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


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 



Speed of sound


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


Total energy per unit volume [J/m3]

E, F

Numerical flux


Condensate mass fraction [-]


Tube height [mm]


Characteristic length [mm]


Nucleation rate [l/(m3.s)]




Boltzmann constant [J/K]


Latent heat [J/kg]


Molecular weight [kg/kmol]


Mass [kg]

Prandtl number


Pressure [Pa]


Flat film equilibrium vapour pressure [Pa]


Source term

R, S

Viscous term


Reynolds number [-]

Gas constant [J/(kg-K)]


Droplet radius [m]


Critical droplet radius [m]


Initial degree of supersaturation [-]


Time [s] or temperature [°C]


Temperature [K]


Conservation term

u, v

Cartesian velocity components [m/s]

x, y

Cartesian coordinates [m]


Ratio of specific heats [-]


Accomodation coefficient of nucleation [-]


Coefficient of surface tension [-]


Dynamic viscosity [Pa.s]


Bulk viscosity


Coefficient of second viscosity

ο, η

Generalized coordinates [-]


Condensation coefficient [-] λ


Density [kg/m3]


Surface tension [N/m]


Surface tension of an infinite flat-film [-]



Stagnation state

Plane surface


Liquid or laminar state




Droplet radius






Turbulent state


Dimensional quantity


Nondimensional quantity


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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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