cryogenic cavitation
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Formation of gas bubbles of a flowing liquid in a region where the pressure of the liquid falls below its vapor pressure
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• Good approximation to assume that the critical pressure for the onset of cavitation is the usual vapourpressure.
• Mathematical Analysis
classical Bernoulli equation 𝑝 +1
2𝜌𝑣2 = 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡
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I• High Velocities
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• Pressure decreases below vapor pressure at that Temperature
III• C A V I TAT I O N O C C U R S
• Cryogenic liquids, including oxygen, nitrogen, and hydrogen, are popular fuels
• Propellants because the by-products are clean and the power/gallon ratio is high
• Issue Rocket fuel and oxidizer pumps is the minimumpressure that the design can tolerate for a given inlettemperature and rotating speed
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C R Y O G E N I C E N G I N E S
Low Inlet Pressure/reduce
Tank Weight
Pump Rotational Speeds High
(Reduce Engine weight)
More chances of Cavitation
(pitting, noise)
• The occurrence of cavitation is determined by the condition that the minimum pressure in the flow pmin is lower or at least equal to the vapour pressure pv
• An index that measures the degree of development of cavitation
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• Cavitation in cryogenic fluids generates substantial thermal effects and strong variations in fluid properties, which in turn alters the cavity characteristics
• Water - very large ratio between liquid and vapor densities, around O(105), Negligible thermal effects
• For cryogenic fluids, the liquid/vapor density ratios are not as high
• Other quantities such as latent heat and thermal conductivity can influence the thermal field more substantially
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• Sensitivity of the vapor pressure with respect to temperature
• Clapeyron Eqn:
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Fluid dPv /dT (KPa / K)
Water 0.19
Nitrogen 20
Hydrogen 28
• Significantly higher slopes of pressure-temperature saturation curve than water, vapor pressure can vary substantially due to the thermal effect
• Local temperature drop due to the evaporative cooling is non-negligible in cryogenic liquids
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SubstanceCp
(KJ/Kg.K)Density
RatioThermal
ConductivityL
(kg/K) ∆v
Water(298K) 4200 43220 681 2442 43.35
N2(83K) 2075 95 134 190 0.12
H2(20k) 9484 57 103 446 0.79
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Variation of physical properties for liquid nitrogen and water along saturation curve
• Homogeneous-fluid modeling
• Favre-averaged Navier-Stokes equations
Continuity Equation
Momentum Conservation
Energy Conservation
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Cavitation Modelling
K-ε Turbulence Model
Assumes that the turbulent viscosity is isotropic
Two Transport Equations – Turbulent kinetic Energy and Dissipation
Mixture property,
Enthalpy
Vapor mass fraction
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Transport based Cavitation Model
Rate of Liq./Vapor Evaporation and Condensation
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Boundary Conditionsσ∞=1.7, Re=9.1 × 106, T∞=83.06K And σ∞=1.61,
Re=1.1 × 107, T∞=88.54K
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Cryogenic cavitation Case 290C, the impact of thermal effect on local
cavitation number (μT / μL =103, σ∞=1.7, Re=9.1 × 106, T∞=83.06K)
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• Computational Framework developed for Cavitation
• Prediction of Cavitation made easier
• Cavitation dependent on the inlet turbulent characteristics
• Larger is the inlet velocity, more is the spread in the cavity
• Differences in Cryogenic and Isothermal cavitation
• Evaporative cooling reduces cavitation intensity and results in a shorter cavity size than that under isothermal conditions
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• Knapp R.T. , Daily J.W. and Hammitt F.G., “Cavitation. McGraw-Hill”, New York, 1970.
• Hord J., “Cavitation in Liquid Cryogens”, II-Hydrofoil. NASA CR-2156 1973
• Tseng, C., and Wei Shyy. "Turbulence Modeling for Isothermal and Cryogenic Cavitation." AIAA Paper No. 2009-1150. In (2009).
• Zhang, X. B., et al. "Computational fluid dynamic study on cavitation in liquid nitrogen." Cryogenics 48.9 (2008): 432-438.
• Franc, Jean-Pierre. Physics and control of cavitation. GRENOBLE UNIV (FRANCE), 2006.
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Contours of Static Pressure
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Contours of Volume Fraction of vapor
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