Prescribed velocity

PUTBCV Inserts the prescribed velocity boundary values at the allocated place in the vector of unknowns for flow equations. 

Often the inlet device (air supply) in a ventilated room is geometrically complicated. To resolve the flow around such a device would require a very fine grid. Instead of trying to resolve the complex flow near the inlet device, one can choose to use the box method or the prescribed velocity method.Both methods are based on the observation that downstream of the inlet, the flow behaves like a wall jet. Thus it is important that the bound-... 

The other method is the prescribed velocity (PV) method. In this method only the streamwise velocity component U and the temperature profile are prescribed inside the volume ab. The remaining variables ( V, W, k, and e) are solved for as usual in the whole room, including the ab volume. The temperature level has to be readjusted after each iteration to ensure conservation of energy. 

Nielsen, P. V. The prescribed velocity method—A practical procedure for introduction of an air terminal device in CFD calculation. Report R9827, Dept, of Building Technology and Structural Engineering, Aalborg University, Aalborg, 1998. 

Acid flowrates also have to be kept at carefully prescribed velocities. 

The permeate is continuously withdrawn through the membrane from the feed sueam. The fluid velocity, pressure and species concentrations on both sides of the membrane and permeate flux are made complex by the reaction and the suction of the permeate stream and all of them depend on the position, design configurations and operating conditions in the membrane reactor. In other words, the Navier-Stokes equations, the convective diffusion equations of species and the reaction kinetics equations are coupled. The transport equations are usually coupled through the concentration-dependent membrane flux and species concentration gradients at the membrane wall. As shown in Chapter 10, for all the available membrane reactor models, the hydrodynamics is assumed to follow prescribed velocity and sometimes pressure drop equations. This makes the species transport and kinetics equations decoupled and renders the solution of... 

Boundary conditions for the one-dimensional (1.4) and two-dimensional (1.5) models are evident. They are the no-slip condition on the surface and a prescribed velocity value (often, the geostrophic wind velocity Ug) sufficiently far away of the surface ... 

Problem 6-7. Coating Flows The Drag-Out Problem A very important model problem in coating theory is sometimes called the drag-out problem. In this problem, a flat plate is pulled through an interface separating a liquid and a gas at a prescribed velocity U. The primary question is to relate the pull velocity U to the thickness // of the thin film that is deposited on the moving plate. We consider the simplest case in which the plate is perpendicular to the horizontal interface that exists far from the plate. The density of the liquid is p, the viscosity //, and the surface tension y. 

The symbolic operators (87)-(88) for the sphere possess a greater degree of generality than do Faxen s laws. In particular, if we consider any Stokes flow v(r, r/r) vanishing at infinity and satisfying the arbitrary boundary condition V = f(r/r) s f(0, < ) at r = a, then the force on the sphere may be obtained directly from the prescribed velocity boundary condition via the expression... 

Closely related to the preceding is the problem of calculating the pressure drop due to Stokes flow through a cylinder of arbitrary (but constant) cross section for arbitrary boundary conditions on the surfaces bounding the cylinder. A simple application of the Reciprocal theorem (B18) permits one to express this pressure drop directly in terms of the prescribed velocity field on the cylinder walls, top, and bottom. If (v, n) and denote the velocity... 

The standard boundary condition at the outlet is CouUet = 0. In fact, this is an ideal limit of a prescribed velocity v at the outlet /outlet = vcoutieti as v + oo, this tends to Coutiet =0, since /outlet must remain finite. A remarkable fact is that this outlet condition can be reduced to the standard one by adding a thin resistor zone if Cextra = 0,/outlet =/extra and... 

In (Eqs 23-27), the scalars x and t denote spatial coordinate and time, respectively. The symbols u, M and P signify the transverse displacement, the moment, and the moving load, respectively. Furthermore, m represents the distributed mass of the beam, fx the moving mass, and c t) its prescribed velocity in time. It has been assumed that the motion of the discrete moving mass begins at a zero initial time and from an initial location xq on the beam. Finally, S denotes the spatial Dirac s delta function. In order to deal with inelastic behavior, the set of equations 23-27 is supplemented by the state equations and the flow rule. 

The velocity of a molecule, c, is specified by its components m, u, and w in the x, y, and z directions, respectively. If we were to attempt to find the number of molecules with a specific velocity c, we would have an immediate problem of measurement. The more precisely c can be measured, the fewer the molecules that will be found with the prescribed velocity. Rather than attempt unnecessary accuracy, we focus on the quantity F(c) = F(u, v, w), where F(u, v, w) du dv dw is the fraction of molecules with velocity components between u and u + du, v and v + dv, w and w + dw the total number of molecules in this velocity domain is then NF u, v, w) du dv dw. If du, dv, and dw are chosen too small, we again encounter the problem that few molecules will lie in the velocity range of interest and the quantity F(c) might not be a smooth function of c. However, as long as the system of interest is macroscopic, the velocity increments may be prescribed as small as measurement permits there is always an enormous number of molecules in the specified velocity domain and F(c) is a smoothly varying function. 

The exact shape of the velocity profile in the outflow of an impeller does not depend solely on the impeller. It is also affected by such variables as the impeller Reynolds number, impeller off-bottom distance C/T, and impeller diameter D/T. If the flow is fully turbulent (i.e.. Re > Kf ), the impeller outflow profiles are typically independent of Reynolds number. If the flow is flansitional or laminar, however, care should be taken so that the velocity profiles used were either measured at a similar Reynolds number, or that the prescribed velocities are being interpolated from data sets measured over a range of Reynolds numbers. Similarly, for impeller off-bottom clearance and diameter, if data for various C/T and D/T values are available, interpolations can be used to obtain the prescribed velocities for the actual conditions. 

The real challenge experimentally is to hold this shape, yet keep all surfaces moving at the prescribed velocity. Probably the... 

To reduce the fundamental PBE (9.118) into the reduced PBE form (12.399), the following simplifying assumptions are applied (i) steady state, (ii) cross-sectional averaging giving one independent spatial coordinate z, and (iii) prescribed velocity field of the dispersed phase, i.e., v (, z) = v = constant. 

CL Parameter in prescribed velocity profile in laminar boundary layer theory (—)... 

When this equation is solved for given initial and boundary conditions, the distribution of configurations is then obtained for the prescribed velocity gradient field ir(t). 

However, very recently Gotze et al. [38] identified several situations involving rotating flow fields in which fhis asymmetry leads to significant deviations from the behavior of a Newtonian fluid. This includes (1) systems in which boundary conditions are defined by torques rather than prescribed velocities, (2) mixtures of... 

---