Research Papers: Evaporation, Boiling, and Condensation

Condensation of a Quiescent Vapor by a Stagnation-Point Liquid Flow

[+] Author and Article Information
R. Balasubramaniam

Research Associate Professor
National Center for Space Exploration Research,
Case Western Reserve University/NASA Glenn
Research Center,
Mail-Stop 110-3,
Cleveland, OH 44135
e-mail: Ramaswamy.Balasubramaniam-1@nasa.gov

E. Ramé

Universities Space Research Association c/o
NASA Glenn Research Center,
Mail-Stop 110-3,
Cleveland, OH 44135
e-mail: enrique.rame-1@nasa.gov

1Corresponding author.

Manuscript received May 31, 2017; final manuscript received September 14, 2017; published online January 23, 2018. Editor: Portonovo S. Ayyaswamy.

J. Heat Transfer 140(5), 051501 (Jan 23, 2018) (10 pages) Paper No: HT-17-1313; doi: 10.1115/1.4038520 History: Received May 31, 2017; Revised September 14, 2017

We analyze the condensation of a quiescent vapor, that is in equilibrium with its liquid, induced by a stagnation point flow in the liquid. The liquid flow brings subcooled liquid from far away to the interface. The ensuing heat transfer causes the vapor to condense. A similarity formulation for the liquid and vapor flow fields and the liquid temperature field is pursued, and a perturbation solution is performed when the ratio of the product of viscosity and density of the vapor to that of the liquid is small. A two-term higher order asymptotic solution is shown to be in excellent agreement with numerical results. The reduction in the rate of condensation due to the presence of a noncondensable gas in the vapor that is insoluble in the liquid is also analyzed.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Lin, C. S. , and Hasan, M. , 1991, “ Vapor Condensation on Liquid Surface Due to Laminar Jet-Induced Mixing,” J. Thermophys. Heat Transfer., 5(4), pp. 607–612. [CrossRef]
Hasan, M. , and Lin, C. , 1990, “Buoyancy Effects on the Vapor Condensation Rate on a Horizontal Liquid Surface,” AIAA Paper No. AIAA-90-0353.
McQuillen, J. B. , 2016, “Zero Boil-Off Tank (ZBOT) Experiment,” NASA Glenn Research Center, Cleveland, OH, Technical Report No. GRC-E-DAA-TN28967. https://ntrs.nasa.gov/search.jsp?R=20160010275
NASA, 2016, “Zero Boil-Off Tank (ZBOT) Experiment,” National Aeronautics and Space Administration, Washington, DC, accessed Dec. 5, 2017, www.nasa.gov/mission_pages/station/research/experiments/1270.html
Schlichting, H. , 1979, Boundary Layer Theory, McGraw-Hill, New York.
Wang, C. , 1985, “ Stagnation Flow on the Surface of a Quiescent Fluid–An Exact Solution of the Navier-Stokes Equations,” Q. Appl. Math., 43(2), pp. 215–223. [CrossRef]
Gerner, F. , and Tien, C. , 1989, “ Axisymmetric Interfacial Condensation Model,” ASME J. Heat Transfer, 111(2), pp. 503–510. [CrossRef]
Gerner, F. , and Tien, C. , 1990, “ Multi-Component Interfacial Condensation,” Int. J. Heat Mass Transfer, 33(10), pp. 2111–2120. [CrossRef]
Davis, J. , and Yadigaroglu, G. , 2004, “ Direct Contact Condensation in Hemenz Flow Boundary Layers,” Int. J. Heat Mass Transfer, 47(8–9), pp. 1863–1875. [CrossRef]
Sparrow, E. , Minkowycz, W. , and Saddy, M. , 1967, “ Forced Convection Condensation in the Presence of Noncondensables and Interfacial Resistance,” Int. J. Heat Mass Transfer, 10(12), pp. 1829–1845. [CrossRef]
Chung, J. , Ayyaswamy, P. , and Sadhal, S. , 1984, “ Laminar Condensation on a Moving Drop—Part 1: Singular Perturbation Technique,” J. Fluid Mech., 139, pp. 105–130. [CrossRef]
Sadhal, S. , Ayyaswamy, P. , and Chung, J. , 1997, Transport Phenomena With Drops and Bubbles, Springer, New York.
Shankar, P. , 1968, “ A Kinetic Theory of Steady Condensation,” J. Fluid Mech., 40(2), pp. 385–400. [CrossRef]
Batchelor, G. , 1967, An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge, UK.
Shekriladze, I. , and Gomelauri, V. , 1966, “ Theoretical Study of Laminar Film Condensation of Flowing Vapor,” Int. J. Heat Mass Transfer, 9(6), pp. 581–591. [CrossRef]
Griffel, D. , 2002, Applied Functional Analysis (Dover Books on Mathematics), Dover Publications, Mineola, NY.


Grahic Jump Location
Fig. 1

Schematic of condensation induced by a liquid in stagnation point flow

Grahic Jump Location
Fig. 2

Plots of: (a) F(η)−ηversusη (and F(η)versus η in the inset), (b) θ(η)versusη, (c) f(ζ)versusζ, (d) ω(ζ)/ω∞versusζ for Pr = 10, ϵ=0.015, λ=0.015, Sc=0.245. The dot-dashed curve is the leading order solution, the solid curve includes the higher order term, and the dashed curve is the numerical solution. All the curves in the inset in (a), in (b), and the solid and dashed curves in (d) are indistinguishable.

Grahic Jump Location
Fig. 3

Scaled interfacial temperature (dotted curve) and scaled condensation ratio (dashed curve) as a function of the noncondensable mass fraction. Pure vapor: perfluoro-n-hexane, noncondensable: nitrogen, ε=0.0143,λ=0.015,Pr=10,Sc=0.245,M̂=10.286,hfg/RvTsat=9.798,μhfg/(kTl,∞)=2.193,Tv,∞=311K,Tl,∞=301K.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In