R.S. Tankin

Bio: R.S. Tankin is an academic researcher from Northwestern University. The author has contributed to research in topics: Rayleigh number & Convection. The author has an hindex of 4, co-authored 4 publications receiving 189 citations.

Two-phase flow, boiling and condensation in conventional and miniature systems

Abstract: Providing a comprehensive introduction to the fundamentals and applications of flow and heat transfer in conventional and miniature systems, this fully enhanced and updated edition covers all the topics essential for graduate courses on two-phase flow, boiling, and condensation. Beginning with a concise review of single-phase flow fundamentals and interfacial phenomena, detailed and clear discussion is provided on a range of topics, including two-phase hydrodynamics and flow regimes, mathematical modeling of gas-liquid two-phase flows, pool and flow boiling, flow and boiling in mini and microchannels, external and internal-flow condensation with and without noncondensables, condensation in small flow passages, and two-phase choked flow. Numerous solved examples and end-of-chapter problems that include many common design problems likely to be encountered by students, make this an essential text for graduate students. With up-to-date detail on the most recent research trends and practical applications, it is also an ideal reference for professionals and researchers in mechanical, nuclear, and chemical engineering.

A critical review of the flooding literature

Abstract: Countercurrent flow of a gas and a liquid in direct contact with each other is, of necessity, gravity dominated. That is, in the absence of electromagnetic force fields, thermocapillary effects, or concentration-capillary effects, countercurrent flow can be sustained only as a result of the difference in the gravitational force per unit volume on the gas and on the liquid. If the gas and liquid are simultaneously introduced into a porous medium or into a vertical or inclined pipe, the gas tends to rise relative to the liquid. If conditions allow complete separation, it is possible to maintain steady countercurrent flow in which the liquid discharges at the bottom while the gas flows out from the top. The countercurrent flow is opposed by interfacial friction between the phases, which always seems to increase monotonically as the relative countercurrent mean velocity of the phases increases. Hence, for a given geometry and liquid-gas pair, there is a maximum relative velocity that can be sustained in countercurrent flow. This point is known as the onset of flooding. Further increases in gas or liquid input ratas result in only partial delivery of the liquid out of the bottom. Eventually, if the gas velocity becomes sufficiently high, none of the liquid is delivered at the bottom, and fully cocurrent upward flow is established. If the liquid is being introduced from an upper plenum, none will penetrate into the pipe or porous medium when this second critical gas velocity is reached.

Spray jets in a cross-flow

Abstract: When droplets are expelled at a high velocity by a spray, a strong vertical air jet is induced throughout which the smallest droplets are dispersed (their Reynolds numbers associated with their relative motion being small). In our analysis we focus on the interaction between an external cross-flow and this spray jet. This interaction and the distances by which the spray jet and, over a longer distance, the large droplets are deflected are found to depend largely on the ratio of the cross-wind speed to the induced air speed U0/Uj. Using a multi-zone analysis we show that with a weak cross-flow (U0/Uj[les ]0.1), in the region immediately below the nozzle the spray entrains the external cross-flow and acts like a line sink; the streamlines close to the spray curve inwards to the centre, while further away the sink flow is weak and the streamlines follow the cross-wind. The external flow stagnates at a certain distance from the spray centreline which depends on U0/Uj. When U0/Uj[ges ]0.1 the cross-section of the spray jet and its velocity distribution change in the same way as a fluid jet in a cross-flow, whose inertia causes the deflection of the external flow around it and whose surface vorticity causes a pair of axial vortices on the downwind side of the spray. These vortices have a significant effect on the spray because they induce a back flow which reduces the tendency of the small droplets to leave the spray. When the cross-wind is strong (U0/Uj>0.3; U0[ges ]10 m s−1) the flow is too strong to be entrained; in this limit the main effect of the larger spray droplets is simply to resist the cross-flow which causes the cross-flow to slow down as it passes through the spray and to divert some of the cross-flow around the spray jet. Since the cross-flow now passes through the spray it carries the smallest droplets downwind.In this paper analytical models have been developed for all the practical ranges of the ratio of the jet speed to the cross-wind speed. This enables spray drift to be calculated. These models require very little computer time and can be run interactively. Spray droplet trajectories can be plotted straightforwardly for both axisymmetric and flat-fan sprays.

Induced Air Velocity within Droplet Driven Sprays

Abstract: A study of the fundamental mechanics of the droplet and gas motion in liquid sprays is presented in this paper. Only vertical sprays without any externally applied gas flow are considered. First a detailed account of the origin of induced air motion within spray jets is given, and this lays the basis for a new one-dimensional model for predicting the induced axial air velocity. Two main flow zones (zone I and zone II) are identified, where the droplet velocity is much greater and of the same order as the induced air velocity respectively. Within zone I there is a near-sub-zone I , close to the nozzle where the droplet velocities deviate little from their initial values, and it is found that the air velocity decreases or increases to a maximum value, depending on whether its initial value is greater or less than a critical value, which itself is a function of the drag coefficient, the initial spray radius and the droplet velocity. In this zone the average induced air velocity decays more slowly, as z -½ ( z being the downstream distance) than the rate of decay, as z -1 , in regular unforced jets. Further downstream in the adjacent forced jet sub-zone , the drag of the faster moving droplets forces an air jet to develop with a rate of growth that is determined by the turbulence if the angle of the spray droplets is small or by the angle of the spray if the angle is large. In this second sub-zone, which typically extends to the stopping distance of the droplets, the flow is largely independent of the flow in the near sub-zone. The 1D model was applied to a rose-head axisymmetric spray and a flat-fan agricultural spray. The calculations agree closely with experimental observations. To calculate the radial variation of the air velocity a 2D axisymmetric model was developed where the air velocity was obtained in the form of a similarity solution. The predictions were in good agreement with the measurements of Binark & Ranz (1958). Finally it is shown that the 1D and the 2D models are consistent with each other.