Consider the flat plate with a thickness of 1 cm placed to a wind tunnel as shown below. The leading edge is sharp Leading edge star.com of plat plate STAR-CCM+ 1 cm 4m 1 cm Pressure outlet 2m U. inlet 1m 2m 1m Top and bottom surfaces should be pressure outlet BC or slip wall BC. Sides should be symmetry BC. 1) Calculate the average boundary layer thickness for REL 100000, 200000,500000, 2000000, 5000000 (see the relevant lecture notes
a) Prepare a simulation case in STAR-CCM+ so that you can study the development of boundary layer at the mid plane (z=1.0) and the scaling law for the drag coefficient at 𝑅��𝐿 = 100000, 200000, 500000, 2000000, 5000000. Use incompressible air for the simulations. Use k-omega SST turbulence model without any transition model.
b) Make a mesh sufficiently fine, which can resolve the velocity change within the boundary layer at the wall by using the calculated boundary layer thickness at the selected 𝑅𝑒𝐿 .
c) At 𝑅𝑒𝐿 = 100000, 2000000, extract 𝑈𝑥 velocity at x=0.1, 0.2, 0,5, 0.8 m. Find 𝛿 at all locations from the simulations by extracting data from the simulations. Plot dimensional (𝑈𝑥 vs 𝑦) and non-dimensional velocity profiles (𝑈𝑥/𝑈∞ vs 𝑦/𝛿 ), (note that x=0 corresponds to leading edge).
d) Compare the non-dimensional velocity profiles at x=0.8 for 𝑅𝑒𝐿 = 100000, 2000000 together with the analytical velocity profiles given by the equation
𝑈𝑥 / 𝑈∞ = 2 𝜂 − 𝜂 2 𝑤ℎ𝑒𝑟𝑒𝜂 = 𝑦/𝛿 for laminar flow and 𝑈𝑥 / 𝑈∞ = 𝜂 1/7 for turbulent flow
e) Calculate the 𝐶𝐷 for all 𝑅𝑒𝐿 by considering the drag created on the upper surface of the flat plate (note that you should define this surface while preparing the simulation) at the above given 𝑅𝑒𝐿