Sequential Quadratic Programming (SQP) for optimal control in direct numerical simulation of turbulent flow

This paper discusses a kind of optimization problem with linear complementarity constraints, and presents a sequential quadratic programming (SQP) algorithm for solving a stationary point of the problem. The algorithm is a modification of the SQP algorithm proposed by Fukushima et al. [Computational Optimization and Applications, 10 (1998), 5-34], and is based on a reformulation of complementarity condition as a system of linear equations. At each iteration, one quadratic programming and one system of equations needs to be solved, and a curve search is used to yield the step size. Under some appropriate assumptions, including the lower-level strict complementarity, but without the upper-level strict complementarity for the inequality constraints, the algorithm is proved to possess strong convergence and superlinear convergence. Some preliminary numerical results are reported.

Multidisciplinary design optimization (MDO) was performed on a helicopter rotor blade. The blade was modeled as a rigid flapping blade for dynamics; Blade Element Theory (BET) was the analysis approach to model the aerodynamic loading, and a simple linearly elastic hollowed rectangular section was the main structural component. MATLAB was used to solve the flapping differential equations and its Sequential Quadratic Programming (SQP) and Genetic Algorithm (GA) were used for the optimization. A Particle Swarm Optimization (PSO) routine was also tested. The optimization process consisted of three cases. The first case was a simple cantilever beam under centrifugal and an assumed bending loads. The optimization was performed using the SQP, GA, and PSO algorithms. The SQP resulted in the superior design with 75.45 compared to the GA's 87.1 and the PSO's 79.2, but a local minimum was present. The second case was an expansion of the first case by turning it into multidisciplinary problem. Aerodynamics was included in the design variables and objective function. Only the SQP algorithm was used and there was a reduction in hub vertical shear by 33.6%. The blade mass increased by 36.84%. The last case was an improvement to the second by creating a multiobjective problem by including the hub radial shear and the results were improved significantly by reducing the hub vertical shear by 34.06% and radial shear by 17.87% with a reduction of blade mass by 23.86%.

Flow around a wall-mounted cube is an example of a turbulent flow around a three-dimensional bluff body attached to a surface. The main experimentally observed feature of this type of flow is the appearance of complex vortical structures, e.g. a horseshoe vortex originating in front of the body and enveloping it. The current paper is a follow-up to Yakhot, Liu & Nikitin (2006) in which we presented results of direct numerical simulation (DNS) of turbulent flow around a cube. Here, it is shown that unsteadiness of the considered flow is caused by inviscid–viscous interaction between the horseshoe vortex and the narrow band of positive vorticity attached to the surface in front of the cube. Details of the spatio-temporal evolution of large-scale vortical structures, including samples of long-term visualization and turbulence statistics, are presented. For the normal-to-the-wall velocity, in the vicinity of the cube's front face, the results reveal an anomalous probability distribution, namely, a bimodal distribution and one with high kurtosis.

Performance analysis of support vector machine, Gaussian Process Regression, sequential quadratic programming algorithms in modeling hydrogen-rich syngas production from catalyzed co-gasification of biomass wastes from oil palm

High-order gas-kinetic scheme with parallel computation for direct numerical simulation of turbulent flows

Turbulent flows are characterised by a continuum of length and time scales, a feature that introduces some unique problems in relation to the analysis and control of errors in numerical simulations of turbulent flows. In direct numerical simulation (DNS) one attempts to fully resolve the flow field. The primary sources of error in DNS are the aliasing error, which arises due to the evaluation of the nonlinear term on a discrete grid in physical space, and, the truncation error, due to the discretization of the derivative operator. In addition there are the time-stepping errors on account of the temporal discretization. In Large Eddy Simulation (LES) only the large scale flow is computed whereas the collective effect of the small scales are modeled. In that case, in addition to the above three types of errors, there are commutation errors arising out of the averaging process used to derive the LES equations and sub-grid modeling errors that arise because in the absence of a systematic method, the subgrid stress is evaluated using an ad hoc closure model. Methods for analyzing and quantifying these errors in turbulence simulations are discussed. In some instances the analysis points to suitable methods of error control.KeywordsTurbulence, LESDNS, aliasing errortruncation errorsub-grid modeling

Comparison of SQP and AL algorithms for deterministic constrained production optimization of hydrocarbon reservoirs

When applying the sequential quadratic programming (SQP) algorithm to topology optimization, using the quasi-Newton methods or calculating the Hessian matrix directly will result in a considerable amount of calculation, making it computationally infeasible when the number of optimization variables is large. To solve the above problems, this paper creatively proposes a method for calculating the approximate Hessian matrix for structural topology optimization with minimum compliance problems. Then, the second-order Taylor expansion transforms the original problem into a series of separable and easy-to-solve convex quadratic programming (QP) subproblems. Finally, the quadratic programming optimality criteria (QPOC) method and the QP solver of MATLAB are used to solve the subproblems. Compared with other sequential quadratic programming methods, the advantage of the proposed method is that the Hessian matrix is diagonally positive definite and its calculation is simple. Numerical experiments on an MBB beam and cantilever beam verify the feasibility and efficiency of the proposed method.

Optimal Design of Heat Exchanger Networks by Using SQP Algorithm Based on GPU Acceleration

Recently, with the wide adoption of electric vehicles, transportation network has shown different characteristics and been further developed. In this paper, we present a new time-flow impedance function, which may be more realistic than the existing time-flow impedance functions. Based on this new impedance function, we present an optimization model for a mixed-mode traffic network in which battery electric vehicles (BEVs) and gasoline vehicles (GVs) are chosen. We suggest two approaches to handle the model: One is to use the interior point (IP) algorithm and the other is to employ the sequential quadratic programming (SQP) algorithm. Three numerical examples are presented to illustrate the efficiency of these approaches. In particular, our numerical results show that more travelers prefer to choosing BEVs when the distance limit of BEVs is long enough and the unit operating cost of GVs is higher than that of BEVs, and the SQP algorithm is faster than the IP algorithm.

A direct numerical simulation of turbulent channel flow over a compliant surface has been performed to evaluate the friction drag reduction effect. The compliant surface is modelled in a mass, damper and spring system. The material properties are determined so that the wall velocity is in phase with the wall pressure. A slight drag reduction is observed, together with a weak wall displacement of the compliant surface. However, a large-scale pressure field becomes dominant. The typical shape of displacement of the compliant surface is a wave, which is almost longitudinal in the stream-wise direction. This article was chosen from selected Proceedings of the Second International Symposium on Turbulence and Shear Flow Phenomena (KTH-Stockholm, 27-29 June 2001) ed E Lindborg, A Johansson, J Eaton, J Humphrey, N Kasagi, M Leschziner and M Sommerfeld.

For current sequential quadratic programming (SQP) type algorithms, there exist two problems: (i) in order to obtain a search direction, one must solve one or more quadratic programming subproblems per iteration, and the computation amount of this algorithm is very large. So they are not suitable for the large-scale problems; (ii) the SQP algorithms require that the related quadratic programming subproblems be solvable per iteration, but it is difficult to be satisfied. By using e-active set procedure with a special penalty function as the merit function, a new algorithm of sequential systems of linear equations for general nonlinear optimization problems with arbitrary initial point is presented. This new algorithm only needs to solve three systems of linear equations having the same coefficient matrix per iteration, and has global convergence and local superlinear convergence. To some extent, the new algorithm can overcome the shortcomings of the SQP algorithms mentioned above.

Typical engineering rough surfaces show only limited resemblance to the artificially constructed rough surfaces that have been the basis of most previous fundamental research on turbulent flow over rough walls. In this article flow past an irregular rough surface is investigated, based on a scan of a rough graphite surface that serves as a typical example for an irregular rough surface found in engineering applications. The scanned map of surface height versus lateral coordinates is filtered in Fourier space to remove features on very small scales and to create a smoothly varying periodic representation of the surface. The surface is used as a no-slip boundary in direct numerical simulations of turbulent channel flow. For the resolution of the irregular boundary an iterative embedded boundary method is employed. The effects of the surface filtering on the turbulent flow are investigated by studying a series of surfaces with decreasing level of filtering. Mean flow, Reynolds stress and dispersive stress profiles show good agreement once a sufficiently large number of Fourier modes are retained. However, significant differences are observed if only the largest surface features are resolved. Strongly filtered surfaces give rise to a higher mean-flow velocity and to a higher variation of the streamwise velocity in the roughness layer compared with weakly filtered surfaces. In contrast, for the weakly filtered surfaces the mean flow is reversed over most of the lower part of the roughness sublayer and higher levels of dispersive shear stress are found.

Direct numerical simulations of turbulent flow in a driven cavity

Two new methods for the efficient parallel computation of the unsteady incompressible Navier-Stokes equations are presented. Such efficient methods are desired for large scale parallel computations of unsteady turbulent flows such as Direct Numerical Simulations (DNS). The performance of the new methods has a distinct advantage over the artificial compressibility method, in that the methods exhibit robust convergence for a variety of flow problems without extensive need for tuning computational parameters. These methods and others have been implemented in a computer program designed for massively parallel computer architectures, written by the author and used to obtain all results in this work. A DNS of a film-cooling jet is performed in order to evaluate the accuracy of the modeled expressions in the k-e turbulence model. Using the results of the DNS, the terms in the exact and modeled k-e equations are computed. These terms are examined to see where the models fail for these flows. DNS budgets for k and dissipation in a film cooling jet flow are presented to provide turbulence modelers with information as to where the models used to replace the exact k-e equations need improvement for this particular type of flow. A DNS of a pulsed jet is performed to analyze the effect of external pulsing on the flow structures and the resulting mixing of the jet with the crossflow. As the problem is inherently unsteady, the key to the successful prediction of such flows is the ability to resolve the dynamics of all important flow structures resulting from the interaction of the unsteady pulsed jet with the crossflow. In the present work massless particles are released into the flow at various locations. These particles are colored by their seed locations and residence time, greatly aiding the understanding of the dynamics of the flow. A new origin for the formation of the wake vortices has been discovered for both pulsed and unpulsed jets. Pulsing is shown to drastically change the jet spreading and penetration and to increase the mixing of the jet with the crossflow. A significant asymmetry affecting primarily the wake vortices has been found for certain cases.