Abstract
A method for modelling the flow in a rigid-walled duct with two narrowings has been developed. It has the second order of accuracy in the spatial and the first order of accuracy in the temporal coordinates, provides high stability of the solution, and compared to the similar methods requires much less computational time to obtain a result. According to the method, the stream function and the vorticity are introduced initially, and consequently the transition from the governing equations, as well as the initial and boundary conditions to the proper relationships for the introduced variables is performed. The obtained relationships are rewritten in a non-dimensional form. After that a computational domain and a uniform computational mesh are chosen, and the corresponding discretization of the non-dimensional relationships is performed. Finally, the linear algebraic equations obtained as a result of the discretization are solved.
Highlights
Study of flows in straight channels is an actual problem in many spheres of science and technology
That is due to local changes in the flow structure and character, as well as changes in the flow local and integral characteristics and others are caused by such irregularities in the duct geometry
The other types of channels, their narrowings, fluids and the basic flow are not considered in this paper, because they have been studied not so often compared with the ones mentioned above
Summary
Study of flows in straight channels is an actual problem in many spheres of science and technology. A numerical method to solve a problem of flow in an infinite straight hard-walled channel with two rectangular axisymmetric rigid narrowings has been developed in [14]. An alternative method has been developed to solve the same problem with the stream function, vorticity, and pressure as the variables This method has almost the same order of accuracy and a higher stability of solution, and, due to the use of less powerful mathematical apparatus, requires far less computational time to obtain a result in comparison with the mentioned above. The relationships (3.8) together with the equation (3.4) allow us to write the following conditions for the vorticity at the channel and the walls of narrowings: Sch ,Sih. Regarding the boundary conditions for the pressure, we have (apart from conditions (2.6)) the following two conditions:. As for the initial conditions for , and p , they are equal to zero at the instant of time t 0 (see (2.7)-(3.2)):
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