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    A New Harmonic Balance Approach Using Multidimensional Time 

    Source: Journal of Engineering for Gas Turbines and Power:;2021:;volume( 143 ):;issue: 008:;page 081007-1
    Author(s): Junge, Laura; Frey, Christian; Ashcroft, Graham; Kügeler, Edmund
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: Over the past years, nonlinear frequency-domain methods have become a state-of-the-art technique for the numerical simulation of unsteady flow fields within multistage turbomachinery as they are capable of fully exploiting ...
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    Analyzing Unsteady Turbomachinery Flow Simulations With Mixing Entropy 

    Source: Journal of Turbomachinery:;2024:;volume( 146 ):;issue: 007:;page 71004-1
    Author(s): Frey, Christian; Geihe, Benedict; Junge, Laura
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: The prediction of unsteady aerodynamic loads is a central problem during the design of turbomachinery. Over the last 20 years, harmonic balance methods have been shown to be highly efficient for this task. A CPU-cost optimal ...
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    Forced Response Sensitivity Analysis Using an Adjoint Harmonic Balance Solver 

    Source: Journal of Turbomachinery:;2019:;volume( 141 ):;issue: 003:;page 31014
    Author(s): Engels-Putzka, Anna; Backhaus, Jan; Frey, Christian
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: This paper describes the development and initial application of an adjoint harmonic balance (HB) solver. The HB method is a numerical method formulated in the frequency domain which is particularly suitable for the simulation ...
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    Evaluating the Aerodynamic Damping At Shock Wave Boundary Layer Interacting Flow Conditions With Harmonic Balance 

    Source: Journal of Engineering for Gas Turbines and Power:;2022:;volume( 145 ):;issue: 003:;page 31012-1
    Author(s): Heners, Jan Philipp; Frey, Christian; Grüber, Björn; Carraro, Thomas
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: The aerodynamic damping of a stator vane located in a rear stage of a high pressure compressor is evaluated at transonic flow conditions by numerical means. The results of a solution method based on temporal linearization ...
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    A Low Mach Preconditioned Harmonic Balance Solver for Cavity Flutter Computations 

    Source: Journal of Engineering for Gas Turbines and Power:;2024:;volume( 147 ):;issue: 002:;page 21029-1
    Author(s): Sivel, Pierre; Frey, Christian; Kersken, Hans-Peter; Kügeler, Edmund
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: Labyrinth seal flutter is a critical phenomenon in turbomachinery, as it can lead to severe structural vibrations and potential component damage. Accurate prediction and mitigation of flutter are paramount to ensuring the ...
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    Analysis of Turbomachinery Averaging Techniques 

    Source: Journal of Turbomachinery:;2022:;volume( 145 ):;issue: 005:;page 51006-1
    Author(s): Frey, Christian; Ashcroft, Graham; Müller, Michael; Wellner, Jens
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: In this paper, various averaging techniques commonly used in turbomachinery applications are analyzed. It is shown how the work average relates to Miller’s mechanical work potential and that it is, in a certain way, ...
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    Fully Coupled Analysis of Flutter Induced Limit Cycles: Frequency Versus Time Domain Methods 

    Source: Journal of Engineering for Gas Turbines and Power:;2023:;volume( 145 ):;issue: 007:;page 71009-1
    Author(s): Berthold, Christian; Gross, Johann; Frey, Christian; Krack, Malte
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: To save resources and reduce emissions, it is crucial to reduce weight of aircraft engines and further increase aerodynamic efficiency of gas and steam turbines. For turbine blades, these goals often lead to flutter. Thus, ...
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    Advanced Numerical Methods for the Prediction of Tonal Noise in Turbomachinery—Part I: Implicit Runge–Kutta Schemes 

    Source: Journal of Turbomachinery:;2014:;volume( 136 ):;issue: 002:;page 21002
    Author(s): Ashcroft, Graham; Frey, Christian; Heitkamp, Kathrin; Weckmأ¼ller, Christian
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: This is the first part of a series of two papers on unsteady computational fluid dynamics (CFD) methods for the numerical simulation of aerodynamic noise generation and propagation. In this part, the stability, accuracy, ...
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    Advanced Numerical Methods for the Prediction of Tonal Noise in Turbomachinery—Part II: Time Linearized Methods 

    Source: Journal of Turbomachinery:;2014:;volume( 136 ):;issue: 002:;page 21003
    Author(s): Frey, Christian; Ashcroft, Graham; Kersken, Hans; Weckmأ¼ller, Christian
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: This is the second part of a series of two papers on unsteady computational fluid dynamics (CFD) methods for the numerical simulation of aerodynamic noise generation and propagation. It focuses on the application of ...
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    Using Pseudotime Marching for the Solution of Harmonic Balance Problems 

    Source: Journal of Turbomachinery:;2025:;volume( 147 ):;issue: 009:;page 91007-1
    Author(s): Frey, Christian; Backhaus, Jan; Ashcroft, Graham; Geiser, Georg; Winhart, Benjamin; Stüer, Heinrich
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: The aim of this paper is to study approaches to implement implicit pseudotime marching for the harmonic balance system in the frequency domain. We first give a motivation for using pseudotime marching as a solution technique. ...
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