Stress waves resulting from hypervelocity impact.
Characteristics method for stress waves from hypervelocity impact of circular cylinder on half space, discussing numerical diffusion effect on pressure and flow fields
Chang, T. S.↗
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Numerical computation of transient coaxial entry tube flows
A numerical program was developed to compute transient laminar flows in two dimensions including multicomponent mixing and chemical reaction. The program can compute both incompressible flows and compressible flows at all speeds, and it is applied to describe transient and steady state solutions for low subsonic, coaxial entry, tue flows. Single component, nonreacting flows comprise most of the solutions, but one steady state solution is presented for trace concentration constituents engaging in a second order reaction. Numerical stability was obtained by adding at each calculation point a correction for numerical diffusion errors caused by truncation of the Taylor series used to finite difference the conservation equations. Transient computations were made for fluids initially at rest, then subjected to step velocity inputs that were uniform across each region of the entry plane and were held constant throughout the computation period. For center tube to annulus velocity ratios of 0.5 and 2.0, the bulk fluid in the tube initially moved in plug flow, but strong radial flows developed near the injection plane which moved the fluid into the high shear region between the jets and away from the tube wall.
Wieber, P. R.↗
A high-resolution study of the gas flow in barred spirals
The considered investigation is concerned with conditions in that type of spiral galaxy which is known as a 'barred spiral'. The lack of star formation and the smoothness of the dark dust lanes may indicate that the bar region is pervaded by a more homogeneous interstellar medium with a lower viscosity than that characteristic of the outer regions. The effects of such a reduced viscosity are investigated on the basis of high-resolution time-dependent gasdynamical equations. Calculations modeling the gas flow in a given bar potential are presented. The calculations were performed on grids with various mesh sizes and consequently had different resolutions and numerical viscosities. A reduction in the numerical diffusion and viscosity was accompanied by changes in the flow pattern, including the appearance of a strong shock in the bar region and the occurrence of postshock outflow.
Van Albada, G. D.↗
Finite analytic numerical solution of axisymmetric Navier-Stokes and energy equations
Convective heat transfer for steady state laminar flow in axisymmetric coordinates is considered. Numerical solutions for flow pattern and temperature distribution are obtained by the finite analytic numerical method applied to the Navier-Stokes equations expressed in terms of vorticity and stream function, and the energy equation. The finite analytic numerical method differs from other numerical methods in that it utilizes a local analytic solution in an element of the problem to construct the total numerical solution. Finite analytic solutions of vorticity, stream function, temperature and heat transfer coefficients for flow with Reynolds number of 5.0, 100.0, 1000.0, and 2000.0, and Prandtl number of 0.1, 1.0, and 10.0 with uniform grid sizes are reported for axisymmetric pipe with sudden expansion and contraction. The wall temperature is considered to be isothermal and differs from the inlet temperature. It is shown that the finite analytic solution is stable, converges rapidly, and simulates the convection of fluid flow accurately since the local analytic solution is capable of simulating automatically the influence of skewed convection through the element boundary on the interior nodal values thereby minimizing the false numerical diffusion.
Chen, C.-J.↗
Error reduction program: A progress report
Five finite differences schemes were evaluated for minimum numerical diffusion in an effort to identify and incorporate the best error reduction scheme into a 3D combustor performance code. Based on this evaluated, two finite volume method schemes were selected for further study. Both the quadratic upstream differencing scheme (QUDS) and the bounded skew upstream differencing scheme two (BSUDS2) were coded into a two dimensional computer code and their accuracy and stability determined by running several test cases. It was found that BSUDS2 was more stable than QUDS. It was also found that the accuracy of both schemes is dependent on the angle that the streamline make with the mesh with QUDS being more accurate at smaller angles and BSUDS2 more accurate at larger angles. The BSUDS2 scheme was selected for extension into three dimensions.
Syed, S. A.↗
Flux-vector splitting for the Euler equations
Flux-vector splitting is shown to be the simplest way of implementing upwind differencing for the full or isenthalpic Euler equations combined with the ideal-gas law. The scheme presented produces steady shock profiles with two interior zones. A disadvantage in using flux-vector splitting is that it leads to numerical diffusion of a contact discontinuity at rest. This diffusion, however, can be removed, and present research is aimed at achieving this with minimal computational effort.
Van Leer, B.↗
Solution method for a hovering helicopter rotor using the Euler equations
A method for the calculation of the flow field of a helicopter rotor blade in hover is presented. The approach uses a finite volume solution of the three dimensional Euler equations for the blade near field. In the Euler solver the velocity field is decomposed into two parts. One is the induced velocity of the vortex wake extending below the blade, found from a free wake calculation procedure. The other part is the unknown additional velocity field of the rotor blade. This approach eliminates numerical diffusion of the rolled up wake vorticity due to truncation error and artificial viscosity. Also, the effects of the far wake are included in the limited computational domain. Solutions are presented for an isolated wing and a model helicopter rotor and compared to experiment.
Roberts, T. W.↗
Euler solutions for the flow around a hovering helicopter rotor
A method for computing the flow around a hovering helicopter rotor is presented. The solution procedure is divided into two parts. The first part is a finite volume solution of the Euler equations for the near field flow around a rotor blade. The second part is a free wake approach for determining the wake geometry and induced velocities. These two parts are solved in a coupled fashion. The rolled-up vortex wake of the rotor is included in the Euler computational domain through a nonlinear perturbation technique. This eliminates the numerical diffusion of the wake vorticity due to truncation error and artificial viscosity without the need for excessive grid resolution near the vortex core. The method is used to compute both hovering rotor and wing/vortex interaction flows, and the results are compared to experiment.
Roberts, T. W.↗
Analysis of coaxial spray combustion flames and related numerical issues
An approach to the simulation of strongly coupled multiphase flows in combustion hardware is sketched and its unique requirements highlighted. An example of a successful application to a coaxial injector flame is presented. Furthermore, several numerical issues that tend to interact with the physics of the problem are discussed with special regard to their potential impact on the choices of numerical parameters by the analyst. These include the issues of stability, numerical diffusivity, stiffness, and boundary conditions. The theme of this paper focuses on the intriguing relationships among the grid, the solution algorithm, and the actual physical mechanisms themselves.
Liang, P. Y.↗
User's manual for a TEACH computer program for the analysis of turbulent, swirling reacting flow in a research combustor
Described is a computer program for the analysis of the subsonic, swirling, reacting turbulent flow in an axisymmetric, bluff-body research combustor. The program features an improved finite-difference procedure designed to reduce the effects of numerical diffusion and a new algorithm for predicting the pressure distribution within the combustor. A research version of the computer program described in the report was supplied to United Technologies Research Center by Professor A. D. Gosman and his students, R. Benodeker and R. I. Issa, of Imperial College, London. The Imperial College staff also supplied much of the program documentation. Presented are a description of the mathematical model for flow within an axisymmetric bluff-body combustor, the development of the finite-difference procedure used to represent the system of equations, an outline of the algorithm for determining the static pressure distribution within the combustor, a description of the computer program including its input format, and the results for representative test cases.
Chiappetta, L. M.↗
Impeller shroud to casing leakage flow simulations in the Space Shuttle Main Engine high pressure fuel pump
Quasi-three-dimensional Navier-Stokes calculations were carried out for the Space Shuttle Main Engine high-pressure fuel pump to simulate the impeller shroud to casing leakage flow. This flow geometry was modeled as an axisymmetric cavity flow with a stationary surface representing the casing, and a rotating surface denoting the impeller. A 63 x 81-node mesh provided sufficient resolution in the regions of greatest flow variations and reduced the effects of numerical diffusion. The turbulence field was closed with the high Reynolds number form of the k-epsilon model supplemented with wall functions in the vicinity of the walls. Finally, a parametric study quantified the effects of through mass flow changes on this leakage flow.
Sindir, Munir M.↗
Improved numerical methods for turbulent viscous recirculating flows
The hybrid-upwind finite difference schemes employed in generally available combustor codes possess excessive numerical diffusion errors which preclude accurate quantative calculations. The present study has as its primary objective the identification and assessment of an improved solution algorithm as well as discretization schemes applicable to analysis of turbulent viscous recirculating flows. The assessment is carried out primarily in two dimensional/axisymetric geometries with a view to identifying an appropriate technique to be incorporated in a three-dimensional code.
Turan, A.↗
Studies of pressure-velocity coupling schemes for analysis of incompressible and compressible flows
Two pressure-velocity coupling schemes, both of which solve the fully implicit discretized equations governing the flow of fluids were examined, and the capability of performing large Reynolds number, low Mach number compressible flow calculations were assessed. The semi-implicit iterative SIMPLE algorithm is extended to handle transient compressible flow calculations. This extension takes into account a strong coupling between the pressure and temperature through a correction procedure, based on the equations of state. Results obtained from the extended SIMPLE algorithm are then compared to similar results obtained from the non-iterative PISO algorithm. Both time-dependent and steady state calculations were performed using an axisymmetric 2:1 pipe expansion geometry and laminar flow conditions corresponding to Reynolds number of 1000 and Mach number of 2.0. For calculations simulating a time-dependent compression/expansion process, both schemes exhibit transient features in excellent agreement with each other, and moreover, the PISO method shows a significant computational time reduction of 60 percent over the SIMPLE scheme, regardless of the time step size or grid size employed. The effects of numerical diffusion are shown to be significant in these calculations. For steady state compressible flows, however, the SIMPLE algorithm displays increasing computational efficiency over the PISO method as the time step sizes employed to reach steady state conditions are decreased.
Burgreen, Gregory Wayne↗
Euler equation computations for the flow over a hovering helicopter rotor
A numerical solution technique is developed for computing the flow field around an isolated helicopter rotor in hover. The flow is governed by the compressible Euler equations which are integrated using a finite volume approach. The Euler equations are coupled to a free wake model of the rotary wing vortical wake. This wake model is incorporated into the finite volume solver using a prescribed flow, or perturbation, technique which eliminates the numerical diffusion of vorticity due to the artificial viscosity of the scheme. The work is divided into three major parts: (1) comparisons of Euler solutions to experimental data for the flow around isolated wings show good agreement with the surface pressures, but poor agreement with the vortical wake structure; (2) the perturbation method is developed and used to compute the interaction of a streamwise vortex with a semispan wing. The rapid diffusion of the vortex when only the basic Euler solver is used is illustrated, and excellent agreement with experimental section lift coefficients is demonstrated when using the perturbation approach; and (3) the free wake solution technique is described and the coupling of the wake to the Euler solver for an isolated rotor is presented. Comparisons with experimental blade load data for several cases show good agreement, with discrepancies largely attributable to the neglect of viscous effects. The computed wake geometries agree less well with experiment, the primary difference being that too rapid a wake contraction is predicted for all the cases.
Roberts, Thomas Wesley↗
Developing fluid flow in a curved duct of square cross-section and its fully developed dual solutions
Developing fluid flow in a curved duct of square cross-section is studied numerically by a factored ADI finite-difference method on a staggered grid. A central-difference scheme with primitive variables is used inside the computational domain to reduce numerical diffusion. Two Reynolds numbers, 574 and 790, based upon a bulk velocity and hydraulic diameter are chosen for curvature ratios of 1/6.45 and 1/2.3, respectively. It is found that the secondary flow is far more complicated than expected, with the appearance of at least two pairs of vortices. Main-flow separation is also observed for the higher curvature ratio. Furthermore, it is observed that the flow develops into two quite different states downstream, depending upon the inlet conditions. Solutions of the fully developed Navier-Stokes equations is shown to be not unique beyond a certain critical Reynolds number. Developing flow seems to evolve into the fully developed state along a particular branch into which the fully developed solution bifurcates.
Soh, W. Y.↗
Aerothermal modeling program. Phase 2, element A: Improved numerical methods for turbulent viscous recirculating flows
The objective of this effort is to develop improved numerical schemes for predicting combustor flow fields. Various candidate numerical schemes were evaluated, and promising schemes were selected for detailed assessment. The criteria for evaluation included accuracy, computational efficiency, stability, and ease of extension to multidimensions. The candidate schemes were assessed against a variety of simple one- and two-dimensional problems. These results led to the selection of the following schemes for further evaluation: flux spline schemes (linear and cubic) and controlled numerical diffusion with internal feedback (CONDIF). The incorporation of the flux spline scheme and direct solution strategy in a computer program for three-dimensional flows is in progress.
Karki, K. C.↗
An embedded mesh procedure for leading-edge vortex flows
A cell-vertex scheme is outlined for solving the flow about a delta wing with M (sub infinity) is greater than 1. Embedded regions of mesh refinement allow solutions to be obtained which have much higher resolution than those achieved to date. Effects of mesh refinement and artificial viscosity on the solutions are studied, to determine at what point leading-edge vortex solutions are grid-converged. A macroscale and a microscale for the size of the vortex are defined, and it is shown that the macroscale (which includes the wing surface properties) is converged on a moderately refined grid, while the microscale is very sensitive to grid spacing. The level of numerical diffusion in the core of the vortex is found to be substantial. Comparisons with the experiment are made for two cases which have transonic cross-flow velocities.
Powell, Kenneth G.↗
Multigrid Calculations of a Jet in Crossflow
A series of numerical calculations are made of a jet in crossflow using progressive mesh refinement up to 2.4 million grid points. A solution algorithm that combined the features of a point-coupled solution of the momentum and continuity equations with multigrid acceleration demonstrated efficient convergence of the governing equations. In comparisons with experimental data, some features of the jet flow field were found to be predicted reasonably well, but the results still remain affected by numerical diffusion.
Claus, R. W.↗