Average velocity field

Thus, for statistically stationary flow, the Favre-averaged velocity field satisfies V ((p)(U = 0. 

Under the conditions of turbulence, the time-averaged velocity field is symmetric with respect to the free stagnation plane, provided the flow rates from the two nozzles are equal. The mean axial velocity profile has a similar shape to the curve of uju ) vs x. The gradient of the time-averaged axial velocity takes the maximum at the stagnation plane, while it approaches zero near the nozzle. 

Thus the interstitial velocity, as described by Kowe et al. [353], is effectively the average velocity field experienced by a test body introduced into the flow, which is not located close to any other bodies. Notice that t Uf because u/,- includes contributions from the near field flow from each body. The dipole moment associated with each body moving parallel to the stream is (1 + Cm)(v - up)Vn/2n, where Vb is the volume of a body and Cm its added-mass coefficient. 

Figure 7.6 Relaxation lengthscales of the unfiltered conditional average velocity field normalised by the bubble diameter d as a function of void fraction. (The difference from estimates based on the filtered conditionally averaged velocity field, are negligible). L and L d correspond to decay distance for up and downstream velocity. The theoretical prediction, from (7.29), of the relaxation lengthscale is Ld/d = 2d/aCd, for Ret = 10.

The time-averaged velocity field downstream of the TARS, including axial and tangential mean and turbulent velocity components, was measured using a Phase Doppler Particle Analyzer (PDPA) system. 

F. 5.2 Ensemble average velocity field in grey scale within an aqueous plug at mixture velocity of 0.01 m s (flow rate ratio equal to 1) in a channel of a 0.5 nun ID, and b 1 mm ID. Thirty instantaneous fields were averaged. TBP/[C4mim] [NTf2] (30 %, v/v) as carrier fluid... 

Meinhart CD, Wereley ST, Santiago JG (2000) A PIV algorithm for estimating time-averaged velocity fields. J Fluids Eng 122 285-289. doi 10.1115/ 1.483256... 

The second contribution originates from the product between the gradient of the local kinetic energy of the particles (u — vq) (see also (de Groot Mazur, 1984)), and the relative current J = (u — v)/, where v represents the average velocity field of the particles. 

The Reynolds stresses appearing in the Reynolds equations [8.21], whose solution determines the turbulence-average velocity field, are modeled via the mixing length model (equation [8.28]) such as ... 

In the above equations, represents the density of the gas and liquid phase, V ( is the averaged velocity field of each phase, andp the pressure. There are two terms on the right-hand side of the momentum equation that require special attention ... 

Turbnlent flows contain a spectrum of eddies of different size, intensity, and lifetime. However, each eddy has an element of simple shear or extension, and creates forces that lead to drop deformation. The drop sees a time-dependent deformation field even if the Reynolds-averaged velocity field does not vary in space. This is illnstrated in Figure 12-2 and is explained more fnlly in Chapter 2. In reality, forces in turbulent stirred vessels arise from both spatial and temporal velocity flnctuations. These arise fi om mean velocity gradients, interacting turbnlent eddies and impingement of jetlike flows on walls, baffles, and impeller blades. 

Velocity perturbations due to a particle are local the average velocity field in the surrounding fluid is the same as if the particles were not present. 

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