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.     

Heat and Mass Transfer in Anisotropic Bodies

This review is aimed, on the one hand, at attracting the researchers' attention to the problems associated with heat transfer in anisotropic bodies and, on the other hand, at analyzing the scanty experience in investigating the heat transfer in anisotropic bodies that has been accumulated over the last 30 years. We treat conjugate heat transfer between boundary layers and anisotropic bodies, and heat transfer under conditions of simultaneous reciprocal influence of anisotropic thermal conductivity and anisotropic filtration upon film cooling of bodies with anisotropic properties. New effects are revealed during simulation of conjugate heat transfer; the law of nonlinear filtration in anisotropic bodies is identified; and the effect of individual components and of the orientation of the principal axes of thermal conductivity and penetrability tensors on stationary temperature fields and on the distribution of components of the filtration rate is investigated. The results of analytical investigation of heat transfer in anisotropic bodies enables one, under conditions of lack of adequate information, to exactly simulate nonstationary temperature in simplest anisotropic bodies, which may be used as test results. A number of recommendations are formulated for implementation of heat shielding of anisotropic bodies under conditions of their aerogasdynamic heating.     

Modeling of Transient Thermal Contact Resistance out of Conjugate Gradient Method

Temperature profile at contacting pairs of any material combination is crucial in many engineering applications. A new experimental approach is suggested to estimate the contact heat transfer coefficient as well as the thermal contact resistance. This method is based on temperature infrared measurements of contact bodies and then solve the inverse problem with conjugate gradient method. Different affecting parameters are studied namely; surface roughness, presence of interlayer, applied pressure and bodies temperature difference. The time dependant heat transfer coefficients resulting from the proposed method need to be validated by a computer model. Close results are shown with slight deviation by the increase of the applied pressure and the temperature difference.     

含损伤复合材料的湿热弹性响应

依据不可逆热力学理论, 未引入任何附加假设, 建立了湿热弹性各向异性损伤复合材料的一般理论。应用建立损伤本构方程的本构泛函展开法, 推导出湿热弹性损伤材料全部本构方程的一般形式, 其中包括比自由能密度表达式、 应力-应变关系、 熵密度方程、 损伤应变能释放率表达式、 吸湿对偶力表达式、 湿-热-固-损伤耦合的热传导方程和损伤演化方程。研究表明, 在本构方程中含有若干损伤效应函数, 表征损伤对材料宏观力学性能与湿、 热性能的影响, 其具体形式可由细观力学解确定, 从而使连续损伤力学与细观损伤力学有机结合在一起。最后, 从细观力学与实验观测两个角度, 举例说明损伤效应函数与系数张量的确定方法, 为分析变温变湿环境下复合材料的损伤问题提供重要的理论依据。      

Thermoelastic state of layered thermosensitive bodies of revolution for the quadratic dependence of the heat-conduction coefficients

We propose an analytic-numerical method for the solution of one-dimensional static problems of thermoelasticity for layered cylinders and balls subjected to the action of the surface loads for various modes of heating with regard for the quadratic dependence of the heat-conduction coefficients and arbitrary dependences of the other physicomechanical characteristics on temperature. Independently of the number of layers, the problems of heat conduction are reduced, by using the constructed exact solutions of special problems, to the solution of a single nonlinear algebraic equation or a system of two equations of this sort. The solutions of the problems of thermoelasticity are obtained by approximating the coefficients of equations continuous inside each layer by piecewise constant functions with subsequent application of Green’s functions of the problems of statics for many-layer cylinders and balls. We perform the numerical analysis of the temperature fields and the thermoelastic state in two-layer bodies whose outer surface is heated by convective-radiation heat exchange and the inner surface is kept at a constant temperature.     

含有任意多个椭圆孔复合材料层合板的应力场计算

本文应用各向异性弹性力学的复变函数理论,用多保角变换的方法,导出了含有任意多个任意位置椭圆孔的各向异性复合材料板的多复变量应力函数表达式,然后在单位圆周上进行复Fourier级数展开,用待定系数法确定应力函数的未知系数,从而计算弹性板的应力场.编制了相应的多工况运行的FORTRAN77标准化程序,进行了考题和算例分析,给出了级数的收敛状况和孔边周向应力的分布图.      

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.     

Measurement by LASER-Generated Ultrasound of Four Stiffness Coefficients of an Anisotropic Material at Elevated Temperatures

Ultrasonic waves are generated through a composite material by means of a noncontact technique. It uses a Nd:Yag LASER for the generation and an interferometric probe for the detection of acoustic waveforms. From a suitable set of experimental data, an inversion scheme is used for the recovering of four stiffness coefficients. They characterize the elasticity in a principal plane of symmetry of the material which exhibits an orthorhombic symmetry. The measurements are performed at various temperatures, elevated by steps up to 300°C for two specimen. The sensitivity of the method appears convenient to measure the temperature induced stiffness changes. The anisotropic degradation of the material properties are then pointed out.     

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.     

Analysis of anisotropic plate using multiquadric radial basis function

In this paper, multiquadric radial basis function is used for dynamic and static analysis of anisotropic plates. Multiquadric radial basis function is applied for spatial discretization and Newmark implicit scheme is used for temporal discretization. The spatial discretization of the differential equations generates greater number of algebraic equations than the unknown coefficients. The multiple linear regression analysis, which is based on the least squares error norm, is employed to obtain the coefficients. Considering simple supported boundary conditions, an analogy between isotropic skew plates and rectangular anisotropic plates is used for solutions. The effect of fiber orientation is observed in clamped square and rectangular anisotropic plates. The results obtained by this method are compared with those obtained by other analytical methods.     

Heat transfer under conditions of phase transitions in bodies with anisotropic properties

An investigation is made of heat transfer in anisotropic bodies under conditions of phase transformations using the numerical solution of multidimensional unsteady-state problems of the Stefan type. A procedure of solving such problems is suggested. It is demonstrated that the characteristics of thermal conductivity tensors of both phases affect significantly both the temperature fields and the shape and velocity of motion of the boundary of phase transformations. Numerous results are analyzed of the effect which is made on the thermal state of anisotropic body by the orientation of principal axes and principal coefficients of thermal conductivity tensors of both phases.     

A generalized Ritz method for partial differential equations in domains of arbitrary geometry using global shape functions

A boundary element method (BEM)-based variational method is presented for the solution of elliptic PDEs describing the mechanical response of general inhomogeneous anisotropic bodies of arbitrary geometry. The equations, which in general have variable coefficients, may be linear or nonlinear. Using the concept of the analog equation of Katsikadelis the original equation is converted into a linear membrane (Poisson) or a linear plate (biharmonic) equation, depending on the order of the PDE under a fictitious load, which is approximated with radial basis function series of multiquadric (MQ) type. The integral representation of the solution of the substitute equation yields shape functions, which are global and satisfy both essential and natural boundary conditions, hence the name generalized Ritz method. The minimization of the functional that produces the PDE as the associated Euler–Lagrange equation yields not only the Ritz coefficients but also permits the evaluation of optimal values for the shape parameters of the MQs as well as optimal position of their centers, minimizing thus the error. If a functional does not exists or cannot be constructed as it is the usual case of nonlinear PDEs, the Galerkin principle can be applied. Since the arising domain integrals are converted into boundary line integrals, the method is boundary-only and, therefore, it maintains all the advantages of the pure BEM. Example problems are studied, which illustrate the method and demonstrate its efficiency and great accuracy.     

Real modes of vibration and hybrid modal analysis

Based on continuous Hilbert space basis functions and mean square convergence properties of spatial generalised Fourier series a new technique for hybrid modal analysis (HMA) is proposed. The technique utilises a mix of experimental, measured vibration responses and good numerical approximations of well defined, three-dimensional, real, normal modes. The modes are assumed to be solutions to an elastic, eigenvalue problem corresponding to the true geometry of the analysed body or structure. Starting from a known geometry and a suitable set of modes, it is shown that the measured data may be supplemented with spatial information about the whole vibrational displacement field which is correctly represented by the chosen set of complete (Hilbert space), modal basis vector fields. The spatial information is extracted from the measured vibration responses by curve fitting a truncated modal response model to the data. As a result of the curve fit a number of generalised Fourier coefficient spectra are obtained which together with the corresponding modes may be used to predict or simulate responses which were not measured or used in the curve fit. Given also the true mass density field of the body, the time average of the kinetic energy of the whole body may be approximated using only a restricted set of measured vibration responses. The method is completely general and applicable in all cases where the vibrational displacements are small enough compared to the characteristic dimensions of the analysed body. The effect of modal truncation and means to approximate corresponding dynamic displacement residuals are discussed for linear, anisotropic solid bodies and structures with general damping. Modal coupling due to damping and unknown elastic properties are also discussed. The method has been tested, with very good results, on experimental data measured with a laser doppler vibrometer on a plexiglas plate excited with a shaker in the frequency range 25–500 Hz.     

Estimation of temperature distributions and thermal stresses in a functionally graded hollow cylinder simultaneously subjected to inner-and-outer boundary heat fluxes

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to simultaneously estimate the unknown time-dependent inner and outer boundary heat fluxes in a functionally graded hollow circular cylinder from the knowledge of temperature measurements taken within the cylinder. Subsequently, the distributions of temperature and thermal stresses in the cylinder can be determined as well. It is assumed that no prior information is available on the functional forms of the unknown heat fluxes; hence the procedure is classified as the function estimation in inverse calculation. The temperature data obtained from the direct problem are used to simulate the temperature measurements, and the effect of the errors and locations in these measurements upon the precision of the estimated results is also considered. Results show that an excellent estimation on the time-dependent heat fluxes, temperature distributions, and thermal stresses can be obtained for the test case considered in this study.     

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.     

Reconstruction of time-dependent boundary heat flux by a BEM-based inverse algorithm

The objective of this study is to reconstruct an unknown time-dependent heat flux distribution at a surface whose temperature history is provided by a broad-band thermochromic liquid crystal (TLC) thermographic technique. The information given for this inverse problem is the surface temperature history. Although this is not an inverse problem, it is solved as such in order to filter the errors in input temperatures which are reflected in errors in heat fluxes. We minimize a quadratic functional which measures the sum of the squares of the deviation of estimated (computed) temperatures relative to measured temperatures provided by the TLC thermography. The objective function is minimized using the Levenberg–Marquardt method, and we develop an explicit scheme to compute the required sensitivity coefficients. The unknown flux is allowed to vary in space and time. Results are presented for a simulation in which a spatially varying and time-dependent flux is reconstructed over an airfoil.     

Thermoelastic solutions for anisotropic cracked thin films

Thermal stress intensity factors for cracks in anisotropic thin films subjected to uniform heat fluxes are investigated. Based on the method of analytic continuation associated with the alternating technique, the general solution of an anisotropic thin film/substrate under thermal loading is derived. Rapidly convergent series solutions for both the temperature and stress fields are obtained in terms of the corresponding homogeneous potentials. Using the technique of superposition and the Cauchy integral, the solution of the crack problem with arbitrary locations and angles is solved. Some typically numerical results are discussed, showing that a stiffer substrate can efficiently reduce the thermal stress intensity factors of the cracked thin films. The result also shows that the solution is accurate and rapidly converges as the thin film/substrate degenerates to a homogeneous medium.     

An Analytical Study into Conjugate Heat Transfer on the Boundaries of Anisotropic Bodies

A simultaneous analytical solution of the second initial boundary-value problem of thermal conductivity in an anisotropic plate and of the simplest problem of the boundary layer on this plate is used to investigate conjugate heat transfer. The reciprocal influence of heat transfer during a variation of the orientation of the principal axes and coefficients of the thermal conductivity tensor is analyzed. A significant decrease in the heat fluxes from the boundary layer to the plate in the case of the principal axis with a high coefficient of thermal conductivity oriented along the body is demonstrated.     

锅炉炉膛热负荷分布拟合算法研究

锅炉炉膛辐射热负荷测量及分布规律的研究可为蒸发受热面及节流孔设计提供必需的数据。提出了炉 膛热负荷测量数据的处理方法,将测得的热负荷数据转换成相对于蒸发受热面平均热负荷的分配不均系数,该系数是炉膛相对高度的函数,它的多项式回归模型不仅要使误差平方和达到最小,而且根据平均热负荷的定义,多项 式系数还要满足给定的等式约束。对于采用普通燃烧技术和空气分级燃烧技术的两类燃煤锅炉,利用该回归模型拟合炉膛辐射热负荷数据,得到不同的分布规律,并与某300 MW锅炉炉膛热负荷测量数据进行了对比;这种以最 小二乘法为基础的改进回归模型既满足了回归变量的内在联系,又对测量数据进行了最佳逼近。     

Lattice dynamics of layered ferroelectric semiconductor compound TlGaSe2

We present the first-principles calculation of the lattice dynamics of the TlGaSe₂ ternary semiconductor having highly anisotropic crystal structure. Calculations have been performed using open-source code ABINIT on the basis of the density functional perturbation theory within the plane-wave pseudopotential approach. Results on the frequencies of phonon modes in the centre of Brilloin zone and the dispersion of transverse shear acoustic branch of the phonon spectra agree well with the experimental data on Raman scattering, infrared reflectivity and ultrasound wave propagation in TlGaSe₂. The calculated and experimental temperature dependencies of heat capacity are in a good agreement up to the room temperature. Along the layer, the low-frequency acoustic branch displays the bending wave behavior which is characteristic of the layer crystal structures.