Numerical solution of plane viscous shock reflections by Tzu-Sien Shao

Cover of: Numerical solution of plane viscous shock reflections | Tzu-Sien Shao

Published by University of Illinois at Urbana-Champaign in Urbana, Illinois .

Written in English

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Book details

Statementby Tzu-Sien Shao
SeriesReport (University of Illinois Dept. of Computer Science) -- no. 190, Report (University of Illinois Dept. of Computer Science) -- no. 190.
ContributionsUniversity of Illinois at Urbana-Champaign. Department of Computer Science
The Physical Object
Paginationiv, 71 leaves :
Number of Pages71
ID Numbers
Open LibraryOL25511839M

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Journals & Books; Register Sign in. Sign in Register. Journals & Books; Help Download full text in PDF Download. Advanced. Journal of Computational Physics. Volume 1, Issue 3, FebruaryPages Numerical solution of plane viscous shock reflections Cited by: 5. The book is concerned with mathematical modelling of supersonic and hyper­ sonic flows about bodies.

Permanent interest in this topic is stimulated, first of all, by aviation and aerospace engineering. The designing of aircraft and space vehicles requires a more precise prediction of the.

The shock layer flow is bounded by the bow shock wave and the front and lat­ eral parts of the body surface. A conventional approach to calculation of shock layer flows consists in a successive solution of the inviscid gas and boundary layer equations. F c = ρu ρu 2 +P ρuv (ρe+P)u, F d =− 0 τ xx τ xy uτ xx +vτ xy +q x.

(4) G c = ρv ρuv ρv 2 +P (ρe+P)v, G d =− 0 τ yx τ yy uτ yx +vτ yy +q y. where ρ, u, v, ρe, P respectively denote the density, the flow velocity components in the x - and y -directions, the total energy per unit volume and the by: 8.

A Numerical Study of Shock Reflection Phenomena is weaker than the incident shock wave. The plane shock after reflection from the end wall of the tube interacts with the grid-generated turbulent field. In Fv, Gv and Hv are the three viscous flux vectors in.

The viscosity effects on strong and weak shock wave reflection are investigated with the Navier‐Stokes and DSMC flow solvers. It is shown that the viscosity plays a crucial role in the vicinity of. The reflection of a triple-shock configuration was studied numerically in two dimensions using the Navier–Stokes equations.

The flow field was initialized using three shock theory, and the reflection of the triple point on a plane of symmetry was studied. The conditions simulated a stoichiometric methane-oxygen detonation cell at low pressure on time scales preceding ignition when.

Experimental measurements of shock strengths from detonation of long high explosive charges are shown to be in good agreement with the numerical solutions. Read more Book. Colella P., Glaz H.M. () Numerical calculation of complex shock reflections in gases. In: Soubbaramayer, Boujot J.P.

(eds) Ninth International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics, vol   Numerical solution of plane viscous shock reflections Journal of Computational Physics, Vol.

1, No. 3 Finite-difference calculations for hydrodynamic flows containing discontinuities. Read the latest articles of Journal of Computational Physics atElsevier’s leading platform of peer-reviewed scholarly literature.

Numerical study for hysteresis phenomena of shock wave reflection in overexpanded axisymmetric supersonic jet Journal of Thermal Science, Vol. 15, No. 3 Shock-wave flow regimes at entry into the diffuser of a hypersonic ramjet engine: Influence of physical properties of the gas medium.

In aerodynamics, the reflection of shock waves is a topic of interest since the pioneering work of Ernst Mach 1 1. Mach, “ Uber den Verlauf von Funkenwellen in der Ebene und im Raume,” Wiss.

Wien 7, – (). more than a century ago and because of its practical occurrences. It can be broadly classified into two categories, namely, regular and irregular.

Numerical solution of a free-boundary problem in hypersonic flow theory: Nonequilibrium viscous shock layers Journal of Computational Physics, Vol. No. 2 Characteristics of conjugate heat and mass transfer in the flow of supersonic and hypersonic streams over blunt bodies.

Considering weak wave reflections (weak shock wave: M shock wave: M > [3]), Sakurai et al. [4] and Shoev et al.

[5] observed a similar three-shock intersection of a steady Mach. Numerical Investigation of Shock-Reflection Phenomena in Overexpanded Supersonic Jets. Viscous simulation of shock reflection hysteresis in ideal and tapered overexpanded planar nozzles. Transition between regular and Mach shock reflections in plane overexpanded jets.

A numerical solution of the conjugate heat-exchange problem for reflection of a normally incident viscous shock wave from a rigid wall is used to find the nonsteady-state temperature of the wall and the thermal flux into the wall.

The main objectives are to study the influence of the wedge trailing edge corner angle, of the numerical methods and of the viscous effects on the shock wave reflections and on the hysteresis.

Differential equations, Hyperbolic -- Numerical solutions -- Congresses. Differential equations, Parabolic -- Numerical solutions -- Congresses.

Differential equations, Hyperbolic -- Numerical solutions. Differential equations, Parabolic -- Numerical solutions. Shock waves. Viscous flow. Numerisches Verfahren; Strömungsmechanik; Ondes de choc. Conical reflection of shock waves is either the same or very similar to plane wedge reflection under some circumstances.

in steady shock wave reflections. The numerical results were compared. 28 R. Deschambault and I. Glass 1. Introduction The study of oblique shock-wave reflection dates back to Mach ().it has been investigated extensively by many researchers. A comprehensive list of references and more detailed introductions and discussions can be found in Ben-Dor & Glass (,), Ando & Glass (), Lee & Glass () and Shirouzu & Glass ().

[10] proposed an inviscid solution in the plane (ө,p), which was an isentrope emanating from the sonic point of the reflected wave polar (figs.

2b and 10b). a) b) FIGURE 2. Theoretical solutions for irregular reflections in the (ө, p) plane. a) three-shock solution marked as MR; b) sonic. The solution is made of the shock (C 3), which is seen as the shock induced by the ramp at large distance from the wall, and of the states 3 and 6, at the same pressure, and separated in the physical plane by the slip line (Σ).

An intermediate state 4 has to be introduced between 2 and 6. Viscous simulation of shock-reflection hysteresis in overexpanded planar nozzles Mach number 05 Nozzle x-position 10 15 20 25 30 2D viscous interaction between a weak shock-wave and a vortex: This test-case has been chosen to highlight the capability of the present MR method to predict the generation and the transport of acoustic waves during a shock-vortex interaction.

The study is restricted to the interaction of a plane weak shock with a single isentropic vortex. Numerical Study of the Shock Wave Propagation in a Micron-Scale Contracting Channel G.V. Shoeva, Ye.A. Bondara, D.V.

Khotyanovskya, A.N. Kudryavtseva, G. Mirshekarib, M. Brouilletteb and M.S. Ivanova aK h r ist an ovc I uef T l dA p M,ky 4/1 N b R 63 09 bD ep artm nof M c hil E g,U v s é dS b k C J 1K 2R Abstract.

Entry of a shock wave into a microchannel and its propagation in the channel. The Springer edition of this book is an unchanged reprint of Courant and Friedrich's classical treatise which was first published in The basic research for it took place during World War II, but there are many aspects which still make the book interesting as a text and as a reference.

It treats basic aspects of the dynamics of compressible fluids in mathematical form, and attempts to 4/5(1). Belotserkovskii and Yu. Davydov, “Calculation of transonic flows by the large-particle method,” in: Information Bulletin of the Siberian Branch of the Academy of Sciences of the USSR on Numerical Methods of the Mechanics of Continuous Media [in Russian], Vol.

1, No. 6, Novosibirsk (), pp. 19– His triple-shock intersection model showed good agreement with numerical simulations of the weak reflections of shock waves, as mentioned in Ref.

In the vicinity of the triple-shock-wave intersection, the non-Rankine–Hugoniot shock zone is a region in which flow parameters vary continuously and deviate distinctly from the theoretical three. We then establish Model 1 for the upper layer medium of the viscous-elastic HTI sandstone and lower layer medium of the viscous-elastic HTI mudstone in accordance with Table 1, and study the change rules of the reflection coefficient curve in the incidence plane with the azimuth angles of 0°, 45° and 90°, respectively, as shown in Figs 7 –9.

• normal shock standing off leading edge • conical oblique shock away from leading edge • acoustic wave in far field Rarefaction (expansion) wave • lowers density, temperature, and pressure of air continuously and significantly • interactions with bow shock weaken bow shock.

In this paper, the fourth‐order MacCormack scheme with a fourth viscous term is used to improve the solution. It is shown from three sample calculations with acoustic shock waves that the new method is much better than the second‐order MacCormack method.

Its numerical error, on an average, is only one fifth of that in the latter method. The papers presented in this volume focus on new finite difference and finite element approaches for both incompressible and compressible Navier-Stokes equations, with attention also given to viscous-inviscid interaction problems.

Particular topics discussed include some aspects of finite element approximations of incompressible viscous flows, numerical solution of the compressible viscous.

The transition boundary separating the region of regular reflection from the regions of single- transitional- and double-Mach reflections for the collision of a planar shock wave moving in argon and atmospheric air and interacting with an inclined reflecting plane is studied by both analytical methods and high-resolution computational-fluid-dynamic flow-field simulations.

Phase plane diagram Free vibrations with viscous damping 11 Numerical solution of the eigenproblem Introduction Properties of standard eigenvalues and eigenvectors Reflection and refraction of waves at a discontinuity in the system properties.

Numerical Solution of Hyperbolic Partial Differential Equations Propagation and Reflection of a Small-Amplitude Wave Propagation of a Finite-Amplitude Wave: Formation of a Shock An Application to Biological Fluid Dynamics: Flow in an Elastic Tube Appendix 3 Viscous Fluid Flows This paper presents numerical simulation of the evolution of one-dimensional normal shocks, their propagation, reflection and interaction in air using a single diaphragm Riemann shock tube and validate them using experimental results.

Mathematical model is derived for one-dimensional compressible flow of viscous and conducting medium. Numerical methods for the solution of the Orr-Sommerfeld equations are considered.

The problem is stated in §1, and the basic numerical tools (the setting up of the finite difference approximations, and the algorithm for solving the resulting algebraic eigenvalue problem) are developed in §§2 and 3.

A numerical investigation of the interaction of a planar shock wave with a rigid wedge and cone in an air-filled shock tube is performed by computing the unsteady flow field of the interaction process.

The Euler and Navier-Stokes equations are solved in two dimensions to produce flow solutions for regular and Mach reflections with and. @article{osti_, title = {Detailed numerical, graphical, and experimental study of oblique-shock-wave reflections}, author = {Glaz, H M and Colella, P and Glass, I I and Deschambault, R L}, abstractNote = {An extensive series of numerical calculations of oblique-shock-wave reflections in air and argon have been performed using a version of the second-order Eulerian Godunov scheme for.

Numerical solution of the hypersonic viscous-shock-layer equations for laminar, transitional, and turbulent flows of a perfect gas over blunt axially symmetric bodies The viscous shock layer equations applicable to hypersonic laminar, transitional, and turbulent flows of a perfect gas over two-dimensional plane or axially symmetric blunt bodies are presented.Fig.

2(a) and (b) show, respectively, the numerical results-2 when k = 0 and when k = From the figure, we can see that the numerical solution and the accurate solution are in good-4 agreement. In addition, when k is less than or equal to 10, the shock wave travels only one mesh point.A new approach for numerical-diffusion control of flux-vector-splitting schemes for viscous-compressible flows Paragmoni Kalita, Anoop K.

Dass, Jongki Hazarika. The flux vector splitting (FVS) schemes are known for their higher resistance to shock instabilities and carbuncle phenomena in high-speed flow computations, which are.

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