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Flow simulation over Airfoil (SHM1) and effect of free-stream turbulence on Lift, Drag and Shedding pattern

Flow over SHM1 Airfoil

•Flow over SHM1 airfoil is computed for zero angle of attack for cruise Reynolds number of 10.3 million.

The flow over SHM1 at zero angle of attack (Re=10.3 million) attains  statistical steady state, separation bubbles are generated and convected near the trailing edge as shown in animation below.

Stream function contours
vortex shedding

Above two figures show stream function and vorticity contour plots, respectively.

Methods/Schemes used in computations

• Convective terms in VTE have been discretized using S-OUCS3 schemes of  Dipankar & Sengupta.
• Diffusion terms in VTE are discretized using CD-2 scheme.
• Four stage Runge-Kutta (RK4) method is used to march forward in time
• BiCGSTAB algorithm is used to solve both the Poisson equations: SFE & PPE (solved explicitly to determine the load parameters).

• For high Re flows, a wide band of scales are excited. To control aliasing error arising out of convection terms, dominant at higher wave numbers, dissipation is added via upwinding the convection terms and by explicitly filtering the solution after every time step using sixth order composite filter [Sengupta et al. (2009)].

Effects on adding FST

Free-stream turbulence is omnipresent in all fluid flows, so its important to include its effects in simulations. Here FST is modelled as described by Sengupta et. al. (2006)

The figure below shows effect of FST in Cl vs time plot

Fluctuations in Cl increases with increase in FST and these fluctuations are present at all frequency levels which is shown in FFT of Cl data shown below.

FFT of Cl shows fluctuations increase with FST that has high amplitudes for low frequencies, which is shown below.

The figures below show effects of FST in Cd vs time plot

Fluctuations in Cd increase with FST and fluctuations are present at all frequencies, shown in FFT of Cd data.

FFT of Cd has high amplitude at low frequencies, shown in figure below.

Effect of FST on shedding pattern are shown below.

The figure (below) shows stream function contours near the trailing edge of SHM1 airfoil, plotted at similar stage of bubble formation and for the same psi (Ψ) contour levels.

From the figure it is noted that the size of bubble on lower surface of the airfoil is larger for all FST cases compared to without FST case.

The figure (below) shows instantaneous vorticity contours near the trailing edge of SHM1 airfoil, plotted for same vorticity contours and at approximately similar stage of shedding.

From the figure (vorticity contours) it is observed that the size of the vortex at the bottom of the airfoil is larger for the cases with FST as compared to without FST case.