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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

A new approach to the formulation of scalar flux closure

This report shows that if a stochastic differential equation (Langevin equation) for velocity fluctuation vector is known, it is possible to derive the equations for scalar flux transport. Durbin and Speziale (1994) showed that the second moment of this stochastic differential equation gives an equation for the evolution of Reynolds stress tensor. Similarly, the stochastic equation will give an equation for scalar flux. Therefore, a coupling between these two is present. The basis for the present work is that there should be Langevin equations that can produce acceptable models for both the Reynolds stress tensor and the scalar flux vector. Having found this basic Langevin equation, the amount of work needed to model the second order closure problems is reduced; using the well developed models for Reynolds stress equations, it will be possible to derive corresponding models for scalar flux equation.

Shabany, Y.↗
NASA NTRS1995

Turbulence modeling for non-equilibrium flow

The work performed during this year has involved further assessment and extension of the k-epsilon-v(exp 2) model, and initiation of work on scalar transport. The latter is introduced by the contribution of Y. Shabany to this volume. Flexible, computationally tractable models are needed for engineering CFD. As computational technology has progressed, the ability and need to use elaborate turbulence closure models has increased. The objective of our work is to explore and develop new analytical frameworks that might extend the applicability of the modeling techniques. In past years the development of a method for near-wall modeling was described. The method has been implemented into a CFD code and its viability has been demonstrated by various test cases. Further tests are reported herein. Non-equilibrium near-wall models are needed for some heat transfer applications. Scalar transport seems generally to be more sensitive to non-equilibrium effects than is momentum transport. For some applications turbulence anisotropy plays a role and an estimate of the full Reynolds stress tensor is needed. We have begun work on scalar transport per se, but in this brief I will only report on an extension of the k-epsilon-v(exp 2) model to predict the Reynolds stress tensor.

Durbin, P. A.↗
NASA NTRS1996

The numerical simulation of multistage turbomachinery flows

The effect of the unsteady flow field in a multistage compressor on the time-averaged performance was assessed. The energy transport by the unsteady deterministic flow field was taken into account. The magnitude of the body force resulting from the aerodynamic loading on a blade row was compared to the gradient of the stress tensor associated with the unsteady time-resolved flow field generated by the blade row. The magnitude of the work performed by these forces was compared to the divergence of the energy correlations produced by the unsteady time-resolved flow field. The stress tensor and the energy correlations are non-negligible in the end wall regions. The results suggest that the turbulence is the primary source of flow mixing in the midspan region.

Adamczyk, John J.↗
NASA NTRS1991

Experimental investigation of turbulent flow through a circular-to-rectangular transition duct

Steady, incompressible, turbulent, swirl-free flow through a circular-to-rectangular transition duck was studied experimentally. The cross-sectional area remains the same at the exit as at the inlet, but varies through the transition section to a maximum value approximately 15 percent above the inlet value. The cross-sectional geometry everywhere along the duct is defined by the equation of a superellipse. Mean and turbulence data were accumulated utilizing pressure and hot-wire instrumentation at five stations along the test section. Data are presented for operating bulk Reynolds numbers of 88,000 and 390,000. Measured quantities include total and static pressure, the three components of the mean velocity vector, and the six components of the Reynolds stress tensor. In addition to the transition duct measurements, a hot-wire technique which relies on the sequential use of single rotatable normal and slant-wire probes was proposed. The technique is applicable for measurement of the total mean velocity vector and the complete Reynolds stress tensor when the primary flow is arbitrarily skewed relative to a plane which lies normal to the probe axis of rotation.

Davis, David O.↗
NASA NTRS1976

Derivation of the Navier-Stokes equation

The proposed approach to the derivation of the Navier-Stokes equation is thought to be more plausible and easier to understand than other derivations that can be found in works on fluid mechanics. The tensor character of the stress is central to the derivation. In particular, a linear relation between stress and strain rate is assumed only for the shear, rather than for the full stress tensor as is done in most other derivations. An assumption for the shear is naturally simpler and easier to verify experimentally. The use of tensor analysis is shown to greatly simplify the derivation.

Deissler, R. G.↗
NASA NTRS2007

Software Tool for Computing Maximum Von Mises Stress

The maximum Van Mises stress and stress direction are of interest far analyzing launch accelerations such as with the Mass Acceleration Curves developed by JPL. Maximum launch stresses can be combined with appropriate load cases at consistent locations with resulting stress tensors. Maximum Van Mises stress is also of interest for understanding maximum operational loading such as traverse events. - For example, planetary traversing simulations may prescribe bounding acceleration values during traverse for a rover such as Mars Science Lab (MSL) in (X,Y,Z) of the rover. - Such accelerations can be really in any directions for many parts such as a mast or head mounted components which can be in numerous configurations and orientations when traversing a planet surface.

software↗
NASA NTRSDate not supplied

Nonlinear Homogenization of Finitely Deformed Viscoelastic-Viscoplastic Composites Using Mechanics of Structure Genome

The objective of this paper is to develop a micromechanics approach to homogenizing finitely deformed viscoelastic-viscoplastic composites using the mechanics of structure genome. The incremental constitutive relation for glassy polymers, formulated in the spatial configuration, is implemented in the present approach.This involves (1) pulling-back the constitutive model to the material configuration and (2)choosing the deformation gradient tensor and the first Piola–Kirchhoff stress tensor as the strain and the stress measures during homogenization, respectively. An Euler–Newton predictor–corrector method is developed for homogenization. Each step involves formulating a variational statement using the mechanics of structure genome, discretizing the statement in a finite-dimensional space, and solving the problem using an Euler/multilevel Newton method. The present approach is demonstrated by homogenizing fiber- and particle-reinforced composites undergoing uniaxial, biaxial, or shear deformation, at different stain rates.

Multi-scale modeling, High Strain Composites, Visc↗
NASA NTRS1990

A new continuum model for suspensions of gyrotactic micro-organisms

A new continuum model is formulated for dilute suspensions of swimming micro-organisms with asymmetric mass distributions. Account is taken of randomness in a cell's swimming direction, p, by postulating that the probability density function for p satisfies a Fokker-Planck equation analogous to that obtained for colloid suspensions in the presence of rotational Brownian motion. The deterministic torques on a cell, viscous and gravitational, are balanced by diffusion, represented by an isotropic rotary diffusivity Dr, which is unknown a priori, but presumably reflects stochastic influences on the cell's internal workings. When the Fokker-Planck equation is solved, macroscopic quantities such as the average cell velocity Vc, the particle diffusivity tensor D and the effective stress tensor sigma can be computed; Vc and D are required in the cell conservation equation, and sigma in the momentum equation. The Fokker-Planck equation contains two dimensionless parameters, lambda and epsilon; lambda is the ratio of the rotary diffusion time Dr-1 to the torque relaxation time B (balancing gravitational and viscous torques), while epsilon is a scale for the local vorticity or strain rate made dimensionless with B. In this paper we solve the Fokker-Planck equation exactly for epsilon = 0 (lambda arbitrary) and also obtain the first-order solution for small epsilon. Using experimental data on Vc and D obtained with the swimming alga, Chlamydomonas nivalis, in the absence of bulk flow, the epsilon = 0 results can be used to estimate the value of lambda for that species (lambda approximately 2.2; Dr approximately 0.13 s-1). The continuum model for small epsilon is then used to reanalyse the instability of a uniform suspension, previously investigated by Pedley, Hill & Kessler (1988). The only qualitatively different result is that there no longer seem to be circumstances in which disturbances with a non-zero vertical wavenumber are more unstable than purely horizontal disturbances. On the way, it is demonstrated that the only significant contribution to sigma, other than the basic Newtonian stress, is that derived from the stresslets associated with the cells' intrinsic swimming motions.

NASA Discipline Number 28-20↗
NASA NTRS1977

Identification and measurement of combustion noise from a turbofan engine using correlation and coherence techniques

Fluctuating pressure measurements within the combustor and tailpipe of a turbofan engine are made simultaneously with far field acoustic measurements. The pressure measurements within the engine are accomplished with cooled semi-infinite waveguide probes utilizing conventional condenser microphones as the transducers. The measurements are taken over a broad range of engine operating conditions and for 16 far field microphone positions between 10 deg and 160 deg relative to the engine inlet axis. Correlation and coherence techniques are used to determine the relative phase and amplitude relationships between the internal pressures and far field acoustic pressures. The results indicate that the combustor is a low frequency source region for acoustic propagation through the tailpipe and out to the far field. Specifically, it is found that the relation between source pressure and the resulting sound pressure involves a 180 deg phase shift. The latter result is obtained by Fourier transforming the cross correlation function between the source pressure and acoustic pressure after removing the propagation delay time. Further, it is found that the transfer function between the source pressure and acoustic pressure has a magnitude approximately proportional to frequency squared. These results are shown to be consistent with a model using a modified source term in Lighthill's turbulence stress tensor, wherein the fluctuating Reynolds stresses are replaced with the pressure fluctuations due to fluctuating entropy.

Karchmer, A. M.↗
NASA NTRS1994

Acoustics of laminar boundary layers breakdown

Boundary layer flow transition has long been suggested as a potential noise source in both marine (sonar-dome self noise) and aeronautical (aircraft cabin noise) applications, owing to the highly transient nature of process. The design of effective noise control strategies relies upon a clear understanding of the source mechanisms associated with the unsteady flow dynamics during transition. Due to formidable mathematical difficulties, theoretical predictions either are limited to early linear and weakly nonlinear stages of transition, or employ acoustic analogy theories based on approximate source field data, often in the form of empirical correlation. In the present work, an approach which combines direct numerical simulation of the source field with the Lighthill acoustic analogy is utilized. This approach takes advantage of the recent advancement in computational capabilities to obtain detailed information about the flow-induced acoustic sources. The transitional boundary layer flow is computed by solving the incompressible Navier-Stokes equations without model assumptions, thus allowing a direct evaluation of the pseudosound as well as source functions, including the Lighthill stress tensor and the wall shear stress. The latter are used for calculating the radiated pressure field based on the Curle-Powell solution of the Lighthill equation. This procedure allows a quantitative assessment of noise source mechanisms and the associated radiation characteristics during transition from primary instability up to the laminar breakdown stage. In particular, one is interested in comparing the roles played by the fluctuating volume Reynolds stress and the wall-shear-stresses, and in identifying specific flow processes and structures that are effective noise generators.

Wang, Meng↗
NASA NTRS2018

Acoustic Radiation Pressure

The theoretical foundation of acoustic radiation pressure in plane wave beams is reexamined. It is shown from finite deformation theory and the Boltzmann-Ehrenfest Adiabatic Principle that the Brillouin stress tensor (BST) is the radiation stress in Lagrangian coordinates (not Eulerian coordinates) and that the terms in the BST are not the momentum flux density and mean excess Eulerian stress but are simply contributions to the variation in the wave oscillation period resulting from changes in path length and true wave velocity, respectively, from virtual variations in the strain. It is shown that the radiation stress in Eulerian coordinates is the mean Cauchy stress (not the momentum flux density, as commonly assumed) and that Langevin's second relation does not yield an assessment of the mean Eulerian pressure, since the enthalpy used in the traditional derivations is a function of the thermodynamic tensions - not the Eulerian pressure. It is shown that the transformation between Lagrangian and Eulerian quantities cannot be obtained from the commonly-used expansion of one of the quantities in terms of the particle displacement, since the expansion provides only the difference between the value of the quantity at two different points in Cartesian space separated by the displacement. The proper transformation is obtained only by employing the transformation coefficients of finite deformation theory, which are defined in terms of the displacement gradients. Finite deformation theory leads to the result that for laterally unconfined, plane waves the Lagrangian and Eulerian radiation pressures are equal with the value (1/4)(2K) along the direction of wave propagation, where (K) is the mean kinetic energy density, and zero in directions normal to the propagation direction. This is contrary to the Langevin result that the Lagrangian radiation pressure in the propagation direction is equal to (2K) and the BST result that the Eulerian radiation pressure in that direction is the momentum flux density.

Finite deformation theory↗
NASA NTRS1978

Adding stress plot function to NASTRAN

Stress plot function was developed and added to the NASTRAN level 15.5. Computed stress distribution can be displayed by this function, with vectors showing the principal stresses of the finite elements over the specified portions of the structure. NASTRAN is reviewed in the aspect of plotting capabilities. Stress tensor field is examined in preparation of stress display. Then the stress plot function as added to the NASTRAN is described. A sample plotout by this function is shown.

Katoh, S.↗
NASA NTRS1992

Comments on the present state of second-order closure models for incompressible flows

Second-order closure models account for history and nonlocal effects of the mean velocity gradients on the Reynolds stress tensor. Turbulent flows involving body forces or curvature, Reynolds stress relaxational effects, and counter-gradient transport are usually better described. The topics are presented in viewgraph form and include: (1) the Reynolds stress transport equation; (2) issues in second-order closure modeling; and (3) near wall models.

Speziale, Charles G.↗
NASA NTRS1989

On the Nature of Navier-stokes Turbulence

Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, largest Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low-Reynolds-number fully developed turbulence are compared. The solutions, separate exponentially with time, having a positive Liapunov exponent. Thus the turbulence is characterized as chaotic. In a search for solutions which contrast with the turbulent ones, the Reynolds number is reduced. Several qualitatively different flows are noted. These are, fully chaotic, complex period, weakly chaotic, simple periodic, and fixed-point. Of these, only the fully chaotic flows are classified as turbulent. Those flows have both a positive Liapunov exponent and Poincare sections without pattern. By contrast, the weakly chaotic flows have some pattern in their Poincare sections. The fixed-point and periodic flows are nonturbulent, since turbulence, is both time-dependent and aperiodic. Turbulent solutions are obtained in which energy cascades from large to small-scale motions. In general, the spectral energy transfer takes place between wavenumber bands that are considerably separated. The special transfer can occur either as a result of nonlinear turbulence self-interaction or by interaction of turbulence with mean gradients. Turbulent systems are compared with those studied in kinetic theory. The two types of systems are fundamentally different (continuous and dissipative as opposed to discrete and conservative), but there are similarities. For instance, both are nonlinear and show sensitive dependence on initial conditions. Also, the turbulent and molecular stress tensors are identical if the macroscopic velocities for the turbulent stress are replaced by molecular velocities.

Deissler, Robert G.↗
NASA NTRS1985

Particle and field stress balance within a planetary magnetosphere

A technique is developed for experimentally estimating the local tensor stresses within a planetary magnetic field configuration characterized by local spacecraft measurements. Key to the technique is the determination of the shapes of field lines using the symmetry properties of the system coupled with local and instantaneous measurements of the field line inclination angles. The technique is applied here to the inner and middle Saturnian magnetosphere using data returned by the Magnetic Field Experiment on the Voyager 1 spacecraft. It is concluded that the ring current has substantial radial structure, heretofore not shown. Outside about 13 R(s) the newly derived field stresses match remarkably well the funtional variation of the centrifugal corotation stresses of the cool particle population measured previously by the Plasma Science Experiment. Inside about 13 R(s) the key structure in the derived field stresses, a prominent local maximum, matches the approximate position of an apparent strong pressure gradient in the energetic particles characterized by the Low-Energy Charged Particle detectors.

Mauk, B. H.↗
NASA NTRSDate not supplied

Mechanical Erosion Modeling of TPS Materials

This work describes the development of a model that accounts for the additional total surface recession in Thermal Protection Systems materials as a result of mechanical erosion due to high shear conditions during atmospheric entry. A computational solid mechanics capability module was integrated within the Porous material Analysis Toolbox based on OpenFOAM, PATO. The mechanical erosion was modeled in three steps: first, the implemented stress analysis solver module computes the stress and the displacement fields for orthotropic materials using the wall shear stress tensor as a boundary condition; then, regions on the surface where the stress meets the failure criteria are identified; and last, the mesh is moved accordingly to remove the failed material. The outcome is a model of the total recession of the material due to surface chemistry and mechanical erosion. Results will be included in the final paper after verifying and completing the study.

Stress Analysis↗
NASA NTRSDate not supplied

Mechanical Erosion Modeling of TPS Materials

This work describes the development of a model that accounts for the additional surface recession in Thermal Protection Systems (TPS) materials as a result of mechanical erosion due to high shear conditions during atmospheric entry. A computational solid mechanics module was integrated within the Porous material Analysis Toolbox (PATO) based on OpenFOAM. The mechanical erosion was modeled in three steps: first, the implemented stress analysis solver computes the stress and the displacement fields for orthotropic materials using the wall shear stress tensor as a boundary condition; then, regions on the surface where the stress meets the failure criteria are identified; and last, the mesh is moved accordingly to remove the failed material. The outcome is a model capable to predict the total recession of the material due to surface chemistry and mechanical erosion. Results will be included in the final paper after verifying and completing the study.

Stress Analysis↗