Time-periodic Boundary Conditions Research Articles

Space–time computations of exactly time-periodic flows past hydrofoils

The computation of periodic flows is typically conducted over multiple periods. First, a number of periods is used to develop periodic characteristics, and afterwards statistics are collected from averages over multiple periods. As a consequence, it is uncertain whether the numerical results are exactly time-periodic, and additionally, the time domain might be needlessly long. In this article, we circumvent these concerns by using a time-periodic function space. Consequently, the boundary conditions and solutions are exactly periodic. We employ the isogeometric analysis framework to achieve higher-order smoothness in both space and time. The discretization is performed using residual-based variational multiscale modeling and weak boundary conditions are adopted to enhance the accuracy near the moving boundaries of the computational domain. We enforce the time-periodic boundary condition within the isogeometric discretization spaces, which converts the two-dimensional time-dependent problem into a three-dimensional boundary value problem. Furthermore, we determine the boundary velocities of moving hydrofoils directly from the computational mesh and use a conservation methodology for force extraction. Application of the computational setup to heaving and pitching hydrofoils displays very accurate and exactly periodic results for lift and drag.

Artificial neural network approach for MHD mixed convection and entropy generation in a vertical annulus with time periodic thermal boundary conditions in the presence of radial and induced magnetic field

Entropy generation with time periodic thermal boundary conditions have numerous applications in heat exchangers, electronic devices, automatic and thermal control systems. The present research focuses on mixed convective hydromagnetic electrically conducting fluid flow in a vertical annulus using thermodynamic concepts, in the presence of induced magnetic field along with entropy generation and time periodic boundary conditions. The governing equations related to the present model are solved using finite element method. Also to predict heat transport features in the vertical annulus, artificial neural network – backpropogated Levenberg Marquardt algorithm is adopted. The steady and periodic profiles of velocity, skin friction, temperature and induced magnetic field are illustrated graphically for specific range of pertinent parameters to demonstrate significant aspects of the results. It is noted that increase in Hartmann number enhances the entropy generation near the outer cylinder, which illustrates that the fluid friction and magnetic field influence is maximum at the outer cylinder surface. The Bejan number in the annulus reduces with increase in viscous heating parameter. Results indicate that raise in the Prandtl number diminishes the thermal boundary layer thickness. As a result of decrease in the intensity of heating the boundary walls, a raise in Strouhal number lowers the fluid temperature profile. The generalized correlation is expressed to predict heat transport features in the annulus using artificial neural network – backpropogated Levenberg Marquardt algorithm.

Subsonic time-periodic solution to the compressible Euler equations triggered by boundary conditions

In this paper, we consider the one-dimensional isentropic compressible Euler equations with source term β(t,x)ρ|u|αu in a bounded domain, which can be used to describe gas transmission in a nozzle. The model is imposed a subsonic time-periodic boundary condition. The main results reveal that the time-periodic boundary can trigger an unique subsonic time-periodic smooth solution and this unique periodic solution is stable under small perturbations on initial and boundary data. To get the existence of subsonic time-periodic solution, we use the linear iterative skill and transfer the boundary value problem into two initial value ones by using the hyperbolic property of the system, then the corresponding linearized system can be decoupled. The uniqueness is a direct by-product of the stability. There is no small assumptions on coefficient β(t,x).

Unsteady MHD flow in a rotating annular region with Homogeneous–Heterogeneous chemical reactions of Walters’ B fluids: Time-periodic boundary criteria

This paper considers the movement of an incompressible non-Newtonian Walters’ B liquid within a rotating annulus. The flow lies within porous media and is magnetized by a uniform normal magnetic field. Mass transmission is included in the arrangements of homogeneous and heterogeneous chemical reactions (HHCR) with a thermal diffusion effect. Heat diffusion is exposed with a temperature- dependent heat source (THS) and an exponential radial-dependent heat source (ERHS), besides Joule heating and viscous dissipations. The mathematical construction is shown by momentum, energy and concentration of chemical materials equations along with time-periodic boundary conditions. The innovation of this study stems from considering mass transfer utilizing HHCR, with thermal diffusion effects in the flow within a rotating annulus, trying to understand the effect of these reactions on the flow and related applications. The principal regulating the structure of nonlinear partial differential equations is transferred by ordinary ones utilizing appropriate similarity analysis. These equations are analyzed by the homotopy perturbation method. Subsequently, the analytical solutions of the main profiles are obtained, and a graphical construction is established to clarify the effects of the relevant physical elements. It is observed that the velocity waves decrease with annulus width enlargement and increase with the wave phase amplitude. With an increase in all significant parameters, heat transmission gets better. Furthermore, as the strength of HHCR is increased, the concentration of molecules decreases. These outcomes are significant in several applications like cancer therapy, biochemical manufacturing purposes through reactors, where biochemical interactions can be regulated by accurate control of various parameters.

Asymptotic solitons of the focusing Kundu-Eckhaus equation with time-periodic boundary condition

Asymptotic solitons of the focusing Kundu-Eckhaus equation with time-periodic boundary condition

Coseismic site response and slope instability using periodic boundary conditions in the material point method

This paper proposed the explicit generalized-α time scheme and periodic boundary conditions in the material point method (MPM) for the simulation of coseismic site response. The proposed boundary condition uses an intuitive particle-relocation algorithm ensuring material points always remain within the computational mesh. The explicit generalized-α time scheme was implemented in MPM to enable the damping of spurious high frequency oscillations. Firstly, the MPM was verified against finite element method (FEM). Secondly, ability of the MPM in capturing the analytical transfer function was investigated. Thirdly, a symmetric embankment was adopted to investigate the effects of ground motion arias intensity (Ia), geometry dimensions, and constitutive models. The results show that the larger the model size, the higher the crest runout and settlement for the same ground motion. When using a Mohr-Coulomb model, the crest runout increases with increasing Ia. However, if the strain-softening law is activated, the results are less influenced by the ground motion. Finally, the MPM results were compared with the Newmark sliding block solution. The simplified analysis herein highlights the capabilities of MPM to capture the full deformation process for earthquake engineering applications, the importance of geometry characterization, and the selection of appropriate constitutive models when simulating coseismic site response and subsequent large deformations.

Ginzburg Landau Model for Nanofluid Convection in the Presence of Time Periodic Plate Modulation

Here we study thermal modulation effect on nanofluid convection and discuss heat and mass transfer in the layer. The non-uniform time periodic boundary conditions of the system are considered. A weak non-linear stability analysis has been performed and obtained heat and mass transfer coefficients as a function of the system parameters. The Ginzburg Landau model was employed to derive nanofluid convective amplitude at different stages of flow disturbances and modulation. Slow variations of time scale shows that thermal modulation impact on transport phenomenon for the case of out phase modulation (OPM) and (lower boundary modulation) LBM. Also the effect of IPM (in-phase modulation) is observed low effect on Nu and which are similar to un-modulation case. It is also justified that LBM restuls are similar to gravity modulation results. It is found that thermal modulation and concentration Rayleigh numbers are either stabilize or destabilize the system. Further, GL model shows better results on regulation of transport process

Subsonic time-periodic solution to compressible Euler equations with damping in a bounded domain

In this paper, we consider the one-dimensional isentropic compressible Euler equations with linear damping β(t,x)ρu in a bounded domain, which can be used to describe the process of compressible flows through a porous medium. And the model is imposed a dissipative subsonic time-periodic boundary condition. Our main results reveal that the time-periodic boundary can trigger a unique subsonic time-periodic smooth solution which is stable under small perturbations on initial data. Moreover, the time-periodic solution possesses higher regularity and stability provided a higher regular boundary condition.

Reaction-Diffusion Dynamics of pH Oscillators in Oscillatory Forced Open Spatial Reactors.

Studying the effect of coupling and forcing of oscillators is a significant area of interest within nonlinear dynamics and has provided evidence of many interesting phenomena, such as synchronization, beating, oscillatory death, and phase resetting. Many studies have also reported along this line in reaction–diffusion systems, which are preferably explored experimentally by using open reactors. These reactors consist of one or two homogeneous (well-stirred) tanks, which provide the boundary conditions for a spatially distributed part. The spatiotemporal dynamics of this configuration in the presence of temporal oscillations in the homogeneous part has not been systematically investigated. This paper aims to explore numerically the effect of time-periodic boundary conditions on the dynamics of open reactors provided by autonomous and forced oscillations in the well-stirred part. A simple model of pH oscillators can produce various phenomena under these conditions, for example, superposition and modulation of spatiotemporal oscillations and forced bursting. The autonomous oscillatory boundary conditions can be generated by the same kinetic instabilities that result in spatiotemporal oscillations in the spatially distributed part. The forced oscillations are induced by sinusoidal modulation on the inflow concentration of the activator in the tank. The simulations confirmed that this type of forcing is more effective when the modulation period is longer than the residence time of the well-stirred part. The use of time-periodic boundary conditions may open a new perspective in the control and design of spatiotemporal phenomena in open one-side-fed and two-side-fed reactors.

Performance evaluation of different pressure-velocity decoupling schemes in built environment simulation

Simulations of indoor airflow can effectively assist in the design of a built environment. However, the intensive computational cost of current computational fluid dynamics (CFD) techniques restricts their efficient deployment, especially in transient airflow simulations. The fast fluid dynamics (FFD) method and fractional-step (FS) method have demonstrated their potential to reduce computational cost by reforming conventional pressure-velocity decoupling algorithms. Thus, this study evaluated the computational accuracy and computational efficiency of four promising schemes, which were chosen and developed from the FFD and FS methods, by applying them to lid-driven cavity flow and forced convection flow. All cases were simulated under constant boundary conditions and periodic boundary conditions with different time step sizes. The results showed that the FS method can achieve similar computational accuracy as the pressure-implicit with splitting operators (PISO) algorithm with approximately half the computational cost. The accuracy of one scheme of the FS method decrease rapidly with increasing time step size. The FFD method can reduce computational cost significantly because it is stable with a large time step size and is more suitable for large-scale numerical simulations. Simulation results of ventilation cases employing these methods also proved that time-periodic boundary conditions induced periodic changes in indoor airflow patterns that could facilitate the dispersion of air pollutants, especially in airflow stagnation areas.

Mathematical Study of Nonlinear Mixed Convection Unsteady Flow in a Parallel Plate Inclined Channel in the Proximity of Time Periodic Boundary Conditions: Flow Reversal

This report is executed to examine the task of assimilating parameters on bipartite convection stream structure in a sloped pipeline while certain plate is disorderly warmed. The dictating motivation and energy identifications are ascertained and consequent expressions for thermal reading, liquid movement, fanning friction and stress flatten are acquired. The purpose of non-linear Boussinesq simulation is to escalate liquid movement, inverse stream generation at the channel plates, stress flatten, and fanning factor. In particular, the liquid motion escalates at the channel left portion and depletes at the channel right portion with the progress of time. A particular case of our development shows an excellent compromise with the previous consequences in the literature.

Transient Three-Dimensional Natural Convection in Confined Porous Media with Time-Periodic Boundary Conditions

Transient three-dimensional natural convection in confined fluid-saturated porous media had been investigated numerically through this work. The geometry selected is a box with time-periodic temperature variation at the vertical sides and constant wall temperature at the top and bottom. In this investigation, the momentum equation of flow through fluid-saturated porous media had been transformed to a vector potential form and solved numerically using the Successive Over Relaxation method while the energy equation is solved using the three-dimensional Alternating Direction Implicit method. The values of the Rayleigh number under investigation are (150, 200, 250 and 300). The results are presented in a form of contour maps for the temperature and a velocity vector maps for the velocity. The results reveal that the temperature within the box is increased as the time or Rayleigh number increase.The Nusselt number varies inversely with the time and directly with the Rayleigh number. Two cell convective patterns are obtained in the y-z

Influence of Heat Generation/Absorption on Mixed Convection Flow Behaviour in the Presence of Lorentz Forces in a Vertical Micro Circular Duct Having Time Periodic Boundary Conditions: Steady Periodic Regime

The problem of mixed convection flow of a heat generating/absorbing fluid in the presence existence of Lorentz forces in a vertical micro circular subjected to a periodic sinusoidal temperature change at the surface has been studied taking the first-order slip and jump effects into consideration. The research analysis is carried out by considering a fully developed parallel flow and steady periodic regime. The governing equations, together with the constraint equations which arise from the definition of mean velocity and temperature, are written in a dimensionless form and mapped into equations in the complex domain. One obtains two independent boundary value problems, which provide the mean value and the oscillating term of the velocity and temperature distributions. These boundary value problems are solved analytically. A parametric study of some of the physical parameters involved in the problem is conducted. The results of this research revealed that the magnetic field has a damping impact on the flow and results in decreases in fluid velocity for both air and water. Furthermore, the presence of the heat generation parameter is seen to enhance the temperature distribution and this is reflected as an increase in the magnitude of the oscillation dimensionless velocity, whereas in the presence of heat absorption a reversed trend occurs.

Nonlinear Mixed Convection Flow in an Inclined Channel with Time-Periodic Boundary Conditions

This article scrutinises the role of nonlinear Boussinesq approximation on mixed convection flow in an inclined channel when one of the walls is kept at constant temperature while is other one is periodically heated. By expanding the Boussinesq approximation up to second degree Taylor series expansion, the governing momentum and energy equations are derived and solved analytically. During the course of graphical and numerical simulations, results show that the role of nonlinear Boussinesq approximation is to increase fluid velocity, interval of reverse flow formation at the walls, pressure drop and fanning frictional factor.

In-plane vibration of a rigid body attached to a flexible rotating beam

The dynamics of rotating systems are conventionally analyzed using models that assume the axis of rotation to be stationary. However, in instances such as helicopters and gas turbines with contra-rotating rotors such models which neglect the complexity arising from the coupling between the stator and the rotor due to their comparable masses can lead to inaccurate predictions. This paper examines the coupled stator-rotor dynamics of a model comprising a rigid (but non-stationary) body which is excited with a flexible rotating beam. Equations of motion governing the model's dynamics are developed and are found to have time-periodic boundary conditions. For the axisymmetric case the system loses its time dependence; the natural frequencies and the mode shapes vary with rotation speed. Specific modes soften within certain speed regimes, while other modes stiffen. Instabilities such as divergence and flutter are observed, and the effects of parameters on the critical speeds are investigated. The non-axisymmetric case is parametrically excited at twice the rotation speed. Floquet theory is employed to develop stability charts; regimes of instability exhibit a definitive structure comprising simple and combination parametric resonances. Temporal responses are modulated, and they exhibit characteristic side-banded frequency spectra.

Mixed Convection Flow Behaviour in Existence of Lorentz Forces in a Vertical Micro Circular Duct having Time Periodic Boundary Conditions: Steady Periodic Regime

The purpose of this research is to study mixed convection flow behaviour in existence of Lorentz forces in a vertical micro circular subjected to a periodic sinusoidal temperature change at the surface. Effects of velocity slip and temperature jump are also taken into consideration. The research analysis is carried out by considering fully developed parallel flow and steady periodic regime. The governing equations, together with the constraint equations with arise from the definition of mean velocity and temperature, are written in a dimensionless form and mapped into equations in the complex domain. One obtains two independent boundary value problems, which provide the mean value and the oscillating term of the velocity and temperature distributions. These boundary value problems are solved analytically. Numerical procedures are examined for various active parameters namely; fluid wall interaction, rarefaction, Hartmann number, Prandtl number, the dimensionless frequency. The results of the research revealed that, magnetic field plays a damping impact in flow and results in decreases in fluid velocity for both air and water. Further, increases the rarefaction parameter and fluid-wall interaction parameter reduces the oscillation amplitude of the dimensionless velocity.

Unsteady natural convection flow of a suspension comprising Nano-Encapsulated Phase Change Materials (NEPCMs) in a porous medium

The free convection phase change heat transfer of a suspension comprising Nano-Encapsulated Phase Change Materials (NEPCMs) in a porous space is theoretically addressed. The core of the nanoparticles is made of a phase change material and encapsulated in a thin shell. Hence, the core of the nanoparticles of the suspension undergoes a phase change at its fusion temperature and release/store large amounts of latent heat. The phase change of nanoparticles is modeled using a sine shape temperature-dependent heat capacity function. Darcy-Brinkman model is used to model the flow in the porous medium. The governing equations including the conservation of mass, momentum, and heat are transformed into a non-dimensional form before being solved by the finite element method in a structured non-uniform mesh. The influence of the porosity, Darcy number, Rayleigh number, fusion temperature of nanoparticles, and the unsteady time-periodic boundary conditions on the thermal behavior of the porous medium in the presence of NEPCM particles is investigated. The results show that the presence of NEPCM particles improves the heat transfer. The increase of porosity improves the heat transfer when the volumetric concentrations of NEPCM particles are higher than 3%. There exists an optimal dimensionless fusion temperature of NEPCM nanoparticles for the interval [0.25; 0.75].

Investigation of using multi-layer PCMs in the tubular heat exchanger with periodic heat transfer boundary condition

Storing and releasing thermal energy at an almost constant temperature is the benefit of employing phase change materials, which makes them a useful material to reduce energy usage in industrial applications. In the present study, the effect of charging and discharging of multi-layers of Phase Change Materials (PCMs) in coaxial cylinders with a time-periodic boundary condition is numerically investigated. The 2D problem is solved with the finite-element method, and convection modeling is also included. The Carman Kozeny model is utilized to control the natural convection velocities in solid and liquid regions. Fifteen cases are introduced so as to capture the effect of arrangements and thicknesses of the PCMs. First simulations were targeted to understand different arrangements effect on melting and transferring heat from the inner tube to the outer wall. Then, different layers’ number and thickness of each section were examined. Results are shown in terms of liquid fractions, temperatures, and velocity streamlines. The results assert that unlike the outer section, the inner one is more susceptible to the change of hot heat transfer fluid (HHTF) temperature. Moreover, the rate of saved energy within PCMs to the inlet energy is calculated for all cases. In the case of one-layer of RT65, the system can only save 23.28% of inlet energy. While in the specific thickness and arrangement of three-layer PCM, the amount of saved energy within the PCMs reach to 41.67%.

Time-periodic solutions to quasilinear hyperbolic systems with time-periodic boundary conditions

For quasilinear hyperbolic systems with time-periodic boundary conditions possessing a dissipative structure, the existence, uniqueness and stability of the time-periodic classical solutions are proved. Moreover, the feedback boundary control with dissipative structure can stabilize the system around the time-periodic solution, provided that the time-periodic boundary conditions are W2,∞ smooth.

Natural Convection Heat and Mass Transfer in the Vertical Cylindrical Porous Channel Under the Effects of Time-Periodic Boundary Condition

Abstract Heat and mass transfer are investigated numerically with steady-state laminar natural convection through a vertical cylindrical enclosure filled with a liquid-saturated porous medium. The vertical wall is under a constant magnetic field and various durations of periodic heating boundary condition; the top and bottom surfaces are kept at a constant cold temperature. Continuity, momentum, and energy equations are transformed to dimensionless equations. The finite difference approach with the line successive over-relaxation (LSOR) method is used to obtain the computational results. This study covers the heat transfer, the temperature distribution, and the velocity field in the domain under the variation of different parameters. The code used is validated by modifying it to analyze the Nusselt number in the existing experimental literature of Izadpanah et al. (1998, “Experimental and Theoretical Studies of Convective Heat Transfer in a Cylindrical Porous Medium,” Int. J. Heat Fluid Flow, 19(6), pp. 629–635). This work shows that Nusselt number decreases (with varying gradient) as the aspect ratio increases, and that it increases as the Rayleigh number increases. The centerline temperature has a proportional relationship with the heating amplitude and the heating period (as the system receives more heat) and is inversely proportional with Rayleigh number. Increasing the Rayleigh number causes increased convective velocity, which affects the position of the hot region, and causes a decrease in the temperature field. Increasing the aspect ratio results in a warm stream at the center of the cylinder, and when the time period of the heating increases, the circulation becomes faster and the intensity of the temperature contour layers decreases. In this work, a correlation for Nu as a function of the mentioned parameters is developed.