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The purpose of this paper is to investigate the two-phase flow problems involving gas–liquid mixture.

The governed equations consist of a range of conservation laws modeling a classification of two-phase flow phenomena subjected to a velocity nonequilibrium for the gas–liquid mixture. Effects of the relative velocity are accounted for in the present model by a kinetic constitutive relation coupled to a collection of specific equations governing mass and volume fractions for the gas phase. Unlike many two-phase models, the considered system is fully hyperbolic and fully conservative. The suggested relaxation approach switches a nonlinear hyperbolic system into a semilinear model that includes a source relaxation term and characteristic linear properties. Notably, this model can be solved numerically without the use of Riemann solvers or linear iterations. For accurate time integration, a high-resolution spatial reconstruction and a Runge–Kutta scheme with decreasing total variation are used to discretize the relaxation system.

The method is used in addressing various nonequilibrium two-phase flow problems, accompanied by a comparative study of different reconstructions. The numerical results demonstrate the suggested relaxation method’s high-resolution capabilities, affirming its proficiency in delivering accurate simulations for flow regimes characterized by strong shocks.

While relaxation methods exhibit notable performance and competitive features, as far as we are aware, there has been no endeavor to address nonequilibrium two-phase flow problems using these methods.

The purpose of this work is to present the implementation of weighted essentially non-oscillatory (WENO) wavelet methods for solving multiphase flow problems. The particular interest is gas–liquid two-phase mixture with velocity non-equilibrium. Numerical simulations are carried out on different scenarios of one-dimensional Riemann problems for gas–liquid flows. Results are validated and qualitatively compared with solutions provided by other standard numerical methods.

This paper extends the framework of WENO wavelet adaptive method to a fully hyperbolic two-phase flow model in a conservative form. The grid adaptivity in each time step is provided by the application of a thresholded interpolating wavelet transform. This facilitates the construction of a small yet effective sparse point representation of the solution. The method of Lax–Friedrich flux splitting is used to resolve the spatial operator in which the flux derivatives are approximated by the WENO scheme.

Hyperbolic models of two-phase flow in conservative form are efficiently solved, as shocks and rarefaction waves are precisely captured by the chosen methodology. Substantial computational gains are obtained through the grid reduction feature while maintaining the quality of the solutions. The results indicate that WENO wavelet methods are robust and sufficient to accurately simulate gas–liquid mixtures.

Resolution of two-phase flows is rarely studied using WENO wavelet methods. It is the first time such a study on the relative velocity is reported in two-phase flows using such methods.

The aim of this work is to quantify the relative importance of the turbulence modelling for cavitating flows in thermal regime. A comparison of various transport-equation turbulence models and a study of the influence of the turbulent Prandtl number appearing in the formulation of the turbulent heat flux are proposed. Numerical simulations are performed on a cavitating Venturi flow for which the running fluid is freon R-114 and results are compared with experimental data.

A compressible, two-phase, one-fluid Navier–Stokes solver has been developed to investigate the behaviour of cavitation models including thermodynamic effects. The code is composed by three conservation laws for mixture variables (mass, momentum and total energy) and a supplementary transport equation for the volume fraction of gas. The mass transfer between phases is closed assuming its proportionality to the mixture velocity divergence.

The influence of turbulence model as regard to the cooling effect due to the vaporization is weak. Only the k – ε Jones–Launder model under-estimates the temperature drop. The amplitude of the wall temperature drop near the Venturi throat increases with the augmentation of the turbulent Prandtl number.

The interaction between Reynolds-averaged Navier–Stokes turbulence closure and non-isothermal phase transition is rarely studied. It is the first time such a study on the turbulent Prandtl number effect is reported in cavitating flows.

This study aims to propose a robust total variation diminishing (TVD) weighted average flux (WAF) finite volume scheme for investigating compressible gas–liquid mixture flows.

This study considers a two-phase flow composed of a liquid containing dispersed gas bubbles. To model this two-phase mixture, this paper uses a homogeneous equilibrium model (HEM) defined by two mass conservation laws for the two phases and a momentum conservation equation for the mixture. It is assumed that the velocity is the same for the two phases, and the density of phases is governed by barotropic laws. By applying the theory of hyperbolic equations, this study establishes an exact solution of the Riemann problem associated with the model equations, which allows to construct an exact Riemann solver within the first-order upwind Godunov scheme as well as a robust TVD WAF scheme.

The ability and robustness of the proposed TVD WAF scheme is validated by testing several two-phase flow problems involving different wave structures of the Riemann problem. Simulation results are compared against analytical solutions and other available numerical methods as well as experimental data in the literature. The proposed approach is much superior to other strategies in terms of the accuracy and ability of reconstruction.

The novelty of this work lies in its methodical extension of a TVD WAF scheme implementing an exact Riemann solver developed for compressible two-phase flows. Furthermore, other novelty lies on the quantitative calculation of different Riemann problem two-phase flows. Simulation results involve the verification of the constructed methods on the exact solutions of HEM without any restriction of variables.

The Purpose of this study is to prove the possibility of developing low cost mechanical anti – lock braking system (ABS) for the passenger’s safety.

The design methodology of the proposed newer mechanical ABS comprises of two units, namely, the braking unit and wheel lock prevention unit. The braking unit actuates the wheel stopping as and when the driver applies the brake, whereas the wheel lock prevention unit initiates wheel release to prevent locking and subsequent slip/skidding. The brake pedal with master cylinder assembly and double-arm cylinder forms the braking unit, brake pad cylinder, movable brake pad, solenoid valve and dynamo forms the wheel lock prevention unit. The dynamo coupled with the rotor energises/de-energises the solenoid values to direct airflow for applying brake and release it, which makes the system less energy-dependent.

The braking unit aids in vehicle stops, by locking the disc with the brake pad actuated by a double-arm cylinder. The dynamo energises the solenoid valve to activate the brake pad cylinder piston for applying the brake on the disc. Instantaneously, on applying the brake the dynamo de-energises the solenoid to divert the pneumatic flow for retracting the brake pad thereby minimizing the braking torque. The baking torque reduction revives the wheel rotating and prevents slip/skidding.

Mechanical ABS preventing wheel lock by torque reduction principle is a novel method that has not been evolved so far. The system was designed with repair/replacement of the parts and subcomponents to support higher affordability on safety grounds.