Surrogate-based Analysis and Optimization

A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities

This paper addresses the solution of bound-constrained optimization problems using algorithms that require only the availability of objective function values but no derivative information. We refer to these algorithms as derivative-free algorithms. Fueled by a growing number of applications in science and engineering, the development of derivative-free optimization algorithms has long been studied, and it has found renewed interest in recent time. Along with many derivative-free algorithms, many software implementations have also appeared. The paper presents a review of derivative-free algorithms, followed by a systematic comparison of 22 related implementations using a test set of 502 problems. The test bed includes convex and nonconvex problems, smooth as well as nonsmooth problems. The algorithms were tested under the same conditions and ranked under several criteria, including their ability to find near-global solutions for nonconvex problems, improve a given starting point, and refine a near-optimal solution. A total of 112,448 problem instances were solved. We find that the ability of all these solvers to obtain good solutions diminishes with increasing problem size. For the problems used in this study, TOMLAB/MULTIMIN, TOMLAB/GLCCLUSTER, MCS and TOMLAB/LGO are better, on average, than other derivative-free solvers in terms of solution quality within 2,500 function evaluations. These global solvers outperform local solvers even for convex problems. Finally, TOMLAB/OQNLP, NEWUOA, and TOMLAB/MULTIMIN show superior performance in terms of refining a near-optimal solution.

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Derivative-free optimization: a review of algorithms and comparison of software implementations

The numerical simulation of high Reynolds number flows is hampered by model accuracy if the Reynolds-averaged Navier–Stokes (RANS) equations are used, and by computational cost if direct or large-eddy simulations (LES) that resolve the near-wall layer are employed. The cost of a calculation scales like the Reynolds number to the power 3 for direct numerical simulations, or 2.4 for LES, making the resolution of the wall layer at high Reynolds number infeasible even with the most advanced computers. In LES, an attractive alternative to compute high-Re flows is the use of wall-layer models, in which only the outer layer is resolved, while the near-wall region is modeled. Three broad classes of approaches are presently used: bypassing this region altogether using wall functions, solving a separate set of equations in the near-wall region, weakly coupled to the outer flow, or simulating the near-wall region in a global, Reynolds-averaged, sense. These approaches are discussed and their ranges of applicability are highlighted. Various unresolved issues in wall-layer modeling are presented.

Wall-layer models for large-eddy simulations

A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries

A large-eddy simulation (LES) solver which combines an immersed-boundary technique with a curvilinear structured grid has been developed to study the temporal and spatial dynamics of a rotor tip-clearance flow, with the objective of determining the underlying mechanisms for low pressure fluctuations downstream of the rotor near the endwall. Salient feature of the numerical methodology, including the mesh topology, the treatment of numerical instability for non-dissipative schemes in a highly skewed mesh, and the parallelization of the code for shared memory platforms are discussed. Qualitative agreements have been observed between present LES and experimental measurements. The simulations indicate that the interaction between the moving endwall boundary layer and blade boundary layers and tip-leakage flow creates a highly complicated flow which is dominated by distinct vortical structures including the tip-leakage and tip-separation vortices. These vortical structures are found to convect downstream, expand in size and generate intense turbulent fluctuations in the endwall region.

Large-eddy simulation of a rotor tip-clearance flow

Roughness noise generation mechanisms are investigated using data from large-eddy simulations of turbulent boundary layers at Re� = 3065 over arrays of 10 × 4 roughness elements. Three types of roughness elements, including hemispheres, short cylinders and cuboids are considered, which share the same height of 0.124�, the same element-to-element spacing of 0.727� and the same flow blockage area. The streamwise dipole sound spectra share a common peak at fh/U∞ = 0.17. The surface pressure spectra in the roughness fetch are elevated over all frequencies and have smaller correlation length and time scales than those in the unperturbed smooth-wall boundary layer. The correlation coefficients and coherence between acoustic roughness dipoles and the pressure fluctuations on the rough wall are calculated. Analysis of the results confirms the importance of the impingement of upstream turbulence to dipole sound radiations, especially in the streamwise direction. For roughness shapes with sharp frontal edges, the edge-induced unsteady flow separations and vortex shedding also play important roles to sound generation. Large scale structures in the boundary layer have relatively low influence on roughness dipoles, except for the first rows of elements.

Statistical Analysis of Acoustic-Source Field in Rough-Wall Boundary Layers

The effect of acoustically non-compact step height on sound generation in a turbulent boundary layer is studied by computing sound with a boundary-element method and comparing its results with those obtained with a compact-step-height assumption. When the ratio of acoustic wavelength to the step height is large, good agreements between the two methods in predicted sound spectra and directivities are found, thus validating the previous compact Green’s function solutions. Discrepancies between the two results become significant with decreasing �/h. For mildly non-compact step heights, the sound directivity for forward steps exhibits asymmetry, with the upstream side maintaining an approximate dipole shape while the rest significantly distorted. Dips in sound spectra and multiple lobes in directivity are observed along with significantly enhanced sound power when �/h is sufficiently small, indicating that edge-scattering becomes the dominant source mechanism. These results indicate that the compact-step-height assumption is generally applicable for underwater applications, where small Mach numbers give large �/h for most frequencies of interest. For air vehicles with large Mach numbers, its applicability is much more limited.

Sound Generated by Boundary-Layer Flow over Small Steps: Effect of Step Noncompactness

Using large eddy simulation, Mach 0.4 flow over a hemisphere-on-cylinder turret is simulated to investigate the aero-optical effects caused by turbulent density fluctuations. The height of the cylinder is 0.375 times the hemisphere diameter and the Reynolds number based on the turret diameter and free stream velocity is 460,000. Comparisons are made between calculated OPDrms and previous experimental results, which shows reasonable agreement in trend and magnitude. Using Proper Orthogonal Decomposition (POD), the capability of the simulation to capture spatial structures present in optical wavefronts is also discussed. The POD modes found from the simulated data contain structures similar to those in the experimental data.

LES Analysis of Hemisphere-on-Cylinder Turret Aero-Optics

A large-mode-area (LMA) ytterbium-doped photonic crystal fiber (PCF) with core NA of 0.034 and core diameter of 50 μm was made by the stack-and-draw technique. The core is formed by Yb3+/Al3+/F−/P5+ co-doped silica glass containing 0.09 mol% Yb2O3 with an absorption coefficient at 976 nm up to 3.2 dB/m. The core glass with homogeneous distribution of Yb3+ ions and refractive index difference of 4 × 10−4 compared with pure silica was prepared by the sol-gel method and heat homogenization at 2000°C. Laser power amplification of this LMA PCF was studied using a seed source of 21 ps pulse duration and 48.7 MHz repetition rate at 1030 nm wavelength. With pump power of 520 W, a maximum 272 W (266 kW peak power) quasi-single-mode laser output with M2 of 2.2 was achieved in a 4.7 m fiber length bent at a diameter of 47 cm with slope efficiency of 52%, and no obvious mode instability, stimulated Raman scattering, or thermal damage on the end facet of the fiber were observed.

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Meng Wang

Papers

Large-eddy simulation of a rotor tip-clearance flow

Statistical Analysis of Acoustic-Source Field in Rough-Wall Boundary Layers

Sound Generated by Boundary-Layer Flow over Small Steps: Effect of Step Noncompactness

LES Analysis of Hemisphere-on-Cylinder Turret Aero-Optics

272 W quasi-single-mode picosecond pulse laser of ytterbium-doped large-mode-area photonic crystal fiber