Condensers correction factors

A computer program developed hy Volta handles the problem of condensing in the presence of a noncondensable gas for down-flow of either a saturated or superheated gas-vapor mixture vertical tubes. The program is based on a modification of Colburn-Hougen and Bras and is certainly more accurate and easier to use than the lengthy manual calculations. Although the program was written for vertical tubes, it can be used to approximate the results in a horizontal unit, and if the correction factor between vertical and horizontal tube condensation is applied, the compari-... 

A pure, saturated, vapour will condense at a fixed temperature, at constant pressure. For an isothermal process such as this, the simple logarithmic mean temperature difference can be used in the equation 12.1 no correction factor for multiple passes is needed. The logarithmic mean temperature difference will be given by ... 

When the condensation process is not exactly isothermal but the temperature change is small such as where there is a significant change in pressure, or where a narrow boiling range multicomponent mixture is being condensed the logarithmic temperature difference can still be used but the temperature correction factor will be needed for multipass condensers. The appropriate terminal temperatures should be used in the calculation. 

The ideal gas equation assumes that the force of attraction between gas molecules is zero. The assumption that there is no force of attraction between gas particles is not true. If it was, gases would never condense to form liquids. In reality, there is a small force of attraction between gas molecules that tends to hold the molecules together. This force of attraction has two consequences (1) gases condense to form liquids at low temperatures, and (2) the pressure of a real gas is sometimes smaller than expected for an ideal gas. The correctional factor "a" corrects for the fact that the pressure of a real gas is smaller than expected from the ideal gas equation. 1 point for explaining "a" correctly and 1 point for supporting evidence. 

U0 is called the lattice energy of the crystal JV is Avogadro s number, used to convert energy per ion pair to energy per mole, and a is the correction factor introduced above to account for the repulsion of electron clouds. The lattice energy, t/o, then corresponds to the energy released when the requisite number of positive ions and of negative ions are condensed into an ionic crystal to form one mole of the compound. 

Many attempts have been made to develop PVT relations for detonation products of condensed expls. These product gases, even in the absence of any condensed phase products, are very far from ideal. Thus most EOS for detonation products have included correction factors to account for non-ideality. Most product EOS are semi-empirical because they have to be adjusted to fit expti data. Usually the Abel equation, pv=nRT+atp, is used as a starting point. In the original Abel equation a is a constant covolume, but a constant a does not agree with observation. Therefore various attempts have been made to modify the Abel equation by inclusion of a = a(v) or a = a(p) and so on. The various attempts at obtaining a true EOS are summarized in Vol 4, D268-L to D298-R. Below we will briefly describe a new EOS which was developed recently... 

The functions/s( ) and FA(E) are, respectively, the normalized spectral distribution of the fluorescence of S and the normalized absorption of A, and ES(E) is the normalized absorption of S. A correction factor (e/ec)2 gives the ratio of the electric field amplitude in the vacuum, s, to that in the condensed medium, sc. The parameters Qi are defined according to Equation 6.85,... 

As indicated when K = kXjjT0MCp was first introduced just before Eqn. (12), K is constant with respect to decisions within each feedwater heater or condenser, but is a variable with respect to associated costs. Thus, for example, the dimensionless cost k includes the cost of cooling water inlet filters in the case of the condensers—while for feedwater heaters it includes the cost of the bleed steam duct and tap required for the addition of a new heater. It also includes the cost of end effects (such as headers and water boxes) which will be added automatically to k when the non-linearity correction factors mentioned above are included. When all these corrections are considered, the results of Eqns. (A2) and (A3) appear to be in good agreement with the values found in well-optimized plants (such as the Wisconsin Electric Plant from which the data for this work was taken), but it is beyond the scope of this paper to pursue this matter further. 

Values of the correction factor F according to Ref. 4 are plotted in Figs. 10-8 to 10-11 for several different types of heat exchangers. When a phase change is involved, as in condensation or boiling (evaporation), the fluid normally... 

For low-fin tubes, the laminar condensing coefficient can be calculated by applying an appropriate correction factor F to the value calculated using the preceding equation for laminar-film condensation. The factor F is defined thus ... 

For isothermal condensation, the logarithmic-mean tenperature difference correction factor, F, equals one. Therefore, from Equation 4.7.3 for the existing heat exchanger, the available overall heat-transfer coefficient. 

Two flow models are used to estimate the mean condensation coefficient in horizontal tubes stratified flow. Figure 12.45<3, and annular flow. Figure 2.45b. The stratified flow model represents the limiting condition at low condensate and vapour rates, and the annular model the condition at high vapour and low condensate rates. For the stratified flow model, the condensate film coefficient can be estimated from the Nusselt equation, applying a suitable correction for the reduction in the coefficient caused by the accumulation of condensate in the bottom of the tube. The correction factor will typically be... 

Equations 15 and 16 develop Equation (14) for gas-to-condensed-phase transitions. It would also be desirable to develop Equation (14) for liquid-to-crystalline nucleation to assign physical meaning to An. However, development of Equation (14) is difficult both because d can be a large correction factor for liquid/solid interfaces and because the molecular density differences between liquids and solids are smaller than between gases and condensed phases (Kashchiev 1982). 

In the upper left of the humidity chart is a little insert that gives the value of the small correction factor for the water condensed from the air which leaves the system. Assuming that the water leaves at the dew point of 54°F, read for 49 grains a correction of —0.15 Btu/lb of dry air. You could calculate the same value by taking the enthalpy of liquid water from the steam tables and saying,... 

It is obvious that the flux correction factors cannot be ignored in this particular problem. This is likely to be the case in many condensation problems. 

F (i) — function of concentration of condensable molecules C = panicle-size-dependent correction factor near unity for dp > 0. t... 

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