Search results for: coupled differential equation

Authors: Elio El Kahi, Michel Khouri, Olivier Deck, Pierre Rahme, Rasool Mehdizadeh

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Recent developments in civil engineering create multiple interaction problems between the soil and the structure. One of the major problems is the impact of ground movements on buildings. Consequently, managing risks associated with these movements, requires a determination of the different influencing factors and a specific knowledge of their variability/uncertainty. The main purpose of this research is to study the behavior of structures submitted to differential settlement, in order to assess their vulnerability, taking into consideration the different sources of uncertainties. Analytical approach is applied to investigate on one hand the influence of these uncertainties that are related to the soil, and on the other hand the structure stiffness variation with the presence of openings and the movement transmitted between them as related to the origin and shape of the free-field movement. Results reveal the effect of taking these uncertainties into consideration, and specify the dominant and most significant parameters that control the ground movement associated with the Soil-Structure Interaction (SSI) phenomenon.

Keywords: analytical approach, building, damage, differential settlement, soil-structure interaction, uncertainties

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Authors: Prerana Sharma

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Effect of relativistic nonlinearity on stimulated Raman scattering of the propagating laser beam carrying null intensity in center (hollow Gaussian beam) by excited plasma wave are studied in a collisionless plasma. The construction of the equations is done employing the fluid theory which is developed with partial differential equation and Maxwell’s equations. The analysis is done using eikonal method. The phenonmenon of Stimulated Raman scattering is shown along with the excitation of seed plasma wave. The power of plasma wave and back reflectivity is observed for higher order of hollow Gaussian beam. Back reflectivity is studied numerically for various orders of HGLB with different value of plasma density, laser power and beam radius. Numerical analysis shows that these parameters play vital role on reflectivity characteristics.

Keywords: Hollow Gaussian beam, relativistic nonlinearity, plasma physics, Raman scattering

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Authors: Manu Manu, Pardha J. Saradhi, Ramana M. V. Murthy

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Wind Energy is accepted as one of the most developed, cost effective and proven renewable energy technologies to meet increasing electricity demands in a sustainable manner. Preliminary assessment studies along Indian Coastline by Ministry of New and Renewable Energy have indicated prospects for development of offshore wind power along Tamil Nadu Coast, India. The commercial viability of a wind project mainly depends on wind characteristics on site. Hence, it is internationally recommended to perform site-specific wind resource assessment based on two years’ wind profile as a part of the feasibility study. Conventionally, guy wire met mast are used onshore for the collection of wind profile. Installation of similar structure in offshore requires complex marine spread and are very expensive. In the present study, an attempt is made to develop 120 m long lattice tower supported on the jacket, piled to the seabed at Rameshwaram, Tamil Nadu, India. Offshore met-masts are subjected to combined wind and hydrodynamic loads, and these lateral loads should be safely transferred to soil. The wind loads are estimated based on gust factor method, and the hydrodynamic loads are estimated by Morison’s equation along with suitable wave theory. The soil is modeled as three nonlinear orthogonal springs based on API standards. The structure configuration and optimum member sizes are obtained for extreme cyclone events. The dynamic behavior of mast under coupled wind and wave loads is also studied. The static responses of a mast with jacket type offshore platform have been studied using a frame model in SESAM. It is found from the study that the maximum displacement at the top of the mast for the random wave is 0.003 m and that of the tower for wind is 0.08 m during the steady state. The dynamic analysis results indicate that the structure is safe against coupled wind and wave loading.

Keywords: offshore wind, mast, static, aerodynamic load, hydrodynamic load

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Authors: Elmongi Elbellili, Ben Lauwens, Daan Huybrechs

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The increasing complexity of modern engineering systems presents a challenge to the digital simulation of these systems which usually can be represented by differential equations. The Linearly Implicit Quantized State System (LIQSS) offers an alternative approach to traditional numerical integration techniques for solving Ordinary Differential Equations (ODEs). This method proved effective for handling discontinuous and large stiff systems. However, the inherent discrete nature of LIQSS may introduce oscillations that result in unnecessary computational steps. The current oscillation detection mechanism relies on a condition that checks the significance of the derivatives, but it could be further improved. This paper describes a different cycle detection mechanism and presents the outcomes using LIQSS order one in simulating the Advection Diffusion problem. The efficiency of this new cycle detection mechanism is verified by comparing the performance of the current solver against the new version as well as a reference solution using a Runge-Kutta method of order14.

Keywords: numerical integration, quantized state systems, ordinary differential equations, stiffness, cycle detection, simulation

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Authors: Kushakov Kholmurodjon, Muhammadjonov Akbarshox

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This present paper is devoted to a system of second-order nonlinear differential equations with a special right-hand side, exactly, the linear part and a third-order polynomial of a special form. It is shown that for some relations between the parameters, there is a second-order curve in which trajectories leaving the points of this curve remain in the same place. Thus, the curve is invariant with respect to the given system. Moreover, this system is invariant under a non-degenerate linear transformation of variables. The form of this curve, depending on the relations between the parameters and the eigenvalues of the matrix, is proved. All solutions of this system of differential equations are shown analytically.

Keywords: dynamic system, ellipse, hyperbola, Hess system, polar coordinate system

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Authors: J. A. Gbadeyan, R. A. Kareem

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In this paper, we investigated the effects of unsteady internal heat generation of a two-step exothermic reactive hydromagnetic fluid flow under different chemical kinetics namely: Sensitized, Arrhenius and Bimolecular kinetics through an isothermal wall temperature channel. The resultant modeled nonlinear partial differential equations were simplified and solved using a combined Laplace-Differential Transform Method (LDTM). The solutions obtained were discussed and presented graphically to show the salient features of the fluid flow and heat transfer characteristics.

Keywords: unsteady, reactive, hydromagnetic, couette ow, exothermi creactio

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Authors: Seyed Abolhassan Naeini, Azam Kouhpeyma

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Reduction of water level at which a slope is submerged with it is called drawdown. Draw down can took place rapidly or slowly and in both situations, it can affect slope stability. Using coupled analysis (seepage and stability analysis) causes more accurate results. In this study, the stability of homogeneous embankment is investigated numerically. Slope safety factor changes due to changes in three factors of height, slope and drawdown rate have been investigated and compared. It was found that with increasing height and slope, the safety factor decreases, and with increasing the discharge rate, the safety factor increases.

Keywords: drawdown, slope stability, coupled seepage and stability analysis

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Authors: M. R. Akbari, P. Soleimani, R. Khalili, Sara Akbari

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Analyzing and modeling the vibrational behavior of arched bridges during the earthquake in order to decrease the exerted damages to the structure is a very hard task to do. This item has been done analytically in the present paper for the first time. Due to the importance of building arched bridges as a great structure in the human being civilization and its specifications such as transferring vertical loads to its arcs and the lack of bending moments and shearing forces, this case study is devoted to this special issue. Here, the nonlinear vibration of arched bridges has been modeled and simulated by an arched beam with harmonic vertical loads and its behavior has been investigated by analyzing a nonlinear partial differential equation governing the system. It is notable that the procedure has been done analytically by AGM (Akbari, Ganji Method). Furthermore, comparisons have been made between the obtained results by numerical Method (rkf-45) and AGM in order to assess the scientific validity.

Keywords: new method (AGM), arched beam bridges, angular frequency, harmonic loads

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Authors: Sheryl Avendaño, Miguel Ospina, Hebert Montegranario

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Full Wave Inversion (FWI) is a variant of seismic tomography for obtaining velocity profiles by an optimization process that combine forward modelling (or solution of wave equation) with the misfit between synthetic and observed data. In this research we are modelling wave propagation in a visco-acoustic medium in the frequency domain. We apply finite differences for the numerical solution of the wave equation with a mix between usual and rotated grids, where density depends on velocity and there exists a damping function associated to a linear dissipative medium. The velocity profiles are obtained from an initial one and the data have been modeled for a frequency range 0-120 Hz. By an iterative procedure we obtain an estimated velocity profile in which are detailed the remarkable features of the velocity profile from which synthetic data were generated showing promising results for our method.

Keywords: seismic inversion, full wave inversion, visco acoustic wave equation, finite diffrence methods

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Authors: N. Smaoui, B. Chentouf

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The boundary stabilization problem of the rotating disk-beam system is a topic of interest in research studies. This system involves a flexible beam attached to the center of a disk, and the control and stabilization of this system have been extensively studied. This research focuses on the case where the center of mass is fixed in an inertial frame, and the rotation of the center is non-uniform. The system is represented by a set of nonlinear coupled partial differential equations and ordinary differential equations. The boundary stabilization problem of this system via a delayed boundary control is considered. We assume that the boundary control is either of a force type control or a moment type control and is subject to the presence of a constant time-delay. The aim of this research is threefold: First, we demonstrate that the rotating disk-beam system is well-posed in an appropriate functional space. Then, we establish the exponential stability property of the system. Finally, we provide numerical simulations that illustrate the theoretical findings. The research utilizes the semigroup theory to establish the well-posedness of the system. The resolvent method is then employed to prove the exponential stability property. Finally, the finite element method is used to demonstrate the theoretical results through numerical simulations. The research findings indicate that the rotating disk-beam system can be stabilized using a boundary control with a time delay. The proof of stability is based on the resolvent method and a variation of constants formula. The numerical simulations further illustrate the theoretical results. The findings have potential implications for the design and implementation of control strategies in similar systems. In conclusion, this research demonstrates that the rotating disk-beam system can be stabilized using a boundary control with time delay. The well-posedness and exponential stability properties are established through theoretical analysis, and these findings are further supported by numerical simulations. The research contributes to the understanding and practical application of control strategies for flexible structures, providing insights into the stability of rotating disk-beam systems.

Keywords: rotating disk-beam, delayed force control, delayed moment control, torque control, exponential stability

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Authors: Shidvash Vakilipour, Scott Ormiston, Masoud Mohammadi, Rouzbeh Riazi, Kimia Amiri, Sahar Barati

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Two-phase and multi-phase flows are common flow types in fluid mechanics engineering. Among the basic and applied problems of these flow types, two-phase parallel flow is the one that two immiscible fluids flow in the vicinity of each other. In this type of flow, fluid properties (e.g. density, viscosity, and temperature) are different at the two sides of the interface of the two fluids. The most challenging part of the numerical simulation of two-phase flow is to determine the location of interface accurately. In the present work, a coupled interface tracking algorithm is developed based on Arbitrary Lagrangian-Eulerian (ALE) approach using a cell-centered, pressure-based, coupled solver. To validate this algorithm, an analytical solution for fully developed two-phase flow in presence of gravity is derived, and then, the results of the numerical simulation of this flow are compared with analytical solution at various flow conditions. The results of the simulations show good accuracy of the algorithm despite using a nearly coarse and uniform grid. Temporal variations of interface profile toward the steady-state solution show that a greater difference between fluids properties (especially dynamic viscosity) will result in larger traveling waves. Gravity effect studies also show that favorable gravity will result in a reduction of heavier fluid thickness and adverse gravity leads to increasing it with respect to the zero gravity condition. However, the magnitude of variation in favorable gravity is much more than adverse gravity.

Keywords: coupled solver, gravitational force, interface tracking, Reynolds number to Froude number, two-phase flow

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Authors: Han Xue, Zhang Lanyue

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In order to seek more effective feature extraction technology, feature extraction method based on MFCC combined with vector hydrophone is exposed in the paper. The sound pressure signal and particle velocity signal of two kinds of ships are extracted by using MFCC and its evolution form, and the extracted features are fused by using fisher-ratio and correlated distance criterion. The features are then identified by BP neural network. The results showed that MFCC, First-Order Differential MFCC and Second-Order Differential MFCC features can be used as effective features for recognition of underwater targets, and the fusion feature can improve the recognition rate. Moreover, the results also showed that the recognition rate of the particle velocity signal is higher than that of the sound pressure signal, and it reflects the superiority of vector signal processing.

Keywords: vector information, MFCC, differential MFCC, fusion feature, BP neural network

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Authors: D. S. Naumann, B. J. Evans, O. Hassan

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This paper outlines the development of an automated aerodynamic optimisation algorithm using a novel method of parameterising a computational mesh by employing user–defined control nodes. The shape boundary movement is coupled to the movement of the novel concept of the control nodes via a quasi-1D-linear deformation. Additionally, a second order smoothing step has been integrated to act on the boundary during the mesh movement based on the change in its second derivative. This allows for both linear and non-linear shape transformations dependent on the preference of the user. The domain mesh movement is then coupled to the shape boundary movement via a Delaunay graph mapping. A Modified Cuckoo Search (MCS) algorithm is used for optimisation within the prescribed design space defined by the allowed range of control node displacement. A finite volume compressible NavierStokes solver is used for aerodynamic modelling to predict aerodynamic design fitness. The resulting coupled algorithm is applied to a range of test cases in two dimensions including the design of a subsonic, transonic and supersonic intake and the optimisation approach is compared with more conventional optimisation strategies. Ultimately, the algorithm is tested on a three dimensional wing optimisation case.

Keywords: mesh movement, aerodynamic shape optimization, cuckoo search, shape parameterisation

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Authors: Anyeres N. Atehortua Jimenez, J. David Lambraño, Juan Carlos Muñoz

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Navier-Stokes equations (NSE), which describe the dynamics of a fluid, have an important application on modeling waves used for data inversion techniques as full waveform inversion (FWI). In this work a linearized version of NSE and its variables, neglecting deviatoric terms of stress tensor, is presented. In order to get a theoretical modeling of pressure p(x,t) and wave velocity profile c(x,t), a wave equation of visco-acoustic medium (VAE) is written. A change of variables p(x,t)=q(x,t)h(ρ), is made on the equation for the VAE leading to a well known Klein-Gordon equation (KGE) describing waves propagating in variable density medium (ρ) with dispersive term α^2(x). KGE is reduced to a Poisson equation and solved by proposing a specific function for α^2(x) accounting for the energy dissipation and dispersion. Finally, an integral form solution is derived for p(x,t), c(x,t) and kinematics variables like particle velocity v(x,t), displacement u(x,t) and bulk modulus function k_b(x,t). Further, it is compared this visco-acoustic formulation with another form broadly used in the geophysics; it is argued that this formalism is more general and, given its integral form, it may offer several advantages from the modern parallel computing point of view. Applications to minimize the errors in modeling for FWI applied to oils resources in geophysics are discussed.

Keywords: Navier-Stokes equations, modeling, visco-acoustic, inversion FWI

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Authors: Dler Abdullah Ahmed, Zozan Ahmed Mohammed

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This study looked into contact surface temperature during a pin-on-disk test. Friction and wear between sliding surfaces raised the temperature differential between the contact surface and ambient temperatures Tdiff. Tdiff was significantly influenced by wear test variables. Tdiff rose with the increase of sliding speed and applied load while dropped with the increase in ambient temperature. The highest Tdiff was 289°C during the tests at room temperature and 2.5 m/s sliding speed, while the minimum was only 24 °C during the tests at 400°C and 0.5 m/s. However, the maximum contact temperature Tmax was found during tests conducted at high ambient temperatures. The Tmax was estimated based on the theoretical equation. The comparison of experimental and theoretical Tmax data revealed good agreement.

Keywords: pin on disk test, contact temperature, wear, sliding surface, friction, ambient temperature

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Authors: M. Azarbarmas, J. M. Cabrera, J. Calvo, M. Aghaie-Khafri

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The modeling of hot deformation behavior for unseen conditions is important in metal-forming. In this study, the hot deformation of IN718 has been characterized in the temperature range 950-1100 and strain rate range 0.001-0.1 s-1 using hot compression tests. All stress-strain curves showed the occurrence of dynamic recrystallization. These curves were implemented quantitatively in mathematics, and then constitutive equation indicating the relationship between the flow stress and hot deformation parameters was obtained successfully.

Keywords: compression test, constitutive equation, dynamic recrystallization, hot working

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Authors: A. H. Choudhury

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In this paper, a highly accurate numerical method for the solution of one-dimensional fourth-order wave equation is derived. This hyperbolic problem is solved by using semidiscrete approximations. The space direction is discretized by wavelet-Galerkin method, and the time variable is discretized by using Newmark schemes.

Keywords: hyperbolic problem, semidiscrete approximations, stability, Wavelet-Galerkin Method

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Authors: Muhammad Younis

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In this article, the novel (G′/G)-expansion method is successfully applied to construct the abundant travelling wave solutions to the modified Burgers’ equation with the aid of computation. The method is reliable and useful, which gives more general exact travelling wave solutions than the existing methods. These obtained solutions are in the form of hyperbolic, trigonometric and rational functions including solitary, singular and periodic solutions which have many potential applications in physical science and engineering. Some of these solutions are new and some have already been constructed. Additionally, the constraint conditions, for the existence of the solutions are also listed.

Keywords: traveling wave solutions, NLPDE, computation, integrability

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Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

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In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: dissipation, oscillatory solutions, phase-lag, Runge-Kutta methods

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Authors: Ross Calvert, Colin Whittaker, Alison Raby, Alistair G. L. Borthwick, Ton S. van den Bremer

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Large concentrations of plastic have polluted the seas in the last half century, with harmful effects on marine wildlife and potentially to human health. Plastic pollution will have lasting effects because it is expected to take hundreds or thousands of years for plastic to decay in the ocean. The question arises how waves transport plastic in the ocean. The predominant motion induced by waves creates ellipsoid orbits. However, these orbits do not close, resulting in a drift. This is defined as Stokes drift. If a particle is infinitesimally small and the same density as water, it will behave exactly as the water does, i.e., as a purely Lagrangian tracer. However, as the particle grows in size or changes density, it will behave differently. The particle will then have its own inertia, the fluid will exert drag on the particle, because there is relative velocity, and it will rise or sink depending on the density and whether it is on the free surface. Previously, plastic pollution has all been considered to be purely Lagrangian. However, the steepness of waves in the ocean is small, normally about α = k₀a = 0.1 (where k₀ is the wavenumber and a is the wave amplitude), this means that the mean drift flows are of the order of ten times smaller than the oscillatory velocities (Stokes drift is proportional to steepness squared, whilst the oscillatory velocities are proportional to the steepness). Thus, the particle motion must have the forces of the full motion, oscillatory and mean flow, as well as a dynamic buoyancy term to account for the free surface, to determine whether inertia is important. To track the motion of a floating inertial particle under wave action requires the fluid velocities, which form the forcing, and the full equations of motion of a particle to be solved. Starting with the equation of motion of a sphere in unsteady flow with viscous drag. Terms can added then be added to the equation of motion to better model floating plastic: a dynamic buoyancy to model a particle floating on the free surface, quadratic drag for larger particles and a slope sliding term. Using perturbation methods to order the equation of motion into sequentially solvable parts allows a parametric equation for the transport of inertial finite-sized floating particles to be derived. This parametric equation can then be validated using numerical simulations of the equation of motion and flume experiments. This paper presents a parametric equation for the transport of inertial floating finite-size particles by ocean waves. The equation shows an increase in Stokes drift for larger, less dense particles. The equation has been validated using numerical solutions of the equation of motion and laboratory flume experiments. The difference in the particle transport equation and a purely Lagrangian tracer is illustrated using worlds maps of the induced transport. This parametric transport equation would allow ocean-scale numerical models to include inertial effects of floating plastic when predicting or tracing the transport of pollutants.

Keywords: perturbation methods, plastic pollution transport, Stokes drift, wave flume experiments, wave-induced mean flow

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Authors: Fatima Zohra Mahi, Luca Varani

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We present an analytical model for the calculation of the sensitivity, the spectral current noise and the detectivity for an optically illuminated In0.53Ga0.47As n+nn+ diode. The photocurrent due to the excess carrier is obtained by solving the continuity equation. Moreover, the current noise level is evaluated at room temperature and under a constant voltage applied between the diode terminals. The analytical calculation of the current noise in the n+nn+ structure is developed. The responsivity and the detectivity are discussed as functions of the doping concentrations and the emitter layer thickness in one-dimensional homogeneous n+nn+ structure.

Keywords: detectivity, photodetectors, continuity equation, current noise

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Authors: Sasiwimol Auepong, Raywat Tanadkithirun

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In this work, the problem that squirrels ruin durian, which is an economical fruit in Thailand, is considered. We seek the strategy for the durian farmers to eliminate the squirrels under the consideration that squirrels also provide ecosystem service. The population dynamics of squirrels are constructed to have carrying capacity since we consider the population in a confined area. A performance index indicating the total benefit of a given elimination strategy is provided. It comprises the cost of countermeasures, the loss of resources, and the ecosystem service provided by squirrels. The optimal performance index is numerically solved through the variational inequality using the finite difference method. The optimal strategy to control the squirrel population is also given numerically.

Keywords: controlled stochastic differential equation, durian, finite difference method, performance index, singular stochastic control model, squirrel

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Authors: Alaa Sheta

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Economic Load Dispatch (ELD) is one of the vital optimization problems in power system planning. Solving the ELD problems mean finding the best mixture of power unit outputs of all members of the power system network such that the total fuel cost is minimized while sustaining operation requirements limits satisfied across the entire dispatch phases. Many optimization techniques were proposed to solve this problem. A famous one is the Quadratic Programming (QP). QP is a very simple and fast method but it still suffer many problem as gradient methods that might trapped at local minimum solutions and cannot handle complex nonlinear functions. Numbers of metaheuristic algorithms were used to solve this problem such as Genetic Algorithms (GAs) and Particle Swarm Optimization (PSO). In this paper, another meta-heuristic search algorithm named Differential Evolution (DE) is used to solve the ELD problem in power systems planning. The practicality of the proposed DE based algorithm is verified for three and six power generator system test cases. The gained results are compared to existing results based on QP, GAs and PSO. The developed results show that differential evolution is superior in obtaining a combination of power loads that fulfill the problem constraints and minimize the total fuel cost. DE found to be fast in converging to the optimal power generation loads and capable of handling the non-linearity of ELD problem. The proposed DE solution is able to minimize the cost of generated power, minimize the total power loss in the transmission and maximize the reliability of the power provided to the customers.

Keywords: economic load dispatch, power systems, optimization, differential evolution

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Authors: Romaric Desbrousses, Lan Lin

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The objective of this study is to determine how Canadian seismic design provisions affect the column axial load resistance of moment-resisting frame reinforced concrete buildings subjected to the differential settlement of their foundation. To do so, two four-storey buildings are designed in accordance with the seismic design provisions of the Canadian Concrete Design Standards. One building is located in Toronto, which is situated in a moderate seismic hazard zone in Canada, and the other in Vancouver, which is in Canada’s highest seismic hazard zone. A finite element model of each building is developed using SAP 2000. A 100 mm settlement is assigned to the base of the building’s center column. The axial load resistance of the column is represented by the demand capacity ratio. The analysis results show that settlement-induced tensile axial forces have a particularly detrimental effect on the conventional settling columns of the Toronto buildings which fail at a much smaller settlement that those in the Vancouver buildings. The results also demonstrate that particular care should be taken in the design of columns in short-span buildings.

Keywords: Columns, Demand, Foundation differential settlement, Seismic design, Non-linear analysis

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Authors: F. Rahimi Dehgolan, S. E. Khadem, S. Bab, M. Najafee

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Nowadays, using rotating systems like shafts and disks in industrial machines have been increased constantly. Dynamic stability is one of the most important factors in designing rotating systems. In this study, linear frequencies and stability of a coupled continuous flexible rotor-disk-blades system are studied. The Euler-Bernoulli beam theory is utilized to model the blade and shaft. The equations of motion are extracted using the extended Hamilton principle. The equations of motion have been simplified using the Coleman and complex transformations method. The natural frequencies of the linear part of the system are extracted, and the effects of various system parameters on the natural frequencies and decay rates (stability condition) are clarified. It can be seen that the centrifugal stiffening effect applied to the blades is the most important parameter for stability of the considered rotating system. This result highlights the importance of considering this stiffing effect in blades equation.

Keywords: rotating shaft, flexible blades, centrifugal stiffness, stability

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Authors: Abdulrahman Abdulrahman

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The specific energy equation has many applications in practical channels, such as exponential channels. In this paper, the governing equation of alternate depth ratio for exponential channels, in general, was investigated towards obtaining analytical solution for the alternate depth ratio in three exponential channel shapes, viz., rectangular, triangular, and parabolic channels. The alternate depth ratio for rectangular channels is quadratic; hence it is very simple to solve. While for parabolic and triangular channels, the alternate depth ratio is cubic and quartic equations, respectively, analytical solution for these equations may be achieved easily for a given Froud number. Different examples are solved to prove the efficiency of the proposed solution. Such analytical solution can be easily used in natural rivers and most of practical channels.

Keywords: alternate depth, analytical solution, specific energy, parabolic channel, rectangular channel, triangular channel, open channel flow

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Authors: Yves Lacroix, Van Van Than, Didier Léandri, Pierre Liardet

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The tombolo of Giens is located in the town of Hyères (France). We recall the history of coastal erosion, and prominent factors affecting the evolution of the western tombolo. We then discuss the possibility of stabilizing the western tombolo. Our argumentation relies on a coupled model integrating swells, currents, water levels and sediment transport. We present the conclusions of the simulations of various scenarios, including pre-existing propositions from coastal engineering offices. We conclude that beach replenishment seems to be necessary but not sufficient for the stabilization of the beach. Breakwaters reveal effective particularly in the most exposed northern area. Some solutions fulfill conditions so as to be elected as satisfactory. We give a comparative analysis of the efficiency of 14 alternatives for the protection of the tombolo.

Keywords: breakwaters, coupled models, replenishment, silting

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Authors: Jiahui You, Kyung Jae Lee

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Hydraulic fracturing fluid (HFF) is widely used in shale reservoir productions. HFF contains diverse chemical additives, which result in the dissolution and precipitation of minerals through multiple chemical reactions. In this study, a new pore-scale Darcy–Brinkman–Stokes (DBS) model coupled with Level Set Method (LSM) is developed to address the microscopic phenomena occurring during the iron–HFF interaction, by numerically describing mass transport, chemical reactions, and pore structure evolution. The new model is developed based on OpenFOAM, which is an open-source platform for computational fluid dynamics. Here, the DBS momentum equation is used to solve for velocity by accounting for the fluid-solid mass transfer; an advection-diffusion equation is used to compute the distribution of injected HFF and iron. The reaction–induced pore evolution is captured by applying the LSM, where the solid-liquid interface is updated by solving the level set distance function and reinitialized to a signed distance function. Then, a smoothened Heaviside function gives a smoothed solid-liquid interface over a narrow band with a fixed thickness. The stated equations are discretized by the finite volume method, while the re-initialized equation is discretized by the central difference method. Gauss linear upwind scheme is used to solve the level set distance function, and the Pressure–Implicit with Splitting of Operators (PISO) method is used to solve the momentum equation. The numerical result is compared with 1–D analytical solution of fluid-solid interface for reaction-diffusion problems. Sensitivity analysis is conducted with various Damkohler number (DaII) and Peclet number (Pe). We categorize the Fe (III) precipitation into three patterns as a function of DaII and Pe: symmetrical smoothed growth, unsymmetrical growth, and dendritic growth. Pe and DaII significantly affect the location of precipitation, which is critical in determining the injection parameters of hydraulic fracturing. When DaII<1, the precipitation uniformly occurs on the solid surface both in upstream and downstream directions. When DaII>1, the precipitation mainly occurs on the solid surface in an upstream direction. When Pe>1, Fe (II) transported deeply into and precipitated inside the pores. When Pe<1, the precipitation of Fe (III) occurs mainly on the solid surface in an upstream direction, and they are easily precipitated inside the small pore structures. The porosity–permeability relationship is subsequently presented. This pore-scale model allows high confidence in the description of Fe (II) dissolution, transport, and Fe (III) precipitation. The model shows fast convergence and requires a low computational load. The results can provide reliable guidance for injecting HFF in shale reservoirs to avoid clogging and wellbore pollution. Understanding Fe (III) precipitation, and Fe (II) release and transport behaviors give rise to a highly efficient hydraulic fracture project.

Keywords: reactive-transport , Shale, Kerogen, precipitation

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Authors: W. Meron Mebrahtu, R. Absi

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Velocity distribution in turbulent open-channel flows is organized in a complex manner. This is due to the large spatial and temporal variability of fluid motion resulting from the free-surface turbulent flow condition. This phenomenon is complicated further due to the complex geometry of channels and the presence of solids transported. Thus, several efforts were made to understand the phenomenon and obtain accurate mathematical models that are suitable for engineering applications. However, predictions are inaccurate because oversimplified assumptions are involved in modeling this complex phenomenon. Therefore, the aim of this work is to study velocity distribution profiles and obtain simple, more accurate, and predictive mathematical models. Particular focus will be made on the acceptable simplification of the general transport equations and an accurate representation of eddy viscosity. Wide rectangular open-channel seems suitable to begin the study; other assumptions are smooth-wall, and sediment-free flow under steady and uniform flow conditions. These assumptions will allow examining the effect of the bottom wall and the free surface only, which is a necessary step before dealing with more complex flow scenarios. For this flow condition, two ordinary differential equations are obtained for velocity profiles; from the Reynolds-averaged Navier-Stokes (RANS) equation and equilibrium consideration between turbulent kinetic energy (TKE) production and dissipation. Then different analytic models for eddy viscosity, TKE, and mixing length were assessed. Computation results for velocity profiles were compared to experimental data for different flow conditions and the well-known linear, log, and log-wake laws. Results show that the model based on the RANS equation provides more accurate velocity profiles. In the viscous sublayer and buffer layer, the method based on Prandtl’s eddy viscosity model and Van Driest mixing length give a more precise result. For the log layer and outer region, a mixing length equation derived from Von Karman’s similarity hypothesis provides the best agreement with measured data except near the free surface where an additional correction based on a damping function for eddy viscosity is used. This method allows more accurate velocity profiles with the same value of the damping coefficient that is valid under different flow conditions. This work continues with investigating narrow channels, complex geometries, and the effect of solids transported in sewers.

Keywords: accuracy, eddy viscosity, sewers, velocity profile

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Authors: Revant Nayar

Abstract:

In this work, we recast the equations describing large scale structure, and by extension all nonlinear fluids, in the path integral formalism. We first calculate the well known two and three point functions using Schwinger Keldysh formalism used commonly to perturbatively solve path integrals in non- equilibrium systems. Then we include EFT corrections due to pressure, viscosity, and noise as effects on the time-dependent propagator. We are able to express results for arbitrary two and three point correlation functions in LSS in terms of differential operators acting on a triple K master intergral. We also, for the first time, get analytical results for more general initial conditions deviating from the usual power law P∝kⁿ by introducing a mass scale in the initial conditions. This robust field theoretic formalism empowers us with tools from strongly coupled QFT to study the strongly non-linear regime of LSS and turbulent fluid dynamics such as OPE and holographic duals. These could be used to capture fully the strongly non-linear dynamics of fluids and move towards solving the open problem of classical turbulence.

Keywords: quantum field theory, cosmology, effective field theory, renormallisation

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