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At least 1,315 records · Page 73

A Newton multigrid method for the Euler equations

A multigrid method is used to apply Newton's method to the Euler equations in a two dimensional curvilinear coordinate system. The objective is to obtain rapid convergence for steady state problems. Solutions computed with the method evolve in a non-time-like manner. Stable pressure distributions typically develop in eight to ten Newton-multigrid steps, which is equivalent to the computational work of about 70 iterations with a factored implicit algorithm.

Childs, R. E.↗

Computational design aspects of a NASP nozzle/afterbody experiment

This paper highlights the influence of computational methods on design of a wind tunnel experiment which generically models the nozzle/afterbody flow field of the proposed National Aerospace Plane. The rectangular slot nozzle plume flow field is computed using a three-dimensional, upwind, implicit Navier-Stokes solver. Freestream Mach numbers of 5.3, 7.3, and 10 are investigated. Two-dimensional parametric studies of various Mach numbers, pressure ratios, and ramp angles are used to help determine model loads and afterbody ramp angle and length. It was found that the center of pressure on the ramp occurs at nearly the same location for all ramp angles and test conditions computed. Also, to prevent air liquefaction, it is suggested that a helium-air mixture be used as the jet gas for the highest Mach number test case.

Ruffin, Stephen M.↗

Numerical experiments on transition control in wall-bounded shear flows

Results are presented from a numerical simulation of transition control in plane channel and boundary layer flows. The analysis is based on a pseudo-spectral/finite difference semi-implicit solution procedure employed to numerically integrate the time-dependent, three-dimensional, incompressible Navier-Stokes equations in a doubly periodic domain. In the channel flow, it was found that the active periodic suction/blowing method was effective in controlling strongly three-dimensional disturbances. In the boundary layer, the preliminary analysis indicated that in the early stages, passive control by suction is as effective as active control to suppress instabilities. The current work is focused on a detailed comparison of active and passive control by suction/blowing in the boundary layer.

Biringen, S.↗

Integral solution of unsteady full-potential equation for a transonic pitching airfoil

The unsteady full-potential equation formulation in a moving frame of reference has been has been developed and used to solve unsteady transonic flow problems. An unsteady integral-equation shock-capturing (IE-SC) scheme has been developed. The resulting unsteady IE-SC scheme is applied to a NACA 0012 airfoil undergoing a pitching oscillation. The numerical results are compared with those of an implicit, approximately factored, finite-volume Euler scheme. The present scheme is efficient in terms of the number of iterations as compared to the other existing schemes, which use finite-difference or finite-volume methods.

Kandil, Osama A.↗

Time-accurate Navier-Stokes calculations with multigrid acceleration

An efficient method for calculating unsteady flows is presented, with emphasis on a modified version of the thin-layer Navier-Stokes equations. Fourier stability analysis is used to illustrate the effect of treating the source term implicitly instead of explicity, as well as to illustrate other algorithmic choices. A 2D circular cylinder (with a Reynolds number of 1200 and a Mach number of 0.3) is calculated. The present scheme requires only about 10 percent of the computer time required by global minimum time stepping.

Melson, N. D.↗

Evaluation of Finite-Rate Gas/Surface Interaction Models for a Carbon Based Ablator

Two sets of finite-rate gas-surface interaction model between air and the carbon surface are studied. The first set is an engineering model with one-way chemical reactions, and the second set is a more detailed model with two-way chemical reactions. These two proposed models intend to cover the carbon surface ablation conditions including the low temperature rate-controlled oxidation, the mid-temperature diffusion-controlled oxidation, and the high temperature sublimation. The prediction of carbon surface recession is achieved by coupling a material thermal response code and a Navier-Stokes flow code. The material thermal response code used in this study is the Two-dimensional Implicit Thermal-response and Ablation Program, which predicts charring material thermal response and shape change on hypersonic space vehicles. The flow code solves the reacting full Navier-Stokes equations using Data Parallel Line Relaxation method. Recession analyses of stagnation tests conducted in NASA Ames Research Center arc-jet facilities with heat fluxes ranging from 45 to 1100 wcm2 are performed and compared with data for model validation. The ablating material used in these arc-jet tests is Phenolic Impregnated Carbon Ablator. Additionally, computational predictions of surface recession and shape change are in good agreement with measurement for arc-jet conditions of Small Probe Reentry Investigation for Thermal Protection System Engineering.

Ablation↗

The OpenSE Cookbook: A Practical, Recipe Based Collection of Patterns, Procedures, and Best Practices for Executable Systems Engineering for the Thirty Meter Telescope

The OpenSE Cookbook is an open-sourced collection of patterns, procedures, and best practices targeted for systems engineers who seek guidance on applying model-based and executable systems engineering (MBSE) using SysML. Its content has emerged from the system level modeling effort on the European Framework Program 6 (FP6) and the Thirty Meter Telescope (TMT). The TMT MBSE approach applied the Executable Systems Engineering Method (ESEM) and the open-source Engineering Environment (OpenMBEE) to specify, analyze, and verify requirements of TMT’s Alignment and Phasing System (APS) and the Narrow Field Infrared Adaptive Optics System (NFIRAOS). In these applications, implicit dependencies are made explicit in a formal model through the use of ESEM, OpenMBEE, and SysML modeling constructs. The value proposition for applying this MBSE approach was to establish precise requirements and fine-grained traceability to system designs, and to verify key requirements beginning early in development. The integration of ESEM and the OpenMBEE tooling infrastructure (providing linked-data and web-operability) is a significant added value for the MBSE approach. The APS is responsible for the overall pre-adaptive optics wavefront quality, using starlight to measure wavefront errors and align the TMT optics. In the formally integrated and executable SysML model, simulations are performed to analyze the impact of changed requirements and verify specified constraints for various operational scenarios. The APS team used several modeling patterns to capture information such as the requirements, the operational scenarios, involved subsystems and their interaction points, the estimated or required time durations, and the mass and power consumption. Adaptive optics systems are designed to sense real-time atmospheric turbulence and correct the telescope’s optical beam to remove its effect. The system model for the adaptive optics operational modes was developed to capture sequence behaviors and operational scenarios to run Monte-Carlo simulations for verifying acquisition time, observing efficiency, and operational behavior requirements. The model is particularly useful for investigating the effect of parallelization, identifying interface issues, and re-ordering sequence acquisition tasks. A former version of the Cookbook (which is now updated to MBSE challenges, goals, and lessons learned) included modeling guidelines and conventions for all system aspects, hierarchy levels, and views, which were developed during for the Active Phasing Experiment (APE), an opto-mechatronical system technology demonstrator for the Extremely Large Telescope (ELT). The Cookbook utilizes the above mentioned system models as real-world case-studies to demonstrate and document the applications of the recipes, providing also instructional examples and addressing the available tooling support. The Cookbook is accompanied by a number of SysML models and aodel libraries which facilitate model authoring and maintenance. The Cookbook covers the different aspects of Systems Engineering such as management of Requirements, Design (behavior and structure), Interfaces, Interdisciplinary Integration, Analysis, Trade Studies, and Technical Resources. This paper presents the background, motivation, architecture, and highlights some key content of the Cookbook. For example, interface management, error budget management, requirements verification, Monte Carlo driven analysis, and timing analysis of operational scenarios. The paper discusses how the capabilities of OpenMBEE contributed significantly to the adoption of executable systems engineering.

Brower, Eric↗

Optimization of Desalination Systems with Detailed Water Chemistry through Integration of Reaktoro in WaterTAP

Chemistry predictions are critical for an accurate estimation of performance and costs in desalination process models, which allows for the estimation of the value of new technologies and the viability of treating new water sources. Herein, we present how an implicit function formulation can be used to integrate the chemical modeling package, Reaktoro, into the techno-economic assessment and modeling platform, WaterTAP. This approach resolves the critical issues of integrating large-scale thermodynamic models and databases into equation-oriented process models while allowing more flexibility relative to previously presented surrogate-based methods. We describe how this integration into Pyomo and WaterTAP models is implemented and used through the open-source package Reaktoro-PSE . We first validate this integration approach by performing optimization on a previously presented desalination treatment train with softening and acid addition as the pretreatment steps. Then, to demonstrate the value of this approach, we extend the cost-optimization problem to include the simultaneous addition of lime and soda ash for softening, and HCl and H 2 SO 4 in the acidification steps. Finally, we were able to confirm the previously established results that were obtained by using surrogate models and demonstrate that the implicit function approach enables exploration of different feedwater compositions and a larger number of chemicals and their combinations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Viscous shock layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium

The viscous shock layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially symmetric flow fields. Solutions are obtained using an implicit finite difference scheme and results are presented for hypersonic flow over spherically blunted cone configurations at free stream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.

Anderson, E. C.↗

A conservative type-dependent full potential method for the treatment of supersonic flows with embedded subsonic regions

A nonlinear method based on the full potential equation in conservation form, cast in an arbitrary coordinate system, has been developed to treat predominantly supersonic flows with embedded subsonic regions. This type of flow field occurs frequently near the fuselage-canopy junction area and wing leading edge regions for a moderately swept fighter configuration. The method uses the theory of characteristics to accurately monitor the type-dependent flow field. A conservative switching scheme is developed to transition from the supersonic marching algorithm to a subsonic relaxation procedure, and vice versa. An implicit approximate factorization scheme is employed to solve the finite-differenced equation. Results are shown for a few configurations, including a wing-body-wake realistic fighter model having embedded subsonic regions.

Shankar, V.↗

A multidomain global modeling technique for analysis of Space Shuttle main engine

A multidomain global modeling technique is presented. The purpose of this multidomain methodology is to simultaneously analyze the three-dimensional compressible flow field in Space Shuttle main engine components. This technique provides flexibility and modularity for individual domain and also simplifies the grid generation task for each domain. A two-way coupling procedure is adopted for exchanging interface boundary conditions. This algorithm which requires that the adjacent domains share an overlapping grid slab, is fully conservative and implicit. For non-matching grid systems and for non-overlapping interfaces, an interpolation and/or extrapolation procedure is used when transferring the interface boundary conditions at the adjacent domains. To maintain overall conservation, a flux correction method is subsequently used. The coupling procedure was verified by modeling several geometries with features similar to SSME components. Satisfactory results for all test cases were obtained. Finally, this algorithm has been applied to the SSME flow simulation.

Tam, L. T.↗

Comparison of Implicit Schemes for the Incompressible Navier-Stokes Equations

For a computational flow simulation tool to be useful in a design environment, it must be very robust and efficient. To develop such a tool for incompressible flow applications, a number of different implicit schemes are compared for several two-dimensional flow problems in the current study. The schemes include Point-Jacobi relaxation, Gauss-Seidel line relaxation, incomplete lower-upper decomposition, and the generalized minimum residual method preconditioned with each of the three other schemes. The efficiency of the schemes is measured in terms of the computing time required to obtain a steady-state solution for the laminar flow over a backward-facing step, the flow over a NACA 4412 airfoil, and the flow over a three-element airfoil using overset grids. The flow solver used in the study is the INS2D code that solves the incompressible Navier-Stokes equations using the method of artificial compressibility and upwind differencing of the convective terms. The results show that the generalized minimum residual method preconditioned with the incomplete lower-upper factorization outperforms all other methods by at least a factor of 2.

Rogers, Stuart E.↗

Mixing of supersonic jets including the effects of supersonic jets including the effects of transverse pressure gradient using difference methods

The usual boundary-layer equations describing the steady-state mixing of parallel jets are supplemented by the momentum equation in the direction normal to the flow. This allows detailed computation of the flow field in the mixing region and simultaneous computation of the outer inviscid flow. An explicit and an implicit finite difference scheme have been developed and applied in several illustrative examples. The examples include mixing of planar and axisymmetric supersonic jets of different composition with both matched and unmatched static pressures. Numerical results were compared with available experimental data obtained for the unmatched pressure case.

Kurkov, A. P.↗

Application of a generalized minimal residual method to 2D unsteady flows

A generalized minimum residual scheme (GMRES), previously developed for solving nonlinear and linear systems of equations, has been applied to the numerical solution of 2D unsteady compressible flows. It is found that the use of GMRES significantly increases the time step that may be used, compared to noniterative implicit schemes. The feasibility of reducing the memory requirements of the GMRES scheme using a multigrid strategy has also been explored. Several sample steady and unsteady viscous flow applications are presented.

Hixon, Ray↗

Application of Contraction Mappings to the Control of Nonlinear Systems

The theoretical and applied aspects of successive approximation techniques are considered for the determination of controls for nonlinear dynamical systems. Particular emphasis is placed upon the methods of contraction mappings and modified contraction mappings. It is shown that application of the Pontryagin principle to the optimal nonlinear regulator problem results in necessary conditions for optimality in the form of a two point boundary value problem (TPBVP). The TPBVP is represented by an operator equation and functional analytic results on the iterative solution of operator equations are applied. The general convergence theorems are translated and applied to those operators arising from the optimal regulation of nonlinear systems. It is shown that simply structured matrices and similarity transformations may be used to facilitate the calculation of the matrix Green functions and the evaluation of the convergence criteria. A controllability theory based on the integral representation of TPBVP's, the implicit function theorem, and contraction mappings is developed for nonlinear dynamical systems. Contraction mappings are theoretically and practically applied to a nonlinear control problem with bounded input control and the Lipschitz norm is used to prove convergence for the nondifferentiable operator. A dynamic model representing community drug usage is developed and the contraction mappings method is used to study the optimal regulation of the nonlinear system.

Killingsworth, W. R., Jr.↗

The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas

JOREK is a massively parallel fully implicit non-linear extended magneto-hydrodynamic (MHD) code for realistic tokamak X-point plasmas. It has become a widely used versatile simulation code for studying large-scale plasma instabilities and their control and is continuously developed in an international community with strong involvements in the European fusion research programme and ITER organization. This article gives a comprehensive overview of the physics models implemented, numerical methods applied for solving the equations and physics studies performed with the code. A dedicated section highlights some of the verification work done for the code. A hierarchy of different physics models is available including a free boundary and resistive wall extension and hybrid kinetic-fluid models. The code allows for flux-surface aligned iso-parametric finite element grids in single and double X-point plasmas which can be extended to the true physical walls and uses a robust fully implicit time stepping. Particular focus is laid on plasma edge and scrape-off layer (SOL) physics as well as disruption related phenomena. Among the key results obtained with JOREK regarding plasma edge and SOL, are deep insights into the dynamics of edge localized modes (ELMs), ELM cycles, and ELM control by resonant magnetic perturbations, pellet injection, as well as by vertical magnetic kicks. Also ELM free regimes, detachment physics, the generation and transport of impurities during an ELM, and electrostatic turbulence in the pedestal region are investigated. Regarding disruptions, the focus is on the dynamics of the thermal quench (TQ) and current quench triggered by massive gas injection and shattered pellet injection, runaway electron (RE) dynamics as well as the RE interaction with MHD modes, and vertical displacement events. Also the seeding and suppression of tearing modes (TMs), the dynamics of naturally occurring TQs triggered by locked modes, and radiative collapses are being studied.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A fully implicit scheme for global numerical weather prediction

A fast-slow factored scheme is presented for use with shallow-water primitive equation numerical weather prediction models. The technique was developed to reduce the rotational mode errors which arise when the fast and slow terms of the governing differential equations are treated simultaneously. The method factors out the fast and slow terms along the coordinate directions by means of a modified Crank-Nicolson scheme. A finite-difference spatial discretization is carried out in the zonal and meridional directions to reduce the factorization error to near-zero, and that time steps of 60-90 min can be used to obtain acceptably accurate results, even in the presence of fine spatial structures in the flow.

Augenbaum, J. M.↗

A Parallel Symmetric Successive Overrelaxation Method for OVERFLOW

The block Jacobi symmetric successive overrelaxation (SSOR) algorithm has been reformulated as a parallelized algorithm for the OVERFLOWstructured, overset grid, computational fluid dynamics flow solver. Simple changes to the flow solver required to implement the algorithm are discussed. A series of test cases are presented that demonstrate how the addition of implicit overset boundaries has improved the robustness and nonlinear convergence characteristics of the flow solver.

Computational Fluid Dynamics↗