Predicting Bladerow Interactions Using a Multistage Time-Linearized Navier-Stokes Solver

2002 ◽  
Author(s):  
W. Ning ◽  
Y. S. Li ◽  
R. G. Wells
Keyword(s):  
Unsteady Flow ◽  
Frequency Domain ◽  
Test Data ◽  
Computational Efficiency ◽  
Unsteady Flows ◽  
Navier Stokes ◽  
Test Cases ◽  
Numerical Accuracy ◽  
Flow Solver ◽  
Time Marching

A multistage frequency domain (time-linearized/nonlinear harmonic) Navier-Stokes unsteady flow solver has been developed for predicting unsteady flows induced by bladerow interactions. In this paper, the time-linearized option of the solver has been used to analyze unsteady flows in a subsonic turbine test stage and the DLR transonic counter-rotating shrouded propfan. The numerical accuracy and computational efficiency of the time-linearized viscous methods have been demonstrated by comparing predictions with test data and nonlinear time-marching solutions for these two test cases. It is concluded that the development of efficient frequency domain approaches enables unsteady flow predictions to be used in the design cycles to tackle aeromechanics problems.

Predicting Bladerow Interactions Using a Multistage Time-Linearized Navier-Stokes Solver

2003 ◽  
Vol 125 (1) ◽  
pp. 25-32 ◽  
Author(s):  
W. Ning ◽  
Y. S. Li ◽  
R. G. Wells
Keyword(s):  
Unsteady Flow ◽  
Frequency Domain ◽  
Test Data ◽  
Computational Efficiency ◽  
Unsteady Flows ◽  
Navier Stokes ◽  
Test Cases ◽  
Numerical Accuracy ◽  
Flow Solver ◽  
Time Marching

A multistage frequency domain (time-linearized/nonlinear harmonic) Navier-Stokes unsteady flow solver has been developed for predicting unsteady flows induced by bladerow interactions. In this paper, the time-linearized option of the solver has been used to analyze unsteady flows in a subsonic turbine test stage and the DLR transonic counter-rotating shrouded propfan. The numerical accuracy and computational efficiency of the time-linearized viscous methods have been demonstrated by comparing predictions with test data and nonlinear time-marching solutions for these two test cases. It is concluded that the development of efficient frequency domain approaches enables unsteady flow predictions to be used in the design cycles to tackle aeromechanics problems.

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.

Grid adaptation for unsteady flow computations

1997 ◽  
Vol 211 (4) ◽  
pp. 237-250 ◽  
Author(s):  
C B Allen
Keyword(s):  
Unsteady Flow ◽  
Unsteady Flows ◽  
Processing Unit ◽  
Flow Solver ◽  
Transfinite Interpolation ◽  
Central Processing ◽  
Grid Adaptation ◽  
Euler Flows ◽  
Adaptation Procedure ◽  
Grid Points

A grid adaptation procedure suitable for use during unsteady flow computations is described. Transfinite interpolation is used to generate structured grids for the computation of steady and unsteady Euler flows past aerofoils. This technique is well suited to unsteady flows, since instantaneous grid positions and speeds required by the flow solver are available directly from the algebraic mapping. A different approach to grid adaptation is described, wherein adaptation is performed by redistributing the interpolation parameters, instead of the physical grid positions. This results in the adapted grid positions, and hence speeds, still being available algebraically. Grid adaptation during an unsteady computation is performed continuously by imposing an ‘adaptation velocity’ on grid points, thereby applying the adaptation over several time steps and avoiding the interpolation of the solution from one grid to another, which is associated with instantaneous adaptation. For both steady and unsteady flows the adapted grid technique is shown to produce sharper shock resolution for a very small increase in CPU (central processing unit) requirements.

Simulating Periodic Unsteady Flows Using Cubic-Spline Based Time Collocation Method

2013 ◽  
Author(s):  
Pengcheng Du ◽  
Fangfei Ning
Keyword(s):  
Collocation Method ◽  
Stokes Equations ◽  
Differential Quadrature Method ◽  
Unsteady Flows ◽  
Cubic Spline ◽  
Navier Stokes ◽  
Transonic Compressor ◽  
Compressor Rotor ◽  
Time Marching ◽  
Flow Variables

Time periodical unsteady flows are typical in turbomachinery. Simulating such flows using conventional time marching approach is most accurate but extremely time consuming. In order to achieve a better balance between accuracy and computational expenses, a cubic-spline based time collocation method is proposed. In this method, the time derivatives in the Navier-Stokes equations are obtained by using the differential quadrature method, in which the periodical flow variables are approximated by cubic-splines. Thus, the computation of a time-periodical flow is substituted by several coupled quasi-steady flow computations at sampled instants. The proposed method is then validated against several typical turbomachinery periodical unsteady flows, i.e., transonic compressor rotor flows under circumferential inlet distortions, single stage rotor-stator interactions and IGV-rotor interactions. The results show that the proposed cubic-spline based time collocation method with appropriate time sampling can well resolve the dominant unsteady effects, whilst the computational expenses are kept much less than the traditional time-marching simulation. More importantly, this paper provides a framework on the basis of time collocation method in which one may choose more compatible test functions for the concerned specific unsteady flows so that the better modeling of the flows can be expected.

Numerical Solution of Incompressible Unsteady Flows in Turbomachinery

2000 ◽  
Vol 123 (3) ◽  
pp. 680-685 ◽  
Author(s):  
L. He ◽  
K. Sato
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Time Stepping ◽  
Incompressible Viscous Flow ◽  
Dual Time Stepping

A three-dimensional incompressible viscous flow solver of the thin-layer Navier-Stokes equations was developed for the unsteady turbomachinery flow computations. The solution algorithm for the unsteady flows combines the dual time stepping technique with the artificial compressibility approach for solving the incompressible unsteady flow governing equations. For time accurate calculations, subiterations are introduced by marching the equations in the pseudo-time to fully recover the incompressible continuity equation at each real time step, accelerated with a multi-grid technique. Computations of test cases show satisfactory agreements with corresponding theoretical and experimental results, demonstrating the validity and applicability of the present method to unsteady incompressible turbomachinery flows.

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.

Simulating Periodic Unsteady Flows Using a Cubic-Spline-Based Time Collocation Method

2013 ◽  
Vol 136 (4) ◽  
Author(s):  
Pengcheng Du ◽  
Fangfei Ning
Keyword(s):  
Collocation Method ◽  
Stokes Equations ◽  
Differential Quadrature Method ◽  
Unsteady Flows ◽  
Cubic Spline ◽  
Navier Stokes ◽  
Transonic Compressor ◽  
Compressor Rotor ◽  
Time Marching ◽  
Flow Variables

Time-periodical unsteady flows are typical in turbomachinery. Simulating such flows using a conventional time marching approach is the most accurate but is extremely time consuming. In order to achieve a better balance between accuracy and computational expenses, a cubic-spline-based time collocation method is proposed. In this method, the time derivatives in the Navier–Stokes equations are obtained by using the differential quadrature method, in which the periodical flow variables are approximated by cubic splines. Thus, the computation of a time-periodical flow is substituted by several coupled quasi-steady flow computations at sampled instants. The proposed method is then validated against several typical turbomachinery periodical unsteady flows, i.e., transonic compressor rotor flows under circumferential inlet distortions, single stage rotor–stator interactions, and IGV–rotor interactions. The results show that the proposed cubic-spline-based time collocation method with appropriate time sampling can well resolve the dominant unsteady effects, while the computational expenses are kept much less than the traditional time-marching simulation. More importantly, this paper provides a framework on the basis of a time collocation method in which one may choose more compatible test functions for the concerned specific unsteady flows so that better modeling of the flows can be expected.

Application of a Viscous Through-Flow Model to a Modern Axial Low-Pressure Compressor

2021 ◽  
Author(s):  
Arnaud Budo ◽  
Vincent E. Terrapon ◽  
Maarten Arnst ◽  
Koen Hillewaert ◽  
Sophie Mouriaux ◽  
...  
Keyword(s):  
Flow Model ◽  
Three Dimensional ◽  
Test Case ◽  
Test Cases ◽  
Compressor Stage ◽  
Flow Solver ◽  
Closure Models ◽  
Through Flow ◽  
Time Marching ◽  
Pressure Compressor

Abstract This paper describes the evaluation of a newly developed viscous time-marching through-flow solver to two test cases to assess the applicability of the method using correlations from the literature to modern blade designs. The test cases are the classic axial compressor stage CME2 and a modern highly loaded multi-stage axial low-pressure compressor developed by Safran Aero Boosters. The through-flow solver is based on the Navier-Stokes equations and uses a pseudo-time marching method. The closure models currently include terms of major importance: the blade forces and the Reynolds stress. The results are compared to higher-fidelity results including three-dimensional RANS simulations to assess their reliability for design and off-design conditions. The main originality of this work is the evaluation of the CFD-based method in the context of a compressor with highly three-dimensional blades, as such an analysis is not commonly found in the literature. The solver gives realistic predictions of loss and deviation for the compressor stage CME2 at both design and off-design operating conditions. Regarding the second test case, the through-flow simulations based on theoretically non-adapted correlations for such a compressor are still in good agreement with RANS simulations, although the results for the 2nd test case are probably not as good as for the first. These results are a promising first step towards the use of this through-flow model for industrial design. Regarding the ongoing closure models development, suggestions to extend the loss models to a larger range of designs are discussed.

Unsteady flows in a semi-infinite contracting or expanding pipe

1977 ◽  
Vol 82 (2) ◽  
pp. 371-387 ◽  
Author(s):  
Shigeo Uchida ◽  
Hiroshi Aoki
Keyword(s):  
Unsteady Flow ◽  
Unsteady Flows ◽  
Bronchial Tube ◽  
Reynolds Numbers ◽  
Present Theory ◽  
Navier Stokes ◽  
Axial Motion ◽  
Thin Boundary Layer ◽  
Navier Stokes Equation ◽  
Contraction And Expansion

Physiological pumps produce flows by alternate contraction and expansion of the vessel. When muscles start to squeeze its wall the valve at the upstream end is closed and that at the downstream end is opened, and the fluid is pumped out in the downstream direction. These systems can be modelled by a semi-infinite pipe with one end closed by a compliant membrane which prevents only axial motion of the fluid, leaving radial motion completely unrestricted. In the present paper an exact similar solution of the Navier–Stokes equation for unsteady flow is a semi-infinite contracting or expanding circular pipe is calculated and reveals the following characteristics of this type of flow. In a contracting pipe the effects of viscosity are limited to a thin boundary layer attached to the wall, which becomes thinner for higher Reynolds numbers. In an expanding pipe the flow adjacent to the wall is highly retarded and eventually reverses at Reynolds numbers above a critical value. The pressure gradient along the axis of pipe is favourable for a contracting wall, while it is adverse for an expanding wall in most cases. These solutions are valid down to the state of a completely collapsed pipe, since the nonlinearity is retained in full. The results of the present theory may be applied to the unsteady flow produced by a certain class of forced contractions and expansions of a valved vein or a thin bronchial tube.

Nonlinear Separated Inviscid-Viscous Analysis of Oscillating Cascade Aerodynamics Using an Inverse Integral Method

1999 ◽  
Vol 121 (1) ◽  
pp. 134-144
Author(s):  
J. M. Wolff ◽  
S. Fleeter
Keyword(s):  
Boundary Layer ◽  
Unsteady Flow ◽  
Unsteady Aerodynamics ◽  
Interaction Model ◽  
Separated Flow ◽  
Integral Boundary ◽  
Data Set ◽  
Flow Solver ◽  
Time Marching ◽  
Viscous Solutions

A mathematical model is developed to analyze the unsteady flow through an harmonically oscillating cascade of airfoils, including separated flow. The model incorporates an inverse integral boundary layer solution with the time-marching Euler analysis NPHASE. An embedded composite grid formulation is incorporated, specifically a deforming C-grid embedded in a Cartesian H-grid, thereby simplifying grid generation. To reduce computational requirements, Fourier series unsteady periodic boundary conditions are implemented. The integral turbulent boundary layer model is closed with steady correlations adopted in a quasi-steady manner. To couple the inviscid and viscous solutions, the viscous effect is modeled in the unsteady Euler solution in a quasi-steady manner by a transpiration boundary condition. An isolated airfoil is used to compare the steady interaction model with experimental data. Then a flat plate cascade is used to verify the unsteady flow solver with linear theory predictions. An experimental unsteady aerodynamics data set of a loaded cascade with separated meanflow executing torsional oscillations compared favorably with the analysis. The code is then utilized to study the effect of flow separation on the unsteady aerodynamics.

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