A set of new general unified fluid dynamic equations for arbitrary equation of state

Huang, Daniel; Ke, Hung-Yu; Du, Juan

doi:10.1243/09544062jmes837

Cited by 2 publications

(2 citation statements)

References 7 publications

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“…Three classical turbulent models, namely, Spalart-Allmaras (SA), shear stress transport (SST), and re-normalization group (RNG) k-epsilon, with enhanced wall function turbulence models, are used in this study. An all-speed Roe scheme 32,33 developed from the preconditioned Roe scheme [33][34][35][36] is adopted in the discretization Navier-Stokes equations with essentially weighted non-oscillatory reconstruction methods [37][38][39] for high-order accuracy. Discontinuous Galerkin (DG) method is also considered.…”

Section: Methodsmentioning

confidence: 99%

Numerical investigation of V-shaped riblets and an improved model of riblet effects

Zhang

2017

Proceedings of the Institution of Mechanical Engineers, Part C:

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Symmetric V-shaped riblets are simulated by using the computational fluid dynamic method to understand the riblet effects on the turbulent boundary layer and the skin friction reduction. Three classical turbulence models, namely Spalart–Allmaras, shear stress transport, and re-normalization group k-epsilon models, are investigated under different grid densities. The re-normalization group model produces good results consistent with the experiment, as compared with the existing theoretical and experimental drag results of the flat plate and the V-shaped riblets with different sizes. Simulating V-shaped riblets yield the unexpected discovery that the shear stress transport model produces large errors, and the Spalart–Allmaras model even produces results of qualitative errors. Another finding is that von Kármán’s constants can no longer meet the requirement of describing velocity profiles in the logarithmic law layer. Aside from the traditional shift of the logarithmic law’s intercept, the slope is also changed by riblet height and spacing. Therefore, an improved model of riblet effects is proposed by redefining von Kármán’s constants.

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Section: Methodsmentioning

confidence: 99%

Numerical investigation of V-shaped riblets and an improved model of riblet effects

Zhang

2017

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…For practical computation, the high‐order accuracy methods of space reconstruction, such as the monotone upstream‐centered schemes for conservation laws (MUSCL) , weighted essentially nonoscillatory scheme , and discontinuous Galerkin methods , are often employed. Therefore, the compatibility of the preceding improvement and high‐order reconstruction should be discussed.…”

Section: Numerical Testsmentioning

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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A set of new general unified fluid dynamic equations for arbitrary equation of state

Cited by 2 publications

References 7 publications

Numerical investigation of V-shaped riblets and an improved model of riblet effects

Numerical investigation of V-shaped riblets and an improved model of riblet effects

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

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