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NASA NTRS1983

A generalized computer code for developing dynamic gas turbine engine models (DIGTEM)

This paper describes DIGTEM (digital turbofan engine model), a computer program that simulates two spool, two stream (turbofan) engines. DIGTEM was developed to support the development of a real time multiprocessor based engine simulator being designed at the Lewis Research Center. The turbofan engine model in DIGTEM contains steady state performance maps for all the components and has control volumes where continuity and energy balances are maintained. Rotor dynamics and duct momentum dynamics are also included. DIGTEM features an implicit integration scheme for integrating stiff systems and trims the model equations to match a prescribed design point by calculating correction coefficients that balance out the dynamic equations. It uses the same coefficients at off design points and iterates to a balanced engine condition. Transients are generated by defining the engine inputs as functions of time in a user written subroutine (TMRSP). Closed loop controls can also be simulated. DIGTEM is generalized in the aerothermodynamic treatment of components. This feature, along with DIGTEM's trimming at a design point, make it a very useful tool for developing a model of a specific turbofan engine.

Daniele, C. J.↗

NASA NTRS1984

A generalized computer code for developing dynamic gas turbine engine models (DIGTEM)

Daniele, C. J.↗

NASA NTRS1981

Numerical method for gas dynamics combining characteristic and conservation concepts

An efficient implicit numerical method that solves the compressible Navier-Stokes equations in arbitrary curvilinear coordinates by the finite-volume technique is presented. An intrinsically dissipative difference scheme and a fully implicit treatment of boundary conditions, based on characteristic and conservation concepts, are used to improve stability and accuracy. Efficiency is achieved by using a diagonal form of the implicit algorithm and spatially varying time-steps. Comparisons of various schemes and methods are presented for one- and two-dimensional flows, including transonic separated flow past a thick circular-arc airfoil in a channel. The new method is equal to or better than a version of MacCormack's hybrid method in accuracy and it converges to a steady state up to an order of magnitude faster.

Coakley, T. J.↗

NASA NTRS1985

Application of TVD schemes for the Euler equations of gas dynamics

First-order, second-order, and implicit total variation diminishing (TVD) schemes are reviewed using the modified flux approach. Some transient and steady-state calculations are then carried out to illustrate the applicability of these schemes to the Euler equations. It is shown that the second-order explicit TVD schemes generate good shock resolution for both transient and steady-state one-dimensional and two-dimensional problems. Numerical experiments for a quasi-one-dimensional nozzle problem show that the second-order implicit TVD scheme produces a fairly rapid convergence rate and remains stable even when running with a Courant number of 10 to the 6th.

Yee, H. C.↗

NASA NTRSDate not supplied

Towards Robust and Accurate Implicit Gradient Methods for Second- and Third-Order Nodal-Gradient Cell-Centered Finite-Volume Discretizations on Tetrahedral Grids

In this paper, we introduce implicit gradient methods as alternatives to conventional least-squares gradient methods for second- and third-order nodal-gradient cell-centered finite-volume discretizations, where solutions are stored at cells but gradients are stored at nodes. Because of the unique configuration of solutions and gradients, implicit gradient systems developed for the node-centered edge-based discretization method can be directly applied once the numerical solutions are interpolated from cells to nodes with sufficient accuracy. The resulting defect-correction solver can be loosely coupled with a flow-equation solver, and at convergence, solutions and gradients that satisfy the corresponding residual equations are obtained. Each iteration is relatively cheap compared with least-squares methods involving hundreds of neighbors. Numerical results are presented for accuracy verification studies and some simple but realistic flow problems.

Computational Fluid Dynamics↗

NASA NTRS1981

Fully implicit shock tracking

A tracking method for solving hyperbolic free boundary problems arising in fluid dynamics is presented. The principal feature of the new approach is that the implicit form is used to simultaneously treat both interior points and boundary conditions. In particular, the location of the free boundary (shock) surface is treated implicitly and coupled with all other unknowns. The method is presented in the context of unsteady one-dimensional flow in a variable area duct with an internal shock wave. The fully implicit method and other strategies for advancing the shock are compared for computing a steady solution via a time asymptotic approach. Issues regarding extension of the method to multiple dimensions are also discussed.

Bell, J. B.↗

NASA NTRS1997

On spurious behavior of CFD simulations

Spurious behavior in underresolved grids and/or semi-implicit temporal discretizations for four computational fluid dynamics (CFD) simulations are studied. The numerical simulations consist of (a) a 1-D chemically relaxed nonequilibrium model, (b) the direct numerical simulation (DNS) of 2-D incompressible flow over a backward facing step, (c) a loosely-coupled approach for a 2-D fluid-structure interaction, and (d) a 3-D compressible unsteady flow simulation of vortex breakdown in delta wings. Using knowledge from dynamical systems theory, various types of spurious behaviors that are numerical artifacts were systematically identified. These studies revealed the various possible dangers of misinterpreting numerical simulation of realistic complex flows that are constrained by the available computing power. In large scale computations underresolved grids, semi-implicit procedures, loosely-coupled implicit procedures, and insufficiently long time integration in DNS are most often unavoidable. Consequently, care must be taken in both computation and in interpretation of the numerical data. The results presented confirm the important role that dynamical systems theory can play in the understanding of the nonlinear behavior of numerical algorithms and in aiding the identification of the sources of numerical uncertainties in CFD.

Numerical Solution↗

NASA NTRS1993

A transient FETI methodology for large-scale parallel implicit computations in structural mechanics, part 2

Explicit codes are often used to simulate the nonlinear dynamics of large-scale structural systems, even for low frequency response, because the storage and CPU requirements entailed by the repeated factorizations traditionally found in implicit codes rapidly overwhelm the available computing resources. With the advent of parallel processing, this trend is accelerating because explicit schemes are also easier to parallellize than implicit ones. However, the time step restriction imposed by the Courant stability condition on all explicit schemes cannot yet and perhaps will never be offset by the speed of parallel hardware. Therefore, it is essential to develop efficient and robust alternatives to direct methods that are also amenable to massively parallel processing because implicit codes using unconditionally stable time-integration algorithms are computationally more efficient than explicit codes when simulating low-frequency dynamics. Here we present a domain decomposition method for implicit schemes that requires significantly less storage than factorization algorithms, that is several times faster than other popular direct and iterative methods, that can be easily implemented on both shared and local memory parallel processors, and that is both computationally and communication-wise efficient. The proposed transient domain decomposition method is an extension of the method of Finite Element Tearing and Interconnecting (FETI) developed by Farhat and Roux for the solution of static problems. Serial and parallel performance results on the CRAY Y-MP/8 and the iPSC-860/128 systems are reported and analyzed for realistic structural dynamics problems. These results establish the superiority of the FETI method over both the serial/parallel conjugate gradient algorithm with diagonal scaling and the serial/parallel direct method, and contrast the computational power of the iPSC-860/128 parallel processor with that of the CRAY Y-MP/8 system.

Farhat, Charbel↗

NASA NTRS1978

Filtering of non-linear instabilities

For Courant numbers larger than one and cell Reynolds numbers larger than two, oscillations and in some cases instabilities are typically found with implicit numerical solutions of the fluid dynamics equations. This behavior has sometimes been associated with the loss of diagonal dominance of the coefficient matrix. It is shown that these problems can be related to the choice of the spatial differences, with the resulting instability related to aliasing or nonlinear interaction. Appropriate filtering can reduce the intensity of these oscillations and possibly eliminate the instability. These filtering procedures are equivalent to a weighted average of conservation and nonconservation differencing. The entire spectrum of filtered equations retains a three point character as well as second order spatial accuracy. Burgers equation was considered as a model.

Khosla, P. K.↗

NASA NTRS1979

Filtering of non-linear instabilities

For Courant numbers larger than one and cell Reynolds numbers larger than two, oscillations and in some cases instabilities are typically found with implicit numerical solutions of the fluid dynamics equations. This behavior has sometimes been associated with the loss of diagonal dominance of the coefficient matrix. It is shown here that these problems can in fact be related to the choice of the spatial differences, with the resulting instability related to aliasing or nonlinear interaction. Appropriate 'filtering' can reduce the intensity of these oscillations and in some cases possibly eliminate the instability. These filtering procedures are equivalent to a weighted average of conservation and non-conservation differencing. The entire spectrum of filtered equations retains a three-point character as well as second-order spatial accuracy. Burgers equation has been considered as a model. Several filters are examined in detail, and smooth solutions have been obtained for extremely large cell Reynolds numbers.

Khosla, P. K.↗

NASA NTRS1986

Report on the feasibility of hypercube concurrent processing systems in computational fluid dynamics

The feasibility of using hypercube-connected concurrent processor systems for problems in computational fluid dynamics is studied. Both explicit and implicit numerical methods are considered and several alternative implementations of these methods are evaluated on concurrent processor systems. A Lax-Wendroff explicit method was designed and implemented for the Navier-Stokes equations. The code runs on the Intel iPSC concurrent processor system. Tests of this code show that it is reasonably efficient. The Beam and Warming implicit factored method was designed and implemented for Berger's equation. Preliminary tests show that the efficiency of code is poor.

Bruno, J.↗

NASA NTRS1990

Computation of thermochemical nonequilibrium flows around a simple and a double ellipse

The nonequilibrium viscous reactive flows over a simple and a double ellipse at a 30 degree angle of attack were computed. The geometry and the free stream conditions are given by INRIA/GAMNI/SMAI workshop test cases 6.2-2 and 6.2-4. The governing Navier-Stokes equations coupled with thermochemical nonequilibrium processes are solved numerically using a fully coupled, implicit, finite volume technique with a dynamically adaptive grid. The nonequilibrium gas model and the numerical method used in the calculations are briefly described.

Gokcen, Tahir↗

NASA NTRS1992

A pressure correction method for the calculation of compressible chemical reacting flows

A recently developed noniterative method for the solution of the transient fluid flow equations at all speed is extended to handle chemical reacting flows. The species conservation equations are loosely coupled into the predictor/multicorrector sequence of the solution procedure. A split-operator method separates the chemical kinetics terms from the fluid-dynamical terms, as well as an implicit differencing method enhance the numerical stability. The method was applied for turbulent diffusion flame calculations and for the analyses of high pressure, axisymmetric turbulent hypersonic nozzle flows. The diffusion flame results were compared with a similar pressure method for fast chemistry integration scheme without operator-splitting. Simulations of the nozzle flow indicated that the nonideal intermolecular effects must be included in the analysis and design of high pressure hypersonic nozzle.

Chen, Z. J.↗

NASA NTRS1991

Computation of thermochemical nonequilibrium flows around a simple and a double ellipse

Gokcen, Tahir↗

NASA NTRS1993

Numerical study of shock-induced combustion in methane-air mixtures

The shock-induced combustion of methane-air mixtures in hypersonic flows is investigated using a new reaction mechanism consisting of 19 reacting species and 52 elementary reactions. This reduced model is derived from a full kinetic mechanism via the Detailed Reduction technique. Zero-dimensional computations of several shock-tube experiments are presented first. The reaction mechanism is then combined with a fully implicit Navier-Stokes computational fluid dynamics (CFD) code to conduct numerical simulations of two-dimensional and axisymmetric shock-induced combustion experiments of stoichiometric methane-air mixtures at a Mach number of M = 6.61. Applications to the ram accelerator concept are also presented.

Yungster, Shaye↗

NASA NTRS1993

Numerical simulation of steady and unsteady viscous flow in turbomachinery using pressure based algorithm

The objective of this research is to simulate steady and unsteady viscous flows, including rotor/stator interaction and tip clearance effects in turbomachinery. The numerical formulation for steady flow developed here includes an efficient grid generation scheme, particularly suited to computational grids for the analysis of turbulent turbomachinery flows and tip clearance flows, and a semi-implicit, pressure-based computational fluid dynamics scheme that directly includes artificial dissipation, and is applicable to both viscous and inviscid flows. The values of these artificial dissipation is optimized to achieve accuracy and convergency in the solution. The numerical model is used to investigate the structure of tip clearance flows in a turbine nozzle. The structure of leakage flow is captured accurately, including blade-to-blade variation of all three velocity components, pitch and yaw angles, losses and blade static pressures in the tip clearance region. The simulation also includes evaluation of such quantities of leakage mass flow, vortex strength, losses, dominant leakage flow regions and the spanwise extent affected by the leakage flow. It is demonstrated, through optimization of grid size and artificial dissipation, that the tip clearance flow field can be captured accurately. The above numerical formulation was modified to incorporate time accurate solutions. An inner loop iteration scheme is used at each time step to account for the non-linear effects. The computation of unsteady flow through a flat plate cascade subjected to a transverse gust reveals that the choice of grid spacing and the amount of artificial dissipation is critical for accurate prediction of unsteady phenomena. The rotor-stator interaction problem is simulated by starting the computation upstream of the stator, and the upstream rotor wake is specified from the experimental data. The results show that the stator potential effects have appreciable influence on the upstream rotor wake. The predicted unsteady wake profiles are compared with the available experimental data and the agreement is good. The numerical results are interpreted to draw conclusions on the unsteady wake transport mechanism in the blade passage.

Lakshminarayana, B.↗

NASA NTRS1995

Implicit schemes and parallel computing in unstructured grid CFD

The development of implicit schemes for obtaining steady state solutions to the Euler and Navier-Stokes equations on unstructured grids is outlined. Applications are presented that compare the convergence characteristics of various implicit methods. Next, the development of explicit and implicit schemes to compute unsteady flows on unstructured grids is discussed. Next, the issues involved in parallelizing finite volume schemes on unstructured meshes in an MIMD (multiple instruction/multiple data stream) fashion are outlined. Techniques for partitioning unstructured grids among processors and for extracting parallelism in explicit and implicit solvers are discussed. Finally, some dynamic load balancing ideas, which are useful in adaptive transient computations, are presented.

Venkatakrishnam, V.↗

NASA NTRS1998

Thermal Infrared Remote Sensing for Analysis of Landscape Ecological Processes: Methods and Applications

Thermal Infrared (TIR) remote sensing data can provide important measurements of surface energy fluxes and temperatures, which are integral to understanding landscape processes and responses. One example of this is the successful application of TIR remote sensing data to estimate evapotranspiration and soil moisture, where results from a number of studies suggest that satellite-based measurements from TIR remote sensing data can lead to more accurate regional-scale estimates of daily evapotranspiration. With further refinement in analytical techniques and models, the use of TIR data from airborne and satellite sensors could be very useful for parameterizing surface moisture conditions and developing better simulations of landscape energy exchange over a variety of conditions and space and time scales. Thus, TIR remote sensing data can significantly contribute to the observation, measurement, and analysis of energy balance characteristics (i.e., the fluxes and redistribution of thermal energy within and across the land surface) as an implicit and important aspect of landscape dynamics and landscape functioning. The application of TIR remote sensing data in landscape ecological studies has been limited, however, for several fundamental reasons that relate primarily to the perceived difficulty in use and availability of these data by the landscape ecology community, and from the fragmentation of references on TIR remote sensing throughout the scientific literature. It is our purpose here to provide evidence from work that has employed TIR remote sensing for analysis of landscape characteristics to illustrate how these data can provide important data for the improved measurement of landscape energy response and energy flux relationships. We examine the direct or indirect use of TIR remote sensing data to analyze landscape biophysical characteristics, thereby offering some insight on how these data can be used more robustly to further the understanding and modeling of landscape ecological processes.

Quattrochi, Dale A.↗