Interaction of a Singular Surface with a Characteristic Shock in a Relaxing Gas with Dust Particles

2020 ◽  
Vol 75 (2) ◽  
pp. 119-129 ◽  
Author(s):  
Sheena Mittal ◽  
Jasobanta Jena
Keyword(s):  
Wave Front ◽  
Wave Interaction ◽  
Singular Surface ◽  
Dust Particles ◽  
Shock Acceleration ◽  
Wave Form ◽  
Transmitted Waves ◽  
Governing System ◽  
Characteristic Shock ◽  
Relaxing Gas

AbstractA system of hyperbolic differential equations outlining one-dimensional planar, cylindrical symmetric and spherical symmetric flow of a relaxing gas with dust particles is considered. Singular surface theory used to study different aspects of wave propagation and its culmination to the steepened form. The evolutionary behavior of the characteristic shock is studied. A particular solution of the governing system of equations is used to discuss the steepened wave form, characteristic shock and their interaction. The results of the interaction between the steepened wave front and the characteristic shock using the general theory of wave interaction are discussed. Also, the influence of relaxation and dust parameters on the steepened wave front, the formation of a characteristic shock, reflected and transmitted waves after interaction and a jump in shock acceleration are investigated.

scholarly journals Matrix basis for plane and modal waves in a Timoshenko beam

2016 ◽  
Vol 3 (11) ◽  
pp. 160825 ◽  
Author(s):  
Julio Cesar Ruiz Claeyssen ◽  
Daniela de Rosso Tolfo ◽  
Leticia Tonetto
Keyword(s):  
Closed Form ◽  
Timoshenko Beam ◽  
Plane Waves ◽  
Crack Problem ◽  
Wave Interaction ◽  
Beam Model ◽  
High Frequencies ◽  
Transmitted Waves ◽  
The Matrix ◽  
Non Local

Plane waves and modal waves of the Timoshenko beam model are characterized in closed form by introducing robust matrix basis that behave according to the nature of frequency and wave or modal numbers. These new characterizations are given in terms of a finite number of coupling matrices and closed form generating scalar functions. Through Liouville’s technique, these latter are well behaved at critical or static situations. Eigenanalysis is formulated for exponential and modal waves. Modal waves are superposition of four plane waves, but there are plane waves that cannot be modal waves. Reflected and transmitted waves at an interface point are formulated in matrix terms, regardless of having a conservative or a dissipative situation. The matrix representation of modal waves is used in a crack problem for determining the reflected and transmitted matrices. Their euclidean norms are seen to be dominated by certain components at low and high frequencies. The matrix basis technique is also used with a non-local Timoshenko model and with the wave interaction with a boundary. The matrix basis allows to characterize reflected and transmitted waves in spectral and non-spectral form.

On the near-equilibrium and near-frozen regions in an expansion wave in a relaxing gas

1964 ◽  
Vol 19 (1) ◽  
pp. 81-102 ◽  
Author(s):  
J. G. Jones
Keyword(s):  
Asymptotic Solution ◽  
Simple Wave ◽  
Expansion Wave ◽  
Wave Form ◽  
Time Interval ◽  
Finite Time Interval ◽  
Acoustic Equation ◽  
Equilibrium Region ◽  
Relaxing Gas ◽  
Asymptotic Equilibrium

A weak expansion wave propagating in a relaxing gas is discussed with particular reference to the ‘near-equilibrium’ and ‘near-frozen’ regions. The concept of bulk viscosity is used in conjunction with Burger's equation in the near-equilibrium region. The asymptotic equilibrium simple wave is modified by diffusive regions in the neighbourhood of the first and last rays. It is shown that in the case of a weak expansion wave, Chu's asymptotic solution of the acoustic equation describes the wave-form for a finite time interval before convection effects become noticeable. In the near-frozen region a characteristic perturbation method is used to describe the flow near the wave-front.

Blast waves in dusty gases

1987 ◽  
Vol 414 (1846) ◽  
pp. 197-219 ◽  
Keyword(s):  
Flow Field ◽  
Wave Front ◽  
Blast Wave ◽  
Spherical Layer ◽  
Blast Waves ◽  
Solid Particles ◽  
Dust Particles ◽  
Spatial Density ◽  
Maximum Pressure ◽  
Sharp Maximum

The conservation equations for the flow field developed behind a spherical blast wave propagating into a dusty medium (gas seeded with small uniformly distributed solid particles) are formulated and solved numerically by using the random choice method. The solution was carried out for the following three cases: (1) the dust is uniformly distributed outside the exploding spherical diaphragm; (2) the dust is uniformly distributed inside the exploding spherical diaphragm; (3) the dust is uniformly distributed inside a spherical layer located outside the exploding spherical diaphragm. The solutions obtained were compared with a similar pure-gas case. It was found that the dust presence weakens the blast wave, i. e. the gas velocity, temperature and pressure immediately behind the blast-wave front were lower than those obtained in a similar pure-gas case. The presence of dust changed the flow field behind the blast wave. The typical blast-wave pressure signature (i. e. a monotonic reduction in the pressure after the jump across the blast-wave front) changed to a different shape. Now the pressure increases after the blast-wave front until it reaches a maximum value followed by a monotonic pressure reduction. The maximum pressure is attained between the blast-wave front and the contact surface. Higher values of total pressure are obtained in the dusty gas case. The initial uniform spatial distribution of the dust particles changed into a bell-shaped pattern with a pronounced peak. The development of the sharp maximum in the dust spatial-density distribution might be of interest in assessing the effects of atmospheric nuclear explosions.

Wave front analysis of weak nonlinear waves in a two-phase flow of gas and dust particles

1993 ◽  
Vol 44 (5) ◽  
pp. 799-811
Author(s):  
V. D. Sharma ◽  
R. R. Sharma ◽  
B. D. Pandey ◽  
N. Gupta
Keyword(s):  
Wave Front ◽  
Nonlinear Waves ◽  
Two Phase Flow ◽  
Dust Particles ◽  
Phase Flow ◽  
Two Phase

scholarly journals Methods of simulating the front of the air shock wave for calculating the industrial structure

Vestnik MGSU ◽  
2020 ◽  
pp. 223-234
Author(s):  
Oleg V. Mkrtychev ◽  
Anton Y. Savenkov
Keyword(s):  
Shock Wave ◽  
Wave Front ◽  
Exposure Time ◽  
Shock Wave Front ◽  
Software Package ◽  
Wave Interaction ◽  
Computational Region ◽  
Shock Wave Interaction ◽  
Dynamic Setting ◽  
Dynamic Methods

Introduction. The paper considers existing methods of simulating a wide front of an air shock wave for solving problems of shock wave interaction with an installation using gas-dynamic methods. When solving the problem of the air shock wave interaction with an installation in a dynamic setting, it was revealed that, when simulating a wide front of a distant explosion using point explosions, it is possible to obtain an underestimated time of the shock wave action. This results in a downward bias of loads to the installation. Thus, the loads obtained in this case do not correspond to the loads for which it is necessary to carry out the calculation of industrial installations protected from shock waves in accordance with domestic and international regulatory documents. To eliminate this drawback, another approach is proposed. It consists in setting the load on the computational region in the form of a pressure graph with specified parameters of overpressure and exposure time. Materials and methods. The interaction of the shock wave front with the installation is carried out using numerical simulation in a nonlinear dynamic setting using gas-dynamic methods in the LS-DYNA software package. Results. The following analyses were conducted in the scope of the study: an analysis of existing methods of forming the wide shock wave front of the distant explosion and an analysis of the parameters of the shock wave during the formation of the wide shock wave front of the distant explosion by setting the pressure graph with the specified parameters of the overpressure and the exposure time. Conclusions. The result of the analysis of methods for numerical simulation of the interaction of the air shock wave wide front with the installation showed that simulation of the explosion source in the form of volume elements and simulation of the shock wave using the CONWEP function of the LS-DYNA software package have disadvantages. These disadvantages do not allow obtaining the main parameters of the shock wave for the further use. A method for modeling the wide shock wave front is given by setting a pressure graph at the boundary of the computational region with the required overpressure parameters and exposure time.

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