Numerical Investigation of Cloud Cavitation and Its Induced Shock Waves

2021 ◽  
Author(s):  
Takahiro Ushioku ◽  
Hiroaki Yoshimura
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Multiphase Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Lagrangian Description ◽  
Cloud Cavitation ◽  
Wave Emission ◽  
Set Up ◽  
Unsteady Behavior

Abstract This paper numerically investigates unsteady behavior of cloud cavitation, in particular, to elucidate the induced shock wave emission. To do this, we consider a submerged water-jet injection into still water through a nozzle and make some numerical analysis of two-dimensional multiphase flows by Navier-Stokes equations. In our previous study [7], we have shown that twin vortices symmetrically appear in the injected water, which plays an essential role in performing the unsteady behavior of a cloud of bubbles. In this paper, we further illustrate the elementary process of the emission of the shock waves. First, we set up the mixture model of liquid and gas in Lagrangian description by the SPH method, together with the details on the treatment of boundary conditions. Second, we show the velocity fields of the multiphase flow to illustrate the inception, growth as well as the collapse of the cloud. In particular, we explain the mechanism of the collapse of the cloud in view of the motion of the twin vortices. Further, we investigate the pressure fields of the multiphase flow in order to demonstrate how the shock wave is emitted associated with the collapse of the cloud. Finally, we show that a small shock wave may be released prior to the main shock wave emission.

A note on the solution of the Navier-Stokes equations for a spherically symmetric expansion into a very low pressure

1973 ◽  
Vol 59 (2) ◽  
pp. 391-396 ◽  
Author(s):  
N. C. Freeman ◽  
S. Kumar
Keyword(s):  
Shock Wave ◽  
Reynolds Number ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Low Pressure ◽  
Navier Stokes ◽  
Spherically Symmetric ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Type Flow

It is shown that, for a spherically symmetric expansion of a gas into a low pressure, the shock wave with area change region discussed earlier (Freeman & Kumar 1972) can be further divided into two parts. For the Navier–Stokes equation, these are a region in which the asymptotic zero-pressure behaviour predicted by Ladyzhenskii is achieved followed further downstream by a transition to subsonic-type flow. The distance of this final region downstream is of order (pressure)−2/3 × (Reynolds number)−1/3.

Self-Excited Oscillation of Transonic Flow Around an Airfoil in Two-Dimensional Channel

1989 ◽  
Author(s):  
Kazuomi Yamamoto ◽  
Yoshimichi Tanida
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Transonic Flow ◽  
Stokes Equations ◽  
Flow Region ◽  
Boundary Layer Separation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Layer Separation ◽  
Excited Oscillation

A self-excited oscillation of transonic flow in a simplified cascade model was investigated experimentally, theoretically and numerically. The measurements of the shock wave and wake motions, and unsteady static pressure field predict a closed loop mechanism, in which the pressure disturbance, that is generated by the oscillation of boundary layer separation, propagates upstream in the main flow and forces the shock wave to oscillate, and then the shock oscillation disturbs the boundary layer separation again. A one-dimensional analysis confirms that the self-excited oscillation occurs in the proposed mechanism. Finally, a numerical simulation of the Navier-Stokes equations reveals the unsteady flow structure of the reversed flow region around the trailing edge, which induces the large flow separation to bring about the anti-phase oscillation.

Perturbation Procedures for Nonlinear Viscous Flows

1983 ◽  
Vol 50 (2) ◽  
pp. 265-269
Author(s):  
D. Nixon
Keyword(s):  
Perturbation Theory ◽  
Shock Waves ◽  
Transonic Flow ◽  
Stokes Equations ◽  
Viscous Flows ◽  
Two Dimensions ◽  
Experimental Results ◽  
Navier Stokes ◽  
Navier Stokes Equations

The perturbation theory for transonic flow is further developed for solutions of the Navier-Stokes equations in two dimensions or for experimental results. The strained coordinate technique is used to treat changes in location of any shock waves or large gradients.

Numerical simulation of dispersion and distribution behaviors of hydrogen leakage in the garage with a crossbeam

SIMULATION ◽  
2019 ◽  
Vol 95 (12) ◽  
pp. 1229-1238 ◽  
Author(s):  
Yunhao Li ◽  
Juncheng Jiang ◽  
Yuan Yu ◽  
Qingwu Zhang
Keyword(s):  
Mole Fraction ◽  
Natural Ventilation ◽  
Stokes Equations ◽  
Ventilation System ◽  
Three Dimensional ◽  
Dynamics Simulation ◽  
Navier Stokes ◽  
Explosion Hazard ◽  
Safety Issues ◽  
Set Up

A three-dimensional computational fluid dynamics simulation model resolved by the unsteady Reynolds-Averaged Navier–Stokes equations was developed to predict hydrogen dispersion in an indoor environment. The effect of the height of the crossbeam (Hc) on hydrogen dispersion and distribution behaviors in a four-car garage was numerically investigated under fully confined and natural ventilation conditions. For the fully confined condition, the garage was almost completely filled with a flammable hydrogen cloud at t=600 s. In addition, the volumetric ratio of the flammable region, thickness of the hydrogen stratification, and hydrogen mole fraction all increased as Hc increased. When two symmetric ventilation openings were set up, the volumetric ratio of the flammable region decreased by 50% at t=600 s. Moreover, Hc had evident influence on the vertical distribution of hydrogen mole fraction. In addition, there existed little explosion hazard under the height of 1.6 m. The results show that Hc was a non-negligible factor for the safety design of hydrogen in the garage and Hc=0.12 m was the optimal height of the crossbeam. Furthermore, the ventilation system in the present study cannot completely eliminate the risk of hydrogen explosion. The present risk assessment results can be useful to analyze safety issues in automotive applications of hydrogen.

scholarly journals A Modified Gas-Kinetic Scheme for Turbulent Flow

2014 ◽  
Vol 16 (1) ◽  
pp. 239-263 ◽  
Author(s):  
Marcello Righi
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Numerical Scheme ◽  
Stokes Equations ◽  
Kinetic Scheme ◽  
Navier Stokes ◽  
Turbulent Stress ◽  
Navier Stokes Equations

AbstractThe implementation of a turbulent gas-kinetic scheme into a finite-volume RANS solver is put forward, with two turbulent quantities, kinetic energy and dissipation, supplied by an allied turbulence model. This paper shows a number of numerical simulations of flow cases including an interaction between a shock wave and a turbulent boundary layer, where the shock-turbulent boundary layer is captured in a much more convincing way than it normally is by conventional schemes based on the Navier-Stokes equations. In the gas-kinetic scheme, the modeling of turbulence is part of the numerical scheme, which adjusts as a function of the ratio of resolved to unresolved scales of motion. In so doing, the turbulent stress tensor is not constrained into a linear relation with the strain rate. Instead it is modeled on the basis of the analogy between particles and eddies, without any assumptions on the type of turbulence or flow class. Conventional schemes lack multiscale mechanisms: the ratio of unresolved to resolved scales – very much like a degree of rarefaction – is not taken into account even if it may grow to non-negligible values in flow regions such as shocklayers. It is precisely in these flow regions, that the turbulent gas-kinetic scheme seems to provide more accurate predictions than conventional schemes.

Shock Wave Instability in a Channel with an Expansion Corner

2015 ◽  
Vol 07 (02) ◽  
pp. 1550019 ◽  
Author(s):  
A. Kuzmin
Keyword(s):  
Shock Wave ◽  
Stokes Equations ◽  
Variable Cross Section ◽  
Navier Stokes ◽  
Variable Cross ◽  
Navier Stokes Equations ◽  
Shock Position ◽  
Sonic Surface ◽  
2D And 3D ◽  
Subsonic Region

2D and 3D transonic flows in a channel of variable cross-section are studied numerically using a solver based on the Reynolds-averaged Navier–Stokes equations. The flow velocity is supersonic at the inlet and outlet of the channel. Between the supersonic regions, there is a local subsonic region whose upstream boundary is a shock wave, whereas the downstream boundary is a sonic surface. The sonic surface gives rise to an instability of the shock wave position in the channel. Computations reveal a hysteresis in the shock position versus the inflow Mach number. A dependence of the hysteresis on the velocity profile given at the inlet is examined.

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