Laminar vapor flow

In Table 6.7, C is the Martinelli-Chisholm constant, / is the friction factor, /f is the friction factor based on local liquid flow rate, / is the friction factor based on total flow rate as a liquid, G is the mass velocity in the micro-channel, L is the length of micro-channel, P is the pressure, AP is the pressure drop, Ptp,a is the acceleration component of two-phase pressure drop, APtp f is the frictional component of two-phase pressure drop, v is the specific volume, JCe is the thermodynamic equilibrium quality, Xvt is the Martinelli parameter based on laminar liquid-turbulent vapor flow, Xvv is the Martinelli parameter based on laminar liquid-laminar vapor flow, a is the void fraction, ji is the viscosity, p is the density, is the two-phase frictional... 

In this table the parameters are defined as follows Bo is the boiling number, d i is the hydraulic diameter, / is the friction factor, h is the local heat transfer coefficient, k is the thermal conductivity, Nu is the Nusselt number, Pr is the Prandtl number, q is the heat flux, v is the specific volume, X is the Martinelli parameter, Xvt is the Martinelli parameter for laminar liquid-turbulent vapor flow, Xw is the Martinelli parameter for laminar liquid-laminar vapor flow, Xq is thermodynamic equilibrium quality, z is the streamwise coordinate, fi is the viscosity, p is the density, <7 is the surface tension the subscripts are L for saturated fluid, LG for property difference between saturated vapor and saturated liquid, G for saturated vapor, sp for singlephase, and tp for two-phase. 

Laminar vapor flow This will tend to reduce mass transfer. 

Vapor can condense on a cooled surface in two ways. Attention has mainly been given in this chapter to one of these modes of condensation, i.e.. to him condensation. The classical Nusselt-type analysis for film condensation with laminar film flow has been presented hnd the extension of this analysis to account for effects such as subcooling in the film and vapor shear stress at the outer edge of the film has been discussed. The conditions under which the flow in the film becomes turbulent have also been discussed. More advanced analysis of laminar film condensation based on the use of the boundary layer-type equations have been reviewed. 

Select the calculation method to be used. Condensation on the outside of banks of horizontal tubes can be predicted assuming two mechanisms. The first assumes laminar condensate flow the second assumes that vapor shear dominates the heat transfer. The following equations can be used to predict heat-transfer coefficients for condensation on banks of horizontal tubes For laminar-film condensation,... 

At Reynolds numbers greater than about 30, it is observed that waves form at the liquid-vapor interface although the flow in liquid film remains laminar. I he flow in this case is said to be wavy laminar. The waves at the liquid-vapor interface tend to increase heat transfer. But the waves also complicate the analysis and make it very difficult to obtain analytical solutions. Therefore, we have to rely on experimental studies. The increase in heat transfer due to the wave effect is, on average, about 20 percent, but it can exceed 50 percent. The exact amount of enhancement depends on the Reynolds number. Rased on his experimental studies, Kutateladze (1963) recommended the following relation for the average heat transfer coefficient in wavy laminar condensate flow for p p, and 30 < Re < 1800,... 

In the absence of a strong vapor flow, the condensate film on a vertical surface drains under the influence of gravity only. At low flow rates, the flow is laminar, and a theoretical analysis by Nusselt [35] is applicable. The local value of the coefficient at a distance x from the start of condensation is... 

Suppose that on a vertical wall whose temperature is constant and equal to Ts, stagnant dry saturated vapor is condensing. Let us consider the steady-state problem under the assumption that we have laminar waveless flow in the condensate film. According to [200], we make the following assumptions the film motion is determined by gravity and viscosity forces the heat transfer is only across the film due to heat conduction there is no dynamic interaction between the liquid and vapor phases the temperature on the outer surface of the condensate film is constant and equal to the saturation temperature Tg the physical parameters of the condensate are independent of temperature and the vapor density is small compared with the condensate density the surface tension on the free surface of the film does not affect the flow. 

Mathewson and Smith [317] investigated the effects of acoustic vibrations on condensation of isopropanol vapor flowing downward in a vertical tube. A siren was used to generate a sound field of up to 176 dB at frequencies ranging from 50 to 330 Hz. The maximum improvement in condensing coefficient was found to be about 60 percent at low vapor flow rates. The condensate film under these conditions was normally laminar thus, an intense sound field produced sufficient agitation in the vapor to cause turbulent conditions in the film. The effect of the sound field was considerably diminished as the vapor flow rate increased. 

During steady-state operation, the liquid mass flow rate m, must equal the vapor mass flow rate mv at every axial position, and while the liquid flow regime is always laminar, the vapor flow may be either laminar or turbulent. As a result, the vapor flow regime must be written as a function of the heat flux. Typically, this is done by evaluating the local axial Reynolds number in the vapor stream. It is also necessary to determine whether the flow should be treated as compressible or incompressible by evaluating the local Mach number. 

Outside Horizontal Tubes Condensation on the outside of banks of horizontal tubes can be predicted assuming two mechanisms laminar condensate flow and vapor shear dominated heat transfer. 

Fauske [32] represented a nomograph for tempered reaetions as shown in Figure 12-35. This aeeounts for turbulent flashing flow and requires information about the rate of temperature rise at the relief set pressure. This approaeh also aeeounts for vapor disengagement and frietional effeets ineluding laminar and turbulent flow eonditions. For turbulent flow, the vent area is... 

A deflagration can best be described as a combustion mode in which the propagation rate is dominated by both molecular and turbulent transport processes. In the absence of turbulence (i.e., under laminar or near-laminar conditions), flame speeds for normal hydrocarbons are in the order of 5 to 30 meters per second. Such speeds are too low to produce any significant blast overpressure. Thus, under near-laminar-flow conditions, the vapor cloud will merely bum, and the event would simply be described as a large fiash fire. Therefore, turbulence is always present in vapor cloud explosions. Research tests have shown that turbulence will significantly enhance the combustion rate in defiagrations. 

Equation 2-25 is valid for calculating the head loss due to valves and fittings for all conditions of flows laminar, transition, and turbulent [3], The K values are a related function of the pipe system component internal diameter and the velocity of flow for v-/2g. The values in the standard tables are developed using standard ANSI pipe, valves, and fittings dimensions for each schedule or class [3]. The K value is for the size/type of pipe, fitting, or valve and not for the fluid, regardless of whether it is liquid or gas/vapor. 

Chapter 10 deals with laminar flow in heated capillaries where the meniscus position and the liquid velocity at the inlet are unknown in advance. The approach to calculate the general parameters of such flow is considered in detail. A brief discussion of the effect of operating parameters on the rate of vaporization, the position of the meniscus, and the regimes of flow, is also presented. 

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