Huankun Fu

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

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 of λ2. The vortex ring is not part of the original Λ-vortex but is formed separately. The Λ-vortex cores were originated from the 2D and 3D T-S waves, amplified and became strong by attracting neighbouring spanwise vortex filaments from the boundary shear layer. As the Λ-vortex becomes strong, a strong shear layer is formed above the Λ-vortex roots, which is caused by ejection of the Λ-vortex rotation to bring low speed flow from the bottom of the boundary layer to form an olive-like low speed zone. As a result, the instability of the shear layer leads to the formation of new ring-like vortex tubes one by one.

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

Modified fourier spectral method for non-periodic CFD

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 used the modified Fourier spectral method for non-periodic boundary condition problems. The modified spectral method has two parts, 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 current examples include a 2D Poisson solver and solution for 2-D incompressible driven cavity flow. The method will be further used for simulation of transitional and turbulent flow.

Modified Weighted Compact Scheme for Shock Capturing

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 schemes. In the present work, a new high-order modified weighted compact (MWCS) is proposed for accurate approximation of the derivatives in the governing Euler equations. The basic idea is to add the weighted essentially non-oscillatory scheme (WENO) to weighted compact scheme to make sure the scheme is diagonally dominant, and then add some WENO in additional to make sure that theres some dissipation in the smooth area to avoid oscillations. Formulation and numerical tests are performed for the one-and two-dimensional case and results are compared with the well-established WENO scheme. Nomenclature b a, = start, and end point of the one-dimensional domain

Improvement of Mixing Function for Modified Upwinding Compact Scheme

The compact scheme has high order accuracy and high resolution, but cannot be used to capture the shock. WENO is a great scheme for shock capturing, but is too dissipative for turbulence and small length scales. We developed a modified upwinding compact scheme which uses an effective shock detector to block compact scheme to cross the shock and a control function to mix the flux with WENO scheme near the shock. The new scheme makes the original compact scheme able to capture the shock sharply and, more important, keep high order accuracy and high resolution in the smooth area, which is particularly important for shock boundary layer and shock acoustic interactions. This work is a continuation to modify the control function for the modified up-winding compact scheme (MUCS). Numerical results show the scheme is successful for 2-D Euler.