Search results for: Navier- Stokes equations.

Authors: I. Sarras, G. Gerakios, A. Diamantis, A. I. Dounis, G. P. Syrcos

Abstract:

Global Positioning System (GPS) technology is widely used today in the areas of geodesy and topography as well as in aeronautics mainly for military purposes. Due to the military usage of GPS, full access and use of this technology is being denied to the civilian user who must then work with a less accurate version. In this paper we focus on the estimation of the receiver coordinates ( X, Y, Z ) and its clock bias ( δtr ) of a fixed point based on pseudorange measurements of a single GPS receiver. Utilizing the instantaneous coordinates of just 4 satellites and their clock offsets, by taking into account the atmospheric delays, we are able to derive a set of pseudorange equations. The estimation of the four unknowns ( X, Y, Z , δtr ) is achieved by introducing an extended Kalman filter that processes, off-line, all the data collected from the receiver. Higher performance of position accuracy is attained by appropriate tuning of the filter noise parameters and by including other forms of biases.

Keywords: Extended Kalman filter, GPS, Pseudorange

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Authors: Gholam Reza Koochaki

Abstract:

This work presents the highly accurate numerical calculation of the natural frequencies for functionally graded beams with simply supported boundary conditions. The Timoshenko first order shear deformation beam theory and the higher order shear deformation beam theory of Reddy have been applied to the functionally graded beams analysis. The material property gradient is assumed to be in the thickness direction. The Hamilton-s principle is utilized to obtain the dynamic equations of functionally graded beams. The influences of the volume fraction index and thickness-to-length ratio on the fundamental frequencies are discussed. Comparison of the numerical results for the homogeneous beam with Euler-Bernoulli beam theory results show that the derived model is satisfactory.

Keywords: Functionally graded beam, Free vibration, Hamilton's principle.

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Authors: Viet-Hung Truong, Seung-Eock Kim

Abstract:

This paper presents a robust software package for practical advanced analysis of space steel framed structures. The pre- and post-processors of the presented software package are coded in the C++ programming language while the solver is written by using the FORTRAN programming language. A user-friendly graphical interface of the presented software is developed to facilitate the modeling process and result interpretation of the problem. The solver employs the stability functions for capturing the second-order effects to minimize modeling and computational time. Both the plastic-hinge and fiber-hinge beam-column elements are available in the presented software. The generalized displacement control method is adopted to solve the nonlinear equilibrium equations.

Keywords: Advanced analysis, beam-column, fiber-hinge, plastic hinge, steel frame.

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Authors: L. Tani, N. El Ouzzani

Abstract:

Crosstalk among interconnects and printed-circuit board (PCB) traces is a major limiting factor of signal quality in highspeed digital and communication equipments especially when fast data buses are involved. Such a bus is considered as a planar multiconductor transmission line. This paper will demonstrate how the finite difference time domain (FDTD) method provides an exact solution of the transmission-line equations to analyze the near end and the far end crosstalk. In addition, this study makes it possible to analyze the rise time effect on the near and far end voltages of the victim conductor. The paper also discusses a statistical analysis, based upon a set of several simulations. Such analysis leads to a better understanding of the phenomenon and yields useful information.

Keywords: Multiconductor transmission line, Crosstalk, Finite difference time domain (FDTD), printed-circuit board (PCB), Rise time, Statistical analysis.

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Authors: Hamdy M. Youssef, Eman A. Al-Lehaibi

Abstract:

This paper presents an iteration method for the numerical solutions of a one-dimensional problem of generalized thermoelasticity with one relaxation time under given initial and boundary conditions. The thermoelastic material with variable properties as a power functional graded has been considered. Adomian’s decomposition techniques have been applied to the governing equations. The numerical results have been calculated by using the iterations method with a certain algorithm. The numerical results have been represented in figures, and the figures affirm that Adomian’s decomposition method is a successful method for modeling thermoelastic problems. Moreover, the empirical parameter of the functional graded, and the lattice design parameter have significant effects on the temperature increment, the strain, the stress, the displacement.

Keywords: Adomian, Decomposition Method, Generalized Thermoelasticity, algorithm, empirical parameter, lattice design.

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Authors: Seema Kapoor, Sushil K. Kansal, Baljinder K. Gill, Aarti Sharma, Swati Arora

Abstract:

Isobaric vapor-liquid equilibrium measurements are reported for the binary mixtures of Mesitylene + 1-Heptanol and Mesitylene + 1-Octanol at 97.3 kPa. The measurements have been performed using a vapor recirculating type (modified Othmer's) equilibrium still. Both the mixtures show positive deviation from ideality. The Mesitylene + 1-Heptanol mixture forms an azeotrope whereas Mesitylene + 1- Octanol form a non – azeotropic mixture. The activity coefficients have been calculated taking into consideration the vapor phase nonideality. The data satisfy the thermodynamic consistency tests of Herington, and Hirata. The activity coefficients have been satisfactorily correlated by means of the Margules, Redlich-Kister, Wilson, Black, and NRTL equations. The activity coefficient values have also been obtained by UNIFAC method.

Keywords: Binary mixture, Mesitylene, Vapor-liquid equilibrium, 1-Heptanol, 1-Octanol.

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Authors: H. Sediki, Dj. Ould Abdeslam, T. Otmane-cherif, A. Bechouche, K. Mesbah

Abstract:

This paper explores steady-state characteristics of grid-connected doubly fed induction motor (DFIM) in case of unity power factor operation. Based on the synchronized mathematical model, analytic determination of the control laws is presented and illustrated by various figures to understand the effect of the applied rotor voltage on the speed and the active power. On other hand, unlike previous works where the stator resistance was neglected, in this work, stator resistance is included such that the equations can be applied to small wind turbine generators which are becoming more popular. Finally the work is crowned by integration of the studied induction generator in a wind system where an open loop control is proposed confers a remarkable simplicity of implementation compared to the known methods.

Keywords: DFIM, equivalent circuit, induction machine, steady state

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Authors: Ubonwan Chaiyo, Savitri Garivait, Kobsak Wanthongchai

Abstract:

The study site was located in Ratchaburi Province, Thailand. Four experimental plots in dry dipterocarp forest (DDF) and four plots in mixed deciduous forest (MDF) were set up to estimate the above-ground biomass of tree, sapling and bamboo. The allometry equations were used to investigate above-ground biomass of these vegetation. Seedling and other understory were determined using direct harvesting method. Carbon storage in above-ground biomass was calculated based on IPCC 2006. The results showed that the above-ground biomass of DDF at 20-40% slope, <20% slope and MDF at <20% slope were 91.96, 30.95 and 59.44 ton/ha, respectively. Bamboo covers about half of total aboveground biomass in MDF, which is a specific characteristic of this area. The carbon sequestration potential in above-ground biomass of plot slope range 20-40% DDF, <20% DDF and <20% MDF are 43.22, 14.55 and 27.94 ton C/ha, respectively.

Keywords: Carbon storage, aboveground biomass, tropical deciduous forest, dry dipterocarp forest, mixed deciduous forest.

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Authors: A. Ghafouri, A. Falavand Jozaei, M. Salari

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In this paper, effects of using Alumina-water nanofluid on the rate of heat transfer have been investigated numerically. Physical model is a square enclosure with insulated top and bottom horizontal walls, while the vertical walls are kept at different constant temperatures. Two appropriate models are used to evaluate the viscosity and thermal conductivity of nanofluid. The governing stream-vorticity equations are solved using a second order central finite difference scheme, coupled to the conservation of mass and energy. The study has been carried out for the Richardson number 0.1 to 10 and the solid volume fraction 0 to 0.04. Results are presented by isotherms lines, average Nusselt number and normalized Nusselt number in different range of φ and Ri for forced, combined and natural convection dominated regime. It is found that higher heat transfer rate is predicted when the effects of nanoparticle is taken into account.

Keywords: Nanofluid, Heat Transfer Enhancement, Square Enclosure, Nusselt number.

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Authors: Yanan Yang, Zhigang Wang, Xiang Chen

Abstract:

This paper presents the use of Legendre pseudospectral method for the optimization of finite-thrust orbital transfer for spacecrafts. In order to get an accurate solution, the System-s dynamics equations were normalized through a dimensionless method. The Legendre pseudospectral method is based on interpolating functions on Legendre-Gauss-Lobatto (LGL) quadrature nodes. This is used to transform the optimal control problem into a constrained parameter optimization problem. The developed novel optimization algorithm can be used to solve similar optimization problems of spacecraft finite-thrust orbital transfer. The results of a numerical simulation verified the validity of the proposed optimization method. The simulation results reveal that pseudospectral optimization method is a promising method for real-time trajectory optimization and provides good accuracy and fast convergence.

Keywords: Finite-thrust, Orbital transfer, Legendre pseudospectral method

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Authors: Syeda Maria Ali Shah, Asif Mansoor, Talat Sharafat Rehmani, Safia Mirza

Abstract:

The stock market of any country acts as a predictor of the economy. The spread of the COVID-19 pandemic has severely impacted the global financial markets. Besides, it has also critically affected the economy of Pakistan. In this study, we consider the role of the Karachi Stock Exchange (KSE) with regard to the Pakistan Stock Exchange and quantify the impact on macroeconomic variables in presence of COVID-19. The suitable macroeconomic variables are used to quantify the impact of COVID-19 by developing the stochastic model. The sufficiency of the computed model is attained by means of available techniques in the literature. The estimated equations are used to forecast the impact of pandemic on macroeconomic variables. The constructed model can help the policymakers take counteractive measures for restricting the influence of viruses on the Karachi Stock Market.

Keywords: COVID-19, Karachi Stock Market, macroeconomic variables, stochastic model, forecasting.

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Authors: Mark Watson, J.-F. Bousquet, Adam Forget

Abstract:

A magnetic induction based underwater communication link is evaluated using an analytical model and a custom Finite-Difference Time-Domain (FDTD) simulation tool. The analytical model is based on the Sommerfeld integral, and a full-wave simulation tool evaluates Maxwell’s equations using the FDTD method in cylindrical coordinates. The analytical model and FDTD simulation tool are then compared and used to predict the system performance for various transmitter depths and optimum frequencies of operation. To this end, the system bandwidth, signal to noise ratio, and the magnitude of the induced voltage are used to estimate the expected channel capacity. The models show that in seawater, a relatively low-power and small coils may be capable of obtaining a throughput of 40 to 300 kbps, for the case where a transmitter is at depths of 1 to 3 m and a receiver is at a height of 1 m.

Keywords: Magnetic Induction, FDTD, Underwater Communication, Sommerfeld.

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Authors: Nasser Mohamed Ramli, Mohamad Syafiq Mohamad

Abstract:

Many types of controllers were applied on the continuous stirred tank reactor (CSTR) unit to control the temperature. In this research paper, Proportional-Integral-Derivative (PID) controller are compared with Fuzzy Logic controller for temperature control of CSTR. The control system for temperature non-isothermal of a CSTR will produce a stable response curve to its set point temperature. A mathematical model of a CSTR using the most general operating condition was developed through a set of differential equations into S-function using MATLAB. The reactor model and S-function are developed using m.file. After developing the S-function of CSTR model, User-Defined functions are used to link to SIMULINK file. Results that are obtained from simulation and temperature control were better when using Fuzzy logic control compared to PID control.

Keywords: CSTR, temperature, PID, fuzzy logic.

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Authors: Norazam Arbin, Ishak Hashim

Abstract:

Double-diffusive natural convection in an open top square cavity and heated from the side is studied numerically. Constant temperatures and concentration are imposed along the right and left walls while the heat balance at the surface is assumed to obey Newton-s law of cooling. The finite difference method is used to solve the dimensionless governing equations. The numerical results are reported for the effect of Marangoni number, Biot number and Prandtl number on the contours of streamlines, temperature and concentration. The predicted results for the average Nusselt number and Sherwood number are presented for various parametric conditions. The parameters involved are as follows; the thermal Marangoni number, 0 ≤ MaT ≤1000 , the solutal Marangoni number, 0 1000 c ≤ Ma ≤ , the Biot number, 0 ≤ Bi ≤ 6 , Grashof number, 5 Gr = 10 and aspect ratio 1. The study focused on both flows; thermal dominated, N = 0.8 , and compositional dominated, N = 1.3 .

Keywords: Double-diffusive, Marangoni effects, heat and mass transfer.

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Authors: Inta Volodko, Valentina Koliskina

Abstract:

Linear stability of wake-shear layers in two-phase shallow flows is analyzed in the present paper. Stability analysis is based on two-dimensional shallow water equations. It is assumed that the fluid contains uniformly distributed solid particles. No dynamic interaction between the carrier fluid and particles is expected in the initial moment. Linear stability curves are obtained for different values of the particle loading parameter, the velocity ratio and the velocity deficit. It is shown that the increase in the velocity ratio destabilizes the flow. The particle loading parameter has a stabilizing effect on the flow. The role of the velocity deficit is also destabilizing: the increase of the velocity deficit leads to less stable flow.

Keywords: Linear stability, Shallow flows, Wake-shear flows.

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Authors: Omar Qasaimeh

Abstract:

The effect of the number of quantum dot (QD) layers on the saturated gain of doped QD semiconductor optical amplifiers (SOAs) has been studied using multi-population coupled rate equations. The developed model takes into account the effect of carrier coupling between adjacent layers. It has been found that increasing the number of QD layers (K) increases the unsaturated optical gain for K<8 and approximately has no effect on the unsaturated gain for K ≥ 8. Our analysis shows that the optimum ptype concentration that maximizes the unsaturated optical gain of the ground state is NA Ôëê 0.75 ×1018cm-3 . On the other hand, it has been found that the saturated optical gain for both the ground state and the excited state are strong function of both the doping concentration and K where we find that it is required to dope the dots with n-type concentration for very large K at high photon energy.

Keywords: doping, multilayer, quantum dot optical amplifier, saturated gain.

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Authors: Alexander Babin, Leonid Savin

Abstract:

In the present paper, increasing of energy efficiency of a thrust hybrid bearing with a central feeding chamber is considered. The mathematical model was developed to determine the pressure distribution and the reaction forces, based on the Reynolds equation and static characteristics’ equations. The boundary problem of pressure distribution calculation was solved using the method of finite differences. For various types of lubricants, geometry and operational characteristics, axial gaps can be determined, where the minimal friction coefficient is provided. The next part of the study considers the application of servovalves in order to maintain the desired position of the rotor. The report features the calculation results and the analysis of the influence of the operational and geometric parameters on the energy efficiency of mechatronic fluid-film bearings.

Keywords: Active bearings, energy efficiency, mathematical model, mechatronics, thrust multipad bearing.

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Authors: Mostafa Ghayour, Mohammad Sadegh Golabi

Abstract:

In the recent years, functionally gradient materials (FGMs) have gained considerable attention in the high temperature environment applications. In this paper, free vibration of thin functionally graded cylindrical shell with hole composed of stainless steel and zirconia is studied. The mechanical properties vary smoothly and continuously from one surface to the other according to a volume fraction power-law distribution. The Influence of shell geometrical parameters, variations of volume fractions and boundary conditions on natural frequency is considered. The equations of motion are based on strains-displacement relations from Love-s shell theory and Rayleigh method. The results have been obtained for natural frequencies of cylindrical shell with holes for different shape, number and location in this paper.

Keywords: Functionally gradient material, Vibration, various boundary conditions, cylindrical shells.

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Authors: M. Nassereddine, J. Rizk, A. Hellany, M. Nagrial

Abstract:

The prologue of new High Voltage (HV) transmission mains into the community necessitates earthing design to ensure safety compliance of the system. Conductive structures such as steel or concrete poles are widely used in HV transmission mains. The earth potential rise (EPR) generated by a fault on these structures could result to an unsafe condition. This paper discusses information on the input impedance of the over head earth wire (OHEW) system for finite and infinite transmission mains. The definition of finite and infinite system is discussed, maximum EPR due to pole fault. The simplified equations for EPR assessments are introduced and discussed for the finite and infinite conditions. A case study is also shown.

Keywords: Coupling Factor, Earth Grid, EPR, Fault Current Distribution, High Voltage, Line Impedance, OHEW, Split Factor, Transmission Mains.

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Authors: N.S. Tomer, Phool Singh, Manoj Kumar

Abstract:

The flow and heat transfer characteristics for natural convection along an inclined plate in a saturated porous medium with an applied magnetic field have been studied. The fluid viscosity has been assumed to be an inverse function of temperature. Assuming temperature vary as a power function of distance. The transformed ordinary differential equations have solved by numerical integration using Runge-Kutta method. The velocity and temperature profile components on the plate are computed and discussed in detail for various values of the variable viscosity parameter, inclination angle, magnetic field parameter, and real constant (λ). The results have also been interpreted with the aid of tables and graphs. The numerical values of Nusselt number have been calculated for the mentioned parameters.

Keywords: Heat Transfer, Magnetic Field, Porosity, Viscosity

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Authors: B. Salmasian, A. Rabiee, T. Yousefzadeh

Abstract:

In this research, the risk assessment of radiation hazard for the Research Nuclear Reactor has been studied. In the current study, the MCNPx computational code has been used and coupled with a developed program using MATLAB software to evaluate Total Effective Dose Equivalent (TEDE) and cancer risk according to the BEIR equations for various human organs. In this study, the risk assessment of cancer has been calculated for ten years after exposure, in each of body organs of different ages and sexes. Also, the risk assessment of cancer has been calculated in each of body organs of different ages and sexes due to exposure after the retirement of the reactor staff. According to obtained results, a conservative whole-body dose rate, during a year, is 0.261 Sv and the probability the cancer risk for women is more than men and for children is more than adults. It has been shown that thyroid cancer was more possible than others.

Keywords: MCNPx code, BEIR equation, equivalent dose, risk analysis.

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Authors: T. K. Das, N. Senapatil, R. K. Dhal

Abstract:

An unsteady mixed free convection MHD flow of elastic-viscous incompressible fluid past an infinite vertical porous flat plate is investigated when the presence of heat Source/sink, temperature and concentration are assumed to be oscillating with time and hall effect. The governing equations are solved by complex variable technique. The expressions for the velocity field, temperature field and species concentration are demonstrated in graphs. The effects of the Prandtl number, the Grashof number, modified Grashof number, the Schimidt number, the Hall parameter, Elastic parameter & Magnetic parameter are discussed.

Keywords: MHD, Mixed convective, Elastic-viscous incompressible, rotational, heat transfer, mass transfer, suction and injection.

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Authors: А. Pashayev, D. Askerov, R. Sadiqov, A. Samedov, C. Ardil

Abstract:

In contrast to existing methods which do not take into account multiconnectivity in a broad sense of this term, we develop mathematical models and highly effective combination (BIEM and FDM) numerical methods of calculation of stationary and quasistationary temperature field of a profile part of a blade with convective cooling (from the point of view of realization on PC). The theoretical substantiation of these methods is proved by appropriate theorems. For it, converging quadrature processes have been developed and the estimations of errors in the terms of A.Ziqmound continuity modules have been received. For visualization of profiles are used: the method of the least squares with automatic conjecture, device spline, smooth replenishment and neural nets. Boundary conditions of heat exchange are determined from the solution of the corresponding integral equations and empirical relationships. The reliability of designed methods is proved by calculation and experimental investigations heat and hydraulic characteristics of the gas turbine first stage nozzle blade.

Keywords: Modeling, Simulating, Gas Turbine, Cooled Blades.

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Authors: Thomas Paris, Vincent Bruyere, Patrick Namy

Abstract:

A numerical model is developed to simulate gas blowdowns through a thin tube and a filter (porous media), separating a high pressure gas filled reservoir to low pressure ones. Based on a previous work, a one-dimensional approach is developed by using the finite element method to solve the transient compressible flow and to predict the pressure and temperature evolution in space and time. Mass, momentum, and energy conservation equations are solved in a fully coupled way in the reservoirs, the pipes and the porous media. Numerical results, such as pressure and temperature evolutions, are firstly compared with experimental data to validate the model for different configurations. Couplings between porous media and pipe flow are then validated by checking mass balance. The influence of the porous media and the nature of the gas is then studied for different initial high pressure values.

Keywords: Fluid mechanics, compressible flow, heat transfer, porous media.

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Authors: H. Bayat, M. Majidi, M. Bolhasani, A. Karbalaie Alilou, A. Mirabdolah Lavasani

Abstract:

Unsteady flow and heat transfer from a circular cylinder in cross-flow is studied numerically. The governing equations are solved by using finite volume method. Reynolds number varies in range of 50 to 200; in this range flow is considered to be laminar and unsteady. Al2O3 nanoparticle with volume fraction in range of 5% to 20% is added to pure water. Effects of adding nanoparticle to pure water on lift and drag coefficient and Nusselt number is presented. Addition of Al2O3 has inconsiderable effect on the value of drags and lift coefficient. However, it has significant effect on heat transfer; results show that heat transfer of Al2O3 nanofluid is about 9% to 36% higher than pure water.

Keywords: Nanofluid, heat transfer, unsteady flow, forced convection, cross-flow.

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Authors: Alexander A. Muravyov

Abstract:

A minimal complexity version of component mode synthesis is presented that requires simplified computer programming, but still provides adequate accuracy for modeling lower eigenproperties of large structures and their transient responses. The novelty is that a structural separation into components is done along a plane/surface that exhibits rigid-like behavior, thus only normal modes of each component is sufficient to use, without computing any constraint, attachment, or residual-attachment modes. The approach requires only such input information as a few (lower) natural frequencies and corresponding undamped normal modes of each component. A novel technique is shown for formulation of equations of motion, where a double transformation to generalized coordinates is employed and formulation of nonproportional damping matrix in generalized coordinates is shown.

Keywords: component mode synthesis, finite element models, transient response, nonproportional damping

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Authors: M. Battira, R. Bessaih

Abstract:

We numerically study the three-dimensional magnetohydrodynamics (MHD) stability of oscillatory natural convection flow in a rectangular cavity, with free top surface, filled with a liquid metal, having an aspect ratio equal to A=L/H=5, and subjected to a transversal temperature gradient and a uniform magnetic field oriented in x and z directions. The finite volume method was used in order to solve the equations of continuity, momentum, energy, and potential. The stability diagram obtained in this study highlights the dependence of the critical value of the Grashof number Grcrit , with the increase of the Hartmann number Ha for two orientations of the magnetic field. This study confirms the possibility of stabilization of a liquid metal flow in natural convection by application of a magnetic field and shows that the flow stability is more important when the direction of magnetic field is longitudinal than when the direction is transversal.

Keywords: Natural convection, Magnetic field, Oscillatory, Cavity, Liquid metal.

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Authors: Andre A. Keller

Abstract:

The optimal control is one of the possible controllers for a dynamic system, having a linear quadratic regulator and using the Pontryagin-s principle or the dynamic programming method . Stochastic disturbances may affect the coefficients (multiplicative disturbances) or the equations (additive disturbances), provided that the shocks are not too great . Nevertheless, this approach encounters difficulties when uncertainties are very important or when the probability calculus is of no help with very imprecise data. The fuzzy logic contributes to a pragmatic solution of such a problem since it operates on fuzzy numbers. A fuzzy controller acts as an artificial decision maker that operates in a closed-loop system in real time. This contribution seeks to explore the tracking problem and control of dynamic macroeconomic models using a fuzzy learning algorithm. A two inputs - single output (TISO) fuzzy model is applied to the linear fluctuation model of Phillips and to the nonlinear growth model of Goodwin.

Keywords: fuzzy control, macroeconomic model, multiplier - accelerator, nonlinear accelerator, stabilization policy.

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Authors: Yaoxin Zhang, Yafei Jia, Sam S.Y. Wang

Abstract:

A multi-block algorithm and its implementation in two-dimensional finite element numerical model CCHE2D are presented. In addition to a conventional Lagrangian Interpolation Method (LIM), a novel interpolation method, called Consistent Interpolation Method (CIM), is proposed for more accurate information transfer across the interfaces. The consistent interpolation solves the governing equations over the auxiliary elements constructed around the interpolation nodes using the same numerical scheme used for the internal computational nodes. With the CIM, the momentum conservation can be maintained as well as the mass conservation. An imbalance correction scheme is used to enforce the conservation laws (mass and momentum) across the interfaces. Comparisons of the LIM and the CIM are made using several flow simulation examples. It is shown that the proposed CIM is physically more accurate and produces satisfactory results efficiently.

Keywords: Multi-block algorithm, conservation, interpolation, numerical model, flow simulation.

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Authors: Raisa Kh. Bolotnova, Marat N. Galimzianov, Andrey S. Topolnikov, Uliana O. Agisheva, Valeria A. Buzina

Abstract:

The paper presents the results of theoretical and numerical modeling of propagation of shock waves in bubbly liquids related to nonlinear effects (realistic equation of state, chemical reactions, two-dimensional effects). On the basis on the Rankine- Hugoniot equations the problem of determination of parameters of passing and reflected shock waves in gas-liquid medium for isothermal, adiabatic and shock compression of the gas component is solved by using the wide-range equation of state of water in the analitic form. The phenomenon of shock wave intensification is investigated in the channel of variable cross section for the propagation of a shock wave in the liquid filled with bubbles containing chemically active gases. The results of modeling of the wave impulse impact on the solid wall covered with bubble layer are presented.

Keywords: bubbly liquid, cavitation, equation of state, shock wave

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