Reference

NBS

PUBLICATIONS

NBSIR 85-3287

AlllDb 031LE7

An Experimental/Computational

Investigation of Organized

Motions in Axisymmetric

Coflowing Streams

R. W. Davis

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Center for Chemical Engineering

Gaithersburg, MD 20899

December 1985

Prepared for: ^orce Office of Scientific Research/ N

A

ng Air Force Base

100 lington, DC 20332

.056

85-3287

1985

NBSIR 85-3287 R83 RESEARCH INFORMATIO!;

CEM’i'CS AN EXPERIMENTAL/COMPUTATIONAL

INVESTIGATION OF ORGANIZED

MOTIONS IN AXISYMMETRIC

COFLOWING STREAMS

ClCICx^

R. W. Davis

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Center for Chemical Engineering

Gaithersburg, MD 20899

December 1985

Prepared for; Air Force Office of Scientific Research/NA

Boiling Air Force Base

Washington, DC

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige. Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
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TABLE OF CONTENTS

Abstract 1

Introduction 2

Experimental Results 4

Computational Results 9

Concluding Remarks 14

Acknowledgments 15

References 15
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AN EXPERIMENTAL/COMPUTATIONAL INVESTIGATION

OF ORGANIZED MOTIONS IN AXISYMMETRIC COFLOWING STREAMS

R. W. Davis

Center for Chemical Engineering

National Bureau of Standards

Gaithersburg, MD 20899

A joint experimental/computational investigation of the entrainment

process in the turbulent mixing of a round jet with a coflowing stream has

been carried out. The overall objectives of this work were to identify and

characterize coherent motions in the mixing region, investigate the

dynamical role these motions play in the entrainment process, and determine

the extent to which entrainment is affected by such factors as initial

conditions and forcing.

It has been found experimentally that, in contrast to the free jet and

to previous theoretical’ predictions based on convected free jet velocity

profiles, the coflowing jet undergoes a streamwise evolution in scaling

characteristics. The wake region near the origin of the jet is responsible

for a streamwise variation in spectra and for a streamwise acceleration of

excited waves. Both effects can be scaled by using the average of the jet

core velocity and the local minimum mean velocity. The proper scaling

parameter downstream of the wake region is found to be the same as for a

plane mixing layer, namely, (U. - U )/(U. + U ). Linear parallel flow

J s J s

stability theory has been found to agree qualitatively with the

measurements, but does not produce accurate quantitative predictions of

spatial growth rates.

The computational portion of this investigation has produced numerical

models for forced spatially-developing axisymmetric and two-dimensional

1
mixing layers. The numerical scheme employs quadratic upwind differencing

for convection and a Leith type of temporal differencing in order to solve

the incompressible Navier-Stokes and continuity equations. The applied

forcing function is derived from linear inviscid stability theory. The

resulting large-scale vortex dynamics is visualized by means of streakline

and isovorticity contour plots. It is seen that the vortex merging behavior

in both types of mixing layers is determined by the subharmonics present in

the forcing function. Manipulation of the vortex dynamics in a predictable

fashion is possible through alterations in the frequency content of this

applied forcing. Reynolds number is shown to be of only minor importance.

Computations of differentially-heated two-dimensional mixing layers have

produced some quantitative measures of downstream entrainment and its

relationship to the large-scale structures.

Key Words: Coherent structures; computational methods; fluid dynamics;

hydrodynamic instability; jets; mixing layers; turbulence

Introduction

Rapid mixing in coflowing streams is essential to high performance in

thrust augmenting ejectors and in air breathing combustors where mixing must

be accomplished within the short lengths available in aircraft applications.

Advances in these technologies have been limited to a large extent by an

incomplete understanding of the dynamics of turbulent mixing. While complex

geometries are encountered in applications, the rational development of

these technologies requires a more complete understanding of the fundamental

fluid dynamics in carefully controlled experimental situations involving

simple geometries, such as that discussed herein, where the effects of basic

parameters can be isolated and identified.

2
stimulated both by the classical Reynolds decomposition of the NavierStokes equations and by the experimental ease of acquiring time-averaged

information from fixed probes, traditional approaches to the study of

turbulent mixing have been primarily statistical in nature, regarding

turbulence as an essentially random process involving a continuous

distribution of "eddy" scales. This view has been modified substantially

over the last decade and a half, giving way to a mounting body of

experimental evidence for the existence of highly organized coherent motions

in turbulent flows. The limitations and inadequacies of the traditional

approaches have been well documented in a number of recent and excellent

review papers [1-4], and these arguments will not be repeated here. The

important point is that both flow visualization and minicomputer-based

conditional sampling techniques are leading to a new view of turbulent

motions wherein organized structures play a dominant and deterministic role

in turbulent processes. This, coupled with recent advances in computational

fluid dynamics, has opened the door to a new level of understanding, and it

is this combined approach which has been employed in the present

investigation. This investigation has consisted of a joint experimentalcomputational study of the entrainment process in the turbulent mixing of a

round jet with a coflowing stream. The overall objectives of this work were

to identify and characterize coherent motions in the mixing region,

investigate the dynamical role these motions play in the entrainment

process, and determine the extent to which entrainment is affected by such

factors as initial conditions and forcing.

The results of the present investigation have already been discussed in

detail in a series of technical papers and reports [5-10]. Thus only a

summary of what has been accomplished will be presented here.

3
Experimental Results

Particular experimental objectives included evaluating the

applicability of linear parallel stability theory to the early shear layer,

examining the influence of the inner and outer boundary layers of the jet

apparatus (and the resulting wake region in the early velocity profiles),

and determining the proper relationships between the free and the coflowing

jet characteristics.

The experiments were performed on an air jet apparatus (Fig. 1) mounted

on the test section centerline of the Low Velocity Wind Tunnel at the

National Bureau of Standards [11]. The wind tunnel provided the external

(coflowing) air stream with a turbulence level of 0 . 05 % outside the boundary

layer of the jet apparatus. The inside diameter of the jet tube was 44. -4 ram

(1.75 inches) and the wind tunnel test section 0.91 ra by 0.91 m (3 ft by 3

ft) so that the area ratio was 535:1. Screens and a flow straightener

inside the jet pipe and near the exit produced a jet velocity profile having

a nearly constant velocity core and a nearly uniform core turbulence

intensity of 0.9 to 1.1^. The wind tunnel and the jet were both generally

operated over the speed range of 1 to 6 m/s. The velocity data were

acquired by a minicomputer system [12] from a single hot-wire probe (Pt, 2.5

um by 0.5 ram) and a constant temperature hot-wire anemometer.

It is now widely recognized that acoustic characteristics of a jet

apparatus are of great importance in determining the development of the

shear layer, at least for laminar and quasi-laminar flows [13]. For the

present work the acoustic effects were particularly strong since the

apparatus consisted of a straight pipe of constant diameter only 2.4 m in

length, an effective resonator. To determine the acoustic character istics

,

a microphone was inserted near the closed end of the pipe and low level

4
acoustic waves were excited by a rotating perforated disc located in the air

supply line. The results (Fig. 2) show a set of resonances having a spacing

in frequency corresponding approximately to that predicted by a simple

acoustic analysis.

The stability calculations used here were based on the analysis of

Michalke and Hermann [14] for an incompressible, inviscid, axisymmetric

coflowing jet. The computational procedure used was developed

independently, however, and is reported by Moore [10]. Locally parallel

flow and small amplitude spatially developing disturbances are assumed so

that the Euler equations may be linearized and satisfied by a disturbance of

the form

,, . i(ax - Bt)

p

' = p(r je

where <p may be u, v, or p; a is the complex wave number, 6 the real

frequency, r the radial coordinate, x the streamwise coordinate, and t the

time. These have been nondimensionalized using the jet core velocity, U^. ,

and the inside radius of the jet pipe, R. The resulting equations were then

solved numerically using curves fit to measured mean velocity profiles by a

least squares procedure. Note that these profiles were not derived in any

way from free jet data, but are measured profiles for the coflowing jet.

Thus they include the remnants of the jet-pipe boundary layers which form a

decaying wake-like region.

Neither nonparallel flow nor finite disturbance amplitudes is accounted

for by this analysis. Yet it is quite likely that some of the differences

observed between the analytical results and the measurements are due to

5
these features. There has been some work on extending the basic theory to

slowly diverging flows and to weakly nonlinear flows (see ref. 15 for a

review). Here, however, these aspects have not been pursued.

The mean velocity profiles are complicated functions of radius, r,

downstream distance, x, the core exit velocity of the jet, , and the

velocity of the external stream far from the jet, U^. Five combinations of

Uj and were investigated in detail for which selected profiles are

plotted in Figs. 3~5. The most apparent characteristic of these profiles is

the decaying wake region resulting from the boundary layers on the jet pipe

walls. For purposes of discussion this wake region may be described in

terms of an inner and an outer shear layer with a gradual disappearance of

the outer shear layer. The inner shear layer here is much steeper than the

outer thus having in some ways a much stronger influence on the stability

characteristics. However, these results should be viewed with some caution

since very different characteristics might develop if the outer layer were

steeper than the inner layer. This possibility has not been explored here,

but perhaps warrants further investigation.

It has been found that the effects of a coflowing stream on a round jet

cannot be determined by simply transforming a free jet flowfield to a

coordinate system moving at the coflowing stream velocity, at least not for

facilities in which the flow develops rapidly near the jet origin. The only

exception, it would seem, would be a facility in which acoustic resonances

have been eliminated (in the unstable range of frequencies) and in which the

background disturbances have been reduced to unusually low levels. In such

a flow the streamwise development of waves might extend far beyond the

region where the wake of the jet pipe is important. In most coflowing jets.

6
however, this will not be the case and the wake region must be taken into

account. In that region it has been found that the flow evolves, not simply

in magnitude but in fundamental scaling characteristics. The rapidly

changing velocity profiles cause large variations in the spatial growth

rates of waves leading to streamwise variations in spectra and in wave

speed. The influence of the external stream speed, U^, is not simple,

however. Near the jet origin the spectra and wave speeds are nearly

independent of U^, whereas further downstream the influence is substantial.

Any scaling laws for this flow must be able to account for the observed

evolution. In particular, the usual choices for characteristic velocity,

for instance U. + U , must be modified. An alternative proposed here, U. +

U , where U is the minimum mean speed in a cross-stream profile, is found

m m

^

to satisfactorily scale both spectra and wave speeds. It is furthermore

consistent with the concept that the "inner" shear layer in this coflowing

jet is dominant because it is substantially stronger than the "outer" shear

layer. Since U. + U approaches U. + U downstream, the latter would seem

J m J e

to be the proper characteristic velocity beyond the wake region in the flow.

A simple linear, parallel flow stability theory has not fared badly in

analyzing this flow. In fact, the work of Michalke and Hermann [14]

predicted several of the important characteristics observed in the

experiments, including the shift of spectra to higher frequencies as is

increased for positions not near the jet origin and the streamwise

acceleration of waves. This was despite the use of transformed free jet

profiles. Other predicted results were not borne out, however. A

stretching factor, o’, defined as

7
a’ = 1 + AU

e U.- U

J e

was calculated by Michalke and Hermann [14] who inferred a value A = 1.4 for

the transformed free jet data. In the present work, however, A = 2.0 is

found to provide the best correlation of the coflowing jet measurements.

This is in agreement with experiments on the plane mixing layer. For

A = 2.0, o'(U. - U ) becomes simply U. + U , the characteristic velocity

j e ^ j e’

downstream of the wake region.

Calculations based on the work of Michalke and Hermann [14], but

performed on the measured coflowing jet profiles of the present work,

likewise agreed with several of the trends in the experimental data. In

particular, the cross-stream profiles of wave amplitude compare relatively

well with the measurements as did the wave speeds near the jet origin. The

predictions of streamwise growth were more difficult to compare with the NBS

measurements due to the rapid development of the profiles and corresponding

changes in the calculations. However, the bracketing of the data by the

calculations would seem to indicate at least qualitative agreement. As a

whole the linear, parallel flow, stability theory did not fare badly, but

could possibly be improved by taking into account the nonparallel and weakly

nonlinear aspects of the flow.

Finally, it should again be noted that the complexity of the coflowing

jet configuration and the dependence of the flow properties on so many

factors should be taken into account in any attempts to apply the results

presented here to other facilities. The relative importance of the two

initial boundary layers in particular should be viewed with caution. An

8
interesting, though perhaps difficult, experiment would be to repeat the

measurements performed here but for an apparatus in which the outer boundary

layer is much thinner and steeper than the inner one. This might have

profound effects on the flow characteristics.

Computational Results

The primary computational objective of this investigation was to

develop a numerical model for the large-scale vortex dynamics inside forced

spatially-developing axisymmetric mixing layers. The temporally-developing

case, with its simpler boundary conditions, had been modeled previously

[15], but was not a completely plausible representation of what occurs

inside the mixing layer between a jet and a coflowing stream. The

axisymmetry condition implies that azimuthal instabilities were not

considered here. This is a realistic assumption (at least in the nearfield) provided that axisymmetric forcing is employed.

The axisymmetric mixing layer develops in the region between a jet with

velocity and a coflowing stream with velocity U^. Therefore, at the

upstream boundary of the computational domain (z = 0), a velocity profile

U(r) characteristic of a coflowing jet is specified. This profile contains

a shear layer centered at r = R . which develops into the mixing layer for

z > 0. In an unforced physical experiment, random background noise will

supply the perturbation necessary to trigger roll-up of this shear layer.

The particular component of the background noise which is responsible for

the initial vortex formation can be determined from linear inviscid

stability theory as that frequency which exhibits the largest spatial growth

rate [14]. Thus, for the computations, a perturbation of the form

9
Z A (r) exp {i[R(a )z - 3 t]}

n n n

n

is applied to the vorticity over some streamwise region from z = 0 to

z = Zp >_ 0. Here A^(r) are complex eigenfunctions, is the real part

of a complex a , and 3 is real. When it is desired to match the situation

n n

in an unforced physical experiment, all parameters are chosen so as to

minimize Im(a^) [14, 16]. In the case of a forced physical experiment, the

3^ for n > 1 must be subharmonics of 3^^, i.e., 3^ is an integer multiple of

3 ^, another integer multiple of 3^> etc. [16]. Variations in the amplitude

and domain of the applied perturbation have been found not to affect the

resulting vortex dynamics in any fundamental way. For this study, the

maximum amplitude of the perturbation was about 0.01 U(r) and z = 2R..

P 1

the basic vortex dynamics although the vortices do smear out as Re

decreases

.

A finite difference method was employed here in order to solve the

incompressible Navier-Stokes and continuity equations in primitive variables

on a staggered mesh. This method utilized quadratic upwind differencing for

convection and an explicit Leith-type of temporal differencing [?]. This

leads to effectively third-order accurate spatial differencing as Re ^ oo.

The only relevant stability criterion is that the Courant number be less

than one. This type of differencing scheme has been shown to perform well

in computing vortex shedding from bluff bodies [17, l8]. At each time ‘step

a Poisson equation for pressure was solved by a direct method utilizing the

1 0
FISHPAK package of FORTRAN subprograms for the solution of separable

elliptic partial differential equations developed at NCAR [19]. No

turbulence model was employed in this computation.

The boundary conditions in the radial direction employed here were that

radial derivatives are set to zero along r = 0 (axisymmetry ) , and a simple

asymptotic analysis involving small perturbations about was employed for

large r. The freestream velocity was specified at the outflow boundary

of the mesh by means of an inf inite-to-f inite mapping of the form

C

= K + K^/z, where K and are constants. This transform was employed for

z > 15 R.

.

J

The untransformed portion of the nonuniform mesh used here is shown in

Fig. 6, where it can be seen that mesh points are concentrated in the region

of the initial shear layer near r = 1. The length scales in Fig. 6 are

normalized with respect to R . . All results that follow are nondimensionalJ

ized with respect to R. and U.. Computation times on the NBS UNIVAC 1100/32

3

required to obtain a few unchanging cycles of vortex dynamics were typically

about 3 hours.

A plot of an upstream velocity profile with U./U = 3.33 is shown in

J “

Fig. 7. This profile, consisting of two Gaussians matched (with continuous

first derivatives) at r = 1, is typical of what is found downstream of a jet

nozzle. A linear inviscid stability analysis reveals the most unstable

frequency to be 6^ = 3.^8. The results of perturbing this velocity profile

with B = = B^ (no subharmonics) are shown in Figs. 8 and 9 for Re = n

1000. These two figures illuminate the same flowfield, the first by means
of a streakline plot composed of passive marker particles and the second by

means of isovorticity contours. What is seen here is the formation of

vortices which shear as they move downstream but do not merge. Figures 10

and 11 show the effects of adding a subharmonic (3 = + 3^/2) to the

applied perturbation. A single vortex merging is now seen to occur. Adding

a second subharmonic (3 = 3^+ 3j^/2 + 3^/3) results in two vortex mergings,

as shown in Figs. 12 and 13. Thus, each subharmonic induces one merging, as

seen experimentally in the two-dimensional mixing layer [16]. By applying

only the fundamental and the second subharmonic (3=3^+ 3^/3), three

vortices merge into one (Figs. 14 and 15), a phenomenon also seen

experimentally [16]. Changing the Reynolds number from 1000 to 333 results

in the increased smearing of the vortices (with no change in the merging

behavior) seen in Fig. lo for 3=3^+ 3^/2 + 3^/3. For Re = 10 and this

same 3, the total streamwise energy content integrated across a plane

cutting through the jet as a function of axial distance downstream is shown

in Fig. 17 for each of the three frequencies. The axial locations where

each subharmonic saturates are, in fact, the same as the merging locations

as seen from streakline and isovorticity contour plots. Also, the second

subharmonic saturates at twice the distance from the upstream profile as the

first. All this is, once again, in agreement with experimental results from

the two-dimensional mixing layer [l6].

In fact, once the axisymmetric mixing layer had been modeled, extension

to the two-dimensional case became straightforward. The resulting basic

vortex dynamics was observed to be identical to that seen in the

axisymmetric situation, i.e., each subharmonic induced one merging. A

12
phenomenon clearly seen in the two-dimensional case was "vortex shredding

(Fig. 18). This occurred in the presence of a fundamental and its first

subharmonic when the subharmonic was phase-shifted by <J) = 90°. What is

clearly seen in Fig. 18 is that the vortex centered at x = 110 is being

pulled apart (shredded) by its neighbors. This same sort of phenomenon has

been seen before in computations of temporally-developing mixing layers

[15]. When compared with the normal vortex merging seen in the zero phase

shift case (Fig. 19), it is clear that downstream entrainment is severely

reduced by this shredding phenomenon. Full details on both the axisymmetric

and two-dimensional mixing layer computations are reported in Davis and

Moore [9].

In a further effort to quantify the downstream entrainment process in a

two-dimensional mixing layer, differential heating of the two incoming

streams was applied. With no gravitational effects in the model, the

temperature then acted as a passive contaminant. For the case shown in Fig.

20 (tanh profile at x = 0 with velocity ratio = 3* 33, fundamental plus first

subharmonic present), the upper high speed stream (for y > 0) enters with

temperature T = 1, while the lower stream has T = 0. The following

integrals were then computed:

Aj(x) =1 T dy,

^ —

m

f °

CO

(1 - T) dy,

J n0

13
where in the actual numerical integrations, ^ “ were replaced by _+ 80. When

there is no mixing between the streams, both and are zero everywhere.

Thus, the deviation of these parameters from zero gives a measure of the

mixing which is occurring at a given downstream station. By comparing Figs.

21 and 22 (A^ and A^, respectively) with Fig. 20, the effect of the vortex

dynamics on the mixing can clearly be seen. Peaks and valleys in both A^

and A^ can be directly related to the vertical position of the braid between

the vortices seen in Fig. 20. There is also an asymmetry in the mixing,

with the peak value of A^ being about 50^ greater than that of A^. Thus,

more high speed than low speed fluid is entrained and mixed in the coherent

structures, an effect also observed experimentally [20]. The summation of

A^ and A^ shown in Fig. 23 rev*eals the expected increase in overall mixing

with downstream distance, with the peaks here occurring at the locations of

the vortices in Fig. 20.

Concluding Remarks

Several concluding observations can be made pertaining to the results

presented in the previous two sections. First, linear parallel stability

theory can provide a great deal of useful information regarding the largescale structure of forced mixing layers. The effectiveness of linear theory

in an obviously nonlinear situation has been noted previously [15, 16].

Also, it is clear that modifications such as the addition of nonparallel and

weakly nonlinear effects to the theory could enhance its usefulness. A

second conclusion that can be drawn here is that the downstream development

of the mixing layer (at least in the near-field) can be controlled by
forcing at appropriate frequencies. The presence of subharmonics and their

phase relationships is the determining factor in the downstream behavior of

the large-scale structures. The vortex dynamics, in turn, is the

determining factor in the entrainment characteristics of the mixing layer.

Predictive methods (e.g., gradient diffusion models) which ignore the large

coherent structures are doomed to failure. Finally, it is clear that fully

three-dimensional models will be required to describe the far-field

development of both circular and planar mixing layers. Joint

computational/experimental research efforts would appear to be highly

desirable here. A cooperative effort on joint data analysis techniques

alone would undoubtedly prove extremely beneficial.

Acknowledgments

J. M. McMichael and L. P. Purtell carried out the experimental portion

of this investigation. The contribution of E. F. Moore to the computational

effort was invaluable.

References

1. Laufer, J. , Ann. Rev. Fluid Mech. 7, p. 307 (1975).

2. Roshko, A., AIAA Journal 14 , p. 1349 (1976).

3. Liepmann, K. M., American Scientist 67 , p. 221 (1979).

4. Davies, P.O.A.L. and Yule, A. J. , J. Fluid Mech. 69, p. 513 (1975).

5. McMichael, J. M., Purtell, L. P., Davis, R. W. and Moore, E. F., AIAA

Aerospace Sciences Meeting Paper No. 84-0420 (1984).

6. Purtell, L. P., McMichael, J. M. , Davis, R. W. , and Moore, E. F. , AIAA

Shear Flow Control Conference Paper No. 85-057^ (1985).

15
7.

Davis, R. W., in Computational Techniques and Applications: CTAC-83

(ed. J. Noye and C. Fletcher), North-Holland , Amsterdam, p. 51 (1984).

8. Davis, R. W. and Moore, E. F. , in Ninth International Conference on

Numerical Methods in Fluid Dynamics (ed. Soubbaramayer and J. P.

Boujot), Springer-Verlag Lect. Notes in Physics 218 , p. 180 (1985).

9. Davis, R. W. and Moore, E. F. , Phys. Fluids 28, p. 1626 (1985).

10. Moore, E. F. , National Bureau of Standards Internal Report 83~2686

(1983)

.

11. Purtell, L. P. and Klebanoff, P. S. , National Bureau of Standards Tech.

Note 989 (1979).

12. Purtell, L. P., National Bureau of Standards Tech. Note ll8l (1983).

13. Gutmark, E. and Ho, C.-M., Phys. Fluids 26, p. 2932 (1983).

14. Michalke, A. and Hermann, G. , J. Fluid Mech. 114 , p. 343 (1982).

15. Ho, C.-M. and Huerre, P., Ann. Rev. Fluid Mech. 16 , p. 365 (1984).

16. Ho, C.-M. and Huang, L. S. , J. Fluid Mech. 119 , p. 443 (1982).

17. Davis, R. W. and Moore, E. F. , J. Fluid Mech. 116 , p. 475 (1982).

18. Davis, R. W. , Moore, E. F. and Purtell, L. P., Phys. Fluids 27, p. 46

(1984).

19. Swar ztrauber , P. and Sweet, R. , Nat. Center Atmos. Res. Tech. Note lA109 (1975).

20. Koochesfahani , M. M. , Dimotakis, P. E. and Broadwell, J. E. , AIAA

Journal 23, p. 1191 (1985).

16
Rasponse

dB

Fig. 1. Scheaacic of jet apparatus in wind tunnel.

fig. 5. Mean velocity profiles. U, 6, ” " 1.^- n/s. J
Fig.

6.

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Re

=

10

:

3i

“

3.48,

39

=

1.74,

3-:.

“

1.16.
m^ o

uO

CN !-i <3- (Us • o O I—1

II !-i <Ua

oa

a3

4-1 o •H

I—1 s

II o

OJ II 03 X o u

4-1 3

S-i (U o rH

•H

CO 4-4O

!-l

M

a

C

•H >s X 4-1 •H *H s CJo Q '—1 1 <u CN >

4-1O 33

4-1

H o1—1

C4 • CN

S-l 3 S= O

4-1 II 3O -e- o

LO

4J CNJ •H

CJ •H o 4-1 •

!-l o O> II O

cn CN M cn

00

00

•H o o

stream

velocity

ratio =

3.33.

mb

o o o o o o

r\] — —^ CM ro

o

ro

Fig.

20.

Streakline

plot

of

2-D

mixing

layer

for

Re

=

10

:

“

0.1425,

3^

=

0.07125
'u

Downstream

variation

ofA

at

same

instant

depicted

in

Fig.

20.
Fig.

22.

Downstream

variation

ofA

at

same

instant

depicted

in

Fig.

20.
°y+’y

Downstream

variation

ofA

+A

at

same

instant

depicted

in

Fig.

20.

NBS-1 UA REV. 2-8C) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See in structions)

1. PUBLICATION OR

REPORT NO.

NBSIR 85-3287

2. Performing Organ. Report No. 3. Publication Date

DECEMBER 1985

4 . TITLE AND SUBTITLE

t An Experimental/Computational Investigation of Organized Motions in Axisymmetric

Coflowing Streams

5. AUTHOR(S)

R. W. Davis

6. PERFORMING ORGANIZATION (If joint or other than MBS. see in struction s)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City. State, ZIP)

Air Force Office of Scientific Research/NA

Bolling Air Force Base

v^ashington, DC 20332

10. SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

. bi bliography or literature survey, mention it here)

A joint experimental/computational investigation of the entrainment process in the

turbulent mixing of a round jet with a coflowing stream has been carried out. The

overall objectives of this work were to identify ahd characterize coherent motions

in the mixing region, investigate the dynamical role these motions play in the

entrainment process, and determine the extent to which entrainment is affected by

such factors as initial conditions and forcing.

12. KEY WORDS (S/x to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons

coherent structures; computational methods; fluid dynamics; jets; mixing layers;

stability; turbulence

13. AVAILABILITY

i XI Unlimited

I

; For Official Distribution. Do Not Release to NTIS

I ! Order From Superintendent of Documents, U.S. Government Printing Office, Washington. D.C. 20402.

i X

!

Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGE'

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