Cavitation
Cavitation is defined as the phenomenon of formation of vaporous bubbles if the local pressure is less than the vapor pressure in a flowing liquid. Cavitation can happen in a wide variety of fluid machinery, such as pumps, nozzles, marine propellers and underwater bodies. This is especially true when the working liquid has a very high temperature. Unfortunately the effects of cavitation, with very few exceptions, are undesirable. Uncontrolled cavitation can produce serious and even catastrophic results. Although the cavitation may be due to the poor design, it may occur in even the best-designed equipment when it is operated under normal operating conditions.
The following aspects make the computation of cavitating flow still a challenging problem:
- 1. Interplay between cavitation and turbulence.
- 2. Large density variations across interface.
- 3. Thermal effects associated with cryogenic fluids.
- 4. Complexity of the phase change process.
Our goal is to develop a computational framework consisting of the turbulence closures and a cavitation model capable to predict a reliable simulation of cavitating flow.
Cavitation Model
We have been developing transport equation-based models (TEM) along with suitable turbulence closures and numerical techniques to advance the capability of simulating turbulent cavitating flows. In TEM, a transport equation of the liquid/vapor phase fraction is established with appropriate source terms to regulate the mass transfer between vapor and liquid phases. Different modeling concepts, such as dimensional argument and mass/momentum balance at interface, embodying qualitatively similar source terms with alternate numerical techniques have been proposed by various researchers.
Thermal effects of cryogenic liquids
As phase change occurs for cryogenic liquids such as liquid nitrogen, more substantial temperature drop results from the fluid properties such as smaller density ratio of liquid to vapor phase. Together with thermal-sensible fluid properties, thermal effects for cryogenic cavitation are very important.
We investigate the cryogenic cavitation in 2D quarter hydrofoil with liquid nitrogen as the working liquid, and we can see the flow structure impact due to the thermal effects and the choices of cavitation model. The cavity length in Figure 1(a), under the isothermal assumption by Merkle et al Model, is larger than that of the cavity in Figure 1(b) by using the Sharpy IDM with thermal effects. This means under the same conditions, thermal effects will lower the strength of cavitation.
Figure 1 Cavity shape indicated by liquid volume fraction. Arrows denote streamlines (a) Merkle et al model-isothermal assumption (b)Merkle et al. Model- with thermal effect
Interplay between turbulence and cavitation
Since there is less information and investigation associated with inlet turbulence quantities in the high Reynolds number turbulent flow (Re~106) from experiment, we apply different eddy-to-laminar viscosity ratios at inlet to investigate the sensitivity. The examined hydrofoil is NACA66MOD (AoA=4) with water as working liquid, and isothermal assumption is reasonable for water cavitation due to the less thermal-sensible fluid properties. We do observe the sensitivity from different inlet conditions in terms of pressure distribution and cavity size (the flattened region) along the upper surface in Figure 2. In order to reduce the reliance of eddy viscosity, we impose a filter based on grid spacing (filter-based model, FBM). We can see the uncertainty from eddy viscosity is reduced with filter-based model in Figure 2, and the results are also in good agreements with experimental data.
Figure 2 Isothermal cavitation of NACA66MOD hydrofoil by Merkle et al. Model (AOA=4˚,σ∞=0.91,Re=2×106)
References
[1] Senocak I., and Shyy W., “A Pressure-Based Method for Turbulent Cavitating Flow Compuitations”, Journal of Computational Physics, Vol.176 (2002), no. 2, pp363-383
[2] Senocak I., and Shyy W., “Interfacial Dynamics-Based Modeling of Turbulent Cavitating Flows”, Part-1: Model Development and Steady-State Computations”, International Journal for Numerical Methods in Fluids, Vol.44 (2004), pp975-995
[3] Utturkar Y., Wu J., Wang G., and Shyy W., “Recent Progress in Modeling of Cryogenic Cavitation for Liquid Rocket Propulsion. Progress in Aerospace Sciences”, Vol. 41 (2005), no. 7, pp. 558-608.
[4] Tseng C and Shyy W., ” Turbulence Modeling for Isothermal and Cryogenic Cavitation”, AIAA Paper No. 2009-1150. In 47th AIAA Aerospace Science Meeting. 5-8 January, 2009, Orlando, FL
Researcher
Chien-Chou Tseng