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NASA NTRS1987

Prediction of hypersonic shock-wave/turbulent-boundary-layer interaction flows

Solutions of the Reynolds-averaged Navier-Stokes equations are presented and compared with experimental surface data for a series of hypersonic shock-wave/turbulent-boundary-layer interaction flows. The turbulence models used include algebraic and two-equation eddy-viscosity models developed for transonic and supersonic flows. Also several additional modifications to the two-equation model to account for compressibility effects are developed and used. Although the modifications improve the agreement with the experimental data, no single model or modification correctly predicts all the test cases.

Horstman, C. C.↗

NASA NTRS1983

Stability and Interaction of Coherent Structure in Supersonic Reactive Wakes

A theoretical formulation and analysis is presented for a study of the stability and interaction of coherent structure in reacting free shear layers. The physical problem under investigation is a premixed hydrogen-oxygen reacting shear layer in the wake of a thin flat plate. The coherent structure is modeled as a periodic disturbance and its stability is determined by the application of linearized hydrodynamic stability theory which results in a generalized eigenvalue problem for reactive flows. Detailed stability analysis of the reactive wake for neutral, symmetrical and antisymmetrical disturbance is presented. Reactive stability criteria is shown to be quite different from classical non-reactive stability. The interaction between the mean flow, coherent structure and fine-scale turbulence is theoretically formulated using the von-Kaman integral technique. Both time-averaging and conditional phase averaging are necessary to separate the three types of motion. The resulting integro-differential equations can then be solved subject to initial conditions with appropriate shape functions. In the laminar flow transition region of interest, the spatial interaction between the mean motion and coherent structure is calculated for both non-reactive and reactive conditions and compared with experimental data wherever available. The fine-scale turbulent motion determined by the application of integral analysis to the fluctuation equations. Since at present this turbulence model is still untested, turbulence is modeled in the interaction problem by a simple algebraic eddy viscosity model. The applicability of the integral turbulence model formulated here is studied parametrically by integrating these equations for the simple case of self-similar mean motion with assumed shape functions. The effect of the motion of the coherent structure is studied and very good agreement is obtained with previous experimental and theoretical works for non-reactive flow. For the reactive case, lack of experimental data made direct comparison difficult. It was determined that the growth rate of the disturbance amplitude is lower for reactive case. The results indicate that the reactive flow stability is in qualitative agreement with experimental observation.

Menon, Suresh↗

NASA NTRS1999

Streamwise Vorticity Generation in Laminar and Turbulent Jets

Complex streamwise vorticity fields are observed in the evolution of non-circular jets. Generation mechanisms are investigated via Reynolds-averaged (RANS), large-eddy (LES) and direct numerical (DNS) simulations of laminar and turbulent rectangular jets. Complex vortex interactions are found in DNS of laminar jets, but axis-switching is observed only when a single instability mode is present in the incoming mixing layer. With several modes present, the structures are not coherent and no axis-switching occurs, RANS computations also produce no axis-switching. On the other hand, LES of high Reynolds number turbulent jets produce axis-switching even for cases with several instability modes in the mixing layer. Analysis of the source terms of the mean streamwise vorticity equation through post-processing of the instantaneous results shows that, complex interactions of gradients of the normal and shear Reynolds stresses are responsible for the generation of streamwise vorticity which leads to axis-switching. RANS computations confirm these results. k - epsilon turbulence model computations fail to reproduce the phenomenon, whereas algebraic Reynolds stress model (ASM) computations, in which the secondary normal and shear stresses are computed explicitly, succeeded in reproducing the phenomenon accurately.

Demuren, Aodeji O.↗

DOE OSTI2021

Predictive Battery Lifetime Modeling at the National Renewable Energy Laboratory

Overview of the development of algebraic battery lifetime modeling efforts within NREL's Electrochemical Energy Storage group within the Energy Conversion and Storage Systems Center. Traditional approaches to developing battery lifetime models are compared with a new methodology incorporating machine learning to autonomously identify parsimonious model equations.

ADVANCED PROPULSION SYSTEMS↗

NASA NTRS1992

Robot Control Based On Spatial-Operator Algebra

Method for mathematical modeling and control of robotic manipulators based on spatial-operator algebra providing concise representation and simple, high-level theoretical frame-work for solution of kinematical and dynamical problems involving complicated temporal and spatial relationships. Recursive algorithms derived immediately from abstract spatial-operator expressions by inspection. Transition from abstract formulation through abstract solution to detailed implementation of specific algorithms to compute solution greatly simplified. Complicated dynamical problems like two cooperating robot arms solved more easily.

Rodriguez, Guillermo↗

NASA NTRS1985

Optical linear algebra processors - Noise and error-source modeling

The modeling of system and component noise and error sources in optical linear algebra processors (OLAPs) are considered, with attention to the frequency-multiplexed OLAP. General expressions are obtained for the output produced as a function of various component errors and noise. A digital simulator for this model is discussed.

Casasent, D.↗

NASA NTRS1988

On the validation of a code and a turbulence model appropriate to circulation control airfoils

A computer code for calculating flow about a circulation control airfoil within a wind tunnel test section has been developed. This code is being validated for eventual use as an aid to design such airfoils. The concept of code validation being used is explained. The initial stages of the process have been accomplished. The present code has been applied to a low-subsonic, 2-D flow about a circulation control airfoil for which extensive data exist. Two basic turbulence models and variants thereof have been successfully introduced into the algorithm, the Baldwin-Lomax algebraic and the Jones-Launder two-equation models of turbulence. The variants include adding a history of the jet development for the algebraic model and adding streamwise curvature effects for both models. Numerical difficulties and difficulties in the validation process are discussed. Turbulence model and code improvements to proceed with the validation process are also discussed.

Viegas, J. R.↗

NASA NTRS1987

Duct flow nonuniformities for Space Shuttle Main Engine (SSME)

A three-duct Space Shuttle Main Engine (SSME) Hot Gas Manifold geometry code was developed for use. The methodology of the program is described, recommendations on its implementation made, and an input guide, input deck listing, and a source code listing provided. The code listing is strewn with an abundance of comments to assist the user in following its development and logic. A working source deck will be provided. A thorough analysis was made of the proper boundary conditions and chemistry kinetics necessary for an accurate computational analysis of the flow environment in the SSME fuel side preburner chamber during the initial startup transient. Pertinent results were presented to facilitate incorporation of these findings into an appropriate CFD code. The computation must be a turbulent computation, since the flow field turbulent mixing will have a profound effect on the chemistry. Because of the additional equations demanded by the chemistry model it is recommended that for expediency a simple algebraic mixing length model be adopted. Performing this computation for all or selected time intervals of the startup time will require an abundance of computer CPU time regardless of the specific CFD code selected.

Source record↗

NASA NTRS2005

Heat Transfer on a Flat Plate with Uniform and Step Temperature Distributions

Heat transfer associated with turbulent flow on a step-heated or cooled section of a flat plate at zero angle of attack with an insulated starting section was computationally modeled using the GASP Navier-Stokes code. The algebraic eddy viscosity model of Baldwin-Lomax and the turbulent two-equation models, the K- model and the Shear Stress Turbulent model (SST), were employed. The variations from uniformity of the imposed experimental temperature profile were incorporated in the computations. The computations yielded satisfactory agreement with the experimental results for all three models. The Baldwin- Lomax model showed the closest agreement in heat transfer, whereas the SST model was higher and the K-omega model was yet higher than the experiments. In addition to the step temperature distribution case, computations were also carried out for a uniformly heated or cooled plate. The SST model showed the closest agreement with the Von Karman analogy, whereas the K-omega model was higher and the Baldwin-Lomax was lower.

Bahrami, Parviz A.↗

NASA NTRS1993

Computation of flows in a turn-around duct and a turbine cascade using advanced turbulence models

Numerical investigation has been carried out to evaluate the capability of the Algebraic Reynolds Stress Model (ARSM) and the Nonlinear Stress Model (NLSM) to predict strongly curved turbulent flow in a turn-around duct (TAD). The ARSM includes the near-wall damping term of pressure-strain correlation phi(sub ij,w), which enables accurate prediction of individual Reynolds stress components in wall flows. The TAD mean flow quantities are reasonably well predicted by various turbulence models. The ARSM yields better predictions for both the mean flow and the turbulence quantities than the NLSM and the k-epsilon (k = turbulent kinetic energy, epsilon = dissipation rate of k) model. The NLSM also shows slight improvement over the k-epsilon model. However, all the models fail to capture the recovery of the flow from strong curvature effects. The formulation for phi(sub ij,w) appears to be incorrect near the concave surface. The hybrid k-epsilon/ARSM, Chien's k-epsilon model, and Coakley's q-omega (q = the square root of k, omega = epsilon/k) model have also been employed to compute the aerodynamics and heat transfer of a transonic turbine cascade. The surface pressure distributions and the wake profiles are predicted well by all the models. The k-epsilon model and the k-epsilon/ARSM model provide better predictions of heat transfer than the q-omega model. The k-epsilon/ARSM solutions show significant differences in the predicted skin friction coefficients, heat transfer rates and the cascade performance parameters, as compared to the k-epsilon model. The k-epsilon/ARSM model appears to capture, qualitatively, the anisotropy associated with by-pass transition.

Lakshminarayana, B.↗

NASA NTRS1991

Application of a Reynolds Stress turbulence model to a supersonic hydrogen-air diffusion flame

A second-order differential Reynolds Stress turbulence model has been applied to the Favre-averaged Navier-Stokes equations for the study of supersonic flows undergoing hydrogen-air chemical reactions. An assumed Beta Probability Density Function is applied to account for the chemical source terms in the conservation equations. An algebraic Reynolds Flux model is used for the fluctuating density-velocity as well as the species mass fraction-velocity correlations. The variances of temperature and species fluctuations are also modelled using an algebraic flux technique. A seven-species, seven-reaction finite rate chemistry mechanism is used to simulate the combustion processes. The resulting formulation is validated by comparison with experimental data on reacting supersonic axisymmetric jets. Results obtained for specific conditions indicate that the effect of chemical reaction on the turbulence is significant.

Chandrasekhar, R.↗

DOE OSTI2022

High Order Wall-Modeled Large-Eddy Simulation on Mixed Unstructured Meshes

In the present study, an algebraic equilibrium wall model previously developed for hexahedral elements is extended to handle mixed meshes including prismatic, tetrahedral, and pyramidal elements in the context of a discontinuous high-order method. This extension is needed for complex geometries, for which high-order mixed elements (e.g., tetrahedral and pyramidal elements) are often necessary near solid walls to avoid meshing challenges. Various design decisions are discussed to achieve the best performance on massively parallel CPU/GPU architectures for a production-level high-order large-eddy simulation solver based on the flux reconstruction/correction procedure via reconstruction method, hpMusic. The extension to other elements is first evaluated using a benchmark channel flow problem at various Reynolds numbers. After that, flow over the NASA high-lift Common Research Model (CRM-HL) from the 4th AIAA High-lift Prediction Workshop is computed to further test the new implementation. Computational results at the third- and fourth-order accuracies are compared with experimental data.

Engineering↗

NASA NTRS1990

Nonlinear Reynolds stress models and the renormalization group

The renormalization group is applied to derive a nonlinear algebraic Reynolds stress model of anisotropic turbulence in which the Reynolds stresses are quadratic functions of the mean velocity gradients. The model results from a perturbation expansion that is truncated systematically at second order with subsequent terms contributing no further information. The resulting turbulence model applied to both low and high Reynolds number flows without requiring wall functions or ad hoc modifications of the equations. All constants are derived from the renormalization group procedure; no adjustable constants arise. The model permits inequality of the Reynolds normal stresses, a necessary condition for calculating turbulence-driven secondary flows in noncircular ducts.

Rubinstein, Robert↗

NASA NTRS1987

Navier-Stokes calculations and turbulence modeling in the trailing edge region of a circulation control airfoil

The accurate prediction of turbulent flows over curved surfaces in general and over the trailing edge region of circulation control airfoils in particular requires the coupled efforts of turbulence modelers, numerical analysts and experimentalists. The purpose of the research program in this area is described. Then, the influence on turbulence modeling of the flow characteristics over a typical circulation control wing is discussed. Next, the scope of this effort to study turbulence in the trailing edge region of a circulation control airfoil is presented. This is followed by a brief overview of the computation scheme, including the grid, governing equations, numerical method, boundary conditions and turbulence models applied to date. Then, examples of applications of two algebraic eddy viscosity models to the trailing edge region of a circulation control airfoil is presented. The results from the calculations is summarized, and conclusions drawn based on examples. Finally, the future directions of the program is outlined.

Viegas, John R.↗

NASA NTRS1990

Computation and turbulence modeling for three-dimensional boundary layers including turbomachinery rotor flows

A method is developed for predicting the behavior of three-dimensional, turbulent boundary layers occurring in internal flows, including those on turbomachinery rotor blades. These boundary layers are complex, turbulent, and subject to Coriolis and centrifugal forces. The major thrust of this paper is the development and use of an algebraic Reynolds stress model (ARSM) that captures the changes in turbulent flow structure arising from curvature, rotation, and three dimensionality. The prediction of pressure-driven secondary flow agrees well with the measured data, and all three turbulence models (k-epsilon, algebraic eddy viscosity, and ARSM) show the same level of agreement. The prediction of boundary-layer development on rotor blades shows much better agreement with measurements with the ARSM. It is essential to employ higher-order turbulence models to capture the effects of rotation, curvature, and three dimensionality on boundary layers in turbomachinery.

Zhang, J.↗

NASA NTRS1981

Mathematical modeling and computer simulation of isoelectric focusing with electrochemically defined ampholytes

A mathematical model of isoelectric focusing at the steady state has been developed for an M-component system of electrochemically defined ampholytes. The model is formulated from fundamental principles describing the components' chemical equilibria, mass transfer resulting from diffusion and electromigration, and electroneutrality. The model consists of ordinary differential equations coupled with a system of algebraic equations. The model is implemented on a digital computer using FORTRAN-based simulation software. Computer simulation data are presented for several two-component systems showing the effects of varying the isoelectric points and dissociation constants of the constituents.

Palusinski, O. A.↗

NASA NTRS2008

Pion and Kaon Lab Frame Differential Cross Sections for Intermediate Energy Nucleus-Nucleus Collisions

Space radiation transport codes require accurate models for hadron production in intermediate energy nucleus-nucleus collisions. Codes require cross sections to be written in terms of lab frame variables and it is important to be able to verify models against experimental data in the lab frame. Several models are compared to lab frame data. It is found that models based on algebraic parameterizations are unable to describe intermediate energy differential cross section data. However, simple thermal model parameterizations, when appropriately transformed from the center of momentum to the lab frame, are able to account for the data.

Norbury, John W.↗

DOE OSTI2024

Two-fermion negativity and confinement in the Schwinger model

We consider the fermionic (logarithmic) negativity between two fermionic modes in the Schwinger model. Recent results pointed out that fermionic systems can exhibit stronger entanglement than bosonic systems, exhibiting a negativity that decays only algebraically. The Schwinger model is described by fermionic excitations at short distances, while its asymptotic spectrum is the one of a bosonic theory. We show that the two-mode negativity detects this confining, fermion-to-boson transition, shifting from an algebraic decay to an exponential decay at distances of the order of the de Broglie wavelength of the first excited state. We derive analytical expressions in the massless Schwinger model and confront them with tensor network simulations. We also perform tensor network simulations in the massive model, which is not solvable analytically, and close to the Ising quantum critical point of the Schwinger model, where we show that the negativity behaves as its bosonic counterpart. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗