Present Numerical Technique Research Articles

Investigation of squeezing Cu–water Casson nanofluid flow with an internal heat source through the Bernoulli wavelet method

The present numerical Bernoulli wavelet technique aims at investigating the heat transfer of Casson nanofluid flow squeezed between parallel plates with the influence of an internal heat source. The fundamental governing equations describing the proposed flow problem is expressed in terms of highly nonlinear coupled ordinary differential equations via appropriate similarity transformations. The numerical Bernoulli wavelet method (BWM) is used to solve these nonlinear equations. Numerical outcomes of the BWM are compared with the different numerical results. Comparison between calculated results showed that the BWM is more suitable and correct than the any numerical method. The effects of each parameters, such as the Casson parameter, internal heat generation/absorption parameter, squeezing number, and nanoparticle volume fraction on the velocity and temperature are presented graphically and discussed. Overall, this research provides novel insights into the heat transfer characteristics of Casson nanofluids in squeezing flows with internal heating, which are highly relevant to several industrial processes and biomedical applications.

Numerical study on collapsing cavitation bubble dynamics in cryogenic fluids

The paper addresses the implementation of a dual distribution function multiphase lattice Boltzmann method (DDF-MLBM) for studying the collapse of cavitation bubbles in cryogenic liquids. The present scheme incorporates the energy equation and imposes interparticle interactions and fluid–solid adhesive forces through the exact difference method (EDM). To accurately model phase changes and the molecular complexities of cryogenic fluids like liquid hydrogen (LH2) and liquid nitrogen (LN2), the Peng-Robinson (PR) equation of state is employed along with an acentric factor. The accuracy of the present numerical technique is evaluated using the Laplace law and the Maxwell equal area construction theorem for a two-phase liquid–vapor system in equilibrium. For transient solutions, the study compares results of heterogeneous cavitation with the analytical solution derived from the thermal Rayleigh-Plesset equation. The research investigates the impact of the distance between a cavitation bubble with an adjacent solid wall on velocity, pressure, temperature, and collapse time. Furthermore, it is assessed how surface wettability influences cavitation bubble collapse intensity. Additionally, the paper examines the collapse of a cavitation bubble cluster and evaluates the effects of different physical parameters on the collapse properties of the bubble cluster. The results underscore the significant influence of the distance between cavitation bubbles in the cluster, the distance between bubbles and the adjacent solid surface on the micro-jet velocity. Moreover, it is found that increasing the contact angle of the solid surface enhances the collapse intensity and micro-jet velocity of the collapsing bubble cluster.

Uniformly convergent extended cubic B-spline collocation method for two parameters singularly perturbed time-delayed convection-diffusion problems

This work proposes a uniformly convergent numerical scheme to solve singularly perturbed parabolic problems of large time delay with two small parameters. The approach uses implicit Euler and the exponentially fitted extended cubic B-spline for time and space derivatives respectively. Extended cubic B-splines have advantages over classical B-splines. This is because for a given value of the free parameter lambda the solution obtained by the extended B-spline is better than the solution obtained by the classical B-spline. To confirm the correspondence of the numerical methods with the theoretical results, numerical examples are presented. The present numerical technique converges uniformly, leading to the current study of being more efficient.

Solution of boundary eigenvalue problems and IBVP involving a system of PDEs using the successive linearization method

AbstractThe paper illustrates a numerical technique to solve a system of three partial differential equations that govern the problem of Rayleigh‐Bénard‐Brinkman convection in a two‐dimensional porous rectangular box. As a result of linear and weakly nonlinear stability analyses of the system a boundary eigenvalue problem (BEVP) and an initial boundary value problem (IBVP) arise. Spatial information on the periodicity of the convection cells is first used in the system of PDEs to make it possible for the successive linearization method (SLM) to be applied. The resulting much‐simplified versions of BEVP and the IVP are then solved by direct and time multi‐stepping versions of SLM, respectively. The SLM solution of the BEVP is compared with that obtained through MATLAB routine bvp4c and the multi‐stepping‐SLM solution of the IVP is validated with that of the Runge‐Kutta‐Fehlberg (RKF45) method (using MATLAB routine ode45). The present numerical technique is found to have quadratic convergence for any desired accuracy.

Numerical Study of a Non-Linear Porous Sublimation Problem With Temperature-Dependent Thermal Conductivity and Concentration-Dependent Mass Diffusivity

Abstract Sublimation heat transfer occurs in a wide range of engineering processes, such as accelerated freeze drying (AFD), energy storage, and food technology. Particularly in the microwave AFD process, preservation of material with the least possible energy consumption is desirable. In connection with this, it is of interest to analyze the effect of temperature/concentration dependent heat/mass transfer properties. Given the limited literature available on sublimation, there is a general lack of physical understanding of this particular problem. The present work analyzes the nonlinear sublimation process driven by convective heat/mass transfer and evaporation of water vapor using the Legendre wavelet collocation method (LWCM). Results from the present work are shown to be in excellent agreement with the exact solution of the special case of a linear problem. Further, the present numerical technique shows good agreement with finite difference method in case of a completely nonlinear model. The model is used for a comprehensive investigation of the impact of the problem parameters, on the rate of sublimation. It is found that the sublimation rate increases with increasing values of β1 and decreasing values of β2. The impact of other dimensionless problem parameters such as Péclet numbers Pe1 and Pem, convection due to mass transfer of water vapor β, latent heat of sublimation l0 and Luikov number Lu on sublimation process is also discussed in detail. These observations offer a comprehensive theoretical and mathematical understanding of sublimation heat/mass transfer for improving the performance and efficiency of freeze-drying and related engineering processes.

Transient evolution of electrowetting induced oscillating droplets on hydrophobic substrates

The present work reports numerical and experimental techniques for investigating electrowetting-induced oscillating water droplets for different hydrophobicity conditions of a surface. A phase-field-based code with a dynamic contact angle model is used to study the droplet dynamics. Hydrophobicity of the substrate intensifies the deformation and internal flow structures of the oscillating droplet. It also influences the phase difference between the contact angle and the contact radius, producing three different phase regimes, i.e., in-phase, out-phase, and mixed-phase regimes. The amplitude and frequency of the droplet oscillation change differently with the surface wettability in different phase regimes. Moreover, a simplified analytical model is developed to correlate the maximum amplitude of the oscillating droplet as a function of static contact angle. The formation of convective rolls inside and outside the oscillating droplet is observed at low frequency, which is required in microfluidic mixing and heat transfer applications.

An overset mesh approach for a vibrating cylinder in uniform flow

Abstract This paper has numerically investigated twodimensional laminar flow over a vibrating circular cylinder. Numerical simulation is performed using the dynamic overset mesh method available in commercial software ANSYS FLUENT 19.0. A simple harmonic motion is applied to simulate the cylinder vibration using the user-defined function (UDF) tool in FLUENT. To examine the accuracy and the capability of the present overset mesh approach, two test types of cylinder vibration are simulated: crossflow and inline vibrations. All simulations are performed at a constant Reynolds number (Re = 100) to predict the occurrence of synchronization or lock-in phenomenon. For the case of crossflow vibration, it is observed that lock-in occurs with cylinder oscillation frequency near the Strouhal frequency of the fixed cylinder. However, for the inline vibration, lockin occurs near twice the Strouhal frequency of the fixed cylinder. Furthermore, in the case of crossflow oscillation, the frequency content in the lift coefficients’ time history is successfully linked to the phase portraits’ shape and the vorticity field. The simulation results are consistent with the available published data in the literature. This indicates that the present numerical technique is valid and capable of modeling flows with moving structural systems.

Droplet spreading dynamics on hydrophobic textured surfaces: A lattice Boltzmann study

A three-dimensional (3D) lattice Boltzmann method based on the Allen-Cahn equation (A-C LBM) is employed to study the spreading dynamics of impacting droplets on the hydrophobic flat and textured surfaces. At first, the simulation of the equilibrium state of a droplet and also the impacting droplet spreading on a flat surface are considered at various wetting conditions to examine the accuracy and efficiency of the present numerical technique. The obtained results for these cases show excellent agreement with available theoretical, numerical, and experimental data in the literature that confirms the validity of the A-C LBM employed for simulation of such complex interfacial dynamics. Upon validation, the implemented A-C LBM is applied for investigation of the droplet impingement on the hydrophobic textured surface and the results are compared with those obtained by considering the flat surface. The present study shows that using microscale textures on a hydrophobic surface dramatically reduces the contact area between the impacting droplet and the solid wall due to the momentum redirection phenomenon. Indeed, the hydrophobic surface used with in-plane circular ridges causes the spreading lamella to eject out-of-plane with a liquid bowl shape. This mechanism converts a part of the horizontal momentum of the spreading to the vertical momentum that prevents droplets to have intense interaction. For an impacting droplet at a high Weber number, it is concluded that the geometrical parameters of the ridge dictate the morphology of the spreading on the hydrophobic surface. However, the droplet dynamics at a low Weber number depend on both the texture size and the surface wettability, so that the physical mechanisms of the droplet spreading and lamella ejection dramatically change by variation of these parameters. The obtained results show that when the adhesion force of the substrate is dominant (lower contact angles), the wetting property of the surface plays an effective role than the texture geometry in the formation of the liquid bowl at low Weber numbers. Also, the present study demonstrates the capability of the A-C LBM for the prediction of the studied multiphase flow structures and characteristics with extremely complex interface phenomena.

Thermal buckling analysis of a functionally graded microshell based on higher-order shear deformation and modified couple stress theories

In this study, thermal buckling responses of a functionally graded (FG) cylindrical microshell are investigated. Material properties of the FG microshell are considered to be graded through the thickness based on a simple power-law distribution. The governing equations and associated boundary conditions are derived based on classical higher-order shear deformation theory. Size dependence of the FG microshell is properly characterized based on the modified couple stress theory (MCST). Two types of differential quadrature method (DQM) – polynomial based differential quadrature (PDQ) and Fourier expansion based differential quadrature (FDQ) – are adopted to transform the differential equations into algebraic equations. The standard eigenvalue equation in the whole computational domain is subsequently established to obtain critical buckling temperature. The present numerical technique shows very fast convergence speed and is validated by comparison with available data in the open literature. Parametric studies are provided to demonstrate the influences of the temperature distribution profile, edge boundary conditions, length scale parameter, length-to-radius ratio, FG power-law index on the critical buckling temperature. In addition, the values of critical thermal buckling loads predicted by classical and MCST models are compared.

Kernel functions‐based approach for distributed order diffusion equations

AbstractIn this work, we solve distributed order diffusion equations (DODEs) by applying the theory on reproducing kernel functions (RKFs). The classical numerical quadrature formulae is used to approximate the DODE to a multi‐term Caputo fractional order diffusion equation (FDE). The Mittag‐Leffler RKF is introduced to estimate fractional derivatives of Caputo. And a space–time RKFs collocation scheme is derived for the multi‐term Caputo time FDEs. The accuracy of the present numerical technique is indicated by employing several experiments.

Simulation of the transient current of radiation detector materials using the constrained profile interpolation method

A semi-Lagrangian-type advection scheme, the constrained profile interpolation (CIP) method, is adopted to obtain a numerical solution of a drift–diffusion equation of photo-generated charge carriers in negatively biased, high-resistivity semiconductor detector materials. Transient current waveforms of high-resistivity CdZnTe measured by a time-of-flight (TOF) technique under different bias voltages and various laser excitation intensities, are theoretically reproduced from the temporal evolution of the charge distribution and corresponding internal electric-field evolution, which are derived from the solution of the drift–diffusion equation, in combination with Poisson’s equation. The temporal evolution of the charge distribution and internal electric-field distribution obtained by the present theoretical technique agree very well with those obtained by a Monte Carlo (MC) simulation, an independent numerical technique. We demonstrate the validity of the present numerical technique by reproducing the excitation-intensity dependence of experimental TOF current waveforms measured in a CdZnTe crystal.

Effect of time-dependent inhomogeneous magnetic fields on the particle momentum spectrum in electron-positron pair production

Electron-positron pair production in spatially and temporally inhomogeneous electric and magnetic fields is studied within the Dirac-Heisenberg-Wigner formalism (quantum kinetic theory) through computing the corresponding Wigner functions. The focus is on discussing the particle momentum spectrum regarding signatures of Schwinger and multiphoton pair production. Special emphasis is put on studying the impact of a strong dynamical magnetic field on the particle distribution functions. As the equal-time Wigner approach is formulated in terms of partial integro-differential equations an entire section of the manuscript is dedicated to present numerical solution techniques applicable to Wigner function approaches in general.

A Numerical Study on the Flow Mechanism of Performance Improvement of a Wide-Angle Diffuser by Inserting a Short Splitter Vane

Usage of a wide-angle diffuser may result in unfavorable separated flow and a significant diffuser loss. To improve the performance of the diffusers, inserting short splitter vanes is known as a useful method that has been demonstrated experimentally. Regarding the role of the vane in the diffuser flow, Senoo & Nishi (1977) qualitatively explained that the lift force acting on the vane should be a key factor. However, its quantitative verification remains since then. To challenge this issue, numerical simulations of incompressible flow in a wide angle of 28° two-dimensional diffuser with and without a short splitter vane were conducted in the present study. An improvement of pressure-recovery by the vane and oscillatory flows in the diffuser are reasonably reproduced from comparison with the experimental results made by Cochran & Kline (1958). It is also found that the lift force acting on the vane varies periodically in an opposite phase with the detachment point moved back and forth on a diverging wall, since one vane is not sufficient to fully suppress the flow separation that occurred on the wall and the incoming main-flow shifts toward the other diverging wall in the diffuser. Thus, as a role of splitter vane in the diffuser, “the lift force of the vane is a key factor” may be quantitatively verified from the present numerical simulation. Further, it is confirmed by the local loss analysis that the turbulent kinetic energy production observed in mixing layers contributes most of the loss in the diffuser. Consequently, the present numerical technique may be usable to investigate the flow character in a diffuser with splitter vanes at a design stage.

Subjective speckle suppression for 3D measurement using one-dimensional numerical filtering.

Laser speckle projection is a reliable method to generate statistical illumination patterns for 3D reconstruction purposes as in stereo photogrammetry. This type of pattern has several advantages compared to incoherent methods. However, the biggest disadvantage is given by the coherent noise, the so-called "subjective speckles," developing when a coherently illuminated surface is imaged by a lens system. Some experimental techniques have been published already, being costly in measurement time or leading to loss in light intensity and/or depth of field. In this work we want to present numerical one-dimensional filtering techniques that reduce this kind of noise and increase the performance of 3D reconstruction, while no experimental changes to the classical speckle projection technique have to be made. Therefore, a model describing the expectable contrast reduction is derived, the dependency between filter orientation and setup geometry is investigated, and results from simulations and real experiments are shown. It is found that for small filter sizes the results can be improved independent of the filter, but that in the general case a vertical orientation of the filter towards the setup geometry is most useful.

The reconstructed power spectrum in the Zeldovich approximation

Density-reconstruction sharpens the baryon acoustic oscillations signal by undoing some of the smoothing incurred by nonlinear structure formation. In this paper we present an analytical model for reconstruction based on the Zeldovich approximation, which for the first time includes a complete set of counterterms and bias terms up to quadratic order and can fit real and redshift-space data pre- and post-reconstruction data in both Fourier and configuration space over a wide range of scales. We compare our model to n-body data at z = 0 from the DarkSky simulation [1], finding sub-percent agreement in both real space and in the redshift-space power spectrum monopole out to k = 0.4 h Mpc-1, and out to k = 0.2 h Mpc-1 in the quadrupole, with comparable agreement in configuration space. We compare our model with several popular existing alternatives, updating existing theoretical results for exponential damping in wiggle/no-wiggle splits of the BAO signal and discuss the usually-ignored effect of higher bias contributions on the reconstructed signal. In the appendices, we re-derive the former within our formalism, present exploratory results on higher-order corrections due to nonlinearities inherent to reconstruction, and present numerical techniques with which to calculate the redshift-space power spectrum of biased tracers within the Zeldovich approximation.

Stability Analysis of Shear Deformable Trapezoidal Composite Plates

The stability characteristics of shear deformable trapezoidal composite plates are studied here. Thestrain smoothing technique is employed to approximate the membrane strains and curvatures of the edge-based smoothing cells. The transverse shear strains within the Reissner–Mindlin quadrilateral element are obtained using the edge-consistent interpolation approach. At the beginning, the performance of the present numerical technique is examined for the buckling analysis of trapezoidal panels under in-plane compressive or shear stresses. Thereafter, new results on the buckling and postbuckling behaviors of trapezoidal composite plates are presented, for which comparable numerical results are rare in the literature. Representative numerical results are presented to highlight the interaction between the higher pre-buckling stresses and increased stiffness near the shorter edge with fiber orientation and loading direction on the buckling resistance of trapezoidal panels.

Solitary wave solution of the nonlinear KdV-Benjamin-Bona-Mahony-Burgers model via two meshless methods

A nonlinear wave phenomenon is one of the significant fields of scientific research, which a lot of researchers in the past have deliberated about mathematical models clarifying the treatment. The nonlinear Korteweg-de Vries-Benjamin-Bona-Mahony-Burgers (KdV-BBM-B) model plays an essential role in numerous subjects of engineering and science. This model is numerically approximated by means of the combination of the radial basis function (RBF) and the finite difference (RBF-FD), RBF-pseudospectral (RBF-PS) that are stated in this paper. These methods are meshless, and no obligation is required to linearize the nonlinear parts. The radial kernels are employed to convert the PDE into a system of ODEs. This ODE system is solved with the help of the higher-order ODE solver. In addition, it is indicated that the present numerical techniques are stable. To evaluate the validity and applicability of the aforesaid techniques, the error norms and three invariants I1, I2 and I3 are calculated and displayed both numerically and graphically. The obtained results are compared with previous schemes found in the literature.

An extended polygonal finite element method for large deformation fracture analysis

The modeling of large deformation fracture mechanics has been a challenging problem regarding the accuracy of numerical methods and their ability to deal with considerable changes in deformations of meshes where having the presence of cracks. This paper further investigates the extended finite element method (XFEM) for the simulation of large strain fracture for hyper-elastic materials, in particular rubber ones. A crucial idea is to use a polygonal mesh to represent space of the present numerical technique in advance, and then a local refinement of structured meshes at the vicinity of the discontinuities is additionally established. Due to differences in the size and type of elements at the boundaries of those two regions, hanging nodes produced in the modified mesh are considered as normal nodes in an arbitrarily polygonal element. Conforming these special elements becomes straightforward by the flexible use of basis functions over polygonal elements. Results of this study are shown through several numerical examples to prove its efficiency and accuracy through comparison with former achievements.

Effect of the Boussinesq approximation: Turbulence studies with GRILLIX in slab geometry

The drift‐reduced global Braginskii system is implemented in GRILLIX, a plasma turbulence code that is able to treat diverted geometries by using the flux‐coordinate independent approach (FCI). We solve a four‐field model, evolving the density, the electron temperature, the vorticity, and parallel ion momentum. The difference between the system with the Boussinesq approximation (BS) and the full system (FS) is investigated. The Boussinesq approximation is widely used as it reduces the numerical and computational complexity significantly. In order to understand the impact of the Boussinesq approximation, a periodic flux tube geometry is chosen as the computational domain. The conservation of energy and particles is derived and tested within the code, both in FS and BS. Moreover, we will discuss how the Boussinesq approximation has subtle effects on the energy theorem of the model, and a conserved energy‐like quantity is only obtained if the Boussinesq approximation is applied in a consistent way. We will also present numerical and computational techniques in order to relax the Boussinesq approximation. The code is verified by the method of manufactured solutions, which yields the expected order of accuracy. A fundamental result found in the paper is that the Boussinesq approximation only has a minor effect on non‐linear simulations, at least in the regime studied here.

A Study of Microstructure and Tribological Properties of Al 5083 MMC Processed by Direct Extrusion

In this study, investigations are done on commercially available aluminum-magnesium (Al 5083) alloy. Aluminum 5083 alloy was first cast by using sand casting technique and then subjected to severe plastic deformation (SPD) through a direct extrusion process. To improve properties of the material, severe plastic deformation technique has been widely used over the last two decades. Present numerous experimental techniques of metal forming are available that can apply great strains on materials for better grain refinement, in that SPD is the best technique. To observe the outcome of direct extrusion on Al 5083 alloy, microstructure and mechanical properties of the cast alloy and extruded alloy were examined. Along the transverse planes of the extruded alloy microstructural investigations were carried out using an optical microscope and it discovered that the coarse microstructure of the alloy was refined to a considerable amount. Hardness and tensile strength of the alloy are improved by 10.33% and 9.8% respectively after direct extrusion. Wear resistance of the aluminum 5083 alloy was determined by Pin-on-Disc test apparatus. The grain size of the material is determined by using Olympus microscope. The wear properties of the alloy after direct extrusion were improved considerably along with improvement in hardness and tensile strength. Because of the highly refined grains imparted by direct extrusion process the mechanical properties of the alloy were improved to a certain extent and it makes the alloy to be used in various engineering claims requiring high strength.