On an analytic solution for general unsteady/transient turbulent pipe flow and starting turbulent flow

García, F. J. García; Alvariño, Pablo Fariñas

doi:10.1016/j.euromechflu.2018.11.014

Cited by 17 publications

(23 citation statements)

References 5 publications

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“…(iv) Changes of pressure are transmitted (almost) instantaneously all over the flow, for it is considered incompressible; however, changes in MPG and WSS would take some time to propagate within the flow, for inertia plays a role in U-flows. (v) Under its own dynamics, the ULF tends to follow the behaviour of the MPG, for Π(τ ) is the source of u L (τ, α) (García García & Fariñas Alvariño 2019b,c, 2020, 2021. The u L (τ, α) reacts rather quickly to changes in Π(τ ), although it does not trail the MPG evolution instantaneously.…”

Section: Explanation Of Experiments Destabilising Turbulence In Pipe ...mentioning

confidence: 98%

“…A list of all acronyms used can be found in Appendix A. The present article is the fifth in a series (García García & Fariñas Alvariño 2019 b , c , 2020, 2021) that intends to explain a number of experimental results reported in the literature, which to date remain unexplained.…”

Section: Introductionmentioning

confidence: 99%

“…A few years ago, we finally solved the Reynolds-averaged Navier–Stokes equation (RANSE) for any fully developed incompressible pipe flow (García García 2017; García García & Fariñas Alvariño 2019 b ), a second-order parabolic partial differential equation on the mean-velocity field. The general solution takes the form of a Fourier–Bessel series, rooted in a weighted Hilbert space , which is the functional space where the ensemble-averaged flow fields are defined.…”

Section: Introductionmentioning

confidence: 99%

“…In order to fully understand the coming explanations, a certain knowledge of the TULF scope and methods would be necessary. Therefore, we shall begin this work with some basic notions, albeit a comprehensive account can be found in our previous publications (García García & Fariñas Alvariño 2019 b , c , 2020, 2021). The TULF is a theory heavily based upon mathematical analysis, and most of the concepts that will be introduced, however strange they might appear at first sight, arise out of mathematical necessity.…”

Section: Introductionmentioning

confidence: 99%

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On the analytic explanation of experiments where turbulence vanishes in pipe flow

García

Alvariño²

2022

J. Fluid Mech.

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The present research will provide an analytical explanation to experiments destabilising turbulence in pipe flow reported in Kuehnen et al. (Nat. Phys., vol. 14, 2018, 386–390). Those experiments show four methods by which turbulence vanishes from steady-state pipe flow, without decreasing its bulk velocity, until it becomes completely laminar. The explanation is based on our theory of underlying laminar flow (TULF), which has already been successfully applied to account for other uncommon experiments reported in the literature. The TULF is founded on the Reynolds-averaged Navier–Stokes equations and thus is a theory of ensemble-averaged flows. The zero theorem for steady-state flow is introduced as a universal result that will help explain the laminarisation process described in experiments. After presenting the most comprehensive solution for the mean pipe flow governing equation that, to our knowledge, has ever been reported, we uncover a general sequence for laminarisation, called the laminarisation pattern, and we introduce a mathematical model for it. We show that a drastic decrease in a flow's mean-pressure gradient, while maintaining constant its Reynolds number, is necessary and sufficient to erase turbulence. Equations derived from our model are used to calculate the minimum pressure gradient necessary to cause complete laminarisation in each experiment. Results are then contrasted with reported experimental data, with noticeable agreement. We also propose a figure of merit to assess the efficiency of each laminarisation method. Having disclosed the intrinsic mechanism leading to complete laminarisation, we expect researchers will propose other ingenious methods to achieve it.

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Section: Explanation Of Experiments Destabilising Turbulence In Pipe ...mentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the analytic explanation of experiments where turbulence vanishes in pipe flow

García

Alvariño²

2022

J. Fluid Mech.

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“…Among such solutions, there are solutions for accelerated [5][6][7][8][9], decelerated [10], reverse [11], pulsating [12,13], and other types of flows [14][15][16][17][18][19]. Relatively recently, new solutions have been developed in which a variable viscosity has been introduced during the duration of unsteady pipe flow [20,21], and with the help of newly derived methods, the previously known laminar models can be extended to turbulent flows [22,23].…”

Section: Introductionmentioning

confidence: 99%

About Inverse Laplace Transform of a Dynamic Viscosity Function

et al. 2022

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A dynamic viscosity function plays an important role in water hammer modeling. It is responsible for dispersion and decay of pressure and velocity histories. In this paper, a novel method for inverse Laplace transform of this complicated function being the square root of the ratio of Bessel functions of zero and second order is presented. The obtained time domain solutions are dependent on infinite exponential series and Calogero–Ahmed summation formulas. Both of these functions are based on zeros of Bessel functions. An analytical inverse will help in the near future to derive a complete analytical solution of this unsolved mathematical problem concerning the water hammer phenomenon. One can next present a simplified approximate form of this solution. It will allow us to correctly simulate water hammer events in large ranges of water hammer number, e.g., in oil–hydraulic systems. A complete analytical solution is essential to prevent pipeline failures while still designing the pipe network, as well as to monitor sensitive sections of hydraulic systems on a continuous basis (e.g., against possible overpressures, cavitation, and leaks that may occur). The presented solution has a high mathematical value because the inverse Laplace transforms of square roots from the ratios of other Bessel functions can be found in a similar way.

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Analytical Solutions of Water Hammer in Metal Pipes. Part I—Brief Theoretical Study

Urbanowicz

Bergant

Stosiak

et al. 2022

Structural Integrity

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On an analytic solution for general unsteady/transient turbulent pipe flow and starting turbulent flow

Cited by 17 publications

References 5 publications

On the analytic explanation of experiments where turbulence vanishes in pipe flow

On the analytic explanation of experiments where turbulence vanishes in pipe flow

About Inverse Laplace Transform of a Dynamic Viscosity Function

Analytical Solutions of Water Hammer in Metal Pipes. Part I—Brief Theoretical Study

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