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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Numerical study of hydrogen-air supersonic combustion by using elliptic and parabolized equations

The two-dimensional Navier-Stokes and species continuity equations are used to investigate supersonic chemically reacting flow problems which are related to scramjet-engine configurations. A global two-step finite-rate chemistry model is employed to represent the hydrogen-air combustion in the flow. An algebraic turbulent model is adopted for turbulent flow calculations. The explicit unsplit MacCormack finite-difference algorithm is used to develop a computer program suitable for a vector processing computer. The computer program developed is then used to integrate the system of the governing equations in time until convergence is attained. The chemistry source terms in the species continuity equations are evaluated implicitly to alleviate stiffness associated with fast chemical reactions. The problems solved by the elliptic code are re-investigated by using a set of two-dimensional parabolized Navier-Stokes and species equations. A linearized fully-coupled fully-implicit finite difference algorithm is used to develop a second computer code which solves the governing equations by marching in spce rather than time, resulting in a considerable saving in computer resources. Results obtained by using the parabolized formulation are compared with the results obtained by using the fully-elliptic equations. The comparisons indicate fairly good agreement of the results of the two formulations.

Chitsomboon, T.↗
NASA NTRS1991

Computations of the three-dimensional flow and heat transfer within a coolant passage of a radial turbine blade

A numerical code is developed for computing three-dimensional, turbulent, compressible flow within coolant passages of turbine blades. The code is based on a formulation of the compressible Navier-Stokes equations in a rotating frame of reference in which the velocity dependent variable is specified with respect to the rotating frame instead of the inertial frame. The algorithm employed to obtain solutions to the governing equation is a finite-volume LU algorithm that allows convection, source, as well as diffusion terms to be treated implicitly. In this study, all convection terms are upwind differenced by using flux-vector splitting, and all diffusion terms are centrally differenced. This paper describes the formulation and algorithm employed in the code. Some computed solutions for the flow within a coolant passage of a radial turbine are also presented.

Shih, T. I.-P.↗
NASA NTRS1996

The study of flow pattern and phase-change problem in die casting process

The flow pattern and solidification phenomena in die casting process have been investigated in the first phase study. The flow pattern in filling process is predicted by using a VOF (volume of fluid) method. A good agreement with experimental observation is obtained for filling the water into a die cavity with different gate geometry and with an obstacle in the cavity. An enthalpy method has been applied to solve the solidification problem. By treating the latent heat implicitly into the enthalpy instead of explicitly into the source term, the CPU time can be reduced at least 20 times. The effect of material properties on solidification fronts is tested. It concludes that the dependence of properties on temperature is significant. The influence of the natural convection over the diffusion has also been studied. The result shows that the liquid metal solidification phenomena is diffusion dominant, and the natural convection can affect the shape of the interface. In the second phase study, the filling and solidification processes will be considered simultaneously.

Wang, T. S.↗
NASA NTRS1993

Upwind MacCormack Euler solver with non-equilibrium chemistry

A computer code, designated UMPIRE, is currently under development to solve the Euler equations in two dimensions with non-equilibrium chemistry. UMPIRE employs an explicit MacCormack algorithm with dissipation introduced via Roe's flux-difference split upwind method. The code also has the capability to employ a point-implicit methodology for flows where stiffness is introduced through the chemical source term. A technique consisting of diagonal sweeps across the computational domain from each corner is presented, which is used to reduce storage and execution requirements. Results depicting one dimensional shock tube flow for both calorically perfect gas and thermally perfect, dissociating nitrogen are presented to verify current capabilities of the program. Also, computational results from a chemical reactor vessel with no fluid dynamic effects are presented to check the chemistry capability and to verify the point implicit strategy.

Sherer, Scott E.↗
NASA NTRS1992

Numerical modeling of fluid and electromagnetic phenomena in an arcjet

An explicit numerical technique is used to solve the axisymmetric reduced electromagnetic field equation. The effect of an electrical arc on a viscous, axisymmetric flow is approximated using an implicit thin layer Navier-Stokes solver with additional electromagnetic source terms in conjunction with the explicit finite difference code.

Flowe, Anita C.↗
NASA NTRS1993

Investigation of high-speed free shear flows using improved pressure-strain correlated Reynolds stress turbulence model

A high-speed shear layer is studied using compressibility corrected Reynolds stress turbulence model which employs newly developed model for pressure-strain correlation. MacCormack explicit prediction-corrector method is used for solving the governing equations and the turbulence transport equations. The stiffness arising due to source terms in the turbulence equations is handled by a semi-implicit numerical technique. Results obtained using the new model show a sharper reduction in growth rate with increasing convective Mach number. Some improvements were also noted in the prediction of the normalized streamwise stress and Reynolds shear stress. The computed results are in good agreement with the experimental data.

Tiwari, S. N.↗
NASA NTRS1988

A study of numerical methods for hyperbolic conservation laws with stiff source terms

The proper modeling of nonequilibrium gas dynamics is required in certain regimes of hypersonic flow. For inviscid flow this gives a system of conservation laws coupled with source terms representing the chemistry. Often a wide range of time scales is present in the problem, leading to numerical difficulties as in stiff systems of ordinary differential equations. Stability can be achieved by using implicit methods, but other numerical difficulties are observed. The behavior of typical numerical methods on a simple advection equation with a parameter-dependent source term was studied. Two approaches to incorporate the source term were utilized: MacCormack type predictor-corrector methods with flux limiters, and splitting methods in which the fluid dynamics and chemistry are handled in separate steps. Various comparisons over a wide range of parameter values were made. In the stiff case where the solution contains discontinuities, incorrect numerical propagation speeds are observed with all of the methods considered. This phenomenon is studied and explained.

Leveque, R. J.↗
NASA NTRS1984

Computation of viscous flow in planar and axisymmetric ducts by an implicit marching procedure

A streamwise marching procedure, approximately 200 times faster than a full Navier-Stokes procedure with comparable accuracy, is presented for solving problems of compressible viscous subsonic flow. Results are presented and compared with experimental data for the cases of developing turbulent flow in a circular pipe; turbulent flow in a two-dimensional S-duct; and turbulent flow in a typical subsonic diffuser. Prior to each main marching step, a preliminary marching step is taken in which the integral continuity equation and an uncoupled form of the streamwise momentum equation are solved simultaneously to obtain the viscous pressure correction. During the main marching step the equations for continuity, streamwise momentum, cross-flow momentum, and energy are solved simultaneously as a coupled system using an implicit finite-difference method, with the viscous pressure correction treated as a source term. The analysis may be used for flows with both favorable and adverse pressure gradients and to predict the location of flow separation.

Towne, C. E.↗
NASA NTRS1993

Flux-difference split parabolized Navier-Stokes algorithm for non-equilibrium chemically reacting flows

A flux-difference split explicit finite-difference algorithm is presented for solving the parabolized form of the equations governing three-dimensional nonequilibrium chemically reacting flows. The algorithm is based on an explicit noniterative, upwind space-marching scheme developed by Korte, but differs in that the unsteady Riemann problem, rather than the steady Riemann problem, is solved. The algorithm allows either a second or an approximately third-order accurate upwind treatment of the convection terms by employing the unsteady approximate Riemann solver of Roe. The source terms of the species transport equations are treated in either an explicit or implicit manner, and the species diffusion terms are modeled with either a Fickian or a multicomponent model. A validation of the algorithm is performed by comparing computational results with the 2-D Mach 14, 15 degree compression-corner data of Holden. The three-dimensional capability of the algorithm is demonstrated by computing Mach 2.7 flow over a swept wedge scramjet fuel injector, and three-dimensional reacting flow capability is demonstrated by a computing a shock-jet interaction concept for mixing and combustion enhancement.

White, J. A.↗
NASA NTRS2011

Conjugate Compressible Fluid Flow and Heat Transfer in Ducts

A computational approach to modeling transient, compressible fluid flow with heat transfer in long, narrow ducts is presented. The primary application of the model is for analyzing fluid flow and heat transfer in solid propellant rocket motor nozzle joints during motor start-up, but the approach is relevant to a wide range of analyses involving rapid pressurization and filling of ducts. Fluid flow is modeled through solution of the spatially one-dimensional, transient Euler equations. Source terms are included in the governing equations to account for the effects of wall friction and heat transfer. The equation solver is fully-implicit, thus providing greater flexibility than an explicit solver. This approach allows for resolution of pressure wave effects on the flow as well as for fast calculation of the steady-state solution when a quasi-steady approach is sufficient. Solution of the one-dimensional Euler equations with source terms significantly reduces computational run times compared to general purpose computational fluid dynamics packages solving the Navier-Stokes equations with resolved boundary layers. In addition, conjugate heat transfer is more readily implemented using the approach described in this paper than with most general purpose computational fluid dynamics packages. The compressible flow code has been integrated with a transient heat transfer solver to analyze heat transfer between the fluid and surrounding structure. Conjugate fluid flow and heat transfer solutions are presented. The author is unaware of any previous work available in the open literature which uses the same approach described in this paper.

Cross, M. F.↗
NASA NTRS2016

Assessment of Preconditioner for a USM3D Hierarchical Adaptive Nonlinear Method (HANIM) (Invited)

Enhancements to the previously reported mixed-element USM3D Hierarchical Adaptive Nonlinear Iteration Method (HANIM) framework have been made to further improve robustness, efficiency, and accuracy of computational fluid dynamic simulations. The key enhancements include a multi-color line-implicit preconditioner, a discretely consistent symmetry boundary condition, and a line-mapping method for the turbulence source term discretization. The USM3D iterative convergence for the turbulent flows is assessed on four configurations. The configurations include a two-dimensional (2D) bump-in-channel, the 2D NACA 0012 airfoil, a three-dimensional (3D) bump-in-channel, and a 3D hemisphere cylinder. The Reynolds Averaged Navier Stokes (RANS) solutions have been obtained using a Spalart-Allmaras turbulence model and families of uniformly refined nested grids. Two types of HANIM solutions using line- and point-implicit preconditioners have been computed. Additional solutions using the point-implicit preconditioner alone (PA) method that broadly represents the baseline solver technology have also been computed. The line-implicit HANIM shows superior iterative convergence in most cases with progressively increasing benefits on finer grids.

Pandya, Mohagna J.↗
NASA NTRS1991

Computational aspects of chemically reacting flows

An implicit, time-dependent approach is taken to solve the inviscid conservative equations in a vertex-based finite-volume formulation. The convective fluxes are estimated by a modified Riemann solver, and higher-order accuracy is obtained by means of the MUSCL. Implicit techniques are adopted to deal with the equation stiffness as a result of the clustered grid and chemical source term. The real-gas Roe matrix and the ADI and LU schemes have been tested on the sample problems: hypersonic flow over blunt configurations, such as the forebody of a double ellipse, and the near wake of a conic aerobrake. Temperature distribution and standoff distance are validated against the shock-fitting, central-differencing results. Equilibrium temperature may be recovered by artificially increasing the chemical rates at the wall. The present method satisfactorily resolves the flow structure, including the strong expansion behind the flat base. The relative merits and performance of the real-gas TVD and implicit schemes are discussed briefly.

Li, C. P.↗
NASA NTRS1997

Computation of Reacting Flows in Combustion Processes

The main objective of this research was to develop an efficient three-dimensional computer code for chemically reacting flows. The main computer code developed is ALLSPD-3D. The ALLSPD-3D computer program is developed for the calculation of three-dimensional, chemically reacting flows with sprays. The ALL-SPD code employs a coupled, strongly implicit solution procedure for turbulent spray combustion flows. A stochastic droplet model and an efficient method for treatment of the spray source terms in the gas-phase equations are used to calculate the evaporating liquid sprays. The chemistry treatment in the code is general enough that an arbitrary number of reaction and species can be defined by the users. Also, it is written in generalized curvilinear coordinates with both multi-block and flexible internal blockage capabilities to handle complex geometries. In addition, for general industrial combustion applications, the code provides both dilution and transpiration cooling capabilities. The ALLSPD algorithm, which employs the preconditioning and eigenvalue rescaling techniques, is capable of providing efficient solution for flows with a wide range of Mach numbers. Although written for three-dimensional flows in general, the code can be used for two-dimensional and axisymmetric flow computations as well. The code is written in such a way that it can be run in various computer platforms (supercomputers, workstations and parallel processors) and the GUI (Graphical User Interface) should provide a user-friendly tool in setting up and running the code.

Keith, Theo G., Jr.↗
NASA NTRS2014

High-Order Residual-Distribution Hyperbolic Advection-Diffusion Schemes: 3rd-, 4th-, and 6th-Order

In this paper, spatially high-order Residual-Distribution (RD) schemes using the first-order hyperbolic system method are proposed for general time-dependent advection-diffusion problems. The corresponding second-order time-dependent hyperbolic advection- diffusion scheme was first introduced in [NASA/TM-2014-218175, 2014], where rapid convergences over each physical time step, with typically less than five Newton iterations, were shown. In that method, the time-dependent hyperbolic advection-diffusion system (linear and nonlinear) was discretized by the second-order upwind RD scheme in a unified manner, and the system of implicit-residual-equations was solved efficiently by Newton's method over every physical time step. In this paper, two techniques for the source term discretization are proposed; 1) reformulation of the source terms with their divergence forms, and 2) correction to the trapezoidal rule for the source term discretization. Third-, fourth, and sixth-order RD schemes are then proposed with the above techniques that, relative to the second-order RD scheme, only cost the evaluation of either the first derivative or both the first and the second derivatives of the source terms. A special fourth-order RD scheme is also proposed that is even less computationally expensive than the third-order RD schemes. The second-order Jacobian formulation was used for all the proposed high-order schemes. The numerical results are then presented for both steady and time-dependent linear and nonlinear advection-diffusion problems. It is shown that these newly developed high-order RD schemes are remarkably efficient and capable of producing the solutions and the gradients to the same order of accuracy of the proposed RD schemes with rapid convergence over each physical time step, typically less than ten Newton iterations.

Mazaheri, Alireza R.↗
NASA NTRS1987

Extension of a semi-implicit shock-capturing algorithm for 3-D fully coupled, chemically reacting flows in generalized coordinates

A semiimplicit high-resolution shock-capturing method for multidimensional systems of hyperbolic conservation laws with stiff source terms has been developed by Yee and Shinn (1987). The goal of this work is to extend this method to solve the three-dimensional fully coupled Navier-Stokes equations for a hypersonic chemically reacting flow in generalized coordinates. In this formulation, the global continuity equation was replaced by all the species continuity equations. The shock-capturing technique is a second-order-accurate, symmetric total-variation-diminishing method which accounts fully and directly for the coupling among the fluid and all the species. To verify the current approach, it was implemented into an existing computer code which contained the MacCormack method. Test results for a five-species reacting flow are shown to be oscillation-free around the shock, and the time spent per iteration only doubles when compared to the result using classical way of supplying numerical dissipation. The extra computation is more than justified by the elimination of spurious oscillation and nonlinear instability associated with the classical shock-capturing schemes in computing hypersonic reacting flows.

Shinn, J. L.↗
NASA NTRS1983

A viscous shock-layer flowfield analysis by an explicit-implicit method

An implicit analogue of a widely used explicit method to external axisymmetric laminar flows with strong entropy gradients is extended. The details of the "numerics" of the implicit part are provided in a body oriented coordinate system with a moving outer (shock) boundary during the transient part of the solutions. The limiting values of the Courant number are obtained when the shock boundary is treated explicitly. The solution algorithm outlined includes the treatment of the source term associated with the equations in weak conservation form. From the results obtained for two sample problems, it becomes clear that accuracy of predictions is, indeed, very good at higher values of the Courant number. There is a significant saving in overall computing time, depending on the Courant number used and the flow Reynolds number. These properties combined with the simplicity of programming the implicit analog may appeal to researchers for using it in the analysis of 3-D flow problems.

Gupta, R. M.↗
NASA NTRS1983

Viscous shock-layer flowfield analysis by an explicit-implicit method

The present work extends the recently reported implicit analogue of MacCormack's earlier widely-used explicit method to external axisymmetric laminar flows with strong entropy gradients. The details of the 'numerics' of the implicit part are provided in a body-oriented coordinate system with a moving outer (shock) boundary during the transient part of the solutions. The limiting values of the Courant number are obtained when the shock boundary is treated explicitly. The solution algorithm outlined includes the treatment of the source term associated with the equations in weak conservation form. From the results obtained for two sample problems, it becomes clear that accuracy of predictions is, indeed, very good at higher values of the Courant number. There is a significant saving in overall computing time, depending on the Courant number used and the flow Reynolds number. These properties combined with the simplicity of programming the implicit analogue may appeal to researchers for using it in the analysis of three-dimensional flow problems.

Gupta, R. N.↗
NASA NTRS1997

Incompressible Navier-Stokes Computations for the Development of a Ventricular Assist Device

An incompressible flow analysis code, INS3D, has been applied to the development of a mechanical heart assist device. The solution method is based on the artificial compressibility approach and uses an implicit-upwind differencing scheme together with a Gauss-Seidel line relaxation method. The equations are solved in steadily rotating reference frames and the centrifugal and the Coriolis force terms are included as source terms. The resulting computational procedure is validated for liquid rocket engine analysis and applied subsequently to analyze a Ventricular Assist Device (VAD). A new design configuration is developed which includes an inducer upstream of the impeller main blades, and substantial improvement is observed in the performance of the VAD.

Kiris, Cetin↗