Internal Condensing Flows Inside a Vertical Pipe: Experimental/Computational Investigations of Effects of Constrained and Natural Exit Conditions

Abstract

The flow and heat transfer rates inside a condenser depend on the specification of inlet, wall, and exit conditions. For steady/quasi-steady internal condensing flows (that involve compressible vapor at low Mach Numbers), the vapor’s ability to change its density — and hence interfacial mass transfer rates and associated locations of the interface — allows the flow to have a rather significant dependence on exit conditions. Both experimental and direct computational simulation results presented here show that this is indeed the case for flows of pure vapor experiencing film condensation on the inside walls of a vertical tube. In applications, the totality of boundary conditions are determined not only by the condenser; but also by the flow-loop (or the system) — of which the condenser is only a part. Therefore, the results outlined here should contribute towards a better understanding of the behavior (particularly the extent to which vapor compressibility effects affect the flow regimes of operation — i.e. annular, plug/churn, etc.) and response (transients due to start-up, system instabilities, etc.) of condensers in application systems (e.g. Rankine Cycle power plants, Capillary Pumped Loops, Looped Heat Pipes, etc.). In this connection, an experimental example of a relevant system instability is presented here. In summary, the experimental results presented here, and computational results presented elsewhere, reinforce the fact that there exist multiple steady solutions (with different heat transfer rates) for different exit conditions and that there also exists a “natural” steady solution for straight vertical condensers (circular and rectangular cross-sections).

Effects of exit-condition, gravity, and surface-tension on stability and noise-sensitivity issues for steady condensing flows inside tubes and channels

“…The experimental results (presented elsewhere [3]) also clearly support the computational results that show existence of multiple steady solutions for different prescriptions of steady exit conditions and the existence of a special steady Nomenclature C pI specific heat (J/(kg K)) h fg latent heat, h g À h f (J/kg) Ja…”

“…through the arrangement in Fig. 3 of [3], a range of _ M v = _ M in values is available at the exit), or (b) a constrained or prescribed exit condition, which may arise from downstream constraints in the flow loop or by active downstream flow control (e.g. a specific value of _ M v = _ M in at the exit is prescribed through the arrangement in Fig.…”

“…a specific value of _ M v = _ M in at the exit is prescribed through the arrangement in Fig. 2 of [3]). …”

“…1a) is considered here while some new and improved results for the horizontal and zero gravity channel flow cases-formulated elsewhere [1,2]-are also presented. The results are important for a qualitative understanding of experiments (see, e.g., [3]) dealing with the behavior of a condenser-section (typically of hydraulic diameters in millimeter or sub-millimeter range). They also relate to issues of better design and integration of condensers needed in ground or space based thermal management systems or power systems-both for large scale (such as Looped Heat Pipes, Capillary Pumped Loops, etc.)…”

“…Greek symbols p I non-dimensional pressure h I non-dimensional temperature q I density (kg/m 3 solution associated with the natural exit condition when no exit condition is prescribed. This natural exit condition for unconstrained exit case typically exists only if the flow is parabolic up to the exit location for the gravity dominated cases.…”