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At least 469 records · Page 26

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NASA NTRS1983

Boundary conditions for the solution of compressible Navier-Stokes equations by an implicit factored method

A method is presented for formulating the boundary conditions in implicit finite-difference form needed for obtaining solutions to the compressible Navier-Stokes equations by the Beam and Warming implicit factored method. The usefulness of the method was demonstrated (a) by establishing the boundary conditions applicable to the analysis of the flow inside an axisymmetric piston-cylinder configuration and (b) by calculating velocities and mass fractions inside the cylinder for different geometries and different operating conditions. Stability, selection of time step and grid sizes, and computer time requirements are discussed in reference to the piston-cylinder problem analyzed.

Shih, T. I.-P.↗

NASA NTRS1983

A spectral numerical method for the Navier-Stokes equations with applications to Taylor-Couette flow

A new spectral method for solving the incompressible Navier-Stokes equations in a plane channel and between concentric cylinders is presented. The method uses spectral expansions which inherently satisfy the boundary conditions and the continuity equation and yield banded matrices which are efficiently solved at each time step. In addition, the number of dependent variables is reduced, resulting in a reduction in computer memory requirements. Several test problems have been computed for the channel flow and for flow between concentric cylinders, including Taylor-Couette flow with axisymmetric Taylor vortices and wavy vortices. In all cases, agreement with available experimental and theoretical results is very good.

Moser, R. D.↗

NASA NTRS1984

An incompressible Navier-Stokes flow solver in three-dimensional curvilinear coordinate systems using primitive variables

An implicit, finite-difference computer code has been developed to solve the incompressible Navier-Stokes equations in a three-dimensional, curvilinear coordinate system. The pressure-field solution is based on the pseudo compressibility approach in which the time derivative pressure term is introduced into the mass conservation equation to form a set of hyperbolic equations. The solution procedure employs an implicit, approximate factorization scheme. The Reynolds stresses, that are uncoupled from the implicit scheme, are lagged by one time-step to facilitate implementing various levels of the turbulence model. Test problems for external and internal flows are computed, and the results are compared with existing experimental data. The application of this technique for general three-dimensional problems is then demonstrated.

Kwak, D.↗

NASA NTRS1984

Solution of the Navier-Stokes equations for flow within a 2-D thrust reversing nozzle

Implicit numerical procedures have been developed to solve the Reynold's Averaged Navier-Stokes equations for the flowfield within a two-dimensional thrust reversing engine nozzle. The procedures have been tested on four different thrust reverser nozzle geometries with both fixed and moving walls. The results have compared well with available experimental data.

Maccormack, R. W.↗

NASA NTRS1984

A strongly implicit procedure for the compressible Navier-Stokes equations

The strongly implicit procedure of Stone is used to obtain numerical solutions of the compressible Navier-Stokes equations in conservative form. In contrast to the spatially split Douglas-Gunn type methods, the method is shown to be numerically stable for the three-dimensional wave equation. The method is applied to a variety of external and internal two-dimensional flow problems involving shock wave boundary-layer interaction for both laminar and turbulent flows. The results are in good agreement with other methods and/or experiments. The storage penalty associated with the method is discussed and a simple, yet effective, means of minimizing the problem is presented.

Walters, R. W.↗

NASA NTRS1984

Calculation of steady and oscillating airfoil flow fields via the Navier Stokes equations

A Navier-Stokes calculation procedure is applied to high Reynolds number flow about steady and unsteady airfoils. The procedure solves the ensemble averaged governing equations via a linearized block implicit (LBI) technique which in general converges to a nominal steady flow within 120 time steps. The grid used in the computation is highly stretched thus resolving the turbulent boundary layers. Calculations have been compared with data for both NACA 4412 airfoil at high incidence and an NACA 0012 airfoil oscillating in dynamic stall. In both cases, good agreement is noted between measured and calculated surface pressure distributions.

Shamroth, S. J.↗

NASA NTRS1983

Spatially and spectrally resolved multipoint coherent anti-Stokes Raman scattering from N2 and O2 flows

Single-shot spectrally resolved broadband rotational coherent anti-Stokes Raman scattering (CARS) from multiple points along a line intersecting a flow has been observed for N2 and O2. A large-angle phase-matching configuration was used to achieve spatial resolution of 0.1 mm x 0.1 mm x 0.1 mm for each of 20 points in the interaction volume. Single-shot multipoint CARS of N2 at different temperatures and of several species in a coflowing jet was observed.

Snow, J. B.↗

NASA NTRS1984

A comparative study of the parabolized Navier-Stokes code using various grid-generation techniques

The parabolized Navier-Stokes (PNS) equations are used to calculate the flow-field characteristics about the hypersonic research aircraft X-24C. A comparison of the results obtained using elliptic, hyperbolic, and algebraic grid generators is presented. The outer bow shock is treated as a sharp discontinuity, and the discontinuities within the shock layer are captured. Surface pressures and heat-transfer results at angles of attack of 6 deg and 20 deg, obtained using the three grid generators, are compared. The PNS equations are marched downstream over the body in both Cartesian and cylindrical base coordinate systems, and the results are compared. A robust marching procedure is demonstrated by successfully using large marching step sizes with the implicit shock fitting procedure. A correlation is found between the marching step size, Reynolds number, and the angle of attack at fixed values of smoothing and stability coefficients for the marching scheme.

Kaul, U. K.↗

NASA NTRS1984

Finite-analytic numerical method for unsteady two-dimensional Navier-Stokes equations

A finite analytic (FA) numerical solution is developed for unsteady two-dimensional Navier-Stokes equations. The FA method utilizes the analytic solution in a small local element to formulate the algebraic representation of partial differential equations. The combination of linear and exponential functions that satisfy the governing equation is adopted as the boundary function, thereby improving the accuracy of the finite analytic solution. Two flows, one a starting cavity flow and the other a vortex shedding flow behind a rectangular block, are solved by the FA method. The starting square cavity flow is solved for Reynolds number of 400, 1000, and 2000 to show the accuracy and stability of the FA solution. The FA solution for flow over a rectangular block (H x H/4) predicts the Strouhal number for Reynolds numbers of 100 and 500 to be 0.156 and 0.125. Details of the flow patterns are given. In addition to streamlines and vorticity distribution, rest-streamlines are given to illustrate the vortex motion downstream of the block.

Chen, C.-J.↗

NASA NTRS1984

Navier-Stokes solutions for two-dimensional subsonic base flow

Methods for determining the effects of mass injection from the trailing edge of a bluff body at low speeds and in transonic flow were numerically studied along with an unmodified blunt-based body to gain insight into the effects of vortex shedding on the base drag. The methodology used to obtain finite-difference solutions to the Navier-Stokes equations for subsonic compressible two-dimensional near-wake flows is presented. The effectiveness of an introduced outflow boundary condition which minimizes reflections back into the computational domain was demonstrated with the solution of a model vortex problem. Calculations of the near-wake flow past a circular cylinder were in excellent agreement with experimental data. Laminar-flow solutions for a blunt-based model with and without a base cavity and with mass injection into the wake agreed qualitatively with experimental observations. The drag reduction capability provided by such base modifications was demonstrated.

Rudy, D. H.↗

NASA NTRS1982

Simulation of large turbulent vortex structures with the parabolic Navier-Stokes equations

The theoretical basis for well posed marching of a Parabolic Navier-Stokes (PNS) computational technique for supersonic flow is discussed and examples given to verify the analysis. It is demonstrated that stable computations can be made even with very small steps in the marching direction. The method is applied to cones at large angle of attack in high Reynolds number, supersonic flow. Streamline trajectories generated from the numerical solutions demonstrate the development of vortex structures of the lee side of the cone. Previously announced in STAR as N83-22551

Rakich, J. V.↗

NASA NTRS1984

Parabolized Navier-Stokes analysis of three-dimensional supersonic and subsonic jet mixing problems

Three-dimensional jet mixing problems are addressed by means of two parabolized Navier-Stokes models. The first of these analyzes supersonic, overexpanded or underexpanded nonaxisymmetric jets, and yields results that exhibit complex, three-dimensional interactions. The second model uses the same numerical framework as the first, and analyzes rectangular jets by means of a pressure-split formulation. Square and rectangular mixing jet problems that highlight this model's capabilities and exhibit the distortion of the nearfield jet contours associated with the streamwise vortices generated by two corner regions are presented.

Dash, S. M.↗

NASA NTRS1984

A numerical study of the two- and three-dimensional unsteady Navier-Stokes equations in velocity-vorticity variables using compact difference schemes

A compact finite-difference approximation to the unsteady Navier-Stokes equations in velocity-vorticity variables is used to numerically simulate a number of flows. These include two-dimensional laminar flow of a vortex evolving over a flat plate with an embedded cavity, the unsteady flow over an elliptic cylinder, and aspects of the transient dynamics of the flow over a rearward facing step. The methodology required to extend the two-dimensional formulation to three-dimensions is presented.

Gatski, T. B.↗

NASA NTRS1984

Intensified silicon photodiode array detector linearity Application to coherent anti-Stokes Raman spectroscopy

The linearity of an intensified silicon photodiode array multichannel detector is studied with coherent anti-Stokes Raman and other similar signals. Studies with diffuse and focused (spherically and cylindrically) signals resolved apparent saturation problems which limit the dynamic range of the detector. In addition, it has been shown that there is no short-range wavelength (473-532-nm) dependence on this saturation. Theoretical explanations for these phenomena are also included.

Antcliff, R. R.↗

NASA NTRS1984

Evaluation of a velocity-split solution of the Navier-Stokes equations for fighter forebodies

A velocity-splitting method of solving the three-dimensional Navier-Stokes equations, originally designed for afterbody flows, is examined for its applicability for predicting fighter forebody flows. Results from the AFTEND Code are compared with wind tunnel data for two fighter configurations at a Mach number of 0.9 and angles-of-attack from 0 deg to 20 deg. Results compare well with data, and in areas where data do not exist, the viscous AFTEND results show realistic effects of viscosity compared to inviscid predictions. The inviscid results themselves are in general superior to results obtained from a small-disturbance transonic potential code.

Yaros, S. F.↗

NASA NTRS1984

A second-order accurate parabolized Navier-Stokes algorithm for internal flows

A parabolized implicit Navier-Stokes algorithm which is of second-order accuracy in both the cross flow and marching directions is presented. The algorithm is used to analyze three model supersonic flow problems (the flow over a 10-degree edge). The results are found to be in good agreement with the results of other techniques available in the literature.

Chitsomboon, T.↗

NASA NTRS1984

A Navier-Stokes calculation of the airfoil dynamic stall process

A time dependent Navier-Stokes calculation procedure has been applied to the problem of an NACA 0012 airfoil oscillating in pitch in a low Mach number, high Reynolds number environment. The calculated results show many of the known physical features, including sudden suction surface separation, vortices shed at the leading and trailing edges and the return to attached flow at low incidences. Both the lift and moment coefficient curves show the expected features and the calculated wall pressure coefficients show strong correspondence to measured data.

Shamroth, S. J.↗

NASA NTRS1984

SSME thrust chamber simulation using Navier-Stokes equations

The capability of the PHOENICS fluid dynamics code in predicting two-dimensional, compressible, and reacting flow in the combustion chamber and nozzle of the space shuttle main engine (SSME) was evaluated. A non-orthogonal body fitted coordinate system was used to represent the nozzle geometry. The Navier-Stokes equations were solved for the entire nozzle with a turbulence model. The wall boundary conditions were calculated based on the wall functions which account for pressure gradients. Results of the demonstration test case reveal all expected features of the transonic nozzle flows. Of particular interest are the locations of normal and barrel shocks, and regions of highest temperature gradients. Calculated performance (global) parameters such as thrust chamber flow rate, thrust, and specific impulse are also in good agreement with available data.

Przekwas, A. J.↗