Probabilistic modelling of security of supply in gas networks and evaluation of new infrastructure

Praks, Pavel; Kopustinskas, Vytis; Masera, Marcelo

doi:10.1016/j.ress.2015.08.005

Cited by 130 publications

(77 citation statements)

References 20 publications

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“…A sudden failure of valves or other components, either related to hydraulic systems in civil and mechanical engineering [35][36][37], can cause also change of flow regime. Because of that it is very important to take into consideration also such cases.…”

Section: Discussionmentioning

confidence: 99%

Unified Friction Formulation from Laminar to Fully Rough Turbulent Flow

Brkić¹,

Praks²

2018

Preprint

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This paper gives a new unified formula for the Newtonian fluids valid for all pipe flow regimes from laminar to the fully rough turbulent. It includes laminar, unstable sharp jump from laminar to turbulent, and all types of the turbulent regimes: smooth turbulent regime, partial non-fully developed turbulent and fully developed rough turbulent regime. The formula follows the inflectional form of curves as suggested in Nikuradse's experiment rather than monotonic shape proposed by Colebrook and White. The composition of the proposed unified formula consists of switching functions and of the interchangeable formulas for laminar, smooth turbulent and fully rough turbulent flow. The proposed switching functions provide a smooth and a computationally cheap transition among hydraulic regimes. Thus, the here presented formulation represents a coherent hydraulic model suitable for engineering use. The model is compared to existing literature models, and shows smooth and computationally cheap transitions among hydraulic regimes.

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Section: Discussionmentioning

confidence: 99%

Unified Friction Formulation from Laminar to Fully Rough Turbulent Flow

Brkić¹,

Praks²

2018

Preprint

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“…The results are relevant for all engineering fields that deal with fluid flow through pipes [72][73][74] and the related calculation of hydraulic flow friction.…”

Section: Discussionmentioning

confidence: 99%

Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

Brkić

Ćojbašić

2017

Fluids

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This paper presents evolutionary optimization of explicit approximations of the empirical Colebrook's equation that is used for the calculation of the turbulent friction factor (λ), i.e., for the calculation of turbulent hydraulic resistance in hydraulically smooth and rough pipes including the transient zone between them. The empirical Colebrook's equation relates the unknown flow friction factor (λ) with the known Reynolds number (R) and the known relative roughness of the inner pipe surface (ε/D). It is implicit in the unknown friction factor (λ). The implicit Colebrook's equation cannot be rearranged to derive the friction factor (λ) directly, and therefore, it can be solved only iteratively [λ = f(λ, R, ε/D)] or using its explicit approximations [λ ≈ f(R, ε/D)], which introduce certain error compared with the iterative solution. The optimization of explicit approximations of Colebrook's equation is performed with the aim to improve their accuracy, and the proposed optimization strategy is demonstrated on a large number of explicit approximations published up to date where numerical values of the parameters in various existing approximations are changed (optimized) using genetic algorithms to reduce maximal relative error. After that improvement, the computational burden stays unchanged while the accuracy of approximations increases in some of the cases very significantly.

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“…The procedure proposed in this paper can significantly reduce the computational burden for evaluating complex distribution networks with various applications (water, gas) (Brkić 2009, Brkić 2011a, Praks et al 2015, Praks et al 2017, Brkić 2016. For example, a probabilistic approach using time dependent modeling of distribution or transmission networks requires many millions of evaluations of Colebrook's equation, which means that it is not a computationally cheap task at all.…”

Section: Discussionmentioning

confidence: 99%

One-Log Call Iterative Solution of the Colebrook Equation for Flow Friction Based on Padé Polynomials

Praks¹,

Brkić²

2018

Preprint

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Abstract:The eighty years old empirical Colebrook function widely used as an informal standard for hydraulic resistance relates implicitly the unknown flow friction factor , with the known Reynolds number and the known relative roughness of a pipe inner surface ;. It is based on logarithmic law in the form that captures the unknown flow friction factor in a way from which it cannot be extracted analytically. As an alternative to the explicit approximations or to the iterative procedures that require at least a few evaluations of computationally expensive logarithmic function or non-integer powers, this paper offers an accurate and computationally cheap iterative algorithm based on Padé polynomials with only one -call in total for the whole procedure (expensive -calls are substituted with Padé polynomials in each iteration with the exception of the first). The proposed modification is computationally less demanding compared with the standard approaches of engineering practice, but does not influence the accuracy or the number of iterations required to reach the final balanced solution.

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Probabilistic modelling of security of supply in gas networks and evaluation of new infrastructure

Cited by 130 publications

References 20 publications

Unified Friction Formulation from Laminar to Fully Rough Turbulent Flow

Unified Friction Formulation from Laminar to Fully Rough Turbulent Flow

Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

One-Log Call Iterative Solution of the Colebrook Equation for Flow Friction Based on Padé Polynomials

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Probabilistic modelling of security of supply in gas networks and evaluation of new infrastructure

Cited by 130 publications

References 20 publications

Unified Friction Formulation from Laminar to Fully Rough Turbulent Flow

Unified Friction Formulation from Laminar to Fully Rough Turbulent Flow

Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

One-Log Call Iterative Solution of the Colebrook Equation for Flow Friction Based on Pad&eacute; Polynomials

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One-Log Call Iterative Solution of the Colebrook Equation for Flow Friction Based on Padé Polynomials