Variation Of Velocity Profile Research Articles

Stability analysis of MHD Jeffery–Hamel flow using artificial neural network

The current research explores the useful impact of artificial neural networks (ANN) back-propagation along Levenberg-Marquardt Method (ANN-BLMM), for findng the influence of dimensionless numbers on the flow distribution pertaining magnetohydrodynamics (MHD) Jeffery–Hamel fluid amid two plates which are enclined at angles 2α. We have employed a numerical approach, ANN-BLMM to assess various aspects of our data, including testing, training, validation, Mean Square Errors (MSE), performance, and fitting. The methodology being used has been tested and validated through comparison with other results obtain numerically, showing extreme level of accuracy. Moreover, we have confirmed our findings through error histograms and regression tests. We used OHAM for the data set. Furthermore, we have also explored the influence of Reynolds number (R) on both flow and pressure distribution, visually representing our findings through graphical analysis. We have discussed about the nature and variations of velocity profiles within MHD Jefery–Hamel flow (MHDJHF), taking into account various values of Ha and Re in both convergent and divergent channels. It was discovered that a significant stabilizing influence of an increase in the magnetic field intensity was observed for both diverging and converging channel geometries and as the Hartman numbers rise, so does the fluid velocity. The absolute error is reduced to 10–2 to 10–6.

The groove effect on wake characteristics of rotating cylinders

In the present study, active and passive flow control methods have been implemented to investigate their effects on the wake flow structures of a circular cylinder. Grooves having circular, rectangular, and triangular cross sections have been applied to the cylinders exposed to the rotation rates, α, from 0 to 0.79. The experiments have been conducted by particle image velocimetry at a Reynolds number of Re = 5 × 103. The contour graphics of time-averaged results have been presented. Moreover, the variations in velocity profiles have also been depicted. The experimental results revealed significant variations for flow patterns, wake structures, and turbulence parameters due to the effects of both groove geometries and rotational motion. In the stationary cases, for turbulence intensity, the circular grooved cylinder exhibited a 15% increase, while the triangular grooved cylinder showed a slightly higher increase of around 20% compared to that of the bare cylinder (BC). Conversely, in non-stationary cases, the rectangular grooved cylinder displayed the most prominent reduction in turbulence intensity, decreasing by approximately 10% compared to that of the BC. The groove type has considerably affected the flow structures of the wake regions, especially for the lower rotation rates.

Application of 1D inverse scattering and projection onto convex sets to inversion of seismic data

The Born series provides a framework for constructing a connection between earth model parameters and a wavefield characterised by perturbation about a known reference wavefield. The inverse scattering series provides a linear and a nonlinear expression for approximating earth's model parameters. Based on our results, the linear expression provides an accurate approximation of the 1D depth varying velocity profile. However, with increasing contrast, one has to utilise the nonlinear expression for increased accuracy. In seismic inversion, a major problem relates to the bandlimited nature of recorded seismic data, limiting the inversion for absolute amplitudes. To reconstruct missing low frequencies, we employ a frequency extrapolation method, in this case, projection onto convex sets (POCS) to reconstruct missing low frequencies critical for accurate inversion and reconstruction of depth varying velocity profile. Numerical results on 1D synthetic data and succeeding results on 1D physical modelling data demonstrate the efficiency of POCS in reconstructing critical missing low frequencies and subsequent advantage of nonlinear inverse scattering in approximating the change in velocity profile. In comparison, the linear scattering expression fails to provide a reasonable estimate of reflectors beyond the first interface.

The viscoacoustic Green's function for the Helmholtz equation in a velocity gradient interface model

SUMMARY In viscoacoustically stratified media where the density is constant, 3-D wave propagation in the frequency–radial wavenumber domain is governed by the Helmholtz equation. In the case that the model is a velocity gradient interface where the squared velocity in depth is represented by a smooth Heaviside function of the Fermi–Dirac distribution type, the Helmholtz equation for a point source at arbitrary location is shown to have analytical solution for the Green's function. The velocity depth profile, which is a modification of the Epstein profile which has been thoroughly studied in different branches of physics, is described by four parameters: the velocities at minus and plus infinity, the reference depth of the gradient interface, and its smoothness. The Helmholtz equation is first solved in a model where the point source is absent. The solution to the source-free equation has four unknown constants that must be determined. The radiation conditions at minus and plus infinity and two conditions on the Green's function at the source depth allow the constants to be found. The Green's function solution can be represented in two mathematically equivalent algebraic forms involving ordinary hypergeometric functions. The first form allows a numerically stable implementation over all wavenumber components. The second form allows a physical, intuitive interpretation and is expressed mathematically as the sum of two terms. Each of the terms contains the product of constant-velocity reference phase shift functions and hypergeometric functions which take the role to adjust the amplitude and phase shift calculated by the reference phase shift functions to account for the depth varying velocity profile. Inverse Fourier transforms take the Green's function from the frequency–wavenumber domain to the frequency–space domain or time–space domain. The Green's function solution is valid for any sharpness of the interface. Selected numerical results are presented for the 1-D and 2-D Helmholtz equation to demonstrate the influence of the velocity gradient zone on the wavefield. The 1-D solution in an acoustic model is compared in time domain to the classical finite-difference wave propagation solution. For the purpose of interpretation of seismograms, we model for comparison the wavefield response in a model of two half-spaces in welded contact. For brevity, the latter model is referenced as the HS model.

Inferring spatial variations in velocity profiles and bed geometry of natural debris flows based on discharge estimates from high-frequency 3D LiDAR point clouds; Illgraben, Switzerland

More detailed field measurements are required for a better understanding of surging debris flows. In this work, we analyze a debris flow at the field-scale using timelapse point clouds from a high-resolution, high-frequency 3D LiDAR sensor, which has been installed over a check dam on the fan of the Illgraben catchment in Switzerland. In our investigations, we manually measured the front velocity and tracked individual features such as large boulders and woody debris over a 25 m long channel segment. We observed a change in the front velocity as well as a difference in the velocity of large boulders and woody debris (vboulder≈ 0.6vwood) during the second surge of the event. We also estimated the discharge for different closely spaced channel sections based on automated measurements of the cross-sectional area and the surface velocity, which enabled us to infer spatial variations in the bed geometry and the velocity profile. From the discharge estimates, we then derived the volume of this event. Over the course of the next year, the amount of field-scale LiDAR data from the Illgraben will increase substantially and allow for an even more detailed analysis of fundamental debris-flow processes.

Second-Order Slip Effect on MHD Flow and Radiative Heat Transfer through Porous Medium due to an Exponentially Stretching Sheet

The magnetohydrodynamic (MHD) boundary layer flow and radiative heat transfer with second-order slip condition are investigated in this paper. The fluid flow is considered towards an exponentially stretching sheet. The effect of magnetic field and thermal conductivity are taken into account. The obtained nonlinear mathematical expression of the flow are transformed into ordinary differential equations by similarity transformation. The coupled higher order nonlinear ordinary differential equations are solved numerically. The solution for velocity and temperature profile against the first and second-order slip parameters are analyzed. Significant changes are observed in skin friction coefficient and Local Nusselt number due to the magnetic parameter. The characteristics of the flow are discussed through graphs for different pertinent parameters. The results designate that the Local Nusselt number reduces with the increased value of magnetic parameter but opposite behavior is observed for the skin friction coefficient. The rate of heat transfer decreases with higher value of Prandtl number and enhances for Radiation parameter.
 HIGHLIGHTS
 
 Phenomenon of an exponentially stretching sheet with thermal conductivity also incorporate in fluid flow
 Behavior of magnetic parameter (M) and Radiation parameter (R) are analyzed
 Highly nonlinear mathematical equations are solved numerically
 Variation of velocity profile obtained for the first and second order slip parameters
 
 GRAPHICAL ABSTRACT

Effects of uncertainties in positioning of PIV plane on validation of CFD results of a high-head Francis turbine model

The use of Computational Fluid Dynamics (CFD) for the design of modern hydraulic turbines has increased and matured significantly in the last decades. More recently, CFD is also used to understand how to safely widen the hydraulic turbine operating ranges, and avoid hazardous conditions during transient operation. The accuracy of such CFD results relies on validation with experimental data which contains numerous sources of uncertainties. The present work is focusing on the effects of the uncertainties in the positioning of the experimental Particle Image Velocimetry (PIV) plane on the validation of CFD results of the high-head Francis-99 turbine model. A transient shutdown sequence is considered, where the available experimental and numerical data are considered accurate according to a conventional thorough validation procedure. A part of that validation procedure is the comparison of spatially and temporally varying velocity profiles along three lines of the experimental PIV plane. The positioning of this PIV plane is here considered uncertain, using three translational and three rotational stochastic parameters with uniform probability distribution functions. The validated CFD results are used to extract the data that depends on these uncertainties, while this is not possible for the experimental data. The polynomial chaos expansion method is employed for the Uncertainty Quantification (UQ) study while Sobol’ indices are utilized for the Sensitivity Analysis (SA). The UQ can be used to show how the considered uncertainties impact the extracted components of the velocity field, and the sensitivity analysis reveals the relative contribution of each uncertain parameter to the quantity of interest. For this particular case it is shown that the so-called horizontal velocity component is most sensitive to the plane-normal positioning of the PIV plane. This is also the velocity component where all the numerical results found in the literature differ most from the experimental results. It is also shown that the probability distribution function of the numerical horizontal velocity is covered by the experimental standard deviation bounds, which means that it is quantified that the numerical and experimental results are similar within the range of the uncertainties.

Guidance algorithm for impact time, angle, and acceleration control under varying velocity condition

A highly constrained guidance algorithm is investigated, which is capable of addressing the constraints on impact time, impact angle, and terminal load factor simultaneously, in particular under a challenging condition where the missile's velocity varies passively with time and cannot be adjusted for impact time control. To develop the guidance, a new flight dynamics is established by treating downrange as the independent variable and flight time as a state variable, and then augmented by putting forward an Additional Maneuvering Acceleration Term (AMAT) for impact time control. Based on the dynamics, an impact-angle-constrained optimal guidance problem is proposed and solved to develop a new guidance formula. Further, the generalized semi-analytical solutions for the guidance command and impact time are derived by putting forward and linearizing a novel engagement model, which takes the heading angle, line-of-sight angle, and flight time as the state variables. Especially, in Appendix A, for a special kind of varying velocity profile, the complete closed-form solutions are developed. Subsequently, for addressing the impact time constraint, the impact-time solution is used to determine the parameters of the AMAT. Finally, to control the terminal load factor, two inequalities are created by applying the kinetic energy theorem, and then used to deduce the limits of some complex integral terms appearing in the generalized semi-analytical solutions. By analyzing these limits, the guidance coefficients making the load factor converge to a pre-specified value can be determined. The superiority of the guidance is demonstrated by conducting a large number of trajectory simulations.

Delayed Deceleration Approach Noise Impact and Modeling Validation

A validation methodology and evaluation of delayed deceleration approach performance and noise-impact modeling using noise measurements and radar data are presented. Advanced procedures such as delayed deceleration approaches, where aircraft maintain higher speeds and therefore remain cleanly configured and at lower thrust levels for longer flight periods, can be used for airport noise abatement. Delayed deceleration approaches have been shown in modeling to offer noise reductions before the stabilization point compared to procedures that decelerate early. The delayed deceleration approach validation methodology is demonstrated through monitoring of operational radar data with varying velocity profiles from Boeing 737, Airbus A320, and Embraer E190 flights and comparing modeled sound exposure levels of these procedures with available ground-noise-monitor data at two major airports. Thrust from radar flights was modeled based on weight predicted from final approach speed and assumed configuration. When corrected for atmospheric conditions, modeled noise is shown to be consistent with noise-monitor readings under reasonable flap-deployment schedule assumptions during observed early, intermediate, and delayed deceleration approaches. In addition, delayed deceleration approaches correlated with monitor readings with lower noise levels of an average of 3–6 dB compared to early deceleration approaches across different aircraft types.

Analysis of Onset of Transition Region on a Supersonic Wing

Abstract: Climate change is due to the sole effect of global warming, which is an outcome of Green House Gas (GHG) emissions. The aviation industry is considered to be one of the fastest-growing sources of these emissions. Mitigation of these emissions is a challenging task since it requires the entire world to work hand-in-hand. The International Civil Aviation Organisation (ICAO), an international governing body, has come up with a challenging target of net 50% reduction in global aviation emission by 2050, relative to the emission levels in 2005. To achieve this target, there must at least be 2% improvement in fuel efficiency every year. This 2% efficiency improvement is further split into Aircraft technology improvement (1.1%) and Airport infrastructure improvement (0.9%). This research aims to achieve the 2% improvement by aircraft technology improvement. Over the years, it was evidenced that mitigation of skin-friction drag on the wing would contribute to a majority of the fuel efficiency improvement. Hence, the primary aim is narrowed down to wing skin friction drag. The theory of boundary-layer has been studied thoroughly in this research work. Also, the interaction between the shock-waves and boundary-layer will be briefed in this paper as the baseline aircraft is supersonic. As it was understood as understood over the research that extension of the laminar boundary-layer favours the reduction of skin-friction drag, it is the primary objective of this research work. A Computational Fluid Dynamics (CFD) study on the of the wing aerodynamics has been conducted to enhance the performance of the aircraft and ANSYS Fluent has been used to serve this purpose. The results obtained from ANSYS fluent will be validated in one of the NASA’s open-source tool VSPAero which uses Vortex Lattice Method to model the flow. Turbulent Kinetic Energy technique is used to predict the onset of the transition of the flow. Initial study is performed on the 2D aerofoil and one the most optimum aerofoil is obtained, the study is continued in 3D to understand the effect of cross-flow instabilities. Free-stream velocity profile variation is another reliable technique in predicting the transition and will be discussed in the next volume of the paper. Finally, aerodynamic performance analysis will be performed to obtain the best wing configuration.

Mechanistic Models for USP2 Dissolution Apparatus, Including Fluid Hydrodynamics and Sedimentation

Drug product dissolution is a key input to Physiologically Based Biopharmaceutics Models (PBBM) to be able to predict in vivo dissolution. The integration of product dissolution in PBBMs for immediate release drug products should be mechanistic, i.e. allow to capture the main determinants of the in vitro dissolution experiment, and extract product batch specific parameter(s). This work focussed on the Product Particle Size Distribution (P-PSD), which was previously shown to integrate the effect of dose, volume, solubility (pH), size and concentration of micelles in the calculation of a batch specific input to PBBMs, and proposed new hydrodynamic (HD) models, which integrate the effect of USP2 apparatus paddle rotation speed and medium viscosity on dissolution. In addition, new models are also proposed to estimate the quantitative impact of formulation and drug sedimentation or “coning” on dissolution. Model “HDC-1” predicts coning in the presence of formulation insoluble excipients and “HDC-2” predicts the sedimentation of the drug substance only. These models were parameterized and validated on 166 dissolution experiments and 18 different drugs. The validation showed that the HD model average fold errors (AFE) for dissolution rate prediction of immediate release formulations, is comprised between 0.85 and 1.15, and the absolute average fold errors (AAFE) are comprised between 1.08 and 1.28, which shows satisfactory predictive power. For experiments where coning was suspected, the HDC-1 model improved the precision of the prediction (defined as ratio of “AAFE-1”values) by 2.46 fold compared to HD model. The calculation of a P-PSD integrating the impact of USP2 paddle rotation, medium viscosity and coning, will improve the PBBM predictions, since these parameters could have an influence on in vitro dissolution, and could open the way to better prediction of the effect of prandial state on human exposure, by developing new in silico tools which could integrate variation of velocity profiles due to the chyme viscosity.

Fibers Effects on Contract Turbulence Using a Coupling Euler Model

Fiber additive will induce the rheological behavior of suspension, resulting in variation in velocity profile and fiber orientation especially for the non-dilute case. Based on the fluid-solid coupling dynamics simulation, it shows that the fiber orientation aligns along the streamline more and more quickly in the central turbulent region as the fiber concentration increases, especially contract ratio Cx > 4. However, fibers tend to maintain the original uniform orientation and are rarely affected by the contract ratio in the boundary layer. The fibers orientation in the near semi-dilute phase is lower than that in the dilute phase near the outlet, which may be the result of the hydrodynamic contact lubrication between fibers. The orientation distribution and concentration of the fibers change the viscous flow mechanism of the suspension microscopically, which makes a velocity profile vary with the phase concentration. The velocity profile of the approaching semi-dilute phase sublayer is higher than that of the dilute and semi-dilute phases on the central streamline and in the viscous bottom layer, showing weak drag reduction while the situation is opposite on the logarithmic layer of the boundary layer. The relevant research can provide a process strategy for fiber orientation optimization and rheological control in the industrial applications of suspension.

Effect of wettability on immiscible viscous fingering: Part I. Mechanisms

Most immiscible viscous-fingering experiments have been conducted using Hele-Shaw cells or linear displacements with high permeabilities. In linear displacement experiments, the effect of varying velocity profiles on viscous fingering is not tested. Only a limited number of studies have been conducted in five-spot displacement patterns. These studies have not provided any comparative insight into fingering length scales during high-IFT imbibition and drainage in water-wet and oil-wet porous media, respectively. To eliminate the limitations of previous studies, high-IFT, adverse-viscosity-ratio, water–oil displacements are conducted in a quarter-five-spot pattern with a relatively intermediate permeability under water-wet and oil-wet conditions, respectively. Statistically representative fingering patterns are captured by devising experimental techniques and image analysis algorithms to correlate statistical information including the evolution of the fingering length scales with time in water-wet and oil-wet micromodels. Mechanistic regimes of viscous fingering in imbibition and drainage are proposed. The patterns of fingering suggest a profound effect of wetting properties on the complex interplay between several pore-scale mechanisms during high-IFT, adverse-mobility-ratio imbibition and drainage, including the interfacial energy effects, capillary invasion, transverse flow, viscous crossflow, bypassing, film flow, and tip splitting, shielding, and spreading.

Hydrodynamic Performance of A‐Jacks Concrete Armor Units in Riverbeds around Downstream in Flip Buckets

The jet flipped from flip buckets hits the dam’s downstream side as a free jet with an immense amount of energy, leading to bed erosion. Erosion of river bed materials downstream of dams could affect the performance of dams or power plants by altering the tailwater depth, rendering proper designs of controlling structures or erosion reduction methods highly indispensable in this regard. Hence, the hydrodynamic performance of A‐Jacks concrete armor units in controlling scour was examined in this study. A‐Jacks armors are applicable as a flexible protection without environmental risks often for bed erosion control. The desirable functionality of A‐Jacks armors depends on the flow hydrodynamic parameters such as velocity profile variations (U/UB), the Reynolds stresses ( and τv′w′), and the skin friction coefficient (Cf) created as a consequence of using A‐Jacks armors on beds. The size of A‐Jacks elements can have a role in increasing the flow turbulence to a certain depth so that after the impact of the flow with A‐Jacks armor, the vortices’ intensity as well as the shear stress affecting the bed gradually decreases. The results of the numerical model suggest that the surge in the flow turbulence energy dissipation downstream of flip buckets significantly mitigates the underlying conditions of scouring phenomena, which is evidence of A‐Jacks armors’ acceptable performance in scaling down scour depths.

Shape Effect of Nanosize Particles on Magnetohydrodynamic Nanofluid Flow and Heat Transfer over a Stretching Sheet with Entropy Generation.

Magnetohydrodynamic nanofluid technologies are emerging in several areas including pharmacology, medicine and lubrication (smart tribology). The present study discusses the heat transfer and entropy generation of magnetohydrodynamic (MHD) Ag-water nanofluid flow over a stretching sheet with the effect of nanoparticles shape. Three different geometries of nanoparticles—sphere, blade and lamina—are considered. The problem is modeled in the form of momentum, energy and entropy equations. The homotopy analysis method (HAM) is used to find the analytical solution of momentum, energy and entropy equations. The variations of velocity profile, temperature profile, Nusselt number and entropy generation with the influences of physical parameters are discussed in graphical form. The results show that the performance of lamina-shaped nanoparticles is better in temperature distribution, heat transfer and enhancement of the entropy generation.

Jet preferred mode vs shear layer mode

The effect of acoustic excitation on a low Reynolds number jet with constant centerline velocity u0 but varying velocity profile u(y) is investigated experimentally by particle imaging velocimetry. Different initial conditions at the nozzle orifice are here used with the intent to characterize the relation between the jet preferred mode fp and the natural shear layer mode fn. The jet response to acoustic excitation is described in terms of the centerline velocity decay and the downstream increase in momentum thickness. This study intends to shed some light onto the duality of the two most fundamental flow instabilities and their controversial dependency on each other.

Newtonian heating effect on laminar flow of Casson fluids: Thermal analysis

AbstractIn the present study, free convective, laminar flow of Casson fluid is investigated numerically over a nonlinear stretched sheet to observe the characteristics of heat transfer in the presence of Newtonian heating. Nonlinear differential equations are derived from the present flow by utilizing the appropriate transformations. Thereafter, for the linear stretching case, an exact solution is applied for the momentum equation, and for the nonlinear stretching case, a convergent numerical technique, SRM, is applied. Computations of SRM and exact solutions are displayed through graphs. For various physical parameters, variation in velocity profile is observed by means of numerical computations and presented graphically. For checking the accuracy and convergence of the proposed method, outcomes are validated with the available outcomes in the literature and compared. The outcomes demonstrate that the velocity profile is reduced for the nonlinear stretching parameter effect, and, with increasing , the temperature is decreased and there is a reduction in the thickness of the thermal boundary layer.

Optimal Freewheeling Control of a Heavy-Duty Vehicle Using Mixed Integer Quadratic Programming

Improving the powertrain control of heavy-duty vehicles can be an efficient way to reduce the fuel consumption and thereby reduce both the operating cost and the environmental impact. One way of doing so is by using information about the upcoming driving conditions, known as look-ahead information, in order to coast in gear or to use freewheeling. Controllers using such techniques today mainly exist for vehicles in highway driving. This paper therefore targets how such control can be applied to vehicles with more variations in their velocity. The driving mission of such a vehicle is here formulated as an optimal control problem. The control variables are the tractive force, the braking force, and a Boolean variable representing closed or open powertrain. The problem is solved by a model predictive controller, which at each iteration solves a mixed integer quadratic program. The fuel consumption is compared for four different control policies: a benchmark following the reference of the driving cycle, look-ahead control without freewheeling, freewheeling with the engine idling, and freewheeling with the engine turned off. Simulations on a driving cycle with a varying velocity profile show the potential of saving 11%, 19%, and 23% respectively for the control policies compared with the benchmark, in all cases without increasing the trip time.

Turbulent Drag Reduction Characteristics of Bionic Nonsmooth Surfaces with Jets

Aiming at aerodynamic drag reduction for transportation systems, a new active surface is proposed that combines a bionic nonsmooth surface with a jet. Simulations were performed in the computational fluid dynamics software STAR-CCM+ to investigate the flow characteristics and drag reduction efficiency. The SST K-Omega model was used to enclose the equations. The simulation results showed that when the active surface simultaneously reduced the skin friction and overcame the sharp increase of pressure drag caused by a common nonsmooth surface, the total net drag decreased. The maximum drag reduction ratio reached 19.35% when the jet velocity was 11 m/s. Analyses of the turbulent kinetic energy, pressure distribution, and velocity profile variations showed that the active surface reduced the peak pressure on the windward side of the nonsmooth unit cell, thereby reducing the total pressure drag. Moreover, the recirculation formed in the unit cell transformed the fluid–wall sliding friction into fluid–fluid rolling friction like a rolling bearing, thereby reducing the skin friction. This study provides a new efficient way for turbulent drag reduction to work.

Analysis of a boundary layer flow over moving an exponentially stretching surface with variable viscosity and Prandtl number

AbstractBoundary layer flow phenomenons on a stretching sheet find numerous applications in industrial processes such as manufacture and extraction of rubber and polymer sheets. The current study focuses on two‐dimensional water boundary layer flow on exponential stretching surface with a vertical plate for variable physical properties of fluid such as viscosity and Prandtl number. The Quasilinearization technique has been used on governing equations to transform nonlinear to linear equations and these equations are discretized by finite difference techniques to get numerical solutions. The effect of buoyancy parameters (λ), velocity ratio parameter () and streamwise coordinator (ξ) on velocity profiles (F), temperature profiles (θ), local skin‐friction coefficient (Cfx(ReLξexp(ξ))1/2) and the local Nusselt number (Nux(ReLξexp(ξ))−1/2) has been analyzed graphically based on numerical outcome. The magnitude of velocity profiles increases and temperature profile decreases approximately by 4% and 16% with increases the buoyancy parameter from λ = 1 to λ = 3 at = 0.5 and ξ = 1.0. The skinfriction and heat transfer coefficient increases approximately by 22% and 27% with an increase in ξ from 0.5 to 1.0 at fixed = 0.5 and λ = 1.0. The variations of velocity profiles and temperature profiles have more impact with as compared to ξ and λ. The benchmark studies were carried out to validate the current results with previously published work and found to be in excellent agreement.