FINAL REPORT 

Submitted to the 

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 

LEWIS RESEARCH CENTER 

21000 Brookpark Road 

Cleveland, OH 44135 

Atkntion: Grants Officer 

MS 500-3 15, LeRC 

Grant Title: "Studies of Turbulent Shear Flows and Their Control" 

Grant No.: NAG3-1016 

Duration: 22 February 1989 to 17 October 1992 

Grant Funding: 

Technical Monitors: Drs. E.J. Rice, M.D. Dahl 

Principal Investigator: Joseph T.C. Liu 

SS NO.- 

Institution: Brown University 

Division of Engineering 

Providence, RI 029 12 

IRS No. 05025889 

l%ofessor of Engineering 

Principal Investigator 

Tel(401) 863-2654 

<NASA-CR-194%%4) STUDIES DF 

TURBULENT SWEAR FLOWS AND THEIR 

CONTROL final Report, 2P Feb, 3.989 

- 19 OcL, 1992 (Brown Univ, 3 5 p 

Date: August 30, 1993 

63/34 0185592 
PREFACE

The Final Report is organized in several s_tions, beginning with TECHNICAL

REPORT< and followed by PUBLICATIONS and Activities, are listed under SEMINAR

LECTURES and INVITED INTERNATIONAL VISITS.

Continued interactions between our Grant Activities and research activities at

NASA/Lewis Research Center will be evidenced under (i) SEMINAR LECTURES; ('fi)

continued collaborative efforts, listed under PAPERS, with members of NASA/I__wis

Research Center;, as well as (iii) informal discussions during fi'equent visits to the

Laboratory.

TECHNICAL REPORT

The intent of the original proposal and the work carried out under the grant was to

explore the instabilities of turbulent free shear flows of an incompressible fluid. The

purpose for doing so was that (1.) coherent instabilities are susceptible to control via

upstream forcing and (2.) because at sufficient finite amplitudes, the coherent modes enter

into nonlinear interactions with the rman motion and thus, (3.) through such nonlinear

interactions, the control of mixing and of mean flow spreading can be effected through the

control of the coherent structures.

=

(1.) Five Mode Interactions in Developing Free Shear Flows - We studied aspects of the

nonlinear interactions between five interacting axisymmetric and helical modes at

fundamental and subharmonic frequencies in a spatially developing round jet. Several

simplifying assumptions were made in order to bring out the nonlinear interaction features:

(i) the absence of dynamically participating fine grained turbulence, (ii) the mean flow is

assumed "simila", thereby ruling out its distortion in its detailed distribution (but its

spreading rate modifications are explicitly accounted). The integral energy method was

used to study the nonlinear interactions. The streamwise development of the jet is

obtained in terms of the mean flow shear-layer momentum thickness, the wave-mode

kinetic energies and the wave-mode phase angles. With this method, a system of partial

differential equations is reduced to a system of ordinary equations. The nonlinear

differential equations are solved with initial conditions which are given at the nozzle exit.

It was shown that the initial wave-mode energy densities as well as initial phase angles

play a significant role in the streamwise evolution of the coherent wave modes and rrman

flow. More extensive studies of the five mode interaction problem in the simpler twodimensional shear flow was also perfomae&

Reported in PAPERS: Lee & Liu 1989; 1993

CONFERENCES: Lee & Liu 1989, Horng & Liu 1989, 1990.

(2.) Two- and Three-Frequencies Interactions - The above five mode interactions

involved only two frequencies (but more complicated geometrical modes). This work

involves three frequencies but for two-dimensional modes in a two-dimensional shear
flow. The frequenciesincludethe fundamental (f), and its surrounding higher-frequency

mode (3f/2) and the subharmonic (f/2). The physical rules for the mode interactions are

established and the possibility of shear layer control studied.

New perspectives on the problem of two-frequency, two-dimensional mode interactions in

the present of dynamically participating f'me-grained turbulence were obtained through the

study of nonlinear interactions in the "phase volun_". This consists of trajectories in the

volume occupied from the two nonlinear amplitudes and the turbulent kinetic energy; the

mixing layer growth is not contained in such a three-dimensional representation.

Reported in PAPERS: Nikitopoulos & Liu 1989; Liu & Kaptanoglu 1989a, 1989b.

CONFERENCES: Nikitopoulos & Liu 1989; Liu & Kaptanoglu 1989, 1990.

(3.) Effect of Forcing in Nozzle Exit Turbulence Conditions - The question naturally

arises about the effect of pulsating nozzle exit conditions, for purposes of controlling the

exiting free shear layer, on the turbulence characteristics in the wall region that is about to

leave the nozzle. This brings into the picture of "new" turbulence closure for the

modulated turbulence quantities in the wall layer (or "turbulent Stokes layer"). Rapid

distortion theory was extended to obtain ratios of modulated Reynolds shear stress and

turbulent kinetic energy. Depending on the imposed frequency, turbulence structural non

equilibrium could results. This has wide implications for unsteady nozzle exit conditions

relevant to downstream mixing region development and control.

Reported in PAPERS: Liu & Mankbadi 1991; Mankbadi & Liu 1992.

CONFERENCES: Liu & Mankbadi 1991.

(4.) Reviews - A review of many aspects of nonlinear mode interactions and control of

free shear flows was made, including possibilities of incorporating coherent structures in

turbulence closure.

Reported in PAPERS: Liu 1989, 1990.

CONFERENCES: Liu 1990.

PUBLICATIONS

Liu, J.T.C. 1989 Coherent structures in transitional and turbulent free shear flows. Annual

Reviews of Fluid Mechanics 21,285-315.

Liu, J.T.C. & Kaptanoglu, H.T. 1989a Multiple large-scale coherent structures in free

turbulent shear flows. In advances in Turbulence 2, (H.H. Femholz & H.E. Fiedler, eds.),

pp. 57-61. Springer-Verlag, Berlin.

Liu, J.T.C. & Kaptanoglu, H.T. 1989b Phase-volume representation of two-coherent

mode transition to turbulence in a developing mixing layer. In Proc. 4th Int. Workshop
Nonlinear Processes and Turbulence in Physics. Inst. Theo. Phys., Acad. Sci. Ukrainian

SSR, Kiev.

Lee, S.S. & Liu, J.T.C. 1989 Multiple coherent mode interactions in a developing round

jet. A.I.A.A. Paper No. 89-0967.

Nikitopoulos, D.E. & Liu, J.T.C. 1989 Nonlinear coherent mode interactions and the

control of shear layers. In structure of Turbulence and Drag Reduction, (A. Gyr, ed.), pp.

119-127. Springer-Verlag, Berlin.

Liu, J.T.C. Liu 1990 Possibilities of incorporating coherent structure models in turbulent

shear flow calculations. Appl. Mech. Rev. 43, $210-$213.

Liu, J.T.C. Liu & Mankbadi, R.R. 1991 Wall-layer response in an unsteady turbulent

flow. In Proc. Response of Shear Flows to Imposed Unsteadiness-Assois, France (G.

Binde & D. Ronneberger, eds.).

Mankbadi, R.R. & Liu, J.T.C. 1992 Near-wall response in turbulent shear flows subjected

to imposed unsteadiness. J. Fluid Mech. 238, 55-71.

Lee, S.S. & Liu, J.T.C. 1993 Multiple-coherent mode interactions in a developing round

jet. J. Fluid Mech. 248, 383-401.

CONFERENCE PAPERS READ ON GRANT ACTIVITIES

AIAA 2nd Shear Flow Conference, Tempe, 12-16 March 1989: Lee, S.S & Liu, J.T.C.

"Multiple coherent mode interactions in a developing round jet"

IUTAM 2nd Symposium on Structure of Turbulence and Drag Reduction, E.T.H., Zurich

25-28 July 1989: Nikitopoulos, D.E. & Liu, J.T.C. "Nonlinear coherent mode interactions

and the control of shear layers"

4th International Workshop on Nonlinear Processes and Turbulence in Physics, Institute

for Theoretical Physics, Academy of Sciences of the Ukrainian SSR, Kiev, 9-22 October

1989: Liu, J.T.C. & Kaptanoglu, H.T. "Phase volume representation of two-coherent

mode nansition to turbulence in a mixing layer"

42nd Annual Division of Fluid Dynamics Meeting, APS, Palo Alto, 19-21 November

1989: Horng, A. & Liu, J.T_C. "Five coherent mode interactions in a spatially developing

mixing layer" (Abstract in Bull. Am. Phys. Soc. 34, 2301 (1989))

1lth U.S. National Congress in Applied Mechanics, Symposium on Coherent Structures in

Turbulent Flow, Tucson, 21-25 May 1990: Liu, J.T.C. "Possibilities of incorporating

coherent structure models in calculation of turbulent shear flows"
IUTAM Symposium on Nonlinear Hydrodynamic Stability and Transition, Valbone, 3-8

September 1990: Liu, J.T.C. & Kaptanoglu, H.T. "Phase volume representation of twocoherent mode transition to turbulence in a developing free shear layer"

43rd Annual Division of Fluid Dynamics Meeting, APS, Comell University, 18-20 1990:

Homg, A. & Liu, J.T.C. "Two- and three-dimensional mode interactions in a spatially

developing turbulent shear layer, Ir' (Abstract in Bull. Am. Phys. Soc. 35, 2281 (1990))

Euromech 272, Response of Shear Flows to Imposed Unsteadiness, Assois, 14-18 January

1991: Liu, J.T.C. & Mankbadi, R.R. "Wall layer response in unsteady turbulent flows"

SEMINAR LECTURES ON GRANT ACTIVITIES

NASA, Lewis Research Center, Cleveland, Internal Fluid Mechanics Division Seminar

Series, 17 April 1989: "Applications of Coherent Structure Ideas to Heat Transfer,

Transition and Coherent Flames"

NASA, Lewis Research Center, Cleveland, Internal Fluid Mechanics Seminar, 29 May

1991: "Coherent Structure Theory Applications to Problem in Propulsion Systems"

NASA, Lewis Research Center, Cleveland, Internal Fluid Mechanics Division Seminar

Series, 24 February 1992: "Mode Interactions in Free Shear Flows"

Universita degli Studi di Roma "La Sapienza", Rome, Dipartirnento di Idraulica,

Transporti e Strade Seminari: 8 May 1992: "Two- and Three-Dimensional Mode

interactions in Free Shear Flows"

INVITED INTERNATIONAL VISITS

Institute for Fundamental and Technological Research, Polish Academy of Sciences,

Warsaw, 1 week, Sept. 1989

Institute of Hydrornechanics, Ukrainian Academy of Sciences, Kiev, 1 1.2 weeks, Oct.

1989

CNRS, Lab. d'Aerothermique, Meudon, Dec. 1990 - Jan. 1991

Polytechnika Warszawska, Institute of Aeronautics & Applied Mechanics, Warsaw, 1

week, Jan. 1992

Universita degli Studi di Roma "La Sapienza", Dipart. di Idraulica, Transporte e Strade,

Rome, 1 week, May 19921