Turbulent Couette-Poiseuille Flow with Wall Transpiration: Analytical Study and Direct Numerical Simulation

• Applicant: Dr.-Ing. Georg Khujadze
• Subject Area: Hydraulic and Turbo Engines and Piston Engines
• Term: from 2009 to 2014
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 142255236

• Final Report Year: 2014

Final Report Abstract

A fully developed, turbulent Poiseuille flow with wall transpiration, i.e. uniform blowing and suction on the lower and upper walls, was investigated by numerically and theoretically. 12 full DNS of the flow with different parameters were performed and presented. The results of three different Reynolds numbers (Reτ = 250, 480, 850) were presented. For each Reynolds number the blowing and suction velocity was varied (v0^+ = 0 − 0.05). High resolution requirements in space and time was kept and smooth statistics (one-, two-point) were accumulated during a long simulation times. It was shown that the transpiration velocity brakes a symmetry resulting in the logarithmic scaling law in the core of the channel. The region of validity of the new logarithmic law is very different from the usual near-wall log-law and the slope constant in the core region differs from the von Karman’s constant and is equal to 0.3. Extended forms of the linear viscous sublayer law and the near-wall log-law were derived, which, as a particular case, include these laws for the classical (non-transpiring) case. The viscous sublayer at the suction side has an asymptotic suction profile. The thickness of the sublayer increase at high Reynolds and transpiration numbers. For the near-wall log-law we see an indication that it appears at the moderate transpiration rates (0.05 < v0 /uτ < 0.1) and only at the blowing wall. Finally, from the DNS data we established a relation between the friction velocity uτ and the transpiration v0 which is linear at moderate transpiration rates.

Publications

• Turbulent Poiseuille flow with walltranspiration: analytical study and direct numerical simulation, Journal of Physics: Conf. Ser., v. 318, 022004, 2011
  V. Avsarkisov, M. Oberlack , & G. Khujadze
  
• Turbulent Poiseuille Flow with Uniform Wall Blowing and Suction. PhD Thesis, Fachbereich Maschinenbau, Technische Universität Darmstadt, 2013
  V. Avsarkisov
  
• “New scaling laws for turbulent Poiseuille flow with wall transpiration”, J. Fluid Mech., vol. 746, pp. 99-122, 2014
  V. Avsarkisov, M. Oberlack and S. Hoyas
  
• “Turbulent plane Couette flow at moderately high Reynolds number”, J. Fluid Mech., vol. 751, 2014
  V. Avsarkisov, S. Hoyas, M. Oberlack and J. P. Garcia-Galache