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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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NASA NTRS1994

Multigrid solution of compressible turbulent flow on unstructured meshes using a two-equation model

The steady state solution of the system of equations consisting of the full Navier-Stokes equations and two turbulence equations has been obtained using a multigrid strategy of unstructured meshes. The flow equations and turbulence equations are solved in a loosely coupled manner. The flow equations are advanced in time using a multistage Runge-Kutta time-stepping scheme with a stability-bound local time step, while turbulence equations are advanced in a point-implicit scheme with a time step which guarantees stability and positivity. Low-Reynolds-number modifications to the original two-equation model are incorporated in a manner which results in well-behaved equations for arbitrarily small wall distances. A variety of aerodynamic flows are solved, initializing all quantities with uniform freestream values. Rapid and uniform convergence rates for the flow and turbulence equations are observed.

MULTIGRID SOLUTION↗
NASA NTRS1981

VNAP2: A Computer Program for Computation of Two-dimensional, Time-dependent, Compressible, Turbulent Flow

A computer program, VNAP2, for calculating turbulent (as well as laminar and inviscid), steady, and unsteady flow is presented. It solves the two dimensional, time dependent, compressible Navier-Stokes equations. The turbulence is modeled with either an algebraic mixing length model, a one equation model, or the Jones-Launder two equation model. The geometry may be a single or a dual flowing stream. The interior grid points are computed using the unsplit MacCormack scheme. Two options to speed up the calculations for high Reynolds number flows are included. The boundary grid points are computed using a reference plane characteristic scheme with the viscous terms treated as source functions. An explicit artificial viscosity is included for shock computations. The fluid is assumed to be a perfect gas. The flow boundaries may be arbitrary curved solid walls, inflow/outflow boundaries, or free jet envelopes. Typical problems that can be solved concern nozzles, inlets, jet powered afterbodies, airfoils, and free jet expansions. The accuracy and efficiency of the program are shown by calculations of several inviscid and turbulent flows. The program and its use are described completely, and six sample cases and a code listing are included.

Cline, M. C.↗
NASA NTRS1992

Assessment of closure coefficients for compressible-flow turbulence models

A critical assessment is made of the closure coefficients used for turbulence length scale in existing models of the transport equation, with reference to the extension of these models to compressible flow. It is shown that to satisfy the compressible 'law of the wall', the model coefficients must actually be functions of density gradients. The magnitude of the errors that result from neglecting this dependence on density varies with the variable used to specify the length scale. Among the models investigated, the k-omega model yields the best performance, although it is not completely free from errors associated with density terms. Models designed to reduce the density-gradient effect to an insignificant level are proposed.

Huang, P. G.↗
NASA NTRS1990

Near-wall modelling of compressible turbulent flows

Work was carried out to extend the near-wall models formulated for the incompressible Reynolds stress equations to compressible flows. The idea of splitting the compressible dissipation function into a solenoidal part that is not sensitive to changes of compressibility indicators and a compressible part that is directly affected by these changes is adopted. This means that all models involving the dissipation rate could be expressed in terms of the solenoidal dissipation rate and an equation governing its transport could be formulated to close the set of compressible Reynolds stress equations. The near-wall modelling of the dissipation rate equation is investigated and its behavior near a wall is studied in detail using k-epsilon closure. It is found that all existing modelled equations give the wrong behavior for the dissipation rate near a wall. Improvements are suggested and the resultant behavior is found to be in good agreement with near-wall data. Furthermore, the present modified k-epsilon closure is used too calculate a flat plate boundary layer and the results are compared with four existing k-epsilon closures. These comparisons show that all closures tested give essentially the same flow properties, except in a region very close to the wall. In this region, the present k-epsilon closure calculations are in better agreement with measurements and direct simulation data; in particular, the behavior of the dissipation rate.

So, Ronald M. C.↗
NASA NTRS1986

Uncertainties in hot-wire measurements of compressible turbulent flows implied by comparisons with laser-induced fluorescence

A hot-wire anemometer and a new nonintrusive laser-induced fluorescence (LIF) technique are used to survey a Mach 2 turbulent boundary layer. The hot-wire anemometer's ability to accurately measure mass flux, temperature, and density fluctuations in a compressible flow is examined by comparing its results with those obtained using LIF. Several methods of hot-wire calibration are used, and the uncertainties in their measurements of various fluctuating flow parameters are determined. The results show that although a hot-wire operated at high overheat can measure mass flux fluctuations, temperature and density fluctuations are not determined accurately from such measurements. However, a hot-wire operated at multiple overheats can be used to measure static and total temperature fluctuations. The presence of pressure fluctuations and their correlation with density can prevent the use of hot-wire data to determine density fluctuations.

Mckenzie, R. L.↗
NASA NTRS1990

A numerical method for prediction of compressible turbulent flows with closure models

A new computer code to solve the time averaged Navier-Stokes equations is developed. Many of the state-of-the-art numerical techniques and algorithms have been tested and implemented in the program in order to achieve a better numerical accuracy and code efficiency. Various turbulence models are tested for a wide range of flows. The initial focus has been on two-equation eddy-viscosity models, which are the most advanced available in current compressible flow codes. The long term goal will be to test Reynolds-Stress models and to explore their performance in the high Mach number range. Although testing and improvement of turbulence models for supersonic and hypersonic flows is the primary objective of this research, part of the effort has been devoted to analyzing the vortex breakdown phenomena using new computer programs. Some preliminary results on the breakdown of a vortex flow in a tube are reported. Present calculations are restricted to two dimensional flow geometry.

Huang, P. G.↗
NASA NTRS1994

Three Dimensional Compressible Turbulent Flow Computations for a Diffusing S-Duct With/Without Vortex Generators

Numerical investigations on a diffusing S-duct with/without vortex generators and a straight duct with vortex generators are presented. The investigation consists of solving the full three-dimensional unsteady compressible mass averaged Navier-Stokes equations. An implicit finite volume lower-upper time marching code (RPLUS3D) has been employed and modified. A three-dimensional Baldwin-Lomax turbulence model has been modified in conjunction with the flow physics. A model for the analysis of vortex generators in a fully viscous subsonic internal flow is evaluated. A vortical structure for modeling the shed vortex is used as a source term in the computation domain. The injected vortex paths in the straight duct are compared with the analysis by two kinds of prediction models. The flow structure by the vortex generators are investigated along the duct. Computed results of the flow in a circular diffusing S-duct provide an understanding of the flow structure within a typical engine inlet system. These are compared with the experimental wall static-pressure, static- and total-pressure field, and secondary velocity profiles. Additionally, boundary layer thickness, skin friction values, and velocity profiles in wall coordinates are presented. In order to investigate the effect of vortex generators, various vortex strengths are examined in this study. The total-pressure recovery and distortion coefficients are obtained at the exit of the S-duct. The numerical results clearly depict the interaction between the low velocity flow by the flow separation and the injected vortices.

Cho, Soo-Yong↗
NASA NTRS1978

A three-dimensional turbulent compressible flow model for ejector and fluted mixers

A three dimensional finite element computer code was developed to analyze ejector and axisymmetric fluted mixer systems whose flow fields are not significantly influenced by streamwise diffusion effects. A two equation turbulence model was used to make comparisons between theory and data for various flow fields which are components of the ejector system, i.e., (1) turbulent boundary layer in a duct; (2) rectangular nozzle (free jet); (3) axisymmetric nozzle (free jet); (4) hypermixing nozzle (free jet); and (5) plane wall jet. Likewise, comparisons of the code with analytical results and/or other numerical solutions were made for components of the axisymmetric fluted mixer system. These included: (1) developing pipe flow; (2) developing flow in an annular pipe; (3) developing flow in an axisymmetric pipe with conical center body and no fluting and (4) developing fluted pipe flow. Finally, two demonstration cases are presented which show the code's ability to analyze both the ejector and axisymmetric fluted mixers.

Rushmore, W. L.↗
NASA NTRS1995

Large eddy simulations of compressible turbulent flows

An evaluation of existing models for Large Eddy Simulations (LES) of incompressible turbulent flows has been completed. LES is a computation in which the large, energy-carrying structures to momentum and energy transfer is computed exactly, and only the effect of the smallest scales of turbulence is modeled. That is, the large eddies are computed and the smaller eddies are modeled. The dynamics of the largest eddies are believed to account for most of sound generation and transport properties in a turbulent flow. LES analysis is based on an observation that pressure, velocity, temperature, and other variables are the sum of their large-scale and small-scale parts. For instance, u(i) (velocity) can be written as the sum of bar-u(i) and u(i)-prime, where bar-u(i) is the large-scale and u(i)-prime is the subgrid-scale (SGS). The governing equations for large eddies in compressible flows are obtained after filtering the continuity, momentum, and energy equations, and recasting in terms of Favre averages. The filtering operation maintains only large scales. The effects of the small-scales are present in the governing equations through the SGS stress tensor tau(ij) and SGS heat flux q(i). The mathematical formulation of the Favre-averaged equations of motion for LES is complete.

Porter-Locklear, Freda↗
NASA NTRS2013

Design of a Variational Multiscale Method for Turbulent Compressible Flows

A spectral-element framework is presented for the simulation of subsonic compressible high-Reynolds-number flows. The focus of the work is maximizing the efficiency of the computational schemes to enable unsteady simulations with a large number of spatial and temporal degrees of freedom. A collocation scheme is combined with optimized computational kernels to provide a residual evaluation with computational cost independent of order of accuracy up to 16th order. The optimized residual routines are used to develop a low-memory implicit scheme based on a matrix-free Newton-Krylov method. A preconditioner based on the finite-difference diagonalized ADI scheme is developed which maintains the low memory of the matrix-free implicit solver, while providing improved convergence properties. Emphasis on low memory usage throughout the solver development is leveraged to implement a coupled space-time DG solver which may offer further efficiency gains through adaptivity in both space and time.

Design↗
NASA NTRS1981

A reattaching free shear layer in compressible turbulent flow - A comparison of numerical and experimental results

An investigation of a two-dimensional, free turbulent shear layer reattaching on an inclined surface at Mach 2.92 and at a high Reynolds number is described. The test geometry is specifically designed to isolate the reattachment process of a high-speed separated flow. A numerical solution of the time-dependent, Reynolds-averaged, Navier-Stokes equations for the entire flow field, employing a two-equation eddy viscosity turbulence model, is presented. Detailed comparisons of prediction and experiment are made in the free shear layer, at reattachment, and in the developing boundary layer downstream. These comparisons include mean surface quantities as well as mean and fluctuating flowfield quantities. Although the overall features of this complex flow field are predicted, there are several deficiencies in the numerical solution, particularly in the region downstream of reattachment. Modifications of the turbulence model to correct these deficiencies are discussed.

Horstman, C. C.↗
NASA NTRS1984

A computational study of complex three-dimensional compressible turbulent flow fields

Solutions of the time dependent, Reynolds-averaged, Navier-Stokes equations are presented and are compared with a family of experimental results for the three-dimensional interaction of a shock wave with a turbulent boundary layer. The solutions correctly predict the major features of the flow field independent of the shock strength and the extent of separation when using a two-equation turbulence model with wall functions. The experimentally observed boundary between cylindrical and conical flow regimes is also predicted. However, for the flow fields with large separated zones, the details of the measured pressure distributions are not accurately computed, which indicates a need for improved turbulence modeling and/or grid resolution.

Horstman, C. C.↗
NASA NTRS1991

Multigrid solution of compressible turbulent flow on unstructured meshes using a two-equation model

The system of equations consisting of the full Navier-Stokes equations and two turbulence equations was solved for in the steady state using a multigrid strategy on unstructured meshes. The flow equations and turbulence equations are solved in a loosely coupled manner. The flow equations are advanced in time using a multistage Runge-Kutta time stepping scheme with a stability bound local time step, while the turbulence equations are advanced in a point-implicit scheme with a time step which guarantees stability and positively. Low Reynolds number modifications to the original two equation model are incorporated in a manner which results in well behaved equations for arbitrarily small wall distances. A variety of aerodynamic flows are solved for, initializing all quantities with uniform freestream values, and resulting in rapid and uniform convergence rates for the flow and turbulence equations.

Mavriplis, D. J.↗
NASA NTRS1991

Navier-Stokes computation of compressible turbulent flows with a second order closure

The objective was the development of a complete second order closure for wall bounded flows, including all components of the dissipation rate tensor and a numerical solution procedure for the resulting system of equations. The main topics discussed are the closure of the pressure correlations and the viscous destruction terms in the dissipation rate equations and the numerical solution scheme based on a block-tridiagonal solver for the nine equations required for the prediction of plane or axisymmetric flows.

Dingus, C.↗
NASA NTRS1991

Multigrid solution of compressible turbulent flow on unstructured meshes using a two-equation model

The system of equations consisting of the full Navier-Stokes equations and two turbulence equations has been solved for in the steady-state using a multigrid strategy on unstructured meshes. The flow equations and turbulence equations are solved in a loosely coupled manner. The flow equations are advanced in time using a multistage Runge-Kutta time stepping scheme with a stability bound local time-step, while the turbulence equations are advanced in a point-implicit scheme with a time-step which guarantees stability and positivity. Low Reynolds number modifications to the original two-equation model are incorporated in a manner which results in well behaved equations for arbitrarily small wall distances. A variety of aerodynamic flows are solved for, initializing all quantities with uniform freestream values, and resulting in rapid and uniform convergence rates for the flow and turbulence equations.

Mavriplis, D. J.↗
NASA NTRS1991

Diagonal implicit multigrid solution of compressible turbulent flows

The Caughey (1988) multigrid diagonal implicit algorithm for Euler equations is extended to solve the two-dimensional thin layer Navier-Stokes equations for turbulent transonic flows. To further accelerate convergence to a steady state, the implicit scheme is used within the multigrid method. Results are presented for transonic flows past airfoils, and the flow-field results are compared with other computational data and experiments demonstrating the accuracy of the method.

Varma, R. R.↗