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At least 145 records · Page 8

Computation of steady and unsteady vortex dominated flows

The unsteady Euler equations have been written in the conservation form for the relative motion in a rotating frame of reference. The resulting equations are solved by using a central-difference finite-volume scheme with four-stage Runge-Kutta time stepping. For steady flow problems, local time stepping is used and for unsteady flow problems, the minimum global time stepping is used. A three-dimensional fully vectorized computer program has been developed and applied to steady and unsteady maneuvering delta wing. The capability of the three-dimensional program has been demonstrated for a rigid sharp-edged delta wing undergoing uniform rolling in a conical flow and rolling oscillations in a locally conical flow.

Kandil, Osama A.↗

Numerical analysis of flow through scramjet engine inlets

A set of computer programs was developed to analyze flow through supersonic combustion ramjet (scramjet) inlets. These programs solve either the two or three dimensional Euler/Navier-Stokes equations in full conservation form by MacCormack's explicit or explicit-implicit method. An algebraic two-layer eddy viscosity model is used for turbulent flow calculations. The programs are operational in Control Data CYBER-200 series vector-processing computer system and were optimized to take maximum advantage of the vector processing capability of the system. Since their development, the programs were extensively verified and used to analyze a number of very complex inlet configurations. Results are presented from two-dimensional, quasi-three-dimensional, and three-dimensional analyses of the inlet flow field to illustrate the use of the program.

Kumar, Ajay↗

Numerical modeling of multidimensional flow in seals and bearings used in rotating machinery

The rotordynamic behavior of turbomachinery is critically dependent on fluid dynamic rotor forces developed by various types of seals and bearings. The occurrence of self-excited vibrations often depends on the rotor speed and load. Misalignment and rotor wobbling motion associated with differential clearance were often attributed to stability problems. In general, the rotative character of the flowfield is a complex three dimensional system with secondary flow patterns that significantly alter the average fluid circumferential velocity. A multidimensional, nonorthogonal, body-fitted-grid fluid flow model is presented that describes the fluid dynamic forces and the secondary flow pattern development in seals and bearings. Several numerical experiments were carried out to demonstrate the characteristics of this complex flowfield. Analyses were performed by solving a conservation form of the three dimensional Navier-Stokes equations transformed to those for a rotating observer and using the general-purpose computer code PHOENICS with the assumptions that the rotor orbit is circular and that static eccentricity is zero. These assumptions have enabled a precise steady-state analysis to be used. Fluid injection from ports near the seal or bearing center increased fluid-film direct dynamic stiffness and, in some cases, significantly increased quadrature dynamic stiffness. Injection angle and velocity could be used for active rotordynamic control; for example, injection, when compared with no injection, increased direct dynamic stiffness, which is an important factor for hydrostatic bearings.

Hendricks, R. C.↗

Evaluation of a research circulation control airfoil using Navier-Stokes methods

The compressible Reynolds time averaged Navier-Stokes equations were used to obtain solutions for flows about a two dimensional circulation control airfoil. The governing equations were written in conservation form for a body-fitted coordinate system and solved using an Alternating Direction Implicit (ADI) procedure. A modified algebraic eddy viscosity model was used to define the turbulent characteristics of the flow, including the wall jet flow over the Coanda surface at the trailing edge. Numerical results are compared to experimental data obtained for a research circulation control airfoil geometry. Excellent agreement with the experimental results was obtained.

Shrewsbury, George D.↗

Numerical and analytical study of fluid dynamic forces in seals and bearings

A numerical model based on a transformed, conservative form of the three dimensional Navier-Stokes equation and an analytical model based on lumped fluid parameters are presented and compared with studies of modeled rotor bearing seal systems. The rotor destabilizing factors are related to the rotative character of the flow field. It is shown that these destabilizing factors can be reduced through a decrease in the fluid average circumferential velocity. However, the rotative character of the flow field is a complex three dimensional system with bifurcated secondary flow patterns that significantly alter the fluid circumferential velocity. By transforming the Navier-Stokes equations to those for a rotating observer and using the numerical code PHOENICS-84 with a nonorthogonal body fitted grid, several numerical experiments were carried out to demonstrate the character of this complex flow field. In general, fluid injection and/or preswirl of the flow field opposing the shaft rotation significantly intensified these secondary recirculation zones and thus reduced the average circumferential velocity; injection or preswirl in the direction of rotation significantly weakened these zones.

Tam, L. T.↗

Application of a nonisentropic full potential method to AGARD standard airfoils

An entropy-correction method for the unsteady full potential equation is presented. The unsteady potential equation is modified to model the entropy jumps across shock waves. The conservative form of the modified equation is solved in generalized coordinates using an implicit, approximate factorization method. A flux-biasing differencing method, which generates the proper amounts of artificial viscosity in supersonic regions, is used to discretize the flow equations in space. Calculated results are presented for the NLR 7301, NACA 0012, and NACA 64A010A airfoils. Comparisons of the present method and solutions of the Euler equations are presented for the NLR 7301 airfoil, and comparisons of the present method and experimental data are presented for all three airfoils. The comparisons show that the present method more accurately models solutions of the Euler equations and experiment than does the isentropic potential formulation. In addition, it is shown that modeling shock-generated entropy extends the range of validity of the full potential method.

Whitlow, Woodrow, Jr.↗

Numerical simulation of scramjet inlet flow fields

A computer program was developed to analyze supersonic combustion ramjet (scramjet) inlet flow fields. The program solves the three-dimensional Euler or Reynolds averaged Navier-Stokes equations in full conservation form by either the fully explicit or explicit-implicit, predictor-corrector method of MacCormack. Turbulence is modeled by an algebraic eddy-viscosity model. The analysis allows inclusion of end effects which can significantly affect the inlet flow field. Detailed laminar and turbulent flow results are presented for a symmetric-wedge corner, and comparisons are made with the available experimental results to allow assessment of the program. Results are then presented for two inlet configurations for which experimental results exist at the NASA Langley Research Center.

Kumar, Ajay↗

Application of unsteady aerodynamic methods for transonic aeroelastic analysis

Aerodynamic methods for aeroelastic analysis are applied to various flow problems. These methods include those that solve the three dimensional transonic small disturbance (TSD) potential equation, the two dimensional (2-D) full potential (FP) equation, and the 2-D thin layer Navier-Stokes equations. Flutter analysis performed using TSD aerodynamics show that such methods can be used to analyze some aeroelastic phenomena. For thicker bodies and larger amplitude motions, a nonisentropic FP method is presented. The unsteady FP equation is modified to model the entropy jumps across shock waves. The conservative form of the modified equation is solved in generalized coordinates using an implicit, approximate factorization method. Pressures calculated on the NLR 7301 and NACA 64A010A airfoils using the nonisentropic FP method are presented. It is shown that modeling shock generated entropy extends the range of validity of the FP method. A Navier-Stokes code is correlated with pressures measured on a supercritical airfoil at transonic speeds. When corrections are made for wind tunnel wall effects, the calculations correlate well with the measured data.

Whitlow, Woodrow, Jr.↗

Application of a nonisentropic full potential method to AGARD standard airfoils

An entropy-correction method for the unsteady full potential equation is presented. The unsteady potential equation is modified to model the entropy jumps across shock waves. The conservative form of the modified equation is solved in generalized coordinates using an implicit, approximate factorization method. A flux-biasing differencing method, which generates the proper amounts of artificial viscosity in supersonic regions, is used to discretize the flow equations in space. Calculated results are presented for the NLR 7301, NACA 0012, and NACA 64A010A airfoils. Comparisons of the present method and solutions of the Euler equations are presented for the NLR 7301 airfoil, and comparisons of the present method and experimental data are presented for all three airfoils. The comparisons show that the present method more accurately models solutions of the Euler equations and experiment than does the isentropic potential formulation. In addition, it is shown that modeling shock-generated entropy extends the range of validity of the full potential method.

Whitlow, Woodrow, Jr.↗

Calculation of external-internal flow fields for mixed-compression inlets

Supersonic inlet flows with mixed external-internal compressions were computed using a combined implicit-explicit (Beam-Warming-Steger/MacCormack) method for solving the three-dimensional unsteady, compressible Navier-Stokes equations in conservation form. Numerical calculations were made of various flows related to such inlet operations as the shock-wave intersections, subsonic spillage around the cowl lip, and inlet started versus unstarted conditions. Some of the computed results were compared with wind tunnel data.

Chyu, W. J.↗

Incompressible and anelastic flow simulations on numerically generated grids

In the numerical simulation of incompressible and anelastic flows, it is necessary to solve an elliptic equation at each time step. When the boundaries of such flows are nonrectangular, it may be advantageous to solve the equations on a new, numerically generated coordinate grid, in which the property of orthogonality has been preserved. Flow equations in general curvilinear coordinates maintaining the conservative form are given for both anelastic models using the momentum equations, and for incompressible models, using the vorticity equation. The general problem of grid-generation in two dimensions is presented, and a quasi-conformal transformation technique is discussed in detail. Some examples of grids generated by this technique are exhibited. Three examples of the flow of a stratified fluid over obstacles are presented, in which the grid-generation permits some new results to be obtained.

Sharman, R. D.↗

Computation of steady and unsteady vortex-dominated flows with shock waves

The unsteady Euler equations have been derived in the conservation form for the flow relative motion with respect to a rotating frame of reference. The resulting equations are solved by using a central-difference finite-volume scheme with four-state Runge-Kutta time stepping. For steady flow applications local time stepping is used, and for unsteady applications the minimum global time stepping is used. A three-dimensional fully vectorized computer program has been developed and applied to steady and unsteady maneuvering delta wings. The capability of the three-dimensional program has been demonstrated for a rigid sharp-edged delta wing undergoing uniform rolling in a conical flow and rolling oscillations in a locally conical flow.

Kandil, Osama A.↗

Transonic Navier-Stokes solutions of three-dimensional afterbody flows

The performance of a three-dimensional Navier-Stokes solution technique in predicting the transonic flow past a nonaxisymmetric nozzle was investigated. The investigation was conducted at free-stream Mach numbers ranging from 0.60 to 0.94 and an angle of attack of 0 degrees. The numerical solution procedure employs the three-dimensional, unsteady, Reynolds-averaged Navier-Stokes equations written in strong conservation form, a thin layer assumption, and the Baldwin-Lomax turbulence model. The equations are solved by using the finite-volume principle in conjunction with an approximately factored upwind-biased numerical algorithm. In the numerical procedure, the jet exhaust is represented by a solid sting. Wind-tunnel data with the jet exhaust simulated by high pressure air were also obtained to compare with the numerical calculations.

Compton, William B., III↗

Transonic flow solutions using a composite velocity procedure for potential, Euler and RNS equations

Solutions for transonic viscous and inviscid flows using a composite velocity procedure are presented. The velocity components of the compressible flow equations are written in terms of a multiplicative composite consisting of a viscous or rotational velocity and an inviscid, irrotational, potential-like function. This provides for an efficient solution procedure that is locally representative of both asymptotic inviscid and boundary layer theories. A modified conservative form of the axial momentum equation that is required to obtain rotational solutions in the inviscid region is presented and a combined conservation/nonconservation form is applied for evaluation of the reduced Navier-Stokes (RNS), Euler and potential equations. A variety of results is presented and the effects of the approximations on entropy production, shock capturing, and viscous interaction are discussed.

Gordnier, R. E.↗

3-D composite velocity solutions for subsonic/transonic flows

A composite velocity procedure for the three-dimensional reduced Navier-Stokes equations is developed. In the spirit of matched asymptotic expansions, the velocity components are written as a combination multiplicative and additive composite of viscouslike velocities and pseudopotential or inviscid velocities. The solution procedure is then consistent with both asymptotic inviscid flow and boundary layer theory. For transonic flow cases, the Enquist-Osher flux biasing scheme developed for the full potential equation is used. A quasi-conservation form of the governing equations is used in the shock region to capture the correct rotational shock with the standard nonconservation form of the equations used in nonshock regions. The consistent coupled strongly implicit procedure coupled with a plane relaxation procedure is used to solve the discretized equations.

Gordnier, R. E.↗

A computational study on the interaction between a vortex and a shock wave

A computational study of two-dimensional shock vortex interaction is discussed in this paper. A second order upwind finite volume method is used to solve the Euler equations in conservation form. In this method, the shock wave is captured rather than fitted so that the cases where shock vortex interaction may cause secondary shocks can also be investigated. The effects of vortex strength on the computed flow and acoustic field generated by the interaction are qualitatively evaluated.

Meadows, Kristine R.↗

Numerical simulation of flow through a two-strut scramjet inlet

A three-dimensional, Reynolds-averaged Navier-Stokes code has been used to numerically analyze flow through a two-strut, supersonic combustion ramjet (scramjet) inlet configuration. It solves the governing equations in full conservation form using either a fully explicit or explicit-implicit method. An algebraic, two-layer eddy-viscosity model is used for turbulent flow calculations. The analysis allows inclusion of end effects that are caused by the aft placement of the cowl on the underside of the inlet. A special grid has been developed to accommodate the struts embedded in the inlet flowfield. Detailed numerical results are presented here for the two-strut configuration, and a comparison is made with the available experimental results.

Kumar, Ajay↗

Nonlinear filters for efficient shock computation

A new type of methods for the numerical approximation of hyperbolic conservation laws with discontinuous solution is introduced. The methods are based on standard finite difference schemes. The difference solution is processed with a nonlinear conservation form filter at every time level to eliminate spurious oscillations near shocks. It is proved that the filter can control the total variation of the solution and also produce sharp discrete shocks. The method is simpler and faster than many other high resolution schemes for shock calculations. Numerical examples in one and two space dimensions are presented.

Engquist, Bjorn↗