A Universal Velocity Profile for Near-Wall Flows

A recently developed mixing length model of the turbulent shear stress in pipe flow is used to solve the stream-wise momentum equation for fully-developed channel flow. The solution yields an integral form of the velocity profile that is uniformly valid from the wall to the channel centerline at all Reynolds numbers. The model velocity profile also provides a remarkably accurate fit to simulated and experimental flat plate turbulent boundary layer data. The mixing length function has five free parameters that are selected through an optimization process to provide an accurate fit to data in the range Rtau = 550 to Rtau = 10,023. Since the velocity profile is directly related to the Reynolds shear stress, certain statistical properties of the flow such as turbulent kinetic energy production can be studied. The examples presented here include numerically-simulated channel flow data from Rtau = 550 to Rtau = 8,016, zero pressure gradient boundary layer simulations from Rtau = 1,307 to Rtau = 2,479, and experimental data at Rtau = 2,760 and Rtau = 10,023. The mixing length model is also used in RANS computations of channel flow and boundary layers.