The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Kenneth C. Hall - One of the best experts on this subject based on the ideXlab platform.
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Compact Implementation Strategy for a Harmonic Balance Method Within Implicit Flow Solvers
AIAA Journal, 2013Co-Authors: Jeffrey P Thomas, Earl H. Dowell, Kenneth C. Hall, Chad H. Custer, Christophe Eric CorreAbstract: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 uses an explicit discretization of the Harmonic Balance source term, and no new implicit code development is required. Both of these features enable the Harmonic Balance method to be implemented within existing implicit flow solver codes with minimal modification necessary to the underlying flow solver code. The resulting Harmonic Balance solver can then be used for modeling nonlinear periodic unsteady flows. The methodology is applied to the NASA OVERFLOW flow solver code, and results are presented for transonic viscous flow past an unsteady pitching airfoil section.
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Harmonic Balance methods applied to computational fluid dynamics problems
International Journal of Computational Fluid Dynamics, 2013Co-Authors: Kenneth C. Hall, Kivanc Ekici, Jeffrey P Thomas, Earl H. DowellAbstract: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 method including a classical balancing method with pseudo time relaxation, the nonlinear frequency domain form and the time spectral form. We show that the maximum stable Courant–Friedrichs–Lewy CFL number for explicit schemes is dependent on the grid reduced frequency, a non-dimensional parameter that depends on the cell size, characteristic wave speed, and the highest frequency retained in the Harmonic Balance analysis. We apply the Harmonic Balance methods to several nonlinear unsteady flow problems and show that even strongly nonlinear flows can be modelled accurately with a small number of Harmonics retained in the model.
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Harmonic Balance Analysis of Limit Cycle Oscillations in Turbomachinery
AIAA Journal, 2011Co-Authors: Kivanc Ekici, Kenneth C. HallAbstract:A Harmonic Balance technique for the analysis of limit cycle oscillations of turbomachinery blades is presented. This method couples a computational fluid dynamics model to a single-degree-of-freedom structural dynamic model of the turbomachinery blades. The computational fluid dynamics solver uses a nonlinear frequency-domain (Harmonic Balance) approach that allows one to model the blade row of a turbomachine on a computational grid spanning a single blade passage. Using the Harmonic Balance approach, several solutions, each one corresponding to a different subtime level of the periodic unsteady flow, are computed simultaneously. These subtime-level solutions are coupled to each other in the computational field by a spectral approximation of the time-derivative term in the Navier―Stokes equation and also by application of far-field and periodic boundary conditions. The structural dynamic model is based on a similar approach in which a single vibratory mode of interest is modeled using the Harmonic Balance technique. The two solvers are coupled together through the upwash condition on the surface of the blade and the resulting generalized aerodynamic forces. In the proposed approach, the limit cycle oscillation frequency is treated as another unknown, which is solved iteratively, together with the governing equations of fluid flow and structural dynamics, thereby driving the residual of the aeroelastic problem to convergence in a single computational fluid dynamics run. The accuracy of the new method is compared with two other techniques and it is shown to offer significant computational savings.
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Harmonic Balance analysis of blade row interactions in a transonic compressor
Journal of Propulsion and Power, 2010Co-Authors: Kivanc Ekici, Kenneth C. Hall, Robe E KielbAbstract:In this paper we apply the Harmonic Balance technique to analyze an inlet guide vane and rotor interaction problem, and compare the computed flow solutions to existing experimental data. The computed results, which compare well with the experimental data, demonstrate that the technique can accurately and efficiently model strongly nonlinear periodic flows, including shock/vane interaction and unsteady shock motion. Using the Harmonic Balance approach, each blade row is modeled using a computational grid spanning just a single blade passage regardless of the actual blade counts. For each blade row, several subtime level solutions that span a single time period are stored. These subtime level solutions are related to each other through the time derivative term in the Euler (or Navier―Stokes) equations, which is approximated by a pseudo-spectral operator, by complex periodicity conditions along the periodic boundary of each blade row's computational domain, and by the interface boundary conditions between the vane and rotor. Casting the governing equations in Harmonic Balance form removes the explicit dependence on time. Mathematically, the equations to be solved are similar in form to the steady Euler (or Navier―Stokes) equations with an additional source term proportional to the fundamental frequency of the unsteadiness. Thus, conventional steady-state computational fluid dynamics techniques, including local time stepping and multigrid acceleration, are used to accelerate convergence, resulting in a very efficient unsteady flow solver.
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unsteady flow computation using a Harmonic Balance approach implemented about the overflow 2 flow solver
19th AIAA Computational Fluid Dynamics, 2009Co-Authors: Jeffrey P Thomas, Earl H. Dowell, Chad H Custe, Kenneth C. HallAbstract:A novel approach for implementing a nonlinear unsteady frequency domain Harmonic Balance solution technique about existing implicit computational fluid dynamic flow solvers is presented. This approach uses an explicit discretization of the Harmonic Balance source term, which enables the Harmonic Balance method to be applied to existing implicit flow solvers with minimal need for modification to the underlying implicit flow solver code. The resulting Harmonic Balance solver can then be used for modeling nonlinear periodic unsteady flows. The methodology is applied to the OVERFLOW 2 flow solver code, and results are presented for transonic viscous flow past an unsteady pitching airfoil section. Unsteady aerodynamic and aeroelastic results for the F-16 fighter wing are also presented.
Kivanc Ekici - One of the best experts on this subject based on the ideXlab platform.
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aeroelastic analysis of a wind turbine blade using the Harmonic Balance method
Wind Energy, 2018Co-Authors: Jaso Howiso, Jeffrey P Thomas, Kivanc EkiciAbstract:Most current wind turbine aeroelastic codes rely on the blade element momentum method with empirical corrections to compute aerodynamic forces on the wind turbine blades. While efficient, this method relies on experimental data and does not allow designers much flexibility for alternative blade designs. Unsteady solutions to the Navier-Stokes equations offer a significant improvement in aerodynamic modeling, but these are currently too computationally expensive to be useful in a design situation. However, steady-state solutions to the Navier-Stokes equations are possible with reasonable computation times. The Harmonic Balance method provides a way to represent unsteady, periodic flows through coupled a set of steady-state solutions. This method offers the possibility of unsteady flow solutions at a computational cost on the order of a few steady-state solutions. By coupling a Harmonic Balance driven aerodynamic model with a mode shape-based structural dynamics model, an efficient aeroelastic model for a wind turbine blade driven by the Navier-Stokes equations is developed in this dissertation. For wind turbine flows, turbulence modeling is essential, especially in the transition of the boundary layer from laminar to turbulent. As part of this dissertation, the Spalart-Allmaras turbulence model and the gamma-Re\_theta-t transition model are included in the aerodynamic model. This marks the first time that this transition model, turbulence model, and the Harmonic Balance method have been coupled to study unsteady wind turbine aerodynamics. Results show that the transition model matches experimental data more closely than a fully turbulent model for the onset of both static and dynamic stall. Flutter is of particular interest as turbines continue to increase in size, and longer and softer blades continue to enter the field. In this dissertation, flutter is investigated for the 1.5 MW WindPACT rotor blade. The aeroelastic model created, which incorporates the Harmonic Balance method and a fully turbulent aerodynamic model, is the first of its kind for wind turbine flutter analysis. Predictions match those of other aeroelastic models for the 1.5 MW WindPACT blade, and the first flapwise and edgewise modes are shown to dominate flutter for the rotor speeds considered.
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resolution of gibbs phenomenon using a modified pseudo spectral operator in Harmonic Balance cfd solvers
International Journal of Computational Fluid Dynamics, 2016Co-Authors: Reza Djeddi, Kivanc EkiciAbstract:A new pseudo-spectral operator is developed for time-spectral Harmonic Balance solutions of periodic unsteady flows. The method utilises a mechanism similar to sigma-approximation technique with Lanczos filtering function that alters the inverse of the discrete Fourier transformation matrix, leading to a modified pseudo-spectral operator. The modified operator is then used instead of the original operator that mimics the time-derivative term of the unsteady governing equations. The modified operator is capable of damping high-frequency nonlinearities in the Harmonic Balance solution, thus alleviating the effects of high-frequency oscillations that result in Gibbs-type phenomena. The effectiveness and robustness of the technique are demonstrated through various test cases.
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a discrete adjoint Harmonic Balance method for turbomachinery shape optimization
Aerospace Science and Technology, 2014Co-Authors: Huang Huang, Kivanc EkiciAbstract:Abstract The Harmonic Balance method has seen an increasing popularity in the solution of time-periodic problems because of its computational efficiency and its ability to model dynamically nonlinear fluid phenomena. In addition, the mathematically steady nature of this technique makes it ideal for adjoint sensitivity analysis of unsteady problems. In this work, a novel optimization framework consisting of three components: a Harmonic Balance based unsteady cascade flow solver, an accompanying adjoint solver and a quasi-Newton optimization solver; have been developed. The discrete adjoint solver is obtained with the aid of an automatic differentiation tool, TAPENADE. To demonstrate the efficiency and accuracy of the method, we present shape optimization and adjoint sensitivity computations for a two-dimensional compressor cascade. Steady inverse design of this cascade is performed to investigate the effects of two shape parameterization methods, namely Hicks–Henne bump functions and mesh points. Shape optimization is performed to improve the aerodynamic damping characteristics of a vibrating cascade row. In addition, the unsteady adjoint technique is used to determine the frequency of vibration that would drive the system to limit-cycle, which defines the stability limit of the cascade.
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Harmonic Balance methods applied to computational fluid dynamics problems
International Journal of Computational Fluid Dynamics, 2013Co-Authors: Kenneth C. Hall, Kivanc Ekici, Jeffrey P Thomas, Earl H. DowellAbstract: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 method including a classical balancing method with pseudo time relaxation, the nonlinear frequency domain form and the time spectral form. We show that the maximum stable Courant–Friedrichs–Lewy CFL number for explicit schemes is dependent on the grid reduced frequency, a non-dimensional parameter that depends on the cell size, characteristic wave speed, and the highest frequency retained in the Harmonic Balance analysis. We apply the Harmonic Balance methods to several nonlinear unsteady flow problems and show that even strongly nonlinear flows can be modelled accurately with a small number of Harmonics retained in the model.
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Harmonic Balance Analysis of Limit Cycle Oscillations in Turbomachinery
AIAA Journal, 2011Co-Authors: Kivanc Ekici, Kenneth C. HallAbstract:A Harmonic Balance technique for the analysis of limit cycle oscillations of turbomachinery blades is presented. This method couples a computational fluid dynamics model to a single-degree-of-freedom structural dynamic model of the turbomachinery blades. The computational fluid dynamics solver uses a nonlinear frequency-domain (Harmonic Balance) approach that allows one to model the blade row of a turbomachine on a computational grid spanning a single blade passage. Using the Harmonic Balance approach, several solutions, each one corresponding to a different subtime level of the periodic unsteady flow, are computed simultaneously. These subtime-level solutions are coupled to each other in the computational field by a spectral approximation of the time-derivative term in the Navier―Stokes equation and also by application of far-field and periodic boundary conditions. The structural dynamic model is based on a similar approach in which a single vibratory mode of interest is modeled using the Harmonic Balance technique. The two solvers are coupled together through the upwash condition on the surface of the blade and the resulting generalized aerodynamic forces. In the proposed approach, the limit cycle oscillation frequency is treated as another unknown, which is solved iteratively, together with the governing equations of fluid flow and structural dynamics, thereby driving the residual of the aeroelastic problem to convergence in a single computational fluid dynamics run. The accuracy of the new method is compared with two other techniques and it is shown to offer significant computational savings.
Liping Liu - One of the best experts on this subject based on the ideXlab platform.
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high dimensional Harmonic Balance analysis for second order delay differential equations
Journal of Vibration and Control, 2010Co-Authors: Liping Liu, Tamas KalmarnagyAbstract:This paper demonstrates the utility of the high-dimensional Harmonic Balance (HDHB) method for locating limit cycles of second-order delay-differential equations (DDEs). A matrix version of the HDHB method for systems of DDEs is described in detail. The method has been successfully applied to capture the stable and/or unstable limit cycles in three different models: a machine tool vibration model, the sunflower equation and a circadian rhythm model. The results show excellent agreement with collocation and continuation-based solutions from DDE-BIFTOOL. The advantages of HDHB over the classical Harmonic Balance method are highlighted and discussed.
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a high dimensional Harmonic Balance approach for an aeroelastic airfoil with cubic restoring forces
Journal of Fluids and Structures, 2007Co-Authors: Liping Liu, Earl H. Dowell, Jeffrey P ThomasAbstract: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 limit cycle oscillations. The results are compared with the results from the classical Harmonic Balance approach and from the conventional time marching integration method.
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A novel Harmonic Balance analysis for the Van Der Pol oscillator
International Journal of Non-linear Mechanics, 2007Co-Authors: Liping Liu, Earl H. Dowell, Kenneth C. HallAbstract:Abstract This study focuses on a novel Harmonic Balance formulation, the high-dimensional Harmonic Balance method. To investigate a non-linearity in the damping term, the system chosen for study is the Van der Pol's oscillator. Both unforced and forced oscillators are analyzed. The results from the analysis are compared with those obtained from the classical Harmonic Balance and the time marching (Runge–Kutta) methods.
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Harmonic Balance Approach for an Airfoil with a Freeplay Control Surface
AIAA Journal, 2005Co-Authors: Liping Liu, Earl H. DowellAbstract:The nonlinear aeroelastic response of a two-dimensional airfoil, including a control surface with freeplay placed in an incompressible flow, is studied. The model equations are formulated as a set of first-order ordinary differential equations. First, the dynamic response is investigated by a time integration method, and the time integration results are used for the verification of the Harmonic Balance results. The interesting hysteresis phenomenon and the effect of initial conditions of the subcritical bifurcation are presented. A higher-order Harmonic Balance method is then derived to investigate the high Harmonics of the airfoil motions. The Harmonic Balance prediction is verified by comparison to the results from a numerical time marching integration and also by comparison to results from a previous experiment. Nomenclature a = nondimensional distance of the elastic axis from the midchord, with respect to the semichord B = damping submatrix b = semichord Ch = stiffness (per unit span) of wing in deflection C(k) = generalized Theodorsen function Cα, Cβ = torsional stiffness (per unit span) of wing around a and of aileron around c c = nondimensional distance of the control surface (aileron) hinge line from the midchord, with respect to the semichord
Jaso Howiso - One of the best experts on this subject based on the ideXlab platform.
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aeroelastic analysis of a wind turbine blade using the Harmonic Balance method
Wind Energy, 2018Co-Authors: Jaso Howiso, Jeffrey P Thomas, Kivanc EkiciAbstract:Most current wind turbine aeroelastic codes rely on the blade element momentum method with empirical corrections to compute aerodynamic forces on the wind turbine blades. While efficient, this method relies on experimental data and does not allow designers much flexibility for alternative blade designs. Unsteady solutions to the Navier-Stokes equations offer a significant improvement in aerodynamic modeling, but these are currently too computationally expensive to be useful in a design situation. However, steady-state solutions to the Navier-Stokes equations are possible with reasonable computation times. The Harmonic Balance method provides a way to represent unsteady, periodic flows through coupled a set of steady-state solutions. This method offers the possibility of unsteady flow solutions at a computational cost on the order of a few steady-state solutions. By coupling a Harmonic Balance driven aerodynamic model with a mode shape-based structural dynamics model, an efficient aeroelastic model for a wind turbine blade driven by the Navier-Stokes equations is developed in this dissertation. For wind turbine flows, turbulence modeling is essential, especially in the transition of the boundary layer from laminar to turbulent. As part of this dissertation, the Spalart-Allmaras turbulence model and the gamma-Re\_theta-t transition model are included in the aerodynamic model. This marks the first time that this transition model, turbulence model, and the Harmonic Balance method have been coupled to study unsteady wind turbine aerodynamics. Results show that the transition model matches experimental data more closely than a fully turbulent model for the onset of both static and dynamic stall. Flutter is of particular interest as turbines continue to increase in size, and longer and softer blades continue to enter the field. In this dissertation, flutter is investigated for the 1.5 MW WindPACT rotor blade. The aeroelastic model created, which incorporates the Harmonic Balance method and a fully turbulent aerodynamic model, is the first of its kind for wind turbine flutter analysis. Predictions match those of other aeroelastic models for the 1.5 MW WindPACT blade, and the first flapwise and edgewise modes are shown to dominate flutter for the rotor speeds considered.
Jeffrey P Thomas - One of the best experts on this subject based on the ideXlab platform.
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aeroelastic analysis of a wind turbine blade using the Harmonic Balance method
Wind Energy, 2018Co-Authors: Jaso Howiso, Jeffrey P Thomas, Kivanc EkiciAbstract:Most current wind turbine aeroelastic codes rely on the blade element momentum method with empirical corrections to compute aerodynamic forces on the wind turbine blades. While efficient, this method relies on experimental data and does not allow designers much flexibility for alternative blade designs. Unsteady solutions to the Navier-Stokes equations offer a significant improvement in aerodynamic modeling, but these are currently too computationally expensive to be useful in a design situation. However, steady-state solutions to the Navier-Stokes equations are possible with reasonable computation times. The Harmonic Balance method provides a way to represent unsteady, periodic flows through coupled a set of steady-state solutions. This method offers the possibility of unsteady flow solutions at a computational cost on the order of a few steady-state solutions. By coupling a Harmonic Balance driven aerodynamic model with a mode shape-based structural dynamics model, an efficient aeroelastic model for a wind turbine blade driven by the Navier-Stokes equations is developed in this dissertation. For wind turbine flows, turbulence modeling is essential, especially in the transition of the boundary layer from laminar to turbulent. As part of this dissertation, the Spalart-Allmaras turbulence model and the gamma-Re\_theta-t transition model are included in the aerodynamic model. This marks the first time that this transition model, turbulence model, and the Harmonic Balance method have been coupled to study unsteady wind turbine aerodynamics. Results show that the transition model matches experimental data more closely than a fully turbulent model for the onset of both static and dynamic stall. Flutter is of particular interest as turbines continue to increase in size, and longer and softer blades continue to enter the field. In this dissertation, flutter is investigated for the 1.5 MW WindPACT rotor blade. The aeroelastic model created, which incorporates the Harmonic Balance method and a fully turbulent aerodynamic model, is the first of its kind for wind turbine flutter analysis. Predictions match those of other aeroelastic models for the 1.5 MW WindPACT blade, and the first flapwise and edgewise modes are shown to dominate flutter for the rotor speeds considered.
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Compact Implementation Strategy for a Harmonic Balance Method Within Implicit Flow Solvers
AIAA Journal, 2013Co-Authors: Jeffrey P Thomas, Earl H. Dowell, Kenneth C. Hall, Chad H. Custer, Christophe Eric CorreAbstract: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 uses an explicit discretization of the Harmonic Balance source term, and no new implicit code development is required. Both of these features enable the Harmonic Balance method to be implemented within existing implicit flow solver codes with minimal modification necessary to the underlying flow solver code. The resulting Harmonic Balance solver can then be used for modeling nonlinear periodic unsteady flows. The methodology is applied to the NASA OVERFLOW flow solver code, and results are presented for transonic viscous flow past an unsteady pitching airfoil section.
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Harmonic Balance methods applied to computational fluid dynamics problems
International Journal of Computational Fluid Dynamics, 2013Co-Authors: Kenneth C. Hall, Kivanc Ekici, Jeffrey P Thomas, Earl H. DowellAbstract: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 method including a classical balancing method with pseudo time relaxation, the nonlinear frequency domain form and the time spectral form. We show that the maximum stable Courant–Friedrichs–Lewy CFL number for explicit schemes is dependent on the grid reduced frequency, a non-dimensional parameter that depends on the cell size, characteristic wave speed, and the highest frequency retained in the Harmonic Balance analysis. We apply the Harmonic Balance methods to several nonlinear unsteady flow problems and show that even strongly nonlinear flows can be modelled accurately with a small number of Harmonics retained in the model.
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unsteady flow computation using a Harmonic Balance approach implemented about the overflow 2 flow solver
19th AIAA Computational Fluid Dynamics, 2009Co-Authors: Jeffrey P Thomas, Earl H. Dowell, Chad H Custe, Kenneth C. HallAbstract:A novel approach for implementing a nonlinear unsteady frequency domain Harmonic Balance solution technique about existing implicit computational fluid dynamic flow solvers is presented. This approach uses an explicit discretization of the Harmonic Balance source term, which enables the Harmonic Balance method to be applied to existing implicit flow solvers with minimal need for modification to the underlying implicit flow solver code. The resulting Harmonic Balance solver can then be used for modeling nonlinear periodic unsteady flows. The methodology is applied to the OVERFLOW 2 flow solver code, and results are presented for transonic viscous flow past an unsteady pitching airfoil section. Unsteady aerodynamic and aeroelastic results for the F-16 fighter wing are also presented.
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a high dimensional Harmonic Balance approach for an aeroelastic airfoil with cubic restoring forces
Journal of Fluids and Structures, 2007Co-Authors: Liping Liu, Earl H. Dowell, Jeffrey P ThomasAbstract: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 limit cycle oscillations. The results are compared with the results from the classical Harmonic Balance approach and from the conventional time marching integration method.
