 the sphere Bevilaqua and Lykoudis studied. 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.
-------
SECTION 2
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 atmospheric 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
anemomenter 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 was found to decay as (x/h) '
and the length scale to grow as (x/h) , confirming the predictions of EH.
-1 2
However, the turbulent kinetic energy components decay as (x/h)~ ' and the
turbulent length scale grows as (x/h)0'4 instead of the self preserving solu-
tions of (x/h)~3/2 and (x/h)1/4 which were predicted.
Velocity deficit solutions are found to the equations of motion for three
cases: first, allowing scale-lengths to differ for the lateral and axial
directions with constant viscosity (two scale lengths) second, allowing vis-
cosity to vary continuously 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.
-------
-1 2
The turbulence decayed longitudinally as (x/h) . To describe the be-
havior in the lateral and vertical direction a two-dimensional fit of the data
was found by least-squares-fit using "orthogonal" polynomials. Appropriate
constants were determined from the data which allow a complete description
of the wake turbulence.
Numerical models which predict pollutant concentrations along roadways
can be enhanced by including the physical properties of wakes found in this
study.
-------
SECTION 3
APPARATUS
3.1 WIND TUNNEL
A wind tunnel was constructed especially for this study (Fig 3.1). A
commercially available conveyor-belt assembly was used for the test-section
floor and 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 and 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
TM
directed room air into a section of Verticel (Verticel Co., Englewood Co.:
paper triangular-cell honeycomb; cell length = 0.15 m and hydraulic diameter
= 0.01 m). Two fiberglas 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 con-
traction to a 0.71 m wide by 0.71 m high cross section. A cast aluminum fan
with three blades (diameter of 0.61 m) was powered 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 operation. 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 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%.
In performing additional tests to determine possible Reynolds number
effects and the extent of the blockage effects resulting from the size of the
models, two additional wind tunnels of a more conventional nature were used:
the Fluid Modeling Facility's Meteorological Wind Tunnel (Snyder, 1979), 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 x 1 m high x 3 m long, respectively.
3.2 VELOCITY MEASUREMENTS
Velocities were measured with Thermo-Systems .(St. Paul, Mn.) hot-film
anemometers. X-configured probes (model 1243-20) were used to obtain trans-
verse velocity components as well as the streamwise component. The bridge
outputs of the anemometers (model 1054-A) were suppressed with signal condi-
tioners (model 1057), attenuated, and sent to the laboratory's Digital Equip-
ment 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 displays of results. The probes were calibrated in posi-
tion on the instrument traversing mechanism against a pitot 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 components. Calculated
values were mean streamwise speed, fluctuating streamwise and transverse com-
ponents, and the associated Reynolds stress. Most measurements were made at
100 samples per second for 30 seconds. A few ten-minute samples at 500 samples
per second were taken at 30 heights downwind of the vehicle at various vertical
positions in order to calculate turbulence spectra. From these, an eddy visco-
sity formulation was derived for use in a theory presented below.
3.3 MODEL VEHICLES
Simple block-shaped models were constructed of wood; they had proportions
of height, width and length of a typical automobile (Fig 3.2). Each model
8
-------
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 = .145 m, ground clearance = .009 m, and wheel diameter = .024 m. The
1/8-scale vehicle was four times as large in all respects.
3.4 EMPTY WIND TUNNEL FLOW CHARACTERISTICS
Homogeneity of the mean flow was checked with the tunnel operating at test
condition by measuring vertical profiles at various positions in the test
section. Fig. 3.3 shows profiles on the centerline for distances of 1, 2, 3
and 4 m from the front of the test section. Fig. 3.4 displays the lateral
homogeneity with profiles at a distance of 1 m from the front of the test
section at lateral positions of -.205, 0, and .205 m. The air speed was 1.9
ms ; there was little scatter down to the belt surface.
Vertical profiles of the turbulence intensity at a distance of 1 m from
the front of the test section and lateral positions of ±.205 m are shown in
Fig. 3.5. The turbulence intensity is seen to be constant and below 1% except
very near the belt, where probe sensitivity near the surface is suspect.
3.5 WIND TUNNEL BLOCKAGE EFFECTS AND REYNOLDS NUMBER INDEPENDENCE
In order to determine if the velocity and turbulence profiles for the
large vehicle were affected by blockage in the moving-belt tunnel, several
tests were performed with both the small and large vehicles. These experi-
ments were performed in the moving belt tunnel and in two other wind tunnels
so that various values of the base pressure coefficient,
P - P
rsy. rb
could be determined as a function of Reynolds number and blockage ratio. In
(3.1) PS is the free-stream static (reference) pressure upwind of the vehicle
-------
(F1g. 3.6), P^ 1s the static pressure pleasured on the rear surface, and 1/2
pU^ 1s the reference dynamic pressure.
Now (3.1) can be written as
P - P
'& >
P - P
'* rs
or
f>0 - f»
(3.2)
where P is the local static pressure and P is the total pressure given by
P_ = 1/2
+ Ps . The pressure ratios in (3.2) can be easily determined
from measurements.
In Fig. 3.7 the spanwise variation in C for various blockages is shown.
While the pressure is not constant across the rear as one might expect, the
variation is small, and is most likely due to asymmetries in the vehicles and
the flow not being exactly normal to the front of the vehicles. Since the
pressure variations were small, the pressure at the tap at y/W = -0.25 was
used in all calculations.
In Fig. 3.8 data are presented showing that while -C_ is a function of
pb
blockage ratio it does not appear to be a function of Reynolds number. However,
there was considerable scatter in the data.
The pressure coefficient -C is plotted against blockage ratio in Fig. 3.9.
pb
For the experiments performed in the non-moving belt tunnels, the vehicles were
placed near the tunnel entrance immediately downwind of the contraction. This
insured a small floor boundary layer (thickness fi). The boundary layer was, of
course, relatively more important for the small vehicle than for the large
vehicle. This may be the reason for the sudden change at small blockage ratios
which otherwise is not reasonable.
The drag coefficient, Cn, can be estimated by assuming that the normalized
2
integrated pressure coefficient on the front face is (0.8) , as reported by
10
-------
Mason and Beebe (1978), to give
= (0.8)%(-CP\
(3.3)
Table 3.1 shows the calculated drag coefficient as a function of blockage
where A^ and Ay are the cross-sectional areas of the model and wind tunnel,
respectively.
TABLE 3.1. DRAG COEFFICIENT AS FUNCTION OF BLOCKAGE
(% blockage)
.51
3.84
6.50
0.775
0.876
0.957
We see that the drag coefficient is about 20% greater for the large car in the
moving belt tunnel than for the small car in the same tunnel (Table 3.1).
An empirical formula (Castro and Fackrell, 1978) for estimating the
blockage effect on drag has the form
CD =CD(l-AM/AT)m
(3.4)
where
p
is the observed drag coefficient. For the block vehicle, m was
found to be 3.31. For two-dimensional fence flows, Castro and Fackrell found
m varied between 2.6 and 7.5 depending on the ratio
-------
C, acting on the vehicle to a surface integral of the velocity deficit,
u(x,y,z), assuming that an integral of the surface pressure is small. That
is:
CO CO
,1 T^ J.. J,
(3.5)
A control volume analysis of the conservation of momentum yields a relation
ship for the drag, D, on the vehicle:
x
0.6)
0 "00 -CO -00
where T (x,y,o) is a surface shear stress defined in Appendix A.
i A
A centerline vertical profile of u/U and a lateral profile of u/U at
z/H = 0.5 are plotted in Figs. 3.10 and 3.11, respectively, for the small and
large vehicle at x/H = 15. These two figures imply that the couple computed
from (3.5), scaled by vehicle size, would be approximately equal for both
vehicles. Similarly, the first term on the right side of (3.6) would be the
same for both vehicles. The previously discussed difference in drag coefficients
for the two vehicles can be explained as a difference in the integrated surface
shear, the second term on the right side of (3.6).
Reynolds -number independence of the vehicle wakes is further supported by
a comparison of velocity fluctuations at x/H = 15 shown in Fig. 3.12. Thus,
similar wakes exist for the two sizes of vehicles independent of the somewhat
larger coefficient of drag found for the large vehicle.
In summary, wind tunnel blockage is not a problem and the wake flows are
independent of Reynolds number.
12
-------
SECTION 4
WAKE THEORY AND MEASUREMENT OF VEHICLE WAKE
4.1 REVIEW OF VEHICLE WAKE THEORY
A car moving at speed U through a calm atmosphere (windspeed <1 ms ) is
equivalent to a car held fixed in space over the roadway with the road and
air moving past the car at speed U. The coordinate system used here has its
origin at the rear of the vehicle. Several heights downwind of the vehicle,
beyond the recirculation region, the velocity deviations (u,v,w « U) from the
undisturbed flow are small enough that a perturbation analysis of the equations
of motion can be carried out (details are found in EH). The first equation of
motion has the following linear form
where it is assumed that
(4'2)
and the eddy viscosity can be estimated as
(X) GC,<(xl IAWWC(X), (4.3)
where £(x) is a vertical scale length in the wake and um., (x) is the maximum
max
velocity deficit in the wake.
In this (EH) theory it is implicit that the vertical and lateral length
scales are Identical. The pressure gradient term in (4.1) can be neglected;
13
-------
the solution to the resulting equation is
(4.4)
where
Y[ =
(4.5)
Y and A are constants, and H is the height of the vehicle. The value of A can
be estimated by approximating the couple acting on the vehicle by the drag on
the vehicle times one half the height of the vehicle. This results in (see EH)
we.
(4.6)
The turbulence is estimated by assuming it has a self-preserving form and
that the turbulent kinetic energy is proportional to the eddy shear stresses in
the wake. This yields the results:
rs/a
(4.7)
(4.8)
14
-------
This theory is reasonable for the velocity field except near the surface,
where it is clear that a much stronger shear layer exists than is possible with
a constant eddy viscosity. Also, the theory does not allow for obstacles that
are wider than they are high. Fig. 4.1 shows a centerline velocity profile
taken at x/H = 60 compared with the original theory. It is immediately obvious
that the wake contains a very strong shear layer near the surface that is in-
compatible with a constant eddy viscosity in the vertical direction as proposed
in (4.3).
4.2 VERIFICATION OF THE EH THEORY
One of the important predictions of the theory in EH is that the velocity
deficit and lateral length scale vary as
-------
where
Now (4.10) can be written as
(4.11)
The left hand side of (4.11) was computed from the data on a point by point
basis using cubic spline fits to velocity deficit profiles to obtain |^. Near
oZ
the top of the wake and near the maximum velocity deficit, u'w1 and |^- become
oZ
small so that errors in u'w'/dr) can be large. However, the ratio was found
dZ
to be nearly constant over the range between these extremes and an average value
was computed for each downwind distance. These are plotted in Fig. 4.6 which
shows that the left hand side of (4.11) can be reasonably fitted with a line
of slope -1/2. Since we have already shown that u _ a (n-)" » this implies
max rt
again that
'4 (4.12)
However, the theory developed in EH does not describe the lateral spread
of the wake as well as desired. The EH theory assumes that £(x) is the correct
length scale in both the vertical and lateral directions. This is equivalent
to assuming the vehicle is as wide as it is high which is incorrect. The line
through FV/^) in Fig. 4.6 lies well above the line through u^w7/^) imply-
ing different length scales for the vertical and lateral directions.
4.3 MODIFIED WAKE THEORY
A modified theory which accounts for different scale lengths in the
lateral and vertical directions is derived in Appendix B. The solution for
16
-------
the velocity deficit is the same as (4.4) except that now
(4.,3,
and the constant A in (4.4) is given by
1/4
(4.14)
C
where A and y are constants with values of 1.14 and 0.095, respectively. The
length scales are
4.4 HEIGHT-DEPENDENT-VISCOSITY WAKE THEORY
A further modification to the theory was made in an attempt to improve the
agreement between the theory and data for the region of strong shear near the
surface. The eddy viscosity was allowed to vary in the z direction as described
in Appendix C, where the details of how the height dependence of the eddy
viscosity was determined from spectra of w'2 are also presented. A numerical
solution was then found.
Appendix D contains a simplified approach to a height-dependent eddy
viscosity solution using a linear approximation in the strong shear layer and
dividing the solution of the equation into two regions. The lower region has a
linear increase in eddy viscosity and the upper region has a constant eddy
viscosity. Results from this technique did not differ substantially from the
numerical solution using a continuously variable eddy viscosity and are there-
fore not presented.
17
-------
The three theories, original EH, modified lateral length scale, and
height-dependent-viscosity, are compared with vertical and lateral velocity
deficit profiles in Fig. 4.7 and 4.8, respectively. The height-dependent
eddy viscosity theory lowers the height of the maximum deficit by a factor
of nearly two and increases the shear near the surface (Fig. 4.7). However,
the maximum in the data occurs still lower. The improvement in describing the
lateral extent of the wake by the modified lateral length scale theory is
evident in Fig. 4.8.
Lateral profiles of velocity deficit at a constant similarity height, c,
are shown in Figure 4.9. These profiles are reduced to similarity coordinates
and compared with the height-dependent-viscosity theory in Fig. 4.10. Vertical
profiles of velocity deficit are compared with the height-dependent-viscosity
theory in Fig. 4.11.
4.5 TURBULENT KINETIC ENERGY TERMS
Preliminary analysis of the fluctuating velocity data indicated that the
lateral length scale determined for the velocity deficit would not collapse the
profiles of the turbulent kinetic energy components (TKEC). The decay rate of
the TKEC was also found to be different than that proposed in EH where complete
self-preserving flow was assumed for the wake.
The turbulent energy budget equation can be written (Tennekes and Lumley,
1972)
_L IJ. ^_
Z ui
(4.16)
where
(4.17)
18
-------
and the convention of repeated indices to indicate summation is used.
Assuming as for the velocity deficit solution that longitudinal changes
scale with x, while crosswind changes scale with I1 where a'/x « 1, let
li2 = 1/3 u.u. and make order of magnitude estimates of the terms in (4.16).
Assuming there is only one velocity and length scale in the wake:
j-fij (* ^ V Uo
-------
(4.19)
A transverse Eulerian integral length scale defined by
^vjjjv^ j (4-20)
o V'(o)
was computed from data obtained using two x-film probes. This length scale
is believed (Tennekes and Lumley, 1972) to be comparable to the Lagrangian
integral length scale for most turbulent flows and is thus a measure of the
size of the dominant eddies within the wake. Thus, I1 should be related to
£r; if we empirically determine the x-dependence of i^ and assume I1 « £E
we can evaluate a and 6.
The two probes were calibrated and then positioned in the wake of the
block vehicle at one half of the vehicle height. One probe was positioned on
the wake centerline while the other was moveable in the lateral direction.
Profiles of v'(o) v'(y) were obtained at downwind distances of x/H = 15, 30,
45, and 60 (Fig. 4.12). For the greater downwind distances, v'2 in the wake
was not large compared with background values, so vh'ackaround was subtracted
from v'2(0) for each profile.
The length scale ££ was determined for each of the profiles by a trapezoi-
dal integration. A power-law fit corresponding to a = 0.40 is shown in Fig.
4.13. The value of $ computed from (4.19) is therefore 1.2. Using the computed
length scale £r to normalize the space correlations of Fig. 1 collapses the
data nicely (Fig. 4.14).
The maximum values of u'2 and v'2 were determined from the vertical center-
line profiles obtained at various downwind distances. These are shown in
20
-------
Fig. 4,15 along with the least squared error fit which gives p * 1.2, in
agreement with the Independent estimate from (4,19).
Thus, the vehicle-generated turbulence in the wake was found to decay as
(x/H)"1'2 and the lateral length scale was found to grow as (x/H)0'4.
The spatial variation of the turbulent kinetic energy is assumed to be
given by
(4.22)
u>*2/£H
and
= 1.0, (4.24)
At (x/H) = 30 detailed measurements were taken in the lateral direction
using a 3-min. averaging period. The function F (x,o>) was determined by a
w
least-squares fit using orthogonal polynomials of the fourth degree (Clark,
Kubik and Phillips, 1963):
Fc(x,u) = ₯00 + W^f01* u(₯02 + u (>F03 + u
+ X4 (*40 + ^(^ + w(V42 + u() = 0.0 when:
c c
i) |xj 1 0.55 or | w | >_ 0.64
1i) x ±0-0 and tt >1.82X + 1.15
111) x > 0.0 and u >-1.82x + 1.15
21
-------
The coefficients 1n (4.251 are found 1n Table 4.1. From these data the con-
stants 1n (4.211 were found to be a^ = 0.048, a2 ~ 0.040, and a3 = 0.030.
In Figs. 4.16 to 4.18 normalized cross-sections of the turbulence com-
ponents u'2, and w'2 are shown fitted by the orthogonal polynomials of (4.25).
The contours of FC are presented in Fig. 4.19.
Using (4.21J with the numerical fit from Table 4.1, vertical and lateral
profiles of the fluctuation velocity components can be estimated. Using simi-
larity coordinates, data at various longitudinal distances can be plotted and
compared to these estimates. F1gs. 4.20 to 4.22 show linear and similarity
plots of vertical profiles of u'2, v'2 and w'2, respectively. Figs. 4.23 and
4.24 show linear and similarity plots of lateral profiles u'2 and w'2.
4.6 REYNOLDS STRESSES IN THE WAKE
The wake theories presented in this paper and that of EH make no predictions
regarding the decay of the Reynolds stresses. Bevilaqua and Lykoudis (1978)
define a hierarchy of self-preserving wakes starting with order one, where mean
velocity profiles are self-preserving; order two, where in addition Reynolds
stresses are also self-preserving and so on.
From the data for center!ine variation of the stresses (Fig. 4.25a for
u'w'), it is easy to show that the stresses decay as (x/H) ' and hence using
25
the EH value of (x/H) as the length scale growth rate, the data collapse as
shown in Fig. 4.25b. Fig. 4.25c is the same data plotted using TKEC similarity
coordinates. It is easily seen that the wake is self-preserving of order two
in terms of EH similarity variables. Fig. 4.26a and b show lateral profiles of
u'w1 at various (x/H) distances, and then the same data in EH similarity co-
ordinates. The uV stresses, shown, are similar to the u'w1 stresses.
22
-------
TABLE 4.1 COEFFICIENTS OF POLYNOMIAL TWO-DIMENSIONAL FIT TO TURBULENT
KINETIC ENERGY FUNCTION F .
^00 = 0.3163277 x 10"1
T01 = 0.1130908 x 102
T02 = -0.4320938 x 102
^03 = 0.6065336 x 102
₯04 = -0.3218438 x 102
f20 = -0.1703226
Y21 = -0.8419376 x 10
₯22 = -0.1640925 x 103
Y23 = 0.5061181 x 103
^24 = -0.3599435 x 103
*40 = 0.2386405
*41 * -0.8499160 x 102
*42 = 0.9322793 x 103
^43 = -0.2115435 x 104
744 = 0.1360754 x 104
23
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25
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APPENDIX A
CONTROL VOLUME ANALYSIS
The overturning moment acting on the vehicle can be related to the
velocity deficit in the wake with a control volume analysis. Consider the
control volume enclosed by the box shown in Fig. A-l . The vehicle is excluded
from the control volume and the effects of the vehicle on the flow are combined
into the overturning moment, C. The small areas where the vehicle tires con-
tact the ground are ignored in the analysis.
The vector equation for conservation of moment of momentum is
where z ft is the sum of externally acting moments on the control volume, r is
a position vector, q is the velocity vector (U-u,v,w), n is an outwardly
directed unit vector, t, j\ t are the unit vectors in the x,y,z directions
-> + * ->
respectively, and M = r x F where F is a force on the control surface.
Steady state conditions are assumed, i.e. ^' ' = O . Since the over-
turning moment of the vehicle is about the y-axis, the dot product of j" with
(A-l) is taken; this, together with an assumption of constant density gives
(A-2)
By definition, a shear stress component is positive when the shear stress
and vector outwardly normal to the surface of action both act in the positive
or negative directions. The shear stress, TV , acts in the x.{ direction along
X1xj J
26
-------
a surface normal to the *. direction.
The external moment about the y-axis resulting from forces acting on
Face 1 are due to pressure and shear stress:
-
Combining and integrating over the area of the face yields the total torque
about the y-axis on
2, Y,
Face 1:
o -Y;
In a similar manner the external moments on the other faces are found to be
on
2rt
27
-------
2. Y,
Face 2:
Xi ?,
Face 4: -Xt (X| Vl/
-*, o
Face5:
-x, -Y
<
J /
^ t 2, T2X U^, 2,)] J
Xi Y
Face 6 0 0
(and vehicle surface): \\ [^ * *(*y ^/Oj] Ju^x - L
28
-------
C 1s the overturning moment acting on the vehicle which 1s positive In
the y direction; C 1s the result of all forces from pressure and stress acting
on the surfaces of the vehicle.
Now the left hand side of (A-2) can be written
(A"3)
x,. r,
- C .
We also can write the pressure as the sum of a mean and perturbation
and we assume the perturbation pressure to be zero far upstream of the vehicle,
i.e. p(x-i, y, z) = 0. The T'S may also be considered perturbation quantities
since TUDstream = ^ (uniform flow). Equation A-3 can now be written as
* From symmetry, T (x,Y,,z) =^r (x, -\J,z), etc.
29
-------
2, Y,
O -Y|
Xt.
-"X, o
it
^*< * '{
-c
Now the moment of momentum crossing each face of the control surface must
be computed, i.e. the right hand side of (A-2).
Face (1)
a -
also / x? v;? \. "f - zU and
therefore I = - f 2 U
' ^j j
o -X
30
-------
Face (2)
also trx£)- = 2 U-utvV,,*) - XW(X,-V;,E);
and
Xl
I 2 = -
Face (3) - avv(
v(i f s
also (rx)«J = 2 iy-u)-Xj.w ^J r\.? = U-u . Hewce,
I3 = f
o -^
and
also
and (w«= V
Thus T4r f
-*< o
31
-------
Face C5) ,r*x*
-------
Now |wl£<|u| (from EH), so that X2Uw«zUu in the first integral.
Let Z^froo; then p(x,y,Z1 )-*0, w(x,y,Z1 )~»0, andTzx(x»y»Z1 )->0.
Also let Y]-*oo; then T (x,Y] ,z)^0 and V(X,YI ,z)-»0. Let -Xj»-»,
and since X2 is arbitrary it can be replaced with x, reducing (A-5) to
(A-6)
, - -* j i \
"^ -CD -CD
The first equation of motion in perturbation form is
(A-7)
Since there are no momentum sources in the control volume from x = x to
x = oo » y = -eo to y = oo, z - 0 to z -oot eq. (A-7) holds everywhere
and can be integrated over this volume.
Integrating (A-7) with respect to y from -co to «o yields
O Oo oo ct>
1 \ 3? Ju 4. J. V 3?** ,j 1 f 3?n i
f \3x^^f jr^n^^V (A-8)
-co "~°° -oo ~ce>
_
Now f JIT^ ~ x^5 ~ ) yielding
-co
-co -co -co
Integrating (A-9) with respect to x from x to CD yields
00 OO
X -co X -oo X "00
33
-------
or
' CO CO °0 00
"*"»'
CD CO X -°°
Multiply by z and Integrate with respect to z from 0 to co
OO GO OO OO OO OO 00
0 -«> o-oo O X -c»
o x -oo -oo * o
,00 n
so that (A-12) becomes
C=
o -oo ^ "0° "c°
- CD
0-00 -0) K 0
OO
i ixP^i
-CD C»
34
o-oo 0 -» OM*
And (A-6) can now be written as
oo OQ °o co x
-------
Since
5° *
\T J - V 'i
Now (A-7) can be written for distances sufficiently far downwind that the
perturbation pressure is negligible (see section 4.1), as
. £i "I
+ J
J
Multiply this by z, integrate the right hand side by parts from z = 0 to
and then integrating with respect to y from - oo to cx>, to get
CD GO
or
-00 o
The couple on the vehicle for a given situation is a value that could be
determined by measurement. At distances sufficiently downwind for (A-19) to
hold, we can therefore conclude that the second integral on the right of (A-17)
is a constant, not a function of x. It is assumed that the second integral in
(A-17) 1s small and therefore the couple on the vehicle determines the wake
strength. Hunt (1974) indicates that the second integral can be neglected
for three dimensional objects.
35
-------
When the stress is approximated by a viscosity that varies in the vertical
direction the analysis is similar to that given with the following modifications
Equation (4.1) in section 4.1 takes the form
where H*(x,z) is the vertical dependence of viscosity
Multiplying by z and integrating with respect to y and z yields
oo
y I i_ J ' ' 13 I a U
-a, o jo J* J J*
(A-21) then gives an integral constraint on the definition of H*(x,z) i.e.
CO
(A-22)
since the right hand side of (A-21) must be zero. From (A-21) and (A-22)
oo
0 y (A-23)
The analysis of the couple would be the same since (A-16) would take the form
oo 00
(A-24)
In the work presented in this paper it is assumed that (A-22) is satisfied.
36
-------
APPENDIX B
MULTI -SCALE WAKE THEORY
The following derivation follows very closely the form in EH. The
assumptions are the same as those given in Section 4.1 and we use the same
notation.
The linearized first equation of motion is given
where the shearing stresses are assumed to have the form
where W and H are the width and height of the vehicle, respectively, and
We have allowed for different length scales in the lateral and vertical and
assume them to be related by
As in EH it can be shown that 3p/3x can be neglected. (B-l) now becomes
U/1 1\ 1 (B-5)
37
-------
Assume a solution of the form
where A Is a constant to be determined and f <. 1.
Now, let
= 2/jfut)
-------
From the control volume analysis given in Appendix A the overturning couple on
the vehicle is given by
C
C*r(
O
CO CO
" ~~ * (B-12)
-co o
The approximation on the right is obtained by taking the overturning moment to
be the drag force times one-half the vehicle height.
If we substitute (B-6) into (B-12) the integral constraint becomes
(B-13)
-CO O
Hence,
C
H » or
From (B-ll) and (B-14)
x3 x"3m x"m = constant, /B_15v
-3/4
which implies that m = 3/4. Thus, we have %x(x)<< x and
J?(x)flCx1/4. If we define f(x) = ^AH (x/H)1/4, and note that
= AU (x/H)'3/4, (B-8) becomes
max
39
-------
describing the behavior of the velocity deficit in all planes normal to the
wake.
The solution to (B-16) is known (EH) to be
A ^ / -i \'/z
where JU, ~
The constant A can now be computed using (B-12) and (B-17);
co oo
(B-is)
j
yielding
^ X^ --^ f /Vl
(B-19)
40
-------
The solution for the velocity deficit Is now known (B-6, B-17, and B-19)
except for two constants y and \.
To determine X we use (B-2);
(B-20)
and
^ T*, "V-r (X) = \7\i~> / ( ^ \
(B-21)
The right hand sides of (B-20) and (B-21) have been determined at various
downwind distances by fitting vertical and lateral velocity profiles with cubic
splines which were differentiated to determine the velocity gradients (Fig. B-l),
Above the maximum velocity deficit the velocity gradient was well behaved and
averaged values of -u'w'/(3u/3z) and -u'v'/(3v/3z) are plotted in Fig. 4.5.
The straight lines fitting these points are least squares linear fits to the
data.
The value of A. can now be determined by using, say, x/H = 10 and the
fitted values to the profiles yielding
(B.22)
To determine y we rewrite B-3 as
(B~23)
41
-------
or
l/V (*/H)
(B-24)
At x/H = 10, vT2/U2H2 = (0.007)2 and by use of (B-19) one finds that
- 0,095".
(B-25)
42
-------
APPENDIX C
HEIGHT-DEPENDENT-VISCOSITY WAKE THEORY
Assume the perturbation equation of motion (B-1) can be written as
where H*(x,z) is some function of height having a continuous derivative. From
Appendix B we can express (C-l) and its solution as
(C-2)
^W^l
,*)^)* -J
and
(C-3)
where
(c'4)
43
-------
Substituting (C-3) Into (C-2) yields for f the partial differential
'Xi <\i
equation (H(0 is the transform of H*(x,z) and H(c) <1)
(C-5)
Equation (C-5) can be solved in part by assuming it is separable, i.e.
This yields ^C"6^
and
(C-7)
where (C-7) is subject to the boundary conditions
(C-8)
Analytic solutions are easily found for (C-7) and (C-8) only when H(c) is
a simple function. Hence, (C-7) and (C-8) have been solved numerically using
the Runge-Kutta-Nystrom method (Kreyszig, 1962).
'X/
To arrive at an expression for H(c) we have taken data along the center-
line (y=0) at x/H = 30 for z/H = 0.15, 0.29, 0.44, 0.59, 0.74, 0.88, 1.03, 1.18,
44
-------
1.32, 1.47, 1.76, 2.06, 2.35, and 2.94, which allowed us to compute spectra
at each height (see Fig. C-l). We further assumed that
where (w12) ' is the standard deviation of the vertical velocity, U(c) is the
mean wind speed at height c, and N is the frequency containing the maximum
energy. A best N was determined for each height from the spectra together with
estimated upper and lower bounds. The product (w'2) ' U (?) N is normalized
by dividing by its maximum value. These results together with error ranges
are plotted in Fig. C-2. The following function describing H(e) was found by a
least-squares fit to the data in Fig. C-2, after changing variables from z/H
to c.
(C-11)
3 -0,
In order to describe the vertical change in viscosity we plotted
u'w'/(3u/3z) from data taken with the 1/8 scale block vehicle. The vertical
velocity gradient was estimated at each point with a cubic spline fit. The
estimate naturally contains error and is partly responsible for the scatter in
Fig. C-3. Careful study of Figure C-2 and C-3 shows that, except for scatter,
the trends in both plots are the same and the maximum occurs near z/H = 1.25
in both plots.
45
-------
APPENDIX D
SIMPLIFIED HEIGHT-DEPENDENT-VISCOSITY WAKE THEORY
A simple approximation for the height-dependence of the eddy viscosity can
be made that will lead to an analytic solution. If we assume that viscosity
^
distribution function H (c) has the form
then (C-8) can be solved as follows. Substituting (D-l) and its derivative
into (C-8) yields (assuming 5 < e )
2T = 0. (D-2)
(D-2) can be transformed into a standard form of Kummer's equation by
(Abramowitz and Stegun, 1964)
(D_3)
Eq. (D-2) becomes
46
-------
The general solution to (D-4) is
(D-5)
where A2 and AS are constants and the power series, M(a,b,z), is defined by
where (a)n = a(a+l) (a+2)...(a+n-1) and (a)Q = 1.
In(D-5) , -- (D-7)
While the first part of the solution can be expressed in terms of elementary
functions as
no such simplification appears to be obtainable for M(a,b,z).
-------
In order to match solutions, it is necessary to assume that y and
A (defined in Appendix B) are independent of the assumed form of viscosity
used in each model. Otherwise the c in D-9 and D-8 will not be the same
coordinate.
The two solutions D-5 and D-9 have four unknown constants; therefore, it
is necessary to specify four constraints on the problem.
The boundary condition U(0) = 0 means
° ^ 5=0
which furnishes the first condition. Requiring a continuous solution and
derivative at the matching point ? requires that
and
The fourth condition used is that
max f 1 , f2 = 1.0. (D-12)
With the constraints given in D-10 thru D-12, the normalized variation of
velocity deficit in the vertical can be computed and the lateral variation can
be computed using (C-7).
48
-------
Figure 3.1. The wind tunnel.
49
-------
Figure 3.2. Scale model vehicles.
50
-------
.50
.45
.40
.35
.30
I
.20
.15
.10
.05
T I I I I I I I T
A 1 m FROM TEST SECTION ENTRANCE
O 2m FROM TEST SECTION ENTRANCE
a 3 m FROM TEST SECTION ENTRANCE
4m FROM TEST SECTION ENTRANCE
.4 .6
U, m/s
40
E>*
I I I I I I I I A|
1.0 ' 1.2 1.4 1.6 1.8 ' 2.0
Rgure 3.3. Empty tunnel, mean velocity profiles for four longitudinal positions on
centeriine.
51
-------
50
.45
.40i
.35
.30
-25
.20
.15
.10
.05
i i i i r
A ON CENTERL1NE
O -0.205 m FROM CENTERLINE
O +0.205 m FROM CENTERLINE
i i r
OOA__
a
a
III I I I I I
0 .2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0
U, m/s
Rgure 3.4. Empty tunnel, mean velocity profiles for three lateral positions at a distance
of 1m from the test section entrance.
52
-------
.44
.40
.36
.32
.28
.24
.20
.16
.12
.08*
.04
i i i i i i i i i r
QAO
0 A ON CENTERLINE
D -0.205 m PROM CENTERLINE
° +0.205 m FROM CENTERLINE
AO
G& O
DA O
AID
a&o
A DD
O
43 O
a A o
a A o
a
a A °0
I I I i I I
1° f °|QD
.002 .004 .006 .008 .010 .012 .014 .016 .018 .020 .022
Rgure 3.5. Empty tunnel, turbulence intensity profiles for three lateral positions at a
distance of 1m from the test section entrance.
53
-------
Ps
U.
U-, P,
figure 3.6. Locations of pressure measurements for determining blockage effects.
54
-------
0.3
0?,
O~
0.2
0.1
.0
AM/AT'
O 0.0650, FLOOR MOVING
Q 0.0024, FLOOR FIXED
A 0.0051, FLOOR FIXED
0.0384, FLOOR FIXED
0.0650, FLOOR FIXED
A 0.0041, FLOOR FIXED
-0.4
-0.2
0.2
0.4
y/W
Figure 3.7. Spanwise variation on Cpr- for various blockage ratios,
55
-------
I 1 1 I
1 1
1 1
.3
o
0:2
o
*
\
\
A\
0/f
I
A/
O
D
I I
0.0650, FLOOR
0.0024, FLOOR
0.0051, FLOOR
0.0384, FLOOR
0.0650, FLOOR
0.0041, FLOOR
MOVING
FIXED
FIXED
FIXED
FIXED
FIXED
I
10" 2x104
4x104
6x104
8x104
Re
10s
Figure 3.8. Cpg as function of Reynolds number for various
56
-------
0.3
0.2:
"07
0.1
0.02
U LARGE CAR
O SMALL CAR
0.04
0.06
figure 3.9. Variation of Cp-- with blockage ratio.
57
-------
1/32 SCALE VEHICLE
O 1/8 SCALE VEHICLE
u/U.
Rgure 3.10. Vertical profiles of deficit velocity at x/H = 15, y = 0 for 1/8 and 1/32 scale
vehicles.
58
-------
.20
1/8 SCALE VEHICLE
A 1/32~SCALE VEHICLE
y/W
Rgure 3.11. Lateral profiles of deficit velocity at x/H = 15, z/H = 0.5 for 1/8 and 1/32
scale vehicles.
59
-------
5.0
4.5
4.0
3.5
3.0
5, 2-5
2.0
1.5
1.0
A
A
.025
A 1/32 SCALE VEHICLE
O 1/8 SCALE VEHICLE
B
.050
.075
.100
"(u'2)1'2, m/s
a
i _
o
.125
Rgure 3.12. Vertical profiles of fluctuating velocity component at x/H = 15, y = 0 for
1/8 and 1/32 scale vehicles.
60
-------
2.50
2.25
ZOO
1.75
1.50
1.00:
.75
.50
i i
A 1/8 SCALE VEHICLE
O EHTHEORY
0 .025 .050 .075 .100 .125 .150 .175 .200 .225 .250
u/ET
Figure 4.1. Vertical profile of velocity deficit at x/H = 15, y = 0 for 1/8 scale block
vehicle and EH theory.
61
-------
1.5
5
i L
.1 .2
u/uT
.3
Rgure 4.2. Vertical profiles of velocity deficit for 1/32 scale vehicle, y = 0.
62
-------
0.04
40
X/H
60
80 100
Figure 4.3. Decay of maximum velocity deficit with downwind distance.
63
-------
1.7'
T1.6
I- 1.5
d
:* 1.4
o
1.3
1.1
1.0
10
[x/H]
0.25
20
30
40 50 60
80 100
Rgure 4.4 Rate of growth of the vertical length scale as determined
from velocity profiles.
64
-------
Figure 4.5. Smoke release showing slow growth of the wake.
65
-------
.020
.015
.009
>|c|'.008
~ .007
«
^.006
a.005
i '-004
.003
.002
10
15
-u'v'/[3u], z/H = 0.5
20
30
x/hT
40 50 60 70 80 90 100
Rgure 4.6 Measured Reynolds stress divided by velocity shear as a function of
downwind distance.
66
-------
3.6
3.2
2.8
2.4
2.0
1.6
1.2
0.8
0.4
-0.02
O DATA
.ORIGINAL THEORY [ESKRIDGE AND HUNT, 1979]
.MODIFIED LATERAL LENGTH SCALE THEORY
HEIGHT DEPENDENT EDDY VISCOSITY THEORY
.02 .04
.06
U/U«
.08 .10 .12
.14
Rgure 4.7. Theoretical curves and data for vertical profile of velocity deficit for x/H = 30 and
= 0.
67
-------
ORIGINAL THEORY [ESKRIDGE AND HUNT, 1979]
MODIFIED LATERAL LENGTH SCALE THEORY
HEIGHT DEPENDENT EDDY VISCOSITY THEORY
OOATA
.02 -
0 t-
1.5
y/W
Rgure 4.8. Theoretical curves and data for lateral profile of velocity deficit for x/H = 30 and
z/H = 0.5.
68
-------
Figure 4.9. Lateral profile of velocity deficit at three longitudinal positions at constant £".
69
-------
1.6
1.4! _
1.2
X/H
* ^
: 30, z/H = 0.5
0 i JO
Height dependent eddy
viscosity theory
1 -
s
9
3* 0.8
-N.
i
0.6
0.4
0.2 -
[y/W]/[x/H]
0.2S
Figure 4.10. Theoretical curve and lateral profiles of velocity deficit at constant £ using
similarity coordinates.
70
-------
1.8
tJB
1.4
1.2
o
I 1
^r
i
~ .8
.6
.4
x/H
30
D 60 ~~~
_____ Height dependent eddy
viscosity theory
-0.2 0 .2 .4 .6
.8
K2 .1.4 1.6 1.8
fu/U.]/rx/H1
Rgure 4.11. Theoretical curve and vertical profiles along centerline of velocity deficit using
similarity coordinates.
71
-------
Rgure 4.12. Lateral variation of the correlation of the fluctuating velocity component, v.
72
-------
1.0
.9
.8
.7
.6
.4
I
J I
10
20
30
x/H
40 50 60 80 100
Figure 4.13. Length scale determined from fluctuating velocity component, V.
73
-------
.6
la
-4
.3
.1
x/H
15
30
A 45
060
y/u
Rgure 4.14. Correlation of the fluctuating velocity component in similarity coordinates.
74
-------
.007
.0003
10
60 70 80 90 100
Figure 4.15. Longitudinal variation of the maximum values of the turbulent kinetic energy
components iP and \P together with least squares linear fit
75
-------
H/2
in
CNI
oi
§
CM
12
d
§
d
m
2
CO
0>
«
f
(Q
S
9
0>
§
Q.
I
g
o>
8
o
I
(0
o
o
3=
ii
gz
2~><
o::
(B
-------
in
§
§
8
d
8"
9
I
1
(B
£
V
8 5
*r >
£
o>
2
«
o
S
8
oi
O
SB
<0
O>
-------
H/z
78
-------
I
T3
!!
O
O)
i-a
79
-------
3.0
2,5
2.0
1.0
0.5
I f
I I
1I I 1
x/H
A 15
30
45
O 60
O 80
I I I I
0 .0005 .0010 .0015 .0020 .0025 .0030 .0035 .0040 .0045 .0050
Figure 4.20a. Measured centerline vertical of the turbulent kinetic energy component u at
various downwind distances.
80
-------
.9
.8
.7
1
-
I5
.4
.1
I
x/H
A 15
« 30
45
A 60
0 80
.02
.04
.06
.08
.10
.12
Rgures 4.20b. Measured centeriine vertical variation of u'2 plotted in TKEC similarity
variables compared to eq. 4.21 [solid line].
81
-------
3.0
2,5
2.0
* 1.5 -
1.0
0.5
.0005 .0010 .0015 .0020 .0025 .0030 .0035 .0040 .0045 .0050
2/l|2
V'Z/U
Rgure 4.21 a. Measured centeriine vertical variation of the turbulent kinetic energy
component V2 at various downwind distances.
82
-------
.8
.7
.6
d
.4
.1
A _1_5__
30
45 ^
A 60
O 80
eq 4.21 _
.02
.04
.06
.08
.10
.12
Figure 4.21 b. Measured centeriine vertical variation of v'2 plotted in TKEC similarity
variables compared to eq. 4.21 [solid line].
83
-------
2.5
i i i I i i r IT ri i i I i i i i I i i i i I I i 1 i I i i i i i i i
0 .0005 .001 .0015 .002 .0025 .003 .0035 .004 .0045 .005
Rgure 4.22a. Measured centeriine vertical variation of the turbulent kinetic energy
component w'2 at various downwind distances.
84
-------
.8
.7
.6
^
.4
.3
.1
x/H
15
Q 30
A 60
O 80
i eq 4.21
.02
.04
.06
.08
.10
.12
Rgure 4.22b. Measured centerline vertical variation of w'2 plotted in TKEC similarity
variables compared to eq. 4.21 [solid line].
85
-------
.0036
D! 30, z/H = O.S
O 45
60
y/W
Figure 4.23a. Measured lateral variation of the turbulent kinetic energy component u75 at
various downwind distances.
86
-------
x/H
A 15
30, 2/H = 0.5
45
D 60
eq4.21
I
I
I
I
0 .15 .30 .45 £0 .75 .90 1.05 1.20 1.35
y/[W[x/H]04]
Figure 4.23b. Measured lateral variation of u'2 plotted in TKEC similarity variables
compared to eq. 4.21 [solid line].
87
-------
.0025
.0015
I?
y/W
Figure 4.24a. Measured lateral variation of w at various downwind distances.
-------
.12
x/H
A. 15
30, Z/H = 0.5
45
A 60
eq4.21
A A A
.15 .30 .45 .60 .75 .90 1.05 1.20 1.35
__ y/[w[x/H]04]
Figure 4.24b. Measured lateral variation of w'2 plotted in TKEC similarity variables
compared to eq. 4.21 [solid line].
89
-------
1 -
. -0.0004 -0.0002
.0002
.0004 .0006 .0008
.001 .0012
u'wvu2
Rgure 4.25a. Measured centeriine vertical variation of u'W at various downwind
distances.
90
-------
3.2
2.8
2.4
x
Z
1.2
.8
.4
I I I
A t
A
i
A
x/H
15
A 30
A 60
O 80
a
..D
0*
-0.06 -0.04 -0.02 0 .02 .04 .06 .08 .1 .12
Figure 4.25b. Measured centerline vertical variation of ITw7 in EH similarity coordinates.
91
-------
80
70
60
50
5_ 40
^
. I.
30
20
10
! I
P
A «
' '«
1 I I
x/H
15_
A 30
A 60^
O 80
I I I I
I I
- _ -0.015 -0.01 -0.005 0 .005 .01 .015 .02. .025 .03 .035
u'w'/
Figure 4.25c. Measured centeriine vertical variation of u'w' in TKEC similarity coordinates.
92
-------
.0032
.0028
.0024
.0020
.0016
.0012
.0008
.0004
50
60
Figure 4.26a. Lateral variation of u'W at various downwind distances.
93
-------
1.5
Figure 4.26b. Measured lateral variation of u'w in EH similarity coordinates.
94
-------
, yi,0]
Figure A-1. Control volume for determining the couple.
95
-------
8
-«.
3
i
O DATA
CUBIC SPLINE FIT
Figure B-1. Example of cubic spline fit to velocity profile at x/H = 10, y = 0.
96
-------
0.01
0.001
z
z
0.0001
0.00001
I I I I I 111
III I I I I I-
0.1
1.0
10.0
N
100.0
1000.6
Figure C-1. Example of velocity spectra at x/H = 15. Spike near 20 Hz is due to a vibration
from the moving belt
97
-------
2.4
2.2
2.0
1.8
1.6
1.4
«
1.0
0.8
0.6
0.4
0.2
1 1
I O-
IO
h-O
^
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Rgure C-2. Vertical variation of the eddy viscosity determined from
the spectral data.
98
-------
2.50
2.25
2.00
1.75
1.50
o
1.25
1.00
0.75
0.50 <)
0.25
-0.020 -0.015 -0.010 -0.005
.005 .010 .015 .020
u'w'/[[du/dz]UocH]
Figure C-3. Vertical variation of the eddy viscosity determined from the Reynolds stress
u'w'.
99
-------
TECHNICAL REPORT DATA
{Please read Jmtrucriont on the revene before completing]
1. REPORT NO.
2.
3. RECIPIENT'S ACCESSION>NO.
4. TITLE AND SUBTITLE
S. REPORT DATE
WAKE OF A BLOCK VEHICLE IN A SHEAR-FREE BOUNDARY FLOW
An Experimental and Theoretical Study
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
R.E. Eskridge and R.S. Thompson
8. PERFORMING ORGANIZATION REPORT NO
Fluid Modeling Report No. 13
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Environmental Sciences Research LaboratoryRTF, NC
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
10. PROGRAM ELEMENT NO.
ADTA1D/02-1313 (FY-82)
11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Sciences Research LaboratoryRTF, .NC
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
In-house 1/1/79 to 10/1/81
14. SPONSORING AGENCY CODE
.-?
IS. SUPPLEMENTARY NOTES
16. ABSTRACT
The wake of a moving vehicle was simulated using a specially-constructed wind
tunnel with a moving floor. A "block-shaped" model vehicle was fixed 1n position
over tbe 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 atmospheric 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.
A momentum type wake was observed behind the block-shaped vehicle. The wake
does not have a simple self-preserving form. However, 1t 1s 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 (1979). A theory which considered a height-dependent eddy viscosity was
found to fit the data best.
Length and velocity scales were found for the longitudinal variation of the
turbulent kinetic energy. The lateral variation Is described by a two-dimensional
numerical fit of the crosswind variation of the data.
7.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
e. COSATI Field/Croup
8. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS
UNCLASSIFIED
21. NO. OF PAGES
116
20. SECURITY CLASS (Thispage)
UNCLASSIFIED
22. PRICE
CPA Farm 2220.1 O-73)
100
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