A heated flat plate is suspended in a uniform freestream inside a virtual wind tunnel. The plate has a sharp leading edge (left) and a blunt trailing edge (right). The simulation uses the Lattice Boltzmann Method (D2Q9) with thermal coupling, running entirely on the GPU via WebGPU compute shaders. Four classical phenomena of fluid dynamics and thermodynamics are observable simultaneously.
The Prandtl number Pr = ν / α compares the rate at which momentum diffuses through the fluid (viscosity ν) to the rate at which heat diffuses (thermal diffusivity α). When Pr > 1, heat diffuses slower than momentum, so the thermal boundary layer is thinner than the velocity boundary layer. When Pr < 1, the opposite: heat spreads faster, producing a thicker thermal layer. Air has Pr ≈ 0.71; water has Pr ≈ 7.
Try it: switch to Temperature view and adjust the Viscosity and Diffusivity sliders to see the two boundary layers change relative thickness.In a laminar boundary layer, small perturbations can amplify into traveling waves called Tollmien-Schlichting (T-S) waves. These are the first stage of the laminar-to-turbulent transition. The simulation seeds sinusoidal velocity perturbations at the inlet. Downstream of the leading edge, the boundary layer amplifies certain frequencies, producing visible wave packets that grow in amplitude along the plate.
Try it: enable Tollmien-Schlichting, switch to Vorticity view, and watch wave crests grow as they travel downstream. Adjust Frequency and Amplitude to change the instability character.When flow separates from the blunt trailing edge, alternating vortices are shed from the top and bottom surfaces, forming a staggered pattern called the von Kármán vortex street. This occurs at moderate Reynolds numbers based on the plate thickness Ret = U × t / ν. The shedding frequency follows the Strouhal relationship. Vortex streets appear behind bridges, power lines, submarine periscopes, and any bluff body in a flow.
Try it: switch to Vorticity view. Increase Velocity or reduce Viscosity to push Ret into the shedding regime (60-400) and watch alternating red and blue vortices peel off the trailing edge.An actuator disk placed downstream extracts kinetic energy from the flow by decelerating it. The induction factor a = Cd / (4 + Cd) describes how much the flow slows. The power coefficient Cp = 4a(1 - a)² gives the fraction of upstream kinetic energy extracted. Betz (1919) proved the theoretical maximum is Cp = 16/27 ≈ 0.593, occurring at a = 1/3. This is why real wind turbines cannot exceed about 59% efficiency, regardless of blade design.
Try it: drag the Drag Coeff slider and watch the operating point move on the Betz chart below. At Cd ≈ 1.33, you reach the Betz maximum. Go higher and the disk over-blocks the flow, reducing extraction.