Viscous Gas Flow Research Articles

Self-similar flow behind a shock wave in a gas under the effect of viscosity, heat conduction, and variable ambient density

Self-similar solutions have been investigated to describe the propagation of planar shock waves in a non-ideal gas generated by a piston under viscous stress and heat flux. The equation of state for non-ideal gas incorporates the correction in pressure and volume of the gas. The piston position and ambient density vary exponentially with time. Newton’s law of viscosity is used for the viscous stress and Fourier’s law of heat conduction is taken for heat flux. The viscosity coefficient is taken as constant whereas the thermal conductivity coefficient varies with temperature and density following the power law. The shock jump conditions have been derived for the viscous non-ideal gas using integral form of conservation laws. The shock Reynolds number Re s has been introduced to study the effect of viscosity on shock propagation in non-ideal gas. It is found that similarity solution exists only in an ideal gas under the condition that the ambient density exponent is equal to twice the shock position exponent. This study shows that shock Reynolds number Re s and heat conduction parameter Γ c can be used to control the variation of the flow variables and piston position significantly. The shock strength decreases with increase in the value of shock Reynolds number Re s but is independent of the heat conduction parameter Γ c . The pressure, density, and adiabatic compressibility have significant deviations from high to low viscous flow of ideal gas but the velocity and heat flux undergo negligible change. The results do not support the claim of negligible effect of viscosity in earlier studies and establish the impact of viscosity and heat flux on shock propagation in an ideal gas.

CFD Analysis of Gas-Dynamic and Heat Transfer Processes in a Propulsion System Using Polymer Fuel

In the presented work, a computer model of thermodynamic and gas-dynamic processes in a rocket engine of a new type, which uses solid polymers as fuel is considered. The design feature is the presence of a central body - a gasification chamber, where solid polymer fuel is decomposed into volatiles. To conduct the research, a preliminary thermodynamic analysis of the combustion of gasification products was carried out. Based on the results of the thermodynamic analysis using the mathematical model of the turbulent flow of viscous compressible gas, the processes of gas dynamics and heat transfer in the chamber and nozzle of the rocket engine were simulated. Analyses are made for the geometry of a real experimental sample of a polymer-fueled rocket engine developed at Oles Honchar Dnipro National University (Ukraine), which has passed the first successful tests. As a result of CFD simulation, dynamic and thermal fields in the combustion chamber and engine nozzle were obtained, and ways of further improvement of the design were determined.

Numerical Method for Calculating Plane Flows of Viscous Gas in a Cylinder

To solve scientific, technological and environmental problems in the field of road transport, it is necessary to develop new mathematical models. At this stage of development of internal combustion engines and their parts, it is necessary to model complex hydrodynamic technologies. This necessities revealing different forms of liquid and gas flows with arbitrary initial and boundary conditions for the region under consideration.The work is devoted to modelling a turbulent flow over a plate located in a cylinder. Reynolds-averaged Navier-Stokes equations were used as a mathematical model of the flow. Turbulent viscosity was calculated using the one-equation Spalart-Allmaras turbulence model. To solve the system of hydrodynamic equations, the finite difference method was used. A numerical method for calculating plane flows of viscous gas in a cylinder using turbulence models is presented. Suitable options were selected based on physical assumptions used to develop the models.Recommendations have been developed on the possibility of using the considered turbulence models.

Numerical Studies of the Influence of the Nature of the In-Chamber Flow on the Initial Period of Operation of the Gas Generator

The ignition of a fuel pellet in a gas generator chamber is a time-consuming complex physico-chemical process. During the ignition of the checker, the operating conditions of the device differ significantly from the conditions of its operation in the main area of operation. In particular, an important characteristic of the initial stage is the pattern of flame propagation over the surface of the fuel. A computational algorithm for modeling unsteady turbulent flows of compressible viscous gas based on numerical integration of unsteady equations obtained using physical conservation laws was used to study the vortex flow of gas in the gas generator path and the ignition process of the fuel block. The method used a system of equations written in a cylindrical coordinate system. The computational algorithm is based on a modified flow vector splitting scheme (Steger – Warming scheme). The algorithm has the 2nd order of accuracy in space. The obtained results of numerical simulation of the gas flow in the gas generator allow us to investigate the patterns of development of the ignition process of the fuel block in time, depending on the nature of the gas flow in the combustion chamber.

On One Method for Calculating Nonstationary Heat Transfer between a Gas Flow and a Solid Body

A method for calculating the nonstationary thermal interaction between a viscous gas flow and a solid body is presented. The method consists in direct joint integration over time of the equations of gas dynamics of a multicomponent mixture and the heat equation in a solid on multi-block unstructured meshes. To calculate one time step, the system of governing equations is split into hyperbolic and parabolic subsystems. The numerical method provides approximation of the matching condition (continuity of temperature and the normal component of the heat flux) at the interface between gas and solid and is efficient for nonstationary calculations. The comparison with the analytical solution of the model problem of the interaction of a high-speed flow and a heated plate confirm the efficiency of the method.

Supersonic dusty gas flow past a cylinder in Eulerian–Lagrangian framework

The present study utilizes computational methods to analyze two-dimensional particle-laden flow over a circular cylinder. The effect of seeding of dust particles in the viscous flow of a compressible gas is analyzed. A new solver has been developed for the purpose of studying multi-phase flows in the supersonic regime. Most of the prior research has primarily focused on flows characterized by low Mach numbers and the absence of shock waves, and there have been very few studies dealing with supersonic dusty gas flows. This study considers a supersonic Mach number and investigates the effect of particle size and particle volume fraction on dusty-gas flow over a circular cylinder. The simulation results reveal that the seeding of particles in the flow creates perturbations. The present work also highlights the influence of particles on flow separation and the subsequent increase in the skin friction coefficient and coefficient of drag. The study shows that for supersonic flows, at the same volume fraction, larger particle size creates more instabilities in the flow, while smaller particles are responsible for increased drag on the cylinder, owing to a greater frequency of collisions.

Modeling Object Motion on Arbitrary Unstructured Grids Using an Invariant Principle of Computational Domain Topology: Key Features

This paper uses a finite volume algorithm to address the numerical modeling of fluid flow around moving bodies. The Navier–Stokes equations, which describe the flow of viscous compressible gas, along with key boundary conditions and discretization schemes, are presented. As the motion of boundaries typically leads to changes in the control volumes, the basic discretization schemes need to be adapted. This paper provides a detailed discussion on the adaptation of the initial system to deforming boundaries while preserving communication topology. The method for calculating the boundary velocity is a crucial element of the numerical scheme. The paper proposes an approach to reconstruct the boundary velocity vector using deformation analysis and the condition of geometric conservation. This approach ensures correct simulation results for arbitrary unstructured computational grids. A comparison of two approaches to reconstructing the boundary velocity vector for characteristic aviation problems in the direct formulation is presented. It is shown that the proposed approach allows for more accurate modeling of object motion on arbitrary grids using the “invariant” principle of the computational domain topology.

Accuracy evaluation of modern effective codes by comparing calculated and experimental data on the example of problem about supersonic viscous turbulent gas flow around the tandem of back-forcing and forward-forcing steps

Дано описание различных программных кодов для расчета полей течения в окрестности сложных конфигураций вязким потоком турбулентного сжимаемого газа. Проведена серия тестовых расчетов для тандема трехмерных клиньев разрежения и сжатия. Целью расчетов является анализ точности разрешения отрывных зон с использованием классических и вновь создаваемых методов. Для достижения цели описаны физические особенности течения и выполнено сравнение результатов расчетов, полученных разными кодами в рамках тестового случая «тандем клиньев сжатия и разрежения».

Damping of an Oscillatory System with Incomplete Sealing of the Air Cavity by a Magnetic Fluid

Purpose. Investigate the damping of an oscillatory system with incomplete sealing of the air cavity with a magnetic fluid.Methods. The study was carried out on an experimental setup developed on the basis of known methods and equipment for magnetic measurements and manufactured independently. A ring neodymium magnet (NdFeB alloy) 60x24x10 mm in size was used as a magnetic field source. The magnetic field strength at the center of the magnet, measured with a TPU-01 milliteslamer, is 220 kA/m. An inductor, a GVT-427B amplifier, and a GwInstek GDS-72072 digital oscilloscope were used to display oscillograms. Samples of magnetic fluid based on Fe3O4 magnetite stabilized with oleic acid were studied. Kerosene was used as the carrier liquid.Results. The results of an experimental study of the elasticity and damping of an oscillatory system with incomplete sealing of the air cavity by a magnetic fluid bridge are presented. The level of sealing of the air cavity varies due to the process of pumping gas through capillaries of various radii. To explain the regularities obtained, a model theory is proposed in the approximation of a viscous gas flow according to the Poiseuille law, and the conclusions of the wellknown theory of sound propagation in molecular acoustics and the theory of sound ducts are also drawn. The relaxation mechanism imposes a restriction on the type of vibrational gas flow through the capillaries, which takes into account the "throughput" capacity of the capillaries. The proposed model explains the presence of a maximum in the dependence of the attenuation coefficient on the capillary radius and its decrease with an increase in the volume (height) of the gas cavity.Conclusion. The proposed relaxation theory of vibrational gas flow through capillaries predicts anomalously large damping coefficients and almost complete damping of an oscillatory system with a magnetic fluid inertial element. The use of the data obtained is advisable in the design of new shock absorbers, since a magnetic fluid damper with capillaries is capable of damping low-frequency oscillations.

A Study of Casson Viscous Gas Flows and Heat Transfer Across A Linear Stretching/Shrinking Sheet by Considering Induced Slip, Mass Transpiration, Inclined Magnetic Force, and Radiation Effect

A Study of Casson Viscous Gas Flows and Heat Transfer Across A Linear Stretching/Shrinking Sheet by Considering Induced Slip, Mass Transpiration, Inclined Magnetic Force, and Radiation Effect

Aeroelastic Characteristics of Rotor Blades of Last Stage of a Powerful Steam Turbine

Blades of powerful steam turbines are subjected to significant unsteady loads, which, in some cases, can lead to the appearance of self-excited oscillations or auto-oscillations. These fluctuations are extremely dangerous and negatively affect the life time of the blading. When developing new or upgrading existing turbine stages, it is necessary to carry out research on the aeroelastic behavior of the rotor blades. As a result of the modernization of a low-pressure cylinder of a 1000 MW steam turbine, the length of the rotor blades of the last stage increased to 1650 mm. In this regard, a numerical analysis of the aeroelastic characteristics of the last-stage rotor blades in the nominal operation mode was carried out. The analysis used the method of solving the coupled problem of unsteady aerodynamics and elastic blade vibrations, which allows the prediction of the amplitude-frequency spectrum of unsteady loads and blade vibrations in a viscous gas flow. The paper presents the results of numerical analysis of aeroelastic characteristics of the last stage rotor blades both for the mode of controlled harmonic oscillations with a given amplitude and inter-blade phase shift, and for the mode of coupled oscillations of the blades under influence of unsteady aerodynamic forces. The results of the simulation of coupled oscillations of blades for the first five natural forms are presented in the form of the time distribution of displacement of the blade peripheral cross-section, as well as the time distribution of forces and moments acting on the peripheral cross-section. The corresponding amplitude-frequency spectra of displacements and loads in the peripheral section are also given. The results of the calculations showed a positive damping of oscillations, the absence of flutter and auto-oscillations for the first five natural forms of oscillations of the blades in the nominal operation mode of the steam turbine

Duality of the Stream Pattern of Supersonic Viscous Gas Flow past a Blunt-Fin Junction: the Effect of a Low Sweep Angle

Duality of the Stream Pattern of Supersonic Viscous Gas Flow past a Blunt-Fin Junction: the Effect of a Low Sweep Angle

Mass transfer of viscous gas flow over porous stretching/shrinking sheet in the presence of slip and mass transpiration

AbstractThe effect of the mass transpiration parameter on the viscous gas flow past a porous stretching/shrinking sheet in the presence of Navier's slip is investigated, and also, the mass transfer characteristics are examined. The physical flow problem executes the Navier–Stokes and the mass equation, which forms the system of nonlinear partial differential equations. These are transformed via similarity variables into a system of ordinary differential equations. The slip flow model of the total mass transfer on the moving sheet is modeled by introducing gas slip velocity. The total mass transfer on the moving sheet is modeled by inducing slip models of first and second order. Further, the suction which induces the slip velocity as opposed to the surface movement is examined. The mass suction‐induced slip forces the adjacent gases to flow in the reverse direction to sheet movement. Thus, the solution space expands with the slip‐induced suction and sheet movement. In the mass injection case, the induced slip increases the effect of the fluid flow for sheet movement. Upon all previous flow models, the present investigation is significant due as it investigates the mass transfer of viscous gasses flow past a porous medium in the presence of slip and mass transpiration.

Duality of the stream pattern of supersonic viscous gas flow past a blunt-fin junction: effect of a low sweep angle

Results of numerical solution of the problem of supersonic flow past a symmetric blunt fin mounted on a plate with a developing boundary layer are presented. Generally, the case considered corresponds to the flow configuration used in the experimental and computational study by Tutty et al. (2013), in which the laminar air flow with the freestream Mach number of 6.7 is considered. Previously, the authors have shown (2020) that for these conditions two stable solutions corresponding to metastable flow states with different configurations of the vortex structure and the pattern of local heat transfer are predicted. In present paper, the influence of a low sweep angle of a blunt leading edge on the vortex structure in the separation region, local heat transfer, and the possibility of obtaining a dual solution are investigated. The bifurcation diagrams showing for two solutions the main horseshoe vortex center location and the length of separation region versus the skew angle are presented.

Analysis of Viscous Gas Flows Pulsation Characteristics in Expanding Conical Nozzles

Analysis of Viscous Gas Flows Pulsation Characteristics in Expanding Conical Nozzles

Aeroelastic Behavior of Long Blades of Last Stage of a 220 MW Steam Turbine

The phenomenon of flutter in steam turbines is quite rare, but when it occurs, the risk of damaging the blades and putting the whole unit out of service increases significantly. Currently, there is a tendency to increase the length of the blades of the last stages of powerful steam turbines, as a result of which the amplitude-frequency characteristics of the blade oscillations change, which can lead to the occurrence of uncontrolled self-excited oscillations. The paper presents the results of a numerical analysis of the aeroelastic characteristics of blade row of the last stage rotor of a 200 MW steam turbine, in which, during modernization, the length of the blades increased to 1200 mm, which made it necessary to check the resistance to flutter in operating modes. The analysis used the method of solving the coupled problem of unsteady aerodynamics and elastic blade vibrations, which allows to predict the amplitude-frequency spectrum of unsteady loads and blade vibrations in a viscous gas flow. The results of the calculations showed the absence of flutter and self-oscillations on the first five natural forms of blade oscillations in the nominal mode of operation of the steam turbine.

Asymmetric Self-Similar Viscous Gas Flows in a Wedge

Asymmetric Self-Similar Viscous Gas Flows in a Wedge

Local existence theorem for micropolar viscous real gas flow with homogeneous boundary conditions

We consider the model for one‐dimensional micropolar, viscous, polytropic, and thermally conductive real gas flow with homogeneous boundary conditions, using the generalized equation of state for pressure. The generalization is shown by the fact that the pressure depends on the mass density as a power function. The governing system of partial differential equations is given in the Lagrangian description. Using the Faedo–Galerkin method and a priori estimates, we prove that the generalized solution exists locally in time.

The mass diffusive model of Svärd simplified to simulate nearly incompressible flows

• A novel model of nearly incompressible viscous flows based on the mass diffusive Svärd equations. • The model is mass and momentum conservative. • Poisson solver-free approach, algorithmic simplicity, easy parallelisation. • Adaptive speed of sound and time step. • Accurate results for 2D and 3D flow cases. A model of viscous gas flows has recently been proposed by Svärd (2018) [27] as a remedy to some physical inconsistencies of the compressible Navier-Stokes equations. We adopt and simplify the model to handle nearly incompressible flows by neglecting the energy conservation law and imposing the isothermal equation of state. For the sake of accuracy and computational efficiency, the artificial speed of sound and the time step are set adaptively during the simulation. The governing equations are solved using 2nd-order central schemes and the skew-symmetric forms are utilised for the hyperbolic terms. Since the explicit time integration is used and the pressure field is obtained from the density via the equation of state, no linear systems of equations need to be solved. Moreover, the use of two-point stencils for the discretisation of fluxes and ellipticity-free type of the governing equations make the model simple and efficient in the context of computer implementation and parallel execution. The analysis of accuracy, resolving power and compressible effects is done on the basis of two-dimensional flow simulations: the Taylor-Green vortex (TGV) at Re=300, the doubly periodic shear layer at Re = 10 4 and the lid-driven cavity at Re = 10 3 . The Svärd model, due to the physically-based diffusive term present in the mass conservation equation, reveals to be more accurate than a similar model based on the Navier-Stokes equations, as shown by the error analysis in the 2D TGV case. For the cases studied, the proper value of the Mach number allowing to match the results with those obtained by means of a truly incompressible flow solver is estimated to be approximately 0.05. Direct numerical simulation of three-dimensional TGV at Re = 1600 is performed and shows a good agreement with reference data obtained with truly incompressible solver.

RANS-based numerical simulation of shock wave/turbulent boundary layer interaction induced by a blunted fin normal to a flat plate

Results of refined RANS-based numerical simulation of shock wave/turbulent boundary layer interaction induced by a blunted fin mounted on a flat plate are presented. The RANS equations for compressible viscous gas flow closed by a (varied) eddy-viscosity turbulence model were solved using the finite volume method implemented in the unstructured-grid parallelized in-house code SINF/Flag-S developed at the SPbPU. Detailed numerical data concerning time-averaged characteristics of the separation region and the shock wave/turbulent boundary layer interaction are acquired, including identification of the horse-shoe vortices and their influence on the pressure and shear stress distributions on the streamlined surfaces. A thorough comparison with measurements presented in literature were conducted. Methodical data on the influence of grid resolution and turbulence model on the predicted structure of the viscous-inviscid interaction are obtained and recommendations for achieving a high-quality resolution of the viscous effects and the complex shock-wave pattern of the flow are worked out.