Solution of Inverse Boundary Optimization Problem by Trefftz Method and Exponentially Convergent Scalar Homotopy Algorithm

The inverse boundary optimization problem, governed by the Helmholtz equation, is analyzed by the Trefftz method (TM) and the exponentially convergent scalar homotopy algorithm (ECSHA). In the inverse boundary optimization problem, the position for part of boundary with given boundary condition is unknown, and the position for the rest of boundary with additionally specified boundary conditions is given. Therefore, it is very difficult to handle the boundary optimization problem by any numerical scheme. In order to stably solve the boundary optimization problem, the TM, one kind of boundary-type meshless methods, is adopted in this study, since it can avoid the generation of mesh grid and numerical integration. In the boundary optimization problem governed by the Helmholtz equation, the numerical solution of TM is expressed as linear combination of the T-complete functions. When this problem is considered by TM, a system of nonlinear algebraic equations will be formed and solved by ECSHA which will converge exponentially. The evolutionary process of ECSHA can acquire the unknown coefficients in TM and the spatial position of the unknown boundary simultaneously. Some numerical examples will be provided to demonstrate the ability and accuracy of the proposed scheme. Besides, the stability of the proposed meshless method will be validated by adding some noise into the boundary conditions.     

CFD simulations of droplet and particle agglomeration in an industrial counter-current spray dryer

In this study, CFD simulations of particle and droplet agglomeration in an industrial counter-current spray dryer are presented. For this purpose, a modified form of the stochastic collision agglomeration model is proposed. This model takes into account droplet–droplet collision as well as wet and dry particle interaction. These events are coupled with heat, mass and momentum transfer. A comprehensive moisture evaporation model based on the concept of characteristic drying curve (CDC) was applied to predict the drying kinetics of the detergent slurry. Due to high instability in air flow inside the drying chamber, simulations were carried out under transient condition. A comparison between time-averaged simulation results and measurements, which were performed on an industrial spray drying installation, shows a good agreement. This finding proves the correctness of the developed agglomeration and drying models. The presented methodology of CFD simulations of agglomeration can be used to design or optimise spray-drying installations and to predict the final particle size distribution of the product.     

Meshless point collocation for the numerical solution of Navier-Stokes flow equations inside an evaporating sessile droplet

The Navier-Stokes flow inside an evaporating sessile droplet is studied in the present paper, using sophisticated meshfree numerical methods for the computation of the flow field. This problem relates to numerous modern technological applications, and has attracted several analytical and numerical investigations that expanded our knowledge on the internal microflow during droplet evaporation. Two meshless point collocation methods are applied here to this problem and used for flow computations and for comparison with analytical and more traditional numerical solutions. Particular emphasis is placed on the implementation of the velocity-correction method within the meshless procedure, ensuring the continuity equation with increased precision. The Moving Least Squares (MLS) and the Radial Basis Function (RBF) approximations are employed for the construction of the shape functions, in conjunction with the general framework of the Point Collocation Method (MPC). An augmented linear system for imposing the coupled boundary conditions that apply at the liquid-gas interface, especially the zero shear-stress boundary condition at the interface, is presented. Computations are obtained for regular, Type-I embedded nodal distributions, stressing the positivity conditions that make the matrix of the system stable and convergent. Low Reynolds number (Stokes regime), and elevated Reynolds number (Navier-Stokes regime) conditions have been studied and the solutions are compared to those of analytical and traditional CFD methods. The meshless implementation has shown a relative ease of application, compared to traditional mesh-based methods, and high convergence rate and accuracy.     

Numerical and experimental investigations on the use of mist flow process in refrigerated display cabinets

This study concerns the use of mist flow whereby fine water droplets are injected into the air curtain to improve the performance of Refrigerated Display Cabinets (RDCs). The deposition and evaporation of droplets on the surface of products partially compensate the radiative heat gained by the products by removing from it the amount of latent heat of the evaporated droplets.The experiments were carried out on an actual display cabinet. Numerical modelling was performed using Fluent Computational Fluid Dynamics (CFD) software. In two-phase flow, an Euler–Lagrange approach was adopted to predict the transport of droplets by the air curtain and their spatial distribution on the product surface of the RDC. An original numerical procedure was built in the CFD model in order to compute the deposited droplets while taking into account the evaporative flux of droplets on the product surface.The two-phase flow model was used to analyse the performance of the mist cooling process in terms of surface temperature decrease and the homogeneity of droplet deposition on the product surface of the RDC as a function of inlet droplet injection configurations.     

影响柴油机喷雾数值模拟精度的若干因素分析

为探明影响柴油机喷雾数值模拟精度的若干因素，采用通用商业软件FLUENT对柴油机喷雾特性进行了CFD模拟计算，分别研究了网格尺寸、喷雾粒子数和最大时间步长对油束几何形状及油束贯穿距的影响．结果表明，网格划分的精度和喷雾粒子数量的多少对计算结果的正确性和油束的几何形状有直接的影响，网格尺寸过大或喷雾粒子数过少则喷雾几何形状失真．最大时间步长对数值模拟的精度在一定的范围内影响是比较小的．     

Variable-fidelity optimization: Efficiency and robustness

This paper deals with variable-fidelity optimization, a technique in which the advantages of high- and low-fidelity models are used in an optimization process. The high-fidelity model provides solution accuracy while the low-fidelity model reduces the computational cost. An outline of the theory of the Approximation Management Framework (AMF) proposed by Alexandrov (1996) and Lewis (1996) is given. The AMF algorithm provides the mathematical robustness required for variable-fidelity optimization. This paper introduces a subproblem formulation adapted to a modular implementation of the AMF. Also, we propose two types of second-order corrections (additive and multiplicative) which serve to build the approximation of the high-fidelity model based on the low-fidelity one. Results for a transonic airfoil shape optimization problem are presented. Application of a variable-fidelity algorithm leads to a threefold savings in high-fidelity solver calls, compared to a direct optimization using the high-fidelity solver only. However, premature stops of the algorithm are observed in some cases. A study of the influence of the numerical noise of solvers on robustness deficiency is presented. The study shows that numerical noise artificially introduced into an analytical function causes premature stops of the AMF. Numerical noise observed with our CFD solvers is therefore strongly suspected to be the cause of the robustness problems encountered.     

Extending the functionality of the general‐purpose finite element package SEPRAN by automatic differentiation

From an abstract point of view, a numerical simulation implements a mathematical function that produces some output from some given input. Derivatives (or sensitivities) of the function's output with respect to its input can be obtained—free from truncation error—by using a technique called automatic differentiation. Given a computer code in a high‐level programming language like Fortran, C, or C++, automatic differentiation generates another code capable of computing not only the original function but also its derivatives. Thus, the application of automatic differentiation significantly extends the functionality of a simulation package. For instance, automatic differentiation enables, in a completely mechanical fashion, the usage of derivative‐based optimization algorithms where the evaluation of the objective function comprises some given large‐scale engineering simulation. In this paper, the automatic differentiation tool ADIFOR is used to transform the general‐purpose finite element package SEPRAN. In doing so, we automatically transform the given 400000 lines of Fortran 77 into a new program consisting of 600000 lines of Fortran 77. We compare our approach with a traditional approach based on numerical differentiation and quantify its advantages in terms of accuracy and computational efficiency for a standard fluid flow problem. Copyright © 2003 John Wiley & Sons, Ltd.     

Robust topology optimization under multiple independent uncertainties of loading positions

The topology optimization problem of a continuum structure is further investigated under the independent position uncertainties of multiple external loads, which are now described with an interval vector of uncertain-but-bounded variables. In this study, the structural compliance is formulated with the quadratic Taylor series expansion of multiple loading positions. As a result, the objective gradient information to the topological variables can be evaluated efficiently upon an explicit quadratic expression as the loads deviate from their ideal application points. Based on the minimum (largest absolute) value of design sensitivities, which corresponds to the most sensitive compliance to the load position variations, a two-level optimization algorithm within the non-probabilistic approach is developed upon a gradient-based optimization method. The proposed framework is then performed to achieve the robust optimal configurations of four benchmark examples, and the final designs are compared comprehensively with the traditional topology optimizations under the loading point fixation. It will be observed that the present methodology can provide a remarkably different structural layout with the auxiliary components in the design domain to counteract the load position uncertainties. The numerical results also show that the present robust topology optimization can effectively prevent the structural performance from a noticeable deterioration than the deterministic optimization in the presence of load position disturbances.     

Conference diary

We present a method that has been developed for the construction of grids suitable for a large class of Computational Fluid Dynamics (CFD) solvers. Three independent steps are considered: a multidomain generation, an optimization and an adaptation. The first step handles the complexity of the three-dimensional domain to be meshed and is able to perform an algebraic construction of the grid points within a multidomain topology; any decomposition can be considered and analysed by the algorithm. The second step is able to optimize a mesh with respect to a quality measure defined in terms of cell deformation; a conjugate gradient algorithm drives the nodes up to an equilibrium position that realizes the minimum of a mesh energy quantity. The final step handles the physics of the problem and moves the nodes in order to refine the mesh where anything of interest takes place, while preserving its good metric quality. The three steps have been implemented independently and successfully, as shown by the examples presented.     

Robust topology optimization under load position uncertainty

The topology optimization problem of a continuum structure on the compliance minimization objective is investigated under consideration of the external load uncertainty in its application position with a nonprobabilistic approach. The load position is defined as the uncertain-but-bounded parameter and is represented by an interval variable with a nominal application point. The structural compliance due to the load position deviation is formulated with the quadratic Taylor series expansion. As a result, the objective gradient information to the topological variables can be evaluated efficiently in a quadratic expression. Based on the maximum design sensitivity value, which corresponds to the most sensitive compliance to the uncertain loading position, a single-level optimization approach is suggested by using a popular gradient-based optimality criteria method. The proposed optimization scheme is performed to gain the robust topology optimizations of three benchmark examples, and the final configuration designs are compared comprehensively with the conventional topology optimizations under the loading point fixation. It can be observed that the present method can provide remarkably different material layouts with auxiliary components to accommodate the load position disturbances. The numerical results of the representative examples also show that the structural performances of the robust topology optimizations appear less sensitive to the load position perturbations than the traditional designs.     

On solving three-dimensional open-dimension rectangular packing problems

In this article, a recently proposed three-dimensional open-dimension rectangular packing problem is considered, in which the objective is to find a minimal volume rectangular container that packs a set of rectangular boxes. The literature has tackled small-sized instances of this problem by means of optimization solvers, position-free mixed-integer programming (MIP) formulations and piecewise linearization approaches. In this study, the problem is alternatively addressed by means of grid-based position MIP formulations, whereas still considering optimization solvers and the same piecewise linearization techniques. A comparison of the computational performance of both models is then presented, when tested with benchmark problem instances and with new instances, and it is shown that the grid-based position MIP formulation can be competitive, depending on the characteristics of the instances. The grid-based position MIP formulation is also embedded with real-world practical constraints, such as cargo stability, and results are additionally presented.     

Multi-disciplinary design optimization of a combustor

A technique for design optimization of a combustor is presented. This technique entails the use of computational fluid dynamics (CFD) and mathematical optimization to minimize the combustor exit temperature profile. The empirical and semi-empirical correlations commonly used for optimizing combustor exit temperature profile do not guarantee optimum. As an experimental approach is time consuming and costly, use is made of numerical techniques. However, using CFD without mathematical optimization on a trial and error basis does not guarantee optimal solutions. A better approach, which is often viewed as too expensive, is a combination of the two approaches, thus incorporating the influence of the variables automatically. In this study the combustor exit temperature profile is optimized. The optimum (uniform) combustor exit temperature profile mainly depends on the geometric parameters. Combustor parameters have been used as optimization variables. The combustor investigated is an experimental liquid-fuelled atmospheric combustor with a turbulent diffusion flame. The CFD simulations use the Fluent code with a standard k–? model. The optimization is carried out using the Dynamic-Q algorithm, which is specifically designed to handle constrained problems where the objective and constraint functions are expensive to evaluate. The optimization leads to a more uniform combustor exit temperature profile compared with the original.     

Trajectory optimization for unmanned aerial vehicle formation reconfiguration

The results of trajectory optimization to reconfigure unmanned aerial vehicle (UAV) formation in the event of a critical failure are presented. The formation reconfiguration process includes two distinct manoeuvres: an escape manoeuvre for a malfunctioning UAV and a replacement movement for an alternative UAV related to its position. This article deals with both manoeuvres but focuses more on the replacement movement. The trajectory optimization problem of the escape manoeuvre is formulated as a minimum-time problem to reduce the possibility of collisions resulting from a failure, whereas the problem of the replacement movement is formulated as a final-time fixed minimum-fuel problem to secure the durability of the group of UAVs. These problems are solved by means of sequential quadratic programming. To evaluate the performance of the optimization results, fuel consumption for the replacement movement is considered and optimization of a three-phase reference trajectory is performed. The results show that the trajectory optimization reduces the fuel consumption and saves time.     

Reconstruction method with data from a multiple-site continuous-wave source for three-dimensional optical tomography

A method is presented for reconstruction of the optical absorption coefficient from transmission near-infrared data with a cw source. As it is distinct from other available schemes such as optimization or Newton's iterative method, this method resolves the inverse problem by solving a boundary value problem for a Volterra-type integral-differential equation. It is demonstrated in numerical studies that this technique has a better than average stability with respect to the discrepancy between the initial guess and the actual unknown absorption coefficient. The method is particularly useful for reconstruction from a large data set obtained from a CCD camera. Several numerical reconstruction examples are presented.     

Robin‐Neumann transmission conditions for fluid‐structure coupling: Embedded boundary implementation and parameter analysis

Partitioned procedures are appealing for solving complex fluid‐structure interaction (FSI) problems, as they allow existing computational fluid dynamics (CFD) and computational structural dynamics algorithms and solvers to be combined and reused. However, for problems involving incompressible flow and strong added‐mass effect (eg, heavy fluid and slender structure), partitioned procedures suffer from numerical instability, which typically requires additional subiterations between the fluid and structural solvers, hence significantly increasing the computational cost. This paper investigates the use of Robin‐Neumann transmission conditions to mitigate the above instability issue. Firstly, an embedded Robin boundary method is presented in the context of projection‐based incompressible CFD and finite element–based computational structural dynamics. The method utilizes operator splitting and a modified ghost fluid method to enforce the Robin transmission condition on fluid‐structure interfaces embedded in structured non–body‐conforming CFD grids. The method is demonstrated and verified using the Turek and Hron benchmark problem, which involves a slender beam undergoing large transient deformation in an unsteady vortex‐dominated channel flow. Secondly, this paper investigates the effect of the combination parameter in the Robin transmission condition, ie, α_f, on numerical stability and solution accuracy. This paper presents a numerical study using the Turek and Hron benchmark problem and an analytical study using a simplified FSI model featuring an Euler‐Bernoulli beam interacting with a two‐dimensional incompressible inviscid flow. Both studies reveal a trade‐off between stability and accuracy: smaller values of α_f tend to improve numerical stability, yet deteriorate the accuracy of the partitioned solution. Using the simplified FSI model, the critical value of α_f that optimizes this trade‐off is derived and discussed.     

Droplet size spectra and water-vapor concentration of laboratory water clouds: inversion of Fourier transform infrared (500-5000 cm(-1)) optical-depth measurement

Infrared extinction optical depth (500-5000 cm(-1)) has been measured with a Fourier transform infrared spectrometer for clouds produced with an ultrasonic nebulizer. Direct measurement of the cloud droplet size spectra agree with size spectra retrieved from inversion of the extinction measurements. Both indicate that the range of droplet sizes is 1-14 mum. The retrieval was accomplished with an iterative algorithm that simultaneously obtains water-vapor concentration. The basis set of droplet extinction functions are computed once by using numerical integration of the Lorenz-Mie theory over narrow size bins, and a measured water-vapor extinction curve was used. Extinction and size spectra are measured and computed for both steady-state and dissipating clouds. It is demonstrated that anomalous diffraction theory produces relatively poor droplet size and synthetic extinction spectra and that extinction measurements are helpful in assessing the validity of various theories. Calculations of cloud liquid-water content from retrieved size distributions agree with a parameterization based on optical-depth measurements at a wave number of 906 cm(-1) for clouds that satisfy the size spectral range assumptions of the parameterization. Significance of droplet and vapor contribution to the total optical depth is used to evaluate the reliability of spectral inversions.     

Optimal Design of Trusses Under a Nonconvex Global Buckling Constraint

We propose a novel formulation of a truss design problem involving a constraint on the global stability of the structure due to the linear buckling phenomenon. The optimization problem is modelled as a nonconvex semidefinite programming problem. We propose two techniques for the numerical solution of the problem and apply them to a series of numerical examples.     

CFD-aided population balance modeling of a spray drying process

Due to the widespread application of spray dryers, the model-based optimization and control of the process are of great interest. Therefore, a reduced order model based on a population balance approach for the spray drying process is developed to accurately capture the shrinkage and drying mechanisms. The population balances describe the two-dimensional distribution of the moisture content and the granule size. The model is validated by experiments in a pilot scale spray dryer. Information from CFD simulations and previous single droplet experiments are used to determine suitable model parameters. The results show a good agreement of the model with experimental findings and promote the suitability of the population balance approach. Furthermore, a novel method of extracting information on the trajectories from detailed CFD simulations and inserting them into the reduced order model is presented. This increases the accuracy of the model without changing the computational complexity.     

Optimization-based method for structural damage localization and quantification by means of static displacements computed by flexibility matrix

This article presents an effective method for structural damage identification. The damage diagnosis problem is introduced as an optimization problem which is based on computing static displacements by the flexibility matrix. By utilizing this matrix, the complexity of the static displacement measurements in real cases can be overcome. The optimization problem is solved by a fast evolutionary optimization strategy, named the cuckoo optimization algorithm. The performance of the presented method was demonstrated by studying the benchmark problem provided by the IASC-ASCE Task Group on Structural Health Monitoring, and a numerical example of a frame. Moreover, the robustness of the presented approach was investigated in the presence of some prevalent modelling errors, and also when noisy and incomplete modal data are available. Finally, the efficiency of the proposed method was verified by an experimental study of a five-storey shear building structure. All the obtained results show the good performance of the presented method.     

Droplet velocity and thermal state from hot gas atomization of steel melt: Impact on the quality of the spray-formed tubular deposit

The velocity and thermal behavior (temperature, enthalpy, solid fraction) of atomized droplets in a metal spray play the most important role in the spray forming process. These properties mainly determine the materials yield and the final product quality (e.g., porosity, microstructure) of the as-sprayed materials. Changing the gas temperature in the atomization process directly influences these droplet properties in the spray. To understand the droplet behavior in the spray at various atomization gas temperatures (i.e., room temperature RT 293 K, 573 K, 873 K), numerical simulations using computational fluid dynamics (CFD) techniques have been performed and validated by experiments. A series of atomization runs (powder production and spray-forming with AISI 52100 steel) has been conducted at different atomization gas temperatures and pressures with a close-coupled atomizer (CCA). The in-situ temperature detection of the deposit surface (pyrometer) and in the substrate (thermocouples) has been performed to observe the effect of particle properties on the deposit. The result shows that hot gas atomization provides smaller droplets with faster velocity in the spray, affecting the droplet impact and deformation time in the deposition zone. A higher solid fraction of the smaller droplets by hot gas atomization also reduces the deposit surface temperature. Increasing the substrate diameter further decreases the deposit surface temperature without compromising the deposit quality (i.e., porosity) and also refines the grain size. Pre-heating of the substrate up to 573 K results in lower porosity in the vicinity of the substrate.