Newtonian flow theory for slender bodies in a dusty gas

1981 ◽  
Vol 108 ◽  
pp. 147-157 ◽  
Author(s):  
R. M. Barron ◽  
J. T. Wiley
Keyword(s):  
Shock Wave ◽  
Gas Flow ◽  
The Body ◽  
Dusty Gas ◽  
Newtonian Theory ◽  
Wedge Surface ◽  
Slender Bodies ◽  
Two Phases ◽  
Flow Variables ◽  
Thin Wedge

Hypersonic small-disturbance theory is extended to consider the problem of dusty-gas flow past thin two-dimensional bodies. The mass fraction of suspended particles is assumed to be sufficiently large that the two-way interaction between particle phase and gas phase must be considered. The system of eight governing equations is further reduced by considering the Newtonian approximation γ → 1 andM∞→ ∞. The Newtonian theory up to second order is studied and the equations are solved for the case of a thin wedge at zero angle of attack. Expressions for the streamlines, dust-particle paths, shock-wave location and all flow variables are obtained. It is seen that the presence of the dust increases the pressure along the wedge surface and tends to bend the shock wave towards the body surface. Other effects of the interaction of the two phases are also discussed.

Focusing of inertial particles after the shock-wave intersection point

2007 ◽  
Vol 5 ◽  
pp. 145-150
Author(s):  
I.V. Golubkina
Keyword(s):  
Shock Wave ◽  
Mass Concentration ◽  
Gas Flow ◽  
Intersection Point ◽  
Plane Shock ◽  
Inertial Particles ◽  
Dusty Gas ◽  
Focusing Effect ◽  
Aerodynamic Focusing ◽  
Particle Mass Concentration

The effect of the aerodynamic focusing of inertial particles is investigated in both symmetric and non-symmetric cases of interaction of two plane shock waves in the stationary dusty-gas flow. The particle mass concentration is assumed to be small. Particle trajectories and concentration are calculated numerically with the full Lagrangian approach. A parametric study of the flow is performed in order to find the values of the governing parameters corresponding to the maximum focusing effect.

Axisymmetric hypersonic flow with strong viscous interaction

1968 ◽  
Vol 34 (4) ◽  
pp. 687-703 ◽  
Author(s):  
John Webster Ellinwood ◽  
Harold Mirels
Keyword(s):  
Shock Wave ◽  
Hypersonic Flow ◽  
Power Law ◽  
Axisymmetric Flow ◽  
Strong Shock ◽  
The Body ◽  
Strong Shock Wave ◽  
Viscous Interaction ◽  
Slender Bodies ◽  
Prandtl Numbers

Stewartson's theory for axisymmetric hypersonic flow of a model gas over slender bodies with strong viscous interaction and strong shock wave is extended to power-law viscosity variation and Prandtl numbers other than one. Flow properties at the body surface and shock are obtained without recourse to numerical integration. Numerical computations are presented for axisymmetric flow over a three-quarter power-law body with strong shock wave and viscous interactions that range from weak to strong.

Oblique shock waves in a dusty-gas flow over a wedge

1986 ◽  
Vol 408 (1834) ◽  
pp. 61-78 ◽  
Keyword(s):  
Shock Wave ◽  
Gas Flow ◽  
Deflection Angle ◽  
Equations Of Motion ◽  
Gas Analysis ◽  
Oblique Shock ◽  
Oblique Shock Wave ◽  
Dusty Gas ◽  
Wave Angle ◽  
Flow Deflection

Supersonic flows of a dusty gas past a wedge are studied theoretically. An oblique shock wave emanates from the apex of the wedge at the same angle as in the case of a pure gas, but bends back because of the presence of the particles. It is shown from an equilibrium-gas analysis that the extent of decrease in the shock-wave angle is larger for smaller velocity of the uniform stream. When the flow-deflection angle is small enough, the oblique shock wave developing fully at large distances from the apex has a fully dispersed transition structure. On the other hand, it is partly dispersed when the flow-deflection angle is large. Details of the development of the oblique shock wave as the distance from the apex increases are clarified by solving the equations of motion numerically. The particles colliding with the wedge are assumed to stick to or reflect elastically from its surface. It is shown that the reflected particles affect the flow significantly in the neighbourhood of the wedge.

scholarly journals Interaction of waves in one-dimensional dusty gas flow

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Pooja Gupta ◽  
Rahul Kumar Chaturvedi ◽  
L. P. Singh
Keyword(s):  
Shock Wave ◽  
High Frequency ◽  
Gas Flow ◽  
Ideal Gas ◽  
Transport Equations ◽  
Dust Particles ◽  
Multiple Time Scales ◽  
Dusty Gas ◽  
One Dimensional ◽  
Geometrical Acoustics

AbstractThe present study uses the theory of weakly nonlinear geometrical acoustics to derive the high-frequency small amplitude asymptotic solution of the one-dimensional quasilinear hyperbolic system of partial differential equations characterizing compressible, unsteady flow with generalized geometry in ideal gas flow with dust particles. The method of multiple time scales is applied to derive the transport equations for the amplitude of resonantly interacting high-frequency waves in a dusty gas. These transport equations are used for the qualitative analysis of nonlinear wave interaction process and self-interaction of nonlinear waves which exist in the system under study. Further, the evolutionary behavior of weak shock waves propagating in ideal gas flow with dust particles is examined here. The progressive wave nature of nonresonant waves terminating into the shock wave and its location is also studied. Further, we analyze the effect of the small solid particles on the propagation of shock wave.

Analytical solution for unsteady adiabatic and isothermal flows behind the shock wave in a rotational axisymmetric mixture of perfect gas and small solid particles

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
G. Nath
Keyword(s):  
Shock Wave ◽  
Analytical Solutions ◽  
Mass Concentration ◽  
Solid Particles ◽  
Dusty Gas ◽  
Perfect Gas ◽  
Rotational Parameter ◽  
First Approximation ◽  
Isothermal Flows ◽  
Flow Variables

Abstract The approximate analytical solutions are obtained for adiabatic and isothermal flows behind a cylindrical shock wave in a dusty gas. A mixture of perfect gas and micro size small inert solid particles is taken as the dusty gas. The inert solid particles are distributed continuously in the mixture. It is considered that the equilibrium flow conditions are maintained. The flow variables are expanded in power series to obtain the solution of the problem. The analytical solutions are obtained for the first order approximation in both the adiabatic and isothermal cases. Also, the system of ordinary differential equations for second order approximations to the solution is obtained. The influence of an increase in the ratio of the density of the inert solid particles to the initial density of the perfect gas, the rotational parameter and the mass concentration of inert solid particles in the mixture are discussed on the flow variables for first approximation. Our first approximation to the solution corresponds to the Taylor’s solution for the creation of a blast wave by a strong explosion. A comparison is also made between the solutions for isothermal and adiabatic flows. It is investigated that the density and pressure near the line of symmetry in the case of isothermal flow become zero and hence a vacuum is formed at the axis of symmetry when the flow is isothermal. Also, it is found that an increase in the value of rotational parameter or the mass concentration of solid particles in the mixture has a decaying effect on shock wave. The present work may be used to verify the correctness of the solution obtained by self-similarity and numerical methods.

SHOCK WAVE INTERACTION NEAR A CYLINDER ALIGNED NORMAL TO A BLUNTED PLATE—PART I: GAS FLOW AND HEAT TRANSFER ON A PLATE NEAR A CYLINDER

2018 ◽  
Vol 49 (2) ◽  
pp. 105-118
Author(s):  
Volf Ya. Borovoy ◽  
Vladimir Evguenyevich Mosharov ◽  
Vladimir Nikolaevich Radchenko ◽  
Arkadii Sergeyevich Skuratov
Keyword(s):  
Heat Transfer ◽  
Shock Wave ◽  
Gas Flow ◽  
Wave Interaction ◽  
Shock Wave Interaction ◽  
Flow And Heat Transfer

Analytical solution for unsteady flow behind ionizing shock wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field

2021 ◽  
Vol 76 (3) ◽  
pp. 265-283
Author(s):  
G. Nath
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Analytical Solution ◽  
Axial Magnetic Field ◽  
Order Approximation ◽  
Ideal Gas ◽  
Field Region ◽  
First Order ◽  
First Order Approximation ◽  
Flow Variables

Abstract The approximate analytical solution for the propagation of gas ionizing cylindrical blast (shock) wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field is investigated. The axial and azimuthal components of fluid velocity are taken into consideration and these flow variables, magnetic field in the ambient medium are assumed to be varying according to the power laws with distance from the axis of symmetry. The shock is supposed to be strong one for the ratio C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ to be a negligible small quantity, where C 0 is the sound velocity in undisturbed fluid and V S is the shock velocity. In the undisturbed medium the density is assumed to be constant to obtain the similarity solution. The flow variables in power series of C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ are expanded to obtain the approximate analytical solutions. The first order and second order approximations to the solutions are discussed with the help of power series expansion. For the first order approximation the analytical solutions are derived. In the flow-field region behind the blast wave the distribution of the flow variables in the case of first order approximation is shown in graphs. It is observed that in the flow field region the quantity J 0 increases with an increase in the value of gas non-idealness parameter or Alfven-Mach number or rotational parameter. Hence, the non-idealness of the gas and the presence of rotation or magnetic field have decaying effect on shock wave.

Evolution of weak shock wave in two-dimensional steady supersonic flow in dusty gas

2019 ◽  
Vol 160 ◽  
pp. 552-557 ◽  
Author(s):  
Rahul Kumar Chaturvedi ◽  
Pooja Gupta ◽  
L.P. Singh
Keyword(s):  
Shock Wave ◽  
Supersonic Flow ◽  
Weak Shock ◽  
Weak Shock Wave ◽  
Dusty Gas ◽  
Two Dimensional
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