Incompressible Model Research Articles

Unconditional finite amplitude stability of a fluid in a mechanically isolated vessel with spatially non-uniform wall temperature

We investigate finite amplitude stability of spatially inhomogeneous steady state of an incompressible viscoelastic fluid which occupies a mechanically isolated vessel with walls kept at spatially non-uniform temperature. For a wide class of incompressible viscoelastic models including the Oldroyd-B model, the Giesekus model, the FENE-P model, the Johnson--Segalman model, and the Phan--Thien--Tanner model we prove that the steady state is stable subject to any finite perturbation.

Tolman length of simple droplet: Theoretical study and molecular dynamics simulation* *Project supported by the National Key Research and Development Program of China (Grant No. 2016YFB0700500), the Scientific Research and Innovation Team of Cangzhou Normal University, China (Grant No. cxtdl1907), the Key Scientific Study Program of Hebei Provincial Higher Education Institution, China (Grant No. ZD2020410), the Cangzhou Natural Science Foundation,

In 1949, Tolman found the relation between the surface tension and Tolman length, which determines the dimensional effect of the surface tension. Tolman length is the difference between the equimolar surface and the surface of tension. In recent years, the magnitude, expression, and sign of the Tolman length remain an open question. An incompressible and homogeneous liquid droplet model is proposed and the approximate expression and sign for Tolman length are derived in this paper. We obtain the relation between Tolman length and the radius of the surface of tension (R s) and found that they increase with the R s decreasing. The Tolman length of plane surface tends to zero. Taking argon for example, molecular dynamics simulation is carried out by using the Lennard–Jones (LJ) potential between atoms at a temperature of 90 K. Five simulated systems are used, with numbers of argon atoms being 10140, 10935, 11760, 13500, and 15360, respectively. By methods of theoretical study and molecular dynamics simulation, we find that the calculated value of Tolman length is more than zero, and it decreases as the size is increased among the whole size range. The value of surface tension increases with the radius of the surface of tension increasing, which is consistent with Tolman’s theory. These conclusions are significant for studying the size dependence of the surface tension.

Entropy anatomization on Marangoni Maxwell fluid over a rotating disk with nonlinear radiative flux and Arrhenius activation energy

Numerical analysis is performed for an incompressible Marangoni Maxwell nanofluid flow model under the implications of thermophoresis, brownian motion and nonlinear radiation over a convectively heated rotating disk. The second law of thermodynamics is also incorporated. The system that comprises differential equations of partial derivatives is remodeled into the system of differential equations via similarity transformations and then solved numerically through the Runge-Kutta-Fehlberg with shooting technique. The physical parameters, which emerges from the derived system are discussed in graphical formats. The significant outcomes of the current investigation are that the velocity filed decays for a higher magnetic parameter, the heat transfer rate is enhanced with the incremental values of radiation parameter and Prandtl number. Further, the entropy generation rate decreases with the fluid parameter while that peters out the Bejan number.

High Reynolds number and high Weissenberg number Oldroyd-B model with dissipation

We give a small data global well-posedness result for an incompressible Oldroyd-B model with wave-number dissipation in the equation of stress tensor. The result is uniform in solvent Reynolds numbers and requires only fractional wave number-dependent dissipation $$(-\Delta )^{\beta }$$ , $$\beta \ge \frac{1}{2}$$ in the added stress.

Large eddy simulation of a double-injection cycle and the impact of the needle motion on the sac-volume flow characteristics of a single-orifice diesel injector

Study of the flow within diesel injector has gained in importance over the years as several authors have reported that the injector flow in the sac volume highly influenced the nozzle-flow characteristics at low lifts. Few studies have, however, characterized the sac volume and its dynamics. Thus, this paper reports on a numerical characterization of the needle displacement effects (static vs dynamic) on the internal flow of a sac-volume, single-hole diesel injector. To this end, a transient double-injection “closing-opening-closing-opening” cycle was simulated with a monophasic incompressible CFD model in combination with a moving mesh strategy to capture axial needle displacement. A large eddy simulation (LES) approach was chosen to gain better insight into the complexity of this unsteady turbulent flow. The emphasis of the paper is on the dynamic effects of needle movement on the sac flow, while static needle LES results are also shown to illustrate differences. The main findings reported herein are that the dynamic model shows a hysteresis effect associated with the needle motion between opening/closing phases. Quantitatively, the transient needle movement caused a difference in mass flow rate between the sac entrance and exit that was found to reach a maximum of [Formula: see text]. The hysteresis effect was found to be more pronounced at low needle lifts; both static and dynamic models seem to have performed similarly at very high needle lifts. Qualitatively, the LES sac-volume flow representations revealed a fuel jet attachment/detachment with needle movement, while static partial-lift simulations always predict an attached fuel jet. Further analysis of sac vortex dynamics revealed a high-energy vortex-structure breakdown just before the nozzle entrance that could help explain the higher turbulence production reported in the literature, both experimentally and numerically, at low needle lifts.

Low Mach number limit for the compressible inertial Qian-Sheng model of liquid crystals: Convergence for classical solutions

<p style='text-indent:20px;'>In this paper we study the incompressible limit of the compressible inertial Qian-Sheng model for liquid crystal flow. We first derive the uniform energy estimates on the Mach number <inline-formula><tex-math id="M1">\begin{document}$ \epsilon $\end{document}</tex-math></inline-formula> for both the compressible system and its differential system with respect to time under uniformly in <inline-formula><tex-math id="M2">\begin{document}$ \epsilon $\end{document}</tex-math></inline-formula> small initial data. Then, based on these uniform estimates, we pass to the limit in the compressible system as <inline-formula><tex-math id="M3">\begin{document}$ \epsilon \rightarrow 0 $\end{document}</tex-math></inline-formula>, so that we establish the global classical solution of the incompressible system by compactness arguments. We emphasize that, on global in time existence of the incompressible inertial Qian-Sheng model under small size of initial data, the range of our assumptions on the coefficients are significantly enlarged, comparing to the results of De Anna and Zarnescu's work [<xref ref-type="bibr" rid="b6">6</xref>]. Moreover, we also obtain the convergence rates associated with <inline-formula><tex-math id="M4">\begin{document}$ L^2 $\end{document}</tex-math></inline-formula>-norm with well-prepared initial data.

Computational and Experimental Study on Pressure Drop in a Fluidised Bed with Different Air Distributor Designs

Fluidised bed combustion (FBC) has been recognised as a suitable technology for converting a wide variety of fuels into energy. In a fluidised bed, the air is passed through a bed of granular solids resting on a distributor plate. Distributor plate plays an essential role as it determines the gas-solid movement and mixing pattern in a fluidised bed. It is believed that the effect of distributor configurations such as variation of free area ratio and air inclination angle through the distributor will affect the operational pressure drop of the fluidised bed. This paper presents an investigation on pressure drop in fluidised bed without the presence of inert materials using different air distributor designs; conventional perforated plate, multi-nozzles, and two newly proposed slotted distributors (45° and 90° inclined slotted distributors). A 3-dimensional Computational Fluid Dynamics (CFD) model is developed and compared with the experimental results. The flow model is based on the incompressible isothermal RNG k-epsilon turbulent model. In the present study, systematic grid-refinement is conducted to make sure that the simulation results are independent of the computational grid size. The non-dimensional wall distance, is examined as a key factor to verify the grid independence by comparing results obtained at different grid resolutions. The multi-nozzles distributor yields higher distributor pressure drop with the averaged maximum value of 749 Pa followed by perforated, 45° and 90° inclined distributors where the maximum pressure drop recorded to be about one-fourth of the value of the multi-nozzles pressure drop. The maximum pressure drop was associated with the higher kinetic head of the inlet air due to the restricted and minimum number of distributor openings and low free area ratio. The results suggested that low-pressure drop operation in a fluidised bed can be achieved with the increase of open area ratio of the distributor.

Simulation of pollutant dispersion in urban street canyons using hybrid rans-les method with two-phase model

In this study, to simulate the pollution treatment as a separated phase a 3D incompressible turbulence model under isothermal conditions was considered. The hybrid RANS-LES method with a sub-grid scale(SGS) technique within the framework of two-phase flow was used to study pollution distribution in urban street canyons. An area source of pollutant with a constant concentration, located in the ground of the street canyon, was used to simulate vehicular emissions. The near-wall regions were simulated using the RANS(k-ε) turbulence model and the rest of the domain was simulated with the LES model. To measure the effect of building height on pollutant dispersion, the parameter AR(Aspect Ratio) was calculated. Also to determine the effect of street width, a new parameter SWV(Street Width Value) was introduced. Governing equations were discretized using the well-known finite volume method on a staggered grid. To increase the accuracy, the second-order Van Leer Method(VLM) was applied and the Volume of Fluid(VOF) method was employed for the description of the interfaces. The Iterative line-by-line TDMA solution procedure and the Strongly Implicit Procedure(SIP) was used for the Pressure Correction Equation. A fine comparison of the results revealed that by increasing SWV, the number of vertical vortices in the canyon streets generally decreased and the vortices grew larger. In addition, increasing AR caused a rise in the pollution volume fraction in the first canyon street. The current numerical results indicate that the AR and SWV influence the flow field and volume fraction of phases inside an isolated street canyon, significantly.

Investigation of the effects of different parameters on the generated pressure waves inside the tunnels

In this research the train movement along the tunnel was simulated numerically, and the time evolution of the flow field in the tunnel was evaluated. The unsteady forms of continuity, Navier–Stokes, and energy equations were applied to solve the compressible viscous flow using the dynamic mesh technique. The importance of using a compressible flow model, even for the low Mach number flow case, was demonstrated. It was shown that even in low train speeds; a compressible model is preferred, as it can predict the pressure fluctuations, while an incompressible model may only be used for predicting the mean pressure. However, in cases where pressure fluctuations are not important, the incompressible model can be used especially for a train with low acceleration. When the trains accelerate, it was found that the initial slope of the pressure curve is proportional to the train acceleration. Therefore, the increase in the train acceleration increases the maximum pressure rise. Also, the first pressure rise depends on the velocity of the train tail as it enters the tunnel. In addition, the earlier equations in the literature for computing the maximum pressure rise, can properly predict the pressure rise of accelerating trains if the train tail velocity, as it enters the tunnel, is used as the velocity scale.

A multi-physics solver for liquid-fueled fast systems based on the discontinuous Galerkin FEM discretization

Performing accurate numerical simulations of molten salt reactors is challenging, especially in case of fast-spectrum designs, due to the unique physics phenomena characterizing these systems. The limitations of codes traditionally used in the nuclear community often require the development of novel high-fidelity multi-physics tools to advance the design of these innovative reactors. In this work, we present the most recent code developed at Delft University of Technology for multi-physics simulations of liquid-fueled fast reactors. The coupling is realized between an incompressible RANS model and an SN neutron transport solver. The models are implemented in two in-house codes, based on the discontinuous Galerkin Finite Element discretization, which guarantees high-quality of the solution. We report and discuss the results of preliminary simulations of the Molten Salt Fast Reactor at steady-state and during a Total Loss of Power transient. Results prove our code has capabilities for steady-state and transient analysis of non-moderated liquid-fueled reactors.

NARMAX Identification Based Closed-Loop Control of Flow Separation over NACA 0015 Airfoil

A closed-loop control algorithm for the reduction of turbulent flow separation over NACA 0015 airfoil equipped with leading-edge synthetic jet actuators (SJAs) is presented. A system identification approach based on Nonlinear Auto-Regressive Moving Average with eXogenous inputs (NARMAX) technique was used to predict nonlinear dynamics of the fluid flow and for the design of the controller system. Numerical simulations based on URANS equations are performed at Reynolds number of 106 for various airfoil incidences with and without closed-loop control. The NARMAX model for flow over an airfoil is based on the static pressure data, and the synthetic jet actuator is developed using an incompressible flow model. The corresponding NARMAX identification model developed for the pressure data is nonlinear; therefore, the describing function technique is used to linearize the system within its frequency range. Low-pass filtering is used to obtain quasi-linear state values, which assist in the application of linear control techniques. The reference signal signifies the condition of a fully re-attached flow, and it is determined based on the linearization of the original signal during open-loop control. The controller design follows the standard proportional-integral (PI) technique for the single-input single-output system. The resulting closed-loop response tracks the reference value and leads to significant improvements in the transient response over the open-loop system. The NARMAX controller enhances the lift coefficient from 0.787 for the uncontrolled case to 1.315 for the controlled case with an increase of 67.1%.

Forced convective Maxwell fluid flow through rotating disk under the thermophoretic particles motion

Numerical analysis is performed for incompressible Maxwell fluid model flow under the implications of thermophoresis and Cattaneo-Christov theory. Fluid motion is initiated by spinning of the disk. The system that comprises differential equations of partial derivatives is remodel into the system of differential equations by similarity transformations and then solved through Runge-Kutta-4 with shooting technique. The physical parameters, which emerging from derived system are discussed in graphical formats. An excellent proficiency of numerical process is analyzed by comparing the results with available literature in limiting scenario. The radial velocity initially improved and then declined by incrementing the Deborah number values. Further, it is executed that the azimuthal velocity field decays for higher magnetic parameter and Deborah number.

Eğrisel Fiber Yollu İkili Motorlu-Kanat Sisteminin Aeroelastik Enerji Optimizasyonu

In the present study, the aeroelastic energy response of a twin-engine composite wing system is optimized based on sequential quadratic programming (SQP) method. The variable stiffness is acquired by constructing laminates of thin wall beam (TWB) with curvilinear fibers having prescribed paths. In order to account the effect of spanwise locations and mass of the engines on the aeroelastic characteristics of TWB, the novel governing equations of motion are obtained using Hamilton's variational principle. The paper aims to exploit desirable fiber paths with improved aeroelastic properties for different twin-engine wing configuration. Ritz based solution methodology is employed to solve the equations with coupled incompressible unsteady aerodynamic model based on Wagner’s function. A novel optimization strategy based on the total energy of the aeroelastic system is introduced. The proposed total energy, as a cost function, is minimized in terms of four optimization variables of two engine’s locations and wing structure curvilinear fiber angle with two design parameters. The total energy is obtained by integrating responses of kinetic and potential energy in a specific time interval. The minimum total energy is an indication of ideal optimization variables which leads to the optimum flutter performance. Numerical results demonstrate the effectiveness of the optimization variables on the total energy of the aeroelastic system and determine the optimal values of introduced variables in case of minimum total energy and improved aeroelastic characteristics.

Dynamic modeling of a radially multilayered tether cable for a remotely-operated underwater vehicle (ROV) based on the absolute nodal coordinate formulation (ANCF)

This research is aimed at the accurate modeling of an ROV's tether cable with a radially multilayered circular cross-section. In the coupled motion analysis of an ROV-tether system, dynamic modeling of a numerical tether continuum, which can accurately reproduce the nonlinear motion behavior of a flexible cable, is crucial since the tether motion greatly affects the ROV's stability. To this end, a new tether cable element based on the multilayered modeling approach is developed. To deal with the inconsistency of the tether's cross-section, the integration domain on the cross-section is divided into subdomains to account for different material properties in each layer and an accurate representation of the tether's cross-section. A Kelvin-Voigt model is employed to account for the viscoelastic behavior of the inner matrix, while nearly incompressible Mooney-Rivlin model is applied for the outer sheath. Structural weakening parameters are applied to modify the beam's strain energy. A new approach for analytical determination of dissipation factors for dilatational and deviatoric responses is proposed. Through validations against the numerical studies and experiment, the effectiveness of the proposed tether cable element is verified.

Magnetohydrodynamic Richtmyer–Meshkov instability under an arbitrarily oriented magnetic field

The effect of an initially uniform magnetic field of arbitrary orientation on the Richtmyer–Meshkov instability in Hall-magnetohydrodynamics (MHD) and ideal MHD is considered. Attention is restricted to the case where the initial density interface has a single-mode sinusoidal perturbation in amplitude and is accelerated by a shock traveling perpendicular to the interface. An incompressible Hall-MHD model for this flow is developed by solving the relevant impulse-driven linearized initial value problem. The ideal MHD theory is naturally obtained by taking the limit of vanishing ion skin depth. It is shown that the out-of-plane magnetic field component normal to both the impulse and the interface perturbation does not affect the evolution of the flow. For all field orientations other than strictly out-of-plane, the growth of interface perturbations is suppressed. However, the suppression is most effective for near tangential fields but becomes less effective with increasing ion skin depth and Larmor radius. The modeled suppression mechanism is transport of vorticity along magnetic field lines via Alfvén fronts in ideal MHD, and via a dispersive wave system in Hall-MHD. Oscillation of the interface growth rate is caused by a continuous phase change of the induced velocities at the interface due to vorticity transport parallel to the perturbation direction in ideal MHD, while it can also result from interfacial vorticity production associated with the ion cyclotron effect in Hall-MHD with a finite Larmor radius. The limiting flow behavior of a large ion-skin-depth is explored. To assess the accuracy and appropriateness of the incompressible model, its ideal MHD predictions are compared to the results of the corresponding shock-driven nonlinear compressible simulations.

Unconditional finite amplitude stability of a viscoelastic fluid in a mechanically isolated vessel with spatially non-uniform wall temperature

We investigate finite amplitude stability of spatially inhomogeneous steady state of an incompressible viscoelastic fluid which occupies a mechanically isolated vessel with walls kept at spatially non-uniform temperature. For a wide class of incompressible viscoelastic models including the Oldroyd-B model, the Giesekus model, the FENE-P model, the Johnson–Segalman model, and the Phan–Thien–Tanner model we prove that the steady state is stable subject to any finite perturbation.

Active flutter control of thin walled wing-engine system using piezoelectric actuators

In the present study, control of a Thin Walled Beam (TWB) wing-engine system is examined applying piezoelectric actuators to enhance the performance of aeroelastic response. The composite piezoelectric governing equations of motion including the structure and electric effects are derived applying Hamilton's principle. Piezoelectric composite plate equations are added to the composite host wing-engine governing system of equations. The incompressible aerodynamic model based on Wagner's function is applied and the Ritz based solution methodology is employed. As a passive control approach, the effects of piezoelectric fiber angles are studied on the time domain response of the high-aspect-ratio wing-engine system. The linear quadratic Gaussian (LQG) control algorithm is applied as a closed-loop active control strategy to enhance the flutter response characteristics of the composite wing-engine system. Numerical results firstly, demonstrate the effectiveness of the active control strategy based on piezocomposite actuator on suppressing the flutter response of the composite wing-engine system and secondly, prove the effect of piezocomposite actuator location and fiber angle orientation on the closed-loop control performance.

Fully discrete finite element approximation of the 2D/3D unsteady incompressible magnetohydrodynamic-Voigt regularization flows

We devote the present paper to a fully discrete finite element scheme for the 2D/3D nonstationary incompressible magnetohydrodynamic-Voigt regularization model. This scheme is based on a finite element approximation for space discretization and the Crank-Nicolson-type scheme for time discretization, which is a two-step method. Moreover, we study stability and convergence of the fully discrete finite element scheme and obtain unconditional stability and error estimates of velocity and magnetic fields, respectively. Finally, several numerical experiments are investigated to confirm our theoretical findings.

A Mass Transport Model for Flows in Channels and Porous Media of Fuel Cells

Low-temperature fuel cells are a promising alternative technology to conventional energy systems such as internal combustion engines. However, their large-scale commercialization is still limited due to several challenges, such as mass transport losses at high power densities [1]. Estimation of gas transport properties in porous materials of fuel cells, such as gas diffusion layers (GDLs), is therefore critical. Several experimental studies in literature estimated the permeability of different GDL samples using a one-dimensional model, which does not account for channel effects [1-6]. Some authors in literature have assumed that the flow is incompressible in their numerical studies [7-10]. This hypothesis is not justified because the error in permeability estimation with an incompressible fluid flow model compared to the estimation with a compressible fluid flow model can be as high as 20% [2]. Numerical models for channels and porous media require volume-averaged formulations, and an in-depth discussion on the physical meaning of density and velocity in these models is seldom found in literature. Also, most of the existing numerical studies neglect the anisotropic nature of GDLs.In this work, a volume-averaged form of the steady-state, compressible, and isothermal Navier-Stokes equations for flows in channels and porous materials is developed and implemented in the open-source framework OpenFCST [11]. Particular attention is given to flows in channels and GDLs of polymer electrolyte fuel cells. The fluid flow model in porous materials is derived by means of the method of volume averaging [12]. A continuous Galerkin finite element method is used to discretize and numerically solve the resulting system of governing equations in the framework of a single domain approach. The coupling boundary conditions at the internal interface between channels and porous media are discussed and a stable non-oscillatory pair of solution variables in the porous domain is obtained. The study reveals that for volume-averaged formulations, the permeability obtained in experiments has to be corrected with the sample porosity. The model is used to estimate in-plane and through-plane permeabilities of fuel cell diffusion media, which is compared to experimental data. Three-dimensional simulations show that channel effects cannot be neglected and therefore one-dimensional models for permeability estimation are limited. Assuming that the fluid is incompressible is only valid for through-plane permeability, and a compressible formulation should be used for in-plane simulations, even at moderate gas flow rates. The suitability of the mathematical model for fuel cell applications is illustrated by estimating the change in pressure drop in a serpentine channel in contact with either a solid wall or a gas diffusion media. An interdigitated channel design is also considered in order to compare the pressure drop and the velocity in the GDL with the results observed with a serpentine channel.

A STUDY OF TRANSIENT FLOWS WITH INTERFACES USING NUMERICAL SOLUTION OF NAVIER–STOKES EQUATIONS

Flows of two immisible fluids are considered taking into account the capillary and gravity forces. The flow is described using a viscous incompressible fluid model within a two-dimensional formulation. The Navier–Stokes equations are solved numerically by an extended finite-element method, which allows for the presence of a strong discontinuity on the interface. The interface location is tracked using the level set method. This approach makes it possible to study flows with a varying topology of the interface. The calculation results are presented for the problems of a rising 2D bubble, development of the Rayleigh–Taylor instability, and a film flowing down a vertical wall in an extended region.