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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Application of unstructured grid methods to steady and unsteady aerodynamic problems

The purpose is to describe the development of unstructured grid methods which have several advantages when compared to methods which make use of structured grids. Unstructured grids, for example, easily allow the treatment of complex geometries, allow for general mesh movement for realistic motions and structural deformations of complete aircraft configurations which is important for aeroelastic analysis, and enable adaptive mesh refinement to more accurately resolve the physics of the flow. Steady Euler calculations for a supersonic fighter configuration to demonstrate the complex geometry capability; unsteady Euler calculations for the supersonic fighter undergoing harmonic oscillations in a complete-vehicle bending mode to demonstrate the general mesh movement capability; and vortex-dominated conical-flow calculations for highly-swept delta wings to demonstrate the adaptive mesh refinement capability are discussed. The basic solution algorithm is a multi-stage Runge-Kutta time-stepping scheme with a finite-volume spatial discretization based on an unstructured grid of triangles in 2D or tetrahedra in 3D. The moving mesh capability is a general procedure which models each edge of each triangle (2D) or tetrahedra (3D) with a spring. The resulting static equilibrium equations which result from a summation of forces are then used to move the mesh to allow it to continuously conform to the instantaneous position or shape of the aircraft. The adaptive mesh refinement procedure enriches the unstructured mesh locally to more accurately resolve the vortical flow features. These capabilities are described in detail along with representative results which demonstrate several advantages of unstructured grid methods. The applicability of the unstructured grid methodology to steady and unsteady aerodynamic problems and directions for future work are discussed.

Batina, John T.↗
NASA NTRS1989

Flux splitting algorithms for two-dimensional viscous flows with finite-rate chemistry

The Roe flux difference splitting method was extended to treat 2-D viscous flows with nonequilibrium chemistry. The derivations have avoided unnecessary assumptions or approximations. For spatial discretization, the second-order Roe upwind differencing is used for the convective terms and central differencing for the viscous terms. An upwind-based TVD scheme is applied to eliminate oscillations and obtain a sharp representation of discontinuities. A two-state Runge-Kutta method is used to time integrate the discretized Navier-Stokes and species transport equations for the asymptotic steady solutions. The present method is then applied to two types of flows: the shock wave/boundary layer interaction problems and the jet in cross flows.

Shuen, Jian-Shun↗
NASA NTRS1990

Conical Euler simulation and active suppression of delta wing rocking motion

A conical Euler code was developed to study unsteady vortex-dominated flows about rolling highly-swept delta wings, undergoing either forced or free-to-roll motions including active roll suppression. The flow solver of the code involves a multistage Runge-Kutta time-stepping scheme which uses a finite volume spatial discretization of the Euler equations on an unstructured grid of triangles. The code allows for the additional analysis of the free-to-roll case, by including the rigid-body equation of motion for its simultaneous time integration with the governing flow equations. Results are presented for a 75 deg swept sharp leading edge delta wing at a freestream Mach number of 1.2 and at alpha equal to 10 and 30 deg angle of attack. A forced harmonic analysis indicates that the rolling moment coefficient provides: (1) a positive damping at the lower angle of attack equal to 10 deg, which is verified in a free-to-roll calculation; (2) a negative damping at the higher angle of attack equal to 30 deg at the small roll amplitudes. A free-to-roll calculation for the latter case produces an initially divergent response, but as the amplitude of motion grows with time, the response transitions to a wing-rock type of limit cycle oscillation. The wing rocking motion may be actively suppressed, however, through the use of a rate-feedback control law and antisymmetrically deflected leading edge flaps. The descriptions of the conical Euler flow solver and the free-to-roll analysis are presented. Results are also presented which give insight into the flow physics associated with unsteady vortical flows about forced and free-to-roll delta wings, including the active roll suppression of this wing-rock phenomenon.

Lee, Elizabeth M.↗
NASA NTRS1991

Rotating bio-reactor cell culture apparatus

A bioreactor system is described in which a tubular housing contains an internal circularly disposed set of blade members and a central tubular filter all mounted for rotation about a common horizontal axis and each having independent rotational support and rotational drive mechanisms. The housing, blade members and filter preferably are driven at a constant slow speed for placing a fluid culture medium with discrete microbeads and cell cultures in a discrete spatial suspension in the housing. Replacement fluid medium is symmetrically input and fluid medium is symmetrically output from the housing where the input and the output are part of a loop providing a constant or intermittent flow of fluid medium in a closed loop.

Schwarz, Ray P.↗
NASA NTRS1990

Prediction of the Thrust Performance and the Flowfield of Liquid Rocket Engines

In an effort to improve the current solutions in the design and analysis of liquid propulsive engines, a computational fluid dynamics (CFD) model capable of calculating the reacting flows from the combustion chamber, through the nozzle to the external plume, was developed. The Space Shuttle Main Engine (SSME) fired at sea level, was investigated as a sample case. The CFD model, FDNS, is a pressure based, non-staggered grid, viscous/inviscid, ideal gas/real gas, reactive code. An adaptive upwinding differencing scheme is employed for the spatial discretization. The upwind scheme is based on fourth order central differencing with fourth order damping for smooth regions, and second order central differencing with second order damping for shock capturing. It is equipped with a CHMQGM equilibrium chemistry algorithm and a PARASOL finite rate chemistry algorithm using the point implicit method. The computed flow results and performance compared well with those of other standard codes and engine hot fire test data. In addition, the transient nozzle flowfield calculation was also performed to demonstrate the ability of FDNS in capturing the flow separation during the startup process.

Wang, T.-S.↗
NASA NTRS1991

Unstructured-grid methods development: Lessons le arned

The development is summarized of unstructured grid methods for the solution of the equations of fluid flow and some of the lessons learned are shared. The 3-D Euler equations are solved, including spatial discretizations, temporal discretizations, and boundary conditions. An example calculation with an upwind implicit method using a CFL (Courant Friedricks Lewy) number of infinity is presented for the Boeing 747 aircraft. The results obtained in less than one hour of CPU time on a Cray-2 computer, thus demonstrating the speed and robustness of the present capability.

Batina, John T.↗
NASA NTRS1991

A fast upwind solver for the Euler equations on three-dimensional unstructured meshes

An upwind scheme is presented for solving the three-dimensional Euler equations on unstructured tetrahedral meshes. Spatial discretization is accomplished by a cell-centered finite-volume formulation using flux-difference splitting. Higher-order differences are formed by a novel cell reconstruction process which results in computational times per cell comparable to those of structured codes. The approach yields highly resolved solutions in regions of smooth flow while avoiding oscillations across shocks without explicit limiting. Solutions are advanced in time by a 3-stage Runge-Kutta time-stepping scheme with convergence accelerated to steady state by local time stepping and implicit residual smoothing. Solutions are presented for a range of configurations in the transonic speed regime to demonstrate code accuracy, speed, and robustness. The results include an assessment of grid sensitivity and convergence acceleration by mesh sequencing.

Frink, Neal T.↗
NASA NTRS1991

Conical Euler methodology for unsteady vortical flows about rolling delta wings

A conical Euler methodology was developed to study unsteady vortex-dominated flows about rolling highly swept delta wings undergoing either forced or free-to-roll motions. The flow solver of the code involves a multistage Runge-Kutta time-stepping scheme which uses a finite-volume spatial discretization of the Euler equations on an unstructured grid of triangles. Results are presented for a 75-deg swept sharp-leading-edge delta wing at a freestream Mach number of 1.2 and at alpha = 10, 20, and 30 deg. At the 10 and 20 deg, forced harmonic analyses indicate that the rolling moment coefficients provide a positive damping which is verified by free-to-roll calculations. In contrast, at 30 deg, a forced harmonic analysis indicates that the rolling moment coefficient provides a negative damping at the small roll amplitudes. A free-to-roll calculation for this case produces an initially divergent response, but as the amplitude of motion grows with time, the response transitions to a wing-rock type of limit cycle oscillation.

Lee, Elizabeth M.↗
NASA NTRS1991

Numerical analysis of a nuclear fuel element for nuclear thermal propulsion

A computational fluid dynamics model with porosity and permeability formulations in the transport equations has been developed to study the concept of nuclear thermal propulsion through the analysis of a pulsed irradiation of a particle bed element (PIPE). The numerical model is a time-accurate pressure-based formulation. An adaptive upwind scheme is employed for spatial discretization. The upwind scheme is based on second- and fourth-order central differencing with adaptive artificial dissipation. Multiblocked porosity regions have been formulated to model the cold frit, particle bed, and hot frit. Multiblocked permeability regions have been formulated to describe the flow shaping effect from the thickness-varying cold frit. Computational results for several zero-power density PIPEs and an elevated-particle-temperature PIPE are presented. The implications of the computational results are discussed.

Wang, Ten-See↗
NASA NTRS1992

Mathematical Modeling Of The Terrain Around A Robot

In conceptual system for modeling of terrain around autonomous mobile robot, representation of terrain used for control separated from representation provided by sensors. Concept takes motion-planning system out from under constraints imposed by discrete spatial intervals of square terrain grid(s). Separation allows sensing and motion-controlling systems to operate asynchronously; facilitating integration of new map and sensor data into planning of motions.

Slack, Marc G.↗
NASA NTRS1991

Progress with multigrid schemes for hypersonic flow problems

Several multigrid schemes are considered for the numerical computation of viscous hypersonic flows. For each scheme, the basic solution algorithm uses upwind spatial discretization with explicit multistage time stepping. Two level versions of the various multigrid algorithms are applied to the two dimensional advection equation, and Fourier analysis is used to determine their damping properties. The capabilities of the multigrid methods are assessed by solving three different hypersonic flow problems. Some new multigrid schemes based on semicoarsening strategies are shown to be quite effective in relieving the stiffness caused by the high aspect ratio cells required to resolve high Reynolds number flows. These schemes exhibit good convergence rates for Reynolds numbers up to 200 x 10(exp 6) and Mach numbers up to 25.

Radespiel, R.↗
NASA NTRS1991

A fast implicit upwind solution algorithm for three-dimensional unstructured dynamic meshes

A fast implicit upwind algorithm for the solution of the time-dependent Euler equations is presented for aerodynamic analysis involving unstructured dynamic meshes. The spatial discretization of the scheme is based on the upwind approach of Roe, referred to as flux-difference splitting (FDS). The FDS approach is naturally dissipative and captures shock waves and contact discontinuities sharply. The temporal discretization of the scheme involves an implicit time-integration using a two-sweep Gauss-Seidel relaxation procedure. The procedure is computationally efficient for either steady or unsteady flow problems. A detailed description is given of the implicit upwind solution algorithm along with results which assess the capability. The results are presented for the NACA 0012 airfoil and for the Boeing 747 aircraft. The 747 geometry includes the fuselage, wing, horizontal and vertical tails, under-wing pylons, and flow-through engine nacelles. Euler solutions for the 747 aircraft on an unstructured tetrahedral mesh containing approximately 100,000 cells were obtained to engineering accuracy in less than one hour CPU time on a Cray-2 computer.

Batina, John T.↗
NASA NTRS1992

Progress in unstructured-grid methods development for unsteady aerodynamic applications

The development of unstructured-grid methods for the solution of the equations of fluid flow and what was learned over the course of the research are summarized. The focus of the discussion is on the solution of the time-dependent Euler equations including spatial discretizations, temporal discretizations, and boundary conditions. An example calculation with an implicit upwind method using a CFL number of infinity is presented for the Boeing 747 aircraft. The results were obtained in less than one hour CPU time on a Cray-2 computer, thus, demonstrating the speed and robustness of the capability. Additional calculations for the ONERA M6 wing demonstrate the accuracy of the method through the good agreement between calculated results and experimental data for a standard transonic flow case.

Batina, John T.↗
NASA NTRS1992

Optimum design of ninety degree bends

An algorithm for the optimum design of an internal flow component to obtain the maximum pressure rise is presented. Maximum pressure rise in a duct with simultaneous turning and diffusion is shown to be related to the control of flow separation on the passage walls. Such a flow is usually associated with downstream conditions that are desirable in turbomachinery and propulsion applications to ensure low loss and stable performance. The algorithm requires the solution of an 'adjoint' problem in addition to the 'direct' equations governing the flow in a body, which in the present analysis are assumed to be the laminar Navier-Stokes equations. The theoretical framework and computational algorithms presented in this study are for the steady Navier-Stokes equations. A procedure is developed for the numerical solution of the adjoint equations. This procedure is coupled with a direct solver in a design iteration loop, that provides a new shape with a higher pressure rise. This procedure is first validated for the design of optimum plane diffusers in two-dimensional flow. The direct Navier-Stokes and the 'adjoint' equations are solved using a finite volume formulation for spatial discretization in an artificial compressibility framework. A simplified version of the above approach is then utilized to design ninety degree diffusing bends. Calculations were carried out for a mean radius ratio at inlet of 2.5 and Reynolds numbers varying from 100 to 500. While at this stage laminar flows is assumed, it is shown that a similar approach can be conceived for turbulent flows.

Modi, Vijay↗
NASA NTRS1992

Upwind scheme for solving the Euler equations on unstructured tetrahedral meshes

An upwind scheme is presented for solving the three-dimensional Euler equations on unstructured tetrahedral meshes. Spatial discretization is accomplished by a cell-centered finite-volume formulation using flux-difference splitting. Higher-order differences are formed by a multidimensional linear reconstruction process. The solution gradients required for the higher-order differenes are computed by a novel approach that yields highly resolved solutions in regions of smooth flow while avoiding oscillations across shocks without explicitly applying a limiter. Solutions are advanced in time by a three-stage Runge-Kutta time-stepping scheme with convergence accelerated to steady state by local time stepping and implicit residual smoothing. Transonic solutions are presented for two meshes around the ONERA M6 wing and demonstrate substantial accuracy and insensitivity to mesh size.

Frink, Neal T.↗
NASA NTRS1992

A fast implicit upwind solution algorithm for three-dimensional unstructured dynamic meshes

A fast implicit upwind algorithm for the solution of the time-dependent Euler equations is presented for aerodynamic analysis involving unstructured dynamic meshes. The spatial discretization of the scheme is based on the upwind approach of Roe, referred to as flux-difference splitting (FDS). The FDS approach is naturally dissipative and captures shock waves and contact discontinuities sharply. The temporal discretization of the scheme involves an implicit time-integration using a two-sweep Gauss-Seidel relaxation procedure. The procedure is computationally efficient for either steady or unsteady flow problems. A detailed description is given of the implicit upwind solution algorithm along with results which assess the capability. The results are presented for the NACA 0012 airfoil and for the Boeing 747 aircraft. The 747 geometry includes the fuselage, wing, horizontal and vertical tails, under-wing pylons, and flow-through engine nacelles. Euler solutions for the 747 aircraft on an unstructured tetrahedral mesh containing approximately 100,000 cells were obtained to engineering accuracy in less than one hour CPU time on a Cray-2 computer.

Batina, John T.↗
NASA NTRS1992

Numerical experiments on a new class of nonoscillatory schemes

Numerical experiments for the SONIC schemes on 2D inviscid, compressible, steady, and unsteady problems are presented. These schemes belong to a new class of uniformly second-order accurate nonoscillatory schemes introduced by Huynh, with the well known UNO2 scheme of Harten and Osher being the most 'diffusive' in this class. The SONIC schemes can also be considered as uniformly second order accurate extensions of the popular TVD schemes. For simplicity, a MUSCL approach for spatial discretization and a Runge-Kutta method for time integration are used. Test problems include steady oblique shock reflection and the well known unsteady double Mach reflection problem. Results confirm that the SONIC schemes are more accurate than their TVD counterparts.

Suresh, Ambady↗
NASA NTRS1992

Unsteady transonic Euler solutions using finite elements

A finite element solution of the unsteady Euler equations is presented and demonstrated for 2D airfoil configurations oscillating in transonic flows. Computations are performed by spatially discretizing the conservation equations using the Galerkin weighted residual method and then employing a multistage Runge-Kutta scheme to march forward in time. A mesh deformation scheme has been developed to efficiently move interior points in a smooth fashion as the airfoil undergoes rigid body pitch and plunge motion. Both steady and unsteady results are presented, and a comparison is made with solutions obtained using finite-volume techniques. The effects of using either a lumped or consistent mass matrix are presented; the finite element method provides an accurate solution for unsteady transonic flows about isolated airfoils.

Davis, Gary A.↗