Convection simulation

Tackley P. J. (2000b) Self-consistent generation of tectonic plates in time-dependent, three-dimensional mantle convection simulations 1. Pseudoplastic yielding. Geochem. Geophys. Geosys. 1. 

Trompert R. and Hansen U. (1998) Mantle convection simulations with rheologies that generate plate-like behaviour. Nature 395, 686-689. 

Trieloff M, Kunz J, Allegre CJ (2002) Noble gas systematics of the Reunion mantle plume source and the origin of primordial noble gases in Earth s mantle. Earth Planet Sei Lett 200 297-313 Trompert R and Hansen U (1998) Mantle convection simulations with rheologies that generate plate-like behaviom. Nature 395 686-689... 

The flow processes are described as Marangoni convections and up to now they were determined by several research centers through numeric simulation works [9]. Due to the... 

The visualization of volumetric properties is more important in other scientific disciplines (e.g., computer tomography in medicine, or convection streams in geology). However, there are also some applications in chemistry (Figure 2-125d), among which only the distribution of water density in molecular dynamics simulations will be mentioned here. Computer visualization of this property is usually realized with two or three dimensional textures [203]. 

The thermal conductivity of polymeric fluids is very low and hence the main heat transport mechanism in polymer processing flows is convection (i.e. corresponds to very high Peclet numbers the Peclet number is defined as pcUUk which represents the ratio of convective to conductive energy transport). As emphasized before, numerical simulation of convection-dominated transport phenomena by the standard Galerkin method in a fixed (i.e. Eulerian) framework gives unstable and oscillatory results and cannot be used. 

A discussion of retention time in rotary Idlns is given in Brit. Chem. Eng., 27-29 (Januaiy 1966). Rotary-ldln heat control is discussed in detail by Bauer [Chem. Eng., 193-200 (May 1954)] and Zubrzycki [Chem. Can., 33-37 (Februaiy 1957)]. Reduction of iron ore in rotaiy Idlns is described by Stewart [Min. Congr J., 34—38 (December 1958)]. The use of balls to improve solids flow is discussed in [Chem. Eng., 120-222 (March 1956)]. Brisbane examined problems of shell deformation [ Min. Eng., 210-212 (Februaiy 1956)]. Instrumentation is discussed by Dixon [Ind. Eng. Chem. Process Des. Dev., 1436-1441 (July 1954)], and a mathematical simulation of a rotaiy Idln was developed by Sass [Ind. Eng. Chem. Process Des. Dev., 532-535 (October 1967)]. This last paper employed the empirical convection heat-transfer coefficient given previously, and its use is discussed in later correspondence [ibid., 318-319 (April 1968)]. 

Yuan, X., Moser, A., Surer, P. Wall functions for numerical simulation of turbulent natura] convection along vertical plates, /nt. J. Heat Mass Transfer, vol. 36, pp. 4477—448,5, 1993. 

In the simulation, the time dependency of the energy release of such sources is defined in so-called schedules. The heat sources transfer energy to the room air by convection and to the surfaces by long-wave radiation. In principle, heat sources can be modeled by two kinds of parameterization ... 

The room models implemented in the codes can be distinguished further by how detailed the models of the energy exchange processes are. Simple models use a combined convective-radiative heat exchange. More complex models use separate paths for these effects. Mixed forms also exist. The different models can also be distinguished by how the problem is solved. The energy balance for the zone is calculated in each time step of the simulation. 

These apparent restrictions in size and length of simulation time of the fully quantum-mechanical methods or molecular-dynamics methods with continuous degrees of freedom in real space are the basic reason why the direct simulation of lattice models of the Ising type or of solid-on-solid type is still the most popular technique to simulate crystal growth processes. Consequently, a substantial part of this article will deal with scientific problems on those time and length scales which are simultaneously accessible by the experimental STM methods on one hand and by Monte Carlo lattice simulations on the other hand. Even these methods, however, are too microscopic to incorporate the boundary conditions from the laboratory set-up into the models in a reahstic way. Therefore one uses phenomenological models of the phase-field or sharp-interface type, and finally even finite-element methods, to treat the diffusion transport and hydrodynamic convections which control a reahstic crystal growth process from the melt on an industrial scale. 

J. Fainberg, H.-J. Leister, G. Mueller. Numerical simulation of the LEC-growth of GaAs crystals with account of high-pressure gas convection. J Cryst Growth 750 517, 1997. 

Zhang, G. ]. and McFarlane, N. A. (1995). Sensitivity of climate simulations to the parameterization of cumulus convection in the Canadian Climate... 

Delete the radial convection term but otherwise run the full simulation. This gives avgC = 0.5197. Now add the radial term to get 0.5347. The change is in the correct direction since velocity profile elongation hurts conversion. 

Forced-Convection Flow. Heat transfer in pol3rmer processing is often dominated by the uVT flow advectlon terms the "Peclet Number" Pe - pcUL/k can be on the order of 10 -10 due to the polymer s low thermal conductivity. However, the inclusion of the first-order advective term tends to cause instabilities in numerical simulations, and the reader is directed to Reference (7) for a valuable treatment of this subject. Our flow code uses a method known as "streamline upwindlng" to avoid these Instabilities, and this example is intended to illustrate the performance of this feature. 

Figure 3. Finite element simulation of plane Couette flow with thermal dissipation and conductive heat transfer. (f) — fixed temperature condition (c) — convective boundary condition.

Gr/v Re = 9.6) without causing recirculation, and thus nonuniform surface flux. Since the disk temperature is fixed in this simulation, a smaller value of the mixed-convection parameter corresponds to a larger value of the disk spin rate. 

Figure 2.9.9(a) shows a schematic representation of a thermal convection cell in Rayleigh-Benard configuration [8]. With a downward temperature gradient one expects convection rolls that are more or less distorted by the tortuosity of the fluid filled pore space. In the absence of any flow obstacles one expects symmetrical convection rolls, such as illustrated by the numerical simulation in Figure 2.9.9(b). 

The spatial temperature distribution established under steady-state conditions is the result both of thermal conduction in the fluid and in the matrix material and of convective flow. Figure 2. 9.10, top row, shows temperature maps representing this combined effect in a random-site percolation cluster. The convection rolls distorted by the flow obstacles in the model object are represented by the velocity maps in Figure 2.9.10. All experimental data (left column) were recorded with the NMR methods described above, and compare well with the simulated data obtained with the aid of the FLUENT 5.5.1 [40] software package (right-hand column). Details both of the experimental set-up and the numerical simulations can be found in Ref. [8], The spatial resolution is limited by the same restrictions associated with spin... 

Fig. 2.9.9 (a) Schematic cross section of a compartments at the top and bottom, respec-convection cell in Rayleigh-Benard configura- tively. (b) Velocity contour plot of typical tion. In the version examined in Refs. [8, 44], a convection rolls expected in the absence of any fluid filled porous model object of section flow obstacles (numerical simulation). 

Fig. 2.9.10 Maps of the temperature and of the experimental data. The right-hand column convection flow velocity in a convection cell in refers to numerical simulations and is marked Rayleigh-Benard configuration (compare with with an index 2. The plots in the first row, (al) Figure 2.9.9). The medium consisted of a and (a2), are temperature maps. All other random-site percolation object of porosity maps refer to flow velocities induced by p = 0.7 filled with ethylene glycol (temperature thermal convection velocity components vx maps) or silicon oil (velocity maps). The left- (bl) and (b2) and vy (cl) and (c2), and the hand column marked with an index 1 represents velocity magnitude (dl) and (d2).

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