Analytical solution of turbulent pipe flow according to second‐gradient theory

Biglarian, Hassan; Beyrami, Hossein; Dorosti, Qaran; Sattari, Amirmohammad

doi:10.1002/apj.1856

Cited by 1 publication

(4 citation statements)

References 13 publications

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“…Wall shear stress and friction velocity can be calculated using equations ( 18), ( 19) and (20). It is possible to construct a radial hydrodynamically developed axial velocity component profile by equations between (11) and (21).…”

Section: Empirical Data and Expressionsmentioning

confidence: 99%

“…For semi-analytical construction of hydrodynamically developed flow axial velocity component radial profile, equations between (11) CFD hydrodynamically developed profiles.…”

Section: Semi-analytical Solutionmentioning

confidence: 99%

“…Additionally, there are more recent analytical solution trials with higher level mathematics [11]. Some instances are provided in the literature survey.…”

Section: Introductionmentioning

confidence: 99%

“…Slaiman et al presents a wide list containing expressions with references for obtaining a general idea about eddy diffusivity models [33]. A more recent and interesting work on analytical solution of turbulent pipe flow is done by Biglarian et al, using second-gradient theory [11]. The linear momentum equation in the case of second-gradient theory for turbulent pipe flow is reduced to an ordinary differential equation of fourth order, which is solved by analytical method.…”

Section: Introductionmentioning

confidence: 99%

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Developing Turbulent Flow in Pipes and Analysis of Entrance Region

Canlı¹,

Ateş²,

Bilir³

2021

Academic Platform Journal of Engineering and Science

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Turbulent flows have complex structures due to its nature and its' analyses are hard either by numerical or experimental means. Hydrodynamic development of turbulent flow is also complex. In this study, velocity and turbulence distributions in hydrodynamic entrance length of pipes are investigated numerically depending on axial and radial locations. Implications of these distributions are qualitatively evaluated in terms of heat transfer. Literature was surveyed for a single empirical expression that provides velocity profile directly according to Reynolds number, radial and axial locations. Requisite for computational fluid dynamics in hydrodynamic entry length of pipes is stressed by assessing turbulence magnitudes in radial and axial directions. Definition of the development length and effects of the definition in respect of heat transfer are discussed. An axisymmetric pipe entrance region was analyzed by means of a commercial CFD code with nondimensional parameters. Therefore, dimensional parameters reduce into one dimensionless independent parameter, i.e. Reynolds number. Four different Reynolds numbers that are 5x10 3 , 1x10 4 , 5x10 4 , 1x10 5 were used in calculations. k-ϵ turbulence model and standard wall functions were used for turbulence modeling. Hydrodynamic entry length, velocity and turbulence values are presented by means of axial and radial profiles. According to the obtained results, two different directions of radial velocity component values exist in the hydrodynamic entry length that would lead to different radial thermal convection effects. It is found that simultaneously developing velocity profiles and turbulence quantities leads to a characteristic centerline velocity profile. Also, it is seen that a good resolution in hydrodynamic entrance length can be easily achieved by computational fluid dynamics. A detailed composition of hydrodynamic turbulent entrance length analysis, its physical explanations due to simultaneously developing hydrodynamic boundary layers and turbulence production, definition aspects of the entrance length in terms of heat transfer and literature survey for analytical solution of the region are provided.

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Section: Empirical Data and Expressionsmentioning

confidence: 99%

“…For semi-analytical construction of hydrodynamically developed flow axial velocity component radial profile, equations between (11) CFD hydrodynamically developed profiles.…”

Section: Semi-analytical Solutionmentioning

confidence: 99%

“…Additionally, there are more recent analytical solution trials with higher level mathematics [11]. Some instances are provided in the literature survey.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations