Search results for: nonlinear Takagi’s equations

Authors: Debjani Chakraborty, Abhijit Chatterjee, Aishwaryaprajna

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Posynomials, a special type of polynomials, having singularities, pose difficulties while solving geometric programming problems. In this paper, a methodology has been proposed and used to obtain extreme values for geometric programming problems by nth degree polynomial interpolation technique. Here the main idea to optimise the posynomial is to fit a best polynomial which has continuous gradient values throughout the range of the function. The approximating polynomial is smoothened to remove the discontinuities present in the feasible region and the objective function. This spatial interpolation method is capable to optimise univariate and multivariate geometric programming problems. An example is solved to explain the robustness of the methodology by considering a bivariate nonlinear geometric programming problem. This method is also applicable for signomial programming problem.

Keywords: geometric programming problem, multivariate optimisation technique, posynomial, spatial interpolation

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Authors: Mahdi Goharrokhi, Rasool Shiri, Eiraj Naser

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A depropanizer column of a particular refinery was redesigned in this work. That is, minimum reflux ratio, minimum number of trays, feed tray location and the hydraulic characteristics of the tower were calculated and compared with the actual values of the existing tower. To Design review of the tower, fundamental equations were used to develop software which its results were compared with two commercial software results. In each case PR EOS was used. Based on the total energy consumption in reboiler and condenser, feed tray location was also determined using case study definition for tower.

Keywords: column, hydraulic design, pressure drop, energy consumption

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Authors: Belloufi Mohammed, Sellami Badreddine

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This paper deals with a new nonlinear modified three-term conjugate gradient algorithm for solving large-scale unstrained optimization problems. The search direction of the algorithms from this class has three terms and is computed as modifications of the classical conjugate gradient algorithms to satisfy both the descent and the conjugacy conditions. An example of three-term conjugate gradient algorithm from this class, as modifications of the classical and well known Hestenes and Stiefel or of the CG_DESCENT by Hager and Zhang conjugate gradient algorithms, satisfying both the descent and the conjugacy conditions is presented. Under mild conditions, we prove that the modified three-term conjugate gradient algorithm with Wolfe type line search is globally convergent. Preliminary numerical results show the proposed method is very promising.

Keywords: unconstrained optimization, three-term conjugate gradient, sufficient descent property, line search

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Authors: Abdulali Bashir Ben Saleh

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The powdered beet red roots (PBRR) were used as an adsorbent to remove dyes namely methylene blue dye (as a typical cationic or basic dye) from aqueous solutions. The present study shows that used beet red roots powder exhibit adsorption trend for the dye. The adsorption processes were carried out at various conditions of concentrations, processing time and a wide range of pH between 2.5-11. Adsorption isotherm equations such as Freundlich, and Langmuir were applied to calculate the values of respective constants. Adsorption study was found that the currently introduced adsorbent can be used to remove cationic dyes such as methylene blue from aqueous solutions.

Keywords: beet red root, removal of deys, methylene blue, adsorption

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Authors: Anamika Paul, Sudipto Sarkar

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The flow behaviour of non-Newtonian fluid is quite complicated, although both the pseudoplastic (n < 1, n being the power index) and dilatant (n > 1) fluids under this category are used immensely in chemical and process industries. A limited research work is carried out for flow over a bluff body in non-Newtonian flow environment. In the present numerical simulation we control the vortices of a square cylinder by placing an upstream vertical splitter plate for pseudoplastic (n=0.8), Newtonian (n=1) and dilatant (n=1.2) fluids. The position of the upstream plate is also varied to calculate the critical distance between the plate and cylinder, below which the cylinder vortex shedding suppresses. Here the Reynolds number is considered as Re = 150 (Re = U∞a/ν, where U∞ is the free-stream velocity of the flow, a is the side of the cylinder and ν is the maximum value of kinematic viscosity of the fluid), which comes under laminar periodic vortex shedding regime. The vertical plate is having a dimension of 0.5a × 0.05a and it is placed at the cylinder centre-line. Gambit 2.2.30 is used to construct the flow domain and to impose the boundary conditions. In detail, we imposed velocity inlet (u = U∞), pressure outlet (Neumann condition), symmetry (free-slip boundary condition) at upper and lower domain. Wall boundary condition (u = v = 0) is considered both on the cylinder and the splitter plate surfaces. The unsteady 2-D Navier Stokes equations in fully conservative form are then discretized in second-order spatial and first-order temporal form. These discretized equations are then solved by Ansys Fluent 14.5 implementing SIMPLE algorithm written in finite volume method. Here, fine meshing is used surrounding the plate and cylinder. Away from the cylinder, the grids are slowly stretched out in all directions. To get an account of mesh quality, a total of 297 × 208 grid points are used for G/a = 3 (G being the gap between the plate and cylinder) in the streamwise and flow-normal directions respectively after a grid independent study. The computed mean flow quantities obtained from Newtonian flow are agreed well with the available literatures. The results are depicted with the help of instantaneous and time-averaged flow fields. Qualitative and quantitative noteworthy differences are obtained in the flow field with the changes in rheology of fluid. Also, aerodynamic forces and vortex shedding frequencies differ with the gap-ratio and power index of the fluid. We can conclude from the present simulation that fluent is capable to capture the vortex dynamics of unsteady laminar flow regime even in the non-Newtonian flow environment.

Keywords: CFD, critical gap-ratio, splitter plate, wake-wake interactions, dilatant, pseudoplastic

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Authors: Mikhail O. Eremin

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Seismic activity around the world is clearly a threat to people's lives, as well as infrastructure and capital construction. It is the instability of the latter to powerful earthquakes that most often causes human casualties. Therefore, during construction it is necessary to take into account the risks of large-scale natural disasters. The task of assessing the risks of natural disasters is one of the most urgent at the present time. The final goal of any study of earthquakes is forecasting. This is especially important for seismically active regions of the planet where earthquakes occur frequently. Gorni Altai is one of such regions. In work, we developed the physical-mathematical model of stress-strain state evolution of loaded geomedium with the purpose of numerical simulation of seismic process accompanying the formation of Chuya-Kuray fault zone Gorni Altay, Russia. We build a structural model on the base of seismotectonic and paleoseismogeological investigations, as well as SRTM-data. Base of mathematical model is the system of equations of solid mechanics which includes the fundamental conservation laws and constitutive equations for elastic (Hooke's law) and inelastic deformation (modified model of Drucker-Prager-Nikolaevskii). An initial stress state of the model correspond to gravitational. Then we simulate an activation of a buried dextral strike-slip paleo-fault located in the basement of the model. We obtain the stages of formation and the structure of Chuya-Kuray fault zone. It is shown that results of numerical simulation are in good agreement with field observations in statistical sense. Simulated seismic process is strongly bound to the faults - lineaments with high degree of inelastic strain localization. Fault zone represents en-echelon system of dextral strike-slips according to the Riedel model. The system of surface lineaments is represented with R-, R'-shear bands, X- and Y-shears, T-fractures. Simulated seismic process obeys the laws of Gutenberg-Richter and Omori. Thus, the model describes a self-similar character of deformation and fracture of rocks and geomedia. We also modified the algorithm of determination of separate slip events in the model due to the features of strain rates dependence vs time.

Keywords: Drucker-Prager model, fault zone, numerical simulation, Riedel bands, seismic process, strike-slip fault

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Authors: Abdullah Al Faruque, Ram Balachandar

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Series of laboratory tests were carried out to study the extent of scour caused by a three-dimensional wall jets exiting from a square cross-section nozzle and into a non-cohesive sand beds. Previous observations have indicated that the effect of the tailwater depth was significant for densimetric Froude number greater than ten. However, the present results indicate that the cut off value could be lower depending on the value of grain size-to-nozzle width ratio. Numbers of equations are drawn out for a better scaling of numerous scour parameters. Also suggested the empirical prediction of scour to predict the scour centre line profile and plan view of scour profile at any particular time.

Keywords: densimetric froude number, jets, nozzle, sand, scour, tailwater, time

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Authors: Pavlo Selyshchev, Tetiana Didenko

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Within the framework of the obstacle radiation hardening and the dislocation climb-glide model a theoretical approach is developed to describe peculiarities of transient plasticity of metal under irradiation. It is considered nonlinear dynamics of accumulation of point defects (vacancies and interstitial atoms). We consider metal under such stress and conditions of irradiation at which creep is determined by dislocation motion: dislocations climb obstacles and glide between obstacles. It is shown that the rivalry between vacancy and interstitial fluxes to dislocation leads to fractures of plasticity time dependence. Simulation and analysis of this phenomenon are performed. Qualitatively different regimes of transient plasticity under irradiation are found. The fracture time is obtained. The theoretical results are compared with the experimental ones.

Keywords: climb and glide of dislocations, fractures of transient plasticity, irradiation, non-linear feed-back, point defects

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Authors: Hamidreza Bayat, Arash Mirabdolah Lavasani, Meysam Bolhasani, Sajad Moosavi

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Heat transfer from flat tube is studied numerically. Reynolds number is defined base on equivalent circular tube which is varied in range of 100 to 300. In these range of Reynolds number flow is considered to be laminar, unsteady, and incompressible. Equations are solved by using finite volume method. Results show that increasing l/D from 1 to 2 has insignificant effect on heat transfer and Nusselt number of flat tube is slightly lower than circular tube. However, thermal-hydraulic performance of flat tube is up to 2.7 times greater than circular tube.

Keywords: laminar flow, flat tube, convective heat transfer, heat exchanger

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Authors: Abbes Lounis, Kahina Louadj, Mohamed Aidene

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This paper presents an optimal control problem applied to a robot; the problem is to determine a command which makes it possible to reach a final state from a given initial state in record time. The approach followed to solve this optimization problem with constraints on the control starts by presenting the equations of motion of the dynamic system then by applying Pontryagin's maximum principle (PMP) to determine the optimal control, and Picard's successive approximation method combined with the shooting method to solve the resulting differential system.

Keywords: robotics, Pontryagin's Maximum Principle, PMP, Picard's method, shooting method, non-linear differential systems

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Authors: Xu Du, Aparna S. Varde

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In this research, we propose to conduct diagnostic and predictive analysis about the key factors and consequences of urban population relocation. To achieve this goal, urban simulation models extract the urban development trends as land use change patterns from a variety of data sources. The results are treated as part of urban big data with other information such as population change and economic conditions. Multiple data mining methods are deployed on this data to analyze nonlinear relationships between parameters. The result determines the driving force of population relocation with respect to urban sprawl and urban sustainability and their related parameters. Experiments so far reveal that data mining methods discover useful knowledge from the multicity urban data. This work sets the stage for developing a comprehensive urban simulation model for catering to specific questions by targeted users. It contributes towards achieving sustainability as a whole.

Keywords: data mining, environmental modeling, sustainability, urban planning

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Authors: Kirill Trapezon, Alexandr Trapezon

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A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.

Keywords: vibrations, plate, method of symmetries, differential equation, factorization, approximation

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Authors: Thibaud Berthomier, Ali Mansour, Luc Bressollette, Frédéric Le Roy, Dominique Mottier, Léo Fréchier, Barthélémy Hermenault

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Deep Venous Thrombosis (DVT) occurs when a thrombus is formed within a deep vein (most often in the legs). This disease can be deadly if a part or the whole thrombus reaches the lung and causes a Pulmonary Embolism (PE). This disorder, often asymptomatic, has multifactorial causes: immobilization, surgery, pregnancy, age, cancers, and genetic variations. Our project aims to relate the thrombus epidemiology (origins, patient predispositions, PE) to its structure using ultrasound images. Ultrasonography and elastography were collected using Toshiba Aplio 500 at Brest Hospital. This manuscript compares two classification approaches: spectral clustering and scattering operator. The former is based on the graph and matrix theories while the latter cascades wavelet convolutions with nonlinear modulus and averaging operators.

Keywords: deep venous thrombosis, ultrasonography, elastography, scattering operator, wavelet, spectral clustering

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Authors: T. Martini, J. M. Martínez

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An algorithmic acceleration strategy based on quasi-Newton (or secant) methods is displayed for address the practical problem of accelerating the convergence of the Newton-Lagrange method in the case of convergence to critical multipliers. Since the Newton-Lagrange iteration converges locally at a linear rate, it is natural to conjecture that quasi-Newton methods based on the so called secant equation and some minimal variation principle, could converge superlinearly, thus restoring the convergence properties of Newton's method. This strategy can also be applied to accelerate the convergence of algorithms applied to fixed-points problems. Computational experience is reported illustrating the efficiency of this strategy to solve fixed-point problems with linear convergence rate.

Keywords: algorithmic acceleration, fixed-point problems, nonlinear programming, quasi-newton method

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Authors: K. Ebrahimi, Sh. Shahid, M. Mohammadi Ghaleni, M. H. Omid

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The longitudinal dispersion coefficient is a crucial parameter for 1-D water quality analysis of riverine flows. So far, different types of empirical equations for estimation of the coefficient have been developed, based on various case studies. The main objective of this paper is to develop an empirical equation for estimation of the coefficient for a riverine flow. For this purpose, a set of tracer experiments was conducted, involving salt tracer, at three sections located in downstream of a lengthy canal. Tracer data were measured in three mixing lengths along the canal including; 45, 75 and 100m. According to the results, the obtained coefficients from new developed empirical equation gave an encouraging level of agreement with the theoretical values.

Keywords: coefficients, dispersion, river, tracer, water quality

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Authors: Sheren H. Salah

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The inverted pendulum is a highly nonlinear and open-loop unstable system. An inverted pendulum (IP) is a pendulum which has its mass above its pivot point. It is often implemented with the pivot point mounted on a cart that can move horizontally and may be called a cart and pole. The characteristics of the inverted pendulum make identification and control more challenging. This paper presents the simulation study of several control strategies for an inverted pendulum system. The goal is to determine which control strategy delivers better performance with respect to pendulum’s angle. The inverted pendulum represents a challenging control problem, which continually moves toward an uncontrolled state. For controlling the inverted pendulum. The simulation study that sliding mode control (SMC) control produced better response compared to Genetic Algorithm Control (GAs) and proportional-integral-derivative(PID) control.

Keywords: Inverted Pendulum (IP) Proportional-Integral-Derivative (PID), Genetic Algorithm Control (GAs), Sliding Mode Control (SMC)

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Authors: Reza Mohammadi

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Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: Ashiq Rahman, Sunil Thapa, Shunyao Fan, Niloy K. Dutta

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A 20-GHz and a 50-GHz pulse train are generated using a fiber ring laser setup that incorporates Rational Harmonic Mode Locking. Two separate experiments were carried out using charcoal nanoparticles and graphene nanoparticles acting as saturable absorbers to reduce the pulse width generated from rational harmonic mode-locking (RHML). Autocorrelator trace shows that the pulse width is reduced from 5.6-ps to 3.2-ps using charcoal at 20-GHz, and to 2.7-ps using graphene at 50-GHz repetition rates, which agrees with the simulation findings. Numerical simulations have been carried out to study the effect of varying the linear and nonlinear absorbance parameters of both absorbers on output pulse widths. Experiments closely agree with the simulations.

Keywords: fiber optics, fiber lasers, mode locking, saturable absorbers

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Authors: Takeru Furuawa, Kohei Takizawa, Daisuke Kuwahara, Shunjiro Shinohara

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In the field of a space propulsion, an electric propulsion system has been developed because its fuel efficiency is much higher than a conventional chemical one. However, the practical electric propulsion systems, e.g., an ion engine, have a problem of short lifetime due to a damage of generation and acceleration electrodes of the plasma. A helicon plasma thruster is proposed as a long-lifetime electric thruster which has non-direct contact electrodes. In this system, both generation and acceleration methods of a dense plasma are executed by antennas from the outside of a discharge tube. Development of the helicon plasma thruster has been conducting under the Helicon Electrodeless Advanced Thruster (HEAT) project. Our helicon plasma thruster has two important processes. First, we generate a dense source plasma using a helicon wave with an excitation frequency between an ion and an electron cyclotron frequencies, fci and fce, respectively, applied from the outside of a discharge using a radio frequency (RF) antenna. The helicon plasma source can provide a high-density (~1019 m-3), a high-ionization ratio (up to several tens of percent), and a high particle generation efficiency. Second, in order to achieve high thrust and specific impulse, we accelerate the dense plasma by the axial Lorentz force fz using the product of the induced azimuthal current jθ and the static radial magnetic field Br, shown as fz = jθ × Br. The HEAT project has proposed several kinds of electrodeless acceleration schemes, and in our particular case, a Rotating Magnetic Field (RMF) method has been extensively studied. The RMF scheme was originally developed as a concept to maintain the Field Reversed Configuration (FRC) in a magnetically confined fusion research. Here, RMF coils are expected to generate jθ due to a nonlinear effect shown below. First, the rotating magnetic field Bω is generated by two pairs of RMF coils with AC currents, which have a phase difference of 90 degrees between the pairs. Due to the Faraday’s law, an axial electric field is induced. Second, an axial current is generated by the effects of an electron-ion and an electron-neutral collisions through the Ohm’s law. Third, the azimuthal electric field is generated by the nonlinear term, and the retarding torque generated by the collision effects again. Then, azimuthal current jθ is generated as jθ = - nₑ er ∙ 2π fRMF. Finally, the axial Lorentz force fz for plasma acceleration is generated. Here, jθ is proportional to nₑ and frequency of RMF coil current fRMF, when Bω is fully penetrated into the plasma. Our previous study has achieved 19 % increase of ion velocity using the 5 MHz and 50 A of the RMF coil power supply. In this presentation, we will show the improvement of the ion velocity using the lower frequency and higher current supplied by RMF power supply. In conclusion, helicon high-density plasma production and electromagnetic acceleration by the RMF scheme with a concept of electrodeless condition have been successfully executed.

Keywords: electric propulsion, electrodeless thruster, helicon plasma, rotating magnetic field

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Authors: Hemant Upadhyay, Tarun Kumar Kundu

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It is utmost important for a blast furnace operator to understand the mechanisms governing the liquid flow, accumulation, drainage and heat transfer between various phases in blast furnace hearth for a stable and efficient blast furnace operation. Abnormal drainage behavior may lead to high liquid build up in the hearth. Operational problems such as pressurization, low wind intake, and lower material descent rates, normally be encountered if the liquid levels in the hearth exceed a critical limit when Hearth coke and Deadman start to float. Similarly, hot metal temperature is an important parameter to be controlled in the BF operation; it should be kept at an optimal level to obtain desired product quality and a stable BF performance. It is not possible to carry out any direct measurement of above due to the hostile conditions in the hearth with chemically aggressive hot liquids. The objective here is to develop a mathematical model to simulate the variation in hot metal / slag accumulation and temperature during the tapping of the blast furnace based on the computed drainage rate, production rate, mass balance, heat transfer between metal and slag, metal and solids, slag and solids as well as among the various zones of metal and slag itself. For modeling purpose, the BF hearth is considered as a pressurized vessel, filled with solid coke particles. Liquids trickle down in hearth from top and accumulate in voids between the coke particles which are assumed thermally saturated. A set of generic mass balance equations gives the amount of metal and slag intake in hearth. A small drainage (tap hole) is situated at the bottom of the hearth and flow rate of liquids from tap hole is computed taking in account the amount of both the phases accumulated their level in hearth, pressure from gases in the furnace and erosion behaviors of tap hole itself. Heat transfer equations provide the exchange of heat between various layers of liquid metal and slag, and heat loss to cooling system through refractories. Based on all that information a dynamic simulation is carried out which provides real time information of liquids accumulation in hearth before and during tapping, drainage rate and its variation, predicts critical event timings during tapping and expected tapping temperature of metal and slag on preset time intervals. The model is in use at JSPL, India BF-II and its output is regularly cross-checked with actual tapping data, which are in good agreement.

Keywords: blast furnace, hearth, deadman, hotmetal

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Authors: Abdelghafour Galadi

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In this paper, accurate power MOSFET models including quasi-saturation effect are presented. These models have no internal node voltages determined by the circuit simulator and use one JFET or one depletion mode MOSFET transistors controlled by an “effective” gate voltage taking into account the quasi-saturation effect. The proposed models achieve accurate simulation results with an average error percentage less than 9%, which is an improvement of 21 percentage points compared to the commonly used standard power MOSFET model. In addition, the models can be integrated in any available commercial circuit simulators by using their analytical equations. A description of the models will be provided along with the parameter extraction procedure.

Keywords: power MOSFET, drift layer, quasi-saturation effect, SPICE model

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Authors: João Paulo Pascon

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A constitutive model accounting for large strains, thermoviscoplasticity, and ductile damage evolution is proposed in the present work. To this end, a fully Lagrangian framework is employed, considering plane stress conditions and multiplicative split of the deformation gradient. The full model includes Gurson’s void growth, nucleation and coalescence, plastic work heating, strain and strain-rate hardening, thermal softening, and heat conductivity. The contribution of the work is the combination of all the above-mentioned features within the finite-strain setting. The model is implemented in a computer code using triangular finite elements and nonlinear analysis. Two mechanical examples involving ductile damage and finite strain levels are analyzed: an inhomogeneous tension specimen and the necking problem. Results demonstrate the capabilities of the developed formulation regarding ductile fracture and large deformations.

Keywords: ductile damage model, finite element method, large strains, thermoviscoplasticity

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Authors: Jeong-Hwan Choi, Hyo-Sang Park, Tae-Hyung Lee

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The transmission tower is one of the crucial lifeline structures in a modern society, and it needs to be protected against extreme loading conditions. However, the transmission tower is a very complex structure and, therefore, it is very difficult to simulate the actual damage and the collapse behavior of the tower structure. In this study, the actual collapse behavior of the transmission tower due to lateral loading conditions such as wind load is evaluated through the computational simulation. For that, a progressive collapse procedure is applied to the simulation. In this procedure, after running the simulation, if a member of the tower structure fails, the failed member is removed and the simulation run again. The 154kV transmission tower is selected for this study. The simulation is performed by nonlinear static analysis procedure, namely pushover analysis, using OpenSEES, an earthquake simulation platform. Three-dimensional finite element models of those towers are developed.

Keywords: transmission tower, OpenSEES, pushover, progressive collapse

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Authors: Fatma Khaled, Khaoula Hidouri, Bechir Chaouachi

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Desalination using solar energy coupled with membrane techniques such as vacuum membrane distillation (VMD) is considered as an interesting alternative for the production of pure water. During this work, a developed model of a polytetrafluoroethylene (PTFE) hollow fiber membrane module of a VMD unit of seawater was carried out. This simulation leads to establishing a comparison between the effects of two different equations of the vaporization latent heat on the membrane surface temperature and on the unit productivity. Besides, in order to study the effect of putting membrane modules in series on the outlet fluid temperature and on the productivity of the process, a simulation was executed.

Keywords: vacuum membrane distillation, membrane module, membrane temperature, productivity

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Authors: N. Targui, H. Kahalerras

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The present work is a numerical simulation of nanofluids flow in a double pipe heat exchanger provided with porous baffles. The hot nanofluid flows in the inner cylinder, whereas the cold nanofluid circulates in the annular gap. The Darcy-Brinkman-Forchheimer model is adopted to describe the flow in the porous regions, and the governing equations with the appropriate boundary conditions are solved by the finite volume method. The results reveal that the addition of metallic nanoparticles enhances the rate of heat transfer in comparison to conventional fluids but this augmentation is accompanied by an increase in pressure drop. The highest heat exchanger performances are obtained when nanoparticles are added only to the cold fluid.

Keywords: double pipe heat exchanger, nanofluids, nanoparticles, porous baffles

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Authors: Mohamed Elshobaki, Alessandro Valiani, Valerio Caleffi

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In this paper, we solve 1-D shallow water equation for sub-critical and super-critical water flow at junction. The water flow at junction has been studied for the last 50 years from the physical-hydraulic point of views and for numerical computations need more attention. For numerical simulation, we need to establish an inner boundary condition at the junction to avoid an oscillation which rise from the waves interactions at the junction. Indeed, we introduce a new boundary condition at the junction based on the mass conservation, total head, and the admissible wave relations between the flow parameters in the three branches to predict the water depths and discharges at the junction. These boundary conditions are valid for sub-critical flow and super-critical flow.

Keywords: numerical simulation, junction flow, sub-critical flow, super-critical flow

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Authors: Brahim Mahfoud, Ali Bendjaghlouli

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Natural convection is simulated in a truncated cone filled with nanofluid. Inclined and top walls have constant temperature where the heat source is located on the bottom wall of the conical container which is thermally insulated. A finite volume approach is used to solve the governing equations using the SIMPLE algorithm for different parameters such as Rayleigh number, inclination angle of inclined walls of the enclosure and heat source length. The results showed an enhancement in cooling system by using a nanofluid, when conduction regime is assisted. The inclination angle of inclined sidewall and heat source length affect the heat transfer rate and the maximum temperature.

Keywords: heat source, truncated cone, nanofluid, natural convection

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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: P. K. Rahul Krishna, S. Sandeep Kumar, Jayanthi Sunder Raj

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The article explores one of the important relations between numbers-the Pythagorean triples (triplets) which finds its application in distance measurement, construction of roads, towers, buildings and wherever Pythagoras theorem finds its application. The Pythagorean triples are numbers, that satisfy the condition “In a given set of three natural numbers, the sum of squares of two natural numbers is equal to the square of the other natural number”. There are numerous methods and equations to obtain the triplets, which have their own merits and demerits. Here, quadratic approach for generating triples uses the hypotenuse leg difference method. The advantage is that variables are few and finally only three independent variables are present.

Keywords: arithmetic progression, hypotenuse leg difference method, natural numbers, Pythagorean triplets, quadratic equation

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Authors: Sanjeet Patra, Soham Roychowdhury

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In recent times, functionally graded dielectric elastomer (FGDE) has gained significant attention within the realm of soft actuation due to its dual capacity to exert highly localized stresses while maintaining its compliant characteristics on application of electro-mechanical loading. Nevertheless, the full potential of dielectric elastomer (DE) has not been fully explored due to their susceptibility to instabilities when subjected to electro-mechanical loads. As a result, study and analysis of such instabilities becomes crucial for the design and realization of dielectric actuators. Prismatic bifurcation is a type of instability that has been recognized in a DE tube. Though several studies have reported on the analysis for prismatic bifurcation in an isotropic DE tube, there is an insufficiency in studies related to prismatic bifurcation of FGDE tubes. Therefore, this paper aims to determine the onset of prismatic bifurcations on an incompressible FGDE tube when subjected to electrical loading across the thickness of the tube and internal pressurization. The analysis has been conducted by imposing two axial boundary conditions on the tube, specifically axially free ends and axially clamped ends. Additionally, the rigidity modulus of the tube has been linearly graded in the direction of thickness where the inner surface of the tube has a lower stiffness than the outer surface. The static equilibrium equations for deformation of the axisymmetric tube are derived and solved using numerical technique. The condition for prismatic bifurcation of the axisymmetric static equilibrium solutions has been obtained by using the linearized incremental constitutive equations. Two modes of bifurcations, corresponding to two different non-circular cross-sectional geometries, have been explored in this study. The outcomes reveal that the FGDE tubes experiences prismatic bifurcation before the Hessian criterion of failure is satisfied. It is observed that the lower mode of bifurcation can be triggered at a lower critical voltage as compared to the higher mode of bifurcation. Furthermore, the tubes with larger stiffness gradient require higher critical voltages for triggering the bifurcation. Moreover, with the increase in stiffness gradient, a linear variation of the critical voltage is observed with the thickness of the tube. It has been found that on applying internal pressure to a tube with low thickness, the tube becomes less susceptible to bifurcations. A thicker tube with axially free end is found to be more stable than the axially clamped end tube at higher mode of bifurcation.

Keywords: critical voltage, functionally graded dielectric elastomer, linearized incremental approach, modulus of rigidity, prismatic bifurcation

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