Kenneth C. Hall

Bio: Kenneth C. Hall is an academic researcher from Duke University. The author has contributed to research in topics: Aerodynamics & Airfoil. The author has an hindex of 44, co-authored 160 publications receiving 6500 citations. Previous affiliations of Kenneth C. Hall include Massachusetts Institute of Technology & Mississippi State University.

Computation of Unsteady Nonlinear Flows in Cascades Using a Harmonic Balance Technique

Abstract: A harmonic balance technique for modeling unsteady nonlinear e ows in turbomachinery is presented. The analysis exploits the fact that many unsteady e ows of interest in turbomachinery are periodic in time. Thus, the unsteady e ow conservation variables may be represented by a Fourier series in time with spatially varying coefe cients. This assumption leads to a harmonic balance form of the Euler or Navier ‐Stokes equations, which, in turn, can be solved efe ciently as a steady problem using conventional computational e uid dynamic (CFD) methods, including pseudotime time marching with local time stepping and multigrid acceleration. Thus, the method is computationally efe cient, at least one to two orders of magnitude faster than conventional nonlinear time-domain CFD simulations. Computational results for unsteady, transonic, viscous e ow in the front stage rotor of a high-pressure compressor demonstrate that even strongly nonlinear e ows can be modeled to engineering accuracy with a small number of terms retained in the Fourier series representation of the e ow. Furthermore, in some cases, e uid nonlinearities are found to be important for surprisingly small blade vibrations.

Modeling of Fluid-Structure Interaction

Abstract: ▪ Abstract The interaction of a flexible structure with a flowing fluid in which it is submersed or by which it is surrounded gives rise to a rich variety of physical phenomena with applications in many fields of engineering, for example, the stability and response of aircraft wings, the flow of blood through arteries, the response of bridges and tall buildings to winds, the vibration of turbine and compressor blades, and the oscillation of heat exchangers. To understand these phenomena we need to model both the structure and the fluid. However, in keeping with the overall theme of this volume, the emphasis here is on the fluid models. Also, the applications are largely drawn from aerospace engineering although the methods and fundamental physical phenomena have much wider applications. In the present article, we emphasize recent developments and future challenges. To provide a context for these, the article begins with a description of the various physical models for a fluid undergoing time-dependent mot...

Proper Orthogonal Decomposition Technique for Transonic Unsteady Aerodynamic Flows

Abstract: A new method for constructing reduced-order models (ROM) of unsteady small-disturbance e ows is presented. The reduced-order models are constructed using basis vectors determined from the proper orthogonal decomposition (POD) of an ensemble of small-disturbance frequency-domain solutions. Each of the individual frequencydomain solutions is computed using an efe cient time-linearized e ow solver. We show that reduced-order models can be constructed using just a handful of POD basis vectors, producing low-order but highly accurate models of the unsteady e ow over a wide range of frequencies. We apply the POD/ROM technique to compute the unsteady aerodynamic and aeroelastic behavior of an isolated transonic airfoil and to a two-dimensional cascade of airfoils.

Nonlinear Inviscid Aerodynamic Effects on Transonic Divergence, Flutter, and Limit-Cycle Oscillations

Abstract: By the use of a state-of-the-art computational e uid dynamic (CFD) method to model nonlinear steady and unsteady transonice owsin conjunction with a linearstructural model,an investigationismadeinto how nonlinear aerodynamics can effect the divergence, e utter, and limit-cycle oscillation (LCO) characteristics of a transonic airfoil cone guration. A single-degree-of-freedom (DOF) model is studied for divergence, and one- and two-DOF models are studied for e utter and LCO. A harmonicbalancemethod in conjunction with the CFD solver is used to determine the aerodynamics for e nite amplitude unsteady excitations of a prescribed frequency. A procedure for determining the LCO solution is also presented. For the cone guration investigated, nonlinear aerodynamic effects are found to produce a favorable transonic divergence trend and unstable and stable LCO solutions, respectively, for the one- and two-DOF e utter models. Nomenclature a = nondimensional location of airfoil elastic axis, e=b b, c = semichord and chord, respectively cl, cm = coefe cients of lift and moment about elastic axis, respectively e = location of airfoil elastic axis, measured positive aft of airfoil midchord h, ® = airfoil plunge and pitch degrees of freedom I® = second moment of inertia of airfoil about elastic axis

Calculation of unsteady flows in turbomachinery using the linearized Euler equations

Abstract: A method for calculating unsteady flows in cascades is presented. The model, which is based on the linearized unsteady Euler equations, accounts for blade loading shock motion, wake motion, and blade geometry. The mean flow through the cascade is determined by solving the full nonlinear Euler equations. Assuming the unsteadiness in the flow is small, then the Euler equations are linearized about the mean flow to obtain a set of linear variable coefficient equations which describe the small amplitude, harmonic motion of the flow. These equations are discretized on a computational grid via a finite volume operator and solved directly subject to an appropriate set of linearized boundary conditions. The steady flow, which is calculated prior to the unsteady flow, is found via a Newton iteration procedure. An important feature of the analysis is the use of shock fitting to model steady and unsteady shocks. Use of the Euler equations with the unsteady Rankine-Hugoniot shock jump conditions correctly models the generation of steady and unsteady entropy and vorticity at shocks. In particular, the low frequency shock displacement is correctly predicted. Results of this method are presented for a variety of test cases. Predicted unsteady transonic flows in channels are compared to full nonlinear Euler solutions obtained using time-accurate, time-marching methods. The agreement between the two methods is excellent for small to moderate levels of flow unsteadiness. The method is also used to predict unsteady flows in cascades due to blade motion (flutter problem) and incoming disturbances (gust response problem).

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

Abstract: Numerical simulation of large-scale dynamical systems plays a fundamental role in studying a wide range of complex physical phenomena; however, the inherent large-scale nature of the models often leads to unmanageable demands on computational resources. Model reduction aims to reduce this computational burden by generating reduced models that are faster and cheaper to simulate, yet accurately represent the original large-scale system behavior. Model reduction of linear, nonparametric dynamical systems has reached a considerable level of maturity, as reflected by several survey papers and books. However, parametric model reduction has emerged only more recently as an important and vibrant research area, with several recent advances making a survey paper timely. Thus, this paper aims to provide a resource that draws together recent contributions in different communities to survey the state of the art in parametric model reduction methods. Parametric model reduction targets the broad class of problems for wh...

Balanced Model Reduction via the Proper Orthogonal Decomposition

Abstract: A new method for performing a balanced reduction of a high-order linear system is presented. The technique combines the proper orthogonal decomposition and concepts from balanced realization theory. The method of snapshotsisused to obtainlow-rank,reduced-rangeapproximationsto thesystemcontrollability and observability grammiansineitherthetimeorfrequencydomain.Theapproximationsarethenusedtoobtainabalancedreducedorder model. The method is particularly effective when a small number of outputs is of interest. It is demonstrated for a linearized high-order system that models unsteady motion of a two-dimensional airfoil. Computation of the exact grammians would be impractical for such a large system. For this problem, very accurate reducedorder models are obtained that capture the required dynamics with just three states. The new models exhibit far superiorperformancethanthosederived using a conventionalproperorthogonal decomposition. Although further development is necessary, the concept also extends to nonlinear systems.

The Method of Proper Orthogonal Decomposition for Dynamical Characterization and Order Reduction of Mechanical Systems: An Overview

Abstract: Modal analysis is used extensively for understanding the dynamic behavior of structures. However, a major concern for structural dynamicists is that its validity is limited to linear structures. New developments have been proposed in order to examine nonlinear systems, among which the theory based on nonlinear normal modes is indubitably the most appealing. In this paper, a different approach is adopted, and proper orthogonal decomposition is considered. The modes extracted from the decomposition may serve two purposes, namely order reduction by projecting high-dimensional data into a lower-dimensional space and feature extraction by revealing relevant but unexpected structure hidden in the data. The utility of the method for dynamic characterization and order reduction of linear and nonlinear mechanical systems is demonstrated in this study.

Nonreflecting boundary conditions for Euler equation calculations

Abstract: We present a unified theory for the construction of steady-state and unsteady nonreflecting boundary conditions for the Euler equations. These allow calculatios to be performed on truncated domains without the generation of spurious nonphysical reflections at the far-field boundaries.

Automatic differentiation in machine learning: a survey

Abstract: Derivatives, mostly in the form of gradients and Hessians, are ubiquitous in machine learning. Automatic differentiation (AD), also called algorithmic differentiation or simply "auto-diff", is a family of techniques similar to but more general than backpropagation for efficiently and accurately evaluating derivatives of numeric functions expressed as computer programs. AD is a small but established field with applications in areas including computational uid dynamics, atmospheric sciences, and engineering design optimization. Until very recently, the fields of machine learning and AD have largely been unaware of each other and, in some cases, have independently discovered each other's results. Despite its relevance, general-purpose AD has been missing from the machine learning toolbox, a situation slowly changing with its ongoing adoption under the names "dynamic computational graphs" and "differentiable programming". We survey the intersection of AD and machine learning, cover applications where AD has direct relevance, and address the main implementation techniques. By precisely defining the main differentiation techniques and their interrelationships, we aim to bring clarity to the usage of the terms "autodiff", "automatic differentiation", and "symbolic differentiation" as these are encountered more and more in machine learning settings.