Rayleigh Flow

For microflow simulations, the statistical scatter associated with DSMC limits its applications to microflows with extremely low velocity. The information preservation (IP) method has been developed to address this issue. The method [7, 8] introduces preserved information velocities. It has been applied to low-speed Couette, Poiseuille, and Rayleigh flows in the sUp, transition, and free molecular flow regimes and to low-speed microflows. For convergence, the... 

The observed effects of heat transfer on the flow in micro-nozzles are readily explained as follows. From compressible Rayleigh flow, it is known that removing heat from a supersonic flow acts to accelerate the flow. At steady-state, the bulk of the flow in the micro-nozzle expander is supersonic, and thus, heat transfer acts to further accelerate the supersonic flow. Concurrently, as the flow is cooled, the exit density p increases. The overall effect is an increase in thrust. Heat extraction from the flow into the substrate increases performance from the subsonic layer point of view as well. For low nozzle wall temperatures, the local sonic velocity is diminished and the near-wall Mach number increases. This phenomenon is the force driving the reduction in subsonic layer size for micro-nozzle flows with heat removal. In fact, with sufficient heat extraction from the flow, the subsonic layer can be reduced to the point where the competing effects of viscous forces and nozzle geometry cause the optimum expander half angle to be shifted from 30° to a more traditional expander half angle of 15°. This is demonstrated in Fig. 7 for isothermal wall temperatures less than 700 K. 

The observed effects of heat transfer on the flow in micronozzles is readily explained as follows. From compressible Rayleigh flow it is known that removing heat from a supersonic flow acts to accelerate the flow. At steady-state, the bulk of the flow in the micro-nozzle expander is super-... 

Circulation of fluid is promoted by surface tension gradients but inhibited by viscosity, which slows the flow, and by molecular diffusion, which tends to even out the concentration differences. The onset of instabibty is described by a critical Marangoni number (Mo), an analogue of the Rayleigh... 

Quiben JM, Thome JR (2007b) Flow pattern based two-phase pressure drop model for horizontal tubes. Part II. New phenomenological model. Int. J. Heat and Fluid Flow. 28(5) 1060-1072 Rayleigh JWS (1917) On the pressure developed in a liquid during the collapse of a spherical cavity. Phil Mag 34 94-98... 

Thermally driven convective instabilities in fluid flow, and, more specifically, Rayleigh-B6nard instabilities are favorite working examples in the area of low-dimensional dynamics of distributed systems (see (14 and references therein). By appropriately choosing the cell dimensions (aspect ratio) we can either drive the system to temporal chaos while keeping it spatially coherent, or, alternatively, produce complex spatial patterns. 

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). 

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).

At low Rayleigh numbers, Wragg (W6) found a smaller Ra dependence, resembling more the dependence in laminar free convection. In this range of Ra numbers, a cellular flow pattern is believed to exist, analogous to that of thermal and surface tension-driven cellular convection (Benard cells F3). In the range where the convection is turbulent, the Ra1/3 dependence has been confirmed over seven powers of Ra by Ravoo (R9), who used a centrifuge to vary the body force at constant bulk composition. 

In acoustic cavitation, some bubbles dramatically expand and violently collapse, which is called the inertial collapse or Rayleigh collapse. It is caused by both the spherically shrinking geometry and the inertia of the surrounding liquid which inwardly flows into the bubble. The bubble collapse is similar to that in hydrodynamic cavitation which is induced by a sudden drop of pressure below the saturated vapor pressure due to a fluid flow through an orifice [92, 93]. At the end of the... 

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