Virtual Nikuradse

Yang, Bobby H.; Joseph, Daniel D.

doi:10.1080/14685240902806491

Cited by 24 publications

(24 citation statements)

References 8 publications

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“…The numerical scheme is similar to that used by Dontsov but uses a friction factor that captures the effect of turbulent flow. Two versions of the friction factor are used: Churchill's friction factor and the “virtual Nikuradse,” where the latter is an approximation fitted to Nikuradse's pipe data . Both friction factors are originally derived for circular pipes.…”

Section: Resultsmentioning

confidence: 99%

“…Variation of the friction factor versus Reynolds number; including Nikuradse's pipe data, the Gauckler‐Manning‐Strickler (GMS) friction factor (Equation ), and approximations of Churchill and Yang and Joseph's virtual Nikuradse approximation [Colour figure can be viewed at wileyonlinelibrary.com]…”

Section: Resultsmentioning

confidence: 99%

“…Variation of the fracture length (left), wellbore width (middle), and wellbore pressure (right) versus Reynolds number that are generated based on the virtual Nikuradse approximation [Colour figure can be viewed at wileyonlinelibrary.com]…”

Section: Resultsmentioning

confidence: 99%

See 2 more Smart Citations

Solution for a plane strain rough‐walled hydraulic fracture driven by turbulent fluid through impermeable rock

Zolfaghari

Dontsov

Bunger

2017

Num Anal Meth Geomechanics

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Summary The impact of turbulent flow on plane strain fluid‐driven crack propagation is an important but still poorly understood consideration in hydraulic fracture modeling. The changes that hydraulic fracturing has experienced over the past decade, especially in the area of fracturing fluids, have played a major role in the transition of the typical fluid regime from laminar to turbulent flow. Motivated by the increasing preponderance of high‐rate, water‐driven hydraulic fractures with high Reynolds number, we present a semianalytical solution for the propagation of a plane strain hydraulic fracture driven by a turbulent fluid in an impermeable formation. The formulation uses a power law relationship between the Darcy‐Weisbach friction factor and the scale of the fracture roughness, where one specific manifestation of this generalized friction factor is the classical Gauckler‐Manning‐Strickler approximation for turbulent flow in a rough‐walled channel. Conservation of mass, elasticity, and crack propagation are also solved simultaneously. We obtain a semianalytical solution using an orthogonal polynomial series. An approximate closed‐form solution is enabled by a choice of orthogonal polynomials embedding the near‐tip asymptotic behavior and thus giving very rapid convergence; a precise solution is obtained with 2 terms of the series. By comparison with numerical simulations, we show that the transition region between the laminar and turbulent regimes can be relatively small so that full solutions can often be well approximated by either a fully laminar or fully turbulent solution.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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Solution for a plane strain rough‐walled hydraulic fracture driven by turbulent fluid through impermeable rock

Zolfaghari

Dontsov

Bunger

2017

Num Anal Meth Geomechanics

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“…Not surprisingly, it has been the subject of careful measurement [1,4]. There is also an array of empirical formulae to predict the friction factor in concrete situations [5,6], culminating with the sheer rendition of Nikuradse's experimental results in analytical form provided by Yang and Joseph [7]. However, the theoretical link between the phenomenological formulae and the experimental results is weak.…”

Section: Introductionmentioning

confidence: 99%

Friction factor for turbulent flow in rough pipes from Heisenberg’s closure hypothesis

Calzetta¹

2009

Phys. Rev. E

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“…The coefficient f in eq. (1) is the so-called friction factor [1][2][3][4][5]. For a given pipe, the friction factor is a function of Reynolds number…”

Section: Introductionmentioning

confidence: 99%

Extension of the momentum transfer model to time-dependent pipe turbulence

Calzetta

2012

Phys. Rev. E

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We analyze a possible extension of Gioia and Chakraborty's momentum transfer model of friction in steady turbulent pipe flows (Phys. Rev. Lett. 96, 044502 (2006)) to the case of time and/or space dependent turbulent flows. The end result is an expression for the stress at the wall as the sum of an steady and a dynamic component. The steady part is obtained by using the instantaneous velocity in the expression for the stress at the wall of a stationary flow. The unsteady part is a weighted average over the history of the flow acceleration, with a weighting function similar to that proposed by Brown (Journal of Sound and Vibration 259, 1011 (2003); ibid. 270, 233 (2004)), but naturally including the effect of spatial derivatives of the mean flow, as in the Brunone model (B. Brunone et al., J. of Water Resources Planning and Management 236 (2000)).

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Virtual Nikuradse

Cited by 24 publications

References 8 publications

Solution for a plane strain rough‐walled hydraulic fracture driven by turbulent fluid through impermeable rock

Solution for a plane strain rough‐walled hydraulic fracture driven by turbulent fluid through impermeable rock

Friction factor for turbulent flow in rough pipes from Heisenberg’s closure hypothesis

Extension of the momentum transfer model to time-dependent pipe turbulence

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