On the direct initiation of a plane detonation wave

1986 ◽  
Vol 408 (1834) ◽  
pp. 129-148 ◽  
Keyword(s):  
Shock Wave ◽  
Detonation Wave ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Combustible Gas ◽  
Direct Initiation ◽  
Time Domains ◽  
History Of ◽  
Plane Detonation

It is assumed that energy is transferred at a rapid rate through a plane wall into a spatially uniform and initially stagnant combustible gas mixture. This action generates a shock wave, just as it does in an inert mixture, and also switches on a significant rate of chemical reaction. The Navier-Stokes equations for plane unsteady flow are integrated numerically in order to reveal the subsequent history of events. Four principal time domains are identified, namely ‘early’, ‘transitional’, ‘formation’ and ‘ZND’. The first contains a conduction-dominated explosion and formation of a shock wave; in the second interval the shock wave is responsible for the acceleration of chemical activity, which becomes intense during the ‘formation’ period. Finally a wave whose structure is in essence that of a ZND detonation wave emerges.

On the evolution of plane detonations

1990 ◽  
Vol 429 (1877) ◽  
pp. 259-283 ◽  
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Unsteady Motion ◽  
Navier Stokes ◽  
Infinite Domain ◽  
Navier Stokes Equations ◽  
Von Neumann ◽  
Combustible Gas ◽  
History Of ◽  
Large Heat

Numerical solutions of the Navier–Stokes equations for the plane one-dimensional unsteady motion of a compressible, combustible gas mixture are used to follow the history of events that are initiated by addition of large heat power through a solid surface bounding an effectively semi­-infinite domain occupied by the gas. Plane Zel’dovich–von Neumann–Doring detonations eventually appear either at the precursor shock (which exists in every set of circumstances) or in the regions, occupied by an unsteady induction-domain and an initially quasi-steady fast-flame, that lie behind the precursor shock.

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.

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.

scholarly journals Прохождение плоской ударной волны через область тлеющего газового разряд

2019 ◽  
Vol 89 (1) ◽  
pp. 42
Author(s):  
Т.А. Лапушкина ◽  
А.В. Ерофеев ◽  
О.А. Азарова ◽  
О.В. Кравченко
Keyword(s):  
Shock Wave ◽  
Stokes Equations ◽  
Wave Structure ◽  
Gas Discharge ◽  
Navier Stokes ◽  
Plane Shock ◽  
Two Dimensional ◽  
Gas Temperature ◽  
Discharge Region ◽  
Navier Stokes Equations

AbstractThe interaction of a plane shock wave ( M = 5) with an ionized plasma region formed before the arrival of a shock wave by a low-current glow gas discharge is considered experimentally and numerically. In the experiment, schlieren images of a moving shock-wave structure resulting from the interaction and consisting of two discontinuities, convex in the direction of motion of the initial wave, are obtained. The propagation of a shock wave over the region of energetic impact is simulated on the basis of the two-dimensional Riemann problem of decay of an arbitrary discontinuity with allowance for the influence of horizontal walls. The systems of Euler and Navier–Stokes equations are solved numerically. The non-equilibrium of the processes in the gas-discharge region was simulated by an effective adiabatic index γ. Based on the calculations performed for equilibrium air (γ = 1.4) and for an ionized nonequilibrium gas medium (γ = 1.2), it is shown that the experimentally observed discontinuities can be interpreted as elements of the solution of the two-dimensional problem of decay of a discontinuity: a shock wave followed by a contact discontinuity. It is shown that a variation in γ affects the shape of the fronts and velocities of the discontinuities obtained. Good agreement is obtained between the experimental and calculated images of density and velocities of the discontinuities at a residual gas temperature in the gas discharge region of 373 K.

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