scholarly journals Quasi-static Flow Model for Predicting the Extreme Values of Air Pocket Pressure in Draining and Filling Operations in Single Water Installations

Water ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 664 ◽  
Author(s):  
Óscar E. Coronado-Hernández ◽  
Vicente S. Fuertes-Miquel ◽  
Daniel Mora-Meliá ◽  
Yamisleydi Salgueiro
Keyword(s):  
Flow Model ◽  
Extreme Values ◽  
Internal Diameter ◽  
Algebraic Equations ◽  
Flow Models ◽  
Numerical Resolution ◽  
Air Pocket ◽  
Water Pipelines ◽  
Thermodynamic Variables ◽  
Static Flow

Inertial models have been used by researchers to simulate the draining and filling processes in water pipelines, based on the evolution of the main hydraulic and thermodynamic variables. These models use complex differential equations, which are solved using advanced numerical codes. In this study, a quasi-static flow model is developed to study these operations in hydraulic installations. The quasi-static flow model represents a simplified formulation compared with inertial flow models, in which its numerical resolution is easier because only algebraic equations must be addressed. Experimental measurements of air pocket pressure patterns were conducted in a 4.36 m long single pipeline with an internal diameter of 42 mm. Comparisons between measured and computed air pocket pressure oscillations indicate how the quasi-static flow model can predict extreme values of air pocket pressure for experimental runs, demonstrating the possibility of selecting stiffness and pipe classes in actual pipelines using this model. Two case studies were analysed to determine the behaviour of the quasi-static flow model in large water pipelines.

Mathematical modelling of salt purification by recrystallization. A cross-current flow model and its comparison with the countercurrent arrangement

1986 ◽  
Vol 51 (11) ◽  
pp. 2489-2501
Author(s):  
Benitto Mayrhofer ◽  
Jana Mayrhoferová ◽  
Lubomír Neužil ◽  
Jaroslav Nývlt
Keyword(s):  
Flow Model ◽  
Current Flow ◽  
Countercurrent Flow ◽  
Flow Models ◽  
Multi Stage ◽  
Stage Crystallization ◽  
The Cross ◽  
Current Flows ◽  
Set Up ◽  
Cross Current

A model is derived for a multi-stage crystallization with cross-current flows of the solution and the crystals being purified. The purity of the product is compared with that achieved in the countercurrent arrangement. A suitable function has been set up which allows the cross-current and countercurrent flow models to be compared and reduces substantially the labour of computation for the countercurrent arrangement. Using the recrystallization of KAl(SO4)2.12 H2O as an example, it is shown that, when the cross-current and countercurrent processes are operated at the same output, the countercurrent arrangement is more advantageous because its solvent consumption is lower.

Study of the Response of PW Traffic Flow Model to a Bottleneck on a Circular Road and its Suitability for Heterogeneous Traffic Conditions

2021 ◽  
Vol 9 (4) ◽  
pp. 460-463
Keyword(s):  
Fluid Flow ◽  
Traffic Flow ◽  
Flow Model ◽  
Equation Model ◽  
Heterogeneous Traffic ◽  
Flow Conditions ◽  
Flow Models ◽  
Traffic Conditions ◽  
Model Response ◽  
Traffic Flow Models

The traffic flow conditions in developing countries are predominantly heterogeneous. The early developed traffic flow models have been derived from fluid flow to capture the behavior of the traffic. The very first two-equation model derived from fluid flow is known as the Payne-Whitham or PW Model. Along with the traffic flow, this model also captures the traffic acceleration. However, the PW model adopts a constant driver behavior which cannot be ignored, especially in the situation of heterogeneous traffic.This research focuses on testing the PW model and its suitability for heterogeneous traffic conditions by observing the model response to a bottleneck on a circular road. The PW model is mathematically approximated using the Roe Decomposition and then the performance of the model is observed using simulations.

scholarly journals A system of conservative regridding for ice/atmosphere coupling in a GCM

2013 ◽  
Vol 6 (4) ◽  
pp. 6493-6568 ◽  
Author(s):  
R. Fischer ◽  
S. Nowicki ◽  
M. Kelley ◽  
G. A. Schmidt
Keyword(s):  
Finite Element ◽  
General Circulation ◽  
Flow Model ◽  
Source Code ◽  
Circulation Model ◽  
Surface Mass Balance ◽  
Ice Flow ◽  
Surface Mass ◽  
Flow Models ◽  
Ice Model

Abstract. The method of elevation classes has proven to be a useful way for a low-resolution general circulation model (GCM) to produce high-resolution downscaled surface mass balance fields, for use in one-way studies coupling GCMs and ice flow models. Past uses of elevation classes have been a cause of non-conservation of mass and energy, caused by inconsistency in regridding schemes chosen to regrid to the atmosphere vs. downscaling to the ice model. This causes problems for two-way coupling. A strategy that resolves this conservation issue has been designed and is presented here. The approach identifies three grids between which data must be regridded, and five transformations between those grids required by a typical coupled GCM–ice flow model. This paper shows how each of those transformations may be achieved in a consistent, conservative manner. These transformations are implemented in GLINT2, a library used to couple GCMs with ice models. Source code and documentation are available for download. Confounding real-world issues are discussed, including the use of projections for ice modeling, how to handle dynamically changing ice geometry, and modifications required for finite element ice models.

Second Order Slip Flow Effects on Heat Transfer Performance of Microchannels

2009 ◽  
Author(s):  
Cem Dolu ◽  
Lu¨tfullah Kuddusi
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Performance ◽  
Flow Model ◽  
Slip Flow ◽  
Second Order ◽  
Flow Models ◽  
Uniform Wall Temperature ◽  
Uniform Wall ◽  
Slip Flow Regime ◽  
Flow Effects

First and second order slip flow models in rectangular microchannels heated at constant and uniform wall temperature are studied. The velocity and temperature profiles for hydrodynamically and thermally developed incompressible slip flow regime available in literature are used. The average nondimensional slip velocity and temperature jump are found by using first and second order slip flow models. The average Nusselt number is also derived by using both first and second order slip flow models. The effects of Knudsen number, aspect ratio and second order slip flow model on the heat transfer characteristics of microchannel are explored.

Gas Temperature Profile Attenuation Through a Multistage Axial-Flow Turbine

2009 ◽  
Author(s):  
Boris I. Mamaev ◽  
Mikhail M. Petukhovskiy
Keyword(s):  
Temperature Profile ◽  
Attenuation Coefficient ◽  
Flow Model ◽  
Axial Flow ◽  
Gas Temperature ◽  
Empirical Coefficient ◽  
Flow Models ◽  
Flow Parameters ◽  
Through Flow ◽  
Full Scale Tests

Nowadays 2D through-flow models are widespread for designing and analysis of a turbine. Unlike 2D calculations, the measurements show that a non-uniform inlet gas temperature profile is strongly attenuated to the outlet of a turbine. This attenuation can be taken into account in through-flow models only using some corrective coefficients. The objective of this work was to find such an empirical coefficient. The results of full-scale tests of several power GTUs and aviation GTEs were employed to obtain values of the temperature profile attenuation coefficient in the through-flow model for various span locations of airfoil rows. During the tests detailed radial-circumferential distributions of the gas temperature upstream of each of rows and downstream of the turbines were measured (in absolute motion for stator and in relative motion for rotor). The values of the attenuation coefficient for airfoil rows of the three front stages were obtained by means comparison of experimental and computed results. The experience shows that the attenuation coefficient is easily incorporated into the 2D gas-dynamic codes. This incorporation allows spanwise distributions of flow parameters to be predicted and the airfoil geometry and cooling mass flow to be chosen more correctly.

scholarly journals The role of mesoscale eddies time and length scales on phytoplankton production

2010 ◽  
Vol 17 (2) ◽  
pp. 177-186 ◽  
Author(s):  
V. Pérez-Muñuzuri ◽  
F. Huhn
Keyword(s):  
Flow Model ◽  
North Atlantic Ocean ◽  
Coupled Model ◽  
Optimal Time ◽  
Phytoplankton Production ◽  
Correlated Noise ◽  
Length Scales ◽  
Flow Models ◽  
The North ◽  
Qualitative Interaction

Abstract. Horizontal mixing has been found to play a crucial role in the development of spatial plankton structures in the ocean. We study the influence of time and length scales of two different horizontal two-dimensional (2-D) flows on the growth of a single phytoplankton patch. To that end, we use a coupled model consisting of a standard three component ecological NPZ model and a flow model able to mimic the mesoscale structures observed in the ocean. Two hydrodynamic flow models are used: a flow based on Gaussian correlated noise, for which the Eulerian length and time scales can be easily controlled, and a multiscale velocity field derived from altimetry data in the North Atlantic ocean. We find the optimal time and length scales for the Gaussian flow model favouring the plankton spread. These results are used for an analysis of a more realistic altimetry flow. We discuss the findings in terms of the time scale of the NPZ model, the qualitative interaction of the flow with the reaction front and a Finite-Time Lyapunov Exponent analysis.

scholarly journals Effect of a Commercial Air Valve on the Rapid Filling of a Single Pipeline: a Numerical and Experimental Analysis

Water ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1814 ◽  
Author(s):  
Óscar E. Coronado-Hernández ◽  
Mohsen Besharat ◽  
Vicente S. Fuertes-Miquel ◽  
Helena M. Ramos
Keyword(s):  
Mathematical Model ◽  
Air Water Interface ◽  
Water Pipelines ◽  
Polytropic Equation ◽  
Pipeline Failure ◽  
Air Valve ◽  
Thermodynamic Variables ◽  
Air Pockets ◽  
The Mathematical Model ◽  
Oscillation Equation

The filling process in water pipelines produces pressure surges caused by the compression of air pockets. In this sense, air valves should be appropriately designed to expel sufficient air to avoid pipeline failure. Recent studies concerning filling maneuvers have been addressed without considering the behavior of air valves. This work shows a mathematical model developed by the authors which is capable of simulating the main hydraulic and thermodynamic variables during filling operations under the effect of the air valve in a single pipeline, which is based on the mass oscillation equation, the air–water interface, the polytropic equation of the air phase, the air mass equation, and the air valve characterization. The mathematical model is validated in a 7.3-m-long pipeline with a 63-mm nominal diameter. A commercial air valve is positioned in the highest point of the hydraulic installation. Measurements indicate that the mathematical model can be used to simulate this phenomenon by providing good accuracy.

The Application of Equivalent Flow Model in Groundwater Resources Loss Estimate of Fractured Rock Tunnel

2011 ◽  
Vol 368-373 ◽  
pp. 1249-1252
Author(s):  
Zhi Chun Liu ◽  
Qian Yang ◽  
Ming Lei Sun
Keyword(s):  
Sustainable Development ◽  
Development Strategy ◽  
Flow Model ◽  
Fractured Rock ◽  
Groundwater Resources ◽  
Environmental Problems ◽  
Flow Models ◽  
Model Fidelity ◽  
Rock Tunnel ◽  
Loss Estimate

This With the deepening of sustainable development strategy, groundwater environmental problems caused by tunnel projects are becoming more and more outstanding. This paper estimate the groundwater resources loss of fractured rock tunnel adopting equivalent flow models. In order to increase the model fidelity, the author considers the nonhomogeneous and anisotropic characteristics of fractured rock. Based on Shibanshan tunnel in Shijiazhuang-Taiyuan passenger line, this paper estimated the groundwater resources loss of fractured rock tunnel in construction stage and operation stage, which provides technical support for decreasing loss of groundwater resources.

Nozzle Flow Model of High Pressure Variable-Rate Spraying Based on PWM Technology

2011 ◽  
Vol 422 ◽  
pp. 208-217 ◽  
Author(s):  
Chang Yuan Zhai ◽  
Xiu Wang ◽  
Da Yin Liu ◽  
Wei Ma ◽  
Yi Jin Mao
Keyword(s):  
High Pressure ◽  
Flow Model ◽  
Hypothesis Test ◽  
Test System ◽  
Nozzle Flow ◽  
Maximum Relative Error ◽  
Variable Rate ◽  
Flow Models ◽  
Pressure Variable ◽  
Variable Rate Spraying

Nozzle flow model for high pressure variable-rate spraying is indispensable when orchard sprayer is controlling liquid flow based on Pulse Width Modulation (PWM) technology. Three flow models for Teejet AITXA 8002, 8003 and 8004 nozzles are obtained by using nozzle flow model test system which is established in this paper. The results from equation hypothesis test and test for lack of fit of flow model shows that those three flow models work well. Nozzle flow model validation trials show that the relative errors of model flow and actual flow are small, while the maximum relative error is 6.50%; the flows characteristics of different nozzles with the same type are almost the same.

scholarly journals Global optimization for the multilevel European gas market system with nonlinear flow models on trees

2022 ◽  
Author(s):  
Lars Schewe ◽  
Martin Schmidt ◽  
Johannes Thürauf
Keyword(s):  
Real World ◽  
Flow Model ◽  
Solution Process ◽  
Nonlinear Flow ◽  
Mixed Integer ◽  
Global Optimality ◽  
Convex Constraints ◽  
Gas Network ◽  
Flow Models ◽  
Gas Market

AbstractThe European gas market is implemented as an entry-exit system, which aims to decouple transport and trading of gas. It has been modeled in the literature as a multilevel problem, which contains a nonlinear flow model of gas physics. Besides the multilevel structure and the nonlinear flow model, the computation of so-called technical capacities is another major challenge. These lead to nonlinear adjustable robust constraints that are computationally intractable in general. We provide techniques to equivalently reformulate these nonlinear adjustable constraints as finitely many convex constraints including integer variables in the case that the underlying network is tree-shaped. We further derive additional combinatorial constraints that significantly speed up the solution process. Using our results, we can recast the multilevel model as a single-level nonconvex mixed-integer nonlinear problem, which we then solve on a real-world network, namely the Greek gas network, to global optimality. Overall, this is the first time that the considered multilevel entry-exit system can be solved for a real-world sized network and a nonlinear flow model.

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