Temperature-Constrained Topology Optimization of Transient Heat Conduction Problems

A regional temperature measure model is constructed to obtain a small number of temperature constraints for local transient temperature control. The temperature sensitivity is derived using the adjoint variable method. The multiple temperature criteria and three-phase topology optimization are further investigated for transient heat conduction design. The material layout design of transient heat conduction is replaced by a static optimization problem, which is subsequently solved by the method of moving asymptotes. Finally, several numerical examples are provided to demonstrate the feasibility and validity of the proposed topology optimization for transient heat conduction problems.     

热负荷阶跃变化条件下热回流式换热系统缺陷机理及优化方法研究

针对国内某北方核电厂的设备冷却水系统热回流式换热器,分析了不同热负荷下热回流式换热系统的稳态特性及负荷阶跃变化下热回流式换热系统缺陷机理,提出了热回流式换热器系统优化方法。研究表明:在不同热负荷下热回流式换热器系统切换的关键是与不同热负荷对应的具有特定温度的伴流的形成;热负荷阶跃变化下状态转换瞬态过程中存在系统缺陷,其根本原因在于单纯采取调节热回流率的方法,具有较大的时间滞后性;调节换热器冷介质侧的流体流量,改变换热器传热系数,强化了对状态改变的快速响应;采取热回流叠加换热器旁流方法,可以解决原有系统状态转换瞬态过程中存在的缺陷。     

Performance Analysis of Heat Sinks With Phase-Change Materials Subjected to Transient and Cyclic Heating

Phase-change cooling technique is a suitable method for thermal management of electronic equipment subjected to transient or cyclic heat loads. The thermal performance of a phase-change based heat sink under cyclic heat load depends on several design parameters, namely, applied heat flux, cooling heat transfer coefficient, thermophysical properties of phase-change materials (PCMs), and physical dimensions of phase-change storage system during melting and freezing processes. A one-dimensional conduction heat transfer model is formulated to evaluate the effectiveness of preliminary design of practical PCM-based energy storage units. In this model, the phase-change process of the PCM is divided into melting and solidification subprocesses, for which separate equations are written. The equations are solved sequentially and an explicit closed-form solution is obtained. The efficacy of analytical model is estimated by comparing with a finite-volume-based numerical solution for both transient and cyclic heat loads.     

Topology optimization for thermal conductors considering design-dependent effects,including heat conduction and convection

In structural designs considering thermal loading, in addition to heat conduction within the structure, the heat convection upon the structure’s surface can significantly influence optimal design configurations. In this paper, we focus on the influence of design-dependent effects upon heat convection and internal heat generation for optimal designs developed using a topology optimization scheme. The method for extracting the structural boundaries for heat convection loads is constructed using a Hat function, and heat convection shape dependencies are taken into account in the heat transfer coefficient using a surrogate model. Several numerical examples are presented to confirm the usefulness of the proposed method.     

Dual-Phase-Lag Heat Conduction in Finite Slabs With Arbitrary Time-Dependent Boundary Heat Flux

Applying a constant or transient heat flux on a plane slab is a common technique in microelectronics technology and material processing, including laser patterning, micromachining, and laser surface treatment processes. Although Fourier's law is typically very precise for evaluating temperatures in solids, a number of experimental observations suggest the existence of non-Fourier transient conduction in these applications. Since the dual-phase-lag (DPL) model of heat conduction can be compatible with the hypothesis of local equilibrium thermodynamics (as shown here), the effects of temperature gradient relaxation time on the non-Fourier hyperbolic conduction in a finite slab subjected to an arbitrary time-dependent surface heat flux is examined by this model. The combination of diffusion- and wave-like features in heat conduction process is properly monitored by the DPL model for two types of heat flow regimes, namely, gradient precedence and flux precedence. The results indicate considerable deviations between the predictions of these regimes.     

THERMOELASTIC TOPOLOGY OPTIMIZATION FOR PROBLEMS WITH VARYING TEMPERATURE FIELDS

Elastic structures that exist in a thermal environment usually experience complex steady-state or transient heat conduction, whereby operational temperatures and stresses may change with time, heat sources, and thermal or kinematic boundary conditions. This article proposes an evolutionary optimization procedure for topology design involving thermoelasticity in which finite element heat analysis, finite element thermoelastic analysis, and subsequently design modification are iteratively carried out. To achieve as efficacious a material usage as possible, the relative efficiency of an element is defined in terms of its thermal stress level. In this article, design cases with uniform temperature fields, nonuniform temperature fields subjected to single or multiple heat load cases, and transient temperature fields are studied. The examples presented show the capabilities of the proposed procedure to solve various thermoelastic problems under varying temperature fields.     

基于元体能量平衡法的垂直U型埋管换热特性的研究

基于元体能量平衡法建立了垂直U型埋管的传热模型,模型考虑了流体温度的沿程变化,并通过引入热干扰角与等效传热间距反映两管脚间的热干扰问题,使之更符合实际的传热情况。通过所建模型对U型埋管的换热特性进行了数值模拟,结果表明:增加土壤与回填物导热系数、管脚间距、管内流体流量及减小管脚热干扰角与进口流体温度(供热工况下)均可以增强埋管的换热效果,其中土壤导热性影响最为显著。但回填物导热系数不可无限制增大,其大小还要考虑对增强管脚间热干扰的影响及其与管脚间距的相互关联性。同时,流量的增加要考虑对流动阻力增加的限制,可以采用变流量设计来进行调节与优化。此外,为了充分发挥地源热泵的能效,实际设计应该考虑埋管、热泵及负荷三者间的相互匹配性。     

Topology optimization of convection-dominated,steady-state heat transfer problems

The current push in the topology optimization community is to apply topology optimization to mechanics problems beyond typical structural design to other physical domains. Here, a framework for topology optimization of nonlinear steady-state heat transfer with conduction, convection, and radiation without explicitly accounting for fluid motion is evaluated. Convection-dominated diffusion problems are susceptible to numerical instabilities that, unless they are handled properly in the analysis, can severely affect the optimization. This numerical instability issue is the focus of this work, its origin is discussed in the context of density-design-variable-based topology optimization, and a method for avoiding such instabilities is described. Several design examples demonstrate the approach.     

SAINT-VENANT TYPE DECAY ESTIMATES FOR TRANSIENT HEAT CONDUCTION IN A COMPOSITE RIGID SEMISPACE

The global and pointwise spatial decay estimates for a solution to the one-dimensional initial-boundary value problem of heat conduction in a composite rigid semispace are presented. Vie global estimates cover: (i) a transient heat conduction problem for an isotropic nonhomogeneous semispace with arbitrary variation with depth of the density, specific heat, and thermal conductivity; (ii) a transient heat conduction problem for an isotropic semispace made of a functionally graded material that composition changes from a ceramic surface at x = 0 to a metal semispacex≥.x₀> 0; and (iii) a transient heat conduction problem for a microperiodic layered semispace. The pointwise spatial decay estimates are confined to homogenized transient heat conduction problems for a microperiodic layered semispace described by an effective modulus theory as well as by a refined averaged theory     

Topological Shape Optimization of Heat Conduction Problems using Level Set Approach

ABSTRACT

A topological shape optimization method for heat conduction problems is developed using a level set method. The level set function obtained from the “Hamilton-Jacobi type” equation is embedded into a fixed initial domain to implicitly represent thermal boundaries and obtain the finite-element response and adjoint sensitivity. The developed method minimizes the thermal compliance, satisfying the constraint of allowable volume by varying the implicit boundary. During optimization, the boundary velocity to integrate the Hamilton-Jacobi equation is obtained from the optimality condition. The newly developed method shows no numerical instability and makes it easy to represent topological shape variations.     

Transient heat flux measurement analysis from coaxial thermocouples at convective based step heat load

The measurement of surface heating rate is an imperative parameter in the force convection ground-based facility for short duration investigation due to the heat transfer rate is changing rapidly. The coaxial thermocouples are suitable to measure the transient heat flux in fast varying heat transfer application because of having fast response time in the range microseconds or less. In this addition, the K-type, E-type, and J-type of coaxial thermocouples are contrived as well as the thermal coefficient resistance (TCR) and sensitivity (S) has been calculated from oil-bath based technique. These handmade coaxial thermocouples are exposed in a forced convection flow facility having three different input step heat loads as well as their transient heat fluxes are estimated using one-dimensional heat conduction modeling for the semi-infinite body. The numerical simulation has also been carried out with the analogous experimental parameters using ANSYS-FLUENT v.15.0 and compared with the outcome of the experimental approach and it is found that the average value of the transient temperatures having 0.3% error and surface heat flux recovered from this temperature is 10%. This study reveals the measuring ability of these handmade coaxial thermocouples at low temperature and low velocity on short duration transient measurements.     

Performance Evaluation of Two Heat Transfer Models of a Walking Beam Type Reheat Furnace

Two different heat transfer models for predicting the transient heat transfer characteristics of the slabs in a walking beam type reheat furnace are compared in this work. The prediction of heat flux on the slab surface and the temperature distribution inside the slab have been determined by considering thermal radiation in the furnace chamber and transient heat conduction in the slab. Both models have been compared for their accuracy and computational time. The furnace is modeled as an enclosure with a radiatively participating medium. In the first model, the three-dimensional (3D) transient heat conduction equation with a radiative heat flux boundary condition is solved using an in-house code. The radiative heat flux incident on the slab surface required in the boundary condition of the conduction code is calculated using the commercial software FLUENT. The second model uses entirely FLUENT along with a user-defined function, which has been developed to account for the movement of slabs. The results obtained from both models have a maximum temperature difference of 2.25%, whereas the computational time for the first model is 3 h and that for the second model is approximately 100 h.     

Transient heat fluxes measurement analysis from platinum based thin film gauges in open and closed cavities

Platinum thin film gauges (PTFGs) measure heat fluxes in the applications involving very short duration of the heating environment. Heat transfer measurement is the frequently used technique for measuring the surface heat flux using thin film gauges. The present investigation has been focused on the design and manufacturing methods for heat transfer gauge, their stability, and dynamic calibrations in certain situations where the heat load suddenly build up. PTFGs measure heat fluxes in heating environments applications during the very duration. The measurement for heat transfer is a technique used often with thin film gauges to measure the surface heat flux. The convection devices are regarded as the best measuring units in short-term transient temperature measurement applications and are usually used when the heat transfer mode is dominant means gas turbine engines, high speed aircraft, etc. In addition to that, there are many difficulties incurred for convection based measurement practically and few interdisciplinary research fields. A convective heat load is provided with a hot air gun to get the temperature signal. By using thin film gauge through present investigations, it is very ambitious to explore the possibility of short term conduction based transient measurements with pure conduction heat transfer mode. A simple experimental set up is used to supply the thin film gauges with heat flux, which is manually manufactured with platinum as a sensing material and quartz as a substrate material. The body's nose tip to high speed flow is expected to be the maximum heat transfer at the stagnation point. The stagnation point probes are fabricated for PTFGs, and baking material is quartz. The recorded temperature histories are compared with the experimentally recorded temperature signals from the gauges through the finite element method. The heat flux forecast was configured by using the one dimension thermal conduction equation convolution integral and by comparison with the heat input loads. This study reveals the ability of PTFGs to be used for a short period.     

Resolution of Unknown Heat Source Inverse Heat Conduction Problems Using Particle Swarm Optimization

The main objective of this article is to solve inverse heat conduction problems with the particle swarm optimization method. An enhanced particle swarm optimization (EPSO) algorithm is proposed to overcome the shortcoming of earlier convergence of standard PSO algorithms. The EPSO is used to estimate the unknown time-dependent heat source in complex regions. Numerical experiments indicate the validity and stability of the EPSO method.     

Inverse Transient Heat Conduction Problems of a Multilayered Functionally Graded Cylinder

Inverse transient heat conduction problems of a multilayered functionally graded (FG) cylinder are presented. The approach is based on measurement of temperature on the outer surface of the cylinder to estimate the heat flux and convection heat transfer coefficient on its inner surface. The non-Fourier heat transfer equation is employed to accurately formulate the problem. The conjugate gradient method (CGM) is used for the optimization procedure and the incremental differential quadrature method (DQM) is applied to solve the direct, sensitivity, and adjoint problems. The accuracy of the presented approach is examined by simulating the exact and noisy data through different examples. Good accuracy of the obtained results validates the presented approach.     

Structured Multiblock Grid Solution of Two-Dimensional Transient Inverse Heat Conduction Problems in Cartesian Coordinate System

ABSTRACT

In this study a structured multiblock grid is used to solve two-dimensional transient inverse heat conduction problems. The multiblock method is implemented for geometric decomposition of the physical domain into regions with blocked interfaces. The finite-element method is employed for direct solution of the transient heat conduction equation in a Cartesian coordinate system. Inverse algorithms used in this research are iterative Levenberg-Marquardt and adjoint conjugate gradient techniques for parameter and function estimations. The measured transient temperature data needed in the inverse solution are given by exact or noisy data. Simultaneous estimation of unknown linear/nonlinear time-varying strengths of two heat sources in two joined surfaces with equal and different heights is obtained for the solution of the inverse problems, and the results of the present study for unknown heat source functions are compared to those of exact functions. This study is an attempt to challenge the goal of combining a multiblock technique with inverse analysis methods. In fact, the structured multiblock grid is capable of providing accurate solutions of inverse heat conduction problems (IHCPs) in industrial configurations, including composite structures. In addition, the multiblock IHCP solver is suitable to estimate unknown parameters and functions in these structures.     

Level Set-based Topological Shape Optimization of Nonlinear Heat Conduction Problems

A level set-based topological shape optimization method is developed for nonlinear heat conduction problems. While minimizing the objective function of instantaneous thermal compliance and satisfying the constraint of allowable volume, solution of the Hamilton-Jacobi equation leads the initial boundary to an optimal one according to the normal velocity field determined from the descent direction of the Lagrangian. To overcome the convergence difficulty in nonlinear problems resulting from introduction of an approximate boundary, an actual boundary is identified by tracking the level set functions and remeshing using Delaunay triangulation. The velocity field outside the actual domain is determined through a velocity extension scheme.     

Topology Optimization of Heat and Mass Transfer Problems: Laminar Flow

The design of efficient structures for heat and mass transfer problems involves the implementation of an appropriate topology optimization strategy in order to fully take into account the bi-objective nature of the problem. This article couples the finite-volume method (FVM), for the direct solver, with the discrete adjoint approach, for the sensitivity analysis, in order to tackle both fluid dynamic and heat transfer optimization in the frame of laminar flows. Details are provided about the sparsity pattern of the discrete adjoint system, which requires special attention to select a suitable matrix iterative solver. Several examples underline the adequacy of topology optimization in conjunction with the FVM for the minimization of the power dissipated by the fluid. Then, a bi-objective problem aiming at minimizing the pressure drop while maximizing the recoverable thermal power is solved by the identification of its Pareto frontier, thanks to an aggregate objective function (AOF) method. The main conclusion deals with the possibility of finding an acceptable trade-off between both objectives and the potential of topology optimization for heat and mass transfer optimization.     

Two-Dimensional Inverse Heat Transfer Analysis of Functionally Graded Materials in Estimating Time-Dependent Surface Heat Flux

Two-dimensional transient inverse heat conduction problem (IHCP) of functionally graded materials (FGMs) is studied herein. A combination of the finite element (FE) and differential quadrature (DQ) methods as a simple, accurate, and efficient numerical method for FGMs transient heat transfer analysis is employed for solving the direct problem. In order to estimate the unknown boundary heat flux in solving the inverse problem, conjugate gradient method (CGM) in conjunction with adjoint problem is used. The results obtained show good accuracy for the estimation of boundary heat fluxes. The effects of measurement errors on the inverse solutions are also discussed.     

Role of Melt Convection on Optimization of PCM-Based Heat Sink Under Cyclic Heat Load

In this article, we study the thermal performance of phase-change material (PCM)-based heat sinks under cyclic heat load and subjected to melt convection. Plate fin type heat sinks made of aluminum and filled with PCM are considered in this study. The heat sink is heated from the bottom. For a prescribed value of heat flux, design of such a heat sink can be optimized with respect to its geometry, with the objective of minimizing the temperature rise during heating and ensuring complete solidification of PCM at the end of the cooling period for a given cycle. For given length and base plate thickness of a heat sink, a genetic algorithm (GA)-based optimization is carried out with respect to geometrical variables such as fin thickness, fin height, and the number of fins. The thermal performance of the heat sink for a given set of parameters is evaluated using an enthalpy-based heat transfer model, which provides the necessary data for the optimization algorithm. The effect of melt convection is studied by taking two cases, one without melt convection (conduction regime) and the other with convection. The results show that melt convection alters the results of geometrical optimization.