On the Hierarchy of Models for Pipe Transients: From Quasi-2D Water Hammer Models to Full 3D CFD Models

2021 ◽  
Author(s):  
Nuno M. C. Martins ◽  
Essam M. Wahba
Keyword(s):  
Stokes Equations ◽  
Cost Effective ◽  
Water Hammer ◽  
Navier Stokes ◽  
Cfd Model ◽  
Navier Stokes Equations ◽  
Cfd Models ◽  
Laminar And Turbulent Flow ◽  
Order Of Magnitude ◽  
Hierarchy Of Models

Abstract A hierarchy of models exists in the literature for the simulation of pipe transients. One-dimensional water hammer models are readily available and provide a cost-effective tool for the analysis of such transients. The main shortcoming of 1D models is the quasi-steady approximation of the frictional term, which results in poor modelling of the attenuation of the transient. To overcome this drawback, quasi-2D water hammer models were introduced, which allow the computation of the unsteady velocity profile and hence provide improved modelling of the attenuation phenomenon. Recently, interest has developed in the use of CFD models based on the Navier-Stokes equations in the simulation of fluid transients. Both axisymmetric CFD models and full 3D CFD models are used in this regard. The aim of the current paper is to carry out a comparative study between the performance of quasi-2D water hammer models, axisymmetric CFD models and full 3D CFD models. Numerical computations using the three models are performed for both laminar and turbulent flow cases. Present results show that the quasi-2D water hammer model and the axisymmetric CFD model provide near identical results in terms of computing the magnitude, phase and attenuation of the transient. Reported results also demonstrate the computational efficiency of the quasi-2D model, which provides results that agree reasonably well with the full 3D CFD model results while using a grid density which is an order of magnitude lower than the grid requirements for the full 3D CFD model.

Flow induced by jets and plumes

1981 ◽  
Vol 108 ◽  
pp. 55-65 ◽  
Author(s):  
W. Schneider
Keyword(s):  
Stokes Equations ◽  
Outer Region ◽  
Reynolds Numbers ◽  
Slip Condition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Laminar Jet ◽  
Order Of Magnitude ◽  
Valid Solution ◽  
Solid Walls

The order of magnitude of the flow velocity due to the entrainment into an axisymmetric, laminar or turbulent jet and an axisymmetric laminar plume, respectively, indicates that viscosity and non-slip of the fluid at solid walls are essential effects even for large Reynolds numbers of the jet or plume. An exact similarity solution of the Navier-Stokes equations is determined such that both the non-slip condition at circular-conical walls (including a plane wall) and the entrainment condition at the jet (or plume) axis are satisfied. A uniformly valid solution for large Reynolds numbers, describing the flow in the laminar jet region as well as in the outer region, is also given. Comparisons show that neither potential flow theory (Taylor 1958) nor viscous flow theories that disregard the non-slip condition (Squire 1952; Morgan 1956) provide correct results if the flow is bounded by solid walls.

scholarly journals Numerical modelling of bank failures during reservoir draw-down

2018 ◽  
Vol 40 ◽  
pp. 03001 ◽  
Author(s):  
Nils Reidar B. Olsen ◽  
Stefan Haun
Keyword(s):  
Stokes Equations ◽  
Limit Equilibrium ◽  
Numerical Algorithms ◽  
High Viscosity ◽  
Navier Stokes ◽  
Bank Failures ◽  
Navier Stokes Equations ◽  
Order Of Magnitude ◽  
Sediment Layers ◽  
Hydropower Reservoir

Numerical algorithms are presented for modeling bank failures during reservoir flushing. The algorithms are based on geotechnical theory and the limit equilibrium approach to find the location and the depth of the slides. The actual movements of the slides are based on the solution of the Navier-Stokes equations for laminar flow with high viscosity. The models are implemented in the SSIIM computer program, which also can be used for modelling erosion of sediments from reservoirs. The bank failure algorithms are tested on the Bodendorf hydropower reservoir in Austria. Comparisons with measurements show that the resulting slides were in the same order of magnitude as the observed ones. However, some scatter on the locations were observed. The algorithms were stable for thick sediment layers, but instabilities were observed for thin sediment layers.

A Quasi-Generalized-Coordinate Approach for Numerical Simulation of Complex Flows

2006 ◽  
Vol 128 (6) ◽  
pp. 1394-1399 ◽  
Author(s):  
Donghyun You ◽  
Meng Wang ◽  
Rajat Mittal ◽  
Parviz Moin
Keyword(s):  
Coordinate System ◽  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Cost Effective ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Curvilinear Coordinate ◽  
Generalized Coordinate

A novel structured grid approach which provides an efficient way of treating a class of complex geometries is proposed. The incompressible Navier-Stokes equations are formulated in a two-dimensional, generalized curvilinear coordinate system complemented by a third quasi-curvilinear coordinate. By keeping all two-dimensional planes defined by constant third coordinate values parallel to one another, the proposed approach significantly reduces the memory requirement in fully three-dimensional geometries, and makes the computation more cost effective. The formulation can be easily adapted to an existing flow solver based on a two-dimensional generalized coordinate system coupled with a Cartesian third direction, with only a small increase in computational cost. The feasibility and efficiency of the present method have been assessed in a simulation of flow over a tapered cylinder.

The Effects of Obstacle and Vent Position on Particle Removal From an Enclosure

2006 ◽  
Author(s):  
M. Hendijanifard ◽  
M. H. Saidi ◽  
M. Taeibi-Rahni
Keyword(s):  
Removal Efficiency ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Particle Removal ◽  
Navier Stokes Equations ◽  
Convection Diffusion ◽  
Step Effect ◽  
Contaminant Particle ◽  
Order Of Magnitude

This paper reports the results of a study of the transient removal of contaminant particle from enclosures. These results are the basic instruments for finding a model for contaminant particle removal from an enclosure containing an obstacle. A numerical CFD code is developed and validated with different cases, then proper two- and three-dimensional cases are modeled and improvements are done. The improvements are done by proper positioning the inlet/outlet vents. The size and position of the obstacle affect the order of magnitude of the convection-diffusion terms in the Navier-Stokes equations, hence results in different phenomena while removing the particles. One of these phenomena, the step effect, is more detailed in reference [41]. The results of these two papers may be compacted into one whole theory, describing the particle removal efficiency from an enclosure as a function of obstacle position and size.

scholarly journals NUMERICAL SIMULATION OF DUST POLLUTION OF WORKING PLACE NEAR COAL DUMP

2021 ◽  
Vol 1 (4(68)) ◽  
pp. 40-45
Author(s):  
M. Biliaiev ◽  
V. Biliaieva ◽  
O. Berlov ◽  
V. Kozachyna
Keyword(s):  
Stokes Equations ◽  
Coal Dust ◽  
Computer Code ◽  
Navier Stokes ◽  
Finite Difference Schemes ◽  
Cfd Model ◽  
Surface Wetting ◽  
Dust Pollution ◽  
Mass Transfer Equation ◽  
Navier Stokes Equations

The problem of estimating the level of air pollution in the working areas near the coal pile is considered. The task is to develop a CFD model that allows to predict the level of air dust pollution, taking into account the process of wetting the surface of the coal pile. To model the process of coal dust transfer in the air, a twodimensional mass transfer equation is used, which takes into account coal dust transfer due to convection and diffusion. The Navier-Stokes equations are used to calculate the air flow field near the coal pile. Finite-difference schemes of splitting are used for numerical integration of modeling equations. Computer code is developed on the basis of created CFD model. The developed code can be used to analyze the effectiveness of the coal surface wetting to reduce dust pollution of work areas near coal piles. The results of a computational experiment are presented.

Nonlinear instability in plane Poiseuille flow: a quantitative comparison between the methods of amplitude expansions and the method of multiple scales

1981 ◽  
Vol 375 (1761) ◽  
pp. 155-167 ◽  
Keyword(s):  
Stream Function ◽  
Stokes Equations ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Navier Stokes ◽  
Plane Poiseuille Flow ◽  
Navier Stokes Equations ◽  
Order Of Magnitude ◽  
Model Equations ◽  
Hydrodynamical Stability

This paper shows that two different expansion procedures for hydrodynamical stability problems are equivalent. The method of multiple scales of Stewartson & Stuart (1971) is extended to calculate the stream function up to order ε 2 . Watson’s (1960) rigorous amplitude expansion of the solution of the Navier-Stokes equations is also used to calculate the stream function up to the same order of magnitude, and a complete equi­valence between the two results is found. An analysis of the Eckhaus model equations has been made and the results are equivalent.

Laminar flow in the entrance region of a smooth pipe

1979 ◽  
Vol 90 (3) ◽  
pp. 433-447 ◽  
Author(s):  
A. K. Mohanty ◽  
S. B. L. Asthana
Keyword(s):  
Boundary Layers ◽  
Stokes Equations ◽  
Velocity Profiles ◽  
Entrance Region ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Fourth Degree ◽  
Boundary Layer Equations ◽  
Inlet Region ◽  
Order Of Magnitude

The entrance region has been divided into two parts, the inlet region and the filled region. At the end of the inlet region, the boundary layers meet at the pipe axis but the velocity profiles are not yet similar. In the filled region, adjustment of the completely viscous profile takes place until the Poiseuille similar profile is attained at the end of it. The boundary-layer equations in the inlet region and the Navier-Stokes equations with order-of-magnitude analysis in the filled region are solved using fourth-degree velocity profiles. The total length of the entrance region so obtained is ξ = x/R Re = 0·150, whereas the boundary layers are observed to meet at approximately one-quarter of the entrance length, i.e. at ξ = 0·036. Experiments reported in the paper corroborate the analytical results.

scholarly journals 3D Flow Structures and Operating Characteristic of an Industrial Fluid Coupling

1995 ◽  
Author(s):  
H. Huitenga ◽  
T. Formanski ◽  
N. K. Mitra ◽  
M. Fiebig
Keyword(s):  
Turbulence Modeling ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Complex Flow ◽  
Navier Stokes Equations ◽  
Laminar And Turbulent Flow ◽  
Fluid Coupling ◽  
Complex Flow Structure ◽  
Insight Into

A liquid circulating between an input rotor and an output rotor transmits power in a fluid coupling. Insight into the flow field is required to influence the transmission behaviour. Parameter studies of model geometries of fluid couplings were presented previously. Laminar and turbulent flow fields and characteristic curves of an actual industrial fluid coupling have been computed from the numerical solution of the three-dimensional, nonsteady Navier-Stokes equations on a body fitted rotating coordinate system. Results show the complex flow structure and vortices that determine the transported angular momentum. Comparison with measured torque suggests that the turbulence modeling by standard k-ϵ model may be inadequate at large slip.

Convergence Acceleration of k-ω Turbulence Equations With Multigrid

2002 ◽  
Author(s):  
Soo Hyung Park ◽  
Chun-ho Sung ◽  
Jang Hyuk Kwon
Keyword(s):  
Multigrid Method ◽  
Stokes Equations ◽  
Computing Time ◽  
Convergence Acceleration ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Loosely Coupled ◽  
Order Of Magnitude ◽  
Simple Limit ◽  
Transonic Airfoil

An efficient implicit multigrid method is presented for the Navier-Stokes and k-ω turbulence equations. Freezing and limiting strategies are applied to improve the robustness and convergence of the multigrid method. In this work, the eddy viscosity and strongly nonlinear production terms of turbulence are frozen in the coarser grids by passing down the values without update of them. The turbulence equations together with the Navier-Stokes equations, however, are consecutively solved on the coarser grids in a loosely coupled fashion. A simple limit for k is also introduced to circumvent slow-down of convergence. Numerical results for the unseparated and separated transonic airfoil flows show that all computations converge well to nine order of magnitude of error without any robustness problem and the computing time is reduced to a factor of about 3 by the present multigrid method.

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