A new method for the numerical solution of time dependent viscous flow

Crane, C. M.

doi:10.1007/bf00385775

Cited by 5 publications

(2 citation statements)

References 10 publications

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“…The problem of the entrance section of a round pipe with a suddenly applied velocity at the entrance of the pipe was solved in [7] with the help of the hypothesis of self-modeling of the velocity profiles in the boundary layer and the impulse equation. A similar problem for the suddenly applied velocity at the inlet at small Reynolds numbers was solved by numerical integration of the Navier-Stokes equation in work [8]. In conditions of periodic disturbance, a thin boundary layer at the inlet of a round pipe was investigated with the help of linear approximations.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Identifying some regularities of the turbulent steady-state plane-parallel motion of incompressible fluid at the entrance length

Sarukhanyan,

Vermishyan,

Kelejyan

et al. 2024

EEJET

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This paper investigates the structural changes in the turbulent motion of an incompressible fluid in the hydrodynamic entrance region of plane-parallel pressure motion. Movement in pressure hydromechanical systems usually occurs in a turbulent regime. Studying the patterns of changes in hydrodynamic parameters under conditions of stationary turbulent pressure motion in the inlet region is a very urgent task. The study was carried out on the basis of boundary layer equations. Taking into account the dependence of changes in the kinematic viscosity coefficient that occur between layers of fluid, a boundary value problem was formed. Analytical solutions have been obtained that make it possible to obtain patterns of changes in velocity and pressure in any effective flow section. Based on the general conclusions of the study, solutions were found for two cases: a) the velocity of the fluid entering the cylindrical pipe is constant; b) the velocity of the incoming fluid has a parabolic distribution. For these cases, using computer analysis of the data obtained, general graphs of velocity changes were constructed in various sections along the hydrodynamic entrance region. These graphs, which display the change in velocity along the entire length of the inlet, make it possible to obtain the velocity of fluid movement at any point along the inlet length and estimate the length of the transition zone. The results obtained are among the least studied issues of classical fluid mechanics and are of important theoretical interest. The results obtained are applicable for the correct construction of the hydrodynamic entrance region of machinery. A calculation formula has been obtained to determine the length of the hydrodynamic inlet region

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Section: Literature Review and Problem Statementmentioning

confidence: 99%

Identifying some regularities of the turbulent steady-state plane-parallel motion of incompressible fluid at the entrance length

Sarukhanyan,

Vermishyan,

Kelejyan

et al. 2024

EEJET

View full text Add to dashboard Cite

show abstract

“…The problem of a round pipe entry region with a suddenly applied velocity at the pipe inlet was solved in [7] using the hypothesis of self-similarity of the velocity profiles in the boundary layer and the momentum equation. Numerical integration of the Navier-Stokes equation solved a similar problem for a suddenly applied velocity at small Reynolds numbers in [8]. Under conditions of periodic perturbation and with the support of linear approximations, a thin boundary layer [9] was studied at the entrance region of a round pipe.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Pattern identification of the non-stationary laminar flow of a viscous fluid in the round pipe inlet section

Sarukhanyan

Vardanyan

Baljyan

et al. 2023

EEJET

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The study of the patterns of change in the hydrodynamic parameters under the conditions of non-stationary flow at the entry of the cylindrical pipe and the initial arbitrary distribution of velocities in the entry section was conducted based on the boundary layer equations. A boundary problem was formed under the axisymmetric change conditions in the flow. The boundary conditions were chosen in accordance with the pattern of an arbitrary distribution of velocities in the entry section. A general solution of the approximating Navier-Stokes equations is presented depending on the initial conditions and the Reynolds number. In accordance with the type of flow, the boundary conditions of the problem are established, and the boundary-value problem is formulated. Regularities for the change in velocities lengthwise in the entrance region have been obtained for a constant and parabolic velocity distribution in the inlet cross-sections. Analytical solutions have been obtained, allowing to obtain patterns of changes in velocities and pressures toward flow at any section and at any time. For the mentioned cases, the composite graphs of velocity changes in different sections along the length of the entrance transition area were constructed by computer analysis, for different time conditions. With the obtained composite graphs, the patterns of change over the entire length of the transition area of the entrance region were constructed, enabling to obtain fluid flow velocity at any point of the section. The length of the transition zone can be estimated based on the condition of reaching a certain percentage (99%) of the maximum velocity of the flow. The proposed solutions create the conditions for correctly constructing separate units of hydromechanical equipment

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Schrifttum

Hoitz

Kremer

1980

Entwicklung Und Anwendung Mathematischer Modelle Für Die Erfassung Der Strömungsvorgänge in Gasbeheizten Industriellen Feuerung

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A new method for the numerical solution of time dependent viscous flow

Cited by 5 publications

References 10 publications

Identifying some regularities of the turbulent steady-state plane-parallel motion of incompressible fluid at the entrance length

Identifying some regularities of the turbulent steady-state plane-parallel motion of incompressible fluid at the entrance length

Pattern identification of the non-stationary laminar flow of a viscous fluid in the round pipe inlet section

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