Local mean velocity

Local mean velocity The magnitude of the time-averaged vector of velocity at a point in an airstream. 

For steady, one-dimensional flow without body forces, with local mean velocity u(x) in a channel of constant cross-sectional area A, the energy conservation equation becomes, approximately (13) ... 

Eulerian equations for the dispersed phase may be derived by several means. A popular and simple way consists in volume filtering of the separate, local, instantaneous phase equations accounting for the inter-facial jump conditions [274]. Such an averaging approach may be restrictive, because particle sizes and particle distances have to be smaller than the smallest length scale of the turbulence. Besides, it does not account for the Random Uncorrelated Motion (RUM), which measures the deviation of particle velocities compared to the local mean velocity of the dispersed phase [280] (see section 10.1). In the present study, a statistical approach analogous to kinetic theory [265] is used to construct a probability density function (pdf) fp cp,Cp, which gives the local instantaneous probable num-... 

Experimental Mj values determined as the difference between the local mean velocities of bubbles and liquid are also shown in Fig, 34 as open keys. For these bubbles, the volume-surface mean diameters J32 have been measured experimentally. The free-rise velocity of the bubbles (Tl, V6) is... 

The local mean velocity may be determined in terms of the phase shift by considering a voxel located at r position. By combining Eq. (34) with Eq. (35), the resulting expression for the signal is an obvious extension to the case found in Eq. (32), which is averaged over the given voxel ... 

The problem in a horizontal plane expresses flow parameter distributions across the water conduit width which is vegetated near one or both banks like the situation shown in Fig. 1.8. It was assumed there that the local mean velocity was averaged over all the flow depth 0 < z < Ox,y). In fact, the flow field in such a geometry, even in the simplest configurations, is completely three-dimensional and is varied in the flow direction Ox, across the conduit Oy, and in the vertical direction Oz, i.e., U = U(x,y, z). It is natural, however, to average the velocities over the whole flow depth [540] ... 

The classical turbulence models express the eddy viscosity algebraically in terms of a turbulence scale and intensity that are related, respectively, to the characteristic length dimensions of the flow field and the local mean velocity gradients. This implies an equilibrium between the local turbulence and the mean motion. This requirement of equilibrium has been relaxed in some eddy viscosity models where the intensity and scale of turbulence used to evaluate the eddy viscosity are expressed by partial differential equations for the turbulence kinetic energy and its dissipation rate. This latter class of models is presented in detail, for example, in Refs. 76 and 77. 

The local mean velocity is related to the mean velocity v in the... 

Turbulent Reynolds Number Slope of the Open Channel Measuring time Absolute temperature Local axial velocity Local mean velocity Fluctuation velocity Shear velocity... 

Wall-bounded turbulent flows are generally subdivided in the direction normal to the wall (y coordinate). To elucidate this, the velocity profile measured in a turbulent channel flow is shown in Fig. 1 with non-dimensional coordinates (inner coordinates). The non-dimensional local mean velocity u = U/u in-... 

The shear stresses over the flow boundaries can be rigorously derived as an integral part of the solution of the flow field only in laminar flows. The need for closure laws arise already in single-phase, steady turbulent flows. The closure problem is resolved by resorting to semi-empirical models, which relate the characteristics of the turbulent flow field to the local mean velocity profile. These models are confronted with experiments, and the model parameters are determined from best fit procedure. For instance, the parameters of the well-known Blasius relations for the wall shear stresses in turbulent flows through conduits are obtained from correlating experimental data of pressure drop. Once established, these closure laws permit formal solution to the problem to be found without any additional information. 

---