PHASE TRANSITIONS IN THE ZERO MACH NUMBER LIMIT OF COMPRESSIBLE TWOPHASE FLOW EQUATIONS

2019 ◽  
Vol 16 (2) ◽  
pp. 351-386
Author(s):  
Hyeonseong Jin
Keyword(s):  
Phase Transitions ◽  
Mach Number ◽  
Flow Equations ◽  
Zero Mach Number Limit

scholarly journals Computing multi-mode shock-induced compressible turbulent mixing at late times

2015 ◽  
Vol 779 ◽  
pp. 411-431 ◽  
Author(s):  
T. Oggian ◽  
D. Drikakis ◽  
D. L. Youngs ◽  
R. J. R. Williams
Keyword(s):  
Mach Number ◽  
Numerical Simulations ◽  
Compressible Flow ◽  
Turbulent Mixing ◽  
Numerical Study ◽  
Mixing Layer ◽  
Suitable Model ◽  
Late Time ◽  
Flow Equations ◽  
Multi Mode

Both experiments and numerical simulations pertinent to the study of self-similarity in shock-induced turbulent mixing often do not cover sufficiently long times for the mixing layer to become developed in a fully turbulent manner. When the Mach number of the flow is sufficiently low, numerical simulations based on the compressible flow equations tend to become less accurate due to inherent numerical cancellation errors. This paper concerns a numerical study of the late-time behaviour of a single-shocked Richtmyer–Meshkov instability (RMI) and the associated compressible turbulent mixing using a new technique that addresses the above limitation. The present approach exploits the fact that the RMI is a compressible flow during the early stages of the simulation and incompressible at late times. Therefore, depending on the compressibility of the flow field, the most suitable model, compressible or incompressible, can be employed. This motivates the development of a hybrid compressible–incompressible solver that removes the low-Mach-number limitations of the compressible solvers, thus allowing numerical simulations of late-time mixing. Simulations have been performed for a multi-mode perturbation at the interface between two fluids of densities corresponding to an Atwood number of 0.5, and results are presented for the development of the instability, mixing parameters and turbulent kinetic energy spectra. The results are discussed in comparison with previous compressible simulations, theory and experiments.

scholarly journals The effect of core size on the speed of compressible hollow vortex streets

2017 ◽  
Vol 836 ◽  
pp. 797-827 ◽  
Author(s):  
Darren G. Crowdy ◽  
Vikas S. Krishnamurthy
Keyword(s):  
Mach Number ◽  
Compressible Flow ◽  
Vortex Core ◽  
Perturbation Expansion ◽  
Core Size ◽  
Flow Equations ◽  
Stable Case ◽  
First Order ◽  
Aspect Ratios ◽  
Vortex Streets

The effect of weak compressibility on the speed of steadily translating staggered vortex streets of hollow vortices in isentropic subsonic flow is studied. A small-Mach-number perturbation expansion about the incompressible solutions for staggered streets of hollow vortices found recently by Crowdy & Green (Phys. Fluids, 2011, vol. 23, 126602) is carried out; the latter solutions provide a desingularization of the classical point vortex streets of von Kármán. The first-order compressible flow correction is calculated. We employ a novel scheme based on a complex variable formulation of the compressible flow equations (the Imai–Lamla method) combined with conformal mapping theory to track the vortex shape in this free boundary problem. The analysis to find the perturbed streamfunction and compressible vortex shapes is greatly facilitated by exploiting a calculus based on use of the Schottky–Klein prime function of a conformally equivalent parametric annulus. It is found that, for a vortex street of specified aspect ratio comprising vortices of specified circulation, the vortex core size is a key determinant of whether compressibility increases or decreases the steady propagation speed (relative to the incompressible street with the same parameters) and that both eventualities are possible. We focus attention on streets with aspect ratios around 0.28, which is close to the neutrally stable case for incompressible flow, and find that a critical vortex core size exists at which compressibility does not affect the speed of the street at first order in the (squared) Mach number. Streets comprising vortices with core size below the critical value speed up due to compressibility; larger vortices slow down.

The interaction of sound with low Mach number wall turbulence, with application to sound propagation in turbulent pipe flow

1979 ◽  
Vol 94 (4) ◽  
pp. 729-744 ◽  
Author(s):  
M. S. Howe
Keyword(s):  
Mach Number ◽  
Pipe Flow ◽  
Sound Propagation ◽  
Turbulent Pipe Flow ◽  
Wall Turbulence ◽  
Rigid Surface ◽  
Low Mach Number ◽  
Flow Equations ◽  
Wide Range ◽  
Good Agreement

This paper discusses the influence of turbulence convection on the formation of acoustic momentum and thermal boundary layers over a rigid surface in the presence of a low Mach number wall-turbulence shear flow. Equations which determine the modified boundary-layer profiles are obtained from a consideration of the relaxation of coherent perturbations in the Reynolds stress. These equations can be solved analytically for a wide range of conditions which are investigated in detail. The theory is applied to the problem of sound propagation in fully-developed turbulent pipe flow, and at low Mach numbers good agreement is obtained between predicted acoustic attenuation rates and experimental results available in the literature.

scholarly journals Cutoff-independent RG flow equations for two-coupled chains model

2014 ◽  
Vol 28 (32) ◽  
pp. 1450247
Author(s):  
Thiago Prudêncio
Keyword(s):  
Phase Transitions ◽  
Energy Scale ◽  
Strongly Correlated Electron ◽  
Flow Equations ◽  
Correlated Electron ◽  
Independent Form ◽  
Cutoff Dependence ◽  
Dependent Form ◽  
Explicit Consideration ◽  
Spinless Case

One-dimensional strongly correlated electron systems coupled via transverse hopping and presence of interband interactions can converge to a Luttinger liquid state or diverge to an even more intricate behavior, as a Mott state. Explicit consideration of the renormalization group (RG) flow of the Fermi points in the Fermi surface, turns the classification of phase transitions more challenging. We reconsider the recent paper for the spinless case [E. Correa and A. Ferraz, Eur. Phys. J. B 87 (2014) 51], where RG flow equations are derived in a cutoff-dependent form up to two-loops order. We demonstrate that the cutoff-dependence can be removed by rewriting the RG flow equations in terms of the energy scale variable. In our paper, the RG flow equations assume a cutoff-independent form and leads to fixed points independent of cutoff choice. The consequence is the invariance under cutoff transformations, more suitable for classifying universality classes and phase transitions.

scholarly journals Fujita–Kato solution for compressible Navier–Stokes equations with axisymmetric initial data and zero Mach number limit

2019 ◽  
Vol 22 (05) ◽  
pp. 1950041
Author(s):  
Boris Haspot
Keyword(s):  
Mach Number ◽  
Initial Data ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Small Initial Data ◽  
Dimension Formula ◽  
Global Strong Solution ◽  
Rotational Part ◽  
Zero Mach Number Limit

In this paper, we investigate the question of the existence of global strong solution for the compressible Navier–Stokes equations for small initial data such that the rotational part of the velocity [Formula: see text] belongs to [Formula: see text] (in dimension [Formula: see text]). We show then an equivalent of the so-called Fujita–Kato theorem to the case of the compressible Navier–Stokes equations when we consider axisymmetric initial data. The main difficulty is linked to the fact that in this case the velocity is not Lipschitz, as a consequence we have to study carefully the coupling between the rotational and irrotational part of the velocity. In a second part, we address the question of convergence to the incompressible model (for ill-prepared initial data) when the Mach number goes to zero.

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