Numerical investigation of the cavitating flow for constant water hammer number

Urbanowicz, Kamil; Bergant, Anton; Karadžić, Uroš; Jing, Haixiao; Kodura, Apoloniusz

doi:10.1088/1742-6596/1736/1/012040

Cited by 10 publications

(7 citation statements)

References 28 publications

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“…This paper presents author's recent developments in general solutions for decomposing modified Calogero-Ahmed series into series built of basic functions, which are Rayleigh series and standard Calogero-Ahmed series. The derived novel formula (7) turned out to be very useful for obtaining the final general solution (13). The presented solutions are very important in order to calculate the coefficients of polynomials that appear in the inverse Laplace transformation of the dynamic viscosity function [20].…”

Section: Discussionmentioning

confidence: 99%

“…To complete the theory about the inverse Laplace transform of the dynamic viscosity function, one more problem need to be solved. Namely, as results from the final general solution (13), it is always based on the standard Calogero-Ahmed series (6), and already Calogero [22] noted that: "... an interesting question is whether it can yield a closed-form expression for the sum for all (positive integral) values of c". So the last step look to be the derivation of a recursive solution (similar to Meimann's for the Rayleigh sums) for the standard Calogero-Ahmed functions:…”

Section: Generalization Of Modified Calogero-ahmed Summation Formulasmentioning

confidence: 99%

“…This solution is in fact a significant extension of the Holmboe's solution, and it is based on unsteady friction term 𝜏 𝑤 = 𝜏 𝑞−𝑠 + 𝜏 𝑢 resulting in an accurate solution, close to numerically predicted normalized pressure 𝑝̂ and velocity 𝑣 ̂ histories (NUM)see figure 1 (𝑡 ̂is the dimensionless time). These simulations were performed for a specific value of an important dimensionless number called water hammer number 𝑊ℎ = (𝜈𝐿)/(𝑐𝑅 2 ) [13]. In the 1990s, these issues were also dealt with by Wang et al [14].…”

Section: Introductionmentioning

confidence: 99%

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On the generalization of Calogero-Ahmed summation formulas

Urbanowicz

Stosiak

Bergant

2022

J. Phys.: Conf. Ser.

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The use of the Laplace transform gives the solution of water hammer equations in the frequency domain. The inverse transform of this solution over the years seemed impossible to derive, due to the significant complexity and the fact that the square root of the Bessel function was embedded in the argument of the resulting hyperbolic functions. In this work, we consider some generalizations that enable the determination of the modified Calogero-Ahmed infinite series. These generalizations will allow us in the near future (using the machine learning and artificial intelligence algorithms) a return to the time domain in a very wide range of the dynamic viscosity function, which plays the most important role in this complex fluid dynamic problem.

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Section: Discussionmentioning

confidence: 99%

Section: Generalization Of Modified Calogero-ahmed Summation Formulasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the generalization of Calogero-Ahmed summation formulas

Urbanowicz

Stosiak

Bergant

2022

J. Phys.: Conf. Ser.

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“…The initial verification of this model presented in recent papers [4,40,41] showed its enormous usefulness, especially in modeling water hammer occurring in water pipe flows (relatively low-viscosity water supply systems). Unfortunately, in typical hydraulic systems, i.e., wherever the working fluid is hydraulic oil (water hammer number 0.05 > Wh > 0.5 [42]), computational compliance was not sufficient. Further attempts of the analytical solution were undertaken by Sobey [43], whose solution, unfortunately, does not take into account the unsteady friction, and Mei-Jing [44,45].…”

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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“…The results of most of the models have been compared to experimental data and satisfactory comparison was achieved even if with different assumptions. Mainly developed within the frame of the water hammer problem, some of them assume that the instantaneous value of the viscous term is related to time evolution of the transient [4], some relate the unsteady contribution to the fluid acceleration [9], further conjectured that the role of viscous terms is not longer described by the Reynolds number [10], dimensional analysis of the 1D and 2D models revealed the role of some dimensionless numbers in the pressure wave attenuation in the water hammer phenomenon [3,8,11]. The problem is still controversial and further efforts seem to be needed.…”

Section: Introductionmentioning

confidence: 99%

New Dimensionless Number for the Transition from Viscous to Turbulent Flow

Nucci

Celli

Pasquali

et al. 2022

Fluids

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Within the framework of Classical Continuum Thermomechanics, we consider an unsteady isothermal flow of a simple isotropic linear viscous fluid in the liquid state to investigate the transient flow conditions. Despite the attention paid to this problem by several research works, it seems that the understanding of turbulence in these flow conditions is controversial. We propose a dimensionless procedure that highlights some aspects related to the transition from viscous to turbulent flow which occurs when a finite amplitude pressure wave travels through the fluid. This kind of transition is demonstrated to be described by a (first) dimensionless number, which involves the bulk viscosity. Furthermore, in the turbulent flow regime, we show the role played by a (second) dimensionless number, which involves the turbulent bulk viscosity, in entropy production. Within the frame of the 1D model, we test the performance of the dimensionless procedure using experimental data on the pressure waves propagation in a long pipe (water hammer phenomenon). The obtained numerical results show good agreement with the experimental data. The results’ inspection confirms the predominant role of the turbulent bulk viscosity on energy dissipation processes.

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Numerical investigation of the cavitating flow for constant water hammer number

Cited by 10 publications

References 28 publications

On the generalization of Calogero-Ahmed summation formulas

On the generalization of Calogero-Ahmed summation formulas

About Inverse Laplace Transform of a Dynamic Viscosity Function

New Dimensionless Number for the Transition from Viscous to Turbulent Flow

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