Vapor shear force

The analysis was later modified to include some of the factors neglected by Nusselt1213. One of these is the effect of buoyancy forces acting on the liquid film. This results in the pl term in Equation 15.80 being replaced by Pl(pl — Pv ) Such buoyancy forces are usually only important close to the critical point. In most cases, the two most important factors that cause a significant deviation from Equation 15.80 are the presence of vapor shear forces and noncondensable gases in the vapor. Vapor shear forces act to increase the heat transfer coefficient, whereas noncondensable gases act to decrease it. 

In order to stimulate condensate motion under zero-G conditions, other forces must replace the gravitational force. This may be done by centrifugal forces, vapor shear forces, surface tension forces, suction forces, and forces created by an electric field. McEver and Hwangbo [133] and Valenzuela et al. [134] describe how surface tension forces may be used to drain a condenser surface in space. Tanasawa [1] reviews electrohydrodynamics (EHD) enhancement of condensation. Bologa et al. [135] showed experimentally that an electric field deforms the liquid-vapor interface, creating local capillary forces that enhance the heat transfer. 

The flow may proceed from laminar wave-free to laminar wavy to turbulent conditions, depending on the film Reynolds number (i.e., the heat flux and length of the tube). In this situation, the average heat transfer coefficient may be calculated using Eq. 14.21. If the vapor velocity is very high, then the flow is controlled by vapor shear forces, and annular flow models described in this chapter are applicable. 

Droplet size, particularly at high velocities, is controlled primarily by the relative velocity between liquid and air and in part by fuel viscosity and density (7). Surface tension has a minor effect. Minimum droplet size is achieved when the nozzle is designed to provide maximum physical contact between air and fuel. Hence primary air is introduced within the nozzle to provide both swid and shearing forces. Vaporization time is characteristically related to the square of droplet diameter and is inversely proportional to pressure drop across the atomizer (7). 

This first term in this equation is the result of the gravitational force on the liquid in the control volume, the second term is due to the viscous shear force, while the third represents the pressure exerted on the control volume due to the gravitational force on vapor. 

This equation indicates that the shear force is equal to the net gravitational force, i.e., the gravitational force on the liquid less the gravitational force that would have acted on the control volume had it contained vapor and not liquid. 

Film condensation on a vertical plate may be analyzed in a manner first proposed by Nusselt [I], Consider the coordinate system shown in Fig. 9-2. The plate temperature is maintained at 7 ,. and the vapor temperature at the edge of the him is the saturation temperature TK. The him thickness is represented by <5, and we choose the coordinate system with the positive direction of. v measured downward, as shown. It is assumed that the viscous shear of the vapor on the him is negligible at y -- 8. It is further assumed that a linear temperature distribution exists between wall and vapor conditions. The weight of the fluid element of thickness dx between y and 8 is balanced by the viscous-shear force at y and the buoyancy force due to the displaced vapor. Thus... 

But the simple no-flow picture of equation 4 can no longer hold in view of equations 7a and 7b. At the liquid-vapor boundary, the viscous shear force must balance the force imposed by surface tension gradients, rjdu/dz = da/dx (z = h). This boundary condition leads to a linear flow profile toward the drying line,... 

Entrainment Limitation. As a result of the high vapor velocities, liquid droplets may be picked up or entrained in the vapor flow and cause excess liquid accumulation in the condenser and hence dryout of the evaporator wick [14]. This phenomenon requires that, for proper operation, the onset of entrainment in countercurrent two-phase flow be avoided. The most commonly quoted criterion to determine this onset is that the Weber number We, defined as the ratio of the viscous shear force to the force resulting from the liquid surface tension,... 

Composite wicking structures accomplish the same type of effect in that the capillary pumping and axial fluid transport are handled independently. In addition to fulfilling this dual purpose, several wick structures physically separate the liquid and vapor flow. This results from an attempt to eliminate the viscous shear force that occurs during countercurrent liquid-vapor flow. 

During shell-side condensation in tube bundles, neighboring tubes disturb the vapor flow field and create condensate that flows from one tube to another under the action of gravity and/or vapor shear stress forces. The effects of local vapor velocity and condensate inundation must, therefore, be properly accounted for when calculating the average heat transfer in the bundle. Marto and Nunn [53], Marto [54], and Fujii [55] provide details of these phenomena. 

Heat transfer coefficients for condensation processes depend on the condensation models involved, condensation rate, flow pattern, heat transfer surface geometry, and surface orientation. The behavior of condensate is controlled by inertia, gravity, vapor-liquid film interfacial shear, and surface tension forces. Two major condensation mechanisms in film condensation are gravity-controlled and shear-controlled (forced convective) condensation in passages where the surface tension effect is negligible. At high vapor shear, the condensate film may became turbulent. 

An interfacial shear may be very important in so-called shear-controlled condensation because downward interfacial shear reduces the critical Re number for onset of turbulence. In such situations, the correlations must include interfacial shear stress, and the determination of the heat transfer coefficient follows the Nusselt-type analysis for zero interfacial shear [76], According to Butterworth [81], data and analyses involving interfacial shear stress are scarce and not comprehensive enough to cover all important circumstances. The calculations should be performed for the local heat transfer coefficient, thus involving step-by-step procedures in any condenser design. The correlations for local heat transfer coefficients are presented in [81] for cases where interfacial shear swamps any gravitational forces in the film or where both vapor shear and gravity are important. 

When vapor is moving at a large approaching velocity, the shear stress between the vapor and the condensate surface must be taken into account (i.e., shear forces are large compared to gravity force). A good review of the work devoted to this problem is found in Rose [85], who provided a detailed discussion of film condensation under forced convection. In Table 17.24, a correlation derived by Fuji et al. [86] and suggested by Butterworth [81] is included for the vapor shear effect. The same equation can be applied for a tube bundle. In such a situation, the approach velocity u should be calculated at the maximum free-flow area cross section within the bundle. 

For an upward flow direction, the shear forces may influence the downward-flow of the condensate, causing an increase of the condensate film thickness. Therefore, the heat transfer coefficient under such conditions shall decrease up to 30 percent compared to the result obtained using the same correlation as the upward-flowing vapor. If the vapor velocity increases substantially, the so-called flooding phenomenon may occur. Under such condition, the shear forces completely prevent the downward condensate flow and flood (block) the tube with the condensate. Prediction of the flooding conditions is discussed by Wallis, as reported by Butterworth [81]. 

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