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.
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Abbreviations
- a:
-
Speed of sound
- C p :
-
Specific heat at constant pressure [J/(kg.K)]
- E s :
-
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]
- Pγ :
-
Prandtl number
- p :
-
Pressure [Pa]
- p∞ :
-
Flat film equilibrium vapour pressure [Pa]
- Q:
-
Source term
- R, S :
-
Viscous term
- Re :
-
Reynolds number [-]
- ℜ :
-
Gas constant [J/(kg-K)]
- γ :
-
Droplet radius [m]
- γ c :
-
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 [-]
- 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
References
Adam, S. and Schnerr, G. H., 1997. “Instabilities and Bifurcation of Non-Equilibrium Two-Phase Flows,”Journal Fluid Mechanics, Vol. 348, pp. 1–28.
Baldwin, B. S. and Lomax, H., 1978. “Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows,”AIAA paper 78-257.
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.
Bull, G. V., 1952, “Investigation into the Operating Cycle of a Two-Dimensional Supersonic Wind Tunnel,”Journal of Aeronautical Sciences, pp. 609-614.
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.
Cagliostro, D. J., 1972, “Periodic Compressible Nozzle Flow caused by Heat Addition due to Condensation,” Ph. D Thesis Yale University. New Haven.
Frank, W., 1985, “Condensation Phenomena in Supersonic Nozzles,”Ada Mechanica, Vol. 54, pp. 135–156.
Friehmelt, H., Koppenwaller. G. and Muller- Eigner, R., 1993, “Calibration and First Results of a Redesigned Ludwieg Expansion Tube,” AIAA Paper 93-5001.
Hill, P. G., 1966, “Condensation of Water Vapour during Supersonic Expansion in Nozzles,”Jour. Fluid Mechanics, Vol. 25, No. 3, pp. 593–620.
Kwon, S. B., 1986, “The Study of Characteristics of Condensation Shock Waves,” Ph. D. Thesis, Kyushu University, Japan.
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.
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.
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.
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.
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).
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).
Wegener P. P. and Mack, L. M., 1958, “Condensation in Supersonic Hypersonic Wind Tunnels,”Adv. in Applied Mechanics, Vol. 5, pp. 307–447.
Wegener, P. P.. 1970, “Nonequilibrium flows Part 2,” Marcel Dekker Inc., pp. 163-242.
Wegener, P. P. and Wu, B., 1977, “Gasdynamics and Homogeneous Nucleation,”Nucleation Phenomena, Vol.7, pp. 325–402. Ed. by A. C. Zettlemoyer.
Wegener. P.P. and Cagliostro, D. J., 1973, “Periodic Nozzle Flow with Heat Addition,”Combustion Science and Technology, Vol. 6, pp. 269–277.
Yee, H. C, 1989, “A Class of High-Resolution Explicit and Implicit Shock-Capturing Methods,” NASA TM-89464.
Zierep. J. and Lin. S., 1967, “Bestimung des kondensationsbeginns kondensation bei entspannung feuchter luft in ueberschallduesen,” Forsch. Ing.-Wes., Vol. 33, pp. 169–172.
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Baek, SC., Kwon, S.B., Kim, HD. et al. Study of moist air flow through the ludwieg tube. KSME International Journal 17, 2066–2077 (2003). https://doi.org/10.1007/BF02982447
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DOI: https://doi.org/10.1007/BF02982447