Cavitation inception of a van der Waals fluid at a sack-wall obstacle

Cavitation in a liquid moving past a constraint is numerically investigated by means of a free-energy lattice Boltzmann simulation based on the van der Waals equation of state. The fluid is streamed past an obstacle and, depending on the pressure drop between inlet and outlet, vapor formation underneath the corner of the sack-wall is observed. The circumstances of cavitation formation are investigated and it is found that the local bulk pressure and mean stress are insufficient to explain the phenomenon. Results obtained in this study strongly suggest that the viscous stress, interfacial contributions to the local pressure, and the Laplace pressure are relevant to the opening of a vapor cavity. This can be described by a generalization of Joseph's criterion that includes these contributions. A macroscopic investigation measuring mass flow rate behavior and discharge coefficient was also performed. As theoretically predicted, mass flow rate increases linearly with the square root of the pressure drop. However, when cavitation occurs, the mass flow growth rate is reduced and eventually it collapses into a choked flow state. In the cavitating regime, as theoretically predicted and experimentally verified, the discharge coefficient grows with the Nurick cavitation number

A review of homogeneous two-phase cavitation models with an emphasis on physical aspects of cavitation

Homogeneous two-phase cavitation models are the preferred models for cavitating flows in large-scale computational fluid dynamics systems. These models use the computationally efficient volume-of-fluids method for multiphase problems. Cavitation phenomena act on magnitudes smaller spacial and temporal scales than the macroscopic bulk flow. The central challenge for homogeneous cavitation models lies therefore in modelling cavitation phenomena on a sub-scale. This review article analyses how the sub-scale modelling of phase transitions and bubble dynamics is realized. In particular, it is emphasized how the underlying model assumptions define the respective cavitation models. Twelve particular approaches to homogeneous cavitating flow modelling have been identified. Their methodology is presented in detail and derived models are highlighted. This article promotes understanding of these models and, in particular, it gives rise to limits of the homogeneous cavitation approach on the basis of the fundamental assumptions. Therewith, this review poses a unified theoretical basis for these models, and leads up to a subsequent study on accuracy and performances of these

Corner transport upwind lattice Boltzmann model for bubble cavitation

Aiming to study the bubble cavitation problem in quiescent and sheared liquids, a third-order isothermal lattice Boltzmann (LB) model that describes a two-dimensional ($2D$) fluid obeying the van der Waals equation of state, is introduced. The evolution equations for the distribution functions in this off-lattice model with 16 velocities are solved using the corner transport upwind (CTU) numerical scheme on large square lattices (up to $6144 \times 6144$ nodes). The numerical viscosity and the regularization of the model are discussed for first and second order CTU schemes finding that the latter choice allows to obtain a very accurate phase diagram of a nonideal fluid. In a quiescent liquid, the present model allows to recover the solution of the $2D$ Rayleigh-Plesset equation for a growing vapor bubble. In a sheared liquid, we investigated the evolution of the total bubble area, the bubble deformation and the bubble tilt angle, for various values of the shear rate. A linear relation between the dimensionless deformation coefficient $D$ and the capillary number $Ca$ is found at small $Ca$ but with a different factor than in equilibrium liquids. A non-linear regime is observed for $Ca \gtrsim 0.2$.Comment: Accepted for publication in Phys. Rev.

Modeling of Turbulent Cavitating Flows.

The goal is to establish a predictive tool for turbulent cavitating flows, including those under cryogenic conditions with noticeable thermal effects. The modeling framework consists of a transport-based cavitation model with ensemble-averaged fluid dynamics equations and turbulence closures. The cavitation models include a phenomenological model with empirical supports and an interfacial dynamics model that utilizes continuity and force balance across the interfaces. For the turbulence closure, a filter-based approach and density correction approach has been imposed to the two equation k-ε model. The reported experimental investigations contain insufficient details regarding the inlet turbulence characteristics of the flow field. However, the inlet turbulent quantities can substantially impact the outcomes because the viscous effect can modify the effective shape of a solid object, which causes noticeable variations in the predicted multiphase flow structures. A filter-based turbulence closure is utilized to reduce the impact of the inlet turbulent quantities based on the local resolution. Its effectiveness is confirmed by both isothermal and cryogenic cavitation. In addition, the thermal effect and the competing effect between the cavitation number and the density ratio effects are investigated by evaporation and condensation dynamics under the cryogenic conditions. Based on the surrogate-based global sensitivity analysis under cryogenic conditions, one can assess the role of model parameters and uncertainties in material properties. It is revealed that variables represented for the evaporation rate are more critical than those for the condensation rate. Furthermore, the recommended model parameter values are optimized by tradeoffs between pressure and temperature predictions. For unsteady cavitating flows, the phenomenological model and interfacial dynamics model are utilized by the turbulence closure with the filter-based approach, the density correction approach, and a hybrid approach that blends the previous two methods. It is discovered that the eddy viscosity near the closure region can significantly influence the capture of the detached cavity. From the experimental validations, no single model combination performs best in all aspects. Furthermore, the implications of the parameters contained in the different cavitation models are investigated. The phase change process is more pronounced near the detached cavity, which is more substantial in the interfacial dynamics model.Ph.D.Mechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/78793/1/tsengch_1.pd

Investigation on the Dispersal Characteristics of Liquid Breakup in Vacuum

This work presents an experimental study on the dispersal characteristics of a liquid jet ejecting into vacuum. The liquid breaking experiments of several kinds of liquid under different pressure and temperature conditions are carried out in a flash chamber. The stability of the jet and the sizes of the droplets or the icing particles formed during liquid flashing dispersing are analyzed. The influences of the superheat degree, spray velocity, and the mass of the volatile liquid mixing in the nonvolatile liquid on these characteristics are discussed. Moreover, the applicability of the two definitions of superheat degree is discussed. The results show that the superheat degree is an important parameter influencing the pattern of the breaking liquid, and the jet velocity has a large influence on the distribution of particle sizes. In addition, mixing some volatile liquid with nonvolatile liquid can enhance the dispersion of the latter

Mesoscopic Methods in Engineering and Science

Matter, conceptually classified into fluids and solids, can be completely described by the microscopic physics of its constituent atoms or molecules. However, for most engineering applications a macroscopic or continuum description has usually been sufficient, because of the large disparity between the spatial and temporal scales relevant to these applications and the scales of the underlying molecular dynamics. In this case, the microscopic physics merely determines material properties such as the viscosity of a fluid or the elastic constants of a solid. These material properties cannot be derived within the macroscopic framework, but the qualitative nature of the macroscopic dynamics is usually insensitive to the details of the underlying microscopic interactions

Modelling cavitation during drop impact on solid surfaces

The impact of liquid droplets on solid surfaces at conditions inducing cavitation inside their volume has rarely been addressed in the literature. A review is conducted on relevant studies, aiming to highlight the differences from non-cavitating impact cases. Focus is placed on the numerical models suitable for the simulation of droplet impact at such conditions. Further insight is given from the development of a purpose-built compressible two-phase flow solver that incorporates a phase-change model suitable for cavitation formation and collapse; thermodynamic closure is based on a barotropic Equation of State (EoS) representing the density and speed of sound of the co-existing liquid, gas and vapour phases as well as liquid-vapour mixture. To overcome the known problem of spurious oscillations occurring at the phase boundaries due to the rapid change in the acoustic impedance, a new hybrid numerical flux discretization scheme is proposed, based on approximate Riemann solvers; this is found to offer numerical stability and has allowed for simulations of cavitation formation during drop impact to be presented for the first time. Following a thorough justification of the validity of the model assumptions adopted for the cases of interest, numerical simulations are firstly compared against the Riemann problem, for which the exact solution has been derived for two materials with the same velocity and pressure fields. The model is validated against the single experimental data set available in the literature for a 2-D planar drop impact case. The results are found in good agreement against these data that depict the evolution of both the shock wave generated upon impact and the rarefaction waves, which are also captured reasonably well. Moreover, the location of cavitation formation inside the drop and the areas of possible erosion sites that may develop on the solid surface, are also well captured by the model. Following model validation, numerical experiments have examined the effect of impact conditions on the process, utilizing both planar and 2-D axisymmetric simulations. It is found that the absence of air between the drop and the wall at the initial configuration can generate cavitation regimes closer to the wall surface, which significantly increase the pressures induced on the solid wall surface, even for much lower impact velocities. A summary highlighting the open questions still remaining on the subject is given at the end