Unified Friction Formulation from Laminar to Fully Rough Turbulent Flow

Brkić, Dejan; Praks, Pavel

doi:10.3390/app8112036

Cited by 39 publications

(24 citation statements)

References 43 publications

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“…Compared with some other experimental findings [3], the Colebrook equation fits the friction factor within a few dozen percent of error [4]. The Colebrook equation over the last 80 years has been seen by the industry as an informal standard for flow friction calculation and has been very well accepted in everyday engineering practice.…”

Section: Introductionmentioning

confidence: 83%

Rational Approximation for Solving an Implicitly Given Colebrook Flow Friction Equation

Praks

Brkić

2019

Mathematics

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The empirical logarithmic Colebrook equation for hydraulic resistance in pipes implicitly considers the unknown flow friction factor. Its explicit approximations, used to avoid iterative computations, should be accurate but also computationally efficient. We present a rational approximate procedure that completely avoids the use of transcendental functions, such as logarithm or non-integer power, which require execution of the additional number of floating-point operations in computer processor units. Instead of these, we use only rational expressions that are executed directly in the processor unit. The rational approximation was found using a combination of a Padé approximant and artificial intelligence (symbolic regression). Numerical experiments in Matlab using 2 million quasi-Monte Carlo samples indicate that the relative error of this new rational approximation does not exceed 0.866%. Moreover, these numerical experiments show that the novel rational approximation is approximately two times faster than the exact solution given by the Wright omega function.

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Section: Introductionmentioning

confidence: 83%

Rational Approximation for Solving an Implicitly Given Colebrook Flow Friction Equation

Praks

Brkić

2019

Mathematics

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“…In Equation (11), ∆p is the pressure loss, ρ is the density, u m is the average fluid velocity, x is the axial distance, d is the pipe diameter, and f f d is the friction factor for the fully developed flow. In general, this coefficient can be approximated as 16/Re [19]. The investigated geometry is shown in Figure 1.…”

Section: Methodsmentioning

confidence: 99%

“…Therefore, the grid arrangement of 4.5 × 10 6 for the computational domain has satisfactory grid independence and is adequate for the resolution of the conjugate heat-transfer problem. The heat-transfer coefficient and pressure drop have been evaluated using Equations (18) and (19).…”

Section: Regression Modelmentioning

confidence: 99%

Development of a Model for Performance Analysis of a Honeycomb Thermal Energy Storage for Solar Power Microturbine Applications

et al. 2019

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Solar power microturbines are required to produce steady power despite the fluctuating solar radiation, with concerns on the dispatchability of such plants where thermal energy storage may offer a solution to address the issue. This paper presents a mathematical model for performance prediction of a honeycomb sensible-heat thermal energy storage designed for application of concentrated solar power microturbine. The focus in the model is to consider the laminar developing boundary layers at the entry of the flow channels, which could have a profound effect on the heat-transfer coefficient due to large velocity and temperature gradients, an effect which has not been considered in the modelling of such storage systems. Analysing the thermal and hydrodynamic boundary layer development, the Nusselt number and the friction factor were evaluated using a validated conjugate heat-transfer method. The simulations results were used to develop accurate regression functions for Nusselt number and friction factor. These formulations have been adopted within a one-dimensional model to evaluate the performance of the storage under different operating conditions. The model was in good agreement with conjugate heat transfer results with maximum relative error below 2%. Two case studies are presented to demonstrate the applicability of the proposed methodology.

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“…As shown in Appendix A of this paper, another formulas are used in the case of waterworks systems [17,18] or ventilation networks [7].…”

Section: Hydraulic Modelmentioning

confidence: 99%

Hardy Cross Method for Pipe Networks

Brkić¹,

Praks²

2019

Preprint

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Hardy Cross originally proposed a method for analysis of flow in networks of conduits or conductors in 1936. His method was the first really useful engineering method in the field of pipe network calculation. Only electrical analogs of hydraulic networks were used before the Hardy Cross method. A problem with the flow resistance versus the electrical resistance makes these electrical analog methods obsolete. The method by Hardy Cross is taught extensively at faculties and it still remains an important tool for analysis of looped pipe systems. Engineers today mostly use a modified Hardy Cross method which threats the whole looped network of pipes simultaneously (use of these methods without computers is practically impossible). A method from the Russian practice published during 1930s, which is similar to the Hardy Cross method, is described, too. Some notes from the life of Hardy Cross are also shown. Finally, an improved version of the Hardy Cross method, which significantly reduces number of iterations, is presented and discussed. Also we tested multi-point iterative methods which can be used as substitution for the Newton-Raphson approach used by Hardy Cross, but this approach didn’t reduce number of required iterations to reach the final balanced solution. Although, many new models have been developed since the time of Hardy Cross, main purpose of this paper is to illustrate the very beginning of modeling of gas and water pipe networks or ventilation systems.

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Unified Friction Formulation from Laminar to Fully Rough Turbulent Flow

Cited by 39 publications

References 43 publications

Rational Approximation for Solving an Implicitly Given Colebrook Flow Friction Equation

Rational Approximation for Solving an Implicitly Given Colebrook Flow Friction Equation

Development of a Model for Performance Analysis of a Honeycomb Thermal Energy Storage for Solar Power Microturbine Applications

Hardy Cross Method for Pipe Networks

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