FLOW AND MIXING DYNAMICS OF PHASE TRANSFORMING MULTICOMPONENT FLUIDS THROUGH THE VAN DER WAALS THEORY OF CAPILLARITY

Cavitation is the conversion of a fluid from liquid to vapor due to depressurization. The process is characterized by non-equilibrium phase change from liquid phase to vapor phase or vice-versa, high speed fluid flow and steep pressure and velocity gradients due to the presence of shock waves. In addition, cavitation is extremely sensitive to the presence of additional components such as non-condensable gases in the phase-transforming fluid. While some aspects of cavitation such as growth, shrinkage and collapse of bubbles are well understood, the formation of vapor from pure liquid continues to be an area of active investigation. Numerous models have been proposed, but they cannot capture all aspects of cavitation mass transfer. One of the existing models, which is based on the van der Waals theory of phase-transformation is called the Navier-Stokes-Korteweg (NSK) model. Although this model can predict cavitation inception, it has not been used to study cavitation inception widely. The reason is that it is computationally very expensive to perform simulations of cavitation at engineering length scales using this model directly. In addition, the structure of the equations does not allow the direct application of most compressible flow solvers. 

Here, we propose a modification to the NSK equations which allows us to understand cavitation inception for pristine phase-transforming fluids in a computationally efficient man- ner. Our proposed algorithm is atleast 108 times faster than state-of-the-art algorithms for NSK equations to understand cavitation inception at length scales of the order of centime- ters. Since cavitation is extremely sensitive to the presence of non-condensable gas bubbles in water, we extend the NSK equations to mixtures of phase-transforming fluids and non- condensable gases. We show numerical examples which prove that our model can capture experimental observations for phase-transforming mixtures at length scales from nanometers to centimeters. Our simulations for cavitating flow of water containing dissolved air past a cylinder show how free stream air nuclei present in water drastically change the amount of liquid that gets converted to vapor in the near-wake region of the cylinder. Our work opens avenues to understand different aspects of cavitation mass transfer in much more detail.