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At least 649 records · Page 36
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NASA NTRS1988

Unsteady aerodynamics of rotor-stator interaction in a turbine stage

The two-dimensional, compressible, unsteady, thin-layer Navier-Stokes equations have been used to study the turbulent flow field of a turbine rotor/stator configuration in the high pressure oxidizer turbopump of the Space Shuttle main engine. The calculations were performed on a system of patched and overlaid grids. The grid system consists of 'O-' and 'H-' grids, with the inner 'O-'grid enclosing the blade surface for an accurate resolution of the leading and trailing edges, while the outer 'H-'grid makes the treatment of boundary conditions easier. The integration scheme used is an iterative, factored, implicit method with numerical fluxes evaluated by the third-order accurate upwind-biased Osher scheme. Computed results in the form of pressure contours, Mach number contours, time-averaged surface pressure, unsteady pressure amplitude and unsteady velocity vectors are presented. Many flow phenomena, such as wake cutting by rotor airfoils and evolution of unsteady passage vortices, are discussed.

Yang, R.-J.↗
NASA NTRS1988

Multi-airfoil Navier-Stokes simulations of turbine rotor-stator interaction

An accurate numerical analysis of the flows associated with rotor-stator configurations in turbomachinery can be extremely helpful in optimizing the performance of turbomachinery. In this study the unsteady, thin-layer, Navier-Stokes equations in two spatial dimensions are solved on a system of patched and overlaid grids for a rotor-stator configuration from an axial turbine. The governing equations are solved using a finite-difference, upwind algorithm that is set in an iterative, implicit framework. Results in the form of pressure contours, time-averaged pressures, unsteady pressure amplitudes and phase are presented. The numerical results are compared with experimental data and the agreement is found to be good. The results are also compared with those of an earlier study which used only one rotor and one stator. The current study uses multiple rotors and stators and a pitch ratio that is much closer to the experimental ratio. Consequently the results of this study are found to be closer to the experimental data.

Rai, Man Mohan↗
NASA NTRS1988

Newton solution of inviscid and viscous problems

The application of Newton iteration to inviscid and viscous airfoil calculations is examined. Spatial discretization is performed using upwind differences with split fluxes. The system of linear equations which arises as a result of linearization in time is solved directly using either a banded matrix solver or a sparse matrix solver. In the latter case, the solver is used in conjunction with the nested dissection strategy, whose implementation for airfoil calculations is discussed. The boundary conditions are also implemented in a fully implicit manner, thus yielding quadratic convergence. Complexities such as the ordering of cell nodes and the use of a far field vortex to correct freestream for a lifting airfoil are addressed. Various methods to accelerate convergence and improve computational efficiency while using Newton iteration are discussed. Results are presented for inviscid, transonic nonlifting and lifting airfoils and also for laminar viscous cases.

Venkatakrishnan, V.↗
NASA NTRS1988

Computations of vortical supersonic flows over a blunt-nose-cylinder at high angles of attack

Three-dimensional, viscous, and separated flows over a blunt-nose-cylinder at 20, 32, and 44-deg attack angles were computed. The approaching freestream was at a Mach number of 1.6 and a unit Reynolds number of 2 x 10 to the 6th/ft with a total temperature of 585 R. The cylinder used for the computations had a length-to-diameter ratio of 6.67 with a base diameter of 3 in. The flowfield was dominated by large-scale and multiple vortices generated by crossflow separation. The effect of turbulence on the flow structure of one case was modeled algebraically with modifications to correct the length and velocity scales in the regions of separation. The mass averaged Navier-Stokes equations were solved by an approximately factored, upwind-biased, implicit, finite volume scheme. The initialization of the flows was enhanced by a mesh sequencing strategy applied to the diagonalized form of the discretized equations. The convergence to steady-state was accelerated by a multigrid algorithm and using the block inversions for the discretized equations. Calculations were compared with experimental results.

Baysal, O.↗
NASA NTRS1988

A longitudinally-patched grid approach with applications to high speed flows

The combined use of an implicit, upwind finite-volume scheme with an 'equivalent' gamma formulation (for real gas effects) and with a three-dimensional conservative patched grid formulation is discussed. Results are presented over a wide Mach number range on both single and patched grids.

Walters, R. W.↗
NASA NTRS1987

A finite difference scheme for three-dimensional steady laminar incompressible flow

A finite difference scheme for three-dimensional steady laminar incompressible flows is presented. The Navier-Stokes equations are expressed conservatively in terms of velocity and pressure increments (delta form). First order upwind differences are used for first order partial derivatives of velocity increments resulting in a diagonally dominant matrix system. Central differences are applied to all other terms for second order accuracy. The SIMPLE pressure correction algorithm is used to satisfy the continuity equation. Numerical results are presented for cubic cavity flow problems for Reynolds numbers up to 2000 and are in good agreement with other numerical results.

Hwang, Danny P.↗
NASA NTRS1987

Low-frequency acoustic propagation in high winds

The effect of refraction due to wind gradients on low-frequency acoustic signals over large propagation distances is considered. The results of an investigation of low-frequency propagation in high winds are presented and compared to normal mode theory for the downwind propagation case. In the downwind direction, the low-frequency signal was channeled close to the ground resulting in a divergence of 3 dB per doubling of propagation distance. Predictions of both ray tracing and normal mode theoretical models supported the downwind cylindrical spreading. In effect, the low-frequency noise signals propagate further in the presence of wind in the downwind direction. No low-frequency acoustic shadow zone was observed in the upwind direction.

Willshire, William L., Jr.↗
NASA NTRS1988

Flow visualization and pressure distributions for an all-body hypersonic aircraft

A CFD code-validation effort has been conducted at the NASA-Ames 3.5-ft hypersonic wind tunnel, using a generic, 'all-body' hypersonic aircraft configuration model. The CFD methods to be validated encompass approximate inviscid ones and the upwind parabolized Navier-Stokes solver code. Flow visualizations and pressure distributions are obtained for the cases of zero and 15 deg angles of attack. A complex leeward flow is observed at angle-of-attack with crossflow separation and vortices, and significant changes are noted in the transition from the forebody's conical to the afterbody's nonconical flows.

Lockman, William K.↗
NASA NTRS1988

Computational validation of a parabolized Navier-Stokes solver on a sharp-nose cone at hypersonic speeds

Perfect gas computational results from a newly-developed upwind, parabolized Navier-Stokes (PNS) solver are compared with an existing set of experimental laminar results for a 10-deg half-angle circular cone at freestream Mach number of 7.95. Comparisons were performed with surface pressure and heat transfer data, as well as with flowfield pitot measurements. The PNS code predicted the surface quantities accurately up through 20-deg angle-of-attack, including crossflow separation, and correctly defined the location of the bow shock and the edge of the boundary layer. The importance of cell Reynolds number, grid density, and thermal boundary conditions to the accurate prediction of the flowfield are examined through numerical emamples.

Huebner, Lawrence D.↗
NASA NTRS1988

Navier-Stokes computation of flow around a round-edged double-delta wing

Computations of three-dimensional vortical flows over a thin round-edged double-delta wing with an aspect ratio of 2.05 are performed using an implicit upwind-relaxation finite-difference scheme. The effects of grid and angle of attack on the Navier-Stokes computations are studied. Coarse-grid calculations can not predict the detailed structures of the vortical flowfields for lack of grid resolution. On the contrary, fine-grid computations show that key features of vortex formation, interaction, and breakdown are simulated. Furthermore, computed lift coefficients and spanswise surface static pressure distributions are in good agreement with the experimental data up to alpha = 25 deg.

Hsu, C.-H.↗
NASA NTRS1988

Cross-B convection of artificially created, negative-ion clouds and plasma depressions - Low-speed flow

A negative-ion, positive-ion plasma produced by the release of an electron attachment chemical into the F region becomes electrically polarized by collisions with neutrals moving across magnetic field lines. The resulting electric field causes E x B drift of the two ion species and the residual electrons. The cross-field flow of the modified ionosphere is computed using a two-dimensional numerical simulation which includes electron attachment and mutual neutralization chemistry, self-consistent electric fields, and three-species plasma transport. The velocity of the plasma is initially in the direction of the neutral wind because the negative-ion cloud is a Pedersen conductivity enhancement. As the positive and negative ions react, the Pedersen conductivity becomes depressed below the ambient value and the velocity of the plasma reverses direction. A plasma hole remains after the positive and negative ions have mutually neutralized. The E x B gradient drift instability produces irregularities on the upwind edge of the hole.

Bernhardt, Paul A.↗
NASA NTRS1988

A comparison of ENO and TVD schemes

The numerical performance of a second-order upwind-based TVD scheme is compared with that of a uniform second-order ENO scheme on shock capturing. The cases considered include flows with Mach numbers of 2.9, 5.0, and 10.0. For cases with Mach numbers of 5.0 and 10.0, the computed ENO results are inferior to the corresponding TVD results.

Chang, Shih-Hung↗
NASA NTRS1988

An algorithm for unsteady flows with strong convection

An implicit ADI numerical method for the calculation of 2-D unsteady flows with strong convection effects is described. The method is based on the conventional Crank-Nicholson approach for parabolic equations but an upwind-downwind differencing is used for the first order spatial derivatives associated with convection. The differencing is carried out in the current and previous time plane in such a way that the algorithm is second order accurate in both space and time. The difference equations are factored into sequential operators, one in each independent spatial variable; the solution at each time step may then be computed as a sequence of tridiagonal matrix problems. The method may be used in a noniterative manner although iteration at each time step is recommended in situations where the effects of convection are strong.

Peridier, Vallorie↗
NASA NTRS1988

Improving the accuracy of central difference schemes

General difference approximations to the fluid dynamic equations require an artificial viscosity in order to converge to a steady state. This artificial viscosity serves two purposes. One is to suppress high frequency noise which is not damped by the central differences. The second purpose is to introduce an entropy-like condition so that shocks can be captured. These viscosities need a coefficient to measure the amount of viscosity to be added. In the standard scheme, a scalar coefficient is used based on the spectral radius of the Jacobian of the convective flux. However, this can add too much viscosity to the slower waves. Hence, it is suggested that a matrix viscosity be used. This gives an appropriate viscosity for each wave component. With this matrix valued coefficient, the central difference scheme becomes closer to upwind biased methods.

Turkel, Eli↗
NASA NTRS1988

A numerical study of ENO and TVD schemes for shock capturing

The numerical performance of a second-order upwind-based total variation diminishing (TVD) scheme and that of a uniform second-order essentially non-oscillatory (ENO) scheme for shock capturing are compared. The TVD scheme used is a modified version of Liou, using the flux-difference splitting (FDS) of Roe and his superbee function as the limiter. The construction of the basic ENO scheme is based on Harten, Engquist, Osher, and Chakravarthy, and the 2-D extensions are obtained by using a Strang-type of fractional-step time-splitting method. Numerical results presented include both steady and unsteady, 1-D and 2-D calculations. All the chosen test problems have exact solutions so that numerical performance can be measured by comparing the computer results to them. For 1-D calculations, the standard shock-tube problems of Sod and Lax are chosen. A very strong shock-tube problem, with the initial density ratio of 400 to 1 and pressure ratio of 500 to 1, is also used to study the behavior of the two schemes. For 2-D calculations, the shock wave reflection problems are adopted for testing. The cases presented in this report include flows with Mach numbers of 2.9, 5.0, and 10.0.

Chang, Shih-Hung↗
NASA NTRS1988

Three-dimensional multigrid algorithms for the flux-split Euler equations

The Full Approximation Scheme (FAS) multigrid method is applied to several implicit flux-split algorithms for solving the three-dimensional Euler equations in a body fitted coordinate system. Each of the splitting algorithms uses a variation of approximate factorization and is implemented in a finite volume formulation. The algorithms are all vectorizable with little or no scalar computation required. The flux vectors are split into upwind components using both the splittings of Steger-Warming and Van Leer. The stability and smoothing rate of each of the schemes are examined using a Fourier analysis of the complete system of equations. Results are presented for three-dimensional subsonic, transonic, and supersonic flows which demonstrate substantially improved convergence rates with the multigrid algorithm. The influence of using both a V-cycle and a W-cycle on the convergence is examined.

Anderson, W. Kyle↗
NASA NTRS1989

Conservation equations and physical models for hypersonic air flows in thermal and chemical nonequilibrium

The conservation equations for simulating hypersonic flows in thermal and chemical nonequilibrium and details of the associated physical models are presented. These details include the curve fits used for defining thermodynamic properties of the 11 species air model, curve fits for collision cross sections, expressions for transport properties, the chemical kinetics models, and the vibrational and electronic energy relaxation models. The expressions are formulated in the context of either a two or three temperature model. Greater emphasis is placed on the two temperature model in which it is assumed that the translational and rotational energy models are in equilibrium at the translational temperature, T, and the vibrational, electronic, and electron translational energy modes are in equilibrium at the vibrational temperature, T sub v. The eigenvalues and eigenvectors associated with the Jacobian of the flux vector are also presented in order to accommodate the upwind based numerical solutions of the complete equation set.

Peter A. Gnoffo↗
NASA NTRS1987

Evaluation of aerothermal modeling computer programs

Various computer programs based upon the SIMPLE or SIMPLER algorithm were studied and compared for numerical accuracy, efficiency, and grid dependency. Four two-dimensional and one three-dimensional code originally developed by a number of research groups were considered. In general, the accuracy and computational efficieny of these TEACH type programs were improved by modifying the differencing schemes and their solvers. A brief description of each program is given. Error reduction, spline flux and second upwind differencing programs are covered.

Hsieh, K. C.↗