Simulations of Hypersonic Rarefied Gas Flows Using DSMC-MLG.

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Book Synopsis Simulations of Hypersonic Rarefied Gas Flows Using DSMC-MLG. by :

Download or read book Simulations of Hypersonic Rarefied Gas Flows Using DSMC-MLG. written by and published by . This book was released on 1997 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The combined Direct Simulation Monte Carlo (DSMC) and Monotonic Lagrangian Grid (MLG) methodologies are used on the massively parallel Connection Machines CM-5 to solve for the properties of a low density hypersonic flow through a channel containing a wedge. Numerical issues related to grid generation around the obstacle, the effects of resolution in terms of the simulated to actual particle ratio, and the use of time-averaging to obtain a statistically converged solution are discussed. A method is presented for quantifying the effects of the grid on the solution. The flow field shows many important aerodynamic features, such as shock waves, boundary layers, expansion fan, and their interactions. Since the flow is so rarefied, these structures are diffuse compared to what is expected in a continuum flow. For example, the reattachment shock behind the trailing edge of the wedge degenerates into a diffuse viscous layer. Other low density effects include the velocity slip, which peaks near the leading edges where the density is low, and temperature jump of the gas adjacent to the solid surfaces, which is highest at the entrance of the channel and decreases further downstream. The calculated skin friction and heat transfer agree well with the Reynolds analogy for boundary layer flow. The computed pressure distributions along the wall are consistent with hypersonic viscous theory and other DSMC calculations.

Advances in an Open-source Direct Simulation Monte Carlo Technique for Hypersonic Rarefied Gas Flows

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ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (141 download)

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Book Synopsis Advances in an Open-source Direct Simulation Monte Carlo Technique for Hypersonic Rarefied Gas Flows by : Abdul Ossman Ahmad

Download or read book Advances in an Open-source Direct Simulation Monte Carlo Technique for Hypersonic Rarefied Gas Flows written by Abdul Ossman Ahmad and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hypersonic vehicles that travel through rarefied gas environments are very expensive to design through experimental methods. In the last few decades major work has been carried out in developing numerical methods to capture these types of flows to a certain degree of accuracy. This accuracy is increased using particle based numerical techniques as opposed to continuum computational fluid dynamics. However, one of the modern problems of particle based techniques is the high computational cost associated with it. This thesis presents an enhanced open-source particle based technique to capture high speed rarefied gas flows. This particle based technique is called dsmcFoam and is based on the direct simulation Monte Carlo technique. As a result of the author's work dsmcFoam has become more efficient and accurate. Benchmark studies of the standard dsmcFoam solver will be presented before introducing the main advances. The results of the benchmark investigations are compared with analytical solutions, other DSMC codes and experimental data available in the literature. And excellent agreement is found when good DSMC practice has been followed. The main advances of dsmcFoam discussed are a routine for selecting collision pairs called the transient adaptive sub-cell (TASC) method and a dynamic wall temperature model (DWTM). The DWTM relates the wall temperature to the heat flux. In addition, verification and validation studies are undertaken of the DWTM. Furthermore, the widely used conventional 8 sub-cell method used to select possible collision pairs becomes very cumbersome to employ properly. This is because many mesh refinement stages are required in order to obtain accurate data. Instead of mesh refinement the TASC technique automatically employs more sub-cells, and these sub-cells are based on the number of particles in a cell. Finally, parallel efficiency tests of dsmcFoam are presented in this thesis along with a new domain decomposition technique for parallel processing. This technique splits up the computational domain based on the number of particles, such that each processor has the same number of particles to work with.

Improved Chemistry Models for DSMC Simulations of Ionized Rarefied Hypersonic Flows

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ISBN 13 :
Total Pages : 432 pages
Book Rating : 4.:/5 (18 download)

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Book Synopsis Improved Chemistry Models for DSMC Simulations of Ionized Rarefied Hypersonic Flows by : Takashi Ozawa

Download or read book Improved Chemistry Models for DSMC Simulations of Ionized Rarefied Hypersonic Flows written by Takashi Ozawa and published by . This book was released on 2007 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Numerical Simulation of Hypersonic Rarefied Flows Using the Second-Order Constitutive Model of the Boltzmann Equation

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ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (115 download)

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Book Synopsis Numerical Simulation of Hypersonic Rarefied Flows Using the Second-Order Constitutive Model of the Boltzmann Equation by : Rho Shin Myong

Download or read book Numerical Simulation of Hypersonic Rarefied Flows Using the Second-Order Constitutive Model of the Boltzmann Equation written by Rho Shin Myong and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Various mathematical theories and simulation methods were developed in the past for describing gas flows in nonequilibrium, in particular, hypersonic rarefied regime. They range from the mesoscale models like the Boltzmann equation, the DSMC, and the high-order hydrodynamic equations. The moment equations can be derived by introducing the statistical averages in velocity space and then combining them with the Boltzmann kinetic equation. In this chapter, on the basis of Eu's generalized hydrodynamics and the balanced closure recently developed by Myong, the second-order constitutive model of the Boltzmann equation applicable for numerical simulation of hypersonic rarefied flows is presented. Multi-dimensional computational models of the second-order constitutive equations are also developed based on the concept of decomposition and method of iterations. Finally, some practical applications of the second-order constitutive model to hypersonic rarefied flows like re-entry vehicles with complicated geometry are described.

Theoretical and Numerical Studies of Rarefied Hypersonic Flows

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ISBN 13 :
Total Pages : 292 pages
Book Rating : 4.:/5 (98 download)

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Book Synopsis Theoretical and Numerical Studies of Rarefied Hypersonic Flows by : Xionghui Huang

Download or read book Theoretical and Numerical Studies of Rarefied Hypersonic Flows written by Xionghui Huang and published by . This book was released on 2014 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation a comprehensive work on theoretical and numerical studies of rarefied hypersonic flows is presented. On the theoretical part, gaskinetic study and exact solutions are obtained for problems related with high speed collisionless round jet: expanding into a vacuum; impinging at a normally set, diffuse or specular reflective plate with finite radius. Several fundamental geometry-velocity relations are utilized in this study and they play crucial roles. These complete results include flowfield properties, and impingement properties at the plate surface. The final results include complex but accurate integrations involving geometry and specific speed ratio factors. Severals numerical simulations with the direct simulation Monte Carlo method validate these analytical exact results. In the numerical part, a multi-dimensional gas-dynamical computational scheme package GRASP-K ("Generalized Rarefied gAs Simulation Package - Kinetic") is presented. This implementation adopts a concept of simulation engine and it utilizes many Object-Oriented Programming features and software engineering design patterns. As a result, this implementation successfully resolves the problem of functionality and interface conflictions for multi-dimension Gas Kinetic Scheme implementations. The package has an open architecture which benefits further development and code maintenance. This package can utilize traditional structured, unstructured or hybrid grids to model multi-dimensional complex geometries and multi-species hypersonic thermo-chemically non equilibrium gas flows. A preliminary test case of a two-species hypersonic flow passing a cylinder and some preliminary results are obtained. The pressure distribution of the gas mixture along the cylinder wall is compared with those in previous works. A Navier-Stokes equations based computational fluid dynamics solver is also incorporated in the package to simulate hypersonic nonequilibrium flows. This solver includes comprehensive chemical reaction models and thermodynamics relations and the phenolic-silica ablation flow simulation is considered. Finite rate chemical reactions, multiple temperature relaxation processes, and ionization phenomena are modeled. Hence the package can be used to simulate multiple-dimensional, non-equilibrium gas flows with multiple species. Simulation results of several hypersonic gas flows over blunted bodies are presented and compared with results in the literature.

Monte Carlo Sensitivity Analyses of DSMC Parameters for Ionizing Hypersonic Flows

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ISBN 13 :
Total Pages : 692 pages
Book Rating : 4.:/5 (15 download)

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Book Synopsis Monte Carlo Sensitivity Analyses of DSMC Parameters for Ionizing Hypersonic Flows by : Kyle J. Higdon

Download or read book Monte Carlo Sensitivity Analyses of DSMC Parameters for Ionizing Hypersonic Flows written by Kyle J. Higdon and published by . This book was released on 2018 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work focuses on the development and sensitivity analyses of a direct simulation Monte Carlo (DSMC) code to understand the complex physical processes that occur during hypersonic entry into a rarefied atmosphere. Simulations are performed on 1-dimensional hypersonic shock scenarios that mimic the conditions of high altitude atmospheric entry to Earth and Saturn with the Computation of Hypersonic Ionizing Particles in Shocks (CHIPS) code. To model hypersonic entry problems accurately, the CHIPS code must resolve nonequilibrium flows and account for a number of complex gas dynamics processes at the molecular level. In this thesis, several high temperature models are added to the CHIPS code including charged particle models and electronic excitation. These models are refined using preliminary sensitivity analyses resulting in improved electronic excitation models and a new backward chemical reaction model. The CHIPS simulations completed in this work reproduce rarefied hypersonic shock tube experiments performed in the Electric Arc Shock Tube (EAST) at NASA Ames Research Center. The CHIPS results are post-processed by the NEQAIR line-by-line radiative solver to compare directly to spectra measured experimentally in EAST. The DSMC techniques used to model hypersonic phenomena require numerous experimentally calibrated parameters. Many of these parameters are inferred from lower temperature experiments, resulting in an unknown amount of uncertainty in the simulated results at the extreme conditions of hypersonic flow. A global Monte Carlo sensitivity analysis is performed by simultaneously varying the CHIPS input parameter values to understand the sensitivity of experimentally measured quantities simulated by the CHIPS and NEQAIR codes. The sensitivity of several of these output quantities is used to rank the input parameters, identifying the most important parameters for the simulation of the hypersonic scenario. It was concluded that experimentally measured radiation intensity is most sensitive to the following key processes: N+e−⇌N++e−+e−, NO+N+⇌N+NO+, N2+N⇌N+N+N, N+O⇌NO++e−, N+N⇌N2++e−, and Z [subscript elec] for N, O, and N2+. In the future, this ranking can be used to identify which input parameters should be experimentally investigated, where model improvements could be beneficial, and aid in reducing the parameter space for DSMC calibrations to experimental data.

Hypersonic Rarefied Flow about a Compression Corner

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ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (11 download)

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Book Synopsis Hypersonic Rarefied Flow about a Compression Corner by : James N. Moss

Download or read book Hypersonic Rarefied Flow about a Compression Corner written by James N. Moss and published by . This book was released on 1991 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

DSMC Simulations of Hypersonic Flows and Comparison With Experiments

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ISBN 13 :
Total Pages : 7 pages
Book Rating : 4.:/5 (742 download)

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Book Synopsis DSMC Simulations of Hypersonic Flows and Comparison With Experiments by :

Download or read book DSMC Simulations of Hypersonic Flows and Comparison With Experiments written by and published by . This book was released on 2005 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents computational results obtained with the direct simulation Monte Carlo (DSMC) method for several biconic test cases in which shock interactions and flow separation-reattachment are key features of the flow. Recent ground-based experiments have been performed for several biconic configurations and surface heating rate and pressure measurements have been proposed for code validation studies. The present focus is to expand on the current validating activities for a relatively new DSMC code called DS2V that Bird (second author) has developed. Comparisons with experiments and other computations help clarify the agreement currently being achieved between computations and experiments and to identify the range of measurement variability of the proposed validation data when benchmarked with respect to the current computations. For the test cases with significant vibrational nonequilibrium, the effect of the vibrational energy surface accommodation on heating and other quantities is demonstrated.

Hypersonic Rarefied Wake Characterization

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Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781722286897
Total Pages : 30 pages
Book Rating : 4.2/5 (868 download)

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Book Synopsis Hypersonic Rarefied Wake Characterization by : National Aeronautics and Space Administration (NASA)

Download or read book Hypersonic Rarefied Wake Characterization written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-07-05 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results of a numerical study using the direct simulation Monte Carlo (DSMC) method are presented for hypersonic rarefied flow over an aeroassisted space transfer vehicle (ASTV). The emphasis of the study is the characterization of the near wake region which includes the ASTV payload. The study covered the transitional flow regime from near continuum to free molecular. Calculations show that the character of the near wake is significantly affected by the presence of the payload. Flow separation occurs when an afterbody is present throughout the transitional flow regime. In contrast, when no afterbody is present, no separation is observed until the flow approaches continuum. Brewer, E. B. Marshall Space Flight Center ...

DSMC Modeling of Vibration-translation Energy Transfer in Hypersonic Rarefied Flows

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ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (11 download)

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Book Synopsis DSMC Modeling of Vibration-translation Energy Transfer in Hypersonic Rarefied Flows by : S. F. Gimelshein

Download or read book DSMC Modeling of Vibration-translation Energy Transfer in Hypersonic Rarefied Flows written by S. F. Gimelshein and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advances in Hypersonics

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Publisher : Springer Science & Business Media
ISBN 13 : 1461203759
Total Pages : 438 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Advances in Hypersonics by : BERTIN

Download or read book Advances in Hypersonics written by BERTIN and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: These three volumes entitled Advances in Hypersonics contain the Proceedings of the Second and Third Joint US/Europe Short Course in Hypersonics which took place in Colorado Springs and Aachen. The Second Course was organized at the US Air Force Academy, USA in January 1989 and the Third Course at Aachen, Germany in October 1990. The main idea of these Courses was to present to chemists, com puter scientists, engineers, experimentalists, mathematicians, and physicists state of the art lectures in scientific and technical dis ciplines including mathematical modeling, computational methods, and experimental measurements necessary to define the aerothermo dynamic environments for space vehicles such as the US Orbiter or the European Hermes flying at hypersonic speeds. The subjects can be grouped into the following areas: Phys ical environments, configuration requirements, propulsion systems (including airbreathing systems), experimental methods for external and internal flow, theoretical and numerical methods. Since hyper sonic flight requires highly integrated systems, the Short Courses not only aimed to give in-depth analysis of hypersonic research and technology but also tried to broaden the view of attendees to give them the ability to understand the complex problem of hypersonic flight. Most of the participants in the Short Courses prepared a docu ment based on their presentation for reproduction in the three vol umes. Some authors spent considerable time and energy going well beyond their oral presentation to provide a quality assessment of the state of the art in their area of expertise as of 1989 and 1991.

Advances in Hypersonics

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Publisher : Springer Science & Business Media
ISBN 13 : 1461203716
Total Pages : 280 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Advances in Hypersonics by : Bertin

Download or read book Advances in Hypersonics written by Bertin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: These three volumes entitled Advances in Hypersonics contain the Proceedings of the Second and Third Joint US/Europe Short Course in Hypersonics which took place in Colorado Springs and Aachen. The Second Course was organized at the US Air Force Academy, USA in January 1989 and the Third Course at Aachen, Germany in October 1990. The main idea of these Courses was to present to chemists, com puter scientists, engineers, experimentalists, mathematicians, and physicists state of the art lectures in scientific and technical dis ciplines including mathematical modeling, computational methods, and experimental measurements necessary to define the aerothermo dynamic environments for space vehicles such as the US Orbiter or the European Hermes flying at hypersonic speeds. The subjects can be grouped into the following areas: Phys ical environments, configuration requirements, propulsion systems (including airbreathing systems), experimental methods for external and internal flow, theoretical and numerical methods. Since hyper sonic flight requires highly integrated systems, the Short Courses not only aimed to give in-depth analysis of hypersonic research and technology but also tried to broaden the view of attendees to give them the ability to understand the complex problem of hypersonic flight. Most of the participants in the Short Courses prepared a docu ment based on their presentation for reproduction in the three vol umes. Some authors spent considerable time and energy going well beyond their oral presentation to provide a quality assessment of the state of the art in their area of expertise as of 1989 and 1991.

Hybrid DSMC-CFD Simulations of Hypersonic Flow Over Sharp and Blunted Bodies

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ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (11 download)

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Book Synopsis Hybrid DSMC-CFD Simulations of Hypersonic Flow Over Sharp and Blunted Bodies by : Wen-Lan Wang

Download or read book Hybrid DSMC-CFD Simulations of Hypersonic Flow Over Sharp and Blunted Bodies written by Wen-Lan Wang and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Hybrid Continuum-rarefied Hypersonics Methodology with Automatic Mesh Optimization

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ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (135 download)

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Book Synopsis A Hybrid Continuum-rarefied Hypersonics Methodology with Automatic Mesh Optimization by : Shrutakeerti Mallikarjun Vagishwari

Download or read book A Hybrid Continuum-rarefied Hypersonics Methodology with Automatic Mesh Optimization written by Shrutakeerti Mallikarjun Vagishwari and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "HALO3D (High-Altitude Low-Orbit, 3D) is a multidisciplinary all-Mach CFD system developed by the McGill CFD Lab to simulate flow fields around hypersonic aircraft whose flight path spans low (continuum) to high (rarefied) altitudes. HALO3D uses an unstructured edge-based finite-element Navier-Stokes (NS) flow solver (HALO3D-NS) for the continuum regime that includes complex thermochemistry. This thesis extends the applicability of HALO3D to the rarefied regime through three significant efforts. First, a rarefied flow solver, HALO3D-DSMC (Direct Simulation Monte Carlo), is developed to tackle the high-altitude flow field. It is a 3D unstructured DSMC code capable of simulating thermochemical non-equilibrium and volume chemistry with sub-cell features for collision pair selection. Validation simulations for HALO3D-DSMC are presented. Second, a HALO3D-HYBRID infrastructure is developed to simulate moderate Knudsen number flows. In a domain consisting of continuum and rarefied patches, the hybrid routine transparently steps between NS and DSMC techniques to calculate a global solution with no user intervention. Delineating the DSMC and NS regions is accomplished by using the gradient length local Knudsen number (Kn_GLL) as a continuum breakdown detector. Cell and node masks based on the Kn_GLL distribution are inputs for mesh population, particle insertion, buffer zone creation, and NS-DSMC boundary condition routines. Bird's leading-edge and 2D cylinder cases are used to demonstrate that a finite-element NS-DSMC hybrid algorithm can be successfully built to address high-Mach flows. Consistent treatment of thermochemical non-equilibrium by both continuum and rarefied modules is found to be necessary to accurately simulate complex flows. Third, is the coupling of HALO3D-DSMC and HALO3D-HYBRID with a powerful in-house solution-driven automatic mesh optimizer, OptiGrid, heavily used in the NS context. A thorough investigation is carried out on scalars and constraints needed to optimize DSMC and hybrid meshes, an aspect that is currently lacking in the literature. Three optimization constraints: the minimum and maximum edge lengths, and a target number of node/cells are studied and applied to the leading-edge case and flows over 2D and 3D cylinder geometries for freestream Knudsen numbers ranging from 0.01 to 0.047. It is shown that an adaptation scalar combination of flow variables such as density, velocities, temperatures, pressure, and Mach number automatically converges to a final optimized mesh through a series of mesh iterations. The adapted meshes gradually improve the solution's quality without necessarily increasing the number of mesh points or cells, even reducing them sometimes. The solutions represented by the final adapted mesh are smooth and free of irregularities. The solutions and meshes of adapted full DSMC simulations and adapted hybrid simulations are seen to match, thus validating the hybrid solver and showcasing the solver-independence aspect of OptiGrid. Further, the optimized hybrid mesh generates buffers with smooth boundaries and consists of coarse NS cells and refined DSMC cells. The cell sizes from NS to DSMC are seen to reduce organically in the shock and boundary layer. This coupled DSMC/hybrid-OptiGrid system can thus simulate complex 3D geometries and multiscale flow features while drastically reducing mesh preparation time as these are automatically adapted to the emerging physics during the iterative solutions. Taken altogether, the DSMC, hybrid NS-DSMC, and mesh optimization efforts form an advanced system to simulate hypersonic flows over complex geometries with controlled precision and at a much lower expense both in the pre-processing and solution phases. These contributions are the essential components of a seamless hybrid solution approach within HALO3D, upon which other functionalities could be easily built in the future"--

Advances in Hypersonics: Computing hypersonic flows

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Publisher : Birkhauser
ISBN 13 : 9780817636722
Total Pages : 0 pages
Book Rating : 4.6/5 (367 download)

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Book Synopsis Advances in Hypersonics: Computing hypersonic flows by : John J. Bertin

Download or read book Advances in Hypersonics: Computing hypersonic flows written by John J. Bertin and published by Birkhauser. This book was released on 1992 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approximate Two Layer (Inviscid/Viscous) Methods to Model Aerothermodynamic Environments.- Second-Order Effects in Hypersonic Boundary Layers.- Unstructured-Grid Algorithms for High-Speed CFD Analysis.- Numerical Simulation of Three-Dimensional Hypersonic Viscous Flows.- Numerical Simulation of Entry Flow over Blunt Swept-Wing Planes.- Viscous Nonequilibrium Flow Calculations.- The Finite Pointset Method for Hypersonic Flows in the Rarefied Gas Regime.- Computation of Flowfields for Hypersonic Flight at High Altitudes.

Modeling of Rarefield Hypersonic Flows Over Spacecraft in Martian Atmosphere Using the DSMC Method

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ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (11 download)

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Book Synopsis Modeling of Rarefield Hypersonic Flows Over Spacecraft in Martian Atmosphere Using the DSMC Method by : S. F. Gimelshein

Download or read book Modeling of Rarefield Hypersonic Flows Over Spacecraft in Martian Atmosphere Using the DSMC Method written by S. F. Gimelshein and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

DSMC Simulation of Separated Flows about Flared Bodies at Hypersonic Conditions

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ISBN 13 :
Total Pages : 30 pages
Book Rating : 4.:/5 (317 download)

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Book Synopsis DSMC Simulation of Separated Flows about Flared Bodies at Hypersonic Conditions by : James N. Moss

Download or read book DSMC Simulation of Separated Flows about Flared Bodies at Hypersonic Conditions written by James N. Moss and published by . This book was released on 2000 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper describes the results of a numerical study of interacting hypersonic flows at conditions that can be produced in ground-based test facilities. The computations are made with the direct simulation Monte Carlo (DSMC) method of Bird. The focus is on Mach 10 flows about flared axisymmetric configurations, both hollow cylinder flares and double cones. The flow conditions are those for which experiments have been or will be performed in the ONERA R5Ch low-density wind tunnel and the Calspan-University of Buffalo Research Center (CUBRC) Large Energy National Shock (LENS) tunnel. The range of flow conditions, model configurations, and model sizes provides a significant range of shock/shock and shock/boundary layer interactions at low Reynolds number conditions. Results presented will highlight the sensitivity of the calculations to grid resolution, contrast the difference in flow structure for hypersonic cold flows and those of more energetic but still low enthalpy flows, and compare the present results with experimental measurements for surface heating, pressure, and extent of separation.