scholarly journals Time-Domain Harmonic Balance Method for Turbomachinery Aeroelasticity

AIAA Journal ◽  
2014 ◽  
Vol 52 (1) ◽  
pp. 62-71 ◽  
Author(s):  
Frédéric Sicot ◽  
Adrien Gomar ◽  
Guillaume Dufour ◽  
Alain Dugeai
Keyword(s):  
Time Domain ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method

Multi-Harmonic Analysis of Dry Friction Damped Systems Using an Incremental Harmonic Balance Method

1985 ◽  
Vol 52 (4) ◽  
pp. 958-964 ◽  
Author(s):  
C. Pierre ◽  
A. A. Ferri ◽  
E. H. Dowell
Keyword(s):  
Time Domain ◽  
Dry Friction ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Frequency Domain Analysis ◽  
Balance Method ◽  
Incremental Harmonic Balance Method ◽  
Incremental Harmonic Balance ◽  
The Time Domain ◽  
Damped Systems

A multi-harmonic, frequency domain analysis of dry friction damped systems is presented which uses an incremental harmonic balance method. When compared with time domain solution methods, it is found that the incremental harmonic balance method can yield very accurate results with some advantages over the time domain methods. Both one and two degree-of-freedom systems are studied.

The Development and Application of a Time-Domain Harmonic Balance Flow Solver

2012 ◽  
Author(s):  
Pengcheng Du ◽  
Fangfei Ning
Keyword(s):  
Time Domain ◽  
Harmonic Balance ◽  
Unsteady Flows ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Computational Time ◽  
Test Cases ◽  
Flow Solver ◽  
The Time Domain ◽  
Time Periodic

Time periodic unsteady flows are often encountered in turbomachinery. Simulating such flows using conventional time marching approach is very time-consuming and hence expensive. To handle this problem, several Fourier-based reduced order models have been developed recently. Among these, the time-domain harmonic balance method solves the governing equations purely in the time domain and there is also no need for the turbulence model to be linearized, making it easy to be implemented in an existing RANS code. Thus, the time-domain harmonic balance method was chosen and incorporated into an in-house Navier-Stokes flow solver. Several test cases were performed for the validations of the developed code. They cover standard unsteady test cases such as the low speed vortex shedding cylinder flow and the Sajben transonic diffuser under periodically oscillating back pressure. Further, two different practical turbomachinery unsteady flows were considered. One is a transonic fan under circumferential inlet distortion and the other is the rotor-stator interactions in a single stage compressor. The results illustrate the capability of the harmonic balance method in capturing the dominant nonlinear effects. The number of harmonics should be retained in the harmonic balance method is depend on the strength of the nonlinear unsteady effects and differs from case to case. With appropriate number of harmonics retained, it can resolve the unsteady flow field satisfactory, meanwhile, reducing the computational time significantly. In a word, the harmonic balance method promise to be an effective way to simulate time periodic unsteady flows.

On the Extension of a Harmonic Balance Method for the Simulation of Compressor Casing Treatments

2016 ◽  
Author(s):  
Christian Voigt ◽  
Graham Ashcroft
Keyword(s):  
Time Domain ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Nonlinear Frequency ◽  
Transonic Compressor ◽  
Frequency Domain Methods ◽  
Blade Tip ◽  
The Time Domain ◽  
Casing Treatments

In recent years both linear and nonlinear frequency domain methods have become increasingly popular in the simulation and investigation of time-periodic flows in turbomachinery. In this work the extension of an alternating frequency/time domain Harmonic Balance method to support arbitrary inter-domain block interfaces, with possibly different frames of reference, is described in detail. The approach outlined is based on the time-domain, area-based interpolation algorithm originally developed for the investigation of casing treatments. In this paper, it is shown that by solving the domain coupling problem in the time-domain it is possible to accurately and efficiently capture the flow physics of such complex, nonlinear problems as blade tip interaction with casing treatments in transonic compressors. To demonstrate and verify the basic algorithm the advection of a simple entropy disturbance in a subsonic duct flow is first computed. Secondly, unsteady flow due to rotor-stator interaction in a transonic compressor stage is simulated and the data compared with reference numerical methods. Finally, to validate the method a single stage transonic axial compressor with casing treatments is simulated and the results are compared with previously published time-domain simulations as well as experimental data based on particle image velocimetry measurements in the blade tip region.

Application of the Harmonic Balance Method in Simulating Almost Periodic Turbomachinery Flows

2014 ◽  
Author(s):  
Pengcheng Du ◽  
Fangfei Ning
Keyword(s):  
Time Domain ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Time Sampling ◽  
Almost Periodic ◽  
Shift Method ◽  
Shape Correction ◽  
Phase Shift Method ◽  
Correction Phase

The time-domain harmonic balance method is now popular in simulating unsteady turbomachinery flows. The essence of this method is that the time marching of a periodic or almost-periodic flow problem is substituted by several coupled steady computations at different time instants in the period of interest. The state-of-the-art non-uniform time sampling algorithm is adopted in our time-domain harmonic balance flow solver to simulate multistage turbomachinery unsteady flows. For a specific blade row in a multi-rows configuration, only the interactions from the adjacent blade rows are considered. A typical highly loaded 1.5 stage fan is studied as validation test case. The results showed that the non-uniform time sampling method is robust regardless of the frequencies considered. In this IGV-Rotor-Stator configuration, the interactions between the upstream-traveling rotor shock and IGV blades and the interactions between the rotor wakes and stator blades are all well captured. Thus, the time-averaged performance map obtained by the harmonic balance method with five resolved frequencies matches well with the reference time-accurate computations. The computational time of this five-frequency harmonic balance simulation is affordable, which ensures the code can be used in performing fast unsteady analysis in the design phase. Besides, the single passage unsteady calculation with the shape-correction phase shift method applied is also performed for comparison purpose. A simple interpolation technique is proposed to update the Fourier coefficients of each disturbance as frequently as possible, thus the convergence speed is enhanced. Similar results can be obtained by this shape-correction phase shift method, making it an alternative unsteady calculation module in an in-house CFD package.

Unsteady Simulation of a 1.5 Stage Turbine Using an Implicitly Coupled Nonlinear Harmonic Balance Method

2012 ◽  
Author(s):  
Chad H. Custer ◽  
Jonathan M. Weiss ◽  
Venkataramanan Subramanian ◽  
William S. Clark ◽  
Kenneth C. Hall
Keyword(s):  
Unsteady Flow ◽  
Time Domain ◽  
Harmonic Balance ◽  
Fourier Coefficients ◽  
Fluid Dynamic ◽  
Time Derivative ◽  
Computational Cost ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Computational Domain

The harmonic balance method implemented within STAR-CCM+ is a mixed frequency/time domain computational fluid dynamic technique, which enables the efficient calculation of time-periodic flows. The unsteady solution is stored at a small number of fixed time levels over one temporal period of the unsteady flow in a single blade passage in each blade row; thus the solution is periodic by construction. The individual time levels are coupled to one another through a spectral operator representing the time derivative term in the Navier-Stokes equation, and at the boundaries of the computational domain through the application of periodic and nonreflecting boundary conditions. The blade rows are connected to one another via a small number of fluid dynamic spinning modes characterized by nodal diameter and frequency. This periodic solution is driven to the correct solution using conventional (steady) CFD acceleration techniques, and thus is computationally efficient. Upon convergence, the time level solutions are Fourier transformed to obtain spatially varying Fourier coefficients of the flow variables. We find that a small number of time levels (or, equivalently, Fourier coefficients) are adequate to model even strongly nonlinear flows. Consequently, the method provides an unsteady solution at a computational cost significantly lower than traditional unsteady time marching methods. The implementation of this nonlinear harmonic balance method within STAR-CCM+ allows for the simulation of multiple blade rows. This capability is demonstrated and validated using a 1.5 stage cold flow axial turbine developed by the University of Aachen. Results produced using the harmonic balance method are compared to conventional time domain simulations using STAR-CCM+, and are also compared to published experimental data. It is shown that the harmonic balance method is able to accurately model the unsteady flow structures at a computational cost significantly lower than unsteady time domain simulation.

scholarly journals A Time-Domain Harmonic Balance Method for Rotor/Stator Interactions

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Frédéric Sicot ◽  
Guillaume Dufour ◽  
Nicolas Gourdain
Keyword(s):  
Time Domain ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Flow Simulation ◽  
Balance Method ◽  
Test Case ◽  
Phase Lag ◽  
Local Flow ◽  
Periodic Rotation ◽  
Time Periodic

In the absence of instabilities, the large deterministic scales of turbomachinery flows resulting from the periodic rotation of blades can be considered periodic in time. Such flows are not simulated with enough efficiency when using classical unsteady techniques as a transient regime must be bypassed. New techniques, dedicated to time-periodic flows and based on Fourier analysis, have been developed recently. Among these, harmonic balance methods cast a time-periodic flow computation in several coupled steady flow computations. A time-domain harmonic balance method is derived and adapted to phase lag periodic conditions to allow the simulation of only one blade passage per row regardless of row blade counts. Sophisticated space and time interpolations are involved and detailed. The test case is a single stage subsonic compressor. A convergence study of the present harmonic balance is performed and compared with a reference well-resolved classical unsteady flow simulation. The results show, on one hand, the good behavior of the harmonic balance and its ability to correctly predict global quantities as well as local flow pattern; on the other hand, the simulation time is drastically reduced.

scholarly journals A Mixed Shooting – Harmonic Balance Method for Unilaterally Constrained Mechanical Systems

2016 ◽  
Vol 63 (2) ◽  
pp. 297-314 ◽  
Author(s):  
Frederic Schreyer ◽  
Remco I. Leine
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Harmonic Balance ◽  
Degrees Of Freedom ◽  
Shooting Method ◽  
Mechanical Systems ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Constrained Mechanical Systems ◽  
Nonlinear Force

Abstract In this paper we present a mixed shooting – harmonic balance method for large linear mechanical systems on which local nonlinearities are imposed. The standard harmonic balance method (HBM), which approximates the periodic solution in frequency domain, is very popular as it is well suited for large systems with many degrees of freedom. However, it suffers from the fact that local nonlinearities cannot be evaluated directly in the frequency domain. The standard HBM performs an inverse Fourier transform, then calculates the nonlinear force in time domain and subsequently the Fourier coefficients of the nonlinear force. The disadvantage of the HBM is that strong nonlinearities are poorly represented by a truncated Fourier series. In contrast, the shooting method operates in time-domain and relies on numerical time-simulation. Set-valued force laws such as dry friction or other strong nonlinearities can be dealt with if an appropriate numerical integrator is available. The shooting method, however, becomes infeasible if the system has many states. The proposed mixed shooting-HBM approach combines the best of both worlds.

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