Direct numerical simulation of isotropic turbulence interacting with a weak shock wave

Interaction of isotropic quasi-incompressible turbulence with a weak shock wave was studied by direct numerical simulations. The effects of the fluctuation Mach number Mt of the upstream turbulence and the shock strength M21 — 1 on the turbulence statistics were investigated. The ranges investigated were 0.0567 ≤ Mt ≤ 0.110 and 1.05 ≤ M1 ≤ 1.20. A linear analysis of the interaction of isotropic turbulence with a normal shock wave was adopted for comparisons with the simulations.Both numerical simulations and the linear analysis of the interaction show that turbulence is enhanced during the interaction with a shock wave. Turbulent kinetic energy and transverse vorticity components are amplified, and turbulent lengthscales are decreased. The predictions of the linear analysis compare favourably with simulation results for flows with M2t < a(M21 — 1) with a ≈ 0.1, which suggests that the amplification mechanism is primarily linear. Simulations also showed a rapid evolution of turbulent kinetic energy just downstream of the shock, a behaviour not reproduced by the linear analysis. Investigation of the budget of the turbulent kinetic energy transport equation shows that this behaviour can be attributed to the pressure transport term.Shock waves were found to be distorted by the upstream turbulence, but still had a well-defined shock front for M2t < a(M21— 1) with a ≈ 0.1). In this regime, the statistics of shock front distortions compare favourably with the linear analysis predictions. For flows with M2t > a(M21— 1 with a ≈ 0.1, shock waves no longer had well-defined fronts: shock wave thickness and strength varied widely along the transverse directions. Multiple compression peaks were found along the mean streamlines at locations where the local shock thickness had increased significantly.

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On the interaction between shock waves and boundary layers

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100026943 ◽

1951 ◽

Vol 47 (3) ◽

pp. 545-553 ◽

Cited By ~ 14

Author(s):

K. Stewartson

Keyword(s):

Boundary Layer ◽

Shock Wave ◽

Reynolds Number ◽

Shock Waves ◽

Boundary Layers ◽

Weak Shock ◽

Boundary Layer Separation ◽

Weak Shock Wave ◽

Layer Separation ◽

Boundary Layer Equations

AbstractThe effect on the boundary-layer equations of a weak shock wave of strength ∈ has been investigated, and it is shown that ifRis the Reynolds number of the boundary layer, separation occurs when ∈ =o(R−i). The boundary-layer assumptions are then investigated and shown to be consistent. It is inferred that separation will occur if a shock wave meets a boundary and the above condition is satisfied.

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Non-linear weak shock diffraction

Journal of the Australian Mathematical Society ◽

10.1017/s144678870000656x ◽

1968 ◽

Vol 8 (4) ◽

pp. 737-754 ◽

Cited By ~ 2

Author(s):

N. J. De Mestre

Keyword(s):

Shock Wave ◽

Shock Front ◽

Weak Shock ◽

Weak Shock Wave ◽

Shadow Region ◽

Ray Theory ◽

Perturbation Expansions ◽

Shock Diffraction ◽

Non Linear ◽

Flow Variables

AbstractPerturbation expansions are sought for the flow variables associated with the diffraction of a plane weak shock wave around convex-angled corners in a polytropic, inviscid, thermally-nonconducting gas. Lighthill's method of strained co-ordinates [4] produces a uniformly valid expansion for most of the diffracted front, while the remainder of this front is treated by a modification of the shock-ray theory of Whitham [6]. The solutions from these approaches are patched just inside the ‘shadow’ region yielding a plausible description of the entire diffracted shock front.

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Virtual motion of real particles

Journal of Fluid Mechanics ◽

10.1017/s0022112010000765 ◽

2010 ◽

Vol 650 ◽

pp. 1-4 ◽

Cited By ~ 9

Author(s):

G. TRYGGVASON

Keyword(s):

Kinetic Energy ◽

Numerical Simulations ◽

Turbulent Kinetic Energy ◽

Multiphase Flows ◽

Isotropic Turbulence ◽

Finite Size ◽

Direct Numerical Simulations ◽

Spherical Particles ◽

Length Scale ◽

Turbulent Eddies

Direct numerical simulations are rapidly becoming one of the most important techniques to examine the dynamics of multiphase flows. Lucci, Ferrante & Elghobashi (J. Fluid Mech., 2010, this issue, vol. 650, pp. 5–55) address several fundamental issues for spherical particles in isotropic turbulence. They show the importance of including the finite size of the particles and discuss how particles of a size comparable to the largest length scale at which viscosity substantially affects the turbulent eddies (i.e. the Taylor microscale) always increase the dissipation of turbulent kinetic energy.

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Corrigendum: Direct numerical simulation of isotropic turbulence interacting with a weak shock wave

Journal of Fluid Mechanics ◽

10.1017/s0022112094000704 ◽

1994 ◽

Vol 264 ◽

pp. 373-374 ◽

Cited By ~ 4

Author(s):

Sangsan Lee ◽

Sanjiva K. Lele ◽

Parviz Moin

Keyword(s):

Numerical Simulation ◽

Shock Wave ◽

Direct Numerical Simulation ◽

Isotropic Turbulence ◽

Weak Shock ◽

Weak Shock Wave

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Interaction of isotropic turbulence with shock waves: effect of shock strength

Journal of Fluid Mechanics ◽

10.1017/s0022112097005107 ◽

1997 ◽

Vol 340 ◽

pp. 225-247 ◽

Cited By ~ 171

Author(s):

SANGSAN LEE ◽

SANJIVA K. LELE ◽

PARVIZ MOIN

Keyword(s):

Shock Wave ◽

Shock Waves ◽

Isotropic Turbulence ◽

Linear Analysis ◽

Shock Capturing ◽

Length Scale ◽

Theoretical Predictions ◽

Unsteady Interaction ◽

Thermodynamic Variables ◽

Turbulence Length

As an extension of the authors' work on isotropic vortical turbulence interacting with a shock wave (Lee, Lele & Moin 1993), direct numerical simulation and linear analysis are performed for stronger shock waves to investigate the effects of the upstream shock-normal Mach number (M1). A shock-capturing scheme is developed to accurately simulate the unsteady interaction of turbulence with shock waves. Turbulence kinetic energy is amplified across the shock wave, and this amplification tends to saturate beyond M1 = 3.0. An existing controversy between experiments and theoretical predictions on length scale change is thoroughly investigated through the shock-capturing simulation: most turbulence length scales decrease across the shock, while the dissipation length scale (ρq3/ε) increases slightly for shock waves with M1<1.65. Fluctuations in thermodynamic variables behind the shock wave are nearly isentropic for M1<1.2, and deviate significantly from isentropy for the stronger shock waves, due to the entropy fluctuation generated through the interaction.

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Reconsideration of the So-Called von Neumann Paradox in the Reflection of a Shock Wave over a Wedge

Materials Science Forum ◽

10.4028/www.scientific.net/msf.566.1 ◽

2007 ◽

Vol 566 ◽

pp. 1-8

Author(s):

Eugene I. Vasilev ◽

Tov Elperin ◽

Gabi Ben-Dor

Keyword(s):

Shock Wave ◽

Shock Waves ◽

Triple Point ◽

Mach Reflection ◽

Weak Shock ◽

Weak Shock Wave ◽

Plane Shock ◽

Von Neumann ◽

Von Neumann Paradox ◽

Guderley Reflection

Numerous experimental investigations on the reflection of plane shock waves over straight wedges indicated that there is a domain, frequently referred to as the weak shock wave domain, inside which the resulted wave configurations resemble the wave configuration of a Mach reflection although the classical three-shock theory does not provide an analytical solution. This paradox is known in the literature as the von Neumann paradox. While numerically investigating this paradox Colella & Henderson [1] suggested that the observed reflections were not Mach reflections but another reflection, in which the reflected wave at the triple point was not a shock wave but a compression wave. They termed them it von Neumann reflection. Consequently, based on their study there was no paradox since the three-shock theory never aimed at predicting this wave configuration. Vasilev & Kraiko [2] who numerically investigated the same phenomenon a decade later concluded that the wave configuration, inside the questionable domain, includes in addition to the three shock waves a very tiny Prandtl-Meyer expansion fan centered at the triple point. This wave configuration, which was first predicted by Guderley [3], was recently observed experimentally by Skews & Ashworth [4] who named it Guderley reflection. The entire phenomenon was re-investigated by us analytically. It has been found that there are in fact three different reflection configurations inside the weak reflection domain: • A von Neumann reflection – vNR, • A yet not named reflection – ?R, • A Guderley reflection – GR. The transition boundaries between MR, vNR, ?R and GR and their domains have been determined analytically. The reported study presents for the first time a full solution of the weak shock wave domain, which has been puzzling the scientific community for a few decades. Although the present study has been conducted in a perfect gas, it is believed that the reported various wave configurations, namely, vNR, ?R and GR, exist also in the reflection of shock waves in condensed matter.

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Investigation of shock-wave deformation history from recovered structure

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100143754 ◽

1986 ◽

Vol 44 ◽

pp. 434-435

Author(s):

M.A. Mogilevsky ◽

L.S. Bushnev

Keyword(s):

Shock Wave ◽

Plastic Deformation ◽

Dislocation Density ◽

Shock Waves ◽

Shock Front ◽

Single Crystals ◽

Residual Deformation ◽

Deformation Structure ◽

Deformation History ◽

Deformation Velocity

Single crystals of Al were loaded by 15 to 40 GPa shock waves at 77 K with a pulse duration of 1.0 to 0.5 μs and a residual deformation of ∼1%. The analysis of deformation structure peculiarities allows the deformation history to be re-established.After a 20 to 40 GPa loading the dislocation density in the recovered samples was about 1010 cm-2. By measuring the thickness of the 40 GPa shock front in Al, a plastic deformation velocity of 1.07 x 108 s-1 is obtained, from where the moving dislocation density at the front is 7 x 1010 cm-2. A very small part of dislocations moves during the whole time of compression, i.e. a total dislocation density at the front must be in excess of this value by one or two orders. Consequently, due to extremely high stresses, at the front there exists a very unstable structure which is rearranged later with a noticeable decrease in dislocation density.

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