Inertia Terms Research Articles

Spatiotemporal linear stability of viscoelastic Saffman–Taylor flows

The temporal and spatiotemporal linear stability analyses of a displaced Oldroyd-B fluid with the mean flow in a horizontally aligned, square, Hele–Shaw cell are reported to identify the regions of topological transition of the advancing interface. The viscosity of the displacing fluid is negligible in comparison to the displaced fluid. While all the inertial terms in the model are retained, the interface is assumed to evolve on a slow timescale compared with the timescale of the perturbation (or the so-called “quasi-stationary” approximation). The parameters governing stability are the Reynolds number Re=b2ρU012η2L, the elasticity number E=12λ(1−ν)η2ρb2, and the ratio of the solvent to the polymer solution viscosity ν=ηsη2, where b,L,U0,ρ,λ are the cell gap, the cell length (or width), the mean flow velocity, the density of the driven fluid, and the polymer relaxation time, respectively. Reasonably good agreement on the relative finger width data computed with our model and the experimental data in the Stokes and the inertial Newtonian regime is found. In the asymptotic limit E(1−ν)≪1, the critical Reynolds number, Rec, diverges as Rec∼[E(1−ν)]−5/3 and the critical wavenumber, αc, increases as αc∼[E(1−ν)]−2/3. In a confined domain, the temporal stability analysis indicates (a) the destabilizing influence of the inertial terms, (b) the destabilizing impact of the finite boundaries near the wall, and (c) the stabilizing impact of elasticity until a critical Reynolds number. The Briggs idea of analytic continuation is deployed to classify regions of absolute and convective instabilities as well as the evanescent modes. The phase diagram reveals the presence of an absolutely unstable region at high values of Reynolds and elasticity number, confirming the role of fluid inertia in triggering a pinch-off.

Simulation of forced convective power law fluid by using Darcy–Brinkman–Forchheimer flow model field

This study investigates the fully developed heat transfer of steady, incompressible and laminar flow of power law fluid saturated porous medium through the rectangular duct by utilizing Darcy–Brinkman–Forchheimer flow model field. Hydrodynamic flow of power law-based fluid within a rectangular duct with porosity has not been reported in the literature. The consideration of Darcy–Brinkman–Forchheimer flow model makes it very much novel in its own right. The main objective of the present study is to explore the modified Darcy parameter on flow and heat transfer characteristics. Numerical results are obtained for different values of Darcy parameter, Da, inertia coefficient, Fr and power law model, n. We note the significant impact of inertial force on flow and heat transfer in the case of dilatant fluid; however, inertial force term can be ignored in the case of pseudo-plastic fluid due to its lower effect. Furthermore, with the decrease in aspect ratio, the effect of the inertial force can be reduced. It is also noted that, axial velocity significantly enhances with Darcy parameter Da. This behavior of the axial velocity is found to be similar for higher inertia coefficient Fr as well.

A Semi-analytical Solution for the Dynamic Analysis of a Rectangular Viscoelastic Plate Subjected to a Moving Inertial Load

A semi-analytical method is developed to determine the response of a thin rectangular plate made of a general viscoelastic material to the excitation of a moving inertial load. The governing equation of the general problem is derived in the Laplace domain, which, for any particular viscoelastic model, is transformable into a system of differential equations in the time domain. Any standard procedure can then be readily employed to solve this system of equations. Using this method, sample response spectra are presented, through which the effect of viscosity, mass and velocity is scrutinized. The results show that, when the viscosity is not large enough, inertial terms cannot be ignored, especially when a heavy load is travelling at a high velocity.

Liquid air energy storage for ancillary services in an integrated hybrid renewable system

High shares of intermittent renewable sources cause volatile frequency movements that could jeopardize the continuous operation of the grid. Liquid Air Energy Storage (LAES) is an emerging technology that not only helps with decarbonisation of energy sectors, but also has potentials for reliable ancillary services. In this paper, a hybrid LAES, wind turbine (WT), and battery energy storage system (BESS) is used to investigate their contributions in fast frequency control. The inertial control, droop control and combined inertial and droop terms are applied on each source of the hybrid renewable system and a comprehensive analysis is conducted to study their impacts on the frequency nadir improvement. The analysis shows that LAES with combined inertial and droop control terms along with inertial control of WT and BESS provide reliable frequency control. To further improve the frequency nadir, a Fuzzy control is proposed and applied on the LAES. The proposed control system provides a more adaptive performance against disturbances. Also, experimental tests are conducted to validate the proposed control method using a real-time hardware-in-the-loop test rig. The simulation and experimental results show that LAES in a hybrid renewable system can significantly contribute to the frequency control when variable gain control schemes are implemented.

Numerical study of laminar natural convection in a half ellipsoid of revolution subjected to heat flux of constant density

In this article, we numerically study the natural convection in a half-eliipsoid of revolution filled with a Newtonian fluid (air). The ellipsoid wall is isothermal which is maintained at a heat flux of constant density. The equations that govern the flow and heat transfer are described by the so-called Navier-Stokes equation of motion accompanied by the so-called Fourier equation of heat. The finite element method is used to solve the system of equations. We consider the effect of the shape factor of the elliptical wall and the Grashof number on the results obtained in the form of streamlines, and mean Nusselt numbers. The Nusselt numbers for natural convection inside a system formed by a rectangular geometry and for a curved shape are comparer and analyzed each other. We find that this number is quite higher for a curved system than that of a planar shape. It shows the importance of the form factor, particularly, in circular shape which is much more advantageous compared to the straight shape.In terms of inertia, the geometry of rounded shape ensures the best distribution of energy. In fact, the half ellipsoidal greenhouse with a circular base studied during this research offers a better distribution for the flow of the convection currents from the bottom to the top of the system.

A simple model for elastic wave propagation in hard sphere-filled random composites.

A simple model is proposed to study wave propagation in hard sphere-reinforced elastic random composites. Compared to existing related models, the proposed model is featured by a modified form of classical elastodynamic equations in which the inertia term is substituted by the acceleration field of the mass centre of a representative unit cell, supplied with a derived simple differential relation between the displacement field of the composite and the displacement field of the mass centre of a representative unit cell. The present model enjoys conceptual and mathematical simplicity although it is restricted to hard sphere-filled elastic composites in which the elastic moduli of embedded spheres are much (at least 4-5 times) stiffer than those of a softer matrix. Explicit formulas are derived for the attenuation coefficient and the effective phase velocity of plane longitudinal P-waves and transverse S-waves. The efficiency and reasonable accuracy of the present model are demonstrated by reasonably good agreement between the predicted results and some established known data. The proposed model could offer a potential general method to study various three-dimensional dynamic problems of hard sphere-filled elastic random composites.

Hygrothermal performance assessment of a bio-based building made with date palm concrete walls

The current research falls within the general context of expanding and developing bio-based materials as insulating and low-cost construction materials. This paper aims to investigate the effect of mass transfer on hygrothermal conditions, and the energy consumption of a building made with date palm concrete (DPC). As well as, highlighting the performance of this new bio-composite material compared to other classical materials. The results were obtained by numerical simulation using EnergyPlus software. Firstly, the hygrothermal model was validated using experimental data. Afterward, the model was used to investigate the influence of moisture transport on indoor temperature, relative humidity, and energy consumption of a DPC building. The results indicate that mass transport through the DPC envelope significantly influences indoor relative humidity and building energy consumption, particularly during the summertime. On the contrary, the indoor temperature remains to be less influenced by mass transport through the building walls. Finally, the hygrothermal performances of DPC and conventional construction materials (Autoclaved Aerated Concrete, AAC) were compared in terms of thermal and hydric inertia, energy saving, and condensation risk. The results show that DPC significantly dampens and delays the temperature variation, mitigates relative humidity variations, and reduces cooling energy, especially in humid and semi-arid climates. Furthermore, DPC ensures that there is no risk of vapor condensation occurring on the envelope's surfaces.

On the auto-oscillation effect of Kaplan rotors during load rejection

High vibrations due to auto-oscillation effects can occur at power units with Kaplan type runner during load rejection. These vibrations may be present in the turbine braking mode when the wicket gates are almost closed, and the rotating runner pushes the water towards the draft tube resulting in higher pressure below the runner blades. The upward leakage flow between runner blades and discharge ring is suspected to cause the vibration phenomenon.Within this contribution, a fluid-structure-interaction (FSI) technique is applied to identify the mechanism of self-excitation. The investigation is carried out on a disk that represents the simplified geometry of a Kaplan runner. Computational fluid dynamics (CFD) simulations are used in order to obtain parameters in terms of stiffness, damping and inertia of the fluid to be applied in the following shaft line analysis. Damped modal analyses of the shaft line allow for evaluation of the stability of natural frequencies and corresponding mode shapes of the shaft line. A resulting negative damping indicates the occurrence of auto-oscillation behavior of the shaft line. For the operating condition under investigation, mode shapes with negative damping are obtained with this approach and a dynamic bending moment on the runner due to lateral movement in combination with a tilting at the runner in these mode shapes is identified as source of instability.Based on these findings, an analytical approach for modeling the relevant effect is derived and compared to CFD result as well as results from acoustic finite element modelling. Finally, conclusions for avoidance of self-excited vibrations at Kaplan runners are proposed.

Strong and linear convergence of projection-type method with an inertial term for finding minimum-norm solutions of pseudomonotone variational inequalities in Hilbert spaces

Strong and linear convergence of projection-type method with an inertial term for finding minimum-norm solutions of pseudomonotone variational inequalities in Hilbert spaces

The negative dielectric permittivity of polycrystalline barium titanate nanofilms under high-strength kHz-AC fields

Unlike the conventional high-frequency dielectric behavior for which the amplitude of the applied field is too small to cause polarization switching, the dynamically-driven polarization reorientation brings remarkable frequency dependence to the nonlinear electromechanical behaviors of ferroelectric nanofilms. In this study, we developed a thermodynamically consistent phase-field model with an introduced second-order kinetic equation to investigate the dynamics of polarization switching in polycrystalline barium titanate nanofilms under high-strength AC fields. The newly introduced kinetic equation consists of an additional dynamic inertial term that brings about collective resonance of polarization within a certain frequency range. Negative dielectric permittivity is observed in a certain frequency band as the applied frequency varies from 30 to 80 kHz, and the maximum absolute value is reached around 40 kHz. It was demonstrated through microstructure-based analysis that such negative dielectric behavior is inherited from the frequency-dependent polarization switching in the nanograins. It also serves as the mechanism for other observed frequency-dependent physical properties, e.g., the remnant polarization, the piezoelectric coefficient at zero electric field and the coercive field. In addition, we further explored the influence of the damping coefficient in the kinetic equation and the influence of the in-plane strain to such frequency-dependent behaviors. It was found that a higher damping coefficient or applied in-plane strain tends to weaken the occurrence of negative permittivity.

Inundation over land with increasing water depth using self-similarity analysis

ABSTRACT This paper describes a self-similarity-analysis-based inundation process in which the water depth at the inlet increases as a power function of time. Numerical analyses of the inundation process are conducted to evaluate the feasibility and stability of two types of regimes: inertia-pressure regime and pressure-friction regime. Numerical simulations using the shallow water equations are conducted to investigate the influence of the increments in scaling coefficient and power which determine the temporal variation of the inlet water depth on the inundation process. Both regimes were realized in the numerical simulations, without considering the friction or inertia terms. Based on the linear stability analysis, it was proved that these processes are stable regardless of the increment in the scaling coefficient of the inlet water depth. The early phase of the inundation process is dominated by the scaling coefficient; whereas, eventually the inundation process depended on power.

Time-Differencing Fundamental Solutions for Plane Elastodynamics

In this paper, new fundamental solutions for dynamic analysis of plane elastodynamics are developed. The governing dynamic differential equations are rewritten by replacing the accelerations with the corresponding displacements at different time steps via a suitable finite difference scheme. The known displacements in initial conditions or from previous time steps are treated as generalized new inertia terms. The unknown displacements at the current time step are added to the governing differential operator to form a new operator. The new time-dependent fundamental solutions are then derived with respect to the new differential operator. The required mathematical derivations are presented in detail. The corresponding integral equations and domain load treatments are also presented. Singular integrals of the derived fundamental solutions are also treated. Several numerical examples are solved to demonstrate the validity and the accuracy of the developed new solutions. The results demonstrated the accuracy of the developed new solutions compared to traditional time domain fundamental solutions.

A novel model of pressure drop for airflow penetrating randomly packed cylindrical particles

Pressure drop is the key factor related to performance and energy consumption of fixed bed. However, the packing of cylindrical particles produces anisotropic gaps and an extremely complex airflow field and makes the formation mechanism of flow resistance undefined. This study conducted a comprehensive investigation on how such factors as the void fraction, diameter, and aspect ratio of cylinders on the flow resistance, in terms of experimental and numerical methods. With the DEM-CFD simulation, the laminar and transitional flow pattern was acquired, and the critical Reynolds number was determined. The expression of void fraction in the inertia term of the original Ergun equation was confirmed not applicable to cylindrical particles, which was proved to be the reason why previous predictions cannot accurately give the flow resistance of packed cylindrical particles. Finally, a new prediction model for the pressure drop of airflow penetrating the packed cylindrical particles was developed.

Dynamic Response and Synchronizing Characteristic for the Dual-Motor Driving System in Non-Inertial System

As one of the typical propulsion systems of the new-energy vehicles (NEVs), the dual-motor driving system (DMDS) is installed and fixed on the bodywork and moves together with the bodywork in space, that is, the DMDS works in non-inertial systems. The previous researches on the DMDS are based on the assumption that the bodywork is stationary. In fact, since the DMDS moves with the bodywork, besides its own excitation forces, it is inevitably affected by the additional inertial terms (AITs) caused by the change in the operating state of the NEVs. In order to investigate the dynamic response and synchronizing characteristic of the DMDS under different motion forms of NEVs, the dynamic model of the DMDS in a non-inertial system is established, considering the permanent magnet synchronous motors (PMSMs), time-varying meshing stiffness and transmission error of gears. Subsequently, the expressions of the AITs are deduced under different non-inertial conditions. The translational motion and circular motion of the vehicle are selected to analyze the dynamic response and synchronizing characteristics of the DMDS in a non-inertial system. The results show that the acceleration has a significant influence on the displacement response of gears, torque and speed of PMSMs, but the torque synchronization and speed synchronization between PMSMs are minimally influenced by both the acceleration and the AITs. Meanwhile, the AITs that affect the displacement response are analyzed and quantified.

Inertial primal-dual dynamics with damping and scaling for linearly constrained convex optimization problems

We propose an inertial primal-dual dynamic with damping and scaling coefficients, which involves inertial terms both for primal and dual variables, for a linearly constrained convex optimization problem in a Hilbert setting. With different choices of damping and scaling coefficients, by a Lyapunov analysis approach, we investigate the asymptotic properties of the dynamic and prove its fast convergence results. Our results can be viewed as extensions of the existing ones on inertial dynamical systems for the unconstrained convex optimization problem to the primal-dual one for the linearly constrained convex optimization problem.

Effect of the inertial term of the ion momentum equation on fluid transport simulation for capacitively coupled plasma sources

Fluid-based simulations are widely used to analyze or optimize capacitively coupled plasma sources. Although the inertial term of the ion momentum equation affects the accuracy of the solutions, the equation has not been considered in the drift-diffusion approximation model in the numerical solution. Therefore, we, herein, improved the accuracy of the model by applying an effective electric field, considering the inertial term. First, the effective electric field, including the ion inertial term of the ion momentum equation, was derived. Subsequently, one-dimensional fluid simulations were conducted. The numerical results were compared with those of one-dimensional particle-in-cell (PIC) simulations. The results of the developed model were similar to those obtained in the case of solving the full-ion momentum equation, as well as more similar to the PIC simulation results than those obtained in the case of the drift-diffusion approximation.

Inertial alternating direction method of multipliers for non-convex non-smooth optimization

In this paper, we propose an algorithmic framework, dubbed inertial alternating direction methods of multipliers (iADMM), for solving a class of nonconvex nonsmooth multiblock composite optimization problems with linear constraints. Our framework employs the general minimization-majorization (MM) principle to update each block of variables so as to not only unify the convergence analysis of previous ADMM that use specific surrogate functions in the MM step, but also lead to new efficient ADMM schemes. To the best of our knowledge, in the nonconvex nonsmooth setting, ADMM used in combination with the MM principle to update each block of variables, and ADMM combined with \emph{inertial terms for the primal variables} have not been studied in the literature. Under standard assumptions, we prove the subsequential convergence and global convergence for the generated sequence of iterates. We illustrate the effectiveness of iADMM on a class of nonconvex low-rank representation problems.

Approximation methods with inertial term for large-scale nonlinear monotone equations

In recent years, systems of nonlinear equations have attracted widespread attention and have been extensively studied. The recent designed Fletcher-Reeves (FR) type methods of Papp and Rapajić [Appl. Math. Comput. 269 (2015) 816–823] [27] are efficient in solving large-scale monotone nonlinear equations due to the simple iterative form. In this paper, we propose an accelerated variant of these FR-type methods for approximating the solutions of nonlinear equations involving monotone and Lipschitz continuous mappings. Under suitable assumptions, we prove that the sequence generated by the new algorithm converges globally. Some numerical results are reported to illustrate the computational performance of the new methods.

Exponential stabilisation analysis of a class of delayed inertial memristive neural networks

This paper focuses on the exponential stabilisation problem of inertial memristive neural networks (IMNNs) with unbounded discrete time-varying delays. The considered IMNNs are modelled by second-order derivatives equations by introducing the inertial terms. By using nonsmooth analysis, Lyapunov stability theory, inequality techniques and integral-differential of Lyapunov functional method, a feedback controller is designed to guarantee pth moment exponential stabilisation of the addressed IMNNs under the framework of Filippov solutions. It is worth noticing that the considered time delays of IMNNs can be unbounded. Finally, a numerical example is presented to illustrate the effectiveness of the main theoretical result.

Inertial Term Accounting in Navier-Stokes Equation of Magnetohydrodynamic Domains Model for a Nematic with Negative Anisotropy of Diamagnetic Susceptibility

Inertial Term Accounting in Navier-Stokes Equation of Magnetohydrodynamic Domains Model for a Nematic with Negative Anisotropy of Diamagnetic Susceptibility