Search results for: fluid
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2176

Search results for: fluid

1216 Multi-Scale Modelling of the Cerebral Lymphatic System and Its Failure

Authors: Alexandra K. Diem, Giles Richardson, Roxana O. Carare, Neil W. Bressloff

Abstract:

Alzheimer's disease (AD) is the most common form of dementia and although it has been researched for over 100 years, there is still no cure or preventive medication. Its onset and progression is closely related to the accumulation of the neuronal metabolite Aβ. This raises the question of how metabolites and waste products are eliminated from the brain as the brain does not have a traditional lymphatic system. In recent years the rapid uptake of Aβ into cerebral artery walls and its clearance along those arteries towards the lymph nodes in the neck has been suggested and confirmed in mice studies, which has led to the hypothesis that interstitial fluid (ISF), in the basement membranes in the walls of cerebral arteries, provides the pathways for the lymphatic drainage of Aβ. This mechanism, however, requires a net reverse flow of ISF inside the blood vessel wall compared to the blood flow and the driving forces for such a mechanism remain unknown. While possible driving mechanisms have been studied using mathematical models in the past, a mechanism for net reverse flow has not been discovered yet. Here, we aim to address the question of the driving force of this reverse lymphatic drainage of Aβ (also called perivascular drainage) by using multi-scale numerical and analytical modelling. The numerical simulation software COMSOL Multiphysics 4.4 is used to develop a fluid-structure interaction model of a cerebral artery, which models blood flow and displacements in the artery wall due to blood pressure changes. An analytical model of a layer of basement membrane inside the wall governs the flow of ISF and, therefore, solute drainage based on the pressure changes and wall displacements obtained from the cerebral artery model. The findings suggest that an active role in facilitating a reverse flow is played by the components of the basement membrane and that stiffening of the artery wall during age is a major risk factor for the impairment of brain lymphatics. Additionally, our model supports the hypothesis of a close association between cerebrovascular diseases and the failure of perivascular drainage.

Keywords: Alzheimer's disease, artery wall mechanics, cerebral blood flow, cerebral lymphatics

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1215 Evaluation of Biological and Confinement Properties of a Bone Substitute to in Situ Preparation Based on Demineralized Bone Matrix for Bone Tissue Regeneration

Authors: Aura Maria Lopera Echavarria, Angela Maria Lema Perez, Daniela Medrano David, Pedronel Araque Marin, Marta Elena Londoño Lopez

Abstract:

Bone regeneration is the process by which the formation of new bone is stimulated. Bone fractures can originate at any time due to trauma, infections, tumors, congenital malformations or skeletal diseases. Currently there are different strategies to treat bone defects that in some cases, regeneration does not occur on its own. That is why they are treated with bone substitutes, which provide a necessary environment for the cells to synthesize new bone. The Demineralized Bone Matrix (DBM) is widely used as a bone implant due to its good properties, such as osteoinduction and bioactivity. However, the use of DBM is limited, because its presentation is powder, which is difficult to implant with precision and is susceptible to migrating to other sites through blood flow. That is why the DBM is commonly incorporated into a variety of vehicles or carriers. The objective of this project is to evaluate the bioactive and confinement properties of a bone substitute based on demineralized bone matrix (DBM). Also, structural and morphological properties were evaluated. Bone substitute was obtained from EIA Biomaterials Laboratory of EIA University and the DBM was facilitated by Tissue Bank Foundation. Morphological and structural properties were evaluated by scanning electron microscopy (SEM), X-ray diffraction (DRX) and Fourier transform infrared spectroscopy with total attenuated reflection (FTIR-ATR). Water absorption capacity and degradation were also evaluated during three months. The cytotoxicity was evaluated by the MTT test. The bioactivity of the bone substitute was evaluated through immersion of the samples in simulated body fluid during four weeks. Confinement tests were performed on tibial fragments of a human donor with bone defects of determined size, to ensure that the substitute remains in the defect despite the continuous flow of fluid. According of the knowledge of the authors, the methodology for evaluating samples in a confined environment has not been evaluated before in real human bones. The morphology of the samples showed irregular surface and presented some porosity. DRX confirmed a semi-crystalline structure. The FTIR-ATR determined the organic and inorganic phase of the sample. The degradation and absorption measurements stablished a loss of 3% and 150% in one month respectively. The MTT showed that the system is not cytotoxic. Apatite clusters formed from the first week were visualized by SEM and confirmed by EDS. These calcium phosphates are necessary to stimulate bone regeneration and thanks to the porosity of the developed material, osteinduction and osteoconduction are possible. The results of the in vitro evaluation of the confinement of the material showed that the migration of the bone filling to other sites is negligible, although the samples were subjected to the passage of simulated body fluid. The bone substitute, putty type, showed stability, is bioactive, non-cytotoxic and has handling properties for specialists at the time of implantation. The obtained system allows to maintain the osteoinductive properties of DBM and it can fill completely fractures in any way; however, it does not provide a structural support, that is, it should only be used to treat fractures without requiring a mechanical load.

Keywords: bone regeneration, cytotoxicity, demineralized bone matrix, hydrogel

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1214 RANS Simulation of the LNG Ship Squat in Shallow Water

Authors: Mehdi Nakisa, Adi Maimun, Yasser M. Ahmed, Fatemeh Behrouzi

Abstract:

Squat is the reduction in under-keel clearance between a vessel at-rest and underway due to the increased flow of water past the moving body. The forward motion of the ship induces a relative velocity between the ship and the surrounding water that causes a water level depression in which the ship sinks. The problem of ship squat is one among the crucial factors affecting the navigation of ships in restricted waters. This article investigates the LNG ship squat, its effects on flow streamlines around the ship hull and ship behavior and motion using computational fluid dynamics which is applied by Ansys-Fluent.

Keywords: ship squat, CFD, confined, mechanic

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1213 Innovative Design of Spherical Robot with Hydraulic Actuator

Authors: Roya Khajepour, Alireza B. Novinzadeh

Abstract:

In this paper, the spherical robot is modeled using the Band-Graph approach. This breed of robots is typically employed in expedition missions to unknown territories. Its motion mechanism is based on convection of a fluid in a set of three donut vessels, arranged orthogonally in space. This robot is a non-linear, non-holonomic system. This paper utilizes the Band-Graph technique to derive the torque generation mechanism in a spherical robot. Eventually, this paper describes the motion of a sphere due to the exerted torque components.

Keywords: spherical robot, Band-Graph, modeling, torque

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1212 3D CFD Modelling of the Airflow and Heat Transfer in Cold Room Filled with Dates

Authors: Zina Ghiloufi, Tahar Khir

Abstract:

A transient three-dimensional computational fluid dynamics (CFD) model is developed to determine the velocity and temperature distribution in different positions cold room during pre-cooling of dates. The turbulence model used is the k-ω Shear Stress Transport (SST) with the standard wall function, the air. The numerical results obtained show that cooling rate is not uniform inside the room; the product at the medium of room has a slower cooling rate. This cooling heterogeneity has a large effect on the energy consumption during cold storage.

Keywords: CFD, cold room, cooling rate, dDates, numerical simulation, k-ω (SST)

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1211 Study of Unsteady Behaviour of Dynamic Shock Systems in Supersonic Engine Intakes

Authors: Siddharth Ahuja, T. M. Muruganandam

Abstract:

An analytical investigation is performed to study the unsteady response of a one-dimensional, non-linear dynamic shock system to external downstream pressure perturbations in a supersonic flow in a varying area duct. For a given pressure ratio across a wind tunnel, the normal shock's location can be computed as per one-dimensional steady gas dynamics. Similarly, for some other pressure ratio, the location of the normal shock will change accordingly, again computed using one-dimensional gas dynamics. This investigation focuses on the small-time interval between the first steady shock location and the new steady shock location (corresponding to different pressure ratios). In essence, this study aims to shed light on the motion of the shock from one steady location to another steady location. Further, this study aims to create the foundation of the Unsteady Gas Dynamics field enabling further insight in future research work. According to the new pressure ratio, a pressure pulse, generated at the exit of the tunnel which travels and perturbs the shock from its original position, setting it into motion. During such activity, other numerous physical phenomena also happen at the same time. However, three broad phenomena have been focused on, in this study - Traversal of a Wave, Fluid Element Interactions and Wave Interactions. The above mentioned three phenomena create, alter and kill numerous waves for different conditions. The waves which are created by the above-mentioned phenomena eventually interact with the shock and set it into motion. Numerous such interactions with the shock will slowly make it settle into its final position owing to the new pressure ratio across the duct, as estimated by one-dimensional gas dynamics. This analysis will be extremely helpful in the prediction of inlet 'unstart' of the flow in a supersonic engine intake and its prominence with the incoming flow Mach number, incoming flow pressure and the external perturbation pressure is also studied to help design more efficient supersonic intakes for engines like ramjets and scramjets.

Keywords: analytical investigation, compression and expansion waves, fluid element interactions, shock trajectory, supersonic flow, unsteady gas dynamics, varying area duct, wave interactions

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1210 A Low-Cost Disposable PDMS Microfluidic Cartridge with Reagent Storage Silicone Blisters for Isothermal DNA Amplification

Authors: L. Ereku, R. E. Mackay, A. Naveenathayalan, K. Ajayi, W. Balachandran

Abstract:

Over the past decade the increase of sexually transmitted infections (STIs) especially in the developing world due to high cost and lack of sufficient medical testing have given rise to the need for a rapid, low cost point of care medical diagnostic that is disposable and most significantly reproduces equivocal results achieved within centralised laboratories. This paper present the development of a disposable PDMS microfluidic cartridge incorporating blisters filled with reagents required for isothermal DNA amplification in clinical diagnostics and point-of-care testing. In view of circumventing the necessity for external complex microfluidic pumps, designing on-chip pressurised fluid reservoirs is embraced using finger actuation and blister storage. The fabrication of the blisters takes into consideration three proponents that include: material characteristics, fluid volume and structural design. Silicone rubber is the chosen material due to its good chemical stability, considerable tear resistance and moderate tension/compression strength. The case of fluid capacity and structural form go hand in hand as the reagent need for the experimental analysis determines the volume size of the blisters, whereas the structural form has to be designed to provide low compression stress when deformed for fluid expulsion. Furthermore, the top and bottom section of the blisters are embedded with miniature polar opposite magnets at a defined parallel distance. These magnets are needed to lock or restrain the blisters when fully compressed so as to prevent unneeded backflow as a result of elasticity. The integrated chip is bonded onto a large microscope glass slide (50mm x 75mm). Each part is manufactured using a 3D printed mould designed using Solidworks software. Die-casting is employed, using 3D printed moulds, to form the deformable blisters by forcing a proprietary liquid silicone rubber through the positive mould cavity. The set silicone rubber is removed from the cast and prefilled with liquid reagent and then sealed with a thin (0.3mm) burstable layer of recast silicone rubber. The main microfluidic cartridge is fabricated using classical soft lithographic techniques. The cartridge incorporates microchannel circuitry, mixing chamber, inlet port, outlet port, reaction chamber and waste chamber. Polydimethylsiloxane (PDMS, QSil 216) is mixed and degassed using a centrifuge (ratio 10:1) is then poured after the prefilled blisters are correctly positioned on the negative mould. Heat treatment of about 50C to 60C in the oven for about 3hours is needed to achieve curing. The latter chip production stage involves bonding the cured PDMS to the glass slide. A plasma coroner treater device BD20-AC (Electro-Technic Products Inc., US) is used to activate the PDMS and glass slide before they are both joined and adequately compressed together, then left in the oven over the night to ensure bonding. There are two blisters in total needed for experimentation; the first will be used as a wash buffer to remove any remaining cell debris and unbound DNA while the second will contain 100uL amplification reagents. This paper will present results of chemical cell lysis, extraction using a biopolymer paper membrane and isothermal amplification on a low-cost platform using the finger actuated blisters for reagent storage. The platform has been shown to detect 1x105 copies of Chlamydia trachomatis using Recombinase Polymerase Amplification (RPA).

Keywords: finger actuation, point of care, reagent storage, silicone blisters

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1209 Flow and Heat Transfer over a Shrinking Sheet: A Stability Analysis

Authors: Anuar Ishak

Abstract:

The characteristics of fluid flow and heat transfer over a permeable shrinking sheet is studied. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the suction parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: dual solutions, heat transfer, shrinking sheet, stability analysis

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1208 Intensification of Heat Transfer Using AL₂O₃-Cu/Water Hybrid Nanofluid in a Circular Duct Using Inserts

Authors: Muluken Biadgelegn Wollele, Mebratu Assaye Mengistu

Abstract:

Nanotechnology has created new opportunities for improving industrial efficiency and performance. One of the proposed approaches to improving the effectiveness of temperature exchangers is the use of nanofluids to improve heat transfer performance. The thermal conductivity of nanoparticles, as well as their size, diameter, and volume concentration, all played a role in influencing the rate of heat transfer. Nanofluids are commonly used in automobiles, energy storage, electronic component cooling, solar absorbers, and nuclear reactors. Convective heat transfer must be improved when designing thermal systems in order to reduce heat exchanger size, weight, and cost. Using roughened surfaces to promote heat transfer has been tried several times. Thus, both active and passive heat transfer methods show potential in terms of heat transfer improvement. There will be an added advantage of enhanced heat transfer due to the two methods adopted; however, pressure drop must be considered during flow. Thus, the current research aims to increase heat transfer by adding a twisted tap insert in a plain tube using a working fluid hybrid nanofluid (Al₂O₃-Cu) with a base fluid of water. A circular duct with inserts, a tube length of 3 meters, a hydraulic diameter of 0.01 meters, and tube walls with a constant heat flux of 20 kW/m² and a twist ratio of 125 was used to investigate Al₂O₃-Cu/H₂O hybrid nanofluid with inserts. The temperature distribution is better than with conventional tube designs due to stronger tangential contact and swirls in the twisted tape. The Nusselt number values of plain twisted tape tubes are 1.5–2.0 percent higher than those of plain tubes. When twisted tape is used instead of plain tube, performance evaluation criteria improve by 1.01 times. A heat exchanger that is useful for a number of heat exchanger applications can be built utilizing a mixed flow of analysis that incorporates passive and active methodologies.

Keywords: nanofluids, active method, passive method, Nusselt number, performance evaluation criteria

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1207 A Xenon Mass Gauging through Heat Transfer Modeling for Electric Propulsion Thrusters

Authors: A. Soria-Salinas, M.-P. Zorzano, J. Martín-Torres, J. Sánchez-García-Casarrubios, J.-L. Pérez-Díaz, A. Vakkada-Ramachandran

Abstract:

The current state-of-the-art methods of mass gauging of Electric Propulsion (EP) propellants in microgravity conditions rely on external measurements that are taken at the surface of the tank. The tanks are operated under a constant thermal duty cycle to store the propellant within a pre-defined temperature and pressure range. We demonstrate using computational fluid dynamics (CFD) simulations that the heat-transfer within the pressurized propellant generates temperature and density anisotropies. This challenges the standard mass gauging methods that rely on the use of time changing skin-temperatures and pressures. We observe that the domes of the tanks are prone to be overheated, and that a long time after the heaters of the thermal cycle are switched off, the system reaches a quasi-equilibrium state with a more uniform density. We propose a new gauging method, which we call the Improved PVT method, based on universal physics and thermodynamics principles, existing TRL-9 technology and telemetry data. This method only uses as inputs the temperature and pressure readings of sensors externally attached to the tank. These sensors can operate during the nominal thermal duty cycle. The improved PVT method shows little sensitivity to the pressure sensor drifts which are critical towards the end-of-life of the missions, as well as little sensitivity to systematic temperature errors. The retrieval method has been validated experimentally with CO2 in gas and fluid state in a chamber that operates up to 82 bar within a nominal thermal cycle of 38 °C to 42 °C. The mass gauging error is shown to be lower than 1% the mass at the beginning of life, assuming an initial tank load at 100 bar. In particular, for a pressure of about 70 bar, just below the critical pressure of CO2, the error of the mass gauging in gas phase goes down to 0.1% and for 77 bar, just above the critical point, the error of the mass gauging of the liquid phase is 0.6% of initial tank load. This gauging method improves by a factor of 8 the accuracy of the standard PVT retrievals using look-up tables with tabulated data from the National Institute of Standards and Technology.

Keywords: electric propulsion, mass gauging, propellant, PVT, xenon

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1206 Critical Parameters of a Square-Well Fluid

Authors: Hamza Javar Magnier, Leslie V. Woodcock

Abstract:

We report extensive molecular dynamics (MD) computational investigations into the thermodynamic description of supercritical properties for a model fluid that is the simplest realistic representation of atoms or molecules. The pair potential is a hard-sphere repulsion of diameter σ with a very short attraction of length λσ. When λ = 1.005 the range is so short that the model atoms are referred to as “adhesive spheres”. Molecular dimers, trimers …etc. up to large clusters, or droplets, of many adhesive-sphere atoms are unambiguously defined. This then defines percolation transitions at the molecular level that bound the existence of gas and liquid phases at supercritical temperatures, and which define the existence of a supercritical mesophase. Both liquid and gas phases are seen to terminate at the loci of percolation transitions, and below a second characteristic temperature (Tc2) are separated by the supercritical mesophase. An analysis of the distribution of clusters in gas, meso- and liquid phases confirms the colloidal nature of this mesophase. The general phase behaviour is compared with both experimental properties of the water-steam supercritical region and also with formally exact cluster theory of Mayer and Mayer. Both are found to be consistent with the present findings that in this system the supercritical mesophase narrows in density with increasing T > Tc and terminates at a higher Tc2 at a confluence of the primary percolation loci. The expended plot of the MD data points in the mesophase of 7 critical and supercritical isotherms in highlight this narrowing in density of the linear-slope region of the mesophase as temperature is increased above the critical. This linearity in the mesophase implies the existence of a linear combination rule between gas and liquid which is an extension of the Lever rule in the subcritical region, and can be used to obtain critical parameters without resorting to experimental data in the two-phase region. Using this combination rule, the calculated critical parameters Tc = 0.2007 and Pc = 0.0278 are found be agree with the values found by of Largo and coworkers. The properties of this supercritical mesophase are shown to be consistent with an alternative description of the phenomenon of critical opalescence seen in the supercritical region of both molecular and colloidal-protein supercritical fluids.

Keywords: critical opalescence, supercritical, square-well, percolation transition, critical parameters.

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1205 A Performance Study of a Solar Heating System on the Microclimate of an Agricultural Greenhouse

Authors: Nora Arbaoui, Rachid Tadili

Abstract:

This study focuses on a solar system designed to heat an agricultural greenhouse. This solar system is based on the heating of a transfer fluid that circulates inside the greenhouse through a solar copper coil integrated into the roof of the greenhouse. The thermal energy stored during the day will be released during the night to improve the microclimate of the greenhouse. This system was tested in a small agricultural greenhouse in order to ameliorate the different operational parameters. The climatic and agronomic results obtained with this system are significant in comparison with a greenhouse with no heating system.

Keywords: solar system, agricultural greenhouse, heating, storage, drying

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1204 Simplified Modelling of Visco-Elastic Fluids for Use in Recoil Damping Systems

Authors: Prasad Pokkunuri

Abstract:

Visco-elastic materials combine the stress response properties of both solids and fluids and have found use in a variety of damping applications – both vibrational and acoustic. Defense and automotive applications, in particular, are subject to high impact and shock loading – for example: aircraft landing gear, firearms, and shock absorbers. Field responsive fluids – a class of smart materials – are the preferred choice of energy absorbents because of their controllability. These fluids’ stress response can be controlled by the application of a magnetic or electric field, in a closed loop. Their rheological properties – elasticity, plasticity, and viscosity – can be varied all the way from that of a liquid such as water to a hard solid. This work presents a simplified model to study the impulse response behavior of such fluids for use in recoil damping systems. The well-known Burger’s equation, in conjunction with various visco-elastic constitutive models, is used to represent fluid behavior. The Kelvin-Voigt, Upper Convected Maxwell (UCM), and Oldroyd-B constitutive models are implemented in this study. Using these models in a one-dimensional framework eliminates additional complexities due to geometry, pressure, body forces, and other source terms. Using a finite difference formulation to numerically solve the governing equation(s), the response to an initial impulse is studied. The disturbance is confined within the problem domain with no-inflow, no-outflow boundary conditions, and its decay characteristics studied. Visco-elastic fluids typically involve a time-dependent stress relaxation which gives rise to interesting behavior when subjected to an impulsive load. For particular values of viscous damping and elastic modulus, the fluid settles into a stable oscillatory state, absorbing and releasing energy without much decay. The simplified formulation enables a comprehensive study of different modes of system response, by varying relevant parameters. Using the insights gained from this study, extension to a more detailed multi-dimensional model is considered.

Keywords: Burgers Equation, Impulse Response, Recoil Damping Systems, Visco-elastic Fluids

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1203 Prompting and Encouraging Community Hydration through Education: A Realist Review and Evaluation Exploring Hydration in a Population at Risk of Frailty

Authors: Mark Davies, Carolyn Wallace, Christina Lloydwin, Tom Powell

Abstract:

Background: Frailty is increasingly recognized as a public health problem within an aging population. It is often characterized as an accumulation of clinical symptoms with progressive decline. We contend that dehydration is potentially the missing link driving the cycle of frailty; it contributes to malnutrition and cognitive decline and is a risk factor for other conditions. Frailty may also impact on fluid intake in cognitively intact older adults, indicating the cyclical nature of dehydration contributing to increasing frailty. Aim: To examine the relationships between fluid, hydration, and frailty in older adults in order to determine what works, for whom, how, why, and in what circumstances. Methods: A Realist Synthesis was first undertaken with n=50 studies, leading to the development of a Refined Programme Theory (RPT) articulating what hydration interventions work, for whom, to what degree, in what contexts, and how & why. Within the subsequent evaluation, the RPT was further confirmed/refuted/refined following semi-structured interviews with n=8 participants (healthcare professionals and patients). The RAMESES Quality Standards were followed throughout the study. Results: The Refined Programme Theory (RPT) highlighted three factors that result in optimized hydration for frail older people, i.e., Developing an Understanding Around Hydration, Empowering Participation, and System Reconfiguration. Our RPT indicates that hydration interventions work by developing an understanding of the importance of hydration, mitigating physical & cognitive barriers, increasing the agency of the patient, using a prompting process to reinforce drinking behavior, and routinizing hydration as a dimension of overall care. Conclusion: The study indicates that a greater understanding of the importance of hydration is required for all parties. Patients also require physical and psychological support if they are to be active agents in meeting their hydration needs. At a wider ‘system’ level, organizations must work in an integrated manner introducing processes that enable continuing professional development (CPD), encourage ongoing holistic assessment, and routinize hydration support.

Keywords: frailty, dehydration, older adults, realist review, realist evaluation

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1202 Modulating Vortex Dynamics Around Circular Cylinder Via Asymmetric Cross-Sectional Profile Morphing: A Comparative Study of Cylindrical and Elliptical Configurations

Authors: Kamila Fethallah, Mahmoud Mekadem, Hamid Ouali

Abstract:

Active flow control around a cylinder is an extensively studied subject in aerodynamics. Researchers apply a range of techniques to alter the fluid flow surrounding a cylindrical body, with the intent of reducing drag, enhancing lift, and optimizing overall aerodynamic performance. This study investigates the manipulation of flow dynamics around a circular cylinder by introducing an original elliptical cylindrical deformation to the traditionally straight section. Through the use of a crank mechanism, precise control of the deformation is achieved, allowing a comprehensive examination of its effects on fluid flow patterns. The main objective of this research is to evaluate the effectiveness of this advanced approach in reducing the drag coefficient and modifying the wake pattern, providing valuable information on flow control and optimization. Experimental results show that varying deformation amplitudes (10%, 15% and 20%) and control frequencies strongly influence drag and flow structure, the maximum reduction in drag coefficient (approximately 44%) observed at 15% amplitude and optimum frequency. The flow structure is strongly influenced by the deformation amplitude and frequency, particularly in the frequency range close to that of the natural shedding. These results suggest that the deformation frequency and amplitude play a crucial role in modifying the flow structure and reducing the drag coefficient. Numerical simulations further support the efficiency of the active flow control technique using cylindrical-elliptical deformation, underlining a consistent drag reduction of up to 42% at extreme deformation conditions (100%). The present study aims at highlighting the potential of this original approach in the enhancement of efficiency and performance of systems involved in energy exchange with fluids. Concluding this, the current study offers fresh routes toward the development of flow control and optimization strategies in a wide range of engineering applications.

Keywords: control frequencies, deformation amplitudes, drag coefficient, elliptical cylindrical deformation, flow dynamics, wake pattern

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1201 Modelling of Solidification in a Latent Thermal Energy Storage with a Finned Tube Bundle Heat Exchanger Unit

Authors: Remo Waser, Simon Maranda, Anastasia Stamatiou, Ludger J. Fischer, Joerg Worlitschek

Abstract:

In latent heat storage, a phase change material (PCM) is used to store thermal energy. The heat transfer rate during solidification is limited and considered as a key challenge in the development of latent heat storages. Thus, finned heat exchangers (HEX) are often utilized to increase the heat transfer rate of the storage system. In this study, a new modeling approach to calculating the heat transfer rate in latent thermal energy storages with complex HEX geometries is presented. This model allows for an optimization of the HEX design in terms of costs and thermal performance of the system. Modeling solidification processes requires the calculation of time-dependent heat conduction with moving boundaries. Commonly used computational fluid dynamic (CFD) methods enable the analysis of the heat transfer in complex HEX geometries. If applied to the entire storage, the drawback of this approach is the high computational effort due to small time steps and fine computational grids required for accurate solutions. An alternative to describe the process of solidification is the so-called temperature-based approach. In order to minimize the computational effort, a quasi-stationary assumption can be applied. This approach provides highly accurate predictions for tube heat exchangers. However, it shows unsatisfactory results for more complex geometries such as finned tube heat exchangers. The presented simulation model uses a temporal and spatial discretization of heat exchanger tube. The spatial discretization is based on the smallest possible symmetric segment of the HEX. The heat flow in each segment is calculated using finite volume method. Since the heat transfer fluid temperature can be derived using energy conservation equations, the boundary conditions at the inner tube wall is dynamically updated for each time step and segment. The model allows a prediction of the thermal performance of latent thermal energy storage systems using complex HEX geometries with considerably low computational effort.

Keywords: modelling of solidification, finned tube heat exchanger, latent thermal energy storage

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1200 Numerical Solution of Momentum Equations Using Finite Difference Method for Newtonian Flows in Two-Dimensional Cartesian Coordinate System

Authors: Ali Ateş, Ansar B. Mwimbo, Ali H. Abdulkarim

Abstract:

General transport equation has a wide range of application in Fluid Mechanics and Heat Transfer problems. In this equation, generally when φ variable which represents a flow property is used to represent fluid velocity component, general transport equation turns into momentum equations or with its well known name Navier-Stokes equations. In these non-linear differential equations instead of seeking for analytic solutions, preferring numerical solutions is a more frequently used procedure. Finite difference method is a commonly used numerical solution method. In these equations using velocity and pressure gradients instead of stress tensors decreases the number of unknowns. Also, continuity equation, by integrating the system, number of equations is obtained as number of unknowns. In this situation, velocity and pressure components emerge as two important parameters. In the solution of differential equation system, velocities and pressures must be solved together. However, in the considered grid system, when pressure and velocity values are jointly solved for the same nodal points some problems confront us. To overcome this problem, using staggered grid system is a referred solution method. For the computerized solutions of the staggered grid system various algorithms were developed. From these, two most commonly used are SIMPLE and SIMPLER algorithms. In this study Navier-Stokes equations were numerically solved for Newtonian flow, whose mass or gravitational forces were neglected, for incompressible and laminar fluid, as a hydro dynamically fully developed region and in two dimensional cartesian coordinate system. Finite difference method was chosen as the solution method. This is a parametric study in which varying values of velocity components, pressure and Reynolds numbers were used. Differential equations were discritized using central difference and hybrid scheme. The discritized equation system was solved by Gauss-Siedel iteration method. SIMPLE and SIMPLER were used as solution algorithms. The obtained results, were compared for central difference and hybrid as discritization methods. Also, as solution algorithm, SIMPLE algorithm and SIMPLER algorithm were compared to each other. As a result, it was observed that hybrid discritization method gave better results over a larger area. Furthermore, as computer solution algorithm, besides some disadvantages, it can be said that SIMPLER algorithm is more practical and gave result in short time. For this study, a code was developed in DELPHI programming language. The values obtained in a computer program were converted into graphs and discussed. During sketching, the quality of the graph was increased by adding intermediate values to the obtained result values using Lagrange interpolation formula. For the solution of the system, number of grid and node was found as an estimated. At the same time, to indicate that the obtained results are satisfactory enough, by doing independent analysis from the grid (GCI analysis) for coarse, medium and fine grid system solution domain was obtained. It was observed that when graphs and program outputs were compared with similar studies highly satisfactory results were achieved.

Keywords: finite difference method, GCI analysis, numerical solution of the Navier-Stokes equations, SIMPLE and SIMPLER algoritms

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1199 In Vitro Digestibility of Grains and Straw of Seventeen Ecotypes of Bitter Vetch (Vicia ervilia) in the North of Morocco

Authors: Boukrouh Soumaya, Cabaraux Jean-François, Avril Claire, Noutfia Ali, Chentouf Mouad

Abstract:

The introduction of marginal leguminous forage species in the diet of ruminants are of great importance. Bitter vetch is a good source of proteins, highly resistant against drought and poor soil conditions. Accordingly; two years field trials (2018/2019 and 2019-2020) were conducted to determine the digestibility of straw and grains of 17 promising bitter vetch ecotypes(Vicia ervilia) in the north of Morocco. In vitro dry and organic matter digestibility, gas production, and kinetics of fermentation of grains and straw were evaluated using gas production technique, pepsin-cellulase enzymatic digestibility of DM (CDDM)and OM (CDOM), as well as protease enzymatic CP degradation (CPD) and in vitro true digestibility, were performed using DAISYII Incubator. In vitro digestibility was performed using gas production method of (Menke et al., 1979) improved by Menke and Steingass (1988). Samples were incubated in glass syringes that contained rumen fluid and incubation solution that conserved in water bath in 39°C during 72 hours. Gas production was recorded after 2, 4, 8, 12, 24, 48, and 72 hours. Studied digestibility parameters were dry and organic matter digestibility, microbial biomass production, partitioning factor, and volatile fatty acids. Enzymatic dry matter digestibility was different (p < 0.05) among grains and straw for all ecotypes. It varied from 804.1 to 957.7 g/kg DM and 270.4 to 412.3 g/kg DM for grains and straw, respectively. Metabolizable energy varied between 11.7 to 14.3 MJ/kg DM and 2.6 to 5.0 MJ/kg DM for grains and straw, respectively. Potential gas production (A), the rate constants (c and d), and lag times of grains and straws from different bitter vetch ecotypes were different (p > 0.05). The results emphasized that in any evaluation of bitter vetch ecotypes, where straw of this legume seed is used as an animal feed, not only seed yield but also yield and quality of straw should be taken into consideration, particularly in areas where straw from this legume is considered as an important feedstuff for ruminants. Enzymatic digestibility was lower than in vitro digestibility by gaz production and by the DAISYII method because rumen fluid contains bacteria than increase digestibility. There was no difference between in vitro digestibility by gaz production and the DAISY II method. The DAISY II method can be used to increase labor efficiency in the in vitro DM digestibility analysis if gaz production is not necessary for analysis.

Keywords: bitter vetch, grains, straw, ecotype, in vitro digestibility, gaz production, enzymatic digestibility

Procedia PDF Downloads 179
1198 A Solar Heating System Performance on the Microclimate of an Agricultural Greenhouse

Authors: Nora Arbaoui, Rachid Tadili

Abstract:

The experiment adopted a natural technique of heating and cooling an agricultural greenhouse to reduce the fuel consumption and CO2 emissions based on the heating of a transfer fluid that circulates inside the greenhouse through a solar copper coil positioned at the roof of the greenhouse. This experimental study is devoted to the performance evaluation of a solar heating system to improve the microclimate of a greenhouse during the cold period, especially in the Mediterranean climate. This integrated solar system for heating has a positive impact on the quality and quantity of the products under the study greenhouse.

Keywords: solar system, agricultural greenhouse, heating, storage

Procedia PDF Downloads 81
1197 Enhancing Heavy Oil Recovery: Experimental Insights into Low Salinity Polymer in Sandstone Reservoirs

Authors: Intisar, Khalifa, Salim, Al Busaidi

Abstract:

Recently, the synergic combination of low salinity water flooding with polymer flooding has been a subject of paramount interest for the oil industry. Numerous studies have investigated the efficiency of enhanced oil recovery using low salinity polymer flooding (LSPF). However, there is no clear conclusion that can explain the incremental oil recovery, determine the main factors controlling the oil recovery process, and define the relative contribution of rock/fluids or fluid/fluid interactions to extra oil recovery. Therefore, this study aims to perform a systematic investigation of the interactions between oil, polymer, low salinity and sandstone rock surface from pore to core scale during LSPF. Partially hydrolyzed polyacrylamide (HPAM) polymer, Boise outcrop, a crude oil sample and reservoir cores from an Omani oil field, and brine at two different salinities were used in the study. Several experimental measurements including static bulk measurements of polymer solutions prepared with brines of high and low salinities, single phase displacement experiments, along with rheological, total organic carbon and ion chromatography measurements to analyze ion exchange reactions, polymer adsorption, and viscosity loss were used. In addition, two-phase experiments were performed to demonstrate the oil recovery efficiency of LSPF. The results revealed that the incremental oil recovery from LSPF was attributed to the combination of the reduction in the water-oil mobility ratio, an increase in the repulsion forces between crude oil/brine/rock interfaces and an increase in pH of the aqueous solution. In addition, lowering the salinity of the make-up brine resulted in a larger conformation (expansion) of the polymer molecules, which in turn resulted in less adsorption and a greater in-situ viscosity without any negative impact on injectivity. This plays a positive role in the oil displacement process. Moreover, the loss of viscosity in the effluent of polymer solutions was lower in low-salinity than in high-salinity brine, indicating that an increase in cations concentration (mainly driven by Ca2+ ions) has stronger effect on the viscosity of high-salinity polymer solution compared with low-salinity polymer.

Keywords: polymer, heavy oil, low salinity, COBR interactions

Procedia PDF Downloads 95
1196 Flow and Heat Transfer of a Nanofluid over a Shrinking Sheet

Authors: N. Bachok, N. L. Aleng, N. M. Arifin, A. Ishak, N. Senu

Abstract:

The problem of laminar fluid flow which results from the shrinking of a permeable surface in a nanofluid has been investigated numerically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. A similarity solution is presented which depends on the mass suction parameter S, Prandtl number Pr, Lewis number Le, Brownian motion number Nb and thermophoresis number Nt. It was found that the reduced Nusselt number is decreasing function of each dimensionless number.

Keywords: Boundary layer, nanofluid, shrinking sheet, Brownian motion, thermophoresis, similarity solution

Procedia PDF Downloads 416
1195 A Simplified Method to Assess the Damage of an Immersed Cylinder Subjected to Underwater Explosion

Authors: Kevin Brochard, Herve Le Sourne, Guillaume Barras

Abstract:

The design of a submarine’s hull is crucial for its operability and crew’s safety, but also complex. Indeed, engineers need to balance lightness, acoustic discretion and resistance to both immersion pressure and environmental attacks. Submarine explosions represent a first-rate threat for the integrity of the hull, whose behavior needs to be properly analyzed. The presented work is focused on the development of a simplified analytical method to study the structural response of a deeply immersed cylinder submitted to an underwater explosion. This method aims to provide engineers a quick estimation of the resulting damage, allowing them to simulate a large number of explosion scenarios. The present research relies on the so-called plastic string on plastic foundation model. A two-dimensional boundary value problem for a cylindrical shell is converted to an equivalent one-dimensional problem of a plastic string resting on a non-linear plastic foundation. For this purpose, equivalence parameters are defined and evaluated by making assumptions on the shape of the displacement and velocity field in the cross-sectional plane of the cylinder. Closed-form solutions for the deformation and velocity profile of the shell are obtained for explosive loading, and compare well with numerical and experimental results. However, the plastic-string model has not yet been adapted for a cylinder in immersion subjected to an explosive loading. In fact, the effects of fluid-structure interaction have to be taken into account. Moreover, when an underwater explosion occurs, several pressure waves are emitted by the gas bubble pulsations, called secondary waves. The corresponding loads, which may produce significant damages to the cylinder, must also be accounted for. The analytical developments carried out to solve the above problem of a shock wave impacting a cylinder, considering fluid-structure interaction will be presented for an unstiffened cylinder. The resulting deformations are compared to experimental and numerical results for different shock factors and different standoff distances.

Keywords: immersed cylinder, rigid plastic material, shock loading, underwater explosion

Procedia PDF Downloads 342
1194 Transient Heat Transfer of a Spiral Fin

Authors: Sen-Yung Lee, Li-Kuo Chou, Chao-Kuang Chen

Abstract:

In this study, the problem of temperature transient response of a spiral fin, with its end insulated, is analyzed with base end subjected to a variation of fluid temperature. The hybrid method of Laplace transforms/Adomian decomposed method-Padé, is applied to the temperature transient response of the fin, the result of the temperature distribution and the heat flux at the base of the spiral fin are obtained, show a good agreement in the physical phenomenon.

Keywords: Laplace transforms, Adomian decomposed method- Padé, transient response, heat transfer

Procedia PDF Downloads 427
1193 Electrospray Plume Characterisation of a Single Source Cone-Jet for Micro-Electronic Cooling

Authors: M. J. Gibbons, A. J. Robinson

Abstract:

Increasing expectations on small form factor electronics to be more compact while increasing performance has driven conventional cooling technologies to a thermal management threshold. An emerging solution to this problem is electrospray (ES) cooling. ES cooling enables two phase cooling by utilising Coulomb forces for energy efficient fluid atomization. Generated charged droplets are accelerated to the grounded target surface by the applied electric field and surrounding gravitational force. While in transit the like charged droplets enable plume dispersion and inhibit droplet coalescence. If the electric field is increased in the cone-jet regime, a subsequent increase in the plume spray angle has been shown. Droplet segregation in the spray plume has been observed, with primary droplets in the plume core and satellite droplets positioned on the periphery of the plume. This segregation is facilitated by inertial and electrostatic effects. This result has been corroborated by numerous authors. These satellite droplets are usually more densely charged and move at a lower relative velocity to that of the spray core due to the radial decay of the electric field. Previous experimental research by Gomez and Tang has shown that the number of droplets deposited on the periphery can be up to twice that of the spray core. This result has been substantiated by a numerical models derived by Wilhelm et al., Oh et al. and Yang et al. Yang et al. showed from their numerical model, that by varying the extractor potential the dispersion radius of the plume also varies proportionally. This research aims to investigate this dispersion density and the role it plays in the local heat transfer coefficient profile (h) of ES cooling. This will be carried out for different extractor – target separation heights (H2), working fluid flow rates (Q), and extractor applied potential (V2). The plume dispersion will be recorded by spraying a 25 µm thick, joule heated steel foil and by recording the thermal footprint of the ES plume using a Flir A-40 thermal imaging camera. The recorded results will then be analysed by in-house developed MATLAB code.

Keywords: electronic cooling, electrospray, electrospray plume dispersion, spray cooling

Procedia PDF Downloads 398
1192 Effects of Polymer Adsorption and Desorption on Polymer Flooding in Waterflooded Reservoir

Authors: Sukruthai Sapniwat, Falan Srisuriyachai

Abstract:

Polymer Flooding is one of the most well-known methods in Enhanced Oil Recovery (EOR) technology which can be implemented after either primary or secondary recovery, resulting in favorable conditions for the displacement mechanism in order to lower the residual oil in the reservoir. Polymer substances can lower the mobility ratio of the whole process by increasing the viscosity of injected water. Therefore, polymer flooding can increase volumetric sweep efficiency, which leads to a better recovery factor. Moreover, polymer adsorption onto rock surface can help decrease reservoir permeability contrast with high heterogeneity. Due to the reduction of the absolute permeability, effective permeability to water, representing flow ability of the injected fluid, is also reduced. Once polymer is adsorbed onto rock surface, polymer molecule can be desorbed when different fluids are injected. This study is performed to evaluate the effects of the adsorption and desorption process of polymer solutions to yield benefits on the oil recovery mechanism. A reservoir model is constructed by reservoir simulation program called STAR® commercialized by the Computer Modeling Group (CMG). Various polymer concentrations, starting times of polymer flooding process and polymer injection rates were evaluated with selected values of polymer desorption degrees including 0, 25, 50, 75 and 100%. The higher the value, the more adsorbed polymer molecules to return back to flowing fluid. According to the results, polymer desorption lowers polymer consumption, especially at low concentrations. Furthermore, starting time of polymer flooding and injection rate affect the oil production. The results show that waterflooding followed by earlier polymer flooding can increase the oil recovery factor while the higher injection rate also enhances the recovery. Polymer concentration is related to polymer consumption due to the two main benefits of polymer flooding control described above. Therefore, polymer slug size should be optimized based on polymer concentration. Polymer desorption causes polymer re-employment that is previously adsorbed onto rock surface, resulting in an increase of sweep efficiency in the further period of polymer flooding process. Even though waterflooding supports polymer injectivity, water cut at the producer can prematurely terminate the oil production. The injection rate decreases polymer adsorption due to decreased retention time of polymer flooding process.

Keywords: enhanced oil recovery technology, polymer adsorption and desorption, polymer flooding, reservoir simulation

Procedia PDF Downloads 333
1191 Two-Dimensional Analysis and Numerical Simulation of the Navier-Stokes Equations for Principles of Turbulence around Isothermal Bodies Immersed in Incompressible Newtonian Fluids

Authors: Romulo D. C. Santos, Silvio M. A. Gama, Ramiro G. R. Camacho

Abstract:

In this present paper, the thermos-fluid dynamics considering the mixed convection (natural and forced convections) and the principles of turbulence flow around complex geometries have been studied. In these applications, it was necessary to analyze the influence between the flow field and the heated immersed body with constant temperature on its surface. This paper presents a study about the Newtonian incompressible two-dimensional fluid around isothermal geometry using the immersed boundary method (IBM) with the virtual physical model (VPM). The numerical code proposed for all simulations satisfy the calculation of temperature considering Dirichlet boundary conditions. Important dimensionless numbers such as Strouhal number is calculated using the Fast Fourier Transform (FFT), Nusselt number, drag and lift coefficients, velocity and pressure. Streamlines and isothermal lines are presented for each simulation showing the flow dynamics and patterns. The Navier-Stokes and energy equations for mixed convection were discretized using the finite difference method for space and a second order Adams-Bashforth and Runge-Kuta 4th order methods for time considering the fractional step method to couple the calculation of pressure, velocity, and temperature. This work used for simulation of turbulence, the Smagorinsky, and Spalart-Allmaras models. The first model is based on the local equilibrium hypothesis for small scales and hypothesis of Boussinesq, such that the energy is injected into spectrum of the turbulence, being equal to the energy dissipated by the convective effects. The Spalart-Allmaras model, use only one transport equation for turbulent viscosity. The results were compared with numerical data, validating the effect of heat-transfer together with turbulence models. The IBM/VPM is a powerful tool to simulate flow around complex geometries. The results showed a good numerical convergence in relation the references adopted.

Keywords: immersed boundary method, mixed convection, turbulence methods, virtual physical model

Procedia PDF Downloads 118
1190 Temporal and Spacial Adaptation Strategies in Aerodynamic Simulation of Bluff Bodies Using Vortex Particle Methods

Authors: Dario Milani, Guido Morgenthal

Abstract:

Fluid dynamic computation of wind caused forces on bluff bodies e.g light flexible civil structures or high incidence of ground approaching airplane wings, is one of the major criteria governing their design. For such structures a significant dynamic response may result, requiring the usage of small scale devices as guide-vanes in bridge design to control these effects. The focus of this paper is on the numerical simulation of the bluff body problem involving multiscale phenomena induced by small scale devices. One of the solution methods for the CFD simulation that is relatively successful in this class of applications is the Vortex Particle Method (VPM). The method is based on a grid free Lagrangian formulation of the Navier-Stokes equations, where the velocity field is modeled by particles representing local vorticity. These vortices are being convected due to the free stream velocity as well as diffused. This representation yields the main advantages of low numerical diffusion, compact discretization as the vorticity is strongly localized, implicitly accounting for the free-space boundary conditions typical for this class of FSI problems, and a natural representation of the vortex creation process inherent in bluff body flows. When the particle resolution reaches the Kolmogorov dissipation length, the method becomes a Direct Numerical Simulation (DNS). However, it is crucial to note that any solution method aims at balancing the computational cost against the accuracy achievable. In the classical VPM method, if the fluid domain is discretized by Np particles, the computational cost is O(Np2). For the coupled FSI problem of interest, for example large structures such as long-span bridges, the aerodynamic behavior may be influenced or even dominated by small structural details such as barriers, handrails or fairings. For such geometrically complex and dimensionally large structures, resolving the complete domain with the conventional VPM particle discretization might become prohibitively expensive to compute even for moderate numbers of particles. It is possible to reduce this cost either by reducing the number of particles or by controlling its local distribution. It is also possible to increase the accuracy of the solution without increasing substantially the global computational cost by computing a correction of the particle-particle interaction in some regions of interest. In this paper different strategies are presented in order to extend the conventional VPM method to reduce the computational cost whilst resolving the required details of the flow. The methods include temporal sub stepping to increase the accuracy of the particles convection in certain regions as well as dynamically re-discretizing the particle map to locally control the global and the local amount of particles. Finally, these methods will be applied on a test case and the improvements in the efficiency as well as the accuracy of the proposed extension to the method are presented. The important benefits in terms of accuracy and computational cost of the combination of these methods will be thus presented as long as their relevant applications.

Keywords: adaptation, fluid dynamic, remeshing, substepping, vortex particle method

Procedia PDF Downloads 266
1189 Simulation of Flow Patterns in Vertical Slot Fishway with Cylindrical Obstacles

Authors: Mohsen Solimani Babarsad, Payam Taheri

Abstract:

Numerical results of vertical slot fishways with and without cylinders study are presented. The simulated results and the measured data in the fishways are compared to validate the application of the model. This investigation is made using FLUENT V.6.3, a Computational Fluid Dynamics solver. Advantages of using these types of numerical tools are the possibility of avoiding the St.-Venant equations’ limitations, and turbulence can be modeled by means of different models such as the k-ε model. In general, the present study has demonstrated that the CFD model could be useful for analysis and design of vertical slot fishways with cylinders.

Keywords: slot Fish-way, CFD, k-ε model, St.-Venant equations’

Procedia PDF Downloads 364
1188 An Object-Oriented Modelica Model of the Water Level Swell during Depressurization of the Reactor Pressure Vessel of the Boiling Water Reactor

Authors: Rafal Bryk, Holger Schmidt, Thomas Mull, Ingo Ganzmann, Oliver Herbst

Abstract:

Prediction of the two-phase water mixture level during fast depressurization of the Reactor Pressure Vessel (RPV) resulting from an accident scenario is an important issue from the view point of the reactor safety. Since the level swell may influence the behavior of some passive safety systems, it has been recognized that an assumption which at the beginning may be considered as a conservative one, not necessary leads to a conservative result. This paper discusses outcomes obtained during simulations of the water dynamics and heat transfer during sudden depressurization of a vessel filled up to a certain level with liquid water under saturation conditions and with the rest of the vessel occupied by saturated steam. In case of the pressure decrease e.g. due to the main steam line break, the liquid water evaporates abruptly, being a reason thereby, of strong transients in the vessel. These transients and the sudden emergence of void in the region occupied at the beginning by liquid, cause elevation of the two-phase mixture. In this work, several models calculating the water collapse and swell levels are presented and validated against experimental data. Each of the models uses different approach to calculate void fraction. The object-oriented models were developed with the Modelica modelling language and the OpenModelica environment. The models represent the RPV of the Integral Test Facility Karlstein (INKA) – a dedicated test rig for simulation of KERENA – a new Boiling Water Reactor design of Framatome. The models are based on dynamic mass and energy equations. They are divided into several dynamic volumes in each of which, the fluid may be single-phase liquid, steam or a two-phase mixture. The heat transfer between the wall of the vessel and the fluid is taken into account. Additional heat flow rate may be applied to the first volume of the vessel in order to simulate the decay heat of the reactor core in a similar manner as it is simulated at INKA. The comparison of the simulations results against the reference data shows a good agreement.

Keywords: boiling water reactor, level swell, Modelica, RPV depressurization, thermal-hydraulics

Procedia PDF Downloads 213
1187 The Soliton Solution of the Quadratic-Cubic Nonlinear Schrodinger Equation

Authors: Sarun Phibanchon, Yuttakarn Rattanachai

Abstract:

The quadratic-cubic nonlinear Schrodinger equation can be explained the weakly ion-acoustic waves in magnetized plasma with a slightly non-Maxwellian electron distribution by using the Madelung's fluid picture. However, the soliton solution to the quadratic-cubic nonlinear Schrodinger equation is determined by using the direct integration. By the characteristics of a soliton, the solution can be claimed that it's a soliton by considering its time evolution and their collisions between two solutions. These results are shown by applying the spectral method.

Keywords: soliton, ion-acoustic waves, plasma, spectral method

Procedia PDF Downloads 413