Physics of turbulence generation and sustenance in a boundary layer

Standard high order methods give rise to spurious oscillations near shocks which can be controlled by using localized artificial viscosity (AV) with high wavenumber bias. Using simulations of compressible isotropic turbulence with optimized high-order schemes at different resolutions we investigated the range of scales where artificial dissipation is active. We observed that the impact of AV was not limited to high wavenumbers. This is especially true for moderately high Mach number isotropic turbulence which spontaneously forms shocklets, for which the AV method is found to excessively damp the dilatational motions. We propose a modified form using a modified coefficient which activates AV only in the regions of strong compression, such as shocks, turning it completely off for turbulence and expansion waves. This is found to give improved statistics for all quantities, not just dilatation. This formulation reverts back to the traditional one for strong shocks, so that its shock capturing capability is not compromised (see Fig. 1).

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A modified artificial viscosity approach for compressible turbulence simulations

This paper addresses the issue of real-time control for applications, subject to physical constraints, involving an energy maximization objective. Typical application areas include renewable energy systems where, in spite of the fact that the raw energy resource is free, the capital and operational costs associated with the energy conversion process are not. In addition, economic energy delivery can only be achieved if the conversion device is operated efficiently. Previous approaches to this problem include model predictive control (MPC), but the computational cost associated with MPC can be high. Pseudospectral solutions show considerable promise in achieving a good balance between performance and computation, but currently available solutions deal with fixed-period optimization. In this paper, a receding horizon real-time pseudospectral control is developed, based on half-range Chebyshev Fourier basis functions, which can accurately represent harmonic signals in the application domain, while also efficiently dealing with the signal truncation effects associated with a receding horizon formulation. An application example, based on a wave energy converter, is used to illustrate the new control algorithm.

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Receding Horizon Pseudospectral Control for Energy Maximization With Application to Wave Energy Devices

Literature review on pressure–velocity decoupling algorithms applied to built-environment CFD simulation

In this paper, two functions are introduced to describe the turbulence generation in late flow transition. One is called the volume omega bar (volume Ω¯), which represents the flow rotation or vortex strength. The other is called the volume vorticity, which shows the flow statistical fluctuations. Although they have very different definitions, one is for fluctuation and the other is for rotation, volume Ω¯ and volume vorticity are found highly correlated with a correlation factor greater than 0.9, which means that there is a very close correlation between flow fluctuation and flow rotation (vortex). While the vorticity flux keeps constant in the late flow transition through the integration over any sections either parallel or perpendicular to the flow direction, the volume Ω¯ is greatly increased along the flow direction during the flow transition process. This means that the vortex structures are greatly built up and rotation becomes more and more dominant. On the other hand, the total volume vorticity i...

Correlation analysis on volume vorticity and vortex in late boundary layer transition

Large vortex structure in late boundary layer transition with an inflow Mach number of 0.5 is studied by DNS (Direct Numerical Simulation) in this paper. First, we found that there are no Λ-vortex tubes, contradicting to what the existing literatures and textbooks addressed. The so-called Λ-vortex is always open on head, which has a different shape from Λ. Λ-vortex is really a pair of open rotation cores with a lower half of the Λ shape. It is also found that the Λ-vortex and ring-like vortex are formed separately and independently. There is no such a process that the Λ-vortex self-deforms to a hairpin vortex at the tip as many literatures indicated. Λ-vortex and ring-like vortex can be visualised by the iso-surface of λ2. However, the iso-surfaces of λ2 only represent rotation cores but not necessarily vortex tubes. In fact, many spanwise vortex filaments can easily penetrate the so-called Λ-vortex (iso-surface of λ2), change the direction toward the streamwise direction, and then leave the iso-surface o...

DNS study on Λ-vortex and vortex ring formation in flow transition at Mach number 0.5

Modified weighted compact scheme with global weights for shock capturing

Standard Fourier spectral method can be used to solve a lot of problems with periodic boundary conditions. However, for non-periodic boundary condition problems, standard Fourier spectral method is not efficient or even useless. This work has developed a new way to use Fourier spectral method for non-periodic boundary condition problems. First, the original function is normalized and then a smooth buffer polynomial is developed to extend the normalized function domain. The new function will be smooth and periodic with both function values and derivatives, which is easy to be treated by standard FFT for high resolution. This method has obtained high order accuracy and high resolution with a penalty of 25% over standard Fourier spectral method, as shown by our examples. The scheme demonstrates to be robust. The method will be further used for simulation of transitional and turbulent flow.

A buffered Fourier spectral method for non-periodic PDE

Standard compact scheme or upwind compact scheme have high order accuracy and high resolution, but cannot capture the shock without oscillations. In this paper, modified compact scheme is developed by using an effective shock detector to block upwinding compact scheme to cross the shock, a control function, and an adaptive scheme which uses some WENO flux near the shock. The new scheme makes the original upwinding compact scheme able to capture the shock sharper than WENO and, more important, keep high order accuracy and high resolution in the smooth area which is particularly important for shock, shock boundary layer interaction and shock acoustic interaction. The scheme is robust and has no case-related coefficients.

New shock detector and improved control function for shock-boundary layer interaction

It is critical for a numerical scheme to obtain numerical results as accurate as possible with limited computational resources. Turbulent processes are very sensitive to numerical dissipation, which may dissipate the small length scales. On the other hand, dealing with shock waves, capturing and reproducing of the discontinuity may lead to non-physical oscillations for non-dissipative high-order schemes. In the present work, a new high-order mixed weighted compact and non-compact difference scheme MWCS hereafter is proposed for accurate approximation of the derivatives in the governing Euler equations. The basic idea is to recover the non-dissipative high-order weighted compact scheme WCS in smooth regions, while linearly combine the WCS with a non-compact scheme, the weighted essentially non-oscillatory WENO scheme, for near-shock areas, by using a shock-detecting function. The proposed formulation does not involve any case-dependent adjustable parameter. A detailed Fourier and local truncation error analysis are used for assessing the dispersion and dissipation characteristics of the scheme. Numerical tests are performed for the one-and two-dimensional case and the results are compared with the well-established WENO scheme and the WCS.

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Huankun Fu

Papers

DNS study on Λ-vortex and vortex ring formation in flow transition at Mach number 0.5

Modified weighted compact scheme with global weights for shock capturing

A buffered Fourier spectral method for non-periodic PDE

New shock detector and improved control function for shock-boundary layer interaction

High-order mixed weighted compact and non-compact scheme for shock and small length scale interaction