Stability of a laminar pipe flow subjected to a step-like increase in the flow rate

Kannaiyan, Ashok; Natarajan, Sekarapandian; Vinoth, B. R.

doi:10.1063/5.0090337

Cited by 8 publications

(5 citation statements)

References 38 publications

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“…Gradual increase in flow rate causes non-periodic non-stationary flow. Analysis of flow stability depending on the ratio of the current flow to the established laminar flow is carried out in work [12]. As a result, the conditions for the stability of the unsteady flow in the pipe are obtained.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

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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%

“…The gradient of pressure change in the direction of movement in a stabilized turbulent flow remains constant, therefore from equation (12) it is possible to get that the tangential stresses in the live section are distributed according to the linear law, therefore:…”

Section: Choosing a Calculation Schemementioning

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

“…A stepwise increase in flow rate causes a non-periodic non-stationary flow. The analysis of the flow stability depending on the ratio of the current flow discharge to the steady-state laminar flow discharge was carried out in [16]. As a result, the conditions for the stability of an non-stationary flow in the pipe are obtained.…”

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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“…Under the conditions of varying the kinematic coefficient of viscosity according to an arbitrary law, the proposed solutions to the momentum equation [12] are represented by the Fourier series and the Bessel and Kelvin functions. Reference [13] analyzed flow stability based on the flow rate ratio to the steady-state laminar flow rate. This analysis led to the establishment of stability conditions for unsteady flow in a pipe.…”

Section: Introductionmentioning

confidence: 99%

Plane-Parallel Laminar Flow of Viscous Fluid in the Transition Zone of the Inlet Section

Sarukhanyan

Vermishyan

Kelejyan

2023

jaer

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A study was conducted to analyze how hydrodynamic parameters change in the entrance region of plane-parallel flow under stationary flow conditions, with an initial arbitrary distribution of velocities in the entrance section. This study was based on boundary layer equations, and a boundary problem was formed under the conditions of plane-parallel flow. The boundary conditions were chosen to reflect the pattern of arbitrary velocity distribution in the entrance section. A general solution of the approximating Navier-Stokes equations is provided, which depends on the initial conditions and the Reynolds number. The boundary conditions are established based on the nature of the motion, and the boundary value problem is described. A method for integrating the boundary value problem has been developed, and regularities for the change in velocities along the length of the inlet section have been obtained for both constant and parabolic velocity distributions in the entrance sections. Analytical solutions have been derived to obtain patterns of velocity and pressure changes in any given flow direction. Through computer analysis, velocity change patterns in various sections along the inlet transition area have been constructed, allowing for the determination of fluid velocity at any point on the section and an estimation of the length of the transition area. These proposed solutions provide a framework for accurately constructing individual units of hydromechanical equipment.

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Stability of a laminar pipe flow subjected to a step-like increase in the flow rate

Cited by 8 publications

References 38 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

Plane-Parallel Laminar Flow of Viscous Fluid in the Transition Zone of the Inlet Section

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