Tangential Stress. Turbulent Viscosity

The Reynolds stress model requires the solution of transport equations for each of the Reynolds stress components as well as for dissipation transport without the necessity to calculate an isotropic turbulent viscosity field. The Reynolds stress turbulence model yield an accurate prediction on swirl flow pattern, axial velocity, tangential velocity and pressure drop on cyclone simulation [7,6,13,10],... 

The RSM solves transport equations for all Reynolds stresses and the dissipation rate e and therefore does not rely on the isotropic turbulent viscosity m,. This makes the RSM suitable to predict even swirling flows, however, the major drawback of this model is the computational effort needed to solve its equations. For 3D simulations, seven additional transport equations must be solved (six for the Reynolds stresses and one for e). However, the RSM is highly recommended if the expected flow field is characterized by anisotropy in the Reynolds stresses as is the case with swirling flows, e.g., cyclones or spray drying with tangential inlet ducts. Crowe (1980) emphasized that the k-e model is not suitable for swirl flow problems. 

Fluid flow past a surface or boundary leads to surface forces acting on it. These surface forces depend on the rate at which fluid is strained by the velocity field. A stress tensor with nine components is used to describe the surface forces on a fluid element. The tangential component of the surface forces with respect to the boundary is known as shear stress. The nature or origin of shear stress depends rai the nature of flow, i.e., laminar or turbulent. The stress components for a laminar flow are functions of the viscosity of the fluid and are known as viscous stresses. The turbulent flow has additional contributions known as Reynolds stresses due to velocity fluctuation, i.e., the stresses of a laminar flow are increased by... 

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