Search results for: incompressible navier-stokes equations

Authors: Rama Bhargava, Mania Goyal

Abstract:

The problem of magnetohydrodynamics boundary layer flow and heat transfer on a permeable stretching surface in a second grade nanofluid under the effect of heat generation and partial slip is studied theoretically. The Brownian motion and thermophoresis effects are also considered. The boundary layer equations governed by the PDE’s are transformed into a set of ODE’s with the help of local similarity transformations. The differential equations are solved by variational finite element method. The effects of different controlling parameters on the flow field and heat transfer characteristics are examined. The numerical results for the dimensionless velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically. The comparison confirmed excellent agreement. The present study is of great interest in coating and suspensions, cooling of metallic plate, oils and grease, paper production, coal water or coal-oil slurries, heat exchangers technology, materials processing exploiting.

Keywords: viscoelastic nanofluid, partial slip, stretching sheet, heat generation/absorption, MHD flow, FEM

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Authors: Yuanhao Gao, Ping Lin, Kees Weijer

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An optimal control system model is proposed for the cell flow in the process of chick embryo gastrulation in this paper. The target is to determine the cellular interaction forces which are hard to measure. This paper will take an approach to investigate the forces with the idea of the inverse problem. By choosing the forces as the control variable and regarding the cell flow as Stokes fluid, an objective functional will be established to match the numerical result of cell velocity with the experimental data. So that the forces could be determined by minimizing the objective functional. The Lagrange multiplier method is utilized to derive the state and adjoint equations consisting the optimal control system, which specifies the first-order necessary conditions. Finite element method is used to discretize and approximate equations. A conjugate gradient algorithm is given for solving the minimum solution of the system and determine the forces.

Keywords: optimal control model, Stokes equation, conjugate gradient method, finite element method, chick embryo gastrulation

Procedia PDF Downloads 259

Authors: Wissem Tighidet, Faïçal Naït Bouda, Moussa Allouche

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The numerical study of the Fluid-Structure Interaction (FSI) in a partially filled flexible tank submitted to a horizontal harmonic excitation motion. It is investigated by using two-way Fluid-Structure Interaction (FSI) in a flexible tank by Coupling between the Transient Structural (Mechanical) and Fluid Flow (Fluent) in ANSYS-Workbench Student version. The Arbitrary Lagrangian-Eulerian (ALE) formulation is adopted to solve with the finite volume method, the Navier-Stokes equations in two phases in a moving domain. The Volume of Fluid (VOF) method is applied to track the free surface. However, the equations of the dynamics of the structure are solved with the finite element method assuming a linear elastic behavior. To conclude, the Fluid-Structure Interaction (IFS) has a vital role in the analysis of the dynamic behavior of the rectangular tank. The results indicate that the flexibility of the tank walls has a significant impact on the amplitude of tank sloshing and the deformation of the free surface as well as the effect of liquid sloshing on wall deformation.

Keywords: arbitrary lagrangian-eulerian, fluid-structure interaction, sloshing, volume of fluid

Procedia PDF Downloads 104

Authors: X. Li, Y. Liu, H. Wong, B. Pardoen, A. Fabbri, F. McGregor, E. Liu

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The target of this paper is to investigate how saturated poroelastic soils subject to freezing temperatures behave and how different boundary conditions can intervene and affect the thermo-hydro-mechanical (THM) responses, based on a particular but classical configuration of a finite homogeneous soil layer studied by Terzaghi. The essential relations on the constitutive behavior of a freezing soil are firstly recalled: ice crystal - liquid water thermodynamic equilibrium, hydromechanical constitutive equations, momentum balance, water mass balance, and the thermal diffusion equation, in general, non-linear case where material parameters are state-dependent. The system of equations is firstly linearized, assuming all material parameters to be constants, particularly the permeability of liquid water, which should depend on the ice content. Two analytical solutions solved by the classic Laplace transform are then developed, accounting for two different sets of boundary conditions. Afterward, the general non-linear equations with state-dependent parameters are solved using a commercial code COMSOL based on finite elements method to obtain numerical results. The validity of this numerical modeling is partially verified using the analytical solution in the limiting case of state-independent parameters. Comparison between the results given by the linearized analytical solutions and the non-linear numerical model reveals that the above-mentioned linear computation will always underestimate the liquid pore pressure and displacement, whatever the hydraulic boundary conditions are. In the nonlinear model, the faster growth of ice crystals, accompanying the subsequent reduction of permeability of freezing soil layer, makes a longer duration for the depressurization of water liquid and slower settlement in the case where the ground surface is swiftly covered by a thin layer of ice, as well as a bigger global liquid pressure and swelling in the case of the impermeable ground surface. Nonetheless, the analytical solutions based on linearized equations give a correct order-of-magnitude estimate, especially at moderate temperature variations, and remain a useful tool for preliminary design checks.

Keywords: chemical potential, cryosuction, Laplace transform, multiphysics coupling, phase transformation, thermodynamic equilibrium

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Authors: Hamidreza Bagheri, Alireza Shariati

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There are many difficulties in the purification of raw components and products. However, researchers are seeking better ways for purification. One of the recent methods is extraction using supercritical fluids. In this study, the phase equilibria of benzoic acid-supercritical carbon dioxide system were investigated. Regarding the phase equilibria of this system, the modeling of solid-supercritical fluid behavior was performed using the Perturbed-Chain Statistical Association Fluid Theory (PC-SAFT) and Peng-Robinson equations of state (PR EoS). For this purpose, five PC-SAFT EoS parameters for pure benzoic acid were obtained using its experimental vapor pressure. Benzoic acid has association sites and the behavior of the benzoic acid-supercritical fluid system was well-predicted using both equations of state, while the binary interaction parameter values for PR EoS were negative. Genetic algorithm, which is one of the most accurate global optimization algorithms, was also used to optimize the pure benzoic acid parameters and the binary interaction parameters. The AAD% value for the PC-SAFT EoS, were 0.22 for the carbon dioxide-benzoic acid system.

Keywords: supercritical fluids, solubility, solid, PC-SAFT EoS, genetic algorithm

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Authors: Yang Zhong, Meijie Xue

Abstract:

The purpose of this paper is to investigate the stresses and excess pore fluid pressure induced by the moving wheel pressure on saturated asphalt pavements, which is one of the reasons for a damage phenomenon in flexible pavement denoted stripping. The saturated asphalt pavement is modeled as multilayered poroelastic half space exerted by a wheel pressure, which is moving at a constant velocity along the surface of the pavement. The governing equations for the proposed analysis are based on the Biot’s theory of dynamics in saturated poroelastic medium. The governing partial differential equations are solved by using Laplace and Hankel integral transforms. The solutions for the stresses and excess pore pressure are expressed in the forms of numerical inversion Laplace and Hankel integral transforms. The numerical simulation results clearly demonstrate the induced deformation and water flow in the asphalt pavement.

Keywords: saturated asphalt pavements, moving loads, excess pore fluid pressure, stress of pavement, biot theory, stress and strain of pavement

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Authors: M. Salmanpour, O. Nourani Zonouz

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In this research, a numerical simulation of an Electrohydrodynamic (EHD) actuator’s effects on the flow around a square cylinder by using a finite volume method has been investigated. This is one of the newest ways for controlling the fluid flows. Two plate electrodes are flush-mounted on the surface of the cylinder and one wire electrode is placed on the line with zero angle of attack relative to the stagnation point and excited with DC power supply. The discharge produces an electric force and changes the local momentum behaviors in the fluid layers. For this purpose, after selecting proper domain and boundary conditions, the electric field relating to the problem has been analyzed and then the results in the form of electrical body force have been entered in the governing equations of fluid field (Navier-Stokes equations). The effect of ionic wind resulted from the Electrohydrodynamic actuator, on the velocity, pressure and the wake behind cylinder has been considered. According to the results, it is observed that the fluid flow accelerates in the nearest wall of the frontal half of the cylinder and the pressure difference between frontal and hinder cylinder is increased.

Keywords: CFD, corona discharge, electro hydrodynamics, flow around square cylinders, simulation

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Authors: Rui Sun, Tamer M. Ismail, Xiaohan Ren, M. Abd El-Salam

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Incineration of municipal solid waste (MSW) is one of the key scopes in the global clean energy strategy. A computational fluid dynamics (CFD) model was established. In order to reveal these features of the combustion process in a fixed porous bed of MSW. Transporting equations and process rate equations of the waste bed were modeled and set up to describe the incineration process, according to the local thermal conditions and waste property characters. Gas phase turbulence was modeled using k-ε turbulent model and the particle phase was modeled using the kinetic theory of granular flow. The heterogeneous reaction rates were determined using Arrhenius eddy dissipation and the Arrhenius-diffusion reaction rates. The effects of primary air flow rate and temperature in the burning process of simulated MSW are investigated experimentally and numerically. The simulation results in bed are accordant with experimental data well. The model provides detailed information on burning processes in the fixed bed, which is otherwise very difficult to obtain by conventional experimental techniques.

Keywords: computational fluid dynamics (CFD) model, waste incineration, municipal solid waste (MSW), fixed bed, primary air

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Authors: Behzad Ali Khan, M. Zubair Akbar Qureshi

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The article analyzes the Darcy Forchheimer 2D Hybrid ferrofluid. The flow of a Hybrid ferrofluid is made due to an unsteady porous channel. The classical liquid water is treated as a based liquid. The flow in the permeable region is characterized by the Darcy-Forchheimer relation. Heat transfer phenomena are studied during the flow. The transformation of a partial differential set of equations into a strong ordinary differential frame is formed through appropriate variables. The numerical Shooting Method is executed for solving the simplified set of equations. In addition, a numerical analysis (ND-Solve) is utilized for the convergence of the applied technique. The influence of some flow model quantities like Pr (Prandtle number), r (porous medium parameter), F (Darcy-porous medium parameter), Re (Reynolds number), Pe (Peclet number) on velocity and temperature field are scrutinized and studied through sketches. Certain physical factors like f ''(η) (skin friction coefficient) and θ^'(η) (rate of heat transfer) are first derived and then presented through tables.

Keywords: darcy forcheimer, hybrid ferro fluid, porous medium, porous channel

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Authors: Tejeet Singh, Ishvneet Singh, Vinay Gupta

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The present study focussed on carrying out the creep analysis in an isotropic thick-walled composite cylindrical pressure vessel composed of aluminium matrix reinforced with silicon-carbide in particulate form. The creep behaviour of the composite material has been described by the threshold stress based creep law. The value of stress exponent appearing in the creep law was selected as 3, 5 and 8. The constitutive equations were developed using well known von-Mises yield criteria. Models were developed to find out the distributions of creep stresses and strain rate in thick-walled composite cylindrical pressure vessels under internal pressure. In order to obtain the stress distributions in the cylinder, the equilibrium equation of the continuum mechanics and the constitutive equations are solved together. It was observed that the radial stress, tangential stress and axial stress increases along with the radial distance. The cross-over was also obtained almost at the middle region of cylindrical vessel for tangential and axial stress for different values of stress exponent. The strain rates were also decreasing in nature along the entire radius.

Keywords: creep, composite, cylindrical vessel, internal pressure

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Authors: Nazish Iftikhar, Adil Jhangeer, Tayyaba Naz

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The universe is expanding at an accelerated rate. Symmetries are useful in understanding universe’s behavior. Emmy Noether reported the relation between symmetries and conservation laws. These symmetries are known as Noether symmetries which correspond to a conserved quantity. In differential equations, conservation laws play an important role. Noether symmetries are helpful in modified theories of gravity. Time independent plane symmetric spacetime was classified by Noether`s theorem. By using Noether`s theorem, set of linear partial differential equations was obtained having A(r), B(r) and F(r) as unknown radial functions. The Lagrangian corresponding to considered spacetime in the Noether equation was used to get Noether operators. Different possibilities of radial functions were considered. Firstly, all functions were same. All the functions were considered as non-zero constant, linear, reciprocal and exponential respectively. Secondly, two functions were proportional to each other keeping third function different. Second case has four subcases in which four different relationships between A(r), B(r) and F(r) were discussed. In all cases, we obtained nontrivial Noether operators including gauge term. Conserved quantities for each Noether operators were also presented.

Keywords: Noether gauge symmetries, radial function, Noether operator, conserved quantities

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Authors: Yasunori Kobori, Futoshi Fukaya, Takuya Arafune, Nobukazu Tsukiji, Nobukazu Takai, Haruo Kobayashi

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This paper proposes an EMI spread spectrum technique to enable to set notch frequencies using pulse coding method for DC-DC switching converters of communication equipment. The notches in the spectrum of the switching pulses appear at the frequencies obtained from empirically derived equations with the proposed spread spectrum technique using the pulse coding methods, the PWM (Pulse Width Modulation) coding or the PCM (Pulse Cycle Modulation) coding. This technique would be useful for the switching converters in the communication equipment which receives standard radio waves, without being affected by noise from the switching converters. In our proposed technique, the notch frequencies in the spectrum depend on the pulse coding method. We have investigated this technique to apply to the switching converters and found that there is good relationship agreement between the notch frequencies and the empirical equations. The notch frequencies with the PWM coding is equal to the equation F=k/(WL-WS). With the PCM coding, that is equal to the equation F=k/(TL-TS).

Keywords: notch frequency, pulse coding, spread spectrum, switching converter

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Authors: Mohamed E. Eleshaky

Abstract:

This paper investigates the dynamic behavior of laminar water flows inside superhydrophobic micro-pipes patterned with square micro-posts features under different operating conditions. It also investigates the effects of air fraction and Reynolds number on the frictional performance of these pipes. Rather than modeling the air-water interfaces of superhydrophobic as a flat inflexible surface, a transient, incompressible, three-dimensional, volume-of-fluid (VOF) methodology has been employed to continuously track the air–water interface shape inside micro-pipes. Also, the entrance effects on the flow field have been taken into consideration. The results revealed the strong dependency of the frictional performance on the air fractions and Reynolds number. The frictional resistance reduction becomes increasingly more significant at large air fractions and low Reynolds numbers. Increasing Reynolds number has an adverse effect on the frictional resistance reduction.

Keywords: drag reduction, laminar flow in micropipes, numerical simulation, superhyrophobic surfaces, microposts

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Authors: Samuel Ahamefula

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Turbulent motion is a highly nonlinear and complex phenomenon, and its modelling is still very challenging. In this study, we developed a hybrid computational approach to accurately simulate fluid turbulence phenomenon. The focus is coupling and transitioning between Direct Numerical Simulation (DNS) and Large Eddy Simulating Wall Models (LES-WM) regions. In the framework, high-order fidelity fluid dynamical methods are utilized to simulate the unsteady compressible Navier-Stokes equations in the Eulerian format on the unstructured moving grids. The coupling and transitioning of DNS and LES-WM are conducted through the linearly staggered Dirichlet-Neumann coupling scheme. The high-fidelity framework is verified and validated based on namely, DNS ability for capture full range of turbulent scales, giving accurate results and LES-WM efficiency in simulating near-wall turbulent boundary layer by using wall models.

Keywords: computational methods, turbulence modelling, turbulence entropy, navier-stokes equations

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Authors: K. Soldatova, Y. Galerkin

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A loading factor performance is necessary for the modeling of centrifugal compressor gas dynamic performance curve. Measured loading factors are linear function of a flow coefficient at an impeller exit. The performance does not depend on the compressibility criterion. To simulate loading factor performances, the authors present two parameters: a loading factor at zero flow rate and an angle between an ordinate and performance line. The calculated loading factor performances of non-viscous are linear too and close to experimental performances. Loading factor performances of several dozens of impellers with different blade exit angles, blade thickness and number, ratio of blade exit/inlet height, and two different type of blade mean line configuration. There are some trends of influence, which are evident – comparatively small blade thickness influence, and influence of geometry parameters is more for impellers with bigger blade exit angles, etc. Approximating equations for both parameters are suggested. The next phase of work will be simulating of experimental performances with the suggested approximation equations as a base.

Keywords: loading factor performance, centrifugal compressor, impeller, modeling

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Authors: Gilbert Makanda

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The problem of free convection from a perforated spinning cone with viscous dissipation, temperature-dependent viscosity, and partial slip was studied. The boundary layer velocity and temperature profiles were numerically computed for different values of the spin, viscosity variation, inertia drag force, Eckert, suction/blowing parameters. The partial differential equations were transformed into a system of ordinary differential equations which were solved using the fourth-order Runge-Kutta method. This paper considered the effect of partial slip and spin parameters on the swirling velocity profiles which are rarely reported in the literature. The results obtained by this method was compared to those in the literature and found to be in agreement. Increasing the viscosity variation parameter, spin, partial slip, Eckert number, Darcian drag force parameters reduce swirling velocity profiles.

Keywords: free convection, suction/injection, partial slip, viscous dissipation

Procedia PDF Downloads 245

Authors: R. Haoui

Abstract:

The purpose of this work is to simulate the flow at the exit of Vulcan 1 engine of European launcher Ariane 5. The geometry of the propellant nozzle is already determined using the characteristics method. The pressure in the outlet section of the nozzle is less than atmospheric pressure on the ground, causing the existence of oblique and normal shock waves at the exit. During the rise of the launcher, the atmospheric pressure decreases and the shock wave disappears. The code allows the capture of shock wave at exit of nozzle. The numerical technique uses the Flux Vector Splitting method of Van Leer to ensure convergence and avoid the calculation instabilities. The Courant, Friedrichs and Lewy coefficient (CFL) and mesh size level are selected to ensure the numerical convergence. The nonlinear partial derivative equations system which governs this flow is solved by an explicit unsteady numerical scheme by the finite volume method. The accuracy of the solution depends on the size of the mesh and also the step of time used in the discretized equations. We have chosen in this study the mesh that gives us a stationary solution with good accuracy.

Keywords: finite volume, lunchers, nozzles, shock wave

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Authors: Humayun R. H. Kabir

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An analytical solution before used for static and free-vibration response has been extended for thermal buckling response on cylindrical panel with anti-symmetric laminations. The partial differential equations that govern kinematic behavior of shells produce five coupled differential equations. The basic displacement and rotational unknowns are similar to first order shear deformation theory---three displacement in spatial space, and two rotations about in-plane axes. No drilling degree of freedom is considered. Boundary conditions are considered as complete hinge in all edges so that the panel respond on thermal inductions. Two sets of double Fourier series are considered in the analytical solution process. The sets are selected that satisfy mixed type of natural boundary conditions. Numerical results are presented for the first 10 eigenvalues, and first 10 mode shapes for Ux, Uy, and Uz components. The numerical results are compared with a finite element based solution.

Keywords: higher order shear deformation, composite, thermal buckling, angle-ply laminations

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Authors: Mostafa Sefidgar, Kaamran Raahemifar, Hossein Bazmara, Madjid Soltani

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The computational methods provide condition for investigation related to the process of drug delivery, such as convection and diffusion of drug in extracellular matrices, and drug extravasation from microvascular. The information of this process clarifies the mechanisms of drug delivery from the injection site to absorption by a solid tumor. In this study, an advanced numerical method is used to solve fluid flow and solute transport equations simultaneously to show how capillary network structure induced by tumor affects drug delivery. The effect of heterogeneous capillary network induced by tumor on interstitial fluid flow and drug delivery is investigated by this multi scale method. The sprouting angiogenesis model is used for generating capillary network induced by tumor. Fluid flow governing equations are implemented to calculate blood flow through the tumor-induced capillary network and fluid flow in normal and tumor tissues. The Starling’s law is used for closing this system of equations and coupling the intravascular and extravascular flows. Finally, convection-diffusion-reaction equation is used to simulate drug delivery. The dynamic approach which changes the capillary network structure based on signals sent by hemodynamic and metabolic stimuli is used in this study for more realistic assumption. The study indicates that drug delivery to solid tumors depends on the tumor induced capillary network structure. The dynamic approach generates the irregular capillary network around the tumor and predicts a higher interstitial pressure in the tumor region. This elevated interstitial pressure with irregular capillary network leads to a heterogeneous distribution of drug in the tumor region similar to in vivo observations. The investigation indicates that the drug transport properties have a significant role against the physiological barrier of drug delivery to a solid tumor.

Keywords: solid tumor, physiological barriers to drug delivery, angiogenesis, microvascular network, solute transport

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Authors: L. Rakesh, T. Y. Heblekar

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This study entails the development and optimization of a mathematical model for a floating drum biogas reactor from first principles using thermal and empirical considerations. The model was derived on the basis of mass conservation, lumped mass heat transfer formulations and empirical biogas formation laws. The treatment leads to a system of coupled nonlinear ordinary differential equations whose solution mapped four-time independent controllable parameters to five output variables which adequately serve to describe the reactor performance. These equations were solved numerically using fourth order Runge-Kutta method for a range of input parameter values. Using the data so obtained an Artificial Neural Network with a single hidden layer was trained using Levenberg-Marquardt Damped Least Squares (DLS) algorithm. This network was then fine-tuned for optimal mapping by varying hidden layer size. This fast forward model was then employed as a health score generator in the Bacterial Foraging Optimization code. The optimal operating state of the simplified Biogas reactor was thus obtained.

Keywords: biogas, floating drum reactor, neural network model, optimization

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Authors: Yuri V. Kim

Abstract:

This article presents a new approach to the Functional Testing of Space Systems (SS). It can be considered as a generic test and used for a wide class of SS that from the point of view of System Dynamics and Control may be described by the ordinary differential equations. Suggested methodology is based on using semi-natural experiment- laboratory stand that doesn’t require complicated, precise and expensive technological control-verification equipment. However, it allows for testing system as a whole totally assembled unit during Assembling, Integration and Testing (AIT) activities, involving system hardware (HW) and software (SW). The test physically activates system input (sensors) and output (actuators) and requires recording their outputs in real time. The data is then inserted in laboratory PC where it is post-experiment processed by Matlab/Simulink Identification Toolbox. It allows for estimating system dynamics in form of estimation of system differential equations by the experimental way and comparing them with expected mathematical model prematurely verified by mathematical simulation during the design process.

Keywords: system dynamics, space system ground tests and space qualification, system dynamics identification, satellite attitude control, assembling, integration and testing

Procedia PDF Downloads 163

Authors: M. Towhidur Rahman, Nasim Zaman Piyas, M. Sadiqul Baree, Shahnewaz Ahmed

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The design of high-speed craft has recently become one of the most active areas of naval architecture. Speed increase makes these vehicles more efficient and useful for military, economic or leisure purpose. The planing hull is designed specifically to achieve relatively high speed on the surface of the water. Speed on the water surface is closely related to the size of the vessel and the installed power. The Savitsky method was first presented in 1964 for application to non-monohedric hulls and for application to stepped hulls. This method is well known as a reliable comparative to CFD analysis of hull resistance. A computer program based on Savitsky’s method has been developed using MATLAB. The power of high-speed vessels has been computed in this research. At first, the program reads some principal parameters such as displacement, LCG, Speed, Deadrise angle, inclination of thrust line with respect to keel line etc. and calculates the resistance of the hull using empirical planning equations of Savitsky. However, some functions used in the empirical equations are available only in the graphical form, which is not suitable for the automatic computation. We use digital plotting system to extract data from nomogram. As a result, value of wetted length-beam ratio and trim angle can be determined directly from the input of initial variables, which makes the power calculation automated without manually plotting of secondary variables such as p/b and other coefficients and the regression equations of those functions are derived by using data from different charts. Finally, the trim angle, mean wetted length-beam ratio, frictional coefficient, resistance, and power are computed and compared with the results of Savitsky and good agreement has been observed.

Keywords: nomogram, planing hull, principal parameters, regression

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Authors: Maciej Major, Izabela Major

Abstract:

The aim of this paper is a numerical analysis of three-layered block design to walls construction subjected to the dynamic load. The block consists of the layers: concrete with rubber pads in shape of crosses, space filled with air and concrete with I-shape rubber pads. The main purpose of rubber inserts embedded during the production process is additional protection against the transversal dynamic load. For the analysis, as rubber, the Zahorski hyperelastic incompressible material model was assumed. A concentrated force as dynamic load applied to the external block surface was investigated. The results for the considered block observed as the stress distribution plot were compared to the results obtained for the solid concrete block. In order to estimate the percentage damping of proposed composite, rubber-concrete block in relation to the solid block the numerical analysis with the use of finite element method based on ADINA software was performed.

Keywords: dynamics, composite, rubber, Zahorski

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Authors: Tejeet Singh, Ishavneet Singh

Abstract:

The present study focused on carrying out the creep analysis in an isotropic thick-walled composite cylindrical pressure vessel composed of aluminum matrix reinforced with silicon-carbide in particulate form. The creep behavior of the composite material has been described by the threshold stress based creep law. The values of stress exponent appearing in the creep law were selected as 3, 5 and 8. The constitutive equations were developed using well known von-Mises yield criteria. Models were developed to find out the distributions of creep stress and strain rate in thick-walled composite cylindrical pressure vessels under internal pressure. In order to obtain the stress distributions in the cylinder, the equilibrium equation of the continuum mechanics and the constitutive equations are solved together. It was observed that the radial stress, tangential stress and axial stress increases along with the radial distance. The cross-over was also obtained almost at the middle region of cylindrical vessel for tangential and axial stress for different values of stress exponent. The strain rates were also decreasing in nature along the entire radius.

Keywords: steady state creep, composite, cylinder, pressure

Procedia PDF Downloads 417

Authors: Romulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales

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This paper presents a rigorous study of advanced functional spaces, with a focus on Sobolev and Besov spaces, to investigate key aspects of fluid dynamics, including the regularity of solutions to the Navier-Stokes equations, hypercomplex bifurcations, and turbulence. We offer a comprehensive analysis of Sobolev embedding theorems in fractional spaces and apply bifurcation theory within quaternionic dynamical systems to better understand the complex behaviors in fluid systems. Additionally, the research delves into energy dissipation mechanisms in turbulent flows through the framework of Besov spaces. Key mathematical tools, such as interpolation theory, Littlewood-Paley decomposition, and energy cascade models, are integrated to develop a robust theoretical approach to these problems. By addressing challenges related to the existence and smoothness of solutions, this work contributes to the ongoing exploration of the open Navier-Stokes problem, providing new insights into the intricate relationship between fluid dynamics and functional spaces.

Keywords: navier-stokes equations, hypercomplex bifurcations, turbulence, sobolev and besov space

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Authors: Xiao-Dong Wang, Wei-Mon Yan

Abstract:

The flow field design in the bipolar plates affects the performance of the proton exchange membrane (PEM) fuel cell. This work adopted a combined optimization procedure, including a simplified conjugate-gradient method and a completely three-dimensional, two-phase, non-isothermal fuel cell model, to look for optimal flow field design for a single serpentine fuel cell of size 9×9 mm with five channels. For the direct solution, the two-fluid method was adopted to incorporate the heat effects using energy equations for entire cells. The model assumes that the system is steady; the inlet reactants are ideal gases; the flow is laminar; and the porous layers such as the diffusion layer, catalyst layer and PEM are isotropic. The model includes continuity, momentum and species equations for gaseous species, liquid water transport equations in the channels, gas diffusion layers, and catalyst layers, water transport equation in the membrane, electron and proton transport equations. The Bulter-Volumer equation was used to describe electrochemical reactions in the catalyst layers. The cell output power density Pcell is maximized subjected to an optimal set of channel heights, H1-H5, and channel widths, W2-W5. The basic case with all channel heights and widths set at 1 mm yields a Pcell=7260 Wm-2. The optimal design displays a tapered characteristic for channels 1, 3 and 4, and a diverging characteristic in height for channels 2 and 5, producing a Pcell=8894 Wm-2, about 22.5% increment. The reduced channel heights of channels 2-4 significantly increase the sub-rib convection and widths for effectively removing liquid water and oxygen transport in gas diffusion layer. The final diverging channel minimizes the leakage of fuel to outlet via sub-rib convection from channel 4 to channel 5. Near-optimal design without huge loss in cell performance but is easily manufactured is tested. The use of a straight, final channel of 0.1 mm height has led to 7.37% power loss, while the design with all channel widths to be 1 mm with optimal channel heights obtained above yields only 1.68% loss of current density. The presence of a final, diverging channel has greater impact on cell performance than the fine adjustment of channel width at the simulation conditions set herein studied.

Keywords: optimization, flow field design, simplified conjugate-gradient method, serpentine flow field, sub-rib convection

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Authors: Gulshan Sachdeva, Ram Bilash

Abstract:

In this paper, the exergy analysis of vapor absorption refrigeration system using LiBr-H2O as working fluid is carried out with the modified Gouy-Stodola approach rather than the classical Gouy-Stodola equation and effect of varying input parameters is also studied on the performance of the system. As the modified approach uses the concept of effective temperature, the mathematical expressions for effective temperature have been formulated and calculated for each component of the system. Various constraints and equations are used to develop program in EES to solve these equations. The main aim of this analysis is to determine the performance of the system and the components having major irreversible loss. Results show that exergy destruction rate is considerable in absorber and generator followed by evaporator and condenser. There is an increase in exergy destruction in generator, absorber and condenser and decrease in the evaporator by the modified approach as compared to the conventional approach. The value of exergy determined by the modified Gouy Stodola equation deviates maximum i.e. 26% in the generator as compared to the exergy calculated by the classical Gouy-Stodola method.

Keywords: exergy analysis, Gouy-Stodola, refrigeration, vapor absorption

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Authors: Carlos Teodoro, Oscar Bautista

Abstract:

In this work, we analyze theoretically the mass transport in a time-periodic electroosmotic flow through a parallel flat plate microchannel under different periodic functions of the applied external electric field. The microchannel connects two reservoirs having different constant concentrations of an electro-neutral solute, and the zeta potential of the microchannel walls are assumed to be uniform. The governing equations that allow determining the mass transport in the microchannel are given by the Poisson-Boltzmann equation, the modified Navier-Stokes equations, where the Debye-Hückel approximation is considered (the zeta potential is less than 25 mV), and the species conservation. These equations are nondimensionalized and four dimensionless parameters appear which control the mass transport phenomenon. In this sense, these parameters are an angular Reynolds, the Schmidt and the Péclet numbers, and an electrokinetic parameter representing the ratio of the half-height of the microchannel to the Debye length. To solve the mathematical model, first, the electric potential is determined from the Poisson-Boltzmann equation, which allows determining the electric force for various periodic functions of the external electric field expressed as Fourier series. In particular, three different excitation wave forms of the external electric field are assumed, a) sawteeth, b) step, and c) a periodic irregular functions. The periodic electric forces are substituted in the modified Navier-Stokes equations, and the hydrodynamic field is derived for each case of the electric force. From the obtained velocity fields, the species conservation equation is solved and the concentration fields are found. Numerical calculations were done by considering several binary systems where two dilute species are transported in the presence of a carrier. It is observed that there are different angular frequencies of the imposed external electric signal where the total mass transport of each species is the same, independently of the molecular diffusion coefficient. These frequencies are called crossover frequencies and are obtained graphically at the intersection when the total mass transport is plotted against the imposed frequency. The crossover frequencies are different depending on the Schmidt number, the electrokinetic parameter, the angular Reynolds number, and on the type of signal of the external electric field. It is demonstrated that the mass transport through the microchannel is strongly dependent on the modulation frequency of the applied particular alternating electric field. Possible extensions of the analysis to more complicated pulsation profiles are also outlined.

Keywords: electroosmotic flow, mass transport, oscillatory flow, species separation

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Authors: Aarthi Sridhar, Henri Gavin, Karah Kelly

Abstract:

Rolling Isolation Systems (RISs) are simple and effective means to mitigate earthquake hazards to equipment in critical and precious facilities, such as hospitals, network collocation facilities, supercomputer centers, and museums. The RIS works by isolating components acceleration the inertial forces felt by the subsystem. The RIS consists of two platforms with counter-facing concave surfaces (dishes) in each corner. Steel balls lie inside the dishes and allow the relative motion between the top and bottom platform. Formerly, a mathematical model for the dynamics of RISs was developed using Lagrange’s equations (LE) and experimentally validated. A new mathematical model was developed using Gauss’s Principle of Least Constraint (GPLC) and verified by comparing impulse response trajectories of the GPLC model and the LE model in terms of the peak displacements and accelerations of the top platform. Mathematical models for the RIS are tedious to derive because of the non-holonomic rolling constraints imposed on the system. However, using Gauss’s Principle of Least constraint to find the equations of motion removes some of the obscurity and yields a system that can be easily extended. Though the GPLC model requires more state variables, the equations of motion are far simpler. The non-holonomic constraint is enforced in terms of accelerations and therefore requires additional constraint stabilization methods in order to avoid the possibility that numerical integration methods can cause the system to go unstable. The GPLC model allows the incorporation of more physical aspects related to the RIS, such as contribution of the vertical velocity of the platform to the kinetic energy and the mass of the balls. This mathematical model for the RIS is a tool to predict the motion of the isolation platform. The ability to statistically quantify the expected responses of the RIS is critical in the implementation of earthquake hazard mitigation.

Keywords: earthquake hazard mitigation, earthquake isolation, Gauss’s Principle of Least Constraint, nonlinear dynamics, rolling isolation system

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Authors: Seyyed Feisal Asbaghian Namin, Reza Pilafkan, Mahmood Kaffash Irzarahimi

Abstract:

TThis paper considers vibration of single-layered graphene sheets using molecular dynamics (MD) and nonlocal elasticity theory. Based on the MD simulations, Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), an open source software, is used to obtain fundamental frequencies. On the other hand, governing equations are derived using nonlocal elasticity and first order shear deformation theory (FSDT) and solved using generalized differential quadrature method (GDQ). The small-scale effect is applied in governing equations of motion by nonlocal parameter. The effect of different side lengths, boundary conditions and nonlocal parameter are inspected for aforementioned methods. Results are obtained from MD simulations is compared with those of the nonlocal elasticity theory to calculate appropriate values for the nonlocal parameter. The nonlocal parameter value is suggested for graphene sheets with various boundary conditions. Furthermore, it is shown that the nonlocal elasticity approach using classical plate theory (CLPT) assumptions overestimates the natural frequencies.

Keywords: graphene sheets, molecular dynamics simulations, fundamental frequencies, nonlocal elasticity theory, nonlocal parameter

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