A multi-dimensional high-order discontinuous Galerkin method based on gas kinetic theory for viscous flow computations

Ren, Xiaodong; Xu, Kun; Shyy, Wei; Gu, Chunwei

doi:10.1016/j.jcp.2015.03.031

Cited by 49 publications

(28 citation statements)

References 21 publications

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“…This result indicates that cells of low Mach number in shock do have obvious effect on MIM and shock instability. [27,28], WENO (the weighted essentially nonoscillatory scheme) [29,30], and DG (the discontinuous Galerkin) methods [31][32][33]. Therefore, the compatibility of preceding improvement and high-order reconstruction should be discussed.…”

Section: Computational Object and Methodsmentioning

confidence: 99%

Role of the momentum interpolation mechanism of the Roe scheme in shock instability

Ren

2016

Numerical Methods in Fluids

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Summary The shock instability phenomenon is a well‐known problem for hypersonic flow computation by the shock‐capturing Roe scheme. The pressure checkerboard is another well‐known problem for low‐Mach‐number flow computation. The momentum interpolation method (MIM) is necessary for low‐Mach‐number flows to suppress the pressure checkerboard problem, and the pressure‐difference‐driven modification for cell face velocity can be regarded as a version of the MIM by subdividing the numerical dissipation of the Roe scheme. In this paper, MIM has been discovered through analysis and numerical tests to have the most important function in shock instability. MIM should be completely removed for nonlinear flows. However, the unexpected MIM is activated on the cell face nearly parallel to the flow for the high‐Mach‐number flows or low‐Mach‐number cells in numerical shock. Therefore, MIM should be retained for low‐Mach‐number flows and be completely removed for high‐Mach‐number flows and low‐Mach‐number cells in numerical shock. For such conditions, two coefficients are designed on the basis of the local Mach number and a shock detector. Thereafter, the improved Roe scheme is proposed. This scheme considers the requirement of MIM for incompressible and compressible flows, and is validated for good performance of numerical tests. An acceptable result can also be obtained with only the Mach number coefficient for general practical computation. Therefore, the objective of decreasing rather than increasing numerical dissipation to cure shock instability can be achieved with simple modification. Moreover, the mechanism of shock instability has been profoundly understood, in which MIM plays the most important role, although it is not the only factor. Copyright © 2016 John Wiley & Sons, Ltd.

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Section: Computational Object and Methodsmentioning

confidence: 99%

Role of the momentum interpolation mechanism of the Roe scheme in shock instability

Ren

2016

Numerical Methods in Fluids

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“…The numerical simulation method is widely applied to evaluate the turbine performance [20,21]. The 3D steadystate numerical simulations in this research were performed using ANSYS CFX [19].…”

Section: Turbine-performance Evaluationmentioning

confidence: 99%

Three-dimensional optimal design of a cooled turbine considering the coolant-requirement change

Wang

et al. 2019

Open Physics

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Cooling technology is widely applied in modern turbines to protect the turbine blades, and extracting high-pressure cooling air from a compressor exerts a remarkable influence on the gas-turbine performance. However, the three-dimensional optimal design of a turbine in modern industrial practice is usually carried out by pursuing high component efficiency without considering possible changes in coolant requirement; hence, it may not exactly lead to improvement in the gas-turbine cycle efficiency. In this study, the turbine stator was twisted and leaned to achieve higher comprehensive efficiency, which is the cycle-based efficiency definition for a cooled turbine that considers both turbine aerodynamic performance and coolant requirement. First, the influence of twist and compound lean on turbine aerodynamic performance, considering stator-hub leakage, was investigated. Then, a method to predict the coolant requirement for turbines with different stator designs was applied, to evaluate coolant-requirement change at the design condition. The optimized turbines were finally compared to demonstrate the necessity of considering the coolant-requirement change in the optimal design. This indicated that proper twisting to open the throat area in the stator hub and compound lean to the pressure surface side could help improve the cooled-turbine comprehensive efficiency.

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“…A positive bow is defined as a positive lean angle at the hub and a negative lean angle at the shroud in comparison with a normal, radially stacked straight blade [18]. It is well acknowledged that the bow is broadly adopted to eliminate corner stall in compressor vanes [17,18]. The bow induces radial forces on the fluids and results in shifting the fluids from the end walls to the midspan, which can reduce endwall loading and postpone the tendency towards corner stall.…”

Section: Bowmentioning

confidence: 99%

Aerodynamic Analysis and Three-Dimensional Redesign of a Multi-Stage Axial Flow Compressor

Tao

et al. 2016

Energies

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This paper describes the introduction of three-dimension (3-D) blade designs into a 5-stage axial compressor with multi-stage computational fluid dynamic (CFD) methods. Prior to a redesign, a validation study is conducted for the overall performance and flow details based on full-scale test data, proving that the multi-stage CFD applied is a relatively reliable tool for the analysis of the follow-up redesign. Furthermore, at the near stall point, the aerodynamic analysis demonstrates that significant separation exists in the last stator, leading to the aerodynamic redesign, which is the focus of the last stator. Multi-stage CFD methods are applied throughout the three-dimensional redesign process for the last stator to explore their aerodynamic improvement potential. An unconventional asymmetric bow configuration incorporated with leading edge re-camber and re-solidity is employed to reduce the high loss region dominated by the mainstream. The final redesigned version produces a 13% increase in the stall margin while maintaining the efficiency at the design point.

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A multi-dimensional high-order discontinuous Galerkin method based on gas kinetic theory for viscous flow computations

Cited by 49 publications

References 21 publications

Role of the momentum interpolation mechanism of the Roe scheme in shock instability

Role of the momentum interpolation mechanism of the Roe scheme in shock instability

Three-dimensional optimal design of a cooled turbine considering the coolant-requirement change

Aerodynamic Analysis and Three-Dimensional Redesign of a Multi-Stage Axial Flow Compressor

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