Vorticity production

The source of vorticity at a solid, no-slip surface is the velocity gradient that is generated in satisfying the no-shp condition. This mechanism yields vorticity of 0(Rel/2) at the body surface. At an interface where the tangential velocity is not zero, on the other hand, vorticity is produced by rotation of fluid elements caused by the surface curvature. This latter mechanism generates vorticity of magnitude proportional to the local curvature of the surface in the direction of the motion of the fluid. As an example of vorticity production in the latter case, we may consider the condition of zero tangential stress at the surface of a bubble whose shape we assume, for simplicity, to be spherical. In this case, for an axisymmetric motion,... 

Figure 1 provides insight into the role of the solenoidal term in vorticity production. If the lines of constant pressure and constant density intersect as shown, the less dense air on the right experiences a greater acceleration due to the pressure gradient force than the heavier air on the left, giving rise to a velocity shear and positive vorticity. The... 

Vapor-Liquid Separation This design problem may be important for a number of reasons. The most important is usually prevention of entrainment because of value or product lost, pollution, contamination of the condensed vapor, or fouling or corrosion of the surfaces on which the vapor is condensed. Vapor-liquid separation in the vapor head may also oe important when spray forms deposits on the w ls, when vortices increase head requirements of circulating pumps, and when shoiT circuiting allows vapor or unflashed liquid to be carried back to the circulating pump ana heating element. 

Convection-based systems fall into two fundamental classes, namely those using a moving electrode in a fixed bulk solution (such as the rotated disc electrode (RDE)) and fixed electrodes with a moving solution (such as flow cells and channel electrodes, and the wall-jet electrode). These convective systems can only be usefully employed if the movement of the analyte solution is reproducible over the face of the electrode. In practice, we define reproducible by ensuring that the flow is laminar. Turbulent flow leads to irreproducible conditions such as the production of eddy currents and vortices and should be avoided whenever possible. 

Measurements showed that the amount of soot produced by the flame was affected by the mixing process between the air jet vortices, the fuel jets, and naturally entrained external air. PIV and smoke flow visualization showed that the air vortices induced strong external air entrainment into the main jet flow very close to the exit plane when the phase angle between the fuel jets and air jet were at the value for minimized soot production. When the wrong phase angle was used, i.e., that which leads to soot formation, the air vorticity coherence was reduced, the vortices appeared to develop further downstream, and the air entrainment at the flame base was significantly reduced. 

The flow involves fuel, F, issuing from a central slot of width D with an oxidizer, O, co-flow with both streams at the reference temperature, Tq. A global single-step, irreversible, exothermic chemical reaction of the type F + rO —> (1 -f r)P with an Arrhenius reaction rate coefiicient is assumed. A hot layer of combustion products, P, at the inlet serves to separate the fuel and oxidizer streams and acts as an ignition source. The inlet conditions for the velocity, temperature, and composition are shown in Fig. 10.2. The ratio of the inlet velocities of the fuel to oxidizer streams is chosen as 4. Inlet velocity forcing is used to induce early roll-up and pairing of the jet shear layer vortices. 

Figure 13.5 Unsteady nonpremixed combustion and fluid dynamics (a) contours of the vorticity magnitude O in planes indicated to the right (6) cross-sectional averaged measures of instantaneous chemical product and product formation (left frame), instantaneous unconstrained and vorticity-bearing (ff > 5% peak-value) streamwise mass flux Q (right frame). 1 — product, 2 — instantaneous production, 3 — Oo = 0, and 4 flo/f peak — 0.05...

Thermal expansion of a gas in a curved flame front leads to the formation of gasdynamic vorticity in the combustion products and is the cause of a flame instability discovered by L. D. Landau, and also by G. Darriet (France), in 1944. It turned out, however, that this instability was very reluctant to exhibit itself in experiments The first explanation of such a phenomenon—using the example of a spherical flame—was given by A. G. Istratov and V. B. Librovich. Ya.B. and his coauthors [34] proposed a method for calculating rapid combustion in a tube containing an elongated flame... 

The flow of combustion products behind the flame front has a non-zero vorticity. When the gas crosses the flame front, which represents the gas-dynamic discontinuity surface where the velocity, pressure, density and gas temperature are step-like changing, the vorticity of combustion products is generated (Zeldovich, 1944, 1966, 1979, 1980 Borisov, 1978 Zeldovich et al. 1979 Tsien, 1951 and Chernyi, 1954). 

Starting from the flame front the intensity of the vortices remains constant along each streamline, so that the region filled by combustion products is a rotational one. In some of the previous works mentioned, however, the existence of the stagnation zone behind the flame front has not been accounted for, so that the quantitative conclusions diflier essentially from those of the hydrodynamic model presently under consideration. It should be noted that the boundary streamline of the stagnation zone is a tangential velocity component discontinuity surface or a vortex sheet. As a consequence of the... 

Consider the condition, which determines the velocity of the curved flame front propagation in the channel. Inside the stagnation zone filled by combustion products the pressure is constant and is equal to the value at infinity (when x = oo). Because of Bernoulli s integral along the streamline restricting the stagnation zone, the gas motion velocity remains unchanged. Since at x = oo the flow is plane-parallel (ptJO = const, v — 0), distributions of velocity u and of the stream function are associated with the vorticity distribution ... 

An effective method of controlling concentration polarization and sustaining productivity involves inducing turbulent vortices on the membrane surface to counteract the forces of solute or particle deposition. The rotating... 

The converter will operate most efficiently when it supplies coating binder at the same rate as it is consumed. Problems may occur when the converter has to be shut off and flushed with water. Channel flow and vortices during the purge with water affect cleaning time and may make it necessary to sewer starch product. In another converter, a single pump is used to transport the starch through the retention vessel. Jet cookers of the venturi type are placed at the entrance to the vessel and at its exit.114 In an alternative design, a retention coil is used instead of a retention vessel.115... 

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