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Induction heating is a process of heat generation which uses metal conductors and the Joule effect. The induction heating process has many applications in industry, such as metal melting, preheating for forging operations, hardening, and welding. A model of induction heating is given by a coupled system of partial differential equations relating temperature field and magnetic potential. Precisely, a coupled system of Maxwell and heat equations is given in the workpiece, while in the exterior domain the Laplace equation for the magnetic potential is formulated. Finally, nonlinear boundary condition for the heat equation, transmission conditions and asymptotic condition for the magnetic potential are given. Solution of such coupled multifield problems requires advanced coupled numerical methods. Therefore, in this paper we present a coupled numerical approach connecting Finite Difference Method and discrete potential theory. The use of discrete potential theory is motivated by the fact that asymptotic conditions are satisfied exactly on the discrete level. Thus, a general scheme for the coupled numerical method is presented in this paper.Induction heating is a process of heat generation which uses metal conductors and the Joule effect. The induction heating process has many applications in industry, such as metal melting, preheating for forging operations, hardening, and welding. A model of induction heating is given by a coupled system of partial differential equations relating temperature field and magnetic potential. Precisely, a coupled system of Maxwell and heat equations is given in the workpiece, while in the exterior domain the Laplace equation for the magnetic potential is formulated. Finally, nonlinear boundary condition for the heat equation, transmission conditions and asymptotic condition for the magnetic potential are given. Solution of such coupled multifield problems requires advanced coupled numerical methods. Therefore, in this paper we present a coupled numerical approach connecting Finite Difference Method and discrete potential theory. The use of discrete potential theory is motivated by the fact that asymptotic condi...

The paper deals with the issues of mathematical modeling of gas-dynamic and thermophysical processes occurring in the internal (working) volume of the air heat curtain (AHC) with a tangential fan. The flow structure in the form of current lines, fields of pressure, temperature, and gas velocity at fan speeds 250 rpm and 1000 rpm are given. It is shown that the structure of the flow does not depend on the fan rotation speed, the speed profiles are self-similar, and the temperature field is invariant concerning the fan rotation speed. Thus, optimization of the air heat curtain structural elements can be carried out at the fixed value of impeller rotation speed, as it does not affect parameters of the output jet. As a result of numerical simulation, it was found that the area of the return flow is formed on the cut of the output diffuser, which significantly reduces the output air jet performance.

The arcticle gives a spatial gas-dynamic formulation of the backpressure problem, which describes the change in pressure in front of an accelerating projectile when it moves along the bore. This takes into account the geometry of the front of the projectile and its influence on the formation of the shock wave. An unsteady spatial flow of the displaced medium ahead of the projectile body without and taking into account the forces of viscosity is considered. The paper considers the solution to the problem of throwing a body using the energy of gunpowder combustion. The internal ballistics problem, which determines the dynamics of the projectile movement, is solved in terms of averaged parameters. A two-step Runge-Kutta scheme with a second order of accuracy is used to numerically integrate a system of ordinary differential equations in time. The control volume method is used for the numerical solution of the system of gas-dynamic equations. The gas parameters at the boundaries of the control volumes are determined using a self-similar solution to the problem of the decay of an arbitrary discontinuity. A comparison is presented of taking into account the backpressure as the pressure behind the detached shock wave, obtained from the analytical solution of the problem of the supersonic motion of a flat piston in a pipe at a constant velocity, and the pressure acting on the projectile, determined from the solution of nonstationary one-dimensional and spatial (axisymmetric) equations of gas dynamics. It was found that taking into account the viscosity practically does not affect the results of calculating the backpressure, while taking into account the shape of the front part of the projectile leads to a significant difference in the pressure fields behind the front of the shock wave compared to the solution in the framework of the one-dimensional formulation of the problem, where the shape of the front part of the projectile cannot be taken into account. It is concluded that this can significantly affect the results of modeling the ballistics of a shot at high throwing speeds.

In this paper we present a numerical study of two streamwise supersonic vortices interaction. A pair of vortices was generated by two coaxial straight wings with sharp leading and trailing edges. Mach number of incoming flow was M∞ = 3. Two configurations are considered: a pair of co-rotating vortices and a pair of counter-rotating vortices. In the case of counter-rotating vortices the wings attack angle was 10 degrees. In the case of co-rotating vortices the attack angle of one of the wings was 10 degrees, the attack angle of other one was -10 degrees. Numerical data were obtained in the domain of 10 wing chords downstream from a wings axis by a computational model based on the URANS equations with SA turbulence model. Numerical simulations were performed on the hybrid supercomputing system K-60 at the Keldysh Institute of Applied Mathematics RAS using the developed software package ARES for 3D turbulent flows modeling on high performance computing systems. This work is a continuation of the series of author’s works dedicated to the supersonic wingtip vortices.

This paper presents a mathematical model and code-implemented engineering calculation technique that allow to study workflow inside a ramjet’s combustion chamber under dynamic variation of external and internal parameters: flight speed, angle of attack, and fuel mass flow rate. To assess adequacy of the mathematical model and the technique, a comparison is performed between results of internal ballistics calculations of a spaceplane’s ramjet obtained by aforementioned mathematical model and by numerical simulation in a computational fluid dynamics software package. This is tested for cruise flight conditions and for dynamic variation of flight parameters and fuel mass flow rate in a wide range. It shows that for a model subsonic flow combustion chamber a satisfactory correlation between these solutions is realized. Transient processes are stable and monotonous for all cases studied, registered oscillations of total pressure and temperature in relation to their stabilized values and weak overshooting have no effect on the engine’s output characteristics.

The paper provides a brief overview of recent computational studies of flow and heat transfer control by rotary oscillations of an infinite circular cylinder at a relatively broad set of imposed frequencies and amplitudes [1, 2]. A study for a previously unreachable high subcritical Reynolds number Re = 1.4 × 105 showed that the efficiency of this control method increases with Re concerning the issue of drag and lift reduction. High-frequency oscillations even lead to around 90 % reduction of the drag. However, the benefits for heat transfer enhancement is not that obvious as the bulk Nusselt number shows only small variations. At the same time its angular distribution around the cylinder becomes much more homogeneous due to oscillations which practically can prevent local overheats.

This paper aims to design a small-scale, compact supersonic wind tunnel nozzle using the method of characteristics and perform computational fluid dynamics (CFD) simulations to validate the design. The wind tunnel is designed to have a test section of 7cm × 7cm and a test section Mach number of 2.0. Simulations were performed for both 3D inviscid and viscous cases and it shows that for both cases, the obtained Mach number conforms with the design requirements. A further study on the effects of different pressure ratios, towards the position of shock waves, shows that an increase in the ratio would result the shock waves to shift downstream.

This paper deals with the frequency response of swirl flow behind an axial swirler. Vortex breakdown resulting in the formation of a precessing vortex core is considered. The influence of the swirl intensity and the nozzle confinement effect on the frequency response of the PVC is studied. Regimes with the presence of PVC were determined using two microphones. The Strouhal number depends linearly on the swirl parameter and weakly on the Reynolds number. The measurement results are used to derive an empirical dependence of the Strouhal number on a modified geometric swirl number. This allows a generalization of the frequency characteristics of swirling flows with a PVC for the class of axial vane swirlers, which are most widely used in engineering.

In this paper an attempt is made to solve the problem of unsteady laminar motion of a dusty viscous incompressible fluid through concentric circular cylinder under time dependent pressure gradient an attempt is made to determine the velocities the fluid to and the dust particles by using finite Hankel transform and Laplace transforms methods.

In this paper, the problem of entropy production on adiabatic propagation of strong spherical imploding shock waves in a dusty gaseous atmosphere having solid body rotation, has been carried out by using CCW theory. The gaseous medium is assumed to be seeded a large number of small spherical solid particles of uniform size. The solid particles are also assumed to be inert and uniformly distributed in the medium. The strength of overtaking waves is estimated under the assumption that both C+ and C− disturbances propagate in the region of same density distribution. Maintaining equilibrium flow conditions, analytical expressions for change in entropy and temperature across the shock front have been derived for both freely propagation as well as under the effect of overtaking disturbances, for the power varying initial density distribution. Neglecting the effect of coriolis forces, the influence of overtaking disturbances on the variation of change in entropy and temperature with propagation distance, mass concentration of solid particles in the mixture, the ratio of solid particles to the initial density of gas, initial angular velocity and the density parameter have been calculated numerically and discussed through graphs. It is found that dust presence in the gases medium has significant effects on the entropy production and temperature. It is shown that the entropy production and temperature are further increasing across the shock in presence of overtaking disturbances. The results obtained here been compared with those for freely propagating shock as well as for the dust free ideal gas.

The current paper presents a semi-analytical solution for the problem of swirl decay under laminar flow in a circular duct with constant value of the radial velocity at the inlet. The swirl velocity equation is solved by the separation of variable technique. Based on the eigenvalues and eigenfunctions corresponding to the solution of main problem it is found that the slowest breakdown processes of eddy structures under laminar viscous flow are described by the exponential function.

The paper presents a method of transient temperature and stress-state estimation in thick-walled pressure components. If complex physical phenomena inside the component make it difficult to define the boundary condition on its inner surface, an inverse boundary problem emerges. The proposed method makes it possible to solve the problem using “measured” temperature histories in easily accessible points located on the component outer surface. The method stability and accuracy are shown by comparing the inverse method results and the exact values obtained from the direct method. The presented method does not require drilling holes for sensors in pressure element walls.

The present paper provides vibration analysis of functionally graded piezoelectric (FGP) actuator due to longitudinal piezoelectric coupling coefficient. In this regard, beam type geometry is taken into consideration. It is assumed that the electric potential has sinusoidal variation along the axial direction. The electro-mechanical properties of Timoshenko beam are supposed to change continuously throughout the thickness based on power law model. The governing equations and end conditions for FGP beam are derived using Hamilton’s principle. A mathematical modeling for clamped-clamped end condition is being obtained. Numerical results are presented to demonstrate the effect of various parameters on natural frequencies of FGP beam.

This paper describes the soil-structure interaction effects in the case of the NPP main buildings with reactor VVER-1200/491 PWR. The simplified 1D and numerical 3D FE models of the subsoil are presented. The main reason of this methodology is proposed the frequency dependent complex function or as a spring-dashpot system, with the spring becoming negative for certain frequencies, which cannot be directly implemented in standard structural analysis codes. The methodology of the calculation of the impedance functions due to dynamic excitation are considered.

Nowadays, utilization of hydropower is still focussed on the development of large dams which have an effect on the natural environment and are often opposed by the people in the region. Producing electricity from small water resources, especially using the gravitational vortex method has currently attracted the interest of researchers. In this paper, a numerical study of the effect of vortex pool variation on the performance and flow field of gravitational water vortex power plant (GWVPP) are investigated. Numerical study based on the volume of fluid (VOF) method is developed in ANSYS FLUENT code program for analyzing the parametric studies of GWVPP. Cylindrical vortex pool coupled with gravitation type water turbine based on Nishi and Inagaki (2017) research, are modified become conical vortex pool type by varying the ratio of inlet diameter and outlet diameter (Din/Dout) by 3.26; 4.9; and 6.12. Turbulent model is approached using RNG k-epsilon and boundary conditions are set 2.838 kg/s for inlet mass flow rate, 0 Pa for open and outlet boundary. As a beginning result, the computational values of this study and experimental data of the torque and turbine output from Nishi and Inagaki (2017) agreed with one another. Later, for conical basin with variation of Din/Dout, it can be shown that the maximum velocity profile achieved in nearly to the discharge hole, in order from 6.12; 4.9; followed by 3.26 of the Din/Dout ratio respectively. It is supported by the increase in the Din/Dout ratio or decrease output hole, the air area increase and creat greater vortex circulation.

The temperature in the nose region of a hypersonic vehicle can be extremely high, for example, reaching approximately 11 000 K at a Mach number of 36 (Apollo reentry). The bow shock wave is normal, or nearly normal, in the nose region of a blunt body. Fortunately, the nose geometry is a spherical sector; therefore, hypersonic aerodynamics near the nose of space vehicle can be studied with a hypersonic axisymmetric CFD code for flows without incidence and this greatly decreases the computational effort. For this reason, the present paper deals with the development of a hypersonic axisymmetric CFD code.

Current research paper deals with the numerical analysis of an idealized fighter jet wing in a multi-module aero-thermal-structural environment during supersonic flights. At high Mach number, heat is generated due to the friction between the body and the fluid flow, which must be considered for structural analyses. Six different Mach numbers ranging from 1.25 to 2.5 are chosen to understand the effect of viscous heating on the wing model. Ansys CFD is coupled with thermal/structural module to calculate the numerical results. It is observed that for Mach number 1.75 and beyond, equivalent Von-mises stress due to pressure load is almost identical. However, with viscous heating consideration, equivalent stress values are increased with higher Mach number which magnifies the significance of thermal loading on the structure

In this paper, a comprehensive numerical study on viscous incompressible fluid flow and heat transfer through a loosely coiled square duct has been presented. Spectral method is used as a basic tool to solve the system of non-linear partial differential equations. Numerical calculations are carried out for the Dean number Dn = 1000 with a temperature difference across the vertical sidewalls for the Grashof number Gr = 100, where the outer wall is heated and the inner wall cooled. A rotation of the duct about the center of curvature is imposed in the positive direction for the Taylor number 0≤Tr≤2000 and combined effects of the centrifugal, Coriolis and buoyancy forces are investigated. First, steady solutions are obtained by the Newton-Raphson iteration method. As a result, three branches of asymmetric steady solutions with two- to four-vortex solutions are obtained. Then, time evolution calculations as well as power spectrum density of the unsteady solutions are obtained and it is found that the unsteady flow undergoes through various flow instabilities, if Tr is increased in the positive direction. Nusselt numbers are calculated as an index of convective heat transfer, and it is found that convective heat transfer is significantly enhanced by the secondary flow. Finally, a comparison between the numerical and experimental investigations has been provided. It is found that there is a good agreement between the numerical and experimental investigations.

The purpose of this paper is to investigate the boundary layer flow and heat transfer of biomagnetic fluid over a stretching/shrinking sheet in the presence of magnetic dipole. We use Lie group transformation to develop similarity transformation. Using this special form of transformation namely Lie group transformation, the governing nonlinear partial differential equations are reduced into a system of couple nonlinear ordinary differential equations subject to associated boundary conditions. The reduced resulting equation are then solved numerically by using MATLAB routine boundary value problem solver bvp4c. The effects of the pertinent parameters such as ferromagnetic parameter, suction parameter, stretching parameter and momentum slip parameter on the flow field and temperature as well as skin friction coefficient and heat transfer rate are presented and discussed through graphically in this study. Results indicate that the dual solutions exits for some specific range of governing parameter. The results of the present study have been compared with those reported by previous results and found a very good agreement that supports the validity of the present analysis and the accuracy of our numerical computations.

In this paper the problem of mutual interaction of incompressible viscous fluid flow with an elastic structure is considered. A model problem of aiflow induced vibratioon of a simplified human vocal folds model is studied. The main attention is paid to the problem of the periodical collisions of vocal folds. First, these collisions are taken into account in the flow model by the application of a suitable inlet boundary condition. Further, in the structure model the contact is resolved with the aid of application of Hertz forces. Numerical results are shown.

In this paper, a spectral-based numerical result is presented for the fully developed two-dimensional flow of viscous incompressible fluid through a rotating curved rectangular duct. The bottom wall of the duct is heated while cooling from the ceiling. A rotation of the duct about the centre of curvature is imposed in the positive direction for the constant Dean number Dn = 1000 over a wide range of the Taylor number 0≤Tr≤2000. First, solution structure of the steady solutions is obtained by the Newton-Raphson iteration method. Then, we investigated unsteady solutions by time evolution calculations justified by power spectrum of the solutions, and it is found that when there is no rotation, the flow is chaotic but as the rotational speed increases, the chaotic flow turns into steady-state flow through periodic or multi-periodic flows. This study shows that combined effects of the centrifugal and Coriolis forces counteract each other in a nonlinear manner which results in to turn the chaotic flow into steady-state flow. The present study demonstrates the role of secondary vortices on convective heat transfer which shows that secondary flow enhances heat transfer in the flow. Typical contours of secondary flow patterns and temperature distribution are also obtained at several values of Tr, and it is found that the unsteady flow consists of two- to eight-vortex solutions if the duct rotation is involved in the present case.

In this paper an oscillatory stream of anelectrically and viscoelasticleading liquid through a porous medium limited by two interminable vertical similar plates is talked about within the sight of heat source and radiation with impact of mass transfer and slip parameter. One of these plates is exposed to a slip-stream condition and other to a no-slip condition. The weight inclination in the channel wavers with time. An attractive field of uniform quality is connected toward the path opposite to the plates. The initiated attractive field is disregarded because of suspicion of little attractive Reynolds number. The temperature contrast of the two plates is additionally accepted sufficiently high to instigate heat transfer because of radiation. A shut form investigative answer for the issue is acquired. The investigative outcomes are assessed statistically and afterward exhibited graphically to talk about in part the impacts of various relevant constraints going into the issue. It is established that the speed profiles increment because of increment in Reynolds number or there is increment in Grashof number for mass transfer and a switch number is noted on the profiles of the speed at whatever point there is an expansion in either attractive parameter or heat source parameter.