Definition of velocity profile for turbulent flow in a circular cylindrical pipe by means of numerical methods

Artem A. Korenevsky GRP Gorizont Moscow, Russian Federation
Michael V. Ryabinin Bauman Moscow State Technical University Moscow, Russian Federation
Determination of flow resistance at unsteady flow condition is still a problem for engineering hydraulic calculations even in a circular pipe. The issue becomes important when considering special practical problems, in particular, hydraulic impact. Such problems include hydraulic fracturing aimed at stimulating oil well productivity. To create calculation programs implementing the mathematical models of this processit is necessary to set the initial conditions not only reflecting the relationship of flow parameters, but also having a convenient representation for further calculations. The article describes a method of the velocity profile construction over the cross section of a circular pipe at steady flow conditions in a form convenient to use in the hydrodynamic calculations. Transformation of the profile differential equation into a discrete analogue for calculations using the non-uniform discretization grid was applied.
Materials and methods
A new method of the velocity profile construction for the five-layer model of turbulent viscosity distribution over the flow cross-section was applied. An original method of selecting simulation parameters was proposed.
It is proposed to use the developed algorithm of the velocity profile construction to set the initial conditions for solving the unsteady flow problems. An example of the calculation, the results of which was used to analyze the accuracy of the method, is provided; and a technique for the rational selection of numerical calculation parameters is proposed.
The proposed method of the velocity profile construction showed high accuracy of the results (for solving practical engineering problems), thereby proving its suitability for practical use. It is should be noted that the constructed velocity profile is of higher quality than all the currently known analytic dependences. The main advantages of this algorithm are its flexibility, programmability and comparatively small ECM computational power demand.
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velocity profile construction mathematical model numerical methods turbulent viscosity turbulent flow