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NASA NTRS1992

Renormalization group methods for the Reynolds stress transport equations

The Yakhot-Orszag renormalization group is used to analyze the pressure gradient-velocity correlation and return to isotropy terms in the Reynolds stress transport equations. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a rapid pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constants are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of deriving higher order nonlinear models by approximating the sums more accurately. The Yakhot-Orszag renormalization group provides a systematic procedure for deriving turbulence models. Typical applications have included theoretical derivation of the universal constants of isotropic turbulence theory, such as the Kolmogorov constant, and derivation of two equation models, again with theoretically computed constants and low Reynolds number forms of the equations. Recent work has applied this formalism to Reynolds stress modeling, previously in the form of a nonlinear eddy viscosity representation of the Reynolds stresses, which can be used to model the simplest normal stress effects. The present work attempts to apply the Yakhot-Orszag formalism to Reynolds stress transport modeling.

Rubinstein, R.↗
NASA NTRS1992

Critical assessment of Reynolds stress turbulence models using homogeneous flows

In modeling the rapid part of the pressure correlation term in the Reynolds stress transport equations, extensive use has been made of its exact properties which were first suggested by Rotta. These, for example, have been employed in obtaining the widely used Launder, Reece and Rodi (LRR) model. Some recent proposals have dropped one of these properties to obtain new models. We demonstrate, by computing some simple homogeneous flows, that doing so does not lead to any significant improvements over the LRR model and it is not the right direction in improving the performance of existing models. The reason for this, in our opinion, is that violation of one of the exact properties can not bring in any new physics into the model. We compute thirteen homogeneous flows using LRR (with a recalibrated rapid term constant), IP and SSG models. The flows computed include the flow through axisymmetric contraction; axisymmetric expansion; distortion by plane strain; and homogeneous shear flows with and without rotation. Results show that for most general representation for a model linear in the anisotropic tensor, performs either better or as good as the other two models of the same level.

Shabbir, Aamir↗
NASA NTRS1992

Experimental investigation of cyclic thermomechanical deformation in torsion

An investigation of thermomechanical testing and deformation behavior of tubular specimens under torsional loading is described. Experimental issues concerning test accuracy and control specific to thermomechanical loadings under a torsional regime are discussed. A series of shear strain-controlled tests involving the nickel-base superalloy Hastelloy X were performed with various temperature excursions and compared to similar thermomechanical uniaxial tests. The concept and use of second invariants of the deviatoric stress and strain tensors as a means of comparing uniaxial and torsional specimens is also briefly presented and discussed in light of previous thermomechanical tests conducted under uniaxial conditions.

Ellis, John R.↗
NASA NTRS1993

Hypersonic three-dimensional nonequilibrium boundary-layer equations in generalized curvilinear coordinates

The basic governing equations for the second-order three-dimensional hypersonic thermal and chemical nonequilibrium boundary layer are derived by means of an order-of-magnitude analysis. A two-temperature concept is implemented into the system of boundary-layer equations by simplifying the rather complicated general three-temperature thermal gas model. The equations are written in a surface-oriented non-orthogonal curvilinear coordinate system, where two curvilinear coordinates are non-orthogonial and a third coordinate is normal to the surface. The equations are described with minimum use of tensor expressions arising from the coordinate transformation, to avoid unnecessary confusion for readers. The set of equations obtained will be suitable for the development of a three-dimensional nonequilibrium boundary-layer code. Such a code could be used to determine economically the aerodynamic/aerothermodynamic loads to the surfaces of hypersonic vehicles with general configurations. In addition, the basic equations for three-dimensional stagnation flow, of which solution is required as an initial value for space-marching integration of the boundary-layer equations, are given along with the boundary conditions, the boundary-layer parameters, and the inner-outer layer matching procedure. Expressions for the chemical reaction rates and the thermodynamic and transport properties in the thermal nonequilibrium environment are explicitly given.

Lee, Jong-Hun↗
NASA NTRS1993

Explicit robust schemes for implementation of a class of principal value-based constitutive models: Symbolic and numeric implementation

The issue of developing effective and robust schemes to implement a class of the Ogden-type hyperelastic constitutive models is addressed. To this end, special purpose functions (running under MACSYMA) are developed for the symbolic derivation, evaluation, and automatic FORTRAN code generation of explicit expressions for the corresponding stress function and material tangent stiffness tensors. These explicit forms are valid over the entire deformation range, since the singularities resulting from repeated principal-stretch values have been theoretically removed. The required computational algorithms are outlined, and the resulting FORTRAN computer code is presented.

Arnold, S. M.↗
NASA NTRS1993

Explicit robust schemes for implementation of general principal value-based constitutive models

The issue of developing effective and robust schemes to implement general hyperelastic constitutive models is addressed. To this end, special purpose functions are used to symbolically derive, evaluate, and automatically generate the associated FORTRAN code for the explicit forms of the corresponding stress function and material tangent stiffness tensors. These explicit forms are valid for the entire deformation range. The analytical form of these explicit expressions is given here for the case in which the strain-energy potential is taken as a nonseparable polynomial function of the principle stretches.

Arnold, S. M.↗
NASA NTRS1993

Point form relativistic quantum mechanics and relativistic SU(6)

The point form is used as a framework for formulating a relativistic quantum mechanics, with the mass operator carrying the interactions of underlying constituents. A symplectic Lie algebra of mass operators is introduced from which a relativistic harmonic oscillator mass operator is formed. Mass splittings within the degenerate harmonic oscillator levels arise from relativistically invariant spin-spin, spin-orbit, and tensor mass operators. Internal flavor (and color) symmetries are introduced which make it possible to formulate a relativistic SU(6) model of baryons (and mesons). Careful attention is paid to the permutation symmetry properties of the hadronic wave functions, which are written as polynomials in Bargmann spaces.

Klink, W. H.↗
NASA NTRS1992

Determining the nuclear equation of state from neutron-star masses and radii

A method is developed for determining the nuclear equation of state directly from a knowledge of the masses and radii of neutron stars. This analysis assumes only that equilibrium neutron-star matter has the stress-energy tensor of an isotropic fluid with a barotropic equation of state, and that general relativity describes a neutron star's internal gravitational field. We present numerical examples which illustrate how well this method will determine the equation of state when the appropriate observational data become available.

Lindblom, Lee↗
NASA NTRS1992

Cold dissipationless collapse of spherical systems - Sensitivity to the initial density law

The collapse of cold, initially spherical systems with varying degrees of central condensation is investigated. The way in which the final shape of a collapsing system depends on the initial density law is examined. For an initial stellar number density rho varies as r exp -n, where n is in the range 0-2.5, the final, nearly prolate shape is given by a/c is approximately equal to 1.28(1 + 0.16 n), where a/c is the ratio of long to short axes of the inertia ellipsoid computed from the moment of inertia tensor of the most tightly bound 80 percent of the mass. The properties associated with the final states in the present computations are also studied. The collapsing systems develop an anisotropic halo dominated by radial orbits surrounding an isotropic core as predicted by Burkert (1990).

Cannizzo, John K.↗
NASA NTRS1992

Intermodulation in the oscillatory magnetoresistance of a two-dimensional electron gas

The oscillatory magnetoresistance wave form of a 2-D electron gas shows multiple structures when two subbands are populated. In addition to high-field oscillations at a frequency equal to the sum of the two frequencies corresponding to the concentrations of the subbands, and to a superposition at intermediate fields, we observed oscillations at the difference frequency at low fields and higher temperatures. The field range at which the frequency difference is observed increases with increasing temperature. The crossover from superposition to frequency difference is accompanied by a beat. Similar beats, whose field location shows identical temperature dependence, can be observed in data obtained by other groups on different structures. The various components of the wave form can be attributed to different phase relations between the diagonal and off-diagonal elements of the conductivity tensor. It is shown how the intermodulation term, when inserted into the extended oscillatory equation, can give rise to all three structures.

Schacham, S. E.↗
NASA NTRS1992

The gravitational wave contribution to cosmic microwave background anisotropies and the amplitude of mass fluctuations from COBE results

A stochastic background of primordial gravitational waves may substantially contribute, via the Sachs-Wolfe effect, to the large-scale cosmic microwave background (CMB) anisotropies recently detected by COBE. This implies a bias in any resulting determination of the primordial amplitude of density fluctuations. We consider the constraints imposed on n is less than 1 ('tilted') power-law fluctuation spectra, taking into account the contribution from both scalar and tensor waves, as predicted by power-law inflation. The gravitational wave contribution to CMB anisotropies generally reduces the required rms level of mass fluctuation, thereby increasing the linear bias parameter, even in models where the spectral index is close to the Harrison-Zel'dovich value n = 1. This 'gravitational wave bias' helps to reconcile the predictions of CDM models with observations on pairwise galaxy velocity dispersion on small scales.

Lucchin, Francesco↗
NASA NTRS1992

Boundary formulations for three-dimensional continuum structural shape sensitivity analysis

The direct, singular, boundary element analysis formulation is shown to provide a basis for a computationally efficient and accurate shape design sensitivity analysis approach for the structural response of three-dimensional solid objects. The theoretical formulation for surface displacement and traction component sensitivities, and all components of the stress tensor is presented along with a formulation for the recovery of displacement and stress components in the interior of the object under consideration. Discussion of computational issues related to the overall efficiency of these formulations is given, along with numerical results to demonstrate the accuracy and efficiency of this approach.

Kane, J. H.↗
NASA NTRS1992

Limits on plasma anisotropy in a tail-like magnetic field

The condition of magnetohydrostatic equilibrium implies tight constraints on the degree of anisotropy that is supportable in a magnetotail field geometry. If the plasma pressure tensor is assumed to be gyrotropic at the tail midplane (z = 0), then equilibrium requires that it also be nearly isotropic there, with P-perpendicular sub 0/P-parallel sub 0 in the range 1 +/- delta square, where delta of about 0.1 is the ratio of the normal field component at the symmetry plane to the field strength in the tail lobe. The upper and the lower limits are essentially equivalent, respectively, to the marginal mirror and firehose stability conditions evaluated at z = 0, which have been invoked previously to limit the degree of anisotropy in the plasma sheet.

Hill, T. W.↗
NASA NTRS1992

Gravity and topography

The paper summarizes the fundamental gravity field constants for Mars and a brief historical review of early determinations and current-day accurate estimates. These include the planetary gravitational constant, global figure, dynamical oblateness, mean density, and rotational period. Topographic results from data acquired from the 1967 opposition to the most recent, 1988, opposition are presented. Both global and selected local topographic variations and features are discussed. The inertia tensor and the nonhydrostatic component of Mars are examined in detail. The dimensionless moment of inertia about the rotational axis is 0.4 for a body of uniform density and 0.37621 if Mars were in hydrostatic equilibrium. By comparing models of both gravity and topography, inferences are made about the degree and depth of compensation in the interior and stresses in the lithosphere.

Esposito, P. B.↗
NASA NTRS1991

Shock waves and the Ffowcs Williams-Hawkings equation

The expansion of the double divergence of the generalized Lighthill stress tensor, which is the basis of the concept of the role played by shock and contact discontinuities as sources of dipole and monopole sound, is presently applied to the simplest transonic flows: (1) a fixed wing in steady motion, for which there is no sound field, and (2) a hovering helicopter blade that produces a sound field. Attention is given to the contribution of the shock to sound from the viewpoint of energy conservation; the shock emerges as the source of only the quantity of entropy.

Isom, Morris P.↗
NASA NTRS1993

Analysis of the anisotropic viscoplastic-damage response of composite laminates - Continuum basis and computational algorithms

The mathematical structure underlying the rate equations of a recently-developed constitutive model for the coupled viscoplastic-damage response of anisotropic composites is critically examined. In this regard, a number of tensor projection operators have been identified, and their properties were exploited to enable the development of a general computational framework for their numerical implementation using the Euler fully-implicit integration method. In particular, this facilitated (i) the derivation of explicit expressions of the (consistent) material tangent stiffnesses that are valid for both three-dimensional as well as subspace (e.g. plane stress) formulations, (ii) the implications of the symmetry or unsymmetry properties of these tangent operators from a thermodynamic standpoint, and (iii) the development of an effective time-step control strategy to ensure accuracy and convergence of the solution. In addition, the special limiting case of inviscid elastoplasticity is treated. The results of several numerical simulations are given to demonstrate the effectiveness of the schemes developed.

Saleeb, A. F.↗
NASA NTRS1993

Triangular spectral elements for incompressible fluid flow

We discuss the use of triangular elements in the spectral element method for direct simulation of incompressible flow. Triangles provide much greater geometric flexibility and are better conditioned and more accurate than quadrilateral elements when small angles arise. We employ a family of tensor product algorithms for triangles, allowing triangular elements to be handled with comparable arithmetic complexity to quadrilateral elements. The triangular discretizations are applied to the Poisson equation and are validated. The triangular discretizations are then applied to the incompressible Navier-Stokes equations, and a laminar channel flow solution is given. The new triangular spectral elements can be combined with standard quadrilateral elements, yielding a general and flexible high order method for complex geometries in two dimensions.

Mavriplis, Catherine↗
NASA NTRS1993

Hybrid simulations of collisionless ion tearing

Ion tearing in a thin collisionless neutral sheet is investigated using hybrid (particle ion, massless fluid electron) simulations in which dissipation effects are included through a model of the full electron pressure tensor in which self-consistently generated anisotropies are reduced via an isotropization time factor. The linear growth rates and ion dynamics are in qualitative agreement with linear theory and one-component simulations. The reconnection rate increases with the isotropization time.

Hesse, Michael↗