S. A. Kolesnik

On inverse boundary thermal conductivity problem of recovery of heat fluxes to the boundaries of anisotropic bodies

A method for solution of the inverse boundary thermal conductivity problem of recovery of the heat fluxes to the structural components of aircraft fabricated of anisotropic materials is proposed. The method is based on a previously obtained analytical solution of a 2D nonstationary thermal conductivity problem in an anisotropic fin under boundary heat transfer. The method consists in parametric identification and finite-element approximation of the dependence of the heat flux on the spatial variable. A regularizing algorithm is developed that permits identification of heat fluxes with large, up to 10%, errors in the experimental temperature values. The results obtained in numerical experiments are analyzed.

The effect of longitudinal nonisothermality on conjugate heat transfer between wall gasdynamic flows and blunt anisotropic bodies

Investigation is performed of the effect of longitudinal nonisothermality on the level of heat fluxes to a blunt anisotropic body from wall gasdynamic flows which differ from those in boundary layers by the inclusion of the second derivatives of gasdynamic characteristics with respect to longitudinal variable. The longitudinal nonisothermality is largely formed by the value of longitudinal component of pressure gradient in nonviscous flow and by the characteristics of the tensor of thermal conductivity of the body subjected to flow. A possibility arises of significantly reducing heat fluxes to the side surface of blunt body by varying the characteristics of anisotropic material of this body.

A methodology for solving inverse coefficient problems of determining nonlinear thermophysical characteristics of anisotropic bodies

A methodology is proposed for solving inverse coefficient thermal-conductivity problems of defining the thermal-conductivity tensor components that depend on the temperature by introducing a quadratic residual functional, its linearization, a minimization iteration algorithm, and a method of parametric identification considering errors in determining the experimental temperature values. The existence and uniqueness of the solution to inverse coefficient problems of nonlinear thermal conductivity in anisotropic bodies at moderate constraints on the descent parameters and the sensitivity matrix norms are proven. The results obtained for carbon-carbon composites support the entire methodology for numerical solution to inverse coefficient problems with an allowable error of the experimental temperature values. The proposed methodology can be applied to define both linear and nonlinear characteristics of anisotropic heat-protection materials used in aircraft and space engineering.

Heat and mass transfer in thermal protection composite materials upon high temperature loading

Heat and mass transfer in thermal protection composite materials, used as heat protection of the structural elements of hypersonic aircrafts, is simulated in this work. Two phases arise upon high-temperature loading of the composite materials: one, unaffected by the decomposition of the binder of the composite material, and the other, a porous residue in which phase transitions are completed. These two phases are separated by a narrow zone of the binder decomposition, limited by moving boundaries of the beginning and end of the phase transformations with gas formation and a variable density of the composite materials. Analytical solutions of the problems of heat and mass transfer are obtained for the first two phases; a transcendental equation for determining the coordinates and velocity of the pyrolysis zone is derived based on these solutions and the balance of heat flows in this zone. The found mass velocity of the pyrolysis zone made it possible to determine the mass generation rate, density, and stagnation pressure of the pyrolysis gases in the decomposition zone, as well as the mass filtration rate in the porous coke residue. The validity of the proposed mathematical model is confirmed by many numerical experiments. The results of some experiments are given as functions of time, temperature, the thermal characteristics, the mass and linear velocities of the pyrolysis zone, the density and stagnation pressure of gases in this area, and the pressure distribution and the mass filtration rate in the resulting porous residue.

Conjugate heat transfer between wall gasdynamic flows and anisotropic bodies

Conjugate heat transfer is investigated between wall gradient gasdynamic flows and anisotropic bodies. Because the degree of anisotropy in a body subjected to flow may be significant (from 1 to 100), the equations of conservation of momentum and energy for wall flows must include the second derivatives of gasdynamic characteristics with respect to longitudinal independent variable. Analysis of the results of conjugate heat transfer between wall gradient gasdynamic flows and anisotropic bodies with the ratio between the diagonal coefficients of thermal conductivity tensor of more than or equal to ten leads one to the conclusion about the possibility of reducing heat fluxes from gasdynamic flows to anisotropic bodies only owing to the variation of the characteristics of thermal conductivity tensor. Analysis is further performed of other results used in making a number of practical recommendations.

Nonstationary heat transfer in anisotropic half-space under the conditions of heat exchange with the environment having a specified temperature

An analytical solution to the problem of heating anisotropic half-space by the environment with a spatially and temporally variable temperature (boundary conditions of the third kind at an anisotropic body) has been obtained for the first time based on the construction of the boundary influence function (the Green’s function), which is determined using the Fourier and Laplace integral transforms. Nonstationary temperature fields in anisotropic blunt bodies have been found under the conditions of aero-gas-dynamic heating of hypersonic aircrafts with different heat-transfer coefficients and incoming-flow temperatures. The solution obtained is recommended for determining the state of thermal protection fabricated from composites which are generally anisotropic.

Modeling of conjugate heat transfer in packets of small-size planar gasdynamic cooled nozzles

A complex physicomathematical formulation and method of solving conjugate heat transfer between viscous gasdynamic and hydraulic flows in packets of planar cooled rocket microthrusters used for the control for spacecrafts and pumping of gasdynamic lasers are presented. The feature of such thrusters is their small size, as a consequence of which the body rapidly warms up and needs special ways of cooling. The immersion technique is proposed for solving heat transfer problems in multiply connected domains which are inherent to cooled microthrusters. It is shown that the cooler removes a considerable amount of heat, especially in the region of the critical cross section of the nozzle.

On the Wave Heat Transfer at Times Comparable with the Relaxation Time upon Intensive Convective-Conductive Heating

The behavior of temperature fields in the vicinity of the boundary of a body at nanosecond durations comparable with relaxation time has been studied on the basis of an analytic solution to the problem of a hyperbolic equation for heat conductivity under the obtained conditions for convective-conductive heat transfer. The presence of first-order damped discontinuities in a temperature profile at a finite rate of the propagation of heat perturbations and convexity of the temperature profile in the vicinity of body boundary have been shown. The method of reduction of restoring relaxation time by experimental values of temperature field has been proposed.

Optimal way for choosing parameters of spacecraft’s screen-vacuum heat insulation

The heat transfer in multiple plate sandwiches of spacecraft’s screen-vacuum heat insulation is simulated for determining the characteristics of heat shielding against long-term solar heat flux. To choose optimal characteristics of heat shielding, it is necessary to determine precisely the number of plates and their peculiarities. The new, absolutely stable method for solving numerically heat transfer problems is presented. We obtain results showing that the screen-vacuum insulation is characterized by low heating-up inertance that is unacceptable. To remove this effect, the inertial heat shielding is used on the internal surface of the heat shielding and its state is examined.

Time-dependent heat transfer in a plate with anisotropy of general form under the action of pulsed heat sources

An analytical solution to the problem of the theory of heat conduction in an anisotropic band under the pulsed (point) action of heat sources has been obtained for the first time by constructing the boundary influence function from using the Fourier and Laplace integral transforms. An arbitrary orientation of the principal axes of the thermal conductivity tensor and arbitrary (including negative) values of the off-diagonal components of the thermal conductivity tensor are taken into account. The found solution is extended to piecewise continuous densities of heat fluxes at the free boundaries of an anisotropic plate. The influences of the principal components and the orientation of the principal axes of the thermal conductivity tensor on time-dependent temperature fields in the anisotropic plate are determined. It is established that there are saddle points and separatrices dividing the temperature field into regions of influence of the boundary heat fluxes. The results are used to solve problems involving the thermal state of thermal protection made of anisotropic materials.