Virtual flow field

These are precisely the same results that we previously obtained and so it would appear that the mean-field approximation used to obtain Eq. (33) is "equivalent to neglecting the difference between the actual and virtual flow fields and... 

Following the verification step, we applied the heat sink methodology to a WS with full cylinders, comprising a flow field solution followed by three virtual... 

In addition to phase change and pyrolysis, mixing between fuel and oxidizer by turbulent motion and molecular diffusion is required to sustain continuous combustion. Turbulence and chemistry interaction is a key issue in virtually all practical combustion processes. The modeling and computational issues involved in these aspects have been covered well in the literature [15, 20-22]. An important factor in the selection of sub-models is computational tractability, which means that the differential or other equations needed to describe a submodel should not be so computationally intensive as to preclude their practical application in three-dimensional Navier-Stokes calculations. In virtually all practical flow field calculations, engineering approximations are required to make the computation tractable. 

Once the mathematical description of dispersion has been clarified, we are left with the task of quantifying the dispersion coefficient, Eiis. Obviously, Edh depends on the characteristics of the flow field, particularly on the velocity shear, dvx/dy and dvx /dz. As it turns out, the shear is directly related to the mean flow velocity vx. In addition, the probability that the water parcels change between different streamlines must also influence dispersion. This probability must be related to the turbulent diffusivity perpendicular to the flow, that is, to vertical and lateral diffusion. At this point it is essential to know whether the lateral and vertical extension of the system is finite or whether the flow is virtually unlimited. For the former (a situation typical for river flow), the dispersion coefficient is proportional to (vx )2 ... 

Forces or stresses are measurable on actual solid surfaces. We are equally interested, if not more interested, in virtual surfaces interior to the flow field that are used to help understand and quantify the intricacies of the flow. In particular, the surfaces of differential control volumes are critical in the derivation of the conservation equations. 

In the following, the use of periodical potentials will be described the periodicity will be denoted T[28]. Switching between two ore more flow patterns is performed inducing chaotic advection. One flow field is maintained in one time interval and another flow field in a second interval. This is repeated with the period T. The switching of the flow fields is accomplished by controlling the distribution of the C, potential created by the electrodes. By flow field alternation, particles virtually expose a zig-zag path, thereby distributing material all over the channel s cross-section. Such transport is similar to efficient stirring. 

The gravitational force is the weakest force in nature, but it binds together the most massive bodies in the universe. The force is in newtons (N) in the SI system,but in dynes in the cgs system (see Appendix, Table A). This force can be rewritten in terms of a vector gravitational field 3>i(r2) experienced by particle 2 at position r2, due to the existence of a particle 1 of mass m t at jt, and mediated by a continuous, if virtual, flow of gravitons emanating from particle 1 ... 

Apart from the drag force, there are three other important forces acting on a dispersed phase particle, namely lift force, virtual mass force and Basset history force. When the dispersed phase particle is rising through the non-uniform flow field of the continuous phase, it will experience a lift force due to vorticity or shear in the continuous phase flow field. Auton (1983) showed that the lift force is proportional to the vector product of the slip velocity and the curl of the liquid velocity. This suggests that lift force acts in a direction perpendicular to both, the direction of slip velocity... 

We conclude that over the continuum scale the determining parameters are the wind speed Uh and turbulence initial parameters of the cloud/plume when it reaches the top of the canopy or, equivalently, the virtual source at the level of the canopy. Using suitable fast approximate models for the flow field over urban areas (e.g. RIMPUFF, FLOWSTAR), the variation of the mean velocity and turbulence above the canopy can be calculated. The FLOWSTAR code (Carruthers et al., 1988 [105]) has been extended to predict how (Uc) varies within the canopy. Dispersion downwind of the canopy can also be estimated using cloud/plume profiles, denoted by Gc,w,GA,w which are shown in Figures 2.20 and 2.22. 

The flow condition was measured in a vessel with dished bottom and turbine stirrer or two different axially working stirrers with a two-component LDA [359], which was operated in back-scattering mode, such that the flow field could be averaged over a long period. The measurements were limited to a vertical plane in the middle between two baffles. The liquid viscosity was varied, so that the flow conditions could be measured both in the virtually laminar zone and in the turbulent zone. The internal liquid circulation and the pumping capacity of the stirrers was determined from the velocity measurements. An increase in the viscosity significantly reduced the rate of liquid circulation, as expected. 

DRE, but they are more susceptible to chain scission in the flow field than short polymers. If a macromolecule has a virtual high molecular weight and can break and reform, it may have improved shear stability. 

Three Dimensionality The flow field in a baffled tank is highly three-dimensional. Baffles both reduce the swirl and produce top to bottom circulation in the tank. Without baffles, any rotating impeller will produce a two-dimensional flow which is mainly rotational. The baffles induce drag and force the swirling fluid up the wall. This transforms a two-dimensional, swirling flow into a three-dimensional flow with low swirl, particularly in the outer third of the tank. A survey of the simulation literature shows that 2D simulations of baffled tanks were virtually abandoned as soon as computational speed would support a 3D approach. No adequate way to model the effect of the baffles in two dimensions was ever found. 

First, an air jet emerging from a single nozzle is considered. In Fig. 1.3, the generated flow field of a nozzle is shown schematically. From the nozzle with the diameter d, the flow exits with the approximately constant speed w. The jet impinges the surface virtually unchanged with a constant velocity as long as... 

Under isothermal conditions, these four equations are sufficient to describe the flow of water (or air and any other gas or liquid with so-called Newtonian behavior of the viscosity). However, in most cases of industrial interest (i.e., at large scale), these equations cannot be solved using analytical techniques. The momentum balance is nonlinear in velocity, which makes analytical solution virtually always impossible. This is reflected in the properties of the flow of water it is in many cases turbulent. This means that the flow is inherently transient in time a steady state solution only exists for the time-averaged flow. The real flow shows a wide variety of structures, both in time and in space the flow field is built up of eddies of all kinds of sizes that have a finite life time. They come and disappear. These eddies make the solution very difficult. However, they are also vital to the processes we are running they make flow so effective in transport and mixing. Without them, we would have to rely on diffusion, which is a very slow process, and life on a larger scale as we know it would not have been possible. 

In the general case, a buoyant jet has an initial momentum. In the region close to discharge, momentum forces dominate the flow, so it behaves like a nonbuoyant jet. There is an intermediate region where the influence of the initial momentum forces becomes smaller and smaller. In the final region, the buoyancy forces completely dominate the flow and it behaves like a plume. When the jet is supplied at an angle to the vertical direction, it is turned upward by the buoyancy forces and behaves virtually like a vertical buoyant jet in a far field. A negative buoyant jet continuously loses momentum due the opposite direction of buoyancy forces to the supply air momentum and eventually turns downward. 

The basic idea of the IBM is that the presence of the solid boundary (fixed or moving) in a fluid can be represented by a virtual body force field Fp applied on the computational grid at the vicinity of solid-flow interface. Thus, the Navier-Stokes equation for this flow system in the Eulerian frame can be given by... 

In the IBM, the presence of the solid boundary (fixed or moving) in the fluid can be represented by a virtual body force field -rp( ) applied on the computational grid at the vicinity of solid-flow interface. Considering the stability and efficiency in a 3-D simulation, the direct forcing scheme is adopted in this model. Details of this scheme are introduced in Section II.B. In this study, a new velocity interpolation method is developed based on the particle level-set function (p), which is shown in Fig. 20. At each time step of the simulation, the fluid-particle boundary condition (no-slip or free-slip) is imposed on the computational cells located in a small band across the particle surface. The thickness of this band can be chosen to be equal to 3A, where A is the mesh size (assuming a uniform mesh is used). If a grid point (like p and q in Fig. 20), where the velocity components of the control volume are defined, falls into this band, that is... 

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