Turbulence modeling for two-dimensional water hammer simulations in the low Reynolds number range

Wahba, Essam

doi:10.1016/j.compfluid.2009.03.007

Cited by 24 publications

(2 citation statements)

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“…Recently, numerical models based on a combination of the Runge-Kutta methods and two-equation turbulence models are receiving attention. Wahba [130,131] modelled twodimensional unsteady pipe flow using mixing-length Baldwin-Lomax and Cebeci-Smith turbulence models, along with the Runge-Kutta method, to integrate mass, momentum, and central differencing for spatial derivatives. Riasi et al [132] used the fourth-order Runge-Kutta scheme along with k − ω and k − ε turbulence models for studying the behaviour of the unsteady turbulent flow.…”

Section: Two-dimensional Numerical Schemesmentioning

confidence: 99%

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An Overview of the Numerical Approaches to Water Hammer Modelling: The Ongoing Quest for Practical and Accurate Numerical Approaches

Pal

Hanmaiahgari

Karney

2021

Water

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Here, recent developments in the key numerical approaches to water hammer modelling are summarized and critiqued. This paper summarizes one-dimensional modelling using the finite difference method (FDM), the method of characteristics (MOC), and especially the more recent finite volume method (FVM). The discussion is briefly extended to two-dimensional modelling, as well as to computational fluid dynamics (CFD) approaches. Finite volume methods are of particular note, since they approximate the governing partial differential equations (PDEs) in a volume integral form, thus intrinsically conserving mass and momentum fluxes. Accuracy in transient modelling is particularly important in certain (typically more nuanced) applications, including fault (leakage and blockage) detection. The FVM, first advanced using Godunov’s scheme, is preferred in cases where wave celerity evolves over time (e.g., due to the release of air) or due to spatial changes (e.g., due to changes in wall thickness). Both numerical and experimental studies demonstrate that the first-order Godunov’s scheme compares favourably with the MOC in terms of accuracy and computational speed; with further advances in the FVM schemes, it progressively achieves faster and more accurate codes. The current range of numerical methods is discussed and illustrated, including highlighting both their limitations and their advantages.

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Section: Two-dimensional Numerical Schemesmentioning

confidence: 99%

“…The available turbulence models for the Reynolds shear stress are based on either steady-state or unsteady-state eddy viscosity distribution. The research approaches [130][131][132][133][134][135]141,142] based on time-varying or time-invariant eddy viscosity distributions are given in Figure 16.…”

Section: Two-dimensional Numerical Schemesmentioning

confidence: 99%