Applicability of Preissmann box scheme for calculation of transcritical flow in pipes

2019 ◽  
Vol 19 (5) ◽  
pp. 1429-1437
Author(s):  
Yanmei Wang ◽  
Chengcai Zhang ◽  
Zhansong Li ◽  
Bin Sun ◽  
Haolan Zhou
Keyword(s):  
Numerical Model ◽  
Momentum Equation ◽  
Internal Boundary ◽  
Urban Drainage ◽  
Box Scheme ◽  
Pipe Networks ◽  
Wide Range ◽  
Transcritical Flow ◽  
Transcritical Flows ◽  
Supercritical Flows

Abstract The accurate computer simulation of pipe flow is of great importance in the design of urban drainage. The Preissmann box scheme is usually used to model a wide range of subcritical and supercritical flows. However, care must be taken over the modelling of transcritical flows since, unless the correct internal boundary conditions are imposed, the scheme becomes unstable. In this paper, using the scheme in conjunction with the reduced momentum equation and applying boundary condition structure inherent to subcritical flow to all regimes, is an approach that enables efficient numerical simulation of transcritical flows in pipe networks. The approach includes three steps. First, a unified mathematical model which is based on the Preissmann slot model is derived. Second, the Preissmann box scheme is used to solve the set of equations, by analyzing and discussing the origin of the invalidity of applying the scheme, and a numerical model suitable for transcritical flow is proposed by the method of changing the convection acceleration term. Third, the numerical model is assessed by comparison with analytical, experimental and numerical results. The proposed models verified that this method can make the Preissmann box scheme applicable to the computation of transcritical flow in pipes.

scholarly journals A pipe network simulation model with dynamic transition between free surface and pressurized flow

2014 ◽  
Vol 7 (1) ◽  
pp. 27-57
Author(s):  
J. Fernández-Pato ◽  
P. García-Navarro
Keyword(s):  
Numerical Simulation ◽  
Numerical Model ◽  
Simulation Model ◽  
Water Pressure ◽  
Laboratory Data ◽  
Finite Volume Methods ◽  
Analytic Solutions ◽  
Pipe Networks ◽  
Network Simulation Model ◽  
Supercritical Flows

Abstract. Water flow numerical simulation in urban pipe systems is one of the topics that shows the need for surface flows and pressurized flows in steady and transient situations. The governing equations for both flow types are different and this must be taken into account in order to get a complete numerical model for solving transients. A numerical simulation model is developed in this work, capable of solving pipe networks mainly unpressurized, with isolated peaks of pressurization. For this purpose, a reformulation of the mathematical model through the Preissmann slot method is proposed. By means of this technique, a reasonable estimation of the water pressure is calculated in cases of pressurization. The numerical model is based on the first order Roe's scheme, in the frame of finite volume methods. It is adapted to abrupt transient situations, with subcritial and supercritical flows. The validation has been done by means of several cases with analytic solutions or empirical laboratory data. It has also been applied to some more complex and realistic cases, like junctions or pipe networks.

Comparison of Four Friction Models: Feature Prediction

2015 ◽  
Vol 11 (3) ◽  
Author(s):  
Yun-Hsiang Sun ◽  
Tao Chen ◽  
Christine Qiong Wu ◽  
Cyrus Shafai
Keyword(s):  
Numerical Model ◽  
Viscous Friction ◽  
Friction Model ◽  
Dynamic Features ◽  
Numerical Predictions ◽  
Wide Range ◽  
Model Predictions ◽  
Friction Models ◽  
Parameter Identifications ◽  
Model Structures

In this paper, we provide not only key knowledge for friction model selection among candidate models but also experimental friction features compared with numerical predictions reproduced by the candidate models. A motor-driven one-dimensional sliding block has been designed and fabricated in our lab to carry out a wide range of control tasks for the friction feature demonstrations and the parameter identifications of the candidate models. Besides the well-known static features such as break-away force and viscous friction, our setup experimentally demonstrates subtle dynamic features that characterize the physical behavior. The candidate models coupled with correct parameters experimentally obtained from our setup are taken to simulate the features of interest. The first part of this work briefly introduces the candidate friction models, the friction features of interest, and our experimental approach. The second part of this work is dedicated to the comparisons between the experimental features and the numerical model predictions. The discrepancies between the experimental features and the numerical model predictions help researchers to judge the accuracy of the models. The relation between the candidate model structures and their numerical friction feature predictions is investigated and discussed. A table that summarizes how to select the most optimal friction model among a variety of engineering applications is presented at the end of this paper. Such comprehensive comparisons have not been reported in previous literature.

scholarly journals A finite-difference convective model for Jupiter's equatorial jet

2006 ◽  
Vol 2 (S239) ◽  
pp. 230-232 ◽  
Author(s):  
Kwing L. Chan
Keyword(s):  
Reynolds Number ◽  
Numerical Model ◽  
Finite Difference ◽  
Spherical Shell ◽  
Reynolds Stress ◽  
Momentum Equation ◽  
Momentum Balance ◽  
Zonal Momentum Balance ◽  
Zonal Momentum ◽  
Convective Model

AbstractWe present results of a numerical model for studying the dynamics of Jupiter's equatorial jet. The computed domain is a piece of spherical shell around the equator. The bulk of the region is convective, with a thin radiative layer at the top. The shell is spinning fast, with a Coriolis number = ΩL/V on the order of 50. A prominent super-rotating equatorial jet is generated, and secondary alternating jets appear in the higher latitudes. The roles of terms in the zonal momentum equation are analyzed. Since both the Reynolds number and the Taylor number are large, the viscous terms are small. The zonal momentum balance is primarily between the Coriolis and the Reynolds stress terms.

scholarly journals Finite volume simulation of unsteady water pipe flow

2014 ◽  
Vol 7 (2) ◽  
pp. 83-92 ◽  
Author(s):  
J. Fernández-Pato ◽  
P. García-Navarro
Keyword(s):  
Numerical Simulation ◽  
Numerical Model ◽  
Finite Volume ◽  
Water Pressure ◽  
Laboratory Data ◽  
Network Models ◽  
Finite Volume Methods ◽  
Analytic Solutions ◽  
Surface Flow ◽  
Pipe Networks

Abstract. The most commonly used hydraulic network models used in the drinking water community exclusively consider fully filled pipes. However, water flow numerical simulation in urban pipe systems may require to model transitions between surface flow and pressurized flow in steady and transient situations. The governing equations for both flow types are different and this must be taken into account in order to get a complete numerical model for solving dynamically transients. In this work, a numerical simulation tool is developed, capable of simulating pipe networks mainly unpressurized, with isolated points of pressurization. For this purpose, the mathematical model is reformulated by means of the Preissmann slot method. This technique provides a reasonable estimation of the water pressure in cases of pressurization. The numerical model is based on the first order Roe's scheme, in the frame of finite volume methods. The novelty of the method is that it is adapted to abrupt transient situations, with subcritical and supercritical flows. The validation has been done by means of several cases with analytic solutions or empirical laboratory data. It has also been applied to some more complex and realistic cases, like junctions or pipe networks.

scholarly journals Evaluating Curb Inlet Efficiency for Urban Drainage and Road Bioretention Facilities

Water ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 851 ◽  
Author(s):  
Li ◽  
Fang ◽  
Chen ◽  
Gong ◽  
Wang ◽  
...  
Keyword(s):  
Overland Flow ◽  
Flow Simulation ◽  
Linear Regression Method ◽  
Urban Drainage ◽  
Regression Equations ◽  
Strongly Correlated ◽  
Wide Range ◽  
Input Parameters ◽  
Longitudinal Slope ◽  
Two Dimensional Flow

An updated two-dimensional flow simulation program, FullSWOF-ZG, which fully (Full) solves shallow water (SW) equations for overland flow (OF) and includes submodules modeling infiltration by zones (Z) and flow interception by grate-inlet (G), was tested with 20 locally depressed curb inlets to validate the inlet efficiency (Eci), and with 80 undepressed curb inlets to validate the inlet lengths (LT) for 100% interception. Previous curb inlet equations were based on certain theoretical approximations and limited experimental data. In this study, 1000 road-curb inlet modeling cases from the combinations of 10 longitudinal slopes (S0, 0.1–1%), 10 cross slopes (Sx, 1.5–6%), and 10 upstream inflows (Qin, 6–24 L/s) were established and modeled to determine LT. The second 1000 modeling cases with the same 10 S0 and 10 Sx and 10 curb inlet lengths (Lci, 0.15–1.5 m) were established to determine Eci. The LT and Eci regression equations were developed as a function of input parameters (S0, Sx, and Qin) and Lci/LT with the multiple linear regression method, respectively. Newly developed regression equations were applied to 10,000 inlet design cases (10 S0, 10 Sx, 10 Qin, and 10 Lci combinations) and comprehensively compared with three equations in previous studies. The 100% intercepted gutter flow (Qg100) equations were derived, and over-prediction of Qg100 from previous methods was strongly correlated to smaller S0. Newly developed equations gave more accurate estimations of LT and Eci over a wide range of input parameters. These equations can be applied to designing urban drainage and road bioretention facilities, since they were developed using a large number of simulation runs with diverse input parameters, but previous methods often overpredict the gutter flow of total interception when the longitudinal slope S0 is small.

Unsteady Flow Structure on a Centrifugal Pump: Experimental and Numerical Approaches

2002 ◽  
Author(s):  
Jose´ Gonza´lez ◽  
Carlos Santolaria ◽  
Eduardo Blanco ◽  
Joaqui´n Ferna´ndez
Keyword(s):  
Numerical Model ◽  
Centrifugal Pump ◽  
Pressure Field ◽  
Pressure Fluctuations ◽  
Side Wall ◽  
Relative Effect ◽  
Pressure Transducers ◽  
Unsteady Pressure ◽  
Blade Passing Frequency ◽  
Wide Range

Both experimental and numerical studies of the unsteady pressure field inside a centrifugal pump have been carried out. The unsteady patterns found for the pressure fluctuations are compared and a further and more detailed flow study from the numerical model developed will be presented in this paper. Measurements were carried out with pressure transducers installed on the volute shroud. At the same time, the unsteady pressure field inside the volute of a centrifugal pump has been numerically modelled using a finite volume commercial code and the dynamic variables obtained have been compared with the experimental data available. In particular, the amplitude of the fluctuating pressure field in the shroud side wall of the volute at the blade passing frequency is successfully captured by the model for a wide range of operating flow rates. Once the developed numerical model has shown its capability in describing the unsteady patterns experimentally measured, an explanation for such patterns is searched. Moreover, the possibilities of the numerical model can be extended to other sections (besides the shroud wall of the volute), which can provide plausible explanations for the dynamic interaction effects between the flow at the impeller exit and the volute tongue at different axial positions. The results of the numerical simulation are focused in the blade passing frequency in order to study the relative effect of the two main phenomena occurring at that frequency for a given position: the blade passing in front of the tongue and the wakes of the blades.

Application of a Simplified Velocity Profile to the Prediction of Pipe-Flow Heat Transfer

1968 ◽  
Vol 90 (2) ◽  
pp. 191-198 ◽  
Author(s):  
R. D. Haberstroh ◽  
L. V. Baldwin
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Velocity Profile ◽  
Pipe Flow ◽  
Energy Equation ◽  
Momentum Equation ◽  
Turbulent Pipe Flow ◽  
Transfer Coefficients ◽  
Constant Property ◽  
Wide Range

The temperature profiles and heat-transfer coefficients are predicted for fully developed turbulent pipe flow with constant wall heat flux for a wide range of Prandtl and Reynolds numbers. The basis for integrating the energy equation comes from a continuously differentiable velocity profile which fits the physical boundary conditions and is a rigorous (though not necessarily unique) solution of the Reynolds equations. This velocity profile is the semiempirical relation proposed by S. I. Pai, reference [12]. The assumptions are those of steady, incompressible, constant-property, fully developed, turbulent flow of Newtonian fluids in smooth, circular pipes with constant heat flux at the wall. The ratio of the turbulent thermal diffusivity to the turbulent momentum diffusivity is taken to be unity. The thermal quantities are obtained by numerical integration of the energy equation, and they are presented as curves and tables. A compact formula for the Nusselt number is given for a wide range of Reynolds and Prandtl numbers. The results degenerate identically to the case of laminar flow. The heat-transfer calculation requires neither adjustable factors nor data-fitting beyond the empirical constants in the momentum equation; thus this analysis constitutes a heat-transfer prediction to be tested against heat-transfer data.

Investigation of a ‘transonic resonance’ with convergent–divergent nozzles

2002 ◽  
Vol 463 ◽  
pp. 313-343 ◽  
Author(s):  
K. B. M. Q. ZAMAN ◽  
M. D. DAHL ◽  
T. J. BENCIC ◽  
C. Y. LOH
Keyword(s):  
Computational Study ◽  
Experimental Studies ◽  
Acoustic Resonance ◽  
Internal Boundary Layer ◽  
Internal Boundary ◽  
Frequency Variation ◽  
Length Scale ◽  
Direct Role ◽  
Wide Range ◽  
Quarter Wave

Experimental studies have shown that convergent–divergent nozzles, when run at low pressure ratios, often undergo a flow resonance accompanied by emission of acoustic tones. The phenomenon, different in characteristics from conventional ‘screech’ tones, is addressed in this paper. Unlike screech, the resonant frequency (fN) increases with increasing supply pressure. There is a ‘staging’ behaviour; odd-harmonic stages resonate at lower pressures while the fundamental occurs in a wide range of higher pressures corresponding to a ‘fully expanded Mach number’ (Mj) around unity. Within a stage, fN varies approximately linearly with Mj; the slope of the variation steepens when the angle of divergence of the nozzle is decreased. Based on the data, correlation equations are provided for the prediction of fN. A companion computational study captures the phenomenon and predicts the frequencies, including the stage jump, quite well. While the underlying mechanisms are not completely understood yet, it is clear that the unsteadiness of a shock occurring within the divergent section plays a direct role. The shock drives the flow downstream like a vibrating diaphragm, and resonance takes place similarly to the (no-flow) acoustic resonance of a conical section having one end closed and the other end open. Thus, the fundamental is accompanied by a standing one-quarter wave within the divergent section, the next stage by a standing three-quarter wave, and so on. The distance from the foot of the shock to the nozzle exit imposes the pertinent length scale. The principal trends in the frequency variation are explained qualitatively from the characteristic variation of that length scale. A striking feature is that tripping of the nozzle's internal boundary layer tends to suppress the resonance. It is likely that the trip effect occurs due to a break in the azimuthal coherence of the unsteady flow.

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