On Allowance for Energy Accommodation in Calculating the Heat Flux from a Spherical Particle at Arbitrary Knudsen Numbers

The present paper considers the problem on the calculation of the heat flux from a uniformly heated spherical particle at arbitrary values of the Knudsen number with allowance for the energyaccommodation effect. The results of numerical calculations of the BGK model of the collision integral are presented.     

Accounting for Energy Accommodation in Calculating the Heat Flux from a Spherical Particle in a Diatomic Gas

The problem of calculation of the heat flux from a uniformly heated spherical particle in a diatomic gas is considered with account for the energy-accommodation effect. The results of numerical calculations for the analog of the BGK collision-integral model are presented.     

The Inclusion of Energy Accommodation in Calculating the Heat Flux from a Spherical Particle in a Polyatomic Gas

The problem on the calculation of the heat flux from a uniformly heated spherical particle in a polyatomic gas is treated with due regard for the effect of energy accommodation. The results of numerical calculations are given for an analog of the Bhatnagar–Gross–Krook model of the collision integral. The distributions of temperature and energy over degrees of freedom are analyzed for the case of their separate excitation.     

Analytical Solution of the Nonhomogeneous Kinetic Equation in the Problem of Isothermal Slip of a Rarefied Gas Along a Solid Spherical Surface

An analytical method of solution of a halfspace boundaryvalue problem for the nonhomogeneous kinetic Boltzmann equation with a collision operator in the form of an ellipsoidalstatistic model in the problem of isothermal slip of a rarefiedgas flow along a solid spherical surface is presented. Within the framework of the considered model, a correction to the coefficient of isothermal slip that is due to the wall curvature is obtained. Comparison with literature data is made.     

Heat Transfer in a Packed Bed at Moderate Values of the Reynolds Number

Results are given of an experimental investigation of the coefficient of wall heat transfer of a round tube filled with a packed medium formed by monodisperse glass spheres of different diameters (d _p = 0.9, 3.2, 8.9 mm) in a stabilized region of heat transfer under conditions of filtering of water and aqueous solution of glycerin. A two-layer model of heat transfer is used to calculate the contribution made by the heat resistance of the flow core and of the wall zone using the measured coefficients of heat transfer and temperature profiles across the packed bed. The form of dependence for the effective coefficient of thermal conductivity is determined. Data are given of the measurement of the coefficient of wall heat transfer of annular channel filled both with a single layer of spheres with packing of two types (cubic and rhombohedral) and with several layers of spheres with random packing in a stabilized region of heat transfer under conditions of filtering of water. It is demonstrated that, in the case of inertial mode of filtering of liquid through the packed bed, the values of the Nusselt number both in the tube and in the annular channel correspond to the relation Nu _e (d _e/D)Pe^1/2 _e . A semi-empirical correlation is suggested, which generalizes well our experimental data (and the data of other authors) on heat transfer in the tube and in the annular channel. A theoretical model is suggested, according to which the variation of heat transfer is defined by the behavior of the effective coefficient of thermal conductivity _ef/ _f Pe^1/2 _d associated with the predominant contribution made to convective heat transfer by the transport processes in vortex cells with closed lines of flow.     

Analysis of the Flow of Rarefied Gas Through a Layer of a Porous Body on the Basis of Direct Numerical Solution of the Kinetic Boltzmann Equation

The problem of the flow of rarefied gas through a layer of a porous body, which is replaced by a homogeneous system of immobile spherical particles, is solved on the basis of the method of direct numerical solution of the kinetic Boltzmann equation. The effect of the spherical particles on the gas molecules is described as a kind of boundary condition distributed in space. Dependences of the density, temperature, and velocity on the coordinate in physical space are obtained; cross sections of the distribution function of the gas molecules by velocities are presented.     

Integration of the Solution of a Mixed Ling Heat Problem

A solution of the Ling heat problem with mixed boundary conditions is obtained using the method of piecewiselinear approximation of the flow. For a constant intensity of the frictional heat flux a resolvent of the kernel of the integral equation of the problem is constructed.     

Study of Particle Motion in He II Counterflow Across a Wide Heat Flux Range

Some discrepancy exists in the results of He II counterflow experiments obtained using particle image velocimetry (PIV) when compared with those obtained using particle tracking velocimetry (PTV): using PIV, it was observed that tracer particles move at roughly half the expected normal fluid velocity, \(v_n/2\), while tracer particles observed using PTV moved at approximately \(v_n\). A suggested explanation is that two different flow regimes were examined since the range of heat flux applied in each experiment was adjacent but non-overlapping. Another PTV experiment attempted to test this model, but the applied heat flux did not overlap with any PIV experiments. We report on the beginnings of a study of solid \(\hbox {D}_2\) particle motion in counterflow using PTV, and the heat flux range overlaps that of all previous visualization studies. The observed particle velocity distribution transitions from a two-peak structure to a single peak as the heat flux is increased. Furthermore, the mean value of one peak in the bi-modal distributions grows at approximately the same rate as \(v_n\), while the mean value of the single-peak distributions grows at roughly \(0.4v_n\), in reasonable agreement with both previous experiments and with the suggested model.     

Formulation and Solution of the Problem on Convection-Conduction Heat Transfer in a System of Slotted Microchannels at a Uniform Temperature of the Frame

The analytical and numerical method of straight lines is used to solve the problem on convection-conduction heat transfer in a system of parallel slotted microchannels with due regard for heat transfer in the upstream region of oxidizer supply to the channels.     

Heat and Particle Transport in the Initial Phase of Ohmic Discharges in the Globus-M Spherical Tokamak

Technical Physics Letters - The results of experiments and simulations of the transport of heat and particles in the Globus-M spherical tokamak are presented. Investigations were carried out in the...     

Application of the Transverse Seebeck Effect to Measurement of Instantaneous Values of a Heat Flux on a Vertical Heated Surface under Conditions of Free-Convection Heat Transfer

The design and features of application of a heat-flux sensor whose operation is based on the transverse Seebeck effect are described. The capabilities of the sensor are demonstrated using the investigation of free-convection heat transfer as an example. The results of measurement of instantaneous values of a heat flux on a heated vertical surface are given for different regimes of air flow in a free-convection boundary layer.     

A Method of Nonstationary Heat Flux Calculation Using the Signal of a Sensor Based on Anisotropic Bismuth Single-Crystal Thermoelements

We propose a method for calculating nonstationary heat fluxes using the electric-response signal of a sensor based on anisotropic bismuth single-crystal thermoelements. Using this method, it is possible to approximately calculate the heat flux during a period of time from ～1 μs to the attainment of a stationary thermal regime. Tests showed that the monitoring of short-term (t ～ 1–10 ms) heat fluxes by bismuth-crystal-based sensors with a crystal length to thickness ratio of above 25 ensures a calculation error not exceeding several percent.     

Supersonic Flow of Viscous Gas in a Flat Channel at High Values of the Reynolds Number

Based on numerical analysis of two-dimensional Reynolds equations using the differential model of turbulence, the structure of flow field and aerodynamic characteristics of a flat channel with variable cross section at the inlet Mach number of four is investigated in the range of Reynolds numbers Re = 10⁵–10⁷. According to the calculation results, the interaction between a shock and a laminar boundary layer results in the emergence of a closed separation zone. During interaction with a turbulent boundary layer, two flow schemes are possible, depending on the intensity of incident shock, namely, without and with separation. The extrapolation of calculation data to nonviscous flow (limiting transition Re ) shows that the classical scheme of regular reflection of the shock from a flat surface corresponds to interaction without separation. Corresponding to interaction with separation is the flow scheme with formation of a small closed separation zone in which a subsonic circulation flow takes place.     

Calculation of the Velocity of Second-Order Thermal Slip Using the Model Kinetic Equation with a Variable Collision Frequency

The problem on the calculation of the second-order thermal slip velocity is solved. For this purpose, an exact solution of an inhomogeneous model Boltzmann kinetic equation with the collision operator in the form corresponding to the BGK model with the collision frequency proportional to the module of intrinsic velocity of gas molecules is constructed. Comparison with the available results is performed.