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At least 289 records · Page 16

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NASA NTRS1989

A three-dimensional upwind parabolized Navier-Stokes code for real gas flows

A real gas, upwind, parabolized Navier-Stokes (PNS) code has been developed to compute the three-dimensional hypersonic flow of equilibrium air around various body shapes. The new code is an extension of the upwind (perfect gas) PNS code of Lawrence et al. (1986). The upwind algorithm is based on Roe's (1981) flux-difference splitting scheme which has been modified to account for real gas effects using the nearly exact approach of Vinokur and Liu (1988). Simplified curve fits are employed to obtain the thermodynamic and transport properties of equilibrium air. The new code has been validated by computing the M-infinity = 25 laminar flow of air over cones at various angles of attack. The results of these computations are compared with the results from a conventional centrally-differenced, real gas PNS code and the previous axisymmetric, upwind, real gas code. The agreement is excellent in all cases.

Tannehill, John C.↗

NASA NTRS1989

Navier-Stokes calculations of transonic flows past cavities

A computational investigation of subsonic and transonic flows past 3-D deep transitional cavities is presented. Computational simulations of these self-induced oscillatory flows were generated through time-accurate solutions of the Reynolds averaged full Navier-Stokes equations, using the explicit MacCormack scheme. The Reynolds stresses were included through the Baldwin-Lomax algebraic turbulence model with certain modifications. Two cases were computed to demonstrate the capability of the numerical scheme in modeling the complex 3-D flow features inside a cavity. The results from an experimental investigation were used not only to benchmark the computations, but also to widen the database used for the discussions and conclusions. The computational results include instantaneous and time averaged flow properties everywhere in the computational zone. Time series analyses were performed for the instantaneous pressure values on the cavity floor. The features of deep and transitional cavity flows, and the effect of the sidewall on the cavity flow flowfield are illustrated through computational graphics.

Baysal, Oktay↗

NASA NTRS1988

An upwind parabolized Navier-Stokes code for real gas flows

A real gas, upwind, parabolized Navier-Stokes (PNS) code has been developed to compute the two-dimensional/axisymmetric hypersonic flow of equilibrium air around various body shapes. The new code is an extension of the upwind (perfect gas) PNS code of Lawrence, Tannehill and Chaussee. The upwind algorithm is based on Roe's flux-difference splitting scheme which has been modified to account for real gas effects. Simplified curve fits are used to obtain the thermodynamic and transport properties of equilibrium air. The new code has been validated by computing the hypersonic laminar flow of air over a flat plate, a wedge, a ramp, and a cone. The results of these computations are compared with the results from a conventional centrally-differenced, real gas, PNS code and the agreement is excellent, except in the vicinity of shock waves where the present code exhibits far superior shock capturing capabilities.

Tannehill, John C.↗

NASA NTRS1991

Navier-Stokes calculations of transonic flows past cavities

Presented in this paper is a computational investigation of subsonic and transonic flows past three-dimensional deep and transitional cavities. Simulations of these self-induced oscillatory flows have been generated through time-accurate solutions of the Reynolds averaged, full Navier-Stokes equations, using the explicit MacCormack scheme. The Reynolds stresses have been included through the Baldwin-Lomax algebraic turbulence model with certain modifications. The computational results include instantaneous and time averaged flow properties. The results of an experimental investigation have been used not only to validate the time-averaged results, but also to investigate the effects of varying the Mach number and the incoming boundary-layer thickness. Time series analyses have been performed for the instantaneous pressure values on the cavity floor and compared with the results obtained by a predictive formula. While most of the comparisons have been favorable, some discrepancies have been observed, particularly on the rear face. The present results help understanding the three-dimensional and unsteady features of the separations, vortices, the shear layer, as well as some of the aeroacoustic phenomena of compressible cavity flows.

Baysal, O.↗

NASA NTRS1989

Parabolized Navier-Stokes algorithm for chemically reacting flows

A second-order parabolized Navier-Stokes algorithm based on the MacCormack (1969) explicit scheme is used to study three-dimensional chemically reacting flows with finite-rate chemistry. The method can treat the chemical source term implicitly, and it accounts for the multicomponent diffusion and convection of the chemical species. The method is demonstrated with the nonreacting case of a Mach-3 flow over a double-wedge compression corner and the case of streamwise hydrogen injection at sonic velocity in a Mach-2.44 vitiated air stream.

Kamath, H.↗

NASA NTRS1989

The numerical solution of the Navier-Stokes equations for 3-dimensional, unsteady, incompressible flows by compact schemes

The present numerical method for the solution of unsteady, incompressible three-dimensional flow Navier-Stokes equations using velocity-vorticity variables and irregular Cartesian grids proceeds by solving: (1) equations of Cauchy-Riemann type for the velocity; and (2) transport-diffusion equations for the vorticity, whose solenoidal vorticity components are generated by a Poisson equation for an appropriate scalar potential. Iterations are used to solve the finite difference equations, facilitating the use of vector and parallel-computing methods; numerical experiments have verified the method's second-order spatial and temporal accuracy.

Gatski, T. B.↗

NASA NTRS1990

Navier-Stokes simulation of transonic afterbody flows with jet exhaust

Three-dimensional Navier-Stokes simulations have been made for the transonic flow past a nonaxisymmetric nozzle typical of those advocated for advanced fighter airplanes. Jet exhaust simulation is evaluated as are the Baldwin-Lomax (1978) and Goldberg (1986) turbulence models. Solutions are presented for Mach numbers of 0.80 and 0.94 at 0-deg angle of attack and a Reynolds number of 20 x 10 to the 6th. The numerical results are compared to wind-tunnel data. They show that including the jet exhaust in the calculations gives the most accurate solution near the nozzle exit. Also, the two turbulence models predict considerably different flow fields.

Compton, William B., III↗

NASA NTRS1990

A review of reduced Navier-Stokes computations for compressible viscous flows

A reduced form of the Navier-Stokes equations, defined by a single composite of the Euler, boundary layer, and triple deck approximations, is considered for the computation of viscous interacting flows. Global pressure or pseudopotential relaxation methods are integrated with coupled sparse matrix direct solvers or coupled strongly implicit ILU algorithms to efficiently capture sharp shocks and regions of recirculation. Solutions are obtained for a variety of 2D and 3D geometries and for Mach numbers (M) spanning the range from incompressible (M = 0) to supersonic (M = 6) flow.

Rubin, S. G.↗

NASA NTRS1989

Navier-Stokes solutions for vortical flows over a tangent-ogive cylinder

Reynolds number (Re) effects on low-speed vortical flows over a 3.5 caliber tangent-ogive cylinders at two angles of attack (alpha = 20 and alpha = 30 degrees) are computationally assessed for Re(D) = 0.2 -3.0 million (D: maximum diameter). The flow field results are steady-state solutions to the three-dimensional, incompressible Navier-Stokes equations in their thin-layer approximation. Using a properly modified algebraic turbulence model, the numerical results are in good to excellent agreement with experiments.

Hartwich, PETER-M.↗

NASA NTRS1988

Navier-Stokes simulation of transonic wing flow fields using a zonal grid approach

The transonic Navier-Stokes code was used to simulate flow fields about isolated wings for workshop wind-tunnel and free-air cases using the thin-layer Reynolds-averaged Navier-Stokes equations. An implicit finite-difference scheme based on a diagonal version of the Beam-Warming algorithm was used to integrate the governing equations. A zonal grid approach was used to allow efficient grid refinement near the wing surface. The flow field was sensitive to the turbulent transition model, and flow unsteadiness was observed for a wind-tunnel case but not for the corresponding free-air case. The specification of experimental pressure at the wind-tunnel exit plane is the primary reason for the difference of these two numerical solutions.

Chaderjian, Neal M.↗

NASA NTRS1988

Navier-Stokes simulation of transonic wing flow fields using a zonal grid approach

Chaderjian, Neal M.↗

NASA NTRS1978

Forebody and afterbody solutions of the Navier-Stokes equations for supersonic flow over blunt bodies in a generalized orthogonal coordinate system

A coordinate transformation, which can approximate many different two-dimensional and axisymmetric body shapes with an analytic function, is used as a basis for solving the Navier-Stokes equations for the purpose of predicting 0 deg angle of attack supersonic flow fields. The transformation defines a curvilinear, orthogonal coordinate system in which coordinate lines are perpendicular to the body and the body is defined by one coordinate line. This system is mapped in to a rectangular computational domain in which the governing flow field equations are solved numerically. Advantages of this technique are that the specification of boundary conditions are simplified and, most importantly, the entire flow field can be obtained, including flow in the wake. Good agreement has been obtained with experimental data for pressure distributions, density distributions, and heat transfer over spheres and cylinders in supersonic flow. Approximations to the Viking aeroshell and to a candidate Jupiter probe are presented and flow fields over these shapes are calculated.

Gnoffo, P. A.↗

NASA NTRS1992

Navier-Stokes simulations of unsteady transonic flow phenomena

Numerical simulations of two classes of unsteady flows are obtained via the Navier-Stokes equations: a blast-wave/target interaction problem class and a transonic cavity flow problem class. The method developed for the viscous blast-wave/target interaction problem assumes a laminar, perfect gas implemented in a structured finite-volume framework. The approximately factored implicit scheme uses Newton subiterations to obtain the spatially and temporally second-order accurate time history of the blast-waves with stationary targets. The inviscid flux is evaluated using either of two upwind techniques, while the full viscous terms are computed by central differencing. Comparisons of unsteady numerical, analytical, and experimental results are made in two- and three-dimensions for Couette flows, a starting shock-tunnel, and a shock-tube blockage study. The results show accurate wave speed resolution and nonoscillatory discontinuity capturing of the predominantly inviscid flows. Viscous effects were increasingly significant at large post-interaction times. While the blast-wave/target interaction problem benefits from high-resolution methods applied to the Euler terms, the transonic cavity flow problem requires the use of an efficient scheme implemented in a geometrically flexible overset mesh environment. Hence, the Reynolds averaged Navier-Stokes equations implemented in a diagonal form are applied to the cavity flow class of problems. Comparisons between numerical and experimental results are made in two-dimensions for free shear layers and both rectangular and quieted cavities, and in three-dimensions for Stratospheric Observatory For Infrared Astronomy (SOFIA) geometries. The acoustic behavior of the rectangular and three-dimensional cavity flows compare well with experiment in terms of frequency, magnitude, and quieting trends. However, there is a more rapid decrease in computed acoustic energy with frequency than observed experimentally owing to numerical dissipation. In addition, optical phase distortion due to the time-varying density field is modelled using geometrical constructs. The computed optical distortion trends compare with the experimentally inferred result, but underpredicts the fluctuating phase difference magnitude.

Atwood, C. A.↗

NASA NTRS1993

Incompressible Navier-Stokes computations of rotating flows

Flow through pump components, such as an inducer and an impeller, is efficiently simulated by solving the incompressible Navier-Stokes equations. The solution method is based on the pseudocompressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. Current computations use one-equation Baldwin-Barth turbulence model which is derived from a simplified form of the standard k-epsilon model equations. The resulting computer code is applied to the flow analysis inside a generic rocket engine pump inducer, a fuel pump impeller, and SSME high-pressure fuel turbopump impeller. Numerical results of inducer flow are compared with experimental measurements. Flow analyses at 80-, 100-, and 120-percent of design conditions are presented.

Kiris, Cetin↗

NASA NTRS1980

Computation of three-dimensional viscous flows with the Navier-Stokes equations

The paper presents computations of three-dimensional viscous flows generated with the General Interpolation Method/STAR code based on the time-averaged Navier-Stokes equations. Calculations are presented for three viscous flow problems, and a two dimensional nozzle-exhaust shear flow case is solved and compared to an inviscid slip-line code. This nozzle-exhaust flow case is then extended to three dimensions and the steady solution displayed at pressure contours in the cross planes. The third problem consists of a simulated two-dimensional aircraft inlet flow which includes calculation of the 'spillage' flow and a shock wave/boundary layer interaction in the nozzle.

Spradley, L. W.↗

NASA NTRS1980

An approximate factorization solution of the Navier-Stokes equations for transonic flow using body-fitted coordinates with application to NACA 64A010 airfoils

The implementation of the approximate factorization algorithm and its ability to efficiently and accurately describe transonic flow about an NACA 64A010 airfoil section is examined. The approximate factorization algorithm is developed from the nondimensional, conservative, vectorized Navier-Stokes equations expressed in curvilinear coordinates. Equations of state and transport coefficient relations appropriate to atmospheric air are appended to close the system of partial differential equations. An algebraic turbulence model is also incorporated into the equation set. This algorithm was verified by investigating the flow about an NACA 64A010 airfoil at 0, 2, and 3.5 deg angle of attack for free-stream conditions of 2,000,000 Reynolds number and 0.8 Mach number. Overall results were in good qualitative agreement with wind tunnel data sets. However, while nondimensional times of six were attained, numerical difficulties prevented any case from reaching a true steady state.

Copper, G. K.↗

NASA NTRS1987

Time-marching solution of incompressible Navier-Stokes equations for internal flow

Primitive variables with central differencing on a staggered grid are used in the present, factored ADI finite-difference scheme for artificial compressibility method solution of the incompressible Navier-Stokes equations, leading to a close coupling between velocity and pressure that both enhances stability and eliminates the need for artificial damping. Computational efficiency is enhanced through the use of a spatially variable, fixed Courant number-based time-step. The numerical results obtained for a driven cavity at Re of 10,000, with local cell Re as high as 100, exhibits no flow variable spatial oscillations on a 40 x 40 stretched grid solution.

Soh, W. Y.↗

NASA NTRS1993

A comparison of two incompressible Navier-Stokes algorithms for unsteady internal flow

A comparative study of two different incompressible Navier-Stokes algorithms for solving an unsteady, incompressible, internal flow problem is performed. The first algorithm uses an artificial compressibility method coupled with upwind differencing and a line relaxation scheme. The second algorithm uses a fractional step method with a staggered grid, finite volume approach. Unsteady, viscous, incompressible, internal flow through a channel with a constriction is computed using the first algorithm. A grid resolution study and parameter studies on the artificial compressibility coefficient and the maximum allowable residual of the continuity equation are performed. The periodicity of the solution is examined and several periodic data sets are generated using the first algorithm. These computational results are compared with previously published results computed using the second algorithm and experimental data.

Wiltberger, N. Lyn↗