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At least 109 records · Page 6
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NASA NTRS1987

Steady bimodal convection in a cylinder at large Prandtl numbers

Steady bimodal convection of an infinite Prandtl-number Boussinesq fluid in a cylinder is considered. An asymptotic analysis similar to the one used by Buell and Catton (1986) for axisymmetric convection yields a solvability condition that determines the radial wavenumber. The analysis is valid for convection far away from the origin, the lateral boundary, and any pattern dislocations. The azimuthal wave number is treated as a parameter, although in real systems it is dependent on the initial and boundary conditions. Results are presented for Rayleigh numbers between 14,000 and 60,000, and for azimuthal wave numbers between 5 and 7. It is shown that for increasing Rayleigh numbers, the selected radial wave number and the heat transfer tend to become independent of the azimuthal wave number. No quantitative experimental data are available, but one qualitative comparison is good.

Buell, Jeffrey C.↗
NASA NTRS1988

Interaction and merging of vortex filaments

The asymptotic solutions of Navier-Stokes equations for vortex filaments of finite strength with small effective vortical cores are summarized with special emphasis placed on the physical meaning and the practical limit to the applicability of the asymptotic solution. Finite-difference solutions of Navier-Stokes equations for the marging of the filament(s) are described with a focus on the development of the approximate boundary conditions for the computational domain. An efficiency study employing a model problem is used to assess the advantages of the present approximate boundary condition method over previously used techniques. Applications of the present method are presented for the motion and decay of a 3:1 elliptic vortex ring, and for the merging process of a pair of coaxial vortex rings. A numerical procedure for the problem of local merging of vortex filaments, which requires the asymptotic analysis as well as the numerical Navier-Stokes solver, is also presented.

Liu, C. H.↗
NASA NTRS1988

Nearly incompressible magnetohydrodynamics at low Mach number

The relationship between compressible and incompressible MHD turbulence at low plasma-frame acoustic Mach numbers is investigated analytically, with a focus on the range of validity of the pseudosound model proposed by Lighthill (1952). The derivation and asymptotic analysis procedures are explained in detail, and consideration is given to the role of number-density fluctuations and Alfven waves in the nearly incompressible model at low Mach numbers. The results are shown to be consistent with the turbulent-density spectrum theory of Montgomery et al. (1987) and applicable to solar-wind Alfven-wave turbulence.

Matthaeus, William H.↗
NASA NTRS1990

Application of a Reynolds stress turbulence model to the compressible shear layer

Theoretically based turbulence models have had success in predicting many features of incompressible, free shear layers. However, attempts to extend these models to the high-speed, compressible shear layer have been less effective. In the present work, the compressible shear layer was studied with a second-order turbulence closure, which initially used only variable density extensions of incompressible models for the Reynolds stress transport equation and the dissipation rate transport equation. The quasi-incompressible closure was unsuccessful; the predicted effect of the convective Mach number on the shear layer growth rate was significantly smaller than that observed in experiments. Having thus confirmed that compressibility effects have to be explicitly considered, a new model for the compressible dissipation was introduced into the closure. This model is based on a low Mach number, asymptotic analysis of the Navier-Stokes equations, and on direct numerical simulation of compressible, isotropic turbulence. The use of the new model for the compressible dissipation led to good agreement of the computed growth rates with the experimental data. Both the computations and the experiments indicate a dramatic reduction in the growth rate when the convective Mach number is increased. Experimental data on the normalized maximum turbulence intensities and shear stress also show a reduction with increasing Mach number.

Sarkar, S.↗
NASA NTRS1990

Application of a Reynolds stress turbulence model to the compressible shear layer

Theoretically based turbulence models have had success in predicting many features of incompressible, free shear layers. However, attempts to extend these models to the high-speed, compressible shear layer have been less effective. In the present work, the compressible shear layer was studied with a second-order turbulence closure, which initially used only variable density extensions of incompressible models for the Reynolds stress transport equation and the dissipation rate transport equation. The quasi-incompressible closure was unsuccessful; the predicted effect of the convective Mach number on the shear layer growth rate was significantly smaller than that observed in experiments. Having thus confirmed that compressibility effects have to be explicitly considered, a new model for the compressible dissipation was introduced into the closure. This model is based on a low Mach number, asymptotic analysis of the Navier-Stokes equations, and on direct numerical simulation of compressible, isotropic turbulence. The use of the new model for the compressible dissipation led to good agreement of the computed growth rates with the experimental data. Both the computations and the experiments indicate a dramatic reduction in the growth rate when the convective Mach number is increased. Experimental data on the normalized maximum turbulence intensities and shear stress also show a reduction with increasing Mach number.

Sarkar, S.↗
NASA NTRS1990

Upwind techniques for flows with multiple translational temperatures

The numerical simulation of high-speed flows out of chemical and thermodynamic equilibrium is considered. A general model for the species internal energy is utilized, which allows for multiple translational temperatures. A study of the characteristic wave speeds for the case of two translational temperatures, one associated with the average thermal speed of the heavy particles and the other associated with the translational temperature of free electrons, yields some very interesting results, with acoustic wave speeds of the symmetric form u + or - a no longer appearing. An asymptotic analysis in terms of small electron mass fractions yields approximate wave speed which recover the symmetric form, with the addition of a new wave speed associated with the electron energy equation.

Cinnella, Pasquale↗
NASA NTRS1989

Analytical and computational models of shells; Proceedings of the Symposium, ASME Winter Annual Meeting, San Francisco, CA, Dec. 10-15, 1989

Topics presented include asymptotic analysis and computation for shells, the edge effects in the Reissner-Mindlin plate theory, nonlinear problems of geometrically exact shell theories, and developments in variational methods for high performance plate and shell elements. Also presented are an assumed strain solid element model for geometrically nonlinear shell analysis, shell finite elements with six degrees of freedom per node, hierarchic plate and shell models based on p-extension, and a simple shell element formulation for large-scale elastoplastic analysis. Also discussed are the assessment of computational models for multilayered composite cylinders, shell models for impact analysis, analysis of shell structures subjected to contact-impacts, and the application of shell theory to cardiac mechanics.

Noor, Ahmed K.↗
NASA NTRS1991

The semi-infinite strip problem in the mechanics of composite materials

Many problems, ranging from interface-fiber fracture to determining the strength of fiber-matrix interfaces in composites, can be greatly assisted by a complete understanding of the boundary value problem of a semi-infinite strip. The specific boundary value problem of a semi-infinite strip with symmetric tractions on the transverse edges and normal loads on the end is investigated in the present study. The nature of the singular behavior in the slope of the end vertical displacement at the corner points is found. An asymptotic analysis of the solution shows that, depending on the nature of the applied stresses in the vicinity of the corner points, the singularity in the slope of the end vertical displacement may either be a power or logarithmic type, both, or not exist at all. Illustrative examples, for which exact or numerical results are known, are given. Numerical procedures are also given. The direct application of the results of the paper are illustrated for several problems in the mechanics of composite materials.

Kaw, Autar K.↗
NASA NTRS1991

Layer tracking, asymptotics, and domain decomposition

A preliminary report is presented on the work on the tracking of internal layers in a singularly-perturbed convection-diffusion equation. It is shown why such tracking may be desirable, and it is also shown how to do it using domain decomposition based on asymptotic analysis.

Brown, D. L.↗
NASA NTRS1992

Two-dimensional stability of laminar flames

The stability of laminar flames was studied numerically and the dependence of stability on finite rate chemistry with low activation energy and variable thermodynamic and transport properties was addressed. The calculations show that activation energy and details of chemistry play a minor role in altering the linear neutral stability results from asymptotic analysis. Variable specific heat makes a marginal change to the stability; variable transport properties, on the other hand, tend to substantially enhance the stability from a critical wave number of about 0.50 to 0.20. Also, the effects of variable properties tend to nullify the effects of nonunity Lewis number. When the Lewis number of a single species is different from unity, as is true in a hydrogen-air premixed flame, the stability results remain close to that of unity Lewis number.

Mukunda, H. S.↗
NASA NTRS1992

Kolmogorov Behavior of Near-Wall Turbulence and Its Application in Turbulence Modeling

The near-wall behavior of turbulence is re-examined in a way different from that proposed by Hanjalic and Launder and followers. It is shown that at a certain distance from the wall, all energetic large eddies will reduce to Kolmogorov eddies (the smallest eddies in turbulence). All the important wall parameters, such as friction velocity, viscous length scale, and mean strain rate at the wall, are characterized by Kolmogorov microscales. According to this Kolmogorov behavior of near-wall turbulence, the turbulence quantities, such as turbulent kinetic energy, dissipation rate, etc. at the location where the large eddies become Kolmogorov eddies, can be estimated by using both direct numerical simulation (DNS) data and asymptotic analysis of near-wall turbulence. This information will provide useful boundary conditions for the turbulent transport equations. As an example, the concept is incorporated in the standard k-epsilon model which is then applied to channel and boundary flows. Using appropriate boundary conditions (based on Kolmogorov behavior of near-wall turbulence), there is no need for any wall-modification to the k-epsilon equations (including model constants). Results compare very well with the DNS and experimental data.

Shih, Tsan-Hsing↗
NASA NTRS1992

Theory of anisotropic thin-walled closed-section beams with hygrothermal effects

A variationally consistent theory is developed in order to derive the governing equations of anisotropic thin-walled beams with closed sections subjected to axial load, torsion, bending and hygrothermal loads. The theory is based on an asymptotical analysis of two-dimensional shell theory. Closed-form expressions for the beam stiffness coefficients, equivalent hygrothermal loads, stress and displacement fields are provided. The influence of material anisotropy and hygrothermal coefficients on the displacement field is identified. The analysis is applied to predict the response of composite beams under thermomechanical loading.

Badir, Ashraf M.↗
NASA NTRS1992

Phase-field model for isothermal phase transitions in binary alloys

A new phase field model is described which models isothermal phase transitions between ideal binary alloy solution phases. Equations are developed for the temporal and spatial variation of the phase field, which describes the identity of the phase, and of the composition. An asymptotic analysis, as the gradient energy coefficient of the phase field becomes small, was conducted. From the analysis, it is shown that the model recovers classical sharp interface models of this situation when the interfacial layers are thin, and they show how to relate the parameters appearing in the phase field model to material and growth parameters in real systems. Further, three stages of temporal evolution are identified: the first corresponding to interfacial genesis which occurs very rapidly; the second to interfacial motion controlled by the local energy difference across the interface and diffusion; the last taking place on a long time scale in which curvature effects are important and which correspond to Ostwald ripening. The results of the numerical calculations are presented.

Wheeler, A. A.↗
NASA NTRS1993

Role of acoustics in flame/vortex interactions

The role of acoustics in flame/vortex interactions is examined via asymptotic analysis and numerical simulation. The model consists of a one-step, irreversible Arrhenius reaction between initially unmixed species occupying adjacent half-planes which are allowed to mix and react by convection and diffusion in the presence of an acoustic field or a time-varying pressure field of small amplitude. The main emphasis is on the influence of the acoustics on the ignition time and flame structure as a function of vortex Reynolds number and initial temperature differences of the reactants.

Jackson, T. L.↗
NASA NTRS1992

Theory of anisotropic thin-walled closed-cross-section beams

A variationally and asymptotically consistent theory is developed in order to derive the governing equations of anisotropic thin-walled beams with closed sections. The theory is based on an asymptotic analysis of two-dimensional shell theory. Closed-form expressions for the beam-stiffness coefficients, stress and displacement fields are provided. The influence of material anisotropy on the displacement field is identified. A comparison with the displacement fields obtained by other analytical developments is performed. The stiffness coefficients and static response are also compared with finite element predictions, closed-form solutions and test data.

Berdichevsky, Victor↗
NASA NTRS1993

Nonlinear Interaction of Frequency-Detuned Modes in Boundary Layers

The present critical-layer asymptotic analysis for the nonlinear interaction of frequency-detuned modes in boundary-layer transition indicates that the interaction between a plane mode at the fundamental frequency and a pair of symmetrical oblique waves at the near-subharmonic frequency amplifies another pair of symmetrical oblique waves at the 'mirror frequency'. This type of interaction is stronger in the frequency-detuned case than the resonant triad case, and leads to a sharp drop in the oblique waves' peak with small detuning.

Mankbadi, Reda R.↗
NASA NTRS1992

A small-scale turbulence model

A model for the small-scale structure of turbulence is reformulated in such a way that it may be conveniently computed. The model is an ensemble of randomly oriented structured two dimensional vortices stretched by an axially symmetric strain flow. The energy spectrum of the resulting flow may be expressed as a time integral involving only the enstrophy spectrum of the time evolving two-dimensional cross section flow, which may be obtained numerically. Examples are given in which a k(exp -5/3) spectrum is obtained by this method without using large wave number asymptotic analysis. The k(exp -5/3) inertial range spectrum is shown to be related to the existence of a self-similar enstrophy preserving range in the two-dimensional enstrophy spectrum. The results are insensitive to time dependence of the strain-rate, including even intermittent on-or-off strains.

Lundgren, T. S.↗
NASA NTRS1994

Ignition dynamics of a laminar diffusion flame in the field of a vortex embedded in a shear flow

The role of streamwise-spanwise vorticity interactions that occur in turbulent shear flows on flame/vortex interactions is examined by means of asymptotic analysis and numerical simulation in the limit of small Mach number. An idealized model is employed to describe the interaction process. The model consists of a one-step, irreversible Arrhenius reaction between initially unmixed species occupying adjacent half-planes which are then allowed to mix and react in the presence of a streamwise vortex embedded in a shear flow. It is found that the interaction of the streamwise vortex with shear gives rise to small-scale velocity oscillations which increase in magnitude with shear strength. These oscillations give rise to regions of strong temperature gradients via viscous heating, which can lead to multiple ignition points and substantially decrease ignition times. The evolution in time of the temperature and mass-fraction fields is followed, and emphasis is placed on the ignition time and structure as a function of vortex and shear strength.

Macaraeg, Michele G.↗