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At least 163 records · Page 9

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NASA NTRS1983

Viscous real gas flowfields about three dimensional configurations

Laminar, real gas hypersonic flowfields over a three dimensional configuration are computed using an unsteady, factored implicit scheme. Local chemical and thermodynamic properties are evaluated by an equilibrium composition method. Transport properties are obtained from individual species properties and application of a mixture rule. Numerical solutions are presented for an ideal gas and equilibrium air for free-stream Mach numbers of 13 and 15 and at various angles of attack. The effect of real gas is to decrease the shock-layer thickness resulting from decreased shock-layer temperatures and corresponding increased density. The combined effects of viscosity and real gas are to increase the subsonic layer near the wall.

Balakrishnan, A.↗

NASA NTRS1983

An experimental and numerical investigation of the impingement of an oblique shock wave on a body of revolution

Attention is given to the experimental study and numerical simulation of the impingement of oblique shock wave on a cylinder, in order both to document the complex three-dimensional shock wave and boundary layer interaction occurring in practical problems (such as stores carriage interference in a supersonic tactical aircraft) and to conduct a critical comparison of experimental measurements and numerical computations for such complex flows. A thin layer approximation of the Navier-Stokes equations was solved by means of a mixed explicit-implicit scheme. Experimental measurements reveal a highly complex flow field with two distinct adjacent separation zones, regions of high cross flow, and multiply reflected shocks and expansion fans.

Brosh, A.↗

NASA NTRS1983

Three-dimensional viscous-flow computations using a directionally hybrid implicit-explicit procedure

A new, directionally dependent, hybrid numerical algorithm for solving the unsteady, three-dimensional Navier-Stokes equations has been developed and used to compute the viscous supersonic flow over complex configurations, which may generate local regions of embedded subsonic or streamwise separated flows or both. The new hybrid implicit-explicit algorithm is derived from the more general implicit Beam-Warming algorithm and is particularly suitable for viscous computations in which the grid spacing in the direction outward from the body is considerably smaller than the spacing in the other two directions. Numerical results obtained from both the hybrid and implicit schemes are presented and compared on the basis of numerical stability, convergence history, and computer and core memory requirements.

Rizk, Y. M.↗

NASA NTRS1983

A time-split finite-volume algorithm for three-dimensional flow-field simulation

A general finite-volume algorithm is developed for solving three-dimensional, time-dependent, compressible Navier-Stokes equations for high Reynolds number flows over an arbitrary geometry. This algorithm adapts MacCormack's (1982) explicit-implicit scheme to a time-split, three-dimensional finite-volume concept in a general coordinate system. It is shown that the thin-layer approximation in all three spatial directions significantly reduces the evaluation of viscous terms and allows the algorithm to solve more complicated geometries with all boundaries in two or all three directions. The calculated results using this method are found to be in good agreement with the experimental measurements of a blunt-fin induced shock wave and boundary-layer interaction problems. Observations of the existence of peak pressure, primary horseshoe and secondary vortices, and reversed supersonic zones show that computational fluid dynamics can effectively supplement the wind tunnel tests for aerodynamic design as well as for understanding basic fluid dynamics.

Hung, C. M.↗

NASA NTRS1984

Multiple steady states for characteristic initial value problems

The time dependent, isentropic, quasi-one-dimensional equations of gas dynamics and other model equations are considered under the constraint of characteristic boundary conditions. Analysis of the time evolution shows how different initial data may lead to different steady states and how seemingly anamolous behavior of the solution may be resolved. Numerical experimentation using time consistent explicit algorithms verifies the conclusions of the analysis. The use of implicit schemes with very large time steps leads to erroneous results.

Salas, M. D.↗

NASA NTRS1986

Application of CFD to aerothermal heating problems

Numerical solutions of the compressible Navier-Stokes equations by an alternating direction implicit scheme, applied to two experimental investigations are presented. The first is cooling by injection of a gas jet through the nose of an ogive-cone, and the second is the aerothermal environment in the gap formed by the wing and elevon section of a test model of the space shuttle. The simulations demonstrate that accurate pressure calculations are easily obtained on a coarse grid, while convergence is obtained after the residual reduces by four orders of magnitude. Accurate heating rates, however, require a fine grid solution, with convergence requiring at least a reduction of six orders of magnitude in the residual. The effect of artificial dissipation on numerical results is also assessed.

Macaraeg, M. G.↗

NASA NTRS1986

Viscous compressible flow direct and inverse computation and illustrations

An algorithm for laminar and turbulent viscous compressible two dimensional flows is presented. For the application of precise boundary conditions over an arbitrary body surface, a body-fitted coordinate system is used in the physical plane. A thin-layer approximation of tne Navier-Stokes equations is introduced to keep the viscous terms relatively simple. The flow field computation is performed in the transformed plane. A factorized, implicit scheme is used to facilitate the computation. Sample calculations, for Couette flow, developing pipe flow, an isolated airflow, two dimensional compressor cascade flow, and segmental compressor blade design are presented. To a certain extent, the effective use of the direct solver depends on the user's skill in setting up the gridwork, the time step size and the choice of the artificial viscosity. The design feature of the algorithm, an iterative scheme to correct geometry for a specified surface pressure distribution, works well for subsonic flows. A more elaborate correction scheme is required in treating transonic flows where local shock waves may be involved.

Yang, T. T.↗

NASA NTRS1986

Application of CFD to aerothermal heating problems

Numerical solutions of the compressible Navier-Stokes equations by an Alternating Direction Implicit scheme, applied to two experimental investigations at NASA Langley Research Center are presented. The first is cooling by injection of a gas jet through the nose of an ogive-cone, and the second is the aerothermal environment in the gap formed by the wing and elevon section of a test model of the Space Shuttle. The simulations demonstrate that accurate pressure calculations are easily obtained on a coarse grid, witih convergence being obtained after the residual reduces by four orders of magnitude. However, accurate heating rates require a fine grid solution, with convergence requiring at least a reduction of six orders of magnitude in the residual. The effect of artificial dissipation on numerical results is also assessed.

Macaraeg, M. G.↗

NASA NTRS1985

A simple, accurate and efficient algorithm for unsteady transonic flow

The derivation of an algorithm for computing an airfoil's response to small unsteady perturbations is described. The analysis of the far-field boundary conditions for the flow field, and the application of the time-linearization technique to develop an accurate description of the flow field are discussed. The treatment of moving shock waves is examined. The alternating direction implicit scheme of Ballhaus and Steger (1975) is utilized for the discretization of the governing equations and boundary conditions. Numerical examples demonstrating the applicability of the time-linearization method to determine the correlation between airfoil and pressure distribution are provided. The effect of wind tunnel walls on unsteady transonic testing is studied.

Fung, K.-Y.↗

NASA NTRS1985

Transonic flow analysis for rotors. Part 2: Three-dimensional, unsteady, full-potential calculation

A numerical method is presented for calculating the three-dimensional unsteady, transonic flow past a helicopter rotor blade of arbitrary geometry. The method solves the full-potential equations in a blade-fixed frame of reference by a time-marching implicit scheme. At the far-field, a set of first-order radiation conditions is imposed, thus minimizing the reflection of outgoing wavelets from computational boundaries. Computed results are presented to highlight radial flow effects in three dimensions, to compare surface pressure distributions to quasi-steady predictions, and to predict the flow field on a swept-tip blade. The results agree well with experimental data for both straight- and swept-tip blade geometries.

Chang, I. C.↗

NASA NTRS1984

Calculation of two- and three-dimensional transonic cascade flow field using the Navier-Stokes equations

A Navier-Stokes analysis employing the time-dependent Linearized Block Implicit scheme (LBI) was applied to two-dimensional and three-dimensional transonic turbulent cascade flows. In general, the geometrical configuration of the turbine blade impacts both the grid construction procedure and the implementation of the numerical algorithm. Since modern turbine blades of interest are characterized by very blunt leading edges, rounded trailing edges and high stacking angles, a robust grid construction procedure is required that can accommodate the severe body shape while resolving regions of large flow gradients. A constructive O-type grid generation technique, suitable for cascades with rounded trailing edges, was developed and used to construct the C3X turbine cascade coordinate grid. Two-dimensional calculations were performed employing the Navier-Stokes procedure for the C3X turbine cascade, and the predicted pressure coefficients and heat transfer rates were compared with the experimental data. Three-dimensional Navier-Stokes calculations were also performed.

Weinberg, B. C.↗

NASA NTRS1986

A locally implicit method for fluid flow problems

The fluid flow inside the space shuttle main engine (SSME) traverses through a complex geometrical configuration. The flow is compressible, viscous, and turbulent with pockets of separated regions. Several computer codes are being developed to solve three dimensional Navier-Stokes equations with different turbulence models for analyzing the SSME internal flow. The locally implicit scheme is a computationally efficient scheme which converges rapidly in multi-grid modes for elliptic problems. It has the promise of providing a rapidly converging algorithm for steady-state viscous flow problems.

Reddy, K. C.↗

NASA NTRS1987

Three-dimensional unsteady Euler solutions for propfans and counter-rotating propfans in transonic flow

An Euler code designed for computing the unsteady, three-dimensional, transonic flow about single-rotating and counter-rotating propfans using dynamic blocked-grids is presented. The algorithm is a finite volume, flux-split, upwind, implicit scheme and solves the equations which have been written in a time-dependent curvilinear coordinate system. Relative motion of the blades for counter-rotating configurations is handled by requiring that grid lines be aligned after each discrete rotation of fore and aft rotor grid blocks. The method by which information is passed across block interfaces, as well as how downstream characteristic outflow boundary conditions which enforce simple radial equilibrium are implemented, is discussed. Comparisons of computed flow-field parameters and propfan performance with experimental data indicate good overall agreement between predictions and measurements.

Whitfield, D. L.↗

NASA NTRS1987

Numerical analysis of discrete fractional integrodifferential structural dampers

This paper develops solution algorithms enabling the handling of the dynamic response of nonlinear structures contained discretely attached dampers modeled by fractional integrodifferential operators of the Grunwald-Liouville-Riemann type. The development consists of two levels of formulation, namely: (1) numerical approximations of fractional operators and, (2) the establishment of global level implicit schemes enabling the solution to nonlinear structural formulations. To generalize the overall results, error estimates are derived for the fractional operator approximation algorithm. These enable an ongoing optimization of solution efficiency for a given error tolerance. To benchmark the scheme, the results of several numerical experiments are presented. These illustrate the numerical characteristics of the overall formulation.

Padovan, Joseph↗

NASA NTRS1988

Primitive numerical simulation of circular Couette flow - Carrousel wind tunnel nonturbulent solutions

The azimuthal-invariant, three-dimensional cylindrical, incompressible Navier-Stokes equations are solved to steady state for a finite-length, physically realistic model. The numerical method relies on an alternating-direction implicit scheme that is formally second-order accurate in space and first-order accurate in time. The equations are linearized and uncoupled by evaluating variable coefficients at the previous time iteration. Wall grid clustering is provided by a Roberts transformation in radial and axial directions. A vorticity-velocity formulation is found to be preferable to a vorticity-streamfunction approach. Subject to no-slip, Dirichlet boundary conditions, except for the inner cylinder rotation velocity (impulsive start-up) and zero-flow initial conditions, nonturbulent solutions are obtained for sub- and supercritical Reynolds numbers of 100 to 400 for a finite geometry where R(outer)/R(inner) = 1.5, H/R(inner) = 0.73, and H/Delta-R = 1.5. An axially-stretched model solution is shown to asymptotically approach the one-dimensional analytic Couette solution at the cylinder midheight. Flowfield change from laminar to Taylor-vortex flow is discussed as a function of Reynolds number. Three-dimensional velocities, vorticity, and streamfunction are presented via two-dimensional graphs and three-dimensional surface and contour plots.

Hasiuk, Jan↗

NASA NTRS1988

Interactive grid generation for turbomachinery flow field simulations

The control point form of algebraic grid generation presented provides the means that are needed to generate well structured grids for turbomachinery flow simulations. It uses a sparse collection of control points distributed over the flow domain. The shape and position of coordinate curves can be adjusted from these control points while the grid conforms precisely to all boundaries. An interactive program called TURBO, which uses the control point form, is being developed. Basic features of the code are discussed and sample grids are presented. A finite volume LU implicit scheme is used to simulate flow in a turbine cascade on the grid generated by the program.

Choo, Yung K.↗

NASA NTRS1989

Full potential unsteady computations including aeroelastic effects

A unified formulation is presented based on the full potential framework coupled with an appropriate structural model to compute steady and unsteady flows over rigid and flexible configurations across the Mach number range. The unsteady form of the full potential equation in conservation form is solved using an implicit scheme maintaining time accuracy through internal Newton iterations. A flux biasing procedure based on the unsteady sonic reference conditions is implemented to compute hyperbolic regions with moving sonic and shock surfaces. The wake behind a trailing edge is modeled using a mathematical cut across which the pressure is satisfied to be continuous by solving an appropriate vorticity convection equation. An aeroelastic model based on the generalized modal deflection approach interacts with the nonlinear aerodynamics and includes both static as well as dynamic structural analyses capability. Results are presented for rigid and flexible configurations at different Mach numbers ranging from subsonic to supersonic conditions. The dynamic response of a flexible wing below and above its flutter point is demonstrated.

Shankar, Vijaya↗

NASA NTRS1989

Compressible studies on dynamic stall

The purpose of this work is to investigate the effects of compressibility on the dynamic stall phenomenon by numerical simulation of the unsteady flow. The full two-dimensional unsteady compressible Navier-Stokes equations are solved for flows over oscillating airfoils and airfoils pitching rapidly to high angles of attack. The free-stream speeds vary from low subsonic with mild compressibility effects, to moderate subsonic where strong compressibility effects appear close to the leading edge at high angles of attack. An Alternating Direction Implicit scheme is implemented for the numerical solution with the viscous terms retained in both directions. The numerical results are compared with available experimental data for a Sikorsky airfoil for compressible high Reynolds number flows. There is good agreement between the computed and measured unsteady lift and pitching moment coefficient time histories. The computed high-speed subsonic unsteady results give a good picture of the entire flow field, and the dynamic stall progression in the compressible flow regime. It was observed that compressibility effects are more severe close to the leading edge at moderate angles of attack, and that the dynamic stall vortex appears at lower angles of attack as the free-stream speed increases.

Ekaterinaris, J. A.↗