Analysis of Sub-Atmospheric Pressures during Emptying of an Irregular Pipeline without an Air Valve Using a 2D CFD Model

Studying sub-atmospheric pressure patterns in emptying pipeline systems is crucial because these processes could cause collapses depending on the installation conditions (the underground pipe covering height, type, fill, and pipeline stiffness class). Pipeline studies have focused more on filling than on emptying processes. This study presents an analysis of the following variables: air pocket pressure, water velocity, and water column length during the emptying of an irregular pipeline without an air valve by two-dimensional computational fluid dynamics (2D CFD) model simulation using the software OpenFOAM. The mathematical model predicts the experimental values of the study variables. Water velocity vectors are also analysed within the experimental facility, assessing the sensitivity of the drain valve to different openings and changes in water column length during the hydraulic phenomenon.

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Assessment of Steady and Unsteady Friction Models in the Draining Processes of Hydraulic Installations

Water ◽

10.3390/w13141888 ◽

2021 ◽

Vol 13 (14) ◽

pp. 1888

Author(s):

Óscar E. Coronado-Hernández ◽

Ivan Derpich ◽

Vicente S. Fuertes-Miquel ◽

Jairo R. Coronado-Hernández ◽

Gustavo Gatica

Keyword(s):

Mathematical Model ◽

Turbulent Flow ◽

Water Velocity ◽

Experimental Facility ◽

Governing Equations ◽

Pressure Oscillations ◽

Air Pocket ◽

Friction Models ◽

The Mathematical Model

The study of draining processes without admitting air has been conducted using only steady friction formulations in the implementation of governing equations. However, this hydraulic event involves transitions from laminar to turbulent flow, and vice versa, because of the changes in water velocity. In this sense, this research improves the current mathematical model considering unsteady friction models. An experimental facility composed by a 4.36 m long methacrylate pipe was configured, and measurements of air pocket pressure oscillations were recorded. The mathematical model was performed using steady and unsteady friction models. Comparisons between measured and computed air pocket pressure patterns indicated that unsteady friction models slightly improve the results compared to steady friction models.

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Pressure oscillation of an air pocket beneath a water column in a vertical riser

Water Science & Technology ◽

10.2166/wst.2020.560 ◽

2020 ◽

Author(s):

Yu Qian ◽

David Z. Zhu

Keyword(s):

Water Column ◽

Film Flow ◽

Pressure Oscillation ◽

Pressure Head ◽

Oscillation Period ◽

Column Length ◽

Filling Process ◽

Initial Water ◽

Air Pocket ◽

Significant Attention

Abstract Storm geysers have received significant attention lately due to its more frequent occurrences and the induced severe local flooding and infrastructure damages. Previous studies suggested that the air pocket pressure oscillated during geyser events especially in rapid filling process, but only the peak values were studied and the oscillation period was not discussed in detail. In this paper, a theoretical model was developed focusing on the period of the pressure oscillation induced by the expansion/compression of the air pocket below a water column in a vertical riser with film flow. It was found that the oscillation period was a function of the initial air pocket volume, initial air pocket pressure head, the riser diameter, and the initial water column length. The oscillation period increased with the air pocket pressure head and the air pocket volume, but decreased with the riser diameter and the polytropic coefficient. The oscillation period increased then decreased with an increasing water column length. Further, when considering the film flow along the riser, the oscillation period decreased slightly from the analytical solution. It was also found that the inflow rate change did not significantly influence the oscillation period.

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Numerical modelling of pipelines with air pockets and air valves

Canadian Journal of Civil Engineering ◽

10.1139/cjce-2016-0209 ◽

2016 ◽

Vol 43 (12) ◽

pp. 1052-1061 ◽

Cited By ~ 10

Author(s):

Vicente S. Fuertes-Miquel ◽

P. Amparo López-Jiménez ◽

F. Javier Martínez-Solano ◽

Gonzalo López-Patiño

Keyword(s):

Numerical Modelling ◽

Water Column ◽

Water Hammer ◽

Extreme Conditions ◽

Residual Velocity ◽

Air Pocket ◽

Air Valve ◽

Air Pockets

This work considers the behaviour of air inside pipes when the air is expelled through air valves. Generally, the air shows isothermal behaviour. Nevertheless, when the transient is very fast, it shows adiabatic behaviour. In a real installation, an intermediate evolution between these two extreme conditions occurs. Thus, it is verified that the results vary significantly depending on the hypothesis adopted. To determine the pressure of the air pocket, the most unfavourable hypothesis (isothermal behaviour) is typically adopted. Nevertheless, from the perspective of the water hammer that takes place when the water column arrives at the air valve and abruptly closes, the most unfavourable hypothesis is the opposite (adiabatic behaviour). In this case, the residual velocity with which the water arrives at the air valve is higher, and, consequently, the water hammer generated is greater.

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Modelling and Simulation of NO2 Dispersion Phenomenon in Atmosphere by Analytical-Experimental Methods

Revista de Chimie ◽

10.37358/rc.08.10.1979 ◽

2008 ◽

Vol 59 (10) ◽

Author(s):

Delia Perju ◽

Harieta Pirlea ◽

Gabriela-Alina Brusturean ◽

Dana Silaghi-Perju ◽

Sorin Marinescu

Keyword(s):

Mathematical Model ◽

Nitrogen Dioxide ◽

Modeling And Simulation ◽

Human Health ◽

Experimental Methods ◽

Negative Effects ◽

Real Situation ◽

Experimental Values ◽

The Mathematical Model

The European laws and recently the Romanian ones impose more and more strict norms to the large nitrogen dioxide polluters. They are obligated to continuously improve the installations and products so that they limit and reduce the nitrogen dioxide pollution, because it has negative effects on the human health and environment. In this paper are presented these researches made within a case study for the Timi�oara municipality, regarding the modeling and simulation of the nitrogen dioxide dispersion phenomenon coming from various sources in atmosphere with the help of analytical-experimental methods. The mathematical model resulting from these researches is accurately enough to describe the real situation. This was confirmed by comparing the results obtained based on the model with real experimental values.

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Implications of sea-ice biogeochemistry for oceanic production and emissions of dimethyl sulfide in the Arctic

Biogeosciences ◽

10.5194/bg-14-3129-2017 ◽

2017 ◽

Vol 14 (12) ◽

pp. 3129-3155 ◽

Cited By ~ 17

Author(s):

Hakase Hayashida ◽

Nadja Steiner ◽

Adam Monahan ◽

Virginie Galindo ◽

Martine Lizotte ◽

...

Keyword(s):

Sea Ice ◽

Water Column ◽

Dimethyl Sulfide ◽

Phytoplankton Bloom ◽

Model Simulation ◽

Field Measurements ◽

Sulfur Cycle ◽

The Arctic ◽

Model Parameters ◽

Ocean Ecosystem

Abstract. Sea ice represents an additional oceanic source of the climatically active gas dimethyl sulfide (DMS) for the Arctic atmosphere. To what extent this source contributes to the dynamics of summertime Arctic clouds is, however, not known due to scarcity of field measurements. In this study, we developed a coupled sea ice–ocean ecosystem–sulfur cycle model to investigate the potential impact of bottom-ice DMS and its precursor dimethylsulfoniopropionate (DMSP) on the oceanic production and emissions of DMS in the Arctic. The results of the 1-D model simulation were compared with field data collected during May and June of 2010 in Resolute Passage. Our results reproduced the accumulation of DMS and DMSP in the bottom ice during the development of an ice algal bloom. The release of these sulfur species took place predominantly during the earlier phase of the melt period, resulting in an increase of DMS and DMSP in the underlying water column prior to the onset of an under-ice phytoplankton bloom. Production and removal rates of processes considered in the model are analyzed to identify the processes dominating the budgets of DMS and DMSP both in the bottom ice and the underlying water column. When openings in the ice were taken into account, the simulated sea–air DMS flux during the melt period was dominated by episodic spikes of up to 8.1 µmol m−2 d−1. Further model simulations were conducted to assess the effects of the incorporation of sea-ice biogeochemistry on DMS production and emissions, as well as the sensitivity of our results to changes of uncertain model parameters of the sea-ice sulfur cycle. The results highlight the importance of taking into account both the sea-ice sulfur cycle and ecosystem in the flux estimates of oceanic DMS near the ice margins and identify key uncertainties in processes and rates that should be better constrained by new observations.

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Microhabitat use by Phalloceros harpagos Lucinda (Cyprinodontiformes: Poeciliidae) from a coastal stream from Southeast Brazil

Neotropical Ichthyology ◽

10.1590/s1679-62252011005000027 ◽

2011 ◽

Vol 9 (3) ◽

pp. 665-672 ◽

Cited By ~ 8

Author(s):

Rosana Mazzoni ◽

Vitor Considera Novaes ◽

Ricardo Iglesias-Rios

Keyword(s):

Water Column ◽

Water Velocity ◽

Microhabitat Use ◽

Mato Grosso ◽

River Bank ◽

Underwater Observation ◽

Electivity Index ◽

Southeast Brazil ◽

Stream Bank ◽

Vegetal Cover

The size-related microhabitat use of Phalloceros harpagos Lucinda, 2008 from Mato Grosso stream (Saquarema - RJ) was examined. We analyzed, during 8.3 h of underwater observation, a 200 m long reach in the upper Mato Grosso stream, quantifying the following microhabitat descriptors: (i) distance from the stream bank, (ii) water column depth, (iii) occurrence on riffle, pool or run mesohabitat, (iv) water velocity, (v) substratum, and (vi) subaquatic vegetal cover. Microhabitat selectivity was analyzed by comparing the microhabitat used by fish and the microhabitat available in the study site. Complementary analyses, based in the Ivlev Electivity Index were applied in order to test selectivity for the microhabitat use. We did not found differences in the microhabitat used by juvenile and adult individuals. Phalloceros harpagos was selective for five among the six analyzed microhabitat descriptors. The occurrence of Phalloceros in the studied stream was limited to shallow pools, close to the river bank, with low water velocities and mud substratum. Vegetal cover was not an important factor in the occurrence of the studied species.

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Journal Bearing: An Integrated CFD-Analytical Approach for the Estimation of the Trajectory and Equilibrium Position

Applied Sciences ◽

10.3390/app10238573 ◽

2020 ◽

Vol 10 (23) ◽

pp. 8573

Author(s):

Franco Concli

Keyword(s):

Fluid Dynamics ◽

Computational Fluid Dynamics ◽

Pressure Distribution ◽

Equilibrium Position ◽

Analytical Approach ◽

Journal Bearing ◽

Cfd Model ◽

Cavitation Model ◽

Computational Fluid Dynamics Cfd ◽

The Mathematical Model

For decades, journal bearings have been designed based on the half-Sommerfeld equations. The semi-analytical solution of the conservation equations for mass and momentum leads to the pressure distribution along the journal. However, this approach admits negative values for the pressure, phenomenon without experimental evidence. To overcome this, negative values of the pressure are artificially substituted with the vaporization pressure. This hypothesis leads to reasonable results, even if for a deeper understanding of the physics behind the lubrication and the supporting effects, cavitation should be considered and included in the mathematical model. In a previous paper, the author has already shown the capability of computational fluid dynamics to accurately reproduce the experimental evidences including the Kunz cavitation model in the calculations. The computational fluid dynamics (CFD) results were compared in terms of pressure distribution with experimental data coming from different configurations. The CFD model was coupled with an analytical approach in order to calculate the equilibrium position and the trajectory of the journal. Specifically, the approach was used to study a bearing that was designed to operate within tight tolerances and speeds up to almost 30,000 rpm for operation in a gearbox.

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An enhanced composting process with bioaugmentation: Mathematical modelling and process optimization

Waste Management & Research ◽

10.1177/0734242x211033712 ◽

2021 ◽

pp. 0734242X2110337

Author(s):

Tea Sokač ◽

Anita Šalić ◽

Dajana Kučić Grgić ◽

Monika Šabić Runjavec ◽

Marijana Vidaković ◽

...

Keyword(s):

Mathematical Model ◽

Model Simulation ◽

Process Conditions ◽

Air Flow Rate ◽

Optimal Process ◽

Composting Process ◽

Different Types ◽

Adiabatic Reactor ◽

The Mathematical Model ◽

Good Agreement

In this paper, two different types of biowaste composting processes were carried out – composting without and with bioaugmentation. All experiments were performed in an adiabatic reactor for 14 days. Composting enhanced with bioaugmentation was the better choice because the thermophilic phase was achieved earlier, making the composting time shorter. Additionally, a higher conversion of substrate (amount of substrate consumed) was also noticed in the process enhanced by bioaugmentation. A mathematical model was developed and process parameters were estimated in order to optimize the composting process. Based on good agreement between experimental data and the mathematical model simulation results, a three-level-four-factor Box-Behnken experimental design was employed to define the optimal process conditions for further studies. It was found that the air flow rate and the mass fraction of the substrate have the most significant effect on the composting process. An improvement of the composting process was achieved after altering the mentioned variables, resulting in shorter composting time and higher conversion of the substrate.

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Study on the Mathematical Model of Vacuum Breaker Valve for Large Air Mass Conditions

Water ◽

10.3390/w11071358 ◽

2019 ◽

Vol 11 (7) ◽

pp. 1358

Author(s):

Zhang ◽

Fan ◽

Yu ◽

Zhang ◽

Lv ◽

...

Keyword(s):

Mathematical Model ◽

Theoretical Basis ◽

Isothermal Process ◽

Air Mass ◽

Protection Scheme ◽

Calculation Results ◽

Air Valve ◽

The Mathematical Model ◽

Valve Model ◽

Derivation Process

The mathematical model of vacuum breaker valve is significant to the protection scheme. The more accurate the vacuum breaker valve model, the more reliable the calculation results. In this study, the application conditions of the air valve model are analyzed according to the assumptions used in the derivation, and the contradictions between these assumptions are proposed. Then, according to the different working characteristics between the vacuum breaker valve on the siphon outlet pipe and the air valve, the vacuum breaker valve model is deduced based on the modified assumptions. In the derivation process, the thermodynamic change of the gas in the vacuum breaker valve is assumed to follow the isentropic process rather than an isothermal process, and the water level in the vacuum breaker valve is considered to be changeable. An engineering case is introduced, and the results calculated according to the vacuum breaker valve model are compared with those resulting from the air valve model. The results indicate that the vacuum breaker valve model is suitable for large air mass conditions and can provide a theoretical basis for the numerical simulation and settings of vacuum breaker valves.

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Mathematical Model of the Piped Vehicle Motion in Piped Hydraulic Transportation of Tube-Contained Raw Material

Mathematical Problems in Engineering ◽

10.1155/2019/3930691 ◽

2019 ◽

Vol 2019 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Yongye Li ◽

Xihuan Sun

Keyword(s):

Mathematical Model ◽

Transportation Cost ◽

Raw Material ◽

Maximum Relative Error ◽

Transportation Energy ◽

Core Components ◽

Vehicle Motion ◽

Motion Characteristics ◽

Experimental Values ◽

The Mathematical Model

The piped hydraulic transportation of tube-contained raw material is an emerging technique for transporting materials. In this technique, the piped vehicle is one of the core components, and its motion characteristics directly determine the transportation energy consumption and the transportation cost of this technique. To study the motion characteristics of the piped vehicle, the force of the piped vehicle was analyzed from the mechanical perspective in this paper. On the assumption that the piped vehicle moved steadily and it had sufficient stiffness, the mathematical model of the piped vehicle motion was established in the turbulent flow according to the stress characteristics of the piped vehicle and the factors influencing its motion characteristics, and then the mathematical model was tested by experiments. The findings show that the calculated values of the velocities of the piped vehicle were identical to the experimental values with changes in various influencing factors. When the flow discharge, the diameter or length of the piped vehicle increased, or the mass of transported material decreased, the velocity of the piped vehicle increased. The maximum relative error did not exceed 9.47%, which proved that the mathematical model of the piped vehicle motion was rational. The results can provide theoretical basis to improve the structure of the piped vehicle and the piped hydraulic transportation technique of tube-contained raw material.

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