Engineering topics

Liu, J. T. C.

Publications and source records attributed to Liu, J. T. C..

At least 19 records

NASA NTRS1993

Multiple large-scale coherent mode interactions in a developing round jet

The integral energy method has been used to study the nonlinear interactions of the large-scale coherent structure in a spatially developing round jet. The streamwise development of a jet is obtained in terms of the mean flow shear-layer momentum thickness, the wave-mode kinetic energy and the wave-mode phase angle. With the energy method, a system of partial differential equations is reduced to a system of ordinary differential equations. The nonlinear differential equations are solved with initial conditions which are given at the nozzle exit. It is shown that the initial wave-mode energy densities as well as the initial phase angles play a significant role in the streamwise evolution of the large-scale coherent wave modes and the mean flow.

Lee, Sang S.↗

NASA NTRS1990

Non-linear coherent mode interactions and the control of shear layers

A nonlinear integral formulation, based on local linear stability considerations, is used to study the collective interactions between discrete wave-modes associated with large-scale structures and the mean flow in a developing shear layer. Aspects of shear layer control are examined in light of the sensitivity of these interactions to the initial frequency parameter, modal energy contents and modal phases. Manipulation of the large-scale structure is argued to be an effective means of controlling the flow, including the small-scale turbulence dominated region far downstream. Cases of fundamental, 1st and 2nd subharmonic forcing are discussed in conjunction with relevant experiments.

Nikitopoulos, D. E.↗

NASA NTRS1989

Multiple coherent mode interaction in a developing round jet

The integral energy method has been used in order to study the nonlinear interactions of the large-scale coherent structure in a spatially developing round jet. The streamwise development of a jet is obtained in terms of the mean flow shear layer momentum thickness, the wave mode kinetic energy and the wave mode phase angle. It is shown that the nonlinear interaction between wave modes is dependent on the wave mode phase angles. The initial wave mode phase angles as well as the initial energy densities play a significant role in the streamwise evolution of the large-scale coherent wave modes and the mean flow.

Lee, S. S.↗

NASA NTRS1989

Coherent structures in transitional and turbulent free shear flows

The development of a quantitative understanding of large-scale coherent structures in shear flows has led to the recognition of their evolutionary features and 'rules' of nonlinear interaction among each other. These determinations, in conjunction with the study of fine-grained turbulence and mean motion, constitute a general view of hydrodynamical instabilities that has resulted in useful concepts for the achievement of shear-flow control. The dynamical role of longitudinal structures in free shear flows is presently exemplified by the axisymmetric and helical modes in a round jet, which resemble the two-dimensional and spanwise-periodic three-dimensional modes in a two-dimensional mean flow.

Liu, J. T. C.↗

NASA NTRS1988

Contributions to the understanding of large-scale coherent structures in developing free turbulent shear flows

The physical problem of large-scale coherent structures in real, developing free turbulent shear flows are discussed from the point of view of a broader interpretation of the nonlinear aspects of hydrodynamic stability. Variations on the Amsden and Harlow problem are considered, and the role of linear theory in nonlinear problems is addressed. Spatially developing two-dimensional coherent structures and three-dimensional nonlinear effects in large-scale coherent mode interactions are considered.

Liu, J. T. C.↗

NASA NTRS1987

Control of free shear layers

The fundamental aspects of controlled multiple coherent mode presence in turbulent shear flows is first discussed, including the supplementary averaging procedures in addition to the Reynolds average and the nonlinear energy transfer mechanisms coupling the coherent modes, mean flow and fine-grained turbulence. Then the problem of a fundamental mode and its subharmonic in a developing mixing layer, the prototype problem of subharmonic cascade, is examined. An integral method is presented which allows the determination of the coherent wave envelope or amplitude simultaneously with the mean flow growth rate and turbulence energy. This is then generalized to the presence of multiple subharmonics using a binary-frequency interaction argument. Free shear layer control is discussed in terms of initial coherent mode amplitudes, dimensionless initial frequencies, phase angle between the modes and fine-grained turbulence levels, in particular, how these parameters could enhance or suppress the shear layer spreading rate and the levels of fine-grained turbulence.

Liu, J. T. C.↗

NASA NTRS1987

Nonlinear binary-mode interactions in a developing mixing layer

This paper presents the formulation and results of two-wave interactions in a spatially developing shear layer, directed at understanding and interpreting the physical mechanisms that underlie the results of quantitative observation. The study confirms the existence of Kelly's (1967) mechanism that augments the growth of a subharmonic disturbance by extracting energy from its fundamental or vice versa. This mechanism is shown to be strongest in the region where the fundamental begins to return energy to the mean flow and the two wave modes are of comparable energy levels. It is found that the initial conditions and, especially, the initial phase angle between the two disturbances play a very significant role in the modal development and that of the shear layer itself. A doubling of the shear-layer thickness is shown to take place; the two successive plateaux in its growth are attributed to the peaking in the energy production rates of the fundamental and subharmonic fluctuations.

Nikitopoulos, D. E.↗

NASA NTRS1986

Contributions to the understanding of large-scale coherent structures in developing free turbulent shear flows

Advances in the mechanics of boundary layer flow are reported. The physical problems of large scale coherent structures in real, developing free turbulent shear flows, from the nonlinear aspects of hydrodynamic stability are addressed. The presence of fine grained turbulence in the problem, and its absence, lacks a small parameter. The problem is presented on the basis of conservation principles, which are the dynamics of the problem directed towards extracting the most physical information, however, it is emphasized that it must also involve approximations.

Liu, J. T. C.↗

NASA NTRS1986

Large-scale coherent structures in free turbulent flows and their aerodynamic sound

After interpreting the observed physical features of large-scale coherent structures in free shear flows on the basis of conservation principles, the role of such structures in sources of turbulent jet sound is discussed. It is found that the lower-frequency sound, which comes from lower-frequency coherent structures peaking further downstream, radiates preferentially nearer the jet axis; the peak radiation moves away from the jet axis as the frequency increases.

Liu, J. T. C.↗

NASA NTRS1984

Sound generated aerodynamically revisited - Large-scale structures in a turbulent jet as a source of sound

The theoretical capability of identifying the source of turbulent jet noise is assessed in comparison with experimental data. Account is taken of axisymmetric and spiral turbulence modes in Lighthill's (1952) formulation of turbulent noise. Coherent structures interacting with the mean flow and the fine-grained turbulence are the primary noise sources, modeled as an oscillating streamwise distribution. Low-frequencies arise farther downstream while high-frequencies congregate close to the nozzle lip. Previous measurements at various exit velocities, angles with respect to the nozzle axis, the Strouhal number and downstream distance are discussed. The model successfully predicted the angular distribution of noise frequency due to coherent structures. Further work is indicated on compressibility effects.

Mankbadi, R.↗

NASA NTRS1981

A study of the interactions between large-scale coherent structures and fine-grained turbulence in a round jet

An approximate energy integral description is used to study the development of large-scale coherent structures in the technologically important problem of the round turbulent jet. The analysis begins from the radially integrated form of the kinetic energy equations of the mean flow, the large-scale structure and the fine-grained turbulence, which are obtained by using the usual Reynolds time average and a conditional average with reference to the frequency of the idealized monochromatic component of the large-scale wavelike structure. This is the basis for obtaining the amplitude equations for the three components of the flow in terms of the mean flow momentum thickness, the large-scale structure kinetic energy and the fine-grained turbulence kinetic energy across the jet.

Mankbadi, R.↗

NASA NTRS1980

On the interactions between large-scale structure and fine-grained turbulence in a free shear flow. III - A numerical solution

The results of a numerical computation of the interactions between the horizontally periodic monochromatic component of a large-scale coherent structure and the fine-grained turbulence in a mixing layer are presented. In the numerical calculations, the appropriate dependent variable is one which comprises both the mean and the large-scale coherent structure. The dynamical equations obtained for such a total coherent structure quantity are identical to the unsteady equations for the mean quantities in the Reynolds sense, except that the fine-grained turbulent stresses are interpreted as being conditionally averaged. It is shown how three dimensional fine-grained turbulence can be produced indirectly from the two dimensional large-scale structure via the isotropizing process of the approximated pressure-strain correlation.

Gatski, T. B.↗

NASA NTRS1978

On the interactions between large-scale structure and fine-grained turbulence in a free shear flow. II - The development of spatial interactions in the mean

The interactions between large-scale structure and fine-grained turbulence in a spatially developing mixing layer are investigated. Both a conditioned average and a time average are employed to separate the nonrandom and random fluctuations in the kinetic energy treatment of the interactions. Shape assumptions applying to the interaction integrals are adopted to obtain a solution to the closure problem. Energy-transfer mechanisms among the mean flow, the fine-grained turbulence and the large-scale structure are discussed. The magnitude of the large-scale structure and its streamwise lifetime both prove to be important in accounting for fine-grained turbulence enhancement.

Alper, A.↗

NASA NTRS1978

The large-scale organized structure in free turbulent shear flow and its radiation properties

Modeling of the large-scale coherent structures in a turbulent free shear flow is described. The objective is to gain insight into the interaction between the large-scale structure and the fine-grained turbulence. Some aerodynamic sound radiation properties of the large-scale structure are examined. It is found that the dominant contributions to the radiation come from shear noise rather than self-noise. The fact that a pure tone excitation leads to broadband amplification is most probably due to the enhancement of the fine-grained turbulence by the coherent structure. Numerical modeling of the coherent structure is also discussed.

Liu, J. T. C.↗

NASA NTRS1977

Aerodynamic sound in a relaxing medium

A theory of aerodynamic sound propagation, when inhomogeneities characterized by a relaxation process are present in both the source and propagation region, is formulated. The details of the relaxation process need not be specified at the outset, although the relaxation process is characterized by a relaxation time and by an equilibrium and a frozen sound speed in a propagation region which is otherwise in equilibrium. Propagation is described in terms of a D'Alembertian characterized by the frozen sound speed relaxing toward one characterized by the equilibrium sound speed, while the source is interpreted in terms of a frozen Lighthill stress tensor relaxing toward the equilibrium stress tensor. An appropriate Green's function for the three-dimensional relaxing wave propagation operator is used to construct an exact integral for the aerodynamic sound. The sound generated far from the source is then estimated in terms of the aerodynamic sound source.

Liu, J. T. C.↗

NASA NTRS1977

The generation of sound by vorticity waves in swirling duct flows

Swirling flow in an axisymmetric duct can support vorticity waves propagating parallel to the axis of the duct. When the cross-sectional area of the duct changes a portion of the wave energy is scattered into secondary vorticity and sound waves. Thus the swirling flow in the jet pipe of an aeroengine provides a mechanism whereby disturbances produced by unsteady combustion or turbine blading can be propagated along the pipe and subsequently scattered into aerodynamic sound. In this paper a linearized model of this process is examined for low Mach number swirling flow in a duct of infinite extent. It is shown that the amplitude of the scattered acoustic pressure waves is proportional to the product of the characteristic swirl velocity and the perturbation velocity of the vorticity wave. The sound produced in this way may therefore be of more significance than that generated by vorticity fluctuations in the absence of swirl, for which the acoustic pressure is proportional to the square of the perturbation velocity. The results of the analysis are discussed in relation to the problem of excess jet noise.

Howe, M. S.↗

NASA NTRS1977

On the large-scale structure in turbulent free shear flows

The interaction between the large-scale structure and the disparately fine-grained turbulence in a free turbulent shear flow, in particular, the mixing region is considered. New results pertaining to the spatial problem are presented. An incompressible fluid is considered. An energy integral description is discussed, giving attention to shape assumptions, the interaction problem, energy transfer mechanisms, the spectral dependence of the interaction, and the control of the large-scale structure.

Liu, J. T. C.↗

NASA NTRS1975

On the development of noise-producing large-scale wavelike eddies in a plane turbulent jet

The paper studies the development of large-scale wavelike eddies in a two-dimensional turbulent jet, extending earlier work on the mixing region (Liu, 1974). The basic mean flow developes from one of mixing-region type with an initially specified boundary-layer thickness into a fully developed jet. This study brings out the role of the varicose and sinuous modes as they develop in a growing mean flow. In general, it is found that, for a given frequency parameter, the varicose mode has a shorter streamwise lifetime than the sinuous mode. For lower frequencies, the latter persists past the end of the potential core only to become subject to dissipation by the enhanced fine-scale turbulent activity in that region.

Merkine, L.-O.↗