Heat-conducting Gas Research Articles

THERMODYNAMIC CHARACTERISTICS OF SWIRLING GAS FLOWS IN SIMULATION OF THEIR OUTPUT TO THE STATIONARY MODE

The method of parallelizing a numerical solution of the complete system of Navier - Stokes equations is used to describe three-dimensional unsteady flows of a viscous compressible heat-conducting gas in ascending swirling flows. In this case, the action of gravity and Coriolis forces is taken into account, the coefficients of viscosity and thermal conductivity are assumed to be constant. The results of numerical calculations of the thermodynamic characteristics of flows on smaller computational grids are presented in simulation of the output to the stationary mode of an ascending swirling air flow in an artificially created tornado. We numerically determined the values of density, temperature, and pressure for various fixed times and for different heights of the calculated region. The research shows that in the process of accelerating the gas flow in the center of vertical region a funnel-shaped region with reduced values of density, temperature, and pressure is observed.

Pyroclast cooling and saturation in water

In the submarine setting pyroclast cooling and saturation, by controlling the buoyancy of individual clasts and surrounding fluid, exert fundamental controls on the dispersal and fate of volcanic material. In this study we use laboratory experiments to understand and quantify how hot and air-filled pyroclasts cool and saturate in liquid water. By measuring internal temperature and clast submerged weight in over thirty experiments, we find that pumice cools and saturates in two stages. We observe that the first stage is marked by much higher rates of cooling and saturation than the second stage and that the transition between stages is sharp. We propose conceptual and quantitative models for each stage of pyroclast cooling and saturation. Specifically we argue that the first stage is defined by the presence of internal steam. That is, hot pyroclasts ingest liquid water and generate steam. Once a clast's internal pore space is filled with steam, heat loss to the surroundings causes condensation of internal vapor and clast saturation. Stage 1 ends when all internal steam has condensed. We test this idea with a Stefan Model with advection and conclude that heat loss, rather than permeability, controls the saturation of pyroclasts above the boiling temperature. We find that permeability matters for air-filled clasts with initial temperatures below the boiling point. Stage 2 begins after all internal vapor has condensed and we propose that stage 2 cooling and saturation are controlled by heat conduction and thermal contraction of trapped gas, respectively. From our understanding of the processes that govern the stage 1 to 2 transition, we derive an empirical average pyroclast cooling rate of q = 7.5 ± 0.5 W cm−2. Finally, we develop quantitative models for cooling-controlled porous clast saturation and for buoyant clast rise to the ocean surface. We find that meter size clasts stay buoyant for more than 10 min - long enough to reach the surface from a depth of 1000 m. The models developed here test our understanding of clast-scale processes and demonstrate that - in hot and porous clasts - the details of internal texture do not matter because clast saturation, and thus buoyancy and fate in the water column, are governed by heat transfer.

Optimal decay estimates in the critical $$L^{p}$$ L p framework for flows of compressible viscous and heat-conductive gases

The global existence issue in critical regularity spaces for the full Navier-Stokes equations satisfied by compressible viscous and heat-conductive gases has been first addressed in \cite{D2}, then recently extended to the general $L^p$ framework in \cite{DH}. In the present work, we establish decay estimates for the global solutions constructed in \cite{DH}, under an additional mild integrability assumption that is satisfied if the low frequencies of the initial data are in $L^{p/2}({\mathbb{R}}^d).$ As a by-product we recover in dimension three the classical decay rate $t^{-\frac34}$ for $t\to+\infty$ that has been observed by A. Matsumura and T. Nishida in \cite{MN2} for solutions with high Sobolev regularity. Compared to a recent paper of us \cite{DX} dedicated to the barotropic case, not only we are able to treat the full system, but we also improve the decay rates for the high frequencies of the solution. We believe the correspondant decay exponents to be optimal.

Dependence of energy characteristics of ascending swirling air flow on velocity of vertical blowing

In the model of a compressible continuous medium, for the complete Navier-Stokes system of equations, an initial boundary problem is proposed that corresponds to the conducted and planned experiments and describes complex three-dimensional flows of a viscous compressible heat-conducting gas in ascending swirling flows that are initiated by a vertical cold blowing. Using parallelization methods, three-dimensional nonstationary flows of a polytropic viscous compressible heat-conducting gas are constructed numerically in different scaled ascending swirling flows under the condition when gravity and Coriolis forces act. With the help of explicit difference schemes and the proposed initial boundary conditions, approximate solutions of the complete system of Navier-Stokes equations are constructed as well as the velocity and energy characteristics of three-dimensional nonstationary gas flows in ascending swirling flows are determined.

THREE-DIMENSIONAL INSTANTANEOUS STREAMLINESOF GAS FLOWS FOR SIMULATION THE STEADY-STATE OUTPUT OF AN ARTIFICIAL TORNADO

The method of parallelizing a numerical solution of the complete system of Navier - Stokes equations is used to describe three-dimensional unsteady flows of a viscous compressible heat-conducting gas in ascending swirling flows. In this case the action of gravity and Coriolis forces is taken into account, and the coefficients of viscosity and thermal conductivity are assumed to be constant. The results of the numerical construction of instantaneous streamlines characterizing complex three-dimensional flows are presented for simulation the steady-state output of an ascend-ing swirling air flow in an artificial tornado.

Diffusive wave in the low Mach limit for non-viscous and heat-conductive gas

The low Mach number limit for one-dimensional non-isentropic compressible Navier–Stokes system without viscosity is investigated, where the density and temperature have different asymptotic states at far fields. It is proved that the solution of the system converges to a nonlinear diffusion wave globally in time as Mach number goes to zero. It is remarked that the velocity of diffusion wave is proportional with the variation of temperature. Furthermore, it is shown that the solution of compressible Navier–Stokes system also has the same phenomenon when Mach number is suitably small.

DETERMINATION OF RUPTURE SOURCES OF TURBINE BLADE PACKETS AT PERFORMANCE OF FORENSIC EXAMINATIONS

The technique ofdetermination of rupture sources of the turbine blades packets, which can be used at performance of forensic expertise is suggested. Its distinctive feature is completeness of the account of the various factors concerning different areas of the applied physics, such as gas dynamics, heat conductivity, thermoelasticity, static and dynamic strength. The following series of calculations was made for acknowledgement of rupture sources of bladed disk. I. Calculation of a viscous compressed subsonic current. II. Calculation periodic gas-dynamic loads operating on the blades. III. Calculation of a non-stationary stress-strain state of the bladed disk under the action of periodic forces. The technique is based on use of the numerical methods of gas dynamics and dynamic strength. The steam current through a turbomachine step calculated with the help of model of the viscous, compressedfluid. The forced vibrations of the bladed disk under the action of the aerodynamic loads are analyzed by the numerical integration of the nonlinearfinite elements design model. Four cases are considered for the numerical calculations of the stress-strain state. I. The clearance in the disk slots are not accounted and the vibrations under the action ofgas-dynamic loads from ideal directing device are investigated. II. The clearance in the disk slots are not accounted and the vibrations under the action of gas- dynamic loads from defective directing device are investigated. III. The clearance in the disk slots are taken into account and the vibrations under the action of gas-dynamic loads from ideal directing device are investigated. IV. The clearance in the disk slots are taken into account and the vibrations under the action of gas-dynamic loads from defective directing device are investigated. It’s established that a source of rupture ofworking blades of a regulating step of a compartment of a high pressure of the steam turbine is damage of blades of the directing device.

EQUIATION OF ENERGY WITH ALLOWANCE OF EFFECTS OF DISSIPATION IN CYLINDRYCAL COORDINATE SYSTEM

Complex flows of a viscous compressible heat-conducting gas in ascending swirling flows have a pro-nounced axial symmetry. Therefore, for the numerical solution of the complete system of Navier - Stokes equations to describe such gas flows, it is desirable to use a cylindrical coordinate system. The paper describes the transformation of the energy equation for a complete system of Navier - Stokes equations with allowance for the dissipative properties of a moving continuous medium. The result of the transformation is the formulation of the energy equation in a cylindrical coordinate system.

MATHEMATICAL MODELING AND CALCULATION OF GAS DYNAMIC CHARACTERISTICS OF FREE THERMAL AIR VORTEX

The article analyzes experimental and analytical studies of ascending swirling air flows. In experimental works such flows are considered from the point of view of the direction of twist, the thermal regimes of heating the underlying surface, the estimation of integral parameters, the method of influence on them, and various methods of visualization. In analytical papers, by constructing solutions of the system of gas dynamics equations, the emergence of a twist of the corresponding direction is proven when there is a gas flow into a vertical cylinder of nonzero radius. In addition, in the numerical modeling of thermal ascending swirling flows, a feature was observed in the behavior of a moving gas at the initial moments of flow formation when the underlying surface was heated locally. This feature consists in the appearance on the boundary of the heating region of counter propagating gas flows with opposite directions of twist. The paper presents the results of numerical simulation of three-dimensional unsteady flows of a compressible viscous heat-conducting gas in thermal swirled vortices with local heating of the underlying surface, taking into account the action of gravity and Coriolis forces.

Entropy balance for the one-dimensional hyperbolic quasi-gasdynamic system of equations

Entropy balance in the one-dimensional hyperbolic quasi-gasdynamic (HQGD) system of equations is analyzed. In particular, in regular flow regimes, it is shown that the behavior of entropy in the HQGD system is mainly determined by terms involving the natural viscosity and thermal conductivity coefficients. The total entropy production differs from the Navier–Stokes equations for viscous compressible heat-conducting gases by O(τ2) terms, where τ is a relaxation parameter. Additionally, a similar analysis of energy balance is performed for the simpler case of the barotropic HQGD system, which is of interest for some applications.

Entropy-conservative spatial discretization of the multidimensional quasi-gasdynamic system of equations

The multidimensional quasi-gasdynamic system written in the form of mass, momentum, and total energy balance equations for a perfect polytropic gas with allowance for a body force and a heat source is considered. A new conservative symmetric spatial discretization of these equations on a nonuniform rectangular grid is constructed (with the basic unknown functions—density, velocity, and temperature—defined on a common grid and with fluxes and viscous stresses defined on staggered grids). Primary attention is given to the analysis of entropy behavior: the discretization is specially constructed so that the total entropy does not decrease. This is achieved via a substantial revision of the standard discretization and applying numerous original features. A simplification of the constructed discretization serves as a conservative discretization with nondecreasing total entropy for the simpler quasi-hydrodynamic system of equations. In the absence of regularizing terms, the results also hold for the Navier–Stokes equations of a viscous compressible heat-conducting gas.

THE THIRD PROJECTION OF THE MOTION EQUATION IN THE CYLINDRICAL COORDINATE SYSTEM

Sophisticated viscous compressible heat-conducting gases arising during heating the vertical field, have a pronounced axial symmetry. Therefore, for the numerical solution of the full Navier-Stokes equations to describe such gas flows is advisable to use a cylindrical coordinate system. This paper describes the transformation of the third projection of the equation of motion of the full Navier-Stokes equations. The result of the transformation is to record the third projection of the equation of motion of a continuous medium in a cylindrical coordinate system.

Theoretical and DSMC Studies on Heat Conduction of Gas Confined in a Cuboid Nanopore

This paper presents a theoretical and numerical study on the heat conduction of gas confined in a cuboid nanopore, in which there exists a temperature difference between the top and bottom walls and the side walls are adiabatic. A modified gas mean free path in confined space is proposed by considering the impact of collisions between molecules and solid surfaces, with which an effective thermal conductivity model of gas in the transition regime is derived. A direct simulation Monte Carlo (DSMC) study on the heat conduction of argon and helium in a cuboid nanopore is carried out to validate the present model. The influences of the Knudsen number and the treatments of boundary conditions on the heat conduction and effective thermal conductivity of gas in nanopores are studied. The temperature jumps and the reduction of heat flux near side walls are analyzed.

Symmetric flows for compressible heat-conducting fluids with temperature dependent viscosity coefficients

We consider the Navier–Stokes equations for compressible heat-conducting ideal polytropic gases in a bounded annular domain when the viscosity and thermal conductivity coefficients are general smooth functions of temperature. A global-in-time, spherically or cylindrically symmetric, classical solution to the initial boundary value problem is shown to exist uniquely and converge exponentially to the constant state as the time tends to infinity under certain assumptions on the initial data and the adiabatic exponent γ. The initial data can be large if γ is sufficiently close to 1. These results are of Nishida–Smoller type and extend the work (Liu et al. (2014) [16]) restricted to the one-dimensional flows.

Supercomputer modeling of flow past hypersonic flight vehicles

A software platform for MPI-based parallel solution of the Navier-Stokes (Euler) equations for viscous heat-conductive compressible perfect gas on 3–D unstructured meshes is developed. The discretization and solution of the Navier-Stokes equations are constructed on generalized S.K. Godunov’s method and the second order approximation in space and time. Developed software platform allows to carry out effectively flow past hypersonic flight vehicles simulations for the Mach numbers 6 and higher, and numerical meshes with up to 1 billion numerical cells and with up to 128 processors.

Adiabatic heating (cooling) of a supercritical fluid with variation in its physical properties

The piston effect (adiabatic heating or cooling) is investigated numerically for a fluid with parameters in the neighborhood of the thermodynamic critical point. The fluid represents a plane layer on one of whose boundaries a jump in temperature takes place. The temperature of the medium is higher than the critical temperature and the mean density is equal to the critical density. The mathematical model includes the Navier–Stokes and energy equations for a heat-conducting compressible gas and the Van der Waals equation of state. The characteristics of the linear piston effect (properties of fluid are almost invariable) are compared the analytic data. The features of the nonlinear piston effect accompanied by significant variation in the physical properties of the medium are investigated.

THE SECOND PROJECTION OF THE MOTION EQUATION IN THE CYLINDRICAL COORDINATE SYSTEM

The complex flows of viscous compressible heat-conducting gas arising during heating the vertical field, have a pronounced axial symmetry. Therefore, for the numerical solution of the complete Navier-Stokes equations system to describe such gas flows it is advisable to use a cylindrical coordinate system. This paper describes a transformation of the second projection of the motion equation of the complete Navier-Stokes equations system. The result of this transformation is writing of the second projection of the equation of a continuous medium motion in the cylindrical coordinate system.

One-dimensional compressible heat-conducting gas with temperature-dependent viscosity

We consider the one-dimensional compressible Navier–Stokes system for a viscous and heat-conducting ideal polytropic gas when the viscosity [Formula: see text] and the heat conductivity [Formula: see text] depend on the specific volume [Formula: see text] and the temperature [Formula: see text] and are both proportional to [Formula: see text] for certain non-degenerate smooth function [Formula: see text]. We prove the existence and uniqueness of a global-in-time non-vacuum solution to its Cauchy problem under certain assumptions on the parameter [Formula: see text] and initial data, which imply that the initial data can be large if [Formula: see text] is sufficiently small. Such a result appears to be the first global existence result for general adiabatic exponent and large initial data when the viscosity coefficient depends on both the density and the temperature.

Experimental Investigation of the Mixed Convection of a Gas in a Rectangular Enclosure with a Local Heat Source and Heat Removal at the Outer Boundaries

The mixed convection of a gas in a parallelepiped with heat conducting walls and a local source of energy at its lower side was investigated experimentally. Local temperatures and velocities of the gas flow at different intensities of its convection in this parallelepiped, characterizing the main mechanisms of the mixed convection of a gas in such a close space, were determined. The results of experimental investigations were compared with corresponding calculation data and were in good agreement with them, which allowed the conclusion that the experimental procedure based on the thermocouple measurements and the use of PIV methods is applicable for analysis of the regimes of flow of a heat-conducting viscous gas. Experiments have shown that the approach developed for the experimental investigation of the mixed convection of a gas in a rectangular enclosure with heat-conducting walls and a local source of energy can be used in fairly wide ranges of change in the main parameters of the gas flow and in the conditions of supply of energy to it.

FIRST PROJECTION OF THE EQUATION OF MOTION IN THE CYLINDRICAL COORDINATE SYSTEM

It is proved that complex flows of the viscous compressible heat-conducting gas, arising during heating the vertical field, have a pronounced axial symmetry. Therefore, for the numerical solution of the full Navier-Stokes equations for description of such gas flows it are advisable to use a cylindrical coordinate system. This paper describes the transformation of the first projection of the equation of motion of the full Navier-Stokes equations system. The result of the transformation is a record of the first projection of the equation of a continuous medium motion in the cylindrical coordinate system.