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Erlebacher, Gordon

Publications and source records attributed to Erlebacher, Gordon.

32 records · Page 2
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NASA NTRS1990

TS - Dean interactions in curved channel flow

A weakly nonlinear theory is developed to study the interaction of TS waves and Dean vortices in curved channel flow. The prediction obtained from the theory agree well with results obtained from direct numerical simulations of curved channel flow, especially for low amplitude disturbances. At low Reynolds numbers the wave interaction is generally stabilizing to both disturbances, though as the Reynolds number increases, many linearly unstable TS waves are further destabilized by the presence of Dean vortices.

Singer, Bart A.↗
NASA NTRS1990

Numerical experiments in supersonic boundary-layer stability

The three-dimensional (3-D) time-dependent compressible Navier-Stokes equations are numerically solved by a Fourier-Chebyshev collocation method to study the stability of supersonic flows over a flat plate. Several direct simulations carried out in this study suggest the existence of a secondary instability that might provide a route to transition. The interaction of the modes involved in the secondary instability is possibly amenable to a Floquet-type analysis. Pertinent differences between this instability and the analogous incompressible K-type secondary instability are pointed out. Some preliminary results of a 2-D direct simulation of the nonlinear evolution of a second mode perturbation wave are also discussed.

Erlebacher, Gordon↗
NASA NTRS1990

The analysis and simulation of compressible turbulence

Compressible turbulent flows at low turbulent Mach numbers are considered. Contrary to the general belief that such flows are almost incompressible (i.e., the divergence of the velocity field remains small for all times), it is shown that even if the divergence of the initial velocity field is negligibly small, it can grow rapidly on a nondimensional time scale which is the inverse of the fluctuating Mach number. An asymptotic theory which enables one to obtain a description of the flow in terms of its divergence-free and vorticity-free components has been developed to solve the initial-value problem. As a result, the various types of low Mach number turbulent regimes have been classified with respect to the initial conditions. Formulae are derived that accurately predict the level of compressibility after the initial transients have disappeared. These results are verified by extensive direct numerical simulations of isotropic turbulence.

Erlebacher, Gordon↗
NASA NTRS1990

On the continuous spectra of the compressible boundary layer stability equations

The branch cuts in the complex frequency plane (omega) that correspond to the continuous spectrum of the two-dimensional compressible boundary layer stability equations are computed by looking for solutions that are pure oscillatory in the free-stream. In the complex omega-plane there are three compressible and one incompressible branch cuts. The compressible branch cuts are given as solutions of third order polynomials. Computations are made for a range of Reynolds and Mach numbers, and also for several streamwise wavenumbers.

Ashpis, David E.↗
NASA NTRS1990

Second mode interactions in supersonic boundary layers

The nonlinear evolution of a two-dimensional second mode unstable wave in a Mach 4.5 wall-bounded flow is computed by solving the full time-dependent compressible Navier-Stokes equations. A highly accurate solution is obtained using spectral collocation methods. It is shown that departure from linearity first occurs in the critical layer due to the cubic nonlinearities in the momentum equation. This is a direct result of the large density perturbations in this regime. Time evolution studies of the growth rate as a function of normal distance from the plate suggests that the mode is evolving toward a nonlinear saturated state, and that this problem is possibly amenable to standard weakly nonlinear perturbation methods.

Erlebacher, Gordon↗
NASA NTRS1989

Direct simulation of compressible turbulence

Several direct simulations of 3-D homogeneous, compressible turbulence are presented with emphasis on the differences with incompressible turbulent simulations. A fully spectral collocation algorithm, periodic in all directions coupled with a 3rd order Runge-Kutta time discretization scheme is sufficient to produce well-resolved flows at Taylor Reynolds numbers below 40 on grids of 128x128x128. A Helmholtz decomposition of velocity is useful to differentiate between the purely compressible effects and those effects solely due to vorticity production. In the context of homogeneous flows, this decomposition in unique. Time-dependent energy and dissipation spectra of the compressible and solenoidal velocity components indicate the presence of localized small scale structures. These structures are strongly a function of the initial conditions. Researchers concentrate on a regime characterized by very small fluctuating Mach numbers Ma (on the order of 0.03) and density and temperature fluctuations much greater than sq Ma. This leads to a state in which more than 70 percent of the kinetic energy is contained in the so-called compressible component of the velocity. Furthermore, these conditions lead to the formation of curved weak shocks (or shocklets) which travel at approximately the sound speed across the physical domain. Various terms in the vorticity and divergence of velocity production equations are plotted versus time to gain some understanding of how small scales are actually formed. Possible links with Burger turbulence are examined. To visualize better the dynamics of the flow, new graphic visualization techniques have been developed. The 3-D structure of the shocks are visualized with the help of volume rendering algorithms developed in-house. A combination of stereographic projection and animation greatly increase the number of visual cues necessary to properly interpret the complex flow.

Zang, T. A.↗
NASA NTRS1989

Non linear evolution of a second mode wave in supersonic boundary layers

Presented here are several direct simulations of one 2-D second mode perturbation wave, superimposed upon a prescribed mean flow. Periodicity is assumed in the streamwise direction (Fourier) and the variables are expanded in Chebyshev series in the direction normal to the flat plate. The code is fully explicit and is time advanced with a 3rd order Runge-Kutta scheme. The second mode wave (R delta prime = 8000), interacts with itself to generate higher streamwise harmonics. Physical parameters are chosen to maximize the linear growth rate at the prescribed Reynolds number. Initial results indicate that the nonlinear processes begin in the critical layer region and are the result of the cubic interactions in the momentum equations, rather than due to the higher streamwise harmonics. Analysis of the various terms in the momentum equations combined with numerical experiments in which various modes are artificially suppressed, lead to the conclusion that asymptotic methods will produce the saturated state in one or two order of magnitude less computer time than that required by the direct numerical simulations.

Erlebacher, Gordon↗
NASA NTRS1989

Non-linear evolution of a second mode wave in supersonic boundary layers

The nonlinear time evolution of a second mode instability in a Mach 4.5 wall-bounded flow is computed by solving the full compressible, time-dependent Navier-Stokes equations. High accuracy is achieved by using a Fourier-Chebyshev collocation algorithm. Primarily inviscid in nature, second modes are characterized by high frequency and high growth rates compared to first modes. Time evolution of growth rate as a function of distance from the plate suggests this problem is amenable to the Stuart-Watson perturbation theory as generalized by Herbert.

Erlebacher, Gordon↗
NASA NTRS1989

Grid generation for the solution of partial differential equations

A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes. The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given.

Eiseman, Peter R.↗
NASA NTRS1988

Stability and transition in supersonic boundary layers

The three-dimensional time-dependent, compressible Navier-Stokes equations are numerically solved by a Fourier-Chebyshev collocation algorithm to study the stability of a Mach 4.5 flow over a flat plate. Several nonlinear direct simulations suggest the existence of a secondary instability which might provide a possible route to transition. Pertinent differences in the energy content of the various Fourier modes between this instability and the more common incompressible K-type instabilities are pointed out.

Erlebacher, Gordon↗
NASA NTRS1987

Grid generation for the solution of partial differential equations

A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes. The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given.

Eiseman, Peter R.↗
NASA NTRS1987

Nonlinear structures in the later stages of transition

The transition to turbulence in low-Reynolds-number channel flow and in a boundary-layer flow (under the conditions studied experimentally by Kovasznay et al., 1962) is investigated by means of high-resolution numerical simulations. The results are presented graphically, and breakdown phenomena are characterized in detail, with a focus on artificially suppressed streamwise vortices, channel-center modes, and the important roles of lambda vortices and mean shear. It is shown that shear-layer roll-up is accurately reproduced by both simulations.

Zang, Thomas A.↗
NASA NTRS1987

Stability and transition in supersonic boundary layers

The full three-dimensional time-dependent compressible Navier-Stokes equations are numerically solved by a Fourier-Chebyshev collocation algorithm to study the stability of supersonic flows over a flat plate. Several non-linear numerical experiments suggest the existence of a secondary instability which might provide a possible route to transition. The interaction of the modes involved in this secondary instability is possibly amenable to a Floquet theory. Pertinent differences between this instability and the more common incompressible K-type instabilities are pointed out.

Erlebacher, Gordon↗