Scholars@Duke
Jeffrey P. Thomas

Jeffrey P. Thomas

Assistant Research Professor in the Thomas Lord Department of Mechanical Engineering and Materials Science
Thomas Lord Department of Mechanical Engineering and Materials Science
jthomas@duke.edu
Box 90300, Durham, NC 27708-0300
237 Hudson Eng Ctr, Durham, NC

Scholarly Works - Journal articles

Nonintrusive Polynomial Chaos Approach for Nonlinear Aeroelastic Uncertainty Quantification

Journal article Journal of Aircraft · December 1, 2025 A point collocation nonintrusive polynomial chaos approach is presented for nonlinear aeroelastic uncertainty quantification analysis. A unique aspect of the approach is the use of a nonlinear frequency-domain harmonic balance aeroelastic solution methodol ... Full text Cite

Convolution/Volterra Reduced-Order Modeling for Nonlinear Aeroelastic Limit Cycle Oscillation Analysis and Control

Journal article AIAA Journal · December 1, 2022 A methodology for leveraging a combination of linear (through convolution integrals) and nonlinear (through Volterra series) reduced-order modeling (ROM) development was demonstrated on both a two-and three-degree-of-freedom (2-DOF and 3-DOF, respectively) ... Full text Cite

Discrete adjoint approach for nonlinear unsteady aeroelastic design optimization

Journal article AIAA Journal · January 1, 2019 Presented is a discrete adjoint approach for computing nonlinear unsteady aeroelastic geometric design sensitivities, which can subsequently be used for nonlinear unsteady aeroelastic geometric design optimization. The methodology is applicable to compress ... Full text Cite

Aeroelastic analysis of a wind turbine blade using the harmonic balance method

Journal article Wind Energy · April 1, 2018 An aeroelastic model for wind turbine blades derived from the unsteady Navier-Stokes equations and a mode shape–based structural dynamics model are presented. For turbulent flows, the system is closed with the Spalart-Allmaras turbulence model. The computa ... Cite

An aeroelastic model for vortex-induced vibrating cylinders subject to frequency lock-in

Journal article Journal of Fluids and Structures · February 1, 2016 This work presents a novel way to calculate the response amplitude of an elastically supported cylinder experiencing vortex-induced vibrations. The method couples a computational fluid dynamic (CFD) model of the shedding vortex flow to a structural model r ... Full text Cite

Vortex-Induced Vibration and Frequency Lock-In of an Airfoil at High Angles of Attack

Journal article Journal of Fluids Engineering Transactions of the ASME · January 1, 2016 Vortex-induced vibration is a fluid instability where vortices due to secondary flows exert a periodic unsteady force on the elastic structure. Under certain circumstances, the shedding frequency can lock into the structure natural frequency and lead to li ... Full text Cite

Store-induced limit-cycle oscillations due to nonlinear wing-store attachment

Journal article Journal of Aircraft · January 1, 2016 Several high-performance fighter aircraft exhibit store-induced limit-cycle oscillations, leading to pilot discomfort, potential structural fatigue, and flight envelope restrictions. The roles of various aerodynamic and structural factors causing the limit ... Full text Cite

Developing a reduced-order model of nonsynchronous vibration in turbomachinery using proper-orthogonal decomposition methods

Journal article Journal of Engineering for Gas Turbines and Power · May 1, 2015 The paper develops a reduced-order model of nonsynchronous vibration (NSV) using proper orthogonal decomposition (POD) methods. The approach was successfully developed and implemented, requiring between two and six POD modes to accurately predict computati ... Full text Cite

Compact implementation strategy for a harmonic balance method within implicit flow solvers

Journal article AIAA Journal · June 1, 2013 A two-step approximate factorization technique for implementing a computationally stable nonlinear unsteady frequency-domain harmonic balance solution method within existing implicit computational fluid dynamic flow solver codes is presented. The approach ... Full text Cite

Harmonic balance methods applied to computational fluid dynamics problems

Journal article International Journal of Computational Fluid Dynamics · February 1, 2013 In this paper, we briefly review the classical harmonic balance method, and describe the adaptation of the method required for its application to computational fluid dynamics models of unsteady time periodic flows. We describe several variations of the met ... Full text Cite

Airfoil transonic flow buffet calculations using the OVERFLOW 2 flow solver

Journal article Collection of Technical Papers AIAA ASME ASCE AHS ASC Structures Structural Dynamics and Materials Conference · December 1, 2011 An investigation of modeling unsteady transonic buffeting flow for the NACA 0012 airfoil when using the NASA OVERFLOW 2 flow solver code is presented. For a fixed freestream Mach number and Reynolds number, buffeting flow is modeled for various angles-of-a ... Full text Cite

Toward a high order throughflow - investigation of the nonlinear harmonic method coupled with an immersed boundary method for the modeling of the circumferential stresses

Journal article Journal of Turbomachinery · May 31, 2011 Capturing a level of modeling of the flow inside a multistage turbomachine, such as unsteadiness for example, can be done at different levels of detail, either by capturing all deterministic features of the flow with a pure unsteady method or by settling f ... Full text Cite

Using automatic differentiation to create a nonlinear reduced-order-model aerodynamic solver

Journal article AIAA Journal · January 1, 2010 A novel nonlinear reduced-order-modeling technique for computational aerodynamics and aeroelasticity is presented. The method is based on a Taylor series expansion of a frequency-domain harmonic balance computational fluid dynamic solver residual. The firs ... Full text Cite

Preliminary flutter design method for supersonic low pressure turbines

Journal article Proceedings of the ASME Turbo Expo · December 1, 2009 The "Tie-Dye" (TD) method is a well-known preliminary flutter design method for subsonic low pressure turbine (LPT) blades. In this paper, a study of 2D mode shape sensitivity using the TD-method for supersonic exit Mach numbers is presented. Using a harmo ... Full text Cite

On the role of the deterministic and circumferential stresses in throughflow calculations

Journal article Journal of Turbomachinery · July 1, 2009 This paper presents a throughflow analysis tool developed in the context of the averagepassage flow model elaborated by Adamczyk. The Adamczyk's flow model describes the 3D time-averaged flow field within a blade row passage. The set of equations that gove ... Full text Cite

Erosion Resistant Coatings for Aircraft Engines

Journal article Vakuum in Forschung Und Praxis · June 1, 2009 Under certain operation conditions, increased amounts of sand particles may be injected into the air inlet duct of jet engines. Because of the high air speed and the high velocity of the compressor blades, an intense material emoval from the airfoils by er ... Full text Cite

Ten years of experience with a small jet engine as a support for education

Journal article Journal of Engineering for Gas Turbines and Power · January 1, 2009 In 1997 the Turbomachinery Group of the University of Liège decided to acquire a small jet engine to illustrate the courses in propulsion and to provide the students with the opportunity to get some experience on data measurement, acquisition, and interpre ... Full text Cite

Improved flutter boundary prediction for an isolated two-degree-of-freedom airfoil

Journal article Journal of Aircraft · January 1, 2009 A novel method of computing the flutter boundary for an isolated airfoil based on a high-fidelity computational fluid dynamics model reveals unusual behavior in a critical transonic range. Inviscid and viscous predictions of the flutter boundary for the tw ... Full text Cite

Theoretical predictions of F-16 fighter limit cycle oscillations for flight flutter testing

Journal article Journal of Aircraft · January 1, 2009 A computational investigation of the flutter onset and limit cycle oscillation behavior of various F-16 fighter weapons and stores configurations is presented. A nonlinear harmonic balance compressible Reynolds-averaged Navier-Stokes computational fluid dy ... Full text Cite

A new solution method for unsteady flows around oscillating bluff bodies

Journal article Solid Mechanics and Its Applications · January 1, 2008 Full text Cite

Fan flutter computations using the harmonic balance method

Journal article 44th AIAA ASME SAE ASEE Joint Propulsion Conference and Exhibit · January 1, 2008 An experimental forward-swept fan encountered flutter at part-speed conditions during wind tunnel testing. A new propulsion aeroelasticity code, based on a computational fluid dynamics (CFD) approach, was used to model the aeroelastic behavior of this fan. ... Full text Cite

A high dimensional harmonic balance approach for an aeroelastic airfoil with cubic restoring forces

Journal article Journal of Fluids and Structures · April 1, 2007 This is a study of a two-dimensional airfoil including a cubic spring stiffness placed in an incompressible flow. A new formulation of the harmonic balance method is employed for the aeroelastic airfoil to investigate the amplitude and frequency of the lim ... Full text Cite

Reduced order nonlinear system identification methodology

Journal article AIAA Journal · August 1, 2006 A new method is presented which enables the identification of a reduced order nonlinear ordinary differential equation (ODE) which can be used to model the behavior of nonlinear fluid dynamics. The method uses a harmonic balance technique and proper orthog ... Full text Cite

A comparison of classical and high dimensional harmonic balance approaches for a Duffing oscillator

Journal article J. Comput. Phys. (USA) · 2006 The present study focuses on a novel harmonic balance formulation, which is much easier to implement than the standard/classical harmonic balance method for complex nonlinear mathematical models and algorithms. Both harmonic balance approaches are applied ... Full text Link to item Cite

Static/dynamic correction approach for reduced-order modeling of unsteady aerodynamics

Journal article Journal of Aircraft · 2006 Presented is a newly devised static/dynamic correction approach for eigenvector expansion based reduced-order modeling (ROM). When compared to the fundamental Ritz ROM formulation, along with the static and multiple static correction ROM approaches, the te ... Cite

Discrete adjoint approach for modeling unsteady aerodynamic design sensitivities

Journal article AIAA Journal · 2005 A discrete adjoint approach is presented for computing steady and unsteady aerodynamic design sensitivities for compressible viscous flows about airfoil configurations. The nominal flow solver method is based on a harmonic balance solution technique, which ... Cite

Higher order harmonic balance analysis for limit cycle oscillations in an airfoil with cubic restoring forces

Journal article Collection of Technical Papers AIAA ASME ASCE AHS ASC Structures Structural Dynamics and Materials Conference · January 1, 2005 This is a study of a two dimensional airfoil including a cubic spring stiffness placed in an incompressible flow. A new formulation of the harmonic balance method is employed for the aeroelastic airfoil to investigate the amplitude and frequency of the lim ... Full text Cite

Limit-cycle oscillations of a typical airfoil in transonic flow

Journal article Journal of Aircraft · 2004 Using an inviscid flow computational-fluid-dynamic model and a harmonic balance flow solver, a parametric investigation of how structural-inertial parameters and freestream Mach number of a transonic flow affect the limit-cycle oscillation characteristics ... Cite

Transonic limit cycle oscillation analysis using reduced order aerodynamic models

Journal article Journal of Fluids and Structures · 2004 Limit cycle oscillations have been observed in flight operations of modern aircraft, wind tunnel experiments and mathematical models. Both fluid and structural nonlinearities are thought to contribute to these phenomena. With recent advances in reduced ord ... Full text Link to item Cite

Modeling viscous transonic limit-cycle oscillation behavior using a harmonic balance approach

Journal article Journal of Aircraft · 2004 Presented is a harmonic-balance computational fluid dynamic approach for modeling limit-cycle oscillation behavior of aeroelastic airfoil configurations in a viscous transonic flow. For the NLR 7301 airfoil configuration studied, accounting for viscous eff ... Cite

Improved understanding of transonic flutter: A three-parameter flutter surface

Journal article Journal of Aircraft · 2004 An understanding of transonic flutter is often critical for high-speed aircraft development. A presentation of the transonic flutter velocity as a function of the Mach number and mass ratio is shown here to provide many advantages. Such a presentation offe ... Cite

Parametric study of flutter for an airfoil in inviscid transonic flow

Journal article Journal of Aircraft · 2003 A parametric study of flutter was conducted for an airfoil in inviscid transonic flow. An inviscid computational flow dynamic harmonic balance aerodynamic-Euler-based code was used for the investigation. The computational efficiency of the time-linearized ... Cite

Three-dimensional transonic aeroelasticity using proper orthogonal decomposition-based reduced-order models

Journal article Journal of Aircraft · 2003 The proper orthogonal decomposition (POD-) based reduced-order modeling technique for modeling unsteady frequency-domain aerodynamics is developed for a large-scale computational model of an inviscid flow transonic wing configuration. When the methodology ... Cite

Computation of unsteady nonlinear flows in cascades using a harmonic balance technique

Journal article AIAA Journal · 2002 A harmonic balance technique for modeling unsteady nonlinear flows in turbomachinery is presented. The analysis exploits the fact that many unsteady flows of interest in turbomachinery are periodic in time. Thus, the unsteady flow conservation variables ma ... Cite

Nonlinear inviscid aerodynamic effects on transonic divergence, flutter, and limit-cycle oscillations

Journal article AIAA Journal · 2002 By the use of a state-of-the-art computational fluid dynamic (CFD) method to model nonlinear steady and unsteady transonic flows in conjunction with a linear structural model, an investigation is made into how nonlinear aerodynamics can effect the divergen ... Cite

Proper orthogonal decomposition technique for transonic unsteady aerodynamic flows

Journal article AIAA Journal · 2000 A new method for constructing reduced-order models (ROM) of unsteady small-disturbance flows is presented. The reduced-order models are constructed using basis vectors determined from the proper orthogonal decomposition (POD) of an ensemble of small-distur ... Cite