Implementation of dual time-stepping strategy of the gas-kinetic scheme for unsteady flow simulations

This paper studies different acceleration techniques for unsteady flow calculations. The results are compared with a non-accelerated, fully-explicit solution in terms of time-averaged pressure distributions, the unsteady pressure and entropy in the frequency domain and the skin friction factor. The numerical method solves the unsteady three-dimensional Navier-Stokes equations via an explicit time-stepping procedure. The flow in the first stage of a modern industrial gas turbine is chosen as a test case. After a description of the numerical method used for the simulation, the test case is introduced. The comparison of the different numerical algorithms for explicit schemes is intended to ease the decision about which acceleration technique to use for calculations as far as accuracy and computational time are concerned. The convergence acceleration methods under consideration are, respectively, explicit time-stepping with implicit residual averaging, explicit time-consistent multigrid and implicit dual time stepping. The investigation and comparison of the different acceleration techniques are applicable to all explicit unsteady flow solvers. As another point of interest, the influence of the stage blade count ratio on the flow field is investigated. For this purpose, a simulation with a stage pitch ratio of unity is compared with a calculation using the real ratio of 78:80, which requires a more sophisticated method for periodic boundary condition treatment. This paper should help to decide whether it is vital from the turbine designer’s point of view to model the real pitch ratio in unsteady flow simulations in turbine stages.

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Comparison of Different Acceleration Techniques and Methods for Periodic Boundary Treatment in Unsteady Turbine Stage Flow Simulations

Journal of Turbomachinery ◽

10.1115/1.555440 ◽

1999 ◽

Vol 122 (2) ◽

pp. 234-246 ◽

Cited By ~ 3

Author(s):

Martin von Hoyningen-Huene ◽

Alexander R. Jung

Keyword(s):

Unsteady Flow ◽

Numerical Method ◽

Periodic Boundary ◽

Computational Time ◽

Test Case ◽

The Real ◽

Flow Simulations ◽

Time Stepping ◽

Acceleration Techniques ◽

Pitch Ratio

This paper studies different acceleration techniques for unsteady flow calculations. The results are compared with a nonaccelerated, fully explicit solution in terms of time-averaged pressure distributions, the unsteady pressure and entropy in the frequency domain, and the skin friction factor. The numerical method solves the unsteady three-dimensional Navier–Stokes equations via an explicit time-stepping procedure. The flow in the first stage of a modern industrial gas turbine is chosen as a test case. After a description of the numerical method used for the simulation, the test case is introduced. The purpose of the comparison of the different numerical algorithms for explicit schemes is to facilitate the decision as to which acceleration technique should be used for calculations with regard to accuracy and computational time. The convergence acceleration methods under consideration are explicit time-stepping with implicit residual averaging, explicit time-consistent multigrid, and implicit dual time stepping. The investigation and comparison of the different acceleration techniques apply to all explicit unsteady flow solvers. This paper also examines the influence of the stage blade count ratio on the flowfield. For this purpose, a simulation with a stage pitch ratio of unity is compared with a calculation using the real ratio of 78:80, which requires a more sophisticated method for periodic boundary condition treatment. This paper should help to decide whether it is crucial from the turbine designer’s point of view to model the real pitch ratio in unsteady flow simulations in turbine stages. [S0889-504X(00)00702-9]

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Code Verification for Unsteady Flow Simulations with High Order Time-Stepping Schemes

47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition ◽

10.2514/6.2009-169 ◽

2009 ◽

Cited By ~ 6

Author(s):

Stephane Etienne ◽

Andre Garon ◽

Dominique Pelletier

Keyword(s):

Unsteady Flow ◽

High Order ◽

Code Verification ◽

Flow Simulations ◽

Time Stepping ◽

High Order Time

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Rotor Cascade Shape Optimization with Unsteady Passing Wakes Using Implicit Dual-Time Stepping and a Genetic Algorithm

International Journal of Rotating Machinery ◽

10.1155/s1023621x03000332 ◽

2003 ◽

Vol 9 (5) ◽

pp. 353-361 ◽

Cited By ~ 1

Author(s):

Eun Seok Lee ◽

George S. Dulikravich ◽

Brian H. Dennis

Keyword(s):

Genetic Algorithm ◽

Unsteady Flow ◽

Shape Optimization ◽

Objective Function ◽

Stokes Equations ◽

Leading Edge ◽

Geometric Parameters ◽

Time Stepping ◽

Acceleration Techniques ◽

Dual Time Stepping

An axial turbine rotor cascade-shape optimization with unsteady passing wakes was performed to obtain an improved aerodynamic performance using an unsteady flow, Reynolds-averaged Navier-Stokes equations solver that was based on explicit, finite difference; Runge-Kutta multistage time marching; and the diagonalized alternating direction implicit scheme. The code utilized Baldwin-Lomax algebraic andk-εturbulence modeling. The full approximation storage multigrid method and preconditioning were implemented as iterative convergence-acceleration techniques. An implicit dual-time stepping method was incorporated in order to simulate the unsteady flow fields. The objective function was defined as minimization of total pressure loss and maximization of lift, while the mass flow rate was fixed during the optimization. The design variables were several geometric parameters characterizing airfoil leading edge, camber, stagger angle, and inter-row spacing. The genetic algorithm was used as an optimizer, and the penalty method was introduced for combining the constraints with the objective function. Each individual's objective function was computed simultaneously by using a 32-processor distributedmemory computer. The optimization results indicated that only minor improvements are possible in unsteady rotor/stator aerodynamics by varying these geometric parameters.

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Application of Harmonic Balance Method to Numerical Model Unsteady Viscous Flow around Oscillating Cascade

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.50-51.583 ◽

2011 ◽

Vol 50-51 ◽

pp. 583-588

Author(s):

Yong Qiang Shi ◽

Qing Zhen Yang ◽

Xin Hai Zhou

Keyword(s):

Unsteady Flow ◽

Harmonic Balance ◽

Present Method ◽

Oscillation Amplitude ◽

Harmonic Balance Method ◽

Hysteresis Effect ◽

Balance Method ◽

Time Stepping ◽

Reduced Frequency ◽

Dual Time Stepping

A harmonic balance approach has been developed to compute nonlinear viscous unsteady flows around oscillating blades. The computed results using two orders harmonic balance method are compared with those by conventional dual-time stepping method. Results obtained with the present method agree well with those from dual-time stepping method, which demonstrate the ability of the present analysis method to model accurately the unsteady flow. Furthermore，the present method is highly efficient. It is about 36 times fast than conventional dual-time stepping method in the present computation. Then the effects of oscillation amplitude and reduced frequency on unsteadiness of flows are studied. The analysis exploits the fact that, (1) the hysteresis effect of unsteady flow is hardly affected by oscillation amplitude, but the first harmonic unsteady pressure across the blade is proportional to oscillation amplitude; (2) the higher the reduced frequency, the wider the range of unsteady aerodynamic forces, the more intense the hysteresis effect.

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Investigation of the Unsteady Flow for the Supersonic Jet Element

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.201-203.2178 ◽

2011 ◽

Vol 201-203 ◽

pp. 2178-2181 ◽

Cited By ~ 1

Author(s):

Yong Xu ◽

Guo Qing Zhang ◽

Fei Wang

Keyword(s):

Unsteady Flow ◽

Viscous Flow ◽

Supersonic Jet ◽

Unsteady Flows ◽

Time Stepping ◽

Dual Time Stepping ◽

Unsteady Viscous Flow ◽

Thrust Fluctuation

The unsteady viscous flow of the supersonic jet element (SJE) was simulated numerically based on CFD technology. A dual time-stepping scheme and AMG scheme were employed to solve the unsteady flows in SJE, and the reasons of thrust fluctuation during the wall-attachment state of SJE are found out. Based on the pressure cloud and streamlines, the vortices generated by the unsteady flow on attached wall had also been investigated and drawn some conclusions.

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Application of Dual Time Stepping to Fully Implicit Runge Kutta Schemes for Unsteady Flow Calculations

22nd AIAA Computational Fluid Dynamics Conference ◽

10.2514/6.2015-2753 ◽

2015 ◽

Cited By ~ 5

Author(s):

Antony Jameson

Keyword(s):

Unsteady Flow ◽

Time Stepping ◽

Fully Implicit ◽

Dual Time Stepping ◽

Runge Kutta

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Investigation of Unsteady Flow in an Axial Compression Based on Double Times Dual Time Stepping

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.757.29 ◽

2015 ◽

Vol 757 ◽

pp. 29-32 ◽

Cited By ~ 1

Author(s):

Fang Xie ◽

Wu Li Chu ◽

Hai Xia Du ◽

Kai Zhou

Keyword(s):

Unsteady Flow ◽

Axial Compression ◽

Leakage Flow ◽

Tip Leakage Flow ◽

Time Step ◽

Tip Leakage ◽

Time Stepping ◽

Dual Time Stepping

A numerical investigate of unsteady (rotor 37) based on dual time step is carried out .Results were used to identify the existence of an interface between the approach fluid and the tip-leakage flow. This paper discusses mechanism of spike stall.

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