Time-Space Spectral Method for Rotor–Rotor/Stator–Stator Interactions

2019 ◽  
Vol 141 (11) ◽  
Author(s):  
Xiuquan Huang ◽  
Ding Xi Wang
Keyword(s):  
Flow Field ◽  
Spectral Method ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Frequency Domain Method ◽  
Test Case ◽  
Flow Solver ◽  
Time Space ◽  
Space Harmonics

Abstract The paper presents a time-space spectral method for an efficient analysis of rotor–rotor/stator–stator interactions in the framework of the time spectral form harmonic balance method. The method treats time and space harmonics in a coherent way and allows for easy choice of time and passage through the introduction of pseudo-shaft frequency and composite frequency. The proposed method can accommodate passage to passage variation of time-averaged flow field and amplitude of unsteady flow field of a given frequency as needed for rotor–rotor/stator–stator interactions. Minimum change is required to extend an existing harmonic balance flow solver to incorporate the proposed method. The proposed method is the most concise and the simplest one of its kind so far. The first three blade rows of a two-stage fan are used as a test case to demonstrate the validity and effectiveness of the proposed method. Numerical results demonstrate the necessity of including rotor–rotor/stator–stator interaction in an analysis using a frequency-domain method and the capability of the proposed method for such a purpose. It is also concluded from the case study that extra spatial and temporal harmonics are needed to adequately analyze a rotor–rotor/stator–stator interaction.

Computing Fluid Structure Interaction Coupling Time Spectral Method (TSM) and Harmonic Balance Method (HBM)

2017 ◽  
Author(s):  
Aude Cadel ◽  
Ghislaine Ngo Boum ◽  
Fabrice Thouverez ◽  
Alain Dugeai ◽  
Marie-Océane Parent
Keyword(s):  
Steady State ◽  
Flow Field ◽  
Spectral Method ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Balance Method ◽  
Integration Scheme ◽  
Fluid Structure ◽  
Time Spectral Method

This paper deals with fluid-structure interactions (FSI), involving a blade profile, submitted to different sources of excitations, as if it were included in a real engine. Two forces of excitation will be considered on the NACA 64A010 airfoil, described in : an external force, due to a forced rotation motion of the blade, and an aerodynamic force, induced by fluid flow around the structure. By using the Harmonic Balance Method, the airfoil’s motion equation becomes an algebraic problem. Then, this system is solved for each frequency of a chosen range. Therefore, the fluid effect on the translation motion of the profile is studied. To compute the time periodic aerodynamic field, the Time Spectral Method, implemented in the Onera’s elsA solver, is used for a fast and efficient resolution. This method relies on a time-integration scheme that turns the resolution of the turbulent Navier-Stokes problem into the resolution of several coupled steady state problems computed at different instants of the time period of the movement. The Theodorsen approach with several hypothesis exposed in allows an analytic estimation of the unsteady lift effort. The two approaches are compared for an imposed motion. In order to predict the dynamic behavior of the system, a fully coupled numerical methodology is developed. For each frequency and at each iteration, TSM supplies the flow field which is used by HBM as a nonlinear excitation on the structure to computate a periodic response and conversely, HBM supplies the new deformed mesh used by TSM to compute the flow field. This strategy has the advantage that all computations take place in the spectral domain, allowing thus to find the steady-state behavior of the fluid and the structure without computing any transient state. The analysis provides the Frequency Forced Response. Some frequencies in the range corresponding to a contribution change between structure and fluid damping are precisely highlighted.

Coupled Time and Passage Spectral Method for an Efficient Resolution of Turbomachinery Far Upstream Wakes

2021 ◽  
pp. 1-17
Author(s):  
Dingxi Wang ◽  
Sen Zhang ◽  
Xiuquan Huang ◽  
Huang Huang
Keyword(s):  
Spectral Method ◽  
Harmonic Balance ◽  
Natural Extension ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Truncated Fourier Series ◽  
Phase Angles ◽  
Numerical Case Study ◽  
Zero Frequency

Abstract The paper proposes a novel numerical method called coupled time and passage spectral method for an efficient resolution of far upstream wakes in an unsteady analysis of flow field within generic multiple blade rows. The proposed method is a very simple and natural extension of the time spectral form harmonic balance method. By including inter-blade phase angle and passage index in a truncated Fourier series, the proposed method is capable of circumventing the limitations of the harmonic balance method in dealing with zero frequency harmonics and time harmonics with the same frequency but different inter blade phase angles. Different from the harmonic balance method, which seeks solutions at different time instants of the same passage, the coupled spectral method seeks solutions at different passages and time instants. Same as the harmonic balance method, all these solutions are connected via a spectral operator. Coupled time and passage sampling is performed using the modified Gram Schmidt process to choose the time and passage pairs which give the most orthogonal rows of an inverse Fourier transform matrix. The coupled time and passage spectral method requires minimum change to an existing harmonic balance solver. A numerical case study has been provided in the paper to demonstrate the expected capability against the harmonic balance method.

Coupled Time and Passage Spectral Method for an Efficient Resolution of Turbomachinery Far Upstream Wakes

2021 ◽  
Author(s):  
Dingxi Wang ◽  
Sen Zhang ◽  
Xiuquan Huang ◽  
Huang Huang
Keyword(s):  
Spectral Method ◽  
Harmonic Balance ◽  
Natural Extension ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Truncated Fourier Series ◽  
Phase Angles ◽  
Numerical Case Study ◽  
Zero Frequency

Abstract The paper proposes a novel numerical method called coupled time and passage spectral method for an efficient resolution of far upstream wakes in an unsteady analysis of flow field within generic multiple blade rows. The proposed method is a very simple and natural extension of the time spectral form harmonic balance method. By including inter blade phase angle and passage index in a truncated Fourier series, the proposed method is capable of circumventing the limitations of the harmonic balance method in dealing with zero frequency harmonics and time harmonics with same frequency but different inter blade phase angles. Different from the harmonic balance method, which seeks solution at different time instants of the same passage, the coupled spectral method seeks solutions at different passages and time instants. Same as the harmonic balance method, all these solutions are connected via a spectral operator. Coupled time and passage sampling is performed using the modified Gram Schmidt process to choose the time and passage pairs which give the most orthogonal rows of an inverse Fourier transform matrix. The coupled time and passage spectral method requires minimum change to an existing harmonic balance solver. A numerical case study has been provided in the paper to demonstrate the expected capability against the harmonic balance method.

Analysis of Transonic Bladerows With Non-Uniform Geometry Using Spectral Method

2020 ◽  
Author(s):  
Feng Wang ◽  
Luca di Mare
Keyword(s):  
Flow Field ◽  
Spectral Method ◽  
Computational Cost ◽  
Leading Edge ◽  
Wave Number ◽  
Efficient Tool ◽  
Flow Solver ◽  
Engine Order ◽  
Harmonic Flow ◽  
Good Agreement

Abstract Turbomachinery blade rows can have non-uniform geometries due to design intent, manufacture errors or wear. When predictions are sought for the effect of such non-uniformities, it is generally the case that whole assembly calculations are needed. A spectral method is used in this paper to approximate the flow fields of the whole assembly but with significantly less computation cost. The method projects the flow perturbations due to the geometry non-uniformity in an assembly in Fourier space, and only one passage is required to compute the flow perturbations corresponding to a certain wave-number of geometry variation. The performance of this method on transonic blade rows is demonstrated on a modern fan assembly. Low engine order and high engine order geometry non-uniformity (e.g. “saw-tooth” pattern) are examined. The non-linear coupling between the flow perturbations and the passage-averaged flow field is also demonstrated. Pressure variations on the blade surface and the potential flow field upstream of the leading edge from the proposed spectral method and the direct whole assembly solutions are compared. Good agreement is observed on both quasi-3D and full 3D cases. A lumped approach to compute deterministic fluxes is also proposed to further reduce the computational cost of the spectral method. The spectral method is formulated in such a way that it can be easily implemented into an existing harmonic flow solver by adding an extra source term, and can be potentially used as an efficient tool for aeromechanical and aeroacoustics design of turbomachinery blade rows.

On the Use of the Automatic Differentiation for Developing a Linear Harmonic Solver

2018 ◽  
Author(s):  
Wei Zhang ◽  
Dingxi Wang ◽  
Xiuquan Huang ◽  
Tianxiao Yang ◽  
Hong Yan ◽  
...  
Keyword(s):  
Harmonic Balance ◽  
Automatic Differentiation ◽  
Harmonic Balance Method ◽  
Source Codes ◽  
Reverse Mode ◽  
Frequency Domain Methods ◽  
The Cost ◽  
Time Periodic ◽  
Small Disturbances

The linear and nonlinear harmonic methods are efficient frequency domain methods for analyzing time periodic unsteady flow fields. They have been widely used in both academia and industry. But the cost and complexity of developing a linear harmonic solver has been limiting its wider applications. On the other hand, the automatic differentiation (AD) has long been used in the CFD community with a focus on generating adjoint codes in a reverse mode. All those AD tools can do a much better job in generating linearized codes in a tangent mode, but so far very little, if any, attention is paid to using AD for developing linear harmonic solvers. The linear harmonic method, in comparison with the harmonic balance method, has its own advantages. For example, it can capture small disturbances very effectively, and avoids aliasing errors which can lead to solution instability since each wave component is solved for separately. This paper presents the effort of using an AD tool to generate major source codes for the development of a linear harmonic solver for analyzing time periodic unsteady flows. It includes the procedures and advice of using AD for such a purpose. A case study is also presented to validate the developed linear harmonic solver.

ANALYSIS OF TRANSONIC BLADEROWS WITH NON-UNIFORM GEOMETRY USING SPECTRAL METHOD

2021 ◽  
pp. 1-27
Author(s):  
Feng Wang ◽  
Luca di Mare
Keyword(s):  
Flow Field ◽  
Spectral Method ◽  
Computational Cost ◽  
Leading Edge ◽  
Wave Number ◽  
Efficient Tool ◽  
Flow Solver ◽  
Engine Order ◽  
Harmonic Flow ◽  
Good Agreement

Abstract Turbomachinery blade rows can have non-uniform geometries due to design intent, manufacture errors or wear. When predictions are sought for the effect of such non-uniformities, it is generally the case that whole assembly calculations are needed. A spectral method is used in this paper to approximate the flow fields of the whole assembly but with significantly less computation cost. The method projects the flow perturbations due to the geometry non-uniformity in an assembly in Fourier space. Only one passage is required to compute the flow perturbations corresponding to a certain wave-number of geometry variation. The performance of this method on transonic blade rows is demonstrated on a modern fan assembly. Low and high engine order geometry non-uniformity (e.g. “saw-tooth” pattern) are examined. The non-linear coupling between the flow perturbations and the passage-averaged flow field is also demonstrated. Pressure variations on the blade surface and the potential flow field upstream of the leading edge from the proposed method and the direct whole assembly solutions are compared. Good agreement is observed on both quasi-3D and full 3D cases. A lumped approach to compute deterministic fluxes is also proposed to further reduce the computational cost of the spectral method. The spectral method is formulated in such a way that it can be easily implemented into an existing harmonic flow solver by adding an extra source term, and can be used as an efficient tool for aeromechanical and aeroacoustics design of turbomachinery blade rows.

scholarly journals Numerical simulation of the non-uniform flow in a full-annulus multi-stage axial compressor with the harmonic balance method

2020 ◽  
Vol 12 (3) ◽  
pp. 168781401989721 ◽  
Author(s):  
Haiou Sun ◽  
Meng Wang ◽  
Zhongyi Wang ◽  
Song Wang ◽  
Franco Magagnato
Keyword(s):  
Flow Field ◽  
Harmonic Balance ◽  
Axial Compressor ◽  
Harmonic Balance Method ◽  
Internal Flow ◽  
Uniform Flow ◽  
Experimental Results ◽  
Balance Method ◽  
Operating Characteristics ◽  
Multi Stage

To improve the understanding of unsteady flow in modern advanced axial compressor, unsteady simulations on full-annulus multi-stage axial compressor are carried out with the harmonic balance method. Since the internal flow in turbomachinery is naturally periodic, the harmonic balance method can be used to reduce the computational cost. In order to verify the accuracy of the harmonic balance method, the numerical results are first compared with the experimental results. The results show that the internal flow field and the operating characteristics of the multi-stage axial compressor obtained by the harmonic balance method coincide with the experimental results with the relative error in the range of 3%. Through the analysis of the internal flow field of the axial compressor, it can be found that the airflow in the clearance of adjacent blade rows gradually changes from axisymmetric to non-axisymmetric and then returns to almost completely axisymmetric distribution before the downstream blade inlet, with only a slight non-axisymmetric distribution, which can be ignored. Moreover, the slight non-axisymmetric distribution will continue to accumulate with the development of the flow and, finally, form a distinct circumferential non-uniform flow field in latter stages, which may be the reason why the traditional single-passage numerical method will cause certain errors in multi-stage axial compressor simulations.

Analysis of the Unsteady Flow in an Aspirated Counter-Rotating Compressor Using the Nonlinear Harmonic Method

2009 ◽  
Author(s):  
Emanuele Guidotti ◽  
Mark G. Turner
Keyword(s):  
Flow Field ◽  
Unsteady Flow ◽  
Frequency Domain ◽  
Navier Stokes ◽  
Test Case ◽  
Numerical Accuracy ◽  
Flow Solver ◽  
Harmonic Method ◽  
Flow Change ◽  
Inlet Boundary Condition

A multistage frequency domain (Nonlinear Harmonic) Navier-Stokes unsteady flow solver has been used to analyze the flow field in the MIT (rotor/rotor) aspirated counter-rotating compressor. The numerical accuracy and computational efficiency of the Nonlinear Harmonic method implemented in Numeca’s Fine/Turbo CFD code has been demonstrated by comparing predictions with experimental data and nonlinear time-accurate solutions for the test case. The comparison is good, especially considering the big savings in time with respect to a time accurate simulation. An imposed inlet boundary condition takes into account the flow change due to the IGV (not simulated in the computational model). Details of the flow field are presented and physical explanations are provided. Also, suggestions and recommendations on the use of the Nonlinear Harmonic method are provided. From this work it can be concluded that the development of efficient frequency domain approaches enables routine unsteady flow predictions to be used in the design of modern turbomachinery.

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.

A Harmonic Balance Technique for Multistage Turbomachinery Applications

2014 ◽  
Author(s):  
Christian Frey ◽  
Graham Ashcroft ◽  
Hans-Peter Kersken ◽  
Christian Voigt
Keyword(s):  
Harmonic Balance ◽  
Simulation Method ◽  
Minor Role ◽  
Frequency Domain Method ◽  
Nonlinear Frequency ◽  
Flow Solver ◽  
Fundamental Frequencies ◽  
Interaction Terms ◽  
A Minor ◽  
The Impact

This article describes a nonlinear frequency domain method for the simulation of unsteady blade row interaction problems across several blade rows in turbomachinery. The capability to efficiently simulate such interactions is crucial for the improvement of the prediction of blade vibrations, tonal noise, and the impact of unsteadiness on aerodynamic performance. The simulation technique presented here is based on the harmonic balance approach and has been integrated into an existing flow solver. A nontrivial issue in the application of harmonic balance methods to turbomachinery flows is the fact that various fundamental frequencies may occur simultaneously in one relative system, each one being due to the interaction of two blade rows. It is shown that, considering the disturbances corresponding to different fundamental frequencies as mutually uncoupled, one can develop an unsteady simulation method which from a practial view point turns out to be highly attractive. On the one hand, it is possible to take into account arbitrarily many nonlinear interaction terms. On the other, the computational efficiency can be increased considerably once it is known that the nonlinear coupling between certain subsets of the harmonics plays only a minor role. To validate the method and demonstrate its accuracy and efficiency a multistage compressor configuration is simulated using both the method described in this article and a conventional time-domain solver.

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