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.

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.

High Order Compact Schemes in Projection Methods for Incompressible Viscous Flows

2011 ◽  
Vol 9 (4) ◽  
pp. 994-1019 ◽  
Author(s):  
Michel Fournié ◽  
Alain Rigal
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Normal Mode Analysis ◽  
Correction Method ◽  
Projection Methods ◽  
High Order ◽  
Mode Analysis ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Von Neumann

AbstractWithin the projection schemes for the incompressible Navier-Stokes equations (namely “pressure-correction” method), we consider the simplest method (of order one in time) which takes into account the pressure in both steps of the splitting scheme. For this scheme, we construct, analyze and implement a new high order compact spatial approximation on nonstaggered grids. This approach yields a fourth order accuracy in space with an optimal treatment of the boundary conditions (without error on the velocity) which could be extended to more general splitting. We prove the unconditional stability of the associated Cauchy problem via von Neumann analysis. Then we carry out a normal mode analysis so as to obtain more precise results about the behavior of the numerical solutions. Finally we present detailed numerical tests for the Stokes and the Navier-Stokes equations (including the driven cavity benchmark) to illustrate the theoretical results.

A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

1989 ◽  
Vol 209 ◽  
pp. 285-308 ◽  
Author(s):  
R. J. Bodonyi ◽  
W. J. C. Welch ◽  
P. W. Duck ◽  
M. Tadjfar
Keyword(s):  
Numerical Solutions ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Surface Geometry ◽  
Navier Stokes Equations ◽  
S Waves ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

NUMERICAL SOLUTIONS OF 2D AND 3D SLAMMING PROBLEMS

2021 ◽  
Vol 153 (A2) ◽  
Author(s):  
Q Yang ◽  
W Qiu
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Type Equation ◽  
The Body ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Highly Nonlinear ◽  
2D And 3D

Slamming forces on 2D and 3D bodies have been computed based on a CIP method. The highly nonlinear water entry problem governed by the Navier-Stokes equations was solved by a CIP based finite difference method on a fixed Cartesian grid. In the computation, a compact upwind scheme was employed for the advection calculations and a pressure-based algorithm was applied to treat the multiple phases. The free surface and the body boundaries were captured using density functions. For the pressure calculation, a Poisson-type equation was solved at each time step by the conjugate gradient iterative method. Validation studies were carried out for 2D wedges with various deadrise angles ranging from 0 to 60 degrees at constant vertical velocity. In the cases of wedges with small deadrise angles, the compressibility of air between the bottom of the wedge and the free surface was modelled. Studies were also extended to 3D bodies, such as a sphere, a cylinder and a catamaran, entering calm water. Computed pressures, free surface elevations and hydrodynamic forces were compared with experimental data and the numerical solutions by other methods.

scholarly journals Mathematical Model for the Electrokinetic Instability of Electrolyte Flow

2019 ◽  
Vol 224 ◽  
pp. 02003
Author(s):  
Andrey Shobukhov
Keyword(s):  
Electric Potential ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Steady State Solution ◽  
Stability Loss ◽  
Navier Stokes ◽  
Ion Distribution ◽  
Navier Stokes Equations ◽  
Dilute Aqueous Solution

We study a one-dimensional model of the dilute aqueous solution of KCl in the electric field. Our model is based on a set of Nernst-Planck-Poisson equations and includes the incompressible fluid velocity as a parameter. We demonstrate instability of the linear electric potential variation for the uniform ion distribution and compare analytical results with numerical solutions. The developed model successfully describes the stability loss of the steady state solution and demonstrates the emerging of spatially non-uniform distribution of the electric potential. However, this model should be generalized by accounting for the convective movement via the addition of the Navier-Stokes equations in order to substantially extend its application field.

Reliability of Convective Diffusion Process in Stenosis Blood Vessels

2008 ◽  
Vol 3 (1) ◽  
Author(s):  
R.K. Saket ◽  
Anil Kumar
Keyword(s):  
Mass Transport ◽  
Diffusion Process ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Wall Stress ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Equations ◽  
Recirculation Flow ◽  
Convection Diffusion Equation

This paper presents a convective dominated reliable diffusion process in an axi-symmetric tube with a local constriction simulating a stenos artery considering the porosity effects. The investigations demonstrate the effects of wall shear stress and recirculation flow on the concentration distribution in the vessels lumen and on wall mass transfer keeping the porosity in view. The flow is governed by the incompressible Navier-Stokes equations for Newtonian fluid in porous medium. The convection diffusion equation has been used for the mass transport. The effect of porosity is examined on the velocity field and wall stress. The numerical solutions of the flow equations and the coupled mass transport equations have been obtained using a finite difference method. This paper explains the reliable effects of flow porosity on the mass transport.

Viscosity Effects on the Radiation Hydrodynamics of Horizontal Cylinders

1991 ◽  
Vol 113 (4) ◽  
pp. 334-343 ◽  
Author(s):  
R. W. Yeung ◽  
C.-F. Wu
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Small Body ◽  
Low Frequency ◽  
Body Motion ◽  
Navier Stokes ◽  
Inviscid Fluid ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Horizontal Cylinders

The problem of a body oscillating in a viscous fluid with a free surface is examined. The Navier-Stokes equations and boundary conditions are linearized using the assumption of small body-motion to wavelength ratio. Generation and diffusion of vorticity, but not its convection, are accounted for. Rotational and irrotational Green functions for a divergent and a vorticity source are presented, with the effects of viscosity represented by a frequency Reynolds number Rσ = g2/νσ3. Numerical solutions for a pair of coupled integral equations are obtained for flows about a submerged cylinder, circular or square. Viscosity-modified added-mass and damping coefficients are developed as functions of frequency. It is found that as Rσ approaches infinity, inviscid-fluid results can be recovered. However, viscous effects are important in the low-frequency range, particularly when Rσ is smaller than O(104).

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