Development of an Edge-Based Harmonic Balance Method for Turbomachinery Flows

2011 ◽  
Author(s):  
Roque Corral ◽  
Javier Crespo
Keyword(s):  
Harmonic Balance ◽  
Stokes Equations ◽  
Computational Cost ◽  
Harmonic Balance Method ◽  
Convergence Acceleration ◽  
Balance Method ◽  
Navier Stokes ◽  
Acceleration Techniques ◽  
Edge Based ◽  
The Time Domain

An harmonic balance method for modeling unsteady nonlinear periodic flows in turbomachinery is presented. The method solves the Reynolds Averaged Navier-Stokes equations in the time domain and may be implemented in a relatively simple way into an existing code including all the standard convergence acceleration techniques used for steady problems. The application of the method to vibrating airfoils and rotorstator interaction is discussed. It is demonstrated that the time spectral scheme may achieve the same temporal accuracy at a lower computational cost at the expense of using more memory.

An Implicit Harmonic Balance Method in Graphics Processing Units for Vibrating Blades

2015 ◽  
Author(s):  
Javier Crespo ◽  
Roque Corral ◽  
Jesus Pueblas
Keyword(s):  
Finite Difference ◽  
Harmonic Balance ◽  
Graphics Processing Units ◽  
Stokes Equations ◽  
Computational Cost ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Transonic Compressor ◽  
Speed Up ◽  
Graphics Processing

An implicit harmonic balance method for modeling the unsteady non-linear periodic flow about vibrating airfoils in turbomachinery is presented. As departing point, an implicit edge-based three-dimensional Reynolds Averaged Navier-Stokes equations solver for unstructured grids that runs both on central processing units (CPUs) and graphics processing units (GPUs) is used. The harmonic balance method performs a spectral discretization of the time derivatives and marches in pseudo-time a new system of equations where the unknowns are the variables at different time samples. The application of the method to vibrating airfoils is discussed. It is shown that a time spectral scheme may achieve the same temporal accuracy at a much lower computational cost than a Backward Finite Difference method at the expense of using more memory. The performance of the implicit solver has been assessed with several application examples. A speed-up factor of 10 is obtained between the spectral and finite difference version of the code whereas and an additional speed-up factor of 10 is obtained when the code is ported to GPUs, totalizing a speed factor of 100. The performance of the solver in GPUs has been assessed using the 10th standard aeroelastic configuration and a transonic compressor.

scholarly journals Implementation and Validation of the Harmonic Balance Method for Temporally Periodic Non–Linear Flows

2016 ◽  
Author(s):  
Hrvoje Jasak ◽  
Gregor Cvijetić
Keyword(s):  
Harmonic Balance ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Navier Stokes ◽  
Scalar Case ◽  
Test Cases ◽  
Navier Stokes Equations ◽  
Non Linear

An efficient method for tackling non-linear, temporally–periodic incompressible flows is presented in this paper. Assuming temporally fully periodic flow, Harmonic Balance method deploys Fourier transformation in order to formulate transient problem as a multiple quasi-steady state problems. The method is implemented in OpenFOAM and developed for a general transport equation and incompressible Navier–Stokes equations. Validation is presented on three test cases: oscillating scalar case for scalar transport validation, a flow around a 2D NACA airfoil and a 3D Onera M6 wing for turbulent incompressible Navier–Stokes validation. For all test cases Harmonic Balance results are compared to transient simulation results. Verification of the model is performed by changing the number of harmonics for all test cases.

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.

Simulation of Unsteady Turbomachinery Flows Using an Implicitly Coupled Nonlinear Harmonic Balance Method

2011 ◽  
Author(s):  
Jonathan M. Weiss ◽  
Venkataramanan Subramanian ◽  
Kenneth C. Hall
Keyword(s):  
Steady State ◽  
Harmonic Balance ◽  
Time Derivative ◽  
Computational Cost ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Computationally Efficient ◽  
State Equations ◽  
Approximate Factorization ◽  
Efficient Manner

A nonlinear harmonic balance method for the simulation of turbomachinery flows is presented. The method is based on representing an unsteady, time periodic flow by a Fourier series in time and then solving a set of mathematically steady-state equations to obtain the Fourier coefficients. The steady-state solutions are stored at discrete time levels distributed throughout one period of unsteadiness and are coupled via the physical time derivative and at periodic boundaries. Implicit coupling between time levels is achieved in a computationally efficient manner through approximate factorization of the linear system that results from the discretized equations. Unsteady, rotor-stator interactions are performed to validate the implementation. Results based on the harmonic balance method are compared against those obtained using a full unsteady, time-accurate calculation using moving meshes. The implicitly coupled nonlinear harmonic balance method is shown to produce a solution of reasonable accuracy compared to the full unsteady approach but with significantly less computational cost.

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.

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.

An Implicit Harmonic Balance Method in Graphics Processing Units for Oscillating Blades

2015 ◽  
Vol 138 (3) ◽  
Author(s):  
Javier Crespo ◽  
Roque Corral ◽  
Jesus Pueblas
Keyword(s):  
Finite Difference ◽  
Harmonic Balance ◽  
Graphics Processing Units ◽  
Stokes Equations ◽  
Computational Cost ◽  
Harmonic Balance Method ◽  
Transonic Compressor ◽  
Central Processing ◽  
Speed Up ◽  
Graphics Processing

An implicit harmonic balance (HB) method for modeling the unsteady nonlinear periodic flow about vibrating airfoils in turbomachinery is presented. An implicit edge-based three-dimensional Reynolds-averaged Navier–Stokes equations (RANS) solver for unstructured grids, which runs both on central processing units (CPUs) and graphics processing units (GPUs), is used. The HB method performs a spectral discretization of the time derivatives and marches in pseudotime, a new system of equations where the unknowns are the variables at different time samples. The application of the method to vibrating airfoils is discussed. It is shown that a time-spectral scheme may achieve the same temporal accuracy at a much lower computational cost than a backward finite-difference method at the expense of using more memory. The performance of the implicit solver has been assessed with several application examples. A speed-up factor of 10 is obtained between the spectral and finite-difference version of the code, whereas an additional speed-up factor of 10 is obtained when the code is ported to GPUs, totalizing a speed factor of 100. The performance of the solver in GPUs has been assessed using the tenth standard aeroelastic configuration and a transonic compressor.

Sign in / Sign up

Export Citation Format

Share Document