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KSME International Journal

, Volume 17, Issue 12, pp 2066–2077 | Cite as

Study of moist air flow through the ludwieg tube

  • Seung-Cheol Baek
  • Soon Bum Kwon
  • Heuy-Dong Kim
  • Toshiaki Setoguchi
  • Sigeru Matsuo
  • Raghu S. Raghunathan
Article

Abstract

The time-dependent behavior of unsteady condensation of moist air through the Ludwieg tube is investigated by using a computational fluid dynamics (CFD) work. The twodimensional, compressible, Navier-Stokes equations, fully coupled with the condensate droplet growth equations, are numerically solved by a third-order MUSCL type TVD finite-difference scheme, with a second-order fractional time step. Baldwin-Lomax turbulence model is employed to close the governing equations. The predicted results are compared with the previous experiments using the Ludwieg tube with a diaphragm downstream. The present computations represent the experimental flows well. The time-dependent unsteady condensation charac-teristics are discussed based upon the present predicted results. The results obtained clearly show that for an initial relative humidity below 30% there is no periodic oscillation of the condensation shock wave, but for an initial relative humidity over 40% the periodic excursions of the condensation shock occurs in the Ludwieg tube, and the frequency increases with the initial relative humidity. It is also found that total pressure loss due to unsteady condensation in the Ludwieg tube should not be ignored even for a very low initial relative humidity and it results from the periodic excursions of the condensation shock wave.

Key Words

Ludwieg Tube Compressible Flow Condensation Shock Wave Periodic Flow Non-Equilibrium Condensation Supersonic Nozzle 

Nomenclature

a

Speed of sound

Cp

Specific heat at constant pressure [J/(kg.K)]

Es

Total energy per unit volume [J/m3]

E, F

Numerical flux

g

Condensate mass fraction [-]

h

Tube height [mm]

h*

Characteristic length [mm]

I

Nucleation rate [l/(m3.s)]

J

Jacobian

k

Boltzmann constant [J/K]

L

Latent heat [J/kg]

M

Molecular weight [kg/kmol]

m

Mass [kg]

Prandtl number

p

Pressure [Pa]

p∞

Flat film equilibrium vapour pressure [Pa]

Q

Source term

R, S

Viscous term

Re

Reynolds number [-]

Gas constant [J/(kg-K)]

γ

Droplet radius [m]

γc

Critical droplet radius [m]

S

Initial degree of supersaturation [-]

t

Time [s] or temperature [°C]

T

Temperature [K]

U

Conservation term

u, v

Cartesian velocity components [m/s]

x, y

Cartesian coordinates [m]

γ

Ratio of specific heats [-]

Γ

Accomodation coefficient of nucleation [-]

ξ

Coefficient of surface tension [-]

μ

Dynamic viscosity [Pa.s]

K

Bulk viscosity

γ

Coefficient of second viscosity

ο, η

Generalized coordinates [-]

ο

Condensation coefficient [-] λ

ρ

Density [kg/m3]

Ő

Surface tension [N/m]

Ő∞

Surface tension of an infinite flat-film [-]

Sub/superscripts

0

Stagnation state

Plane surface

l

Liquid or laminar state

m

Mixture

r

Droplet radius

v

Vapour

S

Saturation

t

Turbulent state

-

Dimensional quantity

*

Nondimensional quantity

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References

  1. Adam, S. and Schnerr, G. H., 1997. “Instabilities and Bifurcation of Non-Equilibrium Two-Phase Flows,”Journal Fluid Mechanics, Vol. 348, pp. 1–28.MATHCrossRefMathSciNetGoogle Scholar
  2. Baldwin, B. S. and Lomax, H., 1978. “Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows,”AIAA paper 78-257.Google Scholar
  3. Barschdorff, D. and Fillipov, G. A., 1970, “Analysis of Certain Special Operating Modes of Laval Nozzles with Local Heat Supply,”Heat Transfer J., Vol. 2, No. 5, pp. 76–87.Google Scholar
  4. Bull, G. V., 1952, “Investigation into the Operating Cycle of a Two-Dimensional Supersonic Wind Tunnel,”Journal of Aeronautical Sciences, pp. 609-614.Google Scholar
  5. Cable, A. J. and Cox, R. N., 1963. “The Ludwieg Pressure Tube Supersonic Wind Tunnel,”The Aeronautical Quarterly, Vol. 14, No. 2, pp. 143–157.Google Scholar
  6. Cagliostro, D. J., 1972, “Periodic Compressible Nozzle Flow caused by Heat Addition due to Condensation,” Ph. D Thesis Yale University. New Haven.Google Scholar
  7. Frank, W., 1985, “Condensation Phenomena in Supersonic Nozzles,”Ada Mechanica, Vol. 54, pp. 135–156.CrossRefGoogle Scholar
  8. Friehmelt, H., Koppenwaller. G. and Muller- Eigner, R., 1993, “Calibration and First Results of a Redesigned Ludwieg Expansion Tube,” AIAA Paper 93-5001.Google Scholar
  9. Hill, P. G., 1966, “Condensation of Water Vapour during Supersonic Expansion in Nozzles,”Jour. Fluid Mechanics, Vol. 25, No. 3, pp. 593–620.CrossRefGoogle Scholar
  10. Kwon, S. B., 1986, “The Study of Characteristics of Condensation Shock Waves,” Ph. D. Thesis, Kyushu University, Japan.Google Scholar
  11. Matsuo, K., Kawagoe, S., Sonoda, K. and Setoguchi, T., 1985a, “Oscillations of Laval Nozzle Flow with Condensation (part 2. on the mechanism of oscillations and their amplitudes),”Bulletin of JSME, Vol. 28, No. 235, pp. 88–93.Google Scholar
  12. Matsuo, K., Kawagoe, S., Sonoda, K. and Sa- kao, K., 1985b, “Studies of Condensation Shock Waves (part 1, mechanism of their formation),”Bulletin of JSME, Vol.28, No. 241, pp. 1416–1422.Google Scholar
  13. Matsuo, K., Kawagoe, S., Sonoda, K. and Setoguchi, T., 1983, “Oscillations of Laval Nozzle Flow with Condensation (part 1, on the range of oscillations and their frequencies),”JSME J., Vol. 26, No. 219, pp. 1556–1562.Google Scholar
  14. Schnerr, G. H. and Dohrmann. U., 1990, “Transonic Flow around Airfoils with Relaxation and Energy Supply by Homogeneous Condensation,”AIAA J., Vol.32, pp. 101–107.CrossRefGoogle Scholar
  15. Setoguchi, T, Matsuo, S. and Kim, H. D., 2001, “Passive Control of the Condensation Shock Wave Oscillations in a Transonic Nozzle,”Journal of Sound and Vibration (to be published).Google Scholar
  16. Setoguchi, T., Kim, H. D. and Matsuo, S., 2001, “Passive Control of the Condensation Shock Wave in a Transonic Nozzle,”Applied Scientific Research, International Journal on the Applications of Fluid Dynamics (to be published).Google Scholar
  17. Wegener P. P. and Mack, L. M., 1958, “Condensation in Supersonic Hypersonic Wind Tunnels,”Adv. in Applied Mechanics, Vol. 5, pp. 307–447.MATHCrossRefGoogle Scholar
  18. Wegener, P. P.. 1970, “Nonequilibrium flows Part 2,” Marcel Dekker Inc., pp. 163-242.Google Scholar
  19. Wegener, P. P. and Wu, B., 1977, “Gasdynamics and Homogeneous Nucleation,”Nucleation Phenomena, Vol.7, pp. 325–402. Ed. by A. C. Zettlemoyer.Google Scholar
  20. Wegener. P.P. and Cagliostro, D. J., 1973, “Periodic Nozzle Flow with Heat Addition,”Combustion Science and Technology, Vol. 6, pp. 269–277.CrossRefGoogle Scholar
  21. Yee, H. C, 1989, “A Class of High-Resolution Explicit and Implicit Shock-Capturing Methods,” NASA TM-89464.Google Scholar
  22. Zierep. J. and Lin. S., 1967, “Bestimung des kondensationsbeginns kondensation bei entspannung feuchter luft in ueberschallduesen,” Forsch. Ing.-Wes., Vol. 33, pp. 169–172.CrossRefGoogle Scholar

Copyright information

© The Korean Society of Mechanical Engineers (KSME) 2003

Authors and Affiliations

  • Seung-Cheol Baek
    • 1
  • Soon Bum Kwon
    • 1
  • Heuy-Dong Kim
    • 2
  • Toshiaki Setoguchi
    • 3
  • Sigeru Matsuo
    • 3
  • Raghu S. Raghunathan
    • 4
  1. 1.Department of Mechanical EngineeringKyungpook National UniversityDaeguKorea
  2. 2.School of Mechanical EngineeringAndong National UniversitySongchun-dong, AndongKorea
  3. 3.Department of Mechanical EngineeringSaga UniversityHonjo-machi, Saga-shi, SagaJapan
  4. 4.School of Aeronautical Engineering, The Queen’sUniversity of BelfastBelfastUK

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