Calculation of Radiation Heat Transfer in Problems of Flow past Bodies with Account for Heat-Shield Coating Mass Loss

Flow past bodies with account for radiation heat transfer near the body nose is considered in connection with the problem of thermal protection of spacecraft entering planetary atmospheres. An approach based on the spherical harmonics method is used for taking radiation into account. The heating and ablation of the heat-shield coating is determined by numerically solving the heat conduction equation with a moving boundary. The thermal problem is solved together with the calculation of the vehicle trajectory, which makes it possible to estimate the effect of the coating mass loss on the trajectory parameters. The approach formulated is realized under the conditions of entry of a spherical segment and a spherically-blunted cone with equal mid-section radii into the Venusian atmosphere. Comparing the results makes it possible to choose the vehicle shape optimal with respect to the thermal regime.     

Optimal discrete distribution of heat flux elements for in-tube laminar forced convection

A new technique is proposed to enhance the heat transfer from a discretely heated pipe to a developing laminar fluid flow. Unlike the common heating situation where the fluid is continuously heated along the pipe wall with uniform heat flux, the proposed technique consists in heating the fluid with stepwise distributed heat flux, namely by placing insulated segments between the heated segments. Applying this technique, the effective length of the thermal entrance region is enlarged and as a result, the average heat transfer is invigorated. In order to maximize the heating performance, an optimal placement of the insulated segments between the heated segments is calculated according to constructal design. This serves to describe the optimal stepwise distribution of the heat flux. Owing that the total heat load is considered fixed, the maximization of the heating performance translates into the minimization of the peak temperature (‘hot spot’) of the pipe wall. The analytical results demonstrate that the optimal location of the insulated segments along with the reduction of the peak temperature strongly depend on the Graetz number. It is also shown that for intermediate values of the Graetz number, the peak temperatures are remarkably reduced in response to the optimal placement of the insulated/heated segments.     

Determination of the body shape for minimum radiative heating along a flight trajectory

Space vehicles are subject to intense aerodynamic heating in planetary entry. According to estimates in [1], the heat shield mass for entry of a probe into the atmospheres of the outer planets can make up 20–50% of its total mass; here the radiative component predominates in the aerodynamic heating. It is therefore interesting to investigate methods of reducing the heat flux to the nose region of a vehicle. Analysis shows [2–6] that, for a given atmospheric composition, the heat-shield weight is determined by the trajectory, the body shape, the heat-protection method, and the chemical composition and the thermophysical and optical properties of the heat shield material. In such a general statement of the problem, optimization of the heat-shield mass depends on many parameters, and has not been solved hitherto. A number of papers have examined simpler problems, associated with reducing spacevehicle heating: optimization of the trajectory from the condition that the total heat flux to the body stagnation point should be a minimum for given probe parameters [2, 3], optimization of the characteristic probe size for a given trajectory [2–4], and optimization of the probe shape in a class of conical bodies at a given trajectory point [3, 5, 6J. In [7] a variational problem was formulated to determine the shape of an axisymmetric body from the condition that the radiative heat flux to the body at a given trajectory point should be a minimum for the entire surface, and an analytical solution was found for this in limiting cases. The present paper investigates a more general variational problem: determination of the shape of an axisymmetric body from the condition that the total radiative influx of heat to the body along its atmospheric trajectory should be a minimum. A solution has been obtained for a class of slender bodies for different isoperimetric conditions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 94–100, March–April, 1978.     

Optimization of tensegrity structures

This paper concerns the design of tensegrity structures with optimal mass-to-stiffness ratio. Starting from an initial layout that defines the largest set of allowed element connections, the procedure seeks the topology, geometry and prestress of the structure that yields optimal designs for different loading scenarios. The design constraints include strength constraints for all elements of the structure, buckling constraints for bars, and shape constraints. The problem formulation accommodates different symmetry constraints for structure parameters and shape. The static response of the structure is computed by using the nonlinear large displacement model. The problem is cast in the form of a nonlinear program. Examples show layouts of 2D and 3D asymmetric and symmetric structures. The influence of the material parameters on the optimal shape of the structure is investigated.     

基于Kriging代理模型的结构形状优化方法研究

建立了一种进行结构形状优化的工程方法。该方法利用试验设计法选取位置变量样本点,并对各个样本点对应的结构进行尺寸优化,然后根据样本点和尺寸优化结果建立Kriging代理模型,再利用遗传算法求出位置变量最优解,进而得到结构最优解。最后进行了15杆平面拱式桁架、悬臂梁和25杆空间桁架三个形状优化算例,算例分析结果表明:该方法思路清晰、适应性强、优化效果明显,具有较大的工程应用价值。     

Determination of the optimal Gabor wavelet shape for the best time-frequency localization using the entropy concept

The continuous Gabor wavelet transform (GWT) has been utilized as an effective and powerful time-frequency analysis tool for identifying the rapidly-varying characteristics of some dispersive wave signals. The effectiveness of the GWT is strongly influenced by the wavelet shape that controls the time-frequency localization property. Therefore, it is very important to choose the right Gabor wavelet shape for given signals. Because the characteristics of signals are rarely known in advance, the determination of the optimal shape is usually difficult. Based on this observation, we aim at developing a systematic method to determine the signal-dependent shape of the Gabor wavelet for the best time-frequency localization. To find the optimal Gabor wavelet shape, we employ the notion of the Shannon entropy that measures the extent of signal energy concentration in the time-frequency plane. To verify the validity of the present approach, we analyze a set of elastic bending wave signals generated by an impact in a solid cylinder.     

Preparation and analysis of different roughness structures for evaporator tubes

The processes of the phase change in boiling occur at the solid–liquid interface by heat transfer from a solid heating surface to the boiling liquid. The characteristic features of the heating surfaces are therefore of great interest to optimize the design of evaporators. The microstructure with all its peaks and cavities influences directly the wetting and rewetting conditions of the heated surface by the boiling liquid and hence bubble formation and heat transfer. The roughness structures of different evaporator copper tubes with 8 or 25 mm diameter are characterized quantitatively with regard to the cavities offered to nucleation. The surfaces of the heating elements are sandblasted by different means resulting in a stochastic microstructure. The surfaces are investigated by a three-dimensional contactless roughness measurement technique combining the stylus technique with the near field acoustic microscopy. The method opens the possibility to obtain results according to standard for practical applications and additionally delivers detailed information about the three-dimensional shape of each cavity within the surface investigated. The analysis of the microstructure implies the total number of cavities, their local and size distribution calculated by the method of the envelope area. The results of the surface analysis are linked to those of heat transfer and bubble formation discussed in a contribution by Kotthoff and Gorenflo.     

Determination of Defect Depth and Size Using Virtual Heat Sources in Pulsed Infrared Thermography

The determination of defect depth and size using Pulsed Infrared Thermography is a critical problem. The problem of defect depth estimation has been previously studied using 1D heat conduction models. Unfortunately, 1D heat conduction based models are generally inadequate in predicting heat flow around defects. In this study, a novel approach based on virtual heat sources is proposed to model heat flow around defects accounting for 2D axisymmetric heat conduction. The proposed approach is used to quantitatively determine the defect depth and size. The validity of the model is established using experiments performed on a stainless steel plate specimen with flat bottom holes at different depths.     

3-D analysis of temperature distribution in the material during pulsed laser and material interaction

Recently, lasers are being increasingly used in the industry owing to their precision and low cost. Material is heated and evaporated during laser and material interaction due to the absorption of laser beams by the material. In this study, a 3-D Laser heating model including evaporation has been solved using the electron- kinetic theory approach. The basis in examining the problem using the kinetic theory approach is to describe the heat conduction through electron-phonon and molecule-phonon collisions. The problem is solved by using the electron-kinetic theory approach in such a way that heat conduction is taken into account until the material is heated to its melting temperature and non-conduction limited heat transfer is considered after the melting temperature is reached. Non-conduction limited heat transfer through the phase change process is resulted from vacancy-molecule collisions. A numerical scheme is introduced to solve the governing equation, owing to the fact that the energy equation resulted is in the form of integro-differential equation. Four different materials, namely iron, nickel, tantalum and titanium are chosen in this study determine the material response to laser pulse heating. For each material, time dependent temperature distribution through the depth of the material and on the surface of the material is computed and analyzed for four different materials.     

Alternative approach in thermal analysis of plate heat exchanger

This paper presents alternative approach in heat transfer analysis of plate heat exchangers. In order to obtain heat transfer rate and effectiveness values of plate heat exchanger, neural network (NN) approach was used. Experimentally, system used in plate heat exchanger for heating and cooling applications was designed and constructed. Experimental data were used for training and testing network. The training and validation were performed with good accuracy. The correlation coefficient obtained when unknown data were applied to the networks was 0.9994 for heat transfer rate and 0.9976 for effectiveness, which is very satisfactory. Using the weights obtained from the trained network, a new formulation is presented for determination of heat transfer rate and effectiveness. This formulation can provide simplicity in thermal analysis of plate heat exchanger. The presented procedure can also help to heat exchanger designer and manufacturer.     

壳体结构优化及其DDDU(W)新版本

本文建立了壳体结构优化的序列二次规划模型,对八节点等参壳单元做了优化处理,扩充了通用结构优化程序DDDU(W)的功能。文末算例表明了算法的合理性与有效性。     

Two-dimensional cellular metals as multifunctional structures: topology optimization

Highly porous two-dimensional (2D) cellular metals have multifunctional attributes, with tailorable structures to achieve multifunctional performance. The focus of this study is to explore the optimal cellular topology of 2D cellular metals for heat dissipation, and to investigate the eligibility of different heat enhancement techniques for more efficient heat dissipation. An analytical approach for the optimal design of metallic 2D cellular materials, cooled by single-phase laminar forced convection in various flow configurations, is proposed and validated by comparison with full numerical simulations. The optimal design is characterized by two subsidiary dimensionless parameters: one reflecting the trade-off between convection and fluid friction, and the other reflecting the optimal balance between conduction and convection. A heat transfer enhancement technique––boundary layer redevelopment––is subsequently introduced and its feasibility examined experimentally. Future research directions in specific areas are discussed.     

Three-dimensional structure optimal design for extending fatigue life by using biological algorithm

This paper presents some applications of a new structural shape optimization procedure for maximizing fatigue life or inspection intervals for damage tolerant structures. In this approach, a new and simple method, which we termed FAST (Failure Analysis of Structures), for estimating the stress intensity factor for cracks at a notch, as well as an extension of the biological algorithm was employed to study the problem of optimization with fatigue life as the design objective. Research by the authors has demonstrated that the optimum shape for minimizing stress is not necessarily the optimum shape for static strength or fatigue life of a damage tolerant structure. The examples are presented that highlight this difference. The optimal shapes for stress are compared with optimized shapes found for static strength with different crack lengths. These are also compared with optimized shapes found for maximum fatigue life. The choice of initial crack size was found to have a significant effect on the optimal shapes for the structures presented.     

Optimum separation of asymmetrically heated sub-channels forming a bundle: influence of simultaneous flow and temperature

This paper focuses on laminar heat and fluid flow in an array of sub-channels placed in an uniform stream, which is characterized by a fixed pressure difference and a developing velocity and temperature. The dominant feature of the study deals with the optimal selection of the plate-to-plate separation between subchannels placed in a specified volume that renders maximum heat transmission from the heated plates to the moving fluid. Asymmetric heating from one plate in a typical sub-channel to either air or water is produced by uniform temperature in one case and uniform heat flux in the other case. Upon relaxing the vital condition of developing velocity, the numerical computations for the optimal separation and the maximum heat transmission incurred in little error for both cooling fluids.     

Optimal Design in Conductivity Under Locally Constrained Heat Flux

This paper addresses the relaxation of an optimal design problem in conductivity under a point-wise constraint on the heat flux. By using a variational approach, developed by the authors in a previous work, we obtained a complete relaxation, involving the explicit computation of constrained quasiconvex envelopes. This relaxed formulation turns out to be very simple in the remarkable compliance case, for which numerical simulations are performed. Those simulations show that our approach and results are interesting from a theoretical point of view as well as from a practical perspective. The emphasis of our work is placed on the local constraint on the heat flux, which seems to be a new ingredient for this kind of optimal design problems.     

THERMOMECHANICAL RESPONSE OF SMA FIBER COMPOSITES WITH NON-UNIFORM TEMPERATURE DISTRIBUTION

A micromechanics method based on the High-Order-Theory developed by Aboudi et al. is used to predict the thermomechanical response of composites reinforced by shape memory alloy (SMA) fibers, and the non-uniform thermal distribution in composite arising from the process of heating or cooling is considered. The numerical development based on this model was coded to predict the thermomechanical response of shape memory alloy fiber/elastomer matrix composite subjected to thermal cycle loading. When the composite is heated, two heating ways, thermal gradients and heat source by passing an electric current through the SMA fibers are imposed on the composite respectively. Upon cooling, the first thermal boundary condition and the second thermal boundary condition are subjected to the composite respectively. A series of stress distributions and temperature distributions for different instants are calculated to reveal the interaction between the SMA material and matrix. It is useful to analyze and design the SMA actuator driven by heat source or the surface temperature.     

Natural convection of an alumina-water nanofluid inside an inclined wavy-walled cavity with a non-uniform heating using Tiwari and Das’ nanofluid model

The present study is devoted to numerical analysis of natural convective heat transfer and fluid flow of alumina-water nanofluid in an inclined wavy-walled cavity under the effect of non-uniform heating. A single-phase nanofluid model with experimental correlations for the nanofluid viscosity and thermal conductivity has been included in the mathematical model. The considered governing equations formulated in dimensionless stream function, vorticity, and temperature have been solved by the finite difference method. The cavity inclination angle and irregular walls (wavy and undulation numbers) are very good control parameters for the heat transfer and fluid flow. Nowadays, optimal parameters are necessary for the heat transfer enhancement in different practical applications. The effects of the involved parameters on the streamlines and isotherms as well as on the average Nusselt number and nanofluid flow rate have been analyzed. It has been found that the heat transfer rate and fluid flow rate are non-monotonic functions of the cavity inclination angle and undulation number.     

A three-dimensional optimal control problem in determining the boundary control heat fluxes

A three-dimensional optimal control algorithm in determining the strength of the unknown optimal boundary control heat fluxes utilizing the Conjugate Gradient Method (CGM) and a general purpose commercial code CFX4.2 is applied successfully in the present study based on the desired domain temperature distributions at the final time of heating. Results obtained by using the conjugate gradient method to solve this three-dimensional optimal control problems are justified based on the numerical experiments. Two different computational domains and two different desired temperature distributions are given and the corresponding optimal control heat fluxes are to be determined. Results show that the optimal control heat fluxes can always be obtained with any arbitrary initial guesses of the boundary fluxes.     

基于拓扑描述函数的连续体结构拓扑优化方法

提出了一种利用拓扑描述函数(TDF)作为拓扑设计变量求解连续体结构拓扑优化问题 的新方法. 优化问题的目标函数是结构的整体柔顺性，约束条件为对于可利用材料的体积限 制. 这种方法不仅可以消除拓扑优化中经常出现的棋盘格式等数值不稳定现象，而且能够有 效地抑制传统算法处理此类优化问题时所引发的边界扩散效应. 与其它的基于水平集描述函 数的拓扑优化方法相比，所提出的算法不仅无需求解控制水平集函数演化的双曲守恒方 程，而且合理地考虑了目标函数的拓扑导数信息，因而使得算法的计算效率有了显著的提高.     

形状记忆合金作动器的设计及优化

采用Ｂｒｉｓｉｏｎ［１］等提出的ＳＭＡ材料的本构关系，分析了形状记忆合金作动器在三种热交换方式（自然冷却、强制冷却和采用半导体热泵技术）下的动力特性，同时研究了ＳＭＡ丝在恒载和载荷变化时对完成正逆相变所用时间的影响，并简单讨论了影响作动器响应的几个因素和改进方法