Ali Alhelfi and Bengt Ake Sunden
The purpose of this paper is to present numerical investigation of the gas/vapor bubble dynamics under the influence of an ultrasonic field to give a more comprehensive…
Abstract
Purpose
The purpose of this paper is to present numerical investigation of the gas/vapor bubble dynamics under the influence of an ultrasonic field to give a more comprehensive understanding of the phenomenon and present new results
Design/methodology/approach
In order to formulate the mathematical model, a set of governing equations for the gas inside the bubble and the liquid surrounding it are used. All hydrodynamics forces acting on the bubble are considered in the typical solution. The systems of equations required to be solved consist of ordinary and partial differential equations, which are both nonlinear and time dependent equations. A fourth order Runge-Kutta method is applied to solve the ordinary differential equations. On the other hand, the finite difference method is employed to solve the partial differential equations and a time-marching technique is applied.
Findings
The numerical model which is developed in the current study permits a correct prediction of the bubble behavior and its characteristics in an acoustic field generated at this occasion.
Originality/value
Previous studies considering numerical simulations of an acoustic bubble were performed based on the polytropic approximation or pressure uniformity models of the contents inside the bubble. In this study, an enhanced numerical model is developed to study the acoustic cavitation phenomenon and the enhancement concerns taking into account both the pressure and temperature gradients inside the bubble as well as heat transfer through the bubble surface into account which is very important to obtain the temperature of the liquid surrounding the bubble surface.
Details
Keywords
This study aims to purpose the idea of a new hybrid approach to examine the approximate solution of the fourth-order partial differential equations (PDEs) with time fractional…
Abstract
Purpose
This study aims to purpose the idea of a new hybrid approach to examine the approximate solution of the fourth-order partial differential equations (PDEs) with time fractional derivative that governs the behaviour of a vibrating beam. The authors have also demonstrated the physical representations of the problem in different fractional order.
Design/methodology/approach
Mohand transform is a new technique that the authors use to reduce the order of fractional problems, and then the homotopy perturbation method can be used to handle the further series solution in the form of convergence. The formulation of Mohand transform and the homotopy perturbation method is known as Mohand homotopy perturbation transform (MHPT). The fractional order in this paper is considered in the Caputo sense.
Findings
The results are formulated in the shape of iterative series and predict the solution close to the exact solution. This successive iteration demonstrates the authenticity and reliability of this scheme.
Research limitations/implications
This paper presents the significance of MHPT such that, firstly, Mohand transform is coupled with homotopy perturbation method and, secondly, the fractional order a is used to show the physical behaviour of the graphical solution.
Practical implications
This study presents the consistency and authenticity of the graphical solution with the exact solutions.
Social implications
This study demonstrates that Mohand transform is capable to handle the fractional order problem without any constraints and assumptions.
Originality/value
A new integral transform has been introduced without any restriction of variables that produces the results in a series form and confirms the validity of the proposed algorithm by graphical illustrations.