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At least 523 records · Page 29

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NASA NTRS1981

Model verification studies using accurate measurements of spin up

The reliability and accuracy of the numerical code for spin up flows in a cylinder by comparing the numerical results against high resolution laser Doppler velocimeter (LDV) measurements of the azimuthal flows were checked. A computer code to generate numerical solution for axisymmetric rotating fluid in a cylinder was obtained and amended for routine use at MSFC. The numerical simulations used the Navier-Stokes equations in axisymmetric form and employed finite difference techniques on both constant and variable grids. The numerical solutions are analyzed to gain further insight into the fundamental questions analyzed in rotating fluid dynamics.

Hyun, J. M.↗

DOE OSTI2024

Tensor Network Space-Time Spectral Collocation Method for Time-Dependent Convection-Diffusion-Reaction Equations

Emerging tensor network techniques for solutions of partial differential equations (PDEs), known for their ability to break the curse of dimensionality, deliver new mathematical methods for ultra-fast numerical solutions of high-dimensional problems. Here, we introduce a Tensor Train (TT) Chebyshev spectral collocation method, in both space and time, for the solution of the time-dependent convection-diffusion-reaction (CDR) equation with inhomogeneous boundary conditions, in Cartesian geometry. Previous methods for numerical solution of time-dependent PDEs often used finite difference for time, and a spectral scheme for the spatial dimensions, which led to a slow linear convergence. Spectral collocation space-time methods show exponential convergence; however, for realistic problems they need to solve large four-dimensional systems. We overcome this difficulty by using a TT approach, as its complexity only grows linearly with the number of dimensions. We show that our TT space-time Chebyshev spectral collocation method converges exponentially, when the solution of the CDR is smooth, and demonstrate that it leads to a very high compression of linear operators from terabytes to kilobytes in TT-format, and a speedup of tens of thousands of times when compared to a full-grid space-time spectral method. These advantages allow us to obtain the solutions at much higher resolutions.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1994

Approximate Solution Methods for Spectral Radiative Transfer in High Refractive Index Layers

Some ceramic materials for high temperature applications are partially transparent for radiative transfer. The refractive indices of these materials can be substantially greater than one which influences internal radiative emission and reflections. Heat transfer behavior of single and laminated layers has been obtained in the literature by numerical solutions of the radiative transfer equations coupled with heat conduction and heating at the boundaries by convection and radiation. Two-flux and diffusion methods are investigated here to obtain approximate solutions using a simpler formulation than required for exact numerical solutions. Isotropic scattering is included. The two-flux method for a single layer yields excellent results for gray and two band spectral calculations. The diffusion method yields a good approximation for spectral behavior in laminated multiple layers if the overall optical thickness is larger than about ten. A hybrid spectral model is developed using the two-flux method in the optically thin bands, and radiative diffusion in bands that are optically thick.

Siegel, R.↗

DOE OSTI2021

Solution Irregularity Remediation for Spatial Discretization Error Estimation for S N Transport Solutions

The discrete ordinates linear Boltzmann transport equation is typically solved in its spatially discretized form, incurring spatial discretization error. Quantification of this error for purposes such as adaptive mesh refinement or error analysis requires an a posteriori estimator, which utilizes the numerical solution to the spatially discretized equation to compute an estimate. Because the quality of the numerical solution informs the error estimate, irregularities, present in the true solution for any realistic problem configuration, tend to cause the largest deviation in the error estimate vis-a-vis the true error. In this paper, an analytical partial singular characteristic tracking (pSCT) procedure for reducing the estimator’s error is implemented within our novel residual source estimator for a zeroth-order discontinuous Galerkin scheme, at the additional cost of a single inner iteration. Here, a metric-based evaluation of the pSCT scheme versus the standard residual source estimator is performed over the parameter range of a Method of Manufactured Solutions test suite. The pSCT scheme generates near-ideal accuracy in the estimate in problems where the dominant source of the estimator’s error is the solution irregularity, namely, problems where the true solution is discontinuous and problems where the true solution’s first derivative is discontinuous and the scattering ratio is low. In problems where the scattering ratio is high and the true solution is discontinuous in the first derivative, the error in the scattering source, which is not converged by the pSCT scheme, is greater than the error incurred due to the irregularity. Ultimately, a pSCT scheme is judged to be useful for error estimation in problems where the computational cost of the scheme is justified. In the presence of many irregularities, such a scheme may be intractable for general use, but in benchmarks, as an analytical tool, or in problems that have nondissipative discontinuities, the scheme may prove invaluable.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1981

Transient dynamic analysis of high-speed lightly loaded cylindrical roller bearings. 2: Computer program and results

The governing differential equations of motion for a high speed cylindrical roller bearing are programmed for numerical solution and plotted output. This computer program has the capability of performing a two dimensional or three dimensional simulation. Two numerical solutions of the governing differential equations were obtained to simulate the motion of a roller bearing, one for the two dimensional equations of motion and one for the three dimensional equations of motion. Computer generated plots were obtained and present such data as roller/cage interaction forces, roller/race traction forces, roller/race relative slip velocities and cage angular speed over a nondimensional time equivalent to 1.2 revolutions of the inner race. Roller axial displacement, roller skew angle, and skew moment are also plotted for the three dimensional solution. The trajectory of the cage center is plotted for both the two dimensional and three dimensional solutions.

Conry, T. F.↗

NASA NTRS1991

Navier-Stokes analysis of turbomachinery blade external heat transfer

The two-dimensional, compressible, thin-layer Navier-Stokes and energy equations were solved numerically to obtain heat transfer rates on turbomachinery blades. The Baldwin-Lomax algebraic model and the q-omega low Reynolds number two-equation model were used for modeling of turbulence. For the numerical solution of the governing equations a four-stage Runge-Kutta solver was employed. The turbulence model equations were solved using an implicit scheme. Numerical solutions are presented for two-dimensional flow within two vane cascades. The heat transfer results and the pressure distributions were compared with published experimental data. The agreement between the numerical calculations and the experimental values were found to be generally favorable. The position of transition from laminar to turbulent flow was also predicted accurately.

Gorla, Rama S. R.↗

NASA NTRS1992

Navier-Stokes analysis of turbomachinery blade external heat transfer

The two-dimensional, compressible, thin-layer Navier-Stokes and energy equations were solved numerically to obtain heat transfer rates on turbomachinery blades. The Baldwin-Lomax algebraic model and the q - omega low Reynolds number, two-equation model were used for modeling of turbulence. For the numerical solution of the governing equations a four-stage Runge-Kutta solver was employed. The turbulence model equations were solved using an implicit scheme. Numerical solutions are presented for two-dimensional flow within two vane cascades. The heat transfer results and the pressure distributions were compared with published experimental data. The agreement between the numerical calculations and the experimental values were found to be generally favorable. The position of transition from laminar to turbulent flow was also predicted accurately.

Ameri, A. A.↗

NASA NTRS1995

On the Nonlinear Evolution of a Stationary Cross-Flow Vortex in a Fully Three-Dimensional Boundary Layer Flow

We consider the nonlinear stability of a fully three-dimensional boundary layer flow in an incompressible fluid and derive an equation governing the nonlinear development of a stationary cross-flow vortex. The amplitude equation is a novel integro-differential equation which has spatial derivatives of the amplitude occurring in the kernal function. It is shown that the evolution of the cross-flow vortex is strongly coupled to the properties of an unsteady wall layer which is in fact driven by an unknown slip velocity, proportional to the amplitude of the cross-flow vortex. The work is extended to obtain the corresponding equation for rotating disk flow. A number of special cases are examined and the numerical solution for one of cases, and further analysis, demonstrates the existence of finite-distance as well as focussing type singularities. The numerical solutions also indicate the presence of a new type of nonlinear wave solution for a certain set of parameter values.

Gajjar, J. S. B.↗

NASA NTRS1992

Upwind schemes and bifurcating solutions in real gas computations

The area of high speed flow is seeing a renewed interest due to advanced propulsion concepts such as the National Aerospace Plane (NASP), Space Shuttle, and future civil transport concepts. Upwind schemes to solve such flows have become increasingly popular in the last decade due to their excellent shock capturing properties. In the first part of this paper the authors present the extension of the Osher scheme to equilibrium and non-equilibrium gases. For simplicity, the source terms are treated explicitly. Computations based on the above scheme are presented to demonstrate the feasibility, accuracy and efficiency of the proposed scheme. One of the test problems is a Chapman-Jouguet detonation problem for which numerical solutions have been known to bifurcate into spurious weak detonation solutions on coarse grids. Results indicate that the numerical solution obtained depends both on the upwinding scheme used and the limiter employed to obtain second order accuracy. For example, the Osher scheme gives the correct CJ solution when the super-bee limiter is used, but gives the spurious solution when the Van Leer limiter is used. With the Roe scheme the spurious solution is obtained for all limiters.

Suresh, Ambady↗

NASA NTRS1991

Derivative interface conditions for multiblock grids

Methods are developed for computing numerical solutions along block boundaries, even when there is a discontinuity in the grid lines or slopes. The technique is based on matching derivatives and does not require overlapping and interpolation of solution values at block boundaries. The comparison of block boundary values is implicit and has proven to be stable for both implicit and explicit numerical algorithms. Examples are included for the numerical solution of the Euler equations for compressible flow on grids with both grid line discontinuities and discontinuous slopes at block boundaries.

Mastin, C. W.↗

DOE OSTI2021

Fast multiscale contrast independent preconditioners for linear elastic topology optimization problems

The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an adjoint analysis, which requires the numerical solution of large high-contrast linear elastic problems with features spanning several length scales. The size of the discretized problems forces the utilization of iterative linear solvers with solution time dependent on the quality of the preconditioner. The lack of clear separation between the scales, as well as the high-contrast, imposes severe challenges on the standard preconditioning techniques. Thus, here we propose new methods for the high-contrast elasticity equation with performance independent of the high-contrast and the multi-scale structure of the elasticity problem. The solvers are based on two-levels domain decomposition techniques with a carefully constructed coarse level to deal with the high-contrast and multi-scale nature of the problem. The construction utilizes spectral equivalence between scalar diffusion and each displacement block of the elasticity problems and, in contrast to previous solutions proposed in the literature, is able to select the appropriate dimension of the coarse space automatically. The new methods inherit the advantages of domain decomposition techniques, such as easy parallelization and scalability. Finally, the presented numerical experiments demonstrate the excellent performance of the proposed methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Optimal Droop Setting for Congestion Reduction in a 100% Grid-Forming Inverter-based Power System

he high penetration of inverter-based resources (IBRs) introduces new challenges to power systems due to the complex inverter control. However, IBRs can be configured to maximize their benefits to improve system resilience and reliability. This paper proposes a steady-state optimization model that aims to mitigate transmission congestion in a 100% grid- forming (GFM) IBR-based power system. This goal is achieved by determining the optimal droop settings for the GFM IBRs under different congestion conditions due to renewable energy and load variations. The numerical solution is rigorously verified by a high-fidelity model of the IEEE 39-bus test system with detailed GFM IBR control in the time-domain electromagnetic transient (EMT) simulation tool PSCAD. The numerical solution and simulation results show a significant congestion reduction while meeting all other operating requirements. It is also observed that the numerical solving time is substantially less compared to the EMT simulation time.

Nguyen, Quan H.↗

NASA NTRS1976

A higher order panel method for general analysis and design applications in subsonic flow

A higher-order panel method is described for numerical solution of boundary-value problems relating to steady inviscid irrotational incompressible subsonic fluid flow in a domain. Both Neumann and Dirichlet boundary conditions are treated; two types of auxiliary conditions are used to remove the degrees of freedom that arise from specifying only the derivative of the perturbation velocity potential. Four general network types and two expansions of the induced potential kernel are employed in the numerical solution. Some results are presented which illustrate the modeling options and numerical characteristics of the method.

Johnson, F. T.↗

NASA NTRS1976

Turbulent viscous-shock-layer solutions with strong vorticity interaction

Numerical solutions of the viscous-shock-layer equations governing laminar and turbulent flows of a perfect gas and radiating and nonradiating mixtures of perfect gases in chemical equilibrium are presented for hypersonic flow over spherically blunted cones and hyperboloids. The results are compared with boundary-layer and inviscid flow-field solutions. The agreement with the inviscid flow field data is satisfactory. The agreement with boundary-layer solutions is good except in regions of strong vorticity interaction. In these flow regions, the viscous-shock-layer solutions appear to be more satisfactory than the boundary-layer solutions.

Anderson, E. C.↗

NASA NTRS1987

Euler solver for three-dimensional supersonic flows with subsonic pockets

A new finite-difference scheme has been developed to solve efficiently the unsteady Euler equations for three-dimensional inviscid supersonic flows with subsonic pockets. The technique utilizes planar Gauss-Seidel relaxation in the marching direction and approximate factorization n the crossflow plane. An 'infinitely large' time step is used in parts of the flowfield where the component of velocity in the marching direction is supersonic - here the Gauss-Seidel sweeps are restricted to the forward direction only, and the procedure reduces to simple space-marching; a finite time step is used in parts of the flowfield where the marching component of velocity is subsonic - here, backward and forward Gauss-Seidel sweeps are employed to allow for upstream and downstream propagation of signals, and a time-asymptotic steady state is obtained. The discretization formulas are based on finite-volume implementation of high accuracy (up to third-order) total variation diminishing formulations. Numerical solutions are obtained for an analytically defined forebody, a realistic fighter configuration, and the Space Shuttle. The results are in very good agreement with available experimental data and numerical solutions of the full-potential equation.

Chakravarthy, Sukumar R.↗

NASA NTRS1994

On the Dynamics of Computing a Chemically Relaxed Nonequilibrium Flow

In order to gain insights into the strong dependence of numerical solutions on initial data for finite time steps, a set of nonlinear test problems rich enough to capture the behavior of difference schemes were recently identified and the numerical basins of attraction for these problems were computed using commonly used time discretizations in CFD. Our study revealed a wealth of surprisingly nonlinear behavior of numerical schemes that were not observed before, in particular for the implicit time discretizations that are commonly used in CFD. The goal of this work is to apply these tools to study a practical model from non-equilibrium flowfield relaxation. This type of problem arises in chemically nonequilibrium hypersonic flows such as in a shock tube experiment or an expanding nozzle. Here we consider a reacting mixture of (N2, N) for an inviscid one-dimensional steady model. Preliminary numerical results indicate that, aside from the possibility of spurious numerical solutions being introduced by the time discretizations, limitations on the model for physical or accurate solutions may also play a part in the dynamics observed.

Sweby, P. K.↗

NASA NTRS1991

A numerical study of the direct contact condensation on a horizontal surface

The results of a numerical study of the direct contact condensation on a slowly moving horizontal liquid surface are presented. The geometrical configuration and the input conditions used to obtain numerical solutions are representative to those of experiments of Celata et al. The effects of Prandtl number (Pr), inflow Reynolds number, and Richardson number on the condensation rate are investigated. Numerical predictions of condensation rate for laminar flow are in good agreement with experimental data. The effect of buoyancy on the condensation rate is characterized by Richardson number. A correlation based on the numerical solutions is developed to predict the average condensation Nusselt number in terms of Richardson number, Peclet number, and inflow Reynolds number.

Hasan, M. M.↗

NASA NTRS1991

A numerical study of the direct contact condensation on a horizontal surface

Hasan, M. M.↗