HEAT AND MASS TRANSFER IN DISPERSED AND POROUS MEDIA
MATHEMATICAL MODELING OF FILTRATION FLOWS FROM FOUNDATION PITS FENCED WITH ZHUKOVSKII SHEET PILES
É. N. Bereslavskii
Consideration is given to the fi ltration of water from foundation pits fenced with Zhukovskii sheet piles through a ground layer underlain by a well-permeable confi ned aquifer on whose roof there is a water-impermeable portion. A mixed multiparametric boundary-value problem of the theory of analytical functions is formulated, which is solved with the Polubarinova-Kochina method. Based on this model, an algorithm of calculation of the fi lrtation characteristics is developed for situations where, in water motion from the foundation pits, one has to take into account the joint infl uence of such important factors, as seepage onto the free surface, upthrust from the water of the underlying highly permeable aquifer, and the presence of the impermeable inclusion on the roof of the latter, on the pattern of the phenomenon. Limiting cases of the model are considered which are related to the absence of one factor characterizing the modeled process (upthrust, an impermeable inclusion, seepage) and to the degeneration of the foundation pits into a submergence band semiinfi nite on the left. A solution of the problem is given for the scheme under the assumption of a fi nite value of the fl ow velocity at the end of a sheet pile; it is a certain analog of the Zhukovskii classical problem.
Keywords: fi ltration, groundwater, Zhukovskii sheet pile, seepage, complex fl ow velocity, Polubarinova-Kochina method, Fuchsian differential equations.
HYDRODYNAMICS OF THE FLUID FILTRATE ON DRILLING-IN
É. M. Abbasov and N. A. Agaeva
The volume of the liquid penetrating into the formation after drilling-in has been determined on the basis of theoretical investigations. The dynamics of change in the bottom-hole pressure has been determined in this process. It has been shown that because of the water hammer, the bottom-hole pressure can be doubled in the presence of large fractures and pores closer to the well-bottom zone.
Keywords: water hammer, bottom-hole pressure, differential equation, Bessel function, period, liquid, fi ltrate.
INFLUENCE OF THE REGIME OF FLOW OF PARTICLES FROM A HYDROCYCLONE ON ITS SEPARATION CHARACTERISTICS
O. V. Matvienko, A. O. Andropova, and M. V. Agafontseva
The infl uence of the presence of an air column in a hydrocyclone and the regime of fl ow of particles through its discharge orifi ces on the separation characteristics of the hydrocyclone was investigated. It was established that the fl ow of heavy particles through the lower discharge orifi ce of the hydrocyclone in the case where its upper discharge orifi ce is isolated from the atmosphere is larger than that in the case of free fl ow of particles to the atmosphere though both two orifi ces of the hydrocyclone. In the case where the lower discharge orifi ce of the hydrocyclone is isolated from the atmosphere, the involvement of light particles from the lower receiving bin into the reverse fl uid fl ow in the axial zone of the hydrocyclone increases the resulting yield of particles through the upper discharge orifi ce of the hydrocyclone.
Keywords: hydrocyclone, separation, air column, free surface, computational hydrodynamics.
MODEL OF MOTION AND SEDIMENTATION OF A CHARGED GAS SUSPENSION IN AN ELECTRIC FIELD
A. L. Tukmakov
We have constructed a model of the dynamics of a charged gas suspension moving in an electric fi eld under the action of interphase friction and Coulomb forces and used it to describe the process of powder coloration. The model incorporates the equations of motion of the carrier and dispersed phases obtained with account for the interphase momentum and energy exchange. The carrier medium is described by a system of Reynolds-averaged Navier–Stokes equations for a compressible heat-conducting gas with a Spalart–Allmaras model. The dispersed phase is given by the mass equation with account for the turbulent diffusion and by the conservation equations of momentum components with account for the action of the Coulomb force and aerodynamic friction, as well as by the internal energy equation. The system is written in generalized coordinates in dimensionless form and is solved by the explicit McCormack method with splitting into spatial directions and by the nonlinear correction scheme. The model is used to investigate the velocity and density fi elds of the gas suspension in the interelectrode space near the surface on which the powder is deposited.
Keywords: two-velocity two-temperature monodispersed gas suspension, electric fi eld, Coulomb force, Navier– Stokes equations, explicit McCormack scheme.
CHANGE IN THE SPECIFIC HEAT CAPACITY OF PARENCHYMAL TISSUES OF APPLES DUE TO DEHYDRATION
V. A. Mikhailik, N. V. Dmitrenko, and Yu. F. Snezhkin
We present the results of measurements of the heat capacity of parenchymal tissues of apples by the differential scanning calorimetry method. An analytical dependence of the specifi c heat capacity of these tissues on their temperature (10–90oC) and moisture (6.8–90%) is proposed. We have considered the boundary conditions under which it is possible to calculate the heat capacity of moist parenchymal tissues of apples containing simultaneously free and bound water by an additive model. Reliable values of the heat capacity of tissues containing only bound water can be obtained only experimentally. In parenchymal tissues of apples with a low moisture content (0.6– 0.43%) in the positive temperature range, a stepwise change in the heat capacity has been revealed.
Keywords: parenchymal tissues of apples, drying, bound water, specifi c heat capacity, devitrifi cation.
ENTRAINED FILM OF ICE–WATER SLURRY WITH IMPINGING SUPERCOOLED WATER DROPLETS
F. Feuillebois, S. Tabakova, S. Radev, and V. Darua
Hitting cold surfaces, such as aircraft ones, supercooled water droplets may freeze immediately. However, glaze ice may also be formed under some conditions: a part of the droplets may freeze, while the rest remains liquid, fl owing on the substrate as a fi lm. This paper proposes a model of a fi lm created by the impact of supercooled droplets on a cylindrical obstacle. The fi lm is a mixture of water and frazil ice, viz. a slurry. The fi lm thickness and volume fraction of ice in the water are expressed by simple analytical formulas obtained from the mass and enthalpy balance laws in the presence of different phenomena responsible for fi lm cooling. The results are compared with the data of existing experiments.
Keywords: ice–water slurry, supercooled water droplets, freezing, impact, liquid fi lm.
THERMAL REGIME IN A BUILDING IN THE PRESENCE OF MIXING OF HEAT CARRIERS FROM DELIVERY AND RETURN PIPELINES
K. O. Sabdenov, B. A. Unaspekov, M. Erzada, and B. A. Igembaev
We consider the problem of establishing a temperature regime in rooms and a heating system on mixing heat carriers fl owing in a delivery and return pipelines. We show that unlimited mixing of heat carriers leads to the leveling of temperatures on the stories of a building and to attainment of a limiting temperature in the building close to the heat carrier temperature in the delivery pipeline of the municipal network. It has been established that if the heat carrier fl ow rate in the heating system does not change in the process of mixing, the temperature in the heating system and the temperature in the rooms of a building can decrease to the outdoor air temperature.
Keywords: heat point, heating system of a building, heat carrier mixing, temperature at the inlet and outlet of the heating system.
THERMOMECHANICS OF ACTIVE THERMAL INSULATION WITH CIRCULAR BLOWING OF THE HEAT CARRIER
Yu. S. Teplitskii, E. A. Pitsukha, V. A. Borodulya and D. G. Belonovicha
We have investigated the infl uence of the nonisothermicity of a granular bed and gas compressibility on the resistance of thermal insulation with circular blowing of the heat carrier. An approximating dependence of the resistance of the bed on its geometric, hydrodynamic, and thermophysical characteristics has been obtained.
Keywords: granular bed, active thermal insulation, cyclone-bed furnace, thermomechanics, bed resistance, thermal conductivity, criterion of active thermal insulation.
ANALYTICAL SOLUTION OF THE PROBLEM ON THE THREE-DIMENSIONAL TRANSIENT HEAT CONDUCTION IN A MULTILAYER CYLINDER
N. Dalir and S. S. Nourazar
An exact analytical solution of the problem on the three-dimensional transient heat conduction in a cylinder with multiple radial layers, in which time-dependent, spatially non-uniform internal volume heat sources are installed, is presented. The transient temperature distribution in this cylinder was determined with the use of the eigenfunction expansion method. The solution obtained is valid for any combination of homogenous fi rst- and second-kind boundary conditions in the angular and axial directions of the cylinder and for the nonhomogeneous third-kind boundary conditions in the radial direction. As a partial case, the problem on the heat conduction in a three-layer semicircular
cylinder was solved.
Keywords: heat conduction, exact analytical solution, transient problem, multiple layers.
HEAT AND MASS TRANSFER IN COMBUSTION PROCESSES
INFLUENCE OF EXPERIMENTAL CONDITIONS ON THE IGNITION CHARACTERISTICS OF DISPERSED WOOD
A. V. Zakharevich
The results of experimental studies of the laws of ignition of dispersed pine by two different methods are presented. The dependences of the ignition delay time on the temperature and sizes of the heating source have been established, and the limiting ignition conditions of the investigated material have been determined. A comparison has been made between the conditions for ignition of wood fragments heated to high temperatures by a massive wafer and by a local energy source. The obtained experimental data form the basis for developing models of ignition of condensed materials under local heating.
Keywords: experimental studies, ignition conditions, dispersed wood, energy source of limited capacity, massive steel wafer, ignition delay time.
NUMERICAL INVESTIGATION OF THE INFLUENCE OF CONVECTION IN A MIXTURE OF COMBUSTION PRODUCTS ON THE INTEGRAL
CHARACTERISTICS OF THE EVAPORATION OF A FINELY ATOMIZED WATER DROP
G. V. Kuznetsov and P. A. Strizhak
A model of the heat-and-mass transfer in the neighborhood of a fi nely atomized water drop moving through the high-temperature products of combustion of materials has been developed for numerical analysis of the macroscopic mechanisms of movement of such a drop in a mixture of combustion products and water vapor with account for the complex of interrelated physical processes and phase transitions taking place in this case. The infl uence of the convection on the integral characteristics of the evaporation of the indicated drop was analyzed and the sizes of its"temperature" and "concentration" wakes were estimated. The conditions under which the integral characteristics
of the evaporation of this drop can be calculated in the diffusion approximation were determined.
Keywords: heat and mass transfer, evaporation, water drop, fi nely atomized water, simulation, fi re suppression.
HYDROGASDYNAMICS IN TECHNOLOGICAL PROCESSES
SIMULATION OF THE WIND EFFECT ON AN ENSEMBLE OF HIGH-RISE BUILDINGS BY MEANS OF MULTIBLOCK COMPUTATIONAL TECHNOLOGIES
S. A. Isaev, P. A. Baranov, Yu. V. Zhukova, A. A. Tereshkin,a and A. E. Usachovd
The numerical simulation of the wind effect on an ensemble of high-rise buildings is based on the solution of Reynoldsaveraged Navier–Stokes equations closed with the help of a shear stress transfer model modifi ed with account for the infl uence of the curvature of streamlines with the use of multiblock computational technologies in the VP2/3 package. It has been shown that the nonstationary aerodynamics of construction ensembles of closely spaced highrise buildings has the characteristic features inherent in tandems of blunt bodies, and the pulsating loads in the lee buildings are largely determined by the self-organization of the jet-vortex structures in the space between buildings.
Keywords: ensemble of high-rise buildings, wind effect, nonstationary fl ow, force loads, pulsations, numerical simulation, multiblock meshes, turbulence models.
NUMERICAL ANALYSIS OF SPATIAL UNSTEADY REGIMES OF CONJUGATE CONVECTIVE-RADIATIVE HEAT TRANSFER IN A CLOSED VOLUME WITH AN ENERGY SOURCE
S. G. Martyushev, I. V. Miroshnichenko, and M. A. Sheremeta,
Unsteady regimes of convective-radiative heat transfer in a cubic enclosure with fi nitely thick heat-conducting walls in the presence of a constant-temperature energy source have been modeled mathematically under the conditions of convective heat exchange with the environment. A mathematical model has been formulated in dimensionless variables "vector potential–vorticity vector–temperature;" the model was realized numerically by the fi nite-difference method. An analysis of radiative heat transfer has been made on the basis of the surface-radiation pproximation with the balance method in Polyak′s version. Three-dimensional temperature and velocity fi elds and dependences for the average Nusselt number have been obtained; they refl ect the infl uence of the reduced emissivity factor of interior surfaces of enclosing walls, of the relative thermal conductivity, and of the unsteadiness factor on the fl ow regimes and heat transfer.
Keywords: conjugate heat transfer, surface radiation, closed volume, vector potential, fi nite-difference method.
THERMAL CRISIS OF THE VORTICITY SOURCE AT A CONSTANT PRESSURE
A. N. Kucherov
The thermal crisis of the vorticity source at a given energy input at a constant pressure has been investigated from the viewpoint of a perfect gas model and Euler equations. The energy release rates given per unit mass or unit volume of the gas with vorticity source outfl ow into a vacuum and a submerged space have been considered. The features of analytical solutions for the gas-dynamic parameters in various regimes and for different variants of the vorticity source with energy input, including heat removal, have been investigated. The boundaries of the region of energy input at a constant pressure have been determined.
Keywords: gas, source, sink, vorticity source, energy input, circulation, fl ow rate, pressure, Mach number, flow choking, thermal crisis, heat removal.
NONSTATIONARY MOVEMENT OF A GENERALIZED NEWTONIAN LIQUID ABOUT A SOLID BODY
A. V. Perminov
UDC 532.135, 532.501.32
Nonstationary fl ows of dilatant and pseudoplastic liquids, classifi ed among the Newtonian liquids, about a solid body were investigated. A pulsating fl ow of a dilatant liquid and the averaged fl ow of this liquid arising on the basis of its pulsating fl ow in the boundary layer near an infi nite solid cylinder were numerically calculated for the case of high-frequency transverse vibrations of the cylinder. A numerical simulation of a fl ow of a pseudoplastic liquid about the indicated cylinder has been performed.
Keywords: Newtonian liquid, dilatant liquid, pseudoplastic liquid, vibrations, averaged fl ow, boundary layer.
INFLUENCE OF PRESSURE PULSATION ON THE DYNAMICS OF FLUID MOTION IN CONCENTRICALLY DISPOSED COMMUNICATING PIPES
É. M. Abbasov and S. A. Imamaliev
We have undertaken a theoretical study of the hydrodynamics of fl uid motion in communicating vertical pipes with different forms of vibrowave effect in the wellhead. The dynamics of the propagation of elastic waves and pressure in the zone of fl uid crossfl ow from one pipe into the other has been examined. The character of change in the bottomhole pressure has been determined. It is shown that in the case of a sawtoothedchange in the pressure of the fl uid pumped into the wellhead, the variation in pressure in the zone of fl uid crossfl ow from one pipe into the other occurs in the form of beats.
Keywords: pulsation, fl uid, effect, Fourier series, Laplace equation, fl ow, mathematical model.
INFLUENCE OF SURFACE TENSION INHOMOGENEITY ON THE WAVE FLOW OF A LIQUID FILM
L. A. Prokudina
This paper presents a mathematical model of the three-dimensional liquid fi lm fl ow taking into account the inhomogeneity of its surface tension in the condensation and evaporation processes. The wave characteristics of this fl ow have been calculated and the instability regions of such fi lms have been determined. The analytical dependence for the wave fl ow of the liquid fi lm in the condensation and evaporation processes taking into account the infl uence of the thermocapillary forces and the surface viscosity on the wave form of the liquid has been obtained.
Keywords: liquid fi lm, instability, increment, phase velocity, nonlinear waves.
OPTIMIZATION OF A RADIAL FLOW HEAT SINK UNDER NATURAL CONVECTION
A steady-state three-dimensional numerical model is developed to predict natural convection heat transfer from a radial fl ow heat sink. The considered medium is air. The effect of several design parameters, such as the fi n length and height, number of fi ns, and the heat sink base radius, on heat transfer is investigated. The Taguchi method, known to be a very useful tool for selecting the best levels of control factors, is employed. Five factors and four levels for each factor are chosen. Sixteen kinds of models are analyzed, and the total heat transfer for each model is obtained. The results are used to estimate the optimum design values of the parameters affecting the heat sink
performance. The reliability of these values is verifi ed. The average heat transfer rate of the optimum model is shown to increase by 60% as compared to the reference model. Finally, the heat transfer data at different outer radii of the radial fl ow heat sink are correlated.
Keywords: natural convection, laminar fl ow, radial fl ow, heat transfer, optimization.
COUETTE LONGITUDINAL TURBULENT FLOW BETWEEN COAXIAL CYLINDERS
V. A. Babkin
Within the framework of the model of anisotropic wall turbulence, an analytical solution is obtained for the problem on turbulent incompressible-fl uid fl ow between two coaxial circular cylinders due to the motion of the internal cylinder along the common axis (Couette fl ow). The velocity profi le and the surface-friction coeffi cient of the internal cylinder are determined. The solution is compared to the existing solutions and to experimental data.
Keywords: wall turbulence, two-layer fl ow in the gap, boundary of fl ow subregions, velocity profi le, surface friction.
TRANSFER PROCESSES IN LOW-TEMPERATURE PLASMA
DYNAMICS OF INTERACTION OF PLASMA COUNTERFLOWS WHEN THE CUMULATIVE ZONE IS BOUNDED BY A PULSED MAGNETIC FIELD
P. P. Khramtsov, O. G. Penyazkov, V. M. Grishchenko,
M. Yu. Chernik, I. A. Shikh, and V. A. Vasetskii
UDC 533.9.082.5; 537.523.2
Results of experimental study of the process of interaction of a pulsed magnetic fi eld and a zone of collision of two opposing compression plasma fl ows have been given. It has been shown that the fi eld of the magnetic trap bounds the region of the cumulative zone due to the compression of a plasma formation resulting from the collision of the two fl ows with simultaneous increase in its glow intensity.
Keywords: cumulative zone, plasma, erosion plasma accelerator, magnetic trap.
INFLUENCE OF DUST CONTENT ON PRIMARY AND SECONDARY WAVES IN THE SPLITTING OF A SHOCK WAVE IN A GLOW-DISCHARGE PLASMA
A. S. Baryshnikov, I. V. Basargin, and M. V. Chistyakova
In the present work, the possibility of using the infl uence of the dust content in the atmosphere, in which a glow discharge is initiated, on the effect of shock-wave splitting and thus on the possibility of fl ight control is elucidated.
Keywords: shock wave, glow discharge, dusty electric plasma.
TRANSFER PROCESSES IN RHEOLOGICAL MEDIA
MATHEMATICAL SIMULATION OF THE SWIRLING FLOW
OF A DILATANT LIQUID IN A CYLINDRICAL CHANNEL
O. V. Matvienko, V. P. Bazuev, and N. K. Dul′zon
The swirling fl ow of a dilatant liquid in a cylindrical channel was investigated. It was established that the effective viscosity of this liquid increases with increase in the shear stresses arising due to the swirling of its fl ow and that the sizes of the recirculation zone and the intensity of recirculation of the liquid in it decrease with increase in its nonlinearity factor.
Keywords: rheology, dilatants liquid, swirling fl ow, computational hydrodynamics.
IMPEDANCE SPECTROSCOPY OF MAGNETIC FLUIDS
V. I. Zubko, D. V. Zubko, and G. N. Sitsko
We have investigated the laws governing the change in the electrophysical properties of decane-, turbine oil-, and kerosene-based magnetic fl uids with the electric fi eld frequency, dispersed phase concentration, and temperature. We have determined the optimal electric fi eld frequencies, dispersed phase concentrations, and temperatures within the limits of which the electrophysical characteristics such as the relative permittivity, specifi c electric resistance, and the loss tangent of a dielectric appear to be the most informative to estimate the structure, composition, and properties of magnetic fl uids.
Keywords: impedance spectroscopy, magnetic fl uids, impedance, electrode cell, turbine oil, decane, kerosene.
ACOUSTIC AND THERMODYNAMIC PROPERTIES OF THE BINARY LIQUID MIXTURE n-OCTANE + n-DODECANE
T. S. Khasanshin, N. V. Golubeva, V. S. Samuilov, and A. P. Shchemelev
The velocity of sound in the binary liquid mixture n-octane + n-dodecane has been investigated by the method of direct measurement of the pulse-transmission time in the interval of temperatures 298–433 K and pressures 0.1–100.1 MPa. The maximum measurement error amounts to 0.1%. The density, isobaric expansion coeffi cient,isobaric and isochoric heat capacities, and isothermal compressibility of a mixture of three compositions have been determined in the intervals of temperatures 298–393 K and pressures 0.1–100 MPa from the data on the velocity of sound. Also, the excess molar volume, the excess isothermal compressibility, and the deviation of the velocity of sound from its value for an ideal liquid have been determined. The coeffi cients of the Tate equation have been computed in the above temperature interval. A table of thermodynamic properties of the mixture has been presented.
Keywords: n-octane, n-dodecane, binary mixtures, velocity of sound, density, heat capacity, compressibility.
A METHOD OF IDENTIFYING THERMOELASTIC CHARACTERISTICS FOR INHOMOGENEOUS BODIES
A. O. Vatul′yan and S. A. Nesterov
We present variants of formulating the inverse coeffi cient problem of thermoelasticity for an inhomogeneous rod and the method of its solution. Investigation of the direct problem is reduced to the solution of a system of 2ndkind integral Fredholm equations in Laplace transforms based on the method of collocations and to the use of the inversion procedure implemented in conformity with the theory of residues. Operator relations that connect the sought and assigned functions are obtained for solving the inverse problem. Results of computational experiments for specifi c laws of inhomogeneity are given.
Keywords: inverse problem, thermoelasticity, inhomogeneous rod, integral equation.
MEASUREMENT OF THE HOT-ROLLED STOCK PARAMETERS
B. T. Budai and N. V. Kasatkin
We show that the rolled-stock parameters can be measured by ecologically pure triangulate optical meters not only for cold-rolled stock but also for hot one.
Keywords: hot-rolled stock, measurement of thickness, optical method, charge-coupling photodetector.
KINETIC THEORY OF TRANSFER PROCESSES
CONDENSATION COEFFICIENT: DEFINITIONS, ESTIMATIONS,
MODERN EXPERIMENTAL AND CALCULATION DATA
UDC 533.72; 538.9
A. P. Kryukov, V. Yu. Levashov, and N. V. Pavlyukevich
A brief analysis of different approaches to the calculation and measurement of the condensation coeffi cient of a vapor is presented. It is shown that, on frequent occasions, calculations give values of this coeffi cient that are at variance with the corresponding experimental data and that the condensation coeffi cient is determined most exactly on the basis of the molecular-kinetic theory. It was established that the spread in the literature data on the measured values of this coeffi cient is explained mainly by the fact that these values were obtained not in the immediate vicinity from the boundary between the gas and liquid phases but at a large distance (as compared to the mean free path of molecules) from it. Results of calculations of the condensation coeffi cient of argon by the method of moleculardynamic simulation are presented.
Keywords: condensation coeffi cient, velocity-distribution function of molecules, molecular-kinetic theory, moleculardynamic simulation.
NUMERICAL VERIFICATION OF THE EXISTENCE OF THE ELASTIC ENERGY LOCALIZATION EFFECT FOR CLOSELY SPACED RIGID DISKS
S. I. Rakin
Based on numerical solution of the linear elasticity theory, the existence of the elastic energy localization effect in a system of closely spaced disks has been confi rmed. It is shown that in contrast to an analogous scalar problem, the arising quadratic form of energy contains a nonzero cross term.
Keywords: elasticity theory, closely spaced disks, energy localization.
CUTTING TOOL WEAR AFTER PULSED LASER PROCESSING IN AIR
S. I. Yares'ko
We have ascertained the infl uence of the oxide fi lm formed on the surface of the laser-processed zone of tool steels by irradiation in air on the wear of the cutting tool. It has been shown that laser pulsed processing makes it possible to infl uence actively the process of its wear. The presence of the oxide fi lm increases the wear stability of the tool in a wide range of cutting speeds, widens the range of cutting regimes in which its least wear is achieved, and minimizes the wear rate. Cutting regimes, in which the highest effi ciency of the irradiated tool is achieved, have been established.
Keywords: laser pulsed processing, cutting tool, wear, oxide film.