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At least 685 records · Page 38

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NASA NTRS1986

Motion and interaction of decaying trailing vortices in spanwise shear wind

A simulation is presented of the drift of trailing vortices in a cross-wind near the ground by an unsteady, two-dimensional, rotational flow field with a concentration of large vorticity in vortical spots (having a finite but small effective size and finite total strength). The problem is analyzed by a combination of the method of matched asymptotic analyses for the decay of the vortical spots and the Euler solution for the unsteady rotational flow. Using the method of averaging, a special numerical method is developed in which the grid size and time step depend only on the length and velocity scales of the background flow and are independent of the effective core size of a vortical spot. The core size can be much smaller than the grid size, whereas the peak velocity in the core is inversely propertional to the spot size. Numerical results are presented to demonstrate the strong interaction between the trajectories of the vortical spots and the change of the vorticity distribution in the background flow field.

Liu, C. H.↗

NASA NTRS1986

Pseudo-time algorithms for the Navier-Stokes equations

A pseudo-time method is introduced to integrate the compressible Navier-Stokes equations to a steady state. This method is a generalization of a method used by Crocco and also by Allen and Cheng. We show that for a simple heat equation that this is just a renormalization of the time. For a convection-diffusion equation the renormalization is dependent only on the viscous terms. We implement the method for the Navier-Stokes equations using a Runge-Kutta type algorithm. This permits the time step to be chosen based on the inviscid model only. We also discuss the use of residual smoothing when viscous terms are present.

Swanson, R. C.↗

NASA NTRS1985

Orbits: Computer simulation

In rotating machinery dynamics an orbit (Lissajous curve) represents the dynamic path of the shaft centerline motion during shaft rotation and resulting precession. The orbit can be observed with an oscilloscope connected to XY promixity probes. The orbits can also be simulated by a computer. The software for HP computer simulates orbits for two cases: (1) Symmetric orbit with four frequency components with different radial amplitudes and relative phase angles; and (2) Nonsymmetric orbit with two frequency components with two different vertical/horizontal amplitudes and two different relative phase angles. Each orbit carries a Keyphasor mark (one-per-turn reference). The frequencies, amplitudes, and phase angles, as well as number of time steps for orbit computation, have to be chosen and introduced to the computer by the user. The orbit graphs can be observed on the computer screen.

Muszynska, A.↗

NASA NTRS1986

Aerodynamics of Engine-Airframe Interaction

The report describes progress in research directed towards the efficient solution of the inviscid Euler and Reynolds-averaged Navier-Stokes equations for transonic flows through engine inlets, and past complete aircraft configurations, with emphasis on the flowfields in the vicinity of engine inlets. The research focusses upon the development of solution-adaptive grid procedures for these problems, and the development of multi-grid algorithms in conjunction with both, implicit and explicit time-stepping schemes for the solution of three-dimensional problems. The work includes further development of mesh systems suitable for inlet and wing-fuselage-inlet geometries using a variational approach. Work during this reporting period concentrated upon two-dimensional problems, and has been in two general areas: (1) the development of solution-adaptive procedures to cluster the grid cells in regions of high (truncation) error;and (2) the development of a multigrid scheme for solution of the two-dimensional Euler equations using a diagonalized alternating direction implicit (ADI) smoothing algorithm.

Caughey, D. A.↗

NASA NTRS1986

Thermodynamic evaluation of transonic compressor rotors using the finite volume approach

A method was developed which calculates two-dimensional, transonic, viscous flow in ducts. The finite volume, time marching formulation is used to obtain steady flow solutions of the Reynolds-averaged form of the Navier Stokes equations. The entire calculation is performed in the physical domain. The method is currently limited to the calculation of attached flows. The features of the current method can be summarized as follows. Control volumes are chosen so that smoothing of flow properties, typically required for stability, is now needed. Different time steps are used in the different governing equations to improve the convergence speed of the viscous calculations. A new pressure interpolation scheme is introduced which improves the shock capturing ability of the method. A multi-volume method for pressure changes in the boundary layer allows calculations which use very long and thin control volumes. A special discretization technique is also used to stabilize these calculations. A special formulation of the energy equation is used to provide improved transient behavior of solutions which use the full energy equation. The method is then compared with a wide variety of test cases. The freestream Mach numbers range from 0.075 to 2.8 in the calculations. Transonic viscous flow in a converging diverging nozzle is calculated with the method; the Mach number upstream of the shock is approximately 1.25. The agreement between the calculated and measured shock strength and total pressure losses is good. Essentially incompressible turbulent boundary layer flow in a adverse pressure gradient is calculated and the computed distribution of mean velocity and shear stress are in good agreement with the measurements. At the other end of the Mach number range, a flat plate turbulent boundary layer with a freestream Mach number of 2.8 is calculated using the full energy equation; the computed total temperature distribution and recovery factor agree well with the measurements when a variable Prandtl number is used through the boundary layer.

Nicholson, S.↗

NASA NTRS1986

Stability analysis of intermediate boundary conditions in approximate factorization schemes

The paper discusses the role of the intermediate boundary condition in the AF2 scheme used by Holst for simulation of the transonic full potential equation. It is shown that the treatment suggested by Holst led to a restriction on the time step and ways to overcome this restriction are suggested. The discussion is based on the theory developed by Gustafsson, Kreiss, and Sundstrom and also on the von Neumann method.

South, J. C., Jr.↗

NASA NTRS1986

Supercomputer implementation of finite element algorithms for high speed compressible flows

Prediction of compressible flow phenomena using the finite element method is of recent origin and considerable interest. Two shock capturing finite element formulations for high speed compressible flows are described. A Taylor-Galerkin formulation uses a Taylor series expansion in time coupled with a Galerkin weighted residual statement. The Taylor-Galerkin algorithms use explicit artificial dissipation, and the performance of three dissipation models are compared. A Petrov-Galerkin algorithm has as its basis the concepts of streamline upwinding. Vectorization strategies are developed to implement the finite element formulations on the NASA Langley VPS-32. The vectorization scheme results in finite element programs that use vectors of length of the order of the number of nodes or elements. The use of the vectorization procedure speeds up processing rates by over two orders of magnitude. The Taylor-Galerkin and Petrov-Galerkin algorithms are evaluated for 2D inviscid flows on criteria such as solution accuracy, shock resolution, computational speed and storage requirements. The convergence rates for both algorithms are enhanced by local time-stepping schemes. Extension of the vectorization procedure for predicting 2D viscous and 3D inviscid flows are demonstrated. Conclusions are drawn regarding the applicability of the finite element procedures for realistic problems that require hundreds of thousands of nodes.

Thornton, E. A.↗

NASA NTRS1986

Development of an explicit multigrid algorithm for quasi-three-dimensional viscous flows in turbomachinery

A rapid quasi three-dimensional analysis was developed for blade-to-blade flows in turbomachinery. The analysis solves the unsteady Euler or thin layer Navier-Stokes equations in a body-fitted coordinate system. It accounts for the effects of rotation, radius change, and stream-surface thickness. The Baldwin-Lomax eddy-viscosity model is used for turbulent flows. The equations which are solved b a two-stage Runge-Kutta scheme made efficient by use of vectorization, a variable time-step, and a flux-based multigrid scheme, are described. A stability analysis is presented for the two-stage. Results for a flat-plate model problem show the applicability of the method to axial, radial, and rotating geometries. Results for a centrifugal impeller and a radial diffuser show that the quasi three-dimensional viscous analysis can be a practical design tool.

Chima, R. V.↗

NASA NTRS1986

Euler solutions for high-speed flow about complex three-dimensional configurations

A numerical algorithm based on a finite-volume explicit scheme with Runge-Kutta time integration of the Euler equations is presented for calculating high-speed three-dimensional flow about complex aerospace configurations. The use of enhancing factors such as artificial dissipative terms, enthalpy damping and local time-stepping are described. An algebraic method for generating quasi-three-dimensional computational grids for realistic aerospace configurations is presented. Computed results for various three-dimensional bodies at different Mach numbers and angles of attack have been obtained using the methods for grid-generation and flow simulation. Comparison of computed and experimental data for an advanced tactical aircraft-like configuration is presented, and a reasonable agreement of the data is noticed.

Moitra, A.↗

NASA NTRS1986

A new approximate LU factorization scheme for the Reynolds-averaged Navier-Stokes equations

A new approximate LU factorization scheme is developed to solve the steady state Reynolds-averaged Navier-Stokes (NS) equations. Central differencing is used for both implicit and explicit operator and special care is taken to obtain well-conditioned factors on the implicit side. The scheme is then analyzed and optimized according to a simple linear analysis. It is unconditionally stable for the model hyperbolic equation in both two- and three-dimensions. However, the requirement for well-conditioned factors has essentially limited the effective time step the scheme can achieve. Supersonic and transonic three-dimensinal flows past a hemisphere cylinder are computed to demonstrate the convergence characteristics of the scheme. A good convergence rate is achieved for the inviscid case. Finally, an explicit eigenvector annihilation procedure is adopted successfully to remove the stiffness caused by the fine grid spacing for viscous flows.

Pan, D.↗

NASA NTRS1985

Calculations of two and three-dimensional transonic cascade flow fields using the Navier-Stokes equations

The multidimensional, ensemble-averaged, compressible, time-dependent Navier-Stokes equations have been used to study the turbulent flow field in two and three-dimensional turbine cascades. The viscous regions of the flow were resolved and non-slip boundary conditions were utilized on solid surfaces. The calculations were performed in a constructive 'O'-type grid which allows representation of the blade rounded trailing edge. Converged solutions were obtained in relatively few time steps (about 80-150) and comparisons for both surface pressure and heat transfer showed good agreement with data. The three-dimensional turbine cascade calculation showed many of the expected flow-field features.

Weinberg, B. C.↗

NASA NTRS1984

An attempt to extend the ATI technique to estimate convective rain volumes using satellite data

Digital satellite and radar data of a thunderstorm event that occurred on June 12, 1981 are examined. The processing of both data sets is described. Cumulative area versus count values, and threshold count values for IR and visible satellite data for 13 consecutive time steps are analyzed. The IR and visible satellite images are compared. The relation between radar reflectivity, temperature, and echo height is studied.

Doneaud, A. A.↗

NASA NTRS1985

A new approach to the free wake problem for hovering rotors

In the present approach to the hovering rotor free wake problem, an influence coefficient solution method is used to find that rotor wake solution which is steady in a reference frame that rotates with the blades; this scheme solves directly for the conditions of free wake equilibrium by a procedure that does not involve time-stepping and the associated use of numerical damping or special convergence methods. The solution method has been implemented in a hover wake computer program having a three-part wake model for the tip vortex. All three wake regions are represented by the new Basic Curved Vortex Elements. Sample hover calculations are presented for single blade and multiblade rotors.

Bliss, D. B.↗

NASA NTRS1986

An implicit flux-difference splitting scheme for three-dimensional, incompressible Navier-Stokes solutions to leading edge vortex flows

A new, implicit finite-difference scheme designed to solve the conservative, flux-difference split Navier-Stokes equations is used to compute incompressible vortex flows around delta wings. The completely vectorizable hybrid algorithm is constructed in delta form for steady state solutions independent of the time-step sizes. The scheme combines approximate factorization in crossflow planes with a symmetric planar Gauss-Seidel relaxation in the remaining spatial direction. The governing equations are solved in curvilinear, body-fitted coordinates for treating complex geometries. The computed flow field results are compared with other theoretical and experimental data.

Hartwich, P.-M.↗

NASA NTRS1986

Accurate solutions for transonic viscous flow over finite wings

An explicit multistage Runge-Kutta type time-stepping scheme is used for solving the three-dimensional, compressible, thin-layer Navier-Stokes equations. A finite-volume formulation is employed to facilitate treatment of complex grid topologies encountered in three-dimensional calculations. Convergence to steady state is expedited through usage of acceleration techniques. Further numerical efficiency is achieved through vectorization of the computer code. The accuracy of the overall scheme is evaluated by comparing the computed solutions with the experimental data for a finite wing under different test conditions in the transonic regime. A grid refinement study ir conducted to estimate the grid requirements for adequate resolution of salient features of such flows.

Vatsa, V. N.↗

NASA NTRS1986

Parametric effects of CFL number and artificial smoothing on numerical solutions using implicit approximate factorization algorithm

An implicit approximate factorization algorithm is employed to quantify the parametric effects of Courant number and artificial smoothing on numerical solutions of the unsteady 3-D Euler equations for a windmilling propeller (low speed) flow field. The results show that propeller global or performance chracteristics vary strongly with Courant number and artificial dissipation parameters, though the variation is such less severe at high Courant numbers. Candidate sets of Courant number and dissipation parameters could result in parameter-dependent solutions. Parameter-independent numerical solutions can be obtained if low values of the dissipation parameter-time step ratio are used in the computations. Furthermore, it is realized that too much artificial damping can degrade numerical stability. Finally, it is demonstrated that highly resolved meshes may, in some cases, delay convergence, thereby suggesting some optimum cell size for a given flow solution. It is suspected that improper boundary treatment may account for the cell size constraint.

Daso, E. O.↗

NASA NTRS1985

High-speed compressible flow and other advection-dominated problems of fluid dynamics

Finite element methods are described for modeling high speed compressible flows with strong advection, problems important to aerodynamics. The situations are characterized by high pressure and temperature gradients, transients and the appearance of discontinuities, factors which require mesh refinement during computations. Techniques are developed for temporal and spatial discretization of a model problem. Several observations are made regarding the explicit and implicit features of the calculations, the use of the Lax-Wendroff scheme to produce a mass-matrix for obtaining accurate results for transients, methods of performing stability analyses, and simplification techniques. Examples are provided of solving the nonlinear shallow-water equations and describing compressible flows, particularly transonic flows. Domain splitting is defined for improving the calculations at each time step and in different parts of the flow regime while simultaneously advancing the calculations towards a solution.

Zienkiewicz, O. C.↗

NASA NTRS1986

Finite-volume and integral-equation techniques for transonic and supersonic vortex-dominated flows

Two computational techniques are developed to calculate the compressible vortex-dominated flows. The first technique is a finite-volume Euler Solver which uses four-Stage Runge-Kutta time stepping with second- and fourth-order dissipation terms. The technique is applied to supersonic conical and three-dimensional flows about sharp- and round-edged delta wings. Attached and separated-flow solutions have been obtained depending on the values of damping coefficients. The second technique is an integral-equation solver of the full potential equation which uses a volume-integral term in addition to the classical surface-integral terms. The technique is applied to transonic three-dimensional flows about sharp-edged delta wings. A hybrid technique which combines the finite-volume and the integral-equation solvers is also presented.

Kandil, O. A.↗