Air with a free stream velocity of 40 ms^-1 flows past a smooth plate which is 3

Question

Air with a free stream velocity of 40 ms^-1 flows past a smooth plate which is 3 m wide and 10 m long in the flow direction. Assuming that air density is equal to 1.2 kg m^-3 and kinematic viscosity is equal to 1.49 10^-5 m^2s^-1, determine The shear stress acting by the flow on the plate 6 m from the leading edge The laminar sublayer thickness 6 m from the leading edge The boundary layer thickness 6 m from the leading edge Explain the meaning of: Reynolds stress tensor Reynolds stress model averaged value turbulent kinetic energy

Explanation / Answer

(b)

i) Reynolds stress tensor A tensor whose components are the components of the Reynolds stress across three mutually perpendicular surfaces

Tensor Properties

Reynolds stress is a 2nd order symmetry tensor.

• Diagonal elements – normal stresses

• Off-Diagonal elements – shear stresses

ii) Reynolds stress model

The Reynold's Stress Models (RSM), also known as the Reynold's Stress Transport (RST) models, are higher level, elaborate turbulence models. The method of closure employed is usually called a Second Order Closure The Reynolds stress model involves calculation of the individual Reynolds stresses.

iii)averaged value

Reynolds averaging to variables that are split into mean and turbulent parts.The Reynolds-averaged equation are time-averaged equations of motion for fluid flow. The idea behind the equations is Reynolds decomposition, whereby an instantaneous quantity is decomposed into its time-averaged and fluctuating quantities

iv)Turbulent kinetic energy

Turbulent kinetic energy is one of the most important variables in micrometeorology. It’s a measure of the intensity of turbulence.

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