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NASA NTRS2001

Unsteady Analysis of Separated Aerodynamic Flows Using an Unstructured Multigrid Algorithm

An implicit method for the computation of unsteady flows on unstructured grids is presented. The resulting nonlinear system of equations is solved at each time step using an agglomeration multigrid procedure. The method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage. Validation of the code using a one-equation turbulence model is performed for the well-known case of flow over a cylinder. A Detached Eddy Simulation model is also implemented and its performance compared to the one equation Spalart-Allmaras Reynolds Averaged Navier-Stokes (RANS) turbulence model. Validation cases using DES and RANS include flow over a sphere and flow over a NACA 0012 wing including massive stall regimes. The project was driven by the ultimate goal of computing separated flows of aerodynamic interest, such as massive stall or flows over complex non-streamlined geometries.

Pelaez, Juan↗

NASA NTRS1995

Analysis of composite ablators using massively parallel computation

In this work, the feasibility of using massively parallel computation to study the response of ablative materials is investigated. Explicit and implicit finite difference methods are used on a massively parallel computer, the Thinking Machines CM-5. The governing equations are a set of nonlinear partial differential equations. The governing equations are developed for three sample problems: (1) transpiration cooling, (2) ablative composite plate, and (3) restrained thermal growth testing. The transpiration cooling problem is solved using a solution scheme based solely on the explicit finite difference method. The results are compared with available analytical steady-state through-thickness temperature and pressure distributions and good agreement between the numerical and analytical solutions is found. It is also found that a solution scheme based on the explicit finite difference method has the following advantages: incorporates complex physics easily, results in a simple algorithm, and is easily parallelizable. However, a solution scheme of this kind needs very small time steps to maintain stability. A solution scheme based on the implicit finite difference method has the advantage that it does not require very small times steps to maintain stability. However, this kind of solution scheme has the disadvantages that complex physics cannot be easily incorporated into the algorithm and that the solution scheme is difficult to parallelize. A hybrid solution scheme is then developed to combine the strengths of the explicit and implicit finite difference methods and minimize their weaknesses. This is achieved by identifying the critical time scale associated with the governing equations and applying the appropriate finite difference method according to this critical time scale. The hybrid solution scheme is then applied to the ablative composite plate and restrained thermal growth problems. The gas storage term is included in the explicit pressure calculation of both problems. Results from ablative composite plate problems are compared with previous numerical results which did not include the gas storage term. It is found that the through-thickness temperature distribution is not affected much by the gas storage term. However, the through-thickness pressure and stress distributions, and the extent of chemical reactions are different from the previous numerical results. Two types of chemical reaction models are used in the restrained thermal growth testing problem: (1) pressure-independent Arrhenius type rate equations and (2) pressure-dependent Arrhenius type rate equations. The numerical results are compared to experimental results and the pressure-dependent model is able to capture the trend better than the pressure-independent one. Finally, a performance study is done on the hybrid algorithm using the ablative composite plate problem. It is found that there is a good speedup of performance on the CM-5. For 32 CPU's, the speedup of performance is 20. The efficiency of the algorithm is found to be a function of the size and execution time of a given problem and the effective parallelization of the algorithm. It also seems that there is an optimum number of CPU's to use for a given problem.

Shia, David↗

NASA NTRS1985

Three dimensional CSCM method for the compressible Navier-Stokes equations with application to a multi-nozzle exhaust flowfield

The effective design of three-dimensional flow systems such as a clustered multinozzle shrouded exhaust system requires detailed analysis of the internal flowfield. It is pointed out that new numerical techniques on the most modern vector computers are making these analyses practicable. In this paper, the upwind differenced implicit conservative supracharacteristics method (CSCM) for three-dimensional viscous flow is presented. The new method is an implicit 'method of planes' symmetric Gauss-Seidel relaxation scheme. The data is conveniently stored on successive planes along the streamwise coordinate, and the system of equations is solved twice in each successive plane of the streamwise coordinate. The developed new three-dimensional compressible Navier-Stokes algorithm combines the best features of the storage and computationally efficient space marching procedures with the generality of time dependent techniques to solve flows with elliptic and streamwise separated flows.

Bardina, J.↗

NASA NTRS1988

Improved 3-D turbomachinery CFD algorithm

The building blocks of a computer algorithm developed for the time-accurate flow analysis of rotating machines are described. The flow model is a finite volume method utilizing a high resolution approximate Riemann solver for interface flux definitions. This block LU implicit numerical scheme possesses apparent unconditional stability. Multi-block composite gridding is used to orderly partition the field into a specified arrangement. Block interfaces, including dynamic interfaces, are treated such as to mimic interior block communication. Special attention is given to the reduction of in-core memory requirements by placing the burden on secondary storage media. Broad applicability is implied, although the results presented are restricted to that of an even blade count configuration. Several other configurations are presently under investigation, the results of which will appear in subsequent publications.

Janus, J. Mark↗

NASA NTRS1995

Implicit method for the computation of unsteady flows on unstructured grids

An implicit method for the computation of unsteady flows on unstructured grids is presented. Following a finite difference approximation for the time derivative, the resulting nonlinear system of equations is solved at each time step by using an agglomeration multigrid procedure. The method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage. Inviscid and viscous unsteady flows are computed to validate the procedure. The issue of the mass matrix which arises with vertex-centered finite volume schemes is addressed. The present formulation allows the mass matrix to be inverted indirectly. A mesh point movement and reconnection procedure is described that allows the grids to evolve with the motion of bodies. As an example of flow over bodies in relative motion, flow over a multi-element airfoil system undergoing deployment is computed.

Venkatakrishnan, V.↗

NASA NTRS1990

Twin-page storage management for rapid transaction-undo recovery

This paper presents and evaluates a new twin-page disk-storage management scheme for rapid database transaction-undo recovery. In contrast to previous twin-page schemes, the present approach uses static page mapping and allows dirty pages in the main memory to be written, at any instant, onto disk without the requirement of undo logging. No explicit undo is required when a transaction is aborted. Transaction undo is implicitly performed by not subsequently fetching from disk the invalid pages updated by the aborted transaction. Performance in terms of disk I/O and CPU overhead for transaction-undo recovery is analyzed and compared with a previous approach TWIST. It is shown that the scheme achieves rapid transaction-undo recovery without degrading average system performance for various workloads, and that the scheme is well suited for applications with a large number of updates and frequent transaction aborts.

Wu, Kun-Lung↗

NASA NTRS2002

Higher Order Time Integration Schemes for the Unsteady Navier-Stokes Equations on Unstructured Meshes

The efficiency gains obtained using higher-order implicit Runge-Kutta schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier-Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each timestep are presented. The first algorithm (NMG) is a pseudo-time-stepping scheme which employs a non-linear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on Inexact Newton's methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson's iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the Generalized Minimal Residual method. Results demonstrating the relative superiority of these Newton's methods based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes with the more efficient nonlinear solvers.

Jothiprasad, Giridhar↗

NASA NTRS1972

A computer program for the geometrically nonlinear static and dynamic analysis of arbitrarily loaded shells of revolution, theory and users manual

A digital computer program known as SATANS (static and transient analysis, nonlinear, shells) for the geometrically nonlinear static and dynamic response of arbitrarily loaded shells of revolution is presented. Instructions for the preparation of the input data cards and other information necessary for the operation of the program are described in detail and two sample problems are included. The governing partial differential equations are based upon Sanders' nonlinear thin shell theory for the conditions of small strains and moderately small rotations. The governing equations are reduced to uncoupled sets of four linear, second order, partial differential equations in the meridional and time coordinates by expanding the dependent variables in a Fourier sine or cosine series in the circumferential coordinate and treating the nonlinear modal coupling terms as pseudo loads. The derivatives with respect to the meridional coordinate are approximated by central finite differences, and the displacement accelerations are approximated by the implicit Houbolt backward difference scheme with a constant time interval. The boundaries of the shell may be closed, free, fixed, or elastically restrained. The program is coded in the FORTRAN 4 language and is dimensioned to allow a maximum of 10 arbitrary Fourier harmonics and a maximum product of the total number of meridional stations and the total number of Fourier harmonics of 200. The program requires 155,000 bytes of core storage.

Ball, R. E.↗

NASA NTRS1977

An implicit factored scheme for the compressible Navier-Stokes equations

An implicit finite difference scheme is developed for the numerical solution of the compressible Navier-Stokes equations in conservation-law form. The algorithm is second-order-time accurate, noniterative, and spatially factored. In order to obtain an efficient factored algorithm, the spatial cross-derivatives are evaluated explicitly. However, the algorithm is unconditionally stable and, although a three-time-level scheme, requires only two-time-levels of data storage. The algorithm is constructed in a 'delta' form (i.e., increments of the conserved variables and fluxes) that provides a direct derivation of the scheme and leads to an efficient computational algorithm. In addition, the delta form has the advantageous property of a steady-state (if one exists) independent of the size of the time step. Numerical results are presented for a two-dimensional shock boundary-layer interaction problem.

Beam, R. M.↗

NASA NTRS2015

Numerical Investigation of Microgravity Tank Pressure Rise Due to Boiling

The ability to control self-pressurization in cryogenic storage tanks is essential for NASAs long-term space exploration missions. Predictions of the tank pressure rise in Space are needed in order to inform the microgravity design and optimization process. Due to the fact that natural convection is very weak in microgravity, heat leaks into the tank can create superheated regions in the liquid. The superheated regions can instigate microgravity boiling, giving rise to pressure spikes during self-pressurization. In this work, a CFD model is developed to predict the magnitude and duration of the microgravity pressure spikes. The model uses the Schrage equation to calculate the mass transfer, with a different accommodation coefficient for evaporation at the interface, condensation at the interface, and boiling in the bulk liquid. The implicit VOF model was used to account for the moving interface, with bounded second order time discretization. Validation of the models predictions was carried out using microgravity data from the Tank Pressure Control Experiment, which flew aboard the Space Shuttle Mission STS-52. Although this experiment was meant to study pressurization and pressure control, it underwent boiling during several tests. The pressure rise predicted by the CFD model compared well with the experimental data. The ZBOT microgravity experiment is scheduled to fly on February 2016 aboard the ISS. The CFD model was also used to perform simulations for setting parametric limits for the Zero-Boil-Off Tank (ZBOT) Experiments Test Matrix in an attempt to avoid boiling in the majority of the test runs that are aimed to study pressure increase rates during self-pressurization. *Supported in part by NASA ISS Physical Sciences Research Program, NASA HQ, USA

pressure rise↗

NASA NTRS1984

A strongly implicit procedure for the compressible Navier-Stokes equations

The strongly implicit procedure of Stone is used to obtain numerical solutions of the compressible Navier-Stokes equations in conservative form. In contrast to the spatially split Douglas-Gunn type methods, the method is shown to be numerically stable for the three-dimensional wave equation. The method is applied to a variety of external and internal two-dimensional flow problems involving shock wave boundary-layer interaction for both laminar and turbulent flows. The results are in good agreement with other methods and/or experiments. The storage penalty associated with the method is discussed and a simple, yet effective, means of minimizing the problem is presented.

Walters, R. W.↗

NASA NTRS1990

A viscoplastic model with application to LiF-22 percent CaF2 hypereutectic salt

A viscoplastic model for class M (metal-like behavior) materials is presented. One novel feature is its use of internal variables to change the stress exponent of creep (where n is approximately = 5) to that of natural creep (where n = 3), in accordance with experimental observations. Another feature is the introduction of a coupling in the evolution equations of the kinematic and isotropic internal variables, making thermal recovery of the kinematic variable implicit. These features enable the viscoplastic model to reduce to that of steady-state creep in closed form. In addition, the hardening parameters associated with the two internal state variables (one scalar-valued, the other tensor-valued) are considered to be functions of state, instead of being taken as constant-valued. This feature enables each internal variable to represent a much wider spectrum of internal states for the material. The model is applied to a LiF-22 percent CaF2 hypereutectic salt, which is being considered as a thermal energy storage material for space-based solar dynamic power systems.

Freed, A. D.↗

NASA NTRS1980

User's guide to the NOZL3D and NOZLIC computer programs

Complete FORTRAN listings and running instructions are given for a set of computer programs that perform an implicit numerical solution to the unsteady Navier-Stokes equations to predict the flow characteristics and performance of nonaxisymmetric nozzles. The set includes the NOZL3D program, which performs the flow computations; the NOZLIC program, which sets up the flow field initial conditions for general nozzle configurations, and also generates the computational grid for simple two dimensional and axisymmetric configurations; and the RGRIDD program, which generates the computational grid for complicated three dimensional configurations. The programs are designed specifically for the NASA-Langley CYBER 175 computer, and employ auxiliary disk files for primary data storage. Input instructions and computed results are given for four test cases that include two dimensional, three dimensional, and axisymmetric configurations.

Thomas, P. D.↗

NASA NTRS1997

Thermal and Hydrologic Signatures of Soil Controls on Evaporation: A Combined Energy and Water Balance Approach with Implications for Remote Sensing of Evaporation

The overall goal of this research is to examine the feasibility of applying a newly developed diagnostic model of soil water evaporation to large land areas using remotely sensed input parameters. The model estimates the rate of soil evaporation during periods when it is limited by the net transport resulting from competing effects of capillary rise and drainage. The critical soil hydraulic properties are implicitly estimated via the intensity and duration of the first stage (energy limited) evaporation, removing a major obstacle in the remote estimation of evaporation over large areas. This duration, or "time to drying" (t(sub d)), is revealed through three signatures detectable in time series of remote sensing variables. The first is a break in soil albedo that occurs as a small vapor transmission zone develops near the surface. The second is a break in either surface to air temperature differences or in the diurnal surface temperature range, both of which indicate increased sensible heat flux (and/or storage) required to balance the decrease in latent heat flux. The third is a break in the temporal pattern of near surface soil moisture. Soil moisture tends to decrease rapidly during stage 1 drying (as water is removed from storage), and then become more or less constant during soil limited, or "stage 2" drying (as water is merely transmitted from deeper soil storage). The research tasks address: (1) improvements in model structure, including extensions to transpiration and aggregation over spatially variable soil and topographic landscape attributes; and (2) applications of the model using remotely sensed input parameters.

Salvucci, Guido D.↗

NASA NTRS2000

Thermal and Hydrologic Signatures of Soil Controls on Evaporation: A Combined Energy and Water Balance Approach with Implications for Remote Sensing of Evaporation

The overall goal of this research is to examine the feasibility of applying a newly developed diagnostic model of soil water evaporation to large land areas using remotely sensed input parameters. The model estimates the rate of soil evaporation during periods when it is limited by the net transport resulting from competing effects of capillary rise and drainage. The critical soil hydraulic properties are implicitly estimated via the intensity and duration of the first stage (energy limited) evaporation, removing a major obstacle in the remote estimation of evaporation over large areas. This duration, or 'time to drying' (t(sub d)) is revealed through three signatures detectable in time series of remote sensing variables. The first is a break in soil albedo that occurs as a small vapor transmission zone develops near the surface. The second is a break in either surface to air temperature differences or in the diurnal surface temperature range, both of which indicate increased sensible heat flux (and/or storage) required to balance the decrease in latent heat flux. The third is a break in the temporal pattern of near surface soil moisture. Soil moisture tends to decrease rapidly during stage I drying (as water is removed from storage), and then become more or less constant during soil limited, or 'stage II' drying (as water is merely transmitted from deeper soil storage). The research tasks address: (1) improvements in model structure, including extensions to transpiration and aggregation over spatially variable soil and topographic landscape attributes; and (2) applications of the model using remotely sensed input parameters.

Salvucci, Guido D.↗

NASA NTRS1977

Implicit approximate-factorization schemes for the efficient solution of steady transonic flow problems

Implicit approximate-factorization algorithms (AF) are developed for the solution of steady-state transonic flow problems. The performance of the AF solution method is evaluated relative to that of the standard solution method for transonic flow problems, successive line over-relaxation (SLOR). Both methods are applied to the solution of the nonlinear, two-dimensional transonic small-disturbance equation. Results indicate that the AF method requires substantially less computer time than SLOR to solve the nonlinear finite-difference matrix equation for a transonic flow field. This increase in computational efficiency is achieved with no appreciable increase in computer storage or coding complexity.

Ballhaus, W. F.↗

NASA NTRS1986

Some design constraints required for the use of generic software in embedded systems: Packages which manage abstract dynamic structures without the need for garbage collection

The embedded systems running real-time applications, for which Ada was designed, require their own mechanisms for the management of dynamically allocated storage. There is a need for packages which manage their own internalo structures to control their deallocation as well, due to the performance implications of garbage collection by the KAPSE. This places a requirement upon the design of generic packages which manage generically structured private types built-up from application-defined input types. These kinds of generic packages should figure greatly in the development of lower-level software such as operating systems, schedulers, controllers, and device driver; and will manage structures such as queues, stacks, link-lists, files, and binary multary (hierarchical) trees. Controlled to prevent inadvertent de-designation of dynamic elements, which is implicit in the assignment operation A study was made of the use of limited private type, in solving the problems of controlling the accumulation of anonymous, detached objects in running systems. The use of deallocator prodecures for run-down of application-defined input types during deallocation operations during satellites.

Johnson, Charles S.↗

NASA NTRS1983

Monotone implicit algorithms for the small-disturbance and full potential equations applied to transonic flows

Numerical calculations of transonic flows by potential equations typically use algorithms that change the method of calculation for regions of subsonic and supersonic flow. In this paper, implicit approximate-factorization algorithms are modified to use the monotonic switch in the type of finite-differencing that was developed by Godunov for the Euler equations. Calculations of flows over airfoils by these algorithms are compared with calculations by other methods that are in common usage. For the small-disturbance potential equation, comparisons are made with the Murman-Cole method and the monotone method of Engquist and Osher for both steady and unsteady flows. For the full potential equation, comparisons are made with the methods of Jameson and of Holst and Ballhaus for steady flows. The comparisons show that the monotone methods are more stable. For steady flows, solutions are obtained for cases where the Murman-Cole switch requires a time step over ten times smaller in order for the calculations to remain stable. These improvements are achieved with no increase in computer storage and only minor modifications in current codes.

Goorjian, P. M.↗