Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session D31: Computational Fluid Dynamics: Sensitivity Analysis, Parameter Estimation, and OptimizationCFD

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Chair: Malgorzata Zimon, IBM Research UK Room: 108 
Sunday, November 19, 2017 2:15PM  2:28PM 
D31.00001: Adjoint Sensitivity Analysis for ScaleResolving Turbulent Flow Solvers Patrick Blonigan, Anirban Garai, Laslo Diosady, Scott Murman Adjointbased sensitivity analysis methods are powerful design tools for engineers who use computational fluid dynamics. In recent years, these engineers have started to use scaleresolving simulations like largeeddy simulations (LES) and direct numerical simulations (DNS), which resolve more scales in complex flows with unsteady separation and jets than the widelyused Reynoldsaveraged NavierStokes (RANS) methods. However, the conventional adjoint method computes large, unusable sensitivities for scaleresolving simulations, which unlike RANS simulations exhibit the chaotic dynamics inherent in turbulent flows. Sensitivity analysis based on leastsquares shadowing (LSS) avoids the issues encountered by conventional adjoint methods, but has a high computational cost even for relatively small simulations [1]. The following talk discusses a more computationally efficient formulation of LSS, ``nonintrusive'' LSS, and its application to turbulent flows simulated with a discontinuousGalkerin spectralelementmethod LES/DNS solver. Results are presented for the minimal flow unit, a turbulent channel flow with a limited streamwise and spanwise domain. \\ \noindent [1] Q. Wang, R. Hui, and P. Blonigan. Least squares shadowing sensitivity analysis of chaotic limit cycle oscillation [Preview Abstract] 
Sunday, November 19, 2017 2:28PM  2:41PM 
D31.00002: Least Squares Shadowing and Lyapunov Covariant Modes of a 3D cylinder flow at Reynolds number 525 Angxiu Ni, Qiqi Wang Many scientific and engineering applications concern how the statistics of chaotic and turbulent flows respond to perturbations in forcing, parameter, geometry, mesh, or boundary conditions. In these flows, a small perturbation in typically results in a large difference in the instantaneous flow field later on, computationally polluting the sensitivity of statistics. Nevertheless, such divergence can be avoided by simultaneously perturbing the initial condition. The Least Squares Shadowing algorithm finds a new flow field satisfying infinitesimally perturbed governing equation such that its difference to the old flow field remains small as time evolves. Such two flow fields are said to be shadowing each other. In this talk, for the flow past a 3D cylinder at Reynolds number 525, we analyze the shadowing directions computed by the Least Squares Shadowing algorithm. We also study byproduct of the algorithm, the Characteristic Lyapunov Modes, which are solutions to the linearized equation that grow or decay at different rates. By doing so, we will reveal the chaotic attractor associated with this flow field and predict how various statistics of the chaotic flow respond to infinitesimal parameter perturbations. [Preview Abstract] 
Sunday, November 19, 2017 2:41PM  2:54PM 
D31.00003: Parameter Estimation for a Pulsating Turbulent Buoyant Jet Using Approximate Bayesian Computation Jason Christopher, Nicholas Wimer, Caelan Lapointe, Torrey Hayden, Ian Grooms, Greg Rieker, Peter Hamlington Approximate Bayesian Computation (ABC) is a powerful tool that allows sparse experimental or other ``truth'' data to be used for the prediction of unknown parameters, such as flow properties and boundary conditions, in numerical simulations of realworld engineering systems. Here we introduce the ABC approach and then use ABC to predict unknown inflow conditions in simulations of a twodimensional (2D) turbulent, hightemperature buoyant jet. For this test case, truth data are obtained from a direct numerical simulation (DNS) with known boundary conditions and problem parameters, while the ABC procedure utilizes lower fidelity large eddy simulations. Using spatiallysparse statistics from the 2D buoyant jet DNS, we show that the ABC method provides accurate predictions of true jet inflow parameters. The success of the ABC approach in the present test suggests that ABC is a useful and versatile tool for predicting flow information, such as boundary conditions, that can be difficult to determine experimentally. [Preview Abstract] 
Sunday, November 19, 2017 2:54PM  3:07PM 
D31.00004: Parameter Optimization for Turbulent Reacting Flows Using Adjoints Caelan Lapointe, Peter E. Hamlington The formulation of a new adjoint solver for topology optimization of turbulent reacting flows is presented. This solver provides novel configurations (e.g., geometries and operating conditions) based on desired system outcomes (i.e., objective functions) for complex reacting flow problems of practical interest. For many such problems, it would be desirable to know optimal values of design parameters (e.g., physical dimensions, fueloxidizer ratios, and inflowoutflow conditions) prior to realworld manufacture and testing, which can be expensive, timeconsuming, and dangerous. However, computational optimization of these problems is made difficult by the complexity of most reacting flows, necessitating the use of gradientbased optimization techniques in order to explore a wide design space at manageable computational cost. The adjoint method is an attractive way to obtain the required gradients, because the cost of the method is determined by the dimension of the objective function rather than the size of the design space. Here, the formulation of a novel solver is outlined that enables gradientbased parameter optimization of turbulent reacting flows using the discrete adjoint method. Initial results and an outlook for future research directions are provided. [Preview Abstract] 
Sunday, November 19, 2017 3:07PM  3:20PM 
D31.00005: An adjointbased framework for maximizing mixing in binary fluids Maximilian Eggl, Peter Schmid Mixing in the inertial, but laminar parameter regime is a common application in a wide range of industries. Enhancing the efficiency of mixing processes thus has a fundamental effect on product quality, material homogeneity and, last but not least, production costs. In this project, we address mixing efficiency in the above mentioned regime (Reynolds number $Re=1000$, Peclet number $Pe=1000$) by developing and demonstrating an algorithm based on nonlinear adjoint looping that minimizes the variance of a passive scalar field which models our binary Newtonian fluids. The numerical method is based on the FLUSI code (Engels et al. 2016), a Fourier pseudospectral code, which we modified and augmented by scalar transport and adjoint equations. Mixing is accomplished by moving stirrers which are numerically modeled using a penalization approach. In our twodimensional simulations we consider rotating circular and elliptic stirrers and extract optimal mixing strategies from the iterative scheme. The case of optimizing shape and rotational speed of the stirrers will be demonstrated. [Preview Abstract] 
Sunday, November 19, 2017 3:20PM  3:33PM 
D31.00006: Using the Levelset Method to Generate Optimizable Geometries for Aerodynamic Applications Jack S. Rossetti, John F. Dannenhoffer III Within the last three decades, topology optimization has grown in popularity in both the structural and fluid dynamics fields. The method is a more general shape optimization, meaning, the final topology of the design does not need to be known beforehand. Currently, the applications of topology optimization in the fluid dynamics field is limited to low Reynolds number flows. At higher Reynolds numbers, inertial effects strongly influence the fluid flow, which makes maintaining smooth boundaries essential. No method exists that represents geometries used for topology optimization with adequately smooth boundaries. Herein, a levelset method for representing geometries using radial basis functions is presented. The levelset method was chosen because of its potential ability to produce smooth boundaries and its uniform parameterization of any shape, thus, no additional grids are required on the design during the optimization process. The levelset method is used to generate various geometries and the design sensitivities, with respect to radial basis function amplitude, will be calculated. Topology optimization will then be then applied to a circular levelset geometry in highspeed 2D crossflow to maximize the lifttodrag ratio and the optimization results will be presented. [Preview Abstract] 
Sunday, November 19, 2017 3:33PM  3:46PM 
D31.00007: Design optimization using adjoint of Longtime LES for the trailing edge of a transonic turbine vane Chaitanya Talnikar, Qiqi Wang Adjointbased design optimization methods have been applied to lowfidelity simulation methods like Reynolds Averaged NavierStokes (RANS) and are useful for designing fluid machinery components. But to reliably capture the complex flow phenomena involved in turbomachinery, high fidelity simulations like large eddy simulation (LES) are required. Unfortunately due to the chaotic dynamics of turbulence, the unsteady adjoint method for LES diverges and produces incorrect gradients. Using a viscosity stabilized unsteady adjoint method developed for LES, the gradient can be obtained with reasonable accuracy. In this paper, design of the trailing edge of a gas turbine inlet guide vane is performed with the objective to reduce stagnation pressure loss and heat transfer over the surface of the vane. Slight changes in the shape of trailing edge can significantly impact these quantities by altering the boundary layer development process and separation points. The trailing edge is parameterized using a linear combination of $5$ convex designs. Bayesian optimization is used as a global optimizer with the objective function evaluated from the LES and gradients obtained using the viscosity adjoint method. Results from the optimization, performed on the supercomputer Mira, are presented. [Preview Abstract] 
Sunday, November 19, 2017 3:46PM  3:59PM 
D31.00008: Drag Reduction of an Airfoil Using Deep Learning Chiyu Jiang, Anzhu Sun, Philip Marcus We reduced the drag of a 2D airfoil by starting with a NACA0012 airfoil and used deep learning methods. We created a database which consists of simulations of 2D external flow over randomly generated shapes. We then developed a machine learning framework for external flow field inference given input shapes. Past work which utilized machine learning in Computational Fluid Dynamics focused on estimations of specific flow parameters, but this work is novel in the inference of entire flow fields. We further showed that learned flow patterns are transferable to cases that share certain similarities. This study illustrates the prospects of deeper integration of databased modeling into current CFD simulation frameworks for faster flow inference and more accurate flow modeling. [Preview Abstract] 
Sunday, November 19, 2017 3:59PM  4:12PM 
D31.00009: Shape Design of Unsteady Forced Heatconvection Fields to Control Temperature Distribution History Eiji Katamine, Naoya Okada This paper presents a numerical solution to shape design of unsteady forced heatconvection fields to control temperature to a prescribed distribution. The square error integral between the actual temperature distributions and the prescribed temperature distributions on the prescribed subdomains during the specified period of time is used as the objective functional. Shape gradient of the shape design problem is derived theoretically using the Lagrange multiplier method, adjoint variable method, and the formulae of the material derivative. Reshaping is carried out by the traction method proposed as an approach to solving shape optimization problems. Numerical analyses program for the shape design is developed based on FreeFem++, and the validity of proposed method is confirmed by results of 2D numerical analyses. [Preview Abstract] 
Sunday, November 19, 2017 4:12PM  4:25PM 
D31.00010: Topology optimization of natural convection: Flow in a differentially heated cavity Clio Saglietti, Philipp Schlatter, Martin Berggren, Dan Henningson The goal of the present work is to develop methods for optimization of the design of natural convection cooled heat sinks, using resolved simulation of both fluid flow and heat transfer. We rely on mathematical programming techniques combined with direct numerical simulations in order to iteratively update the topology of a solid structure towards optimality, i.e. until the design yielding the best performance is found, while satisfying a specific set of constraints. The investigated test case is a twodimensional differentially heated cavity, in which the two vertical walls are held at different temperatures. The buoyancy force induces a swirling convective flow around a solid structure, whose topology is optimized to maximize the heat flux through the cavity. We rely on the spectralelement code Nek5000 to compute a highorder accurate solution of the natural convection flow arising from the conjugate heat transfer in the cavity. The laminar, steadystate solution of the problem is evaluated with a timemarching scheme that has an increased convergence rate; the actual iterative optimization is obtained using a steepestdecent algorithm, and the gradients are conveniently computed using the continuous adjoint equations for convective heat transfer. [Preview Abstract] 
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