Ripples, condensation

Reducing the residual ripple from single-phase rectifiers for currents up to about 20 A and voltages of up to about 20 V can be achieved by filter circuits of choke coils and condensers. For greater output and constant residual ripple independent of load, the only possibility is the three-phase bridge circuit. It is always more satisfactory than a filter circuit. 

When this interaction of transmitted and reflected waves (resulting in ripples or beats), reaches a predetermined intensity, it trips an electronic switch, which then permits an electric charge stored in the firing capacitor (condenser) to flow thru an electric firing squib. 

The question in the title can be reformulated by asking how much can be dug out of an analogy between broken symmetry in dissipative structures (such as the ripple marks generated by wind, i.e., an external perturbation, in an otherwise flat surface of sand) and broken symmetry defined as phenomena of condensed matter systems of the kind observed near the critical points. The value of Anderson s discussion is to be seen more in the deepening of the question itself than in the answer that cannot yet be final, and for the moment, according to the author, appears to be more on the negative side. 

While the fluid dynamics of the actual film-flow process across the disc is daunt-ingly complex, a very approximate interim how model may be based upon Nusselt s treatment of the how of a condensate him. This assumes that the how is stable (i.e., ripple free), that there is no circumferential slip at the disc/liquid surface, and that there is no shear at the gas/liquid interface. The treatment is based... 

For example, suppose that the distillate flowrate from a distillation column is large compared to the reflux. We normally would use distillate to control level in the reflux drum. But suppose the distillate recycles back to the reactor and so we want to control its flow. What manipulator should we use to control reflux drum level We could potentially use condenser cooling rate or reboiler heat input. Either choice would have implications on the control strategy for the column, which would ripple through the control strategy for the rest of the plant. This would lead to control schemes that would never be considered if one looked only at the unit operations in isolation. 

Horizontal In-Shell Condensers The mean condensing coefficient for the outside of a bank of horizontal tubes is calculated from Eq. (5-93) for a single tube, corrected for the number of tubes in a vertical row. For undisturbed laminar flow over all the tubes, Eq. (5-97) is, for realistic condenser sizes, overly conservative because of rippling, splashing, and turbulent flow (Process Heat Transfer, McGraw-Hill, New York, 1950). Kern proposed an exponent of -Ve on the basis of experience, while Freon-11 data of Short and Brown General Discussion on Heat Transfer, Institute of Mechanical Engineers, London, 1951) indicate independence of the number of tube rows. It seems reasonable to use no correction for inviscid liquids and Kern s correction for viscous condensates. For a cylindrical tube bundle, where N varies, it is customary to take N equal to two-thirds of the maximum or centerline value. 

The Reynolds number for condensation on the outer surfaces of vertical tube or plates increases in the flow direction due to the increase of the liquid filn thickness S. The flow of liquid film exhibits different regimes, depending 01 the value of the Reynolds number. It is observed that the outer surface of th liquid film remains smooth and wave-free for about Re < 30, as shown ii Fig. 10 -23, and thus the flow is clearly laminar. Ripples or waves appear 01 the free surface of the condensate flow as the Reynolds number increases, anr the conden.sale flow becomes fully turbulent at about Re 1800. The con densate flow is called wavy-laminar in the range of 450 < Re < 1800 an turbulent for Re > 1800. However, some disagreement exists about the valu of Re at which the flow becomes wavy-laminar or turbulent. 

Nusselt s film condensation theory presumes an even increase in the thickness of the film due to further condensation. However experiments, among others [4.4] to [4.6], have shown that even in a flow that is clearly laminar, waves can develop at the film surface. These types of waves were not only observed on rough but also on polished surfaces. Obviously this means that the disturbances in the velocity that are always present in a stream are not damped under certain conditions, and so waves form. They lead to an improvement in the heat transfer of 10 to 25 % compared to the predictions from Nusselt s theory. According to Grimley [4.7], waves and ripples appear above a critical Reynolds number... 

These equations are strictly valid only for a plane vertical surface. However, they can be used for inside or outside vertical tubes with small error because the condensate film is thin compared with the diameter of a typical tube. Because of rippling and other nonidealities, the predicted coefficients are about 10-20% below experimental values. 

A high vapor velocity, in cross flow on a cylinder, canses rippling and turbulence in the condensate and resnlts in an increase (compared with Eqnation (6.89)) in the heat-transfer coefficient beginning at vapor Reynolds nnmbers (based on maximum vapor velocity flowing around the tnbe and the tube diameter) above 20,000, rising to as mnch as a 10-fold increase at Reynolds nnmbers abont... 

An Important possibility to consider Is that, near P°, Kelvin condensation occurs In ripple and dimple features, so that the surface actually consists of multitudinous patches or lakes" of liquid adsorbate. The model, for a single dimple. Is shown In Figure 9. The dimple Is taken to be a figure of revolution, of... 

The equation for thickness of a falling laminar film was first presented by Nusselt, who used the result to predict heat-transfer coefficients for condensing vapors. Measurements of film thickness on a vertical surface (cos = 1) show that Eq. (5.77) is approximately correct for x 1000, but the thickness actually varies with about 0.45 power of the Reynolds number, and the layers are thinner than predicted at low Nr and thicker than predicted above = 1000. The deviations may be due to ripples or waves in the films, which are apparent even at quite low Reynolds numbers. 

Armbruster and Mitrovic [62] observed that liquid falls from tube to tube in three patterns discrete droplets, jets or columns, and sheets, depending on the flow rate (i.e., film Reynolds number) and fluid properties. In addition, depending on the tube arrangement and spacing, the condensate may cause ripples, waves, and turbulence to occur in the film splashing may occur, as well as nonuniform rivulet runoff of condensate because of tube inclination or local vapor velocity effects. As a result, it is impossible to arrive at an analytical expression to describe these complex bundle phenomena. In general, the effect of inundation may be accounted for using... 

---