Local Flow Properties Research Articles

Inner structures of rapid free-surface granular avalanche over a small bump obstacle: Expansion fan, oblique shock wave, and contact anisotropy

This study investigates the inner flow characteristics of a rapid granular avalanche passing over a small bump obstacle fixed on an inclined chute using the discrete element method. Both the cross-sectional mean flow properties, such as free-surface height, mean flow velocity, and mean stresses, and the inner local flow properties, including granular temperature, coordination number, pressure, contact force orientation, and granular fabrics, were comprehensively investigated. Upstream of the obstacle, a wide compression region where mean stresses strengthen and exhibit anisotropy was observed. Employing the kinetic theory of granular gas, we revealed a smooth supersonic-to-subsonic transition near the obstacle, a phenomenon distinct from typical gas dynamics. These upstream flow phenomena are attributed to the generation of stream-wise-oriented contact force chains as the flow impacts the obstacle. Downstream of the obstacle, a complex non-monotonic expansion–compression–expansion process was observed. We demonstrated that this non-monotonic flow process reflects an inner gasdynamic-like phenomenon characterized by an expansion fan followed by an oblique shock wave. Moreover, the force chains and the inner shock structure were found to significantly influence the evolution of stream-wise velocity profiles. These findings underscore the significance of inner flow structures in shaping the dynamics of granular avalanche flow interacting with obstacles.

A versatile micromodel technology to explore biofilm development in porous media flows.

Bacterial biofilms that grow in porous media are critical to ecosystem processes and applications ranging from soil bioremediation to bioreactors for treating wastewater or producing value-added products. However, understanding and engineering the complex phenomena that drive the development of biofilms in such systems remains a challenge. Here we present a novel micromodel technology to explore bacterial biofilm development in porous media flows. The technology consists of a set of modules that can be combined as required for any given experiment and conveniently tuned for specific requirements. The core module is a 3D-printed micromodel where biofilm is grown into a perfusable porous substrate. High-precision additive manufacturing, in particular stereolithography, is used to fabricate porous scaffolds with precisely controlled architectures integrating flow channels with diameters down to several hundreds of micrometers. The system is instrumented with: ultraviolet-C light-emitting diodes; on-line measurements of oxygen consumption and pressure drop across the porous medium; camera and spectrophotometric cells for the detection of biofilm detachment events at the outlet. We demonstrate how this technology can be used to study the development of Pseudomonas aeruginosa biofilm for several days within a network of flow channels. We find complex dynamics whereby oxygen consumption reaches a steady-state but not the pressure drop, which instead features a permanent regime with large fluctuations. We further use X-ray computed microtomography to image the spatial distribution of biofilms and computational fluid dynamics to link biofilm development with local flow properties. By combining the advantages of additive manufacturing for the creation of reproducible 3D porous microarchitectures with the flow control and instrumentation accuracy of microfluidics, our system provides a platform to study the dynamics of biofilm development in 3D porous media and to rapidly test new concepts in process engineering.

Stratified horizontal convection

Surface differential heating on a stably stratified fluid body drives an overturning circulation confined to the upper fluid region – here coined stratified horizontal convection (SHC). In this manuscript, we investigate the dynamics of SHC via laboratory experiments, exploring local and global flow properties. By considering the available potential energy of the system, we derive a unique length scale of SHC and introduce the Péclet number $Pe$ that captures both the stabilising effect of stratification and the destabilising effect of the baroclinic adjustment. We found that $Pe$ characterises local and global flow properties, including the fluid transport of the overturning circulation, the available mechanical energy and the flow dimensionality. Our study provides insights into the fluid dynamics of stratified environments that experience horizontal convection, such as lakes, oceans and atmospheres.

Computational fluid dynamics simulation of the heterogeneous regime in a large-scale bubble column

Bubble columns are used in many industrial applications, but the complex fluid dynamics phenomena has limited their design and optimization processes. Computational Fluid Dynamics (CFD) is a promising tool to investigate the complex multi-scale flow physics characterising multiphase reactors. In this work, a CFD Eulerian-Eulerian modelling approach is developed to describe the hydrodynamics of a large-scale bubble column operated over a wide range of superficial gas velocities (0.0188 – 0.20 m/s). Available experimental results were used for the model validation. A drag law for oblate bubbles was considered and coupled with a drag modification function to include the effects of bubble–bubble interactions. The numerical approach was tested considering a mono-dispersed approximation and including coalescence and breakup by using a Population Balance Model (PBM). The role played by the lift force was investigated and, for the reactor configuration considered, it turned out to be essential in the description of the local flow properties.

Thermal performance of elliptical pins on a semicircular concave surface in the staggered array jet impingement cooling

In a jet impingement cooling, decreasing heat transfer on the last jet's region due to the strong crossflow significantly increases thermal stress on the material. Thus, the main objectives of this study are to achieve relatively more uniform heat transfer distribution and enhance heat transfer on the surface compared to conventional jet impingement cooling (CJIC) configuration by mounting elliptical pins on the impingement regions. From this point of view, we have investigated the thermal performance of elliptical pins mounted on the impingement region of a staggered array jet impingement cooling (SJIC) on the semicircular concave surface. Numerical analyses were performed under various Reynolds numbers (Re = 5000, 15000, and 25000), jet nozzle-to-target surface spacing (0.5 ≤ G/d ≤ 8.0), and dimensionless orifice plate-target surface gaps (H/d = 4.0 and 8.0). Average Nusselt (Nu) numbers, local Nu contours, flow properties, and Thermal Performance Factor (TPF) on pinned and smooth target surfaces were studied in detail. Results showed that the local and area-averaged Nu numbers increased with reducing G/d and roughening of the surface with elliptical pins compared to conventional SJIC. Maximum heat transfer enhancement was obtained as 55.68% at H/d = 8.0 with extended jets (G/d = 0.5) and elliptical pin roughening surface design. Besides, the highest TPF on the pinned surface is achieved as 1.10 by G/d = 2.0 and H/d = 8.0 at Re = 25000. Furthermore, mounting elliptical pins on the surface provided more uniform heat transfer distribution on the surface compared to flat surface by means of significantly enhancing heat transfer on the last jet region.

Computational Fluid Dynamics Modelling of Two-Phase Bubble Columns: A Comprehensive Review

Bubble columns are used in many different industrial applications, and their design and characterisation have always been very complex. In recent years, the use of Computational Fluid Dynamics (CFD) has become very popular in the field of multiphase flows, with the final goal of developing a predictive tool that can track the complex dynamic phenomena occurring in these types of reactors. For this reason, we present a detailed literature review on the numerical simulation of two-phase bubble columns. First, after a brief introduction to bubble column technology and flow regimes, we discuss the state-of-the-art modelling approaches, presenting the models describing the momentum exchange between the phases (i.e., drag, lift, turbulent dispersion, wall lubrication, and virtual mass forces), Bubble-Induced Turbulence (BIT), and bubble coalescence and breakup, along with an overview of the Population Balance Model (PBM). Second, we present different numerical studies from the literature highlighting different model settings, performance levels, and limitations. In addition, we provide the errors between numerical predictions and experimental results concerning global (gas holdup) and local (void fraction and liquid velocity) flow properties. Finally, we outline the major issues to be solved in future studies.

A numerical wave tank with large eddy simulation for wave breaking

A three-dimensional (3D) numerical wave tank (NWT) is developed based on OpenFOAM. The propagation and breaking of waves with a moderate wavelength that could be generated in the laboratory are studied. The wave periods range from 0.5 to 1.79 s and wave steepness goes up to 0.05. The volume of fluid method (VOF) is employed for interface capturing. The relaxation zone method is implemented for wave generation and absorption at the boundaries. Computationally significant factors like grid size, relaxation weight and time step are investigated to find the optimal parameters of the numerical models for various wave regimes. A relationship between grid size and time step, similar to the wave dispersion relation, is found. The accuracy and performance of the NWT are assessed through the reflecting coefficient, wave damping and phase distortion rates. Simulation conditions are monitored to achieve an error rate of less than 3%. To mitigate the effects of numerical errors on the calculation of the reflection coefficient, a modified version of Goda's approach is proposed. The coefficient of wave reflection at the outlet boundary calculated by the conventional Goda's method is as high as 4.3%. This value can be modified to be less than 2% after utilizing the revised Goda's method. Turbulent flows, especially for the breaking wave regime, are investigated by large eddy simulation. A one-equation sub-grid eddy viscosity model, with coefficients being derived from local flow properties, is employed for turbulence closure. A case study of wave breaking on a fixed bar is simulated. The validation of this NWT model is confirmed by comparing the numerical results with experimental data.

Population Balance Models for Particulate Flows in Porous Media: Breakage and Shear-Induced Events

Transport and particulate processes are ubiquitous in environmental, industrial and biological applications, often involving complex geometries and porous media. In this work we present a general population balance model for particle transport at the pore-scale, including aggregation, breakage and surface deposition. The various terms in the equations are analysed with a dimensional analysis, including a novel collision-induced breakage mechanism, and split into one- and two-particles processes. While the first are linear processes, they might both depend on local flow properties (e.g. shear). This means that the upscaling (via volume averaging and homogenisation) to a macroscopic (Darcy-scale) description requires closures assumptions. We discuss this problem and derive an effective macroscopic term for the shear-induced events, such as breakage caused by shear forces on the transported particles. We focus on breakage events as prototype for linear shear-induced events and derive upscaled breakage frequencies in periodic geometries, starting from nonlinear power-law dependence on the local fluid shear rate. Results are presented for a two-dimensional channel flow and a three dimensional regular arrangement of spheres, for arbitrarily fast (mixing-limited) events. Implications for linearised shear-induced collisions are also discussed. This work lays the foundations of a new general framework for multiscale modelling of particulate flows.

Turbulent flow characteristics in an 84-pin rod bundle for typical and damaged spacer grids

Hexagonal rod bundles arranged in a tightly packed triangular lattice are extensively used for heat transfer and energy generation applications. Staggered spacer grids are used to maintain the structural integrity of gas-cooled fast reactor (GFR) fuel assemblies, while inducing localized turbulence in flow. Damage to these spacer grids results in a disruption of flow fields within these hexagonal fuel bundles. Experimental flow visualizations are critical to identify the differences in local flow properties that the structural damage may cause. This experimental research investigates the flow-field characteristics at a near-wall and center plane in a prototypical 84-pin GFR fuel assembly. Newly installed typical spacers and spacers subject to naturally occurring damage due to material degradation over prolonged experimentation were investigated. Velocity fields were acquired by utilizing the matched-index-of-refraction method to obtain time-resolved particle image velocimetry measurements for a Reynolds number of 12 000. Reynolds decomposition statistical results divulged differences in the time-averaged velocity, velocity fluctuations, flow anisotropy, and Reynolds stress distributions. Galilean decomposition demarcated the influence of spacer grid damage on the velocity fields. To extract turbulent structures and elucidate mechanisms of flow instabilities, proper orthogonal decomposition analysis was employed. Reduced order flow reconstructions enabled the application of vortex identification algorithms to determine the spatial and statistical characteristics of vortices generated. This research work provides unique experimental data on the spacer grid condition-dependent flow. The results offer a deeper understanding of fluid dynamics behavior to support GFR rod bundle design efforts and computational fluid dynamics model validation.

The influence of Variable Geometry Control on a R290 Ejector Refrigeration System

The large-scale deployment of ejector refrigeration systems (i.e., solar-based ejector refrigeration systems), although representing a promising alternative compared with mechanical compressor ones, is hindered due to limitations regarding ejector control modes. Indeed, ejectors are fluid-dynamics controlled devices and, because of their fixed geometry, they operate at their highest efficiency in a narrow range of operating conditions, which is in contrast with the dynamic pressure and temperature levels characterizing real applications. In this context, variable geometry ejectors (VGE) represent a promising solution to increase the flexibility and operation range of this component. The present study aims to extend the present body of knowledge regarding VGE systems, evaluating the impact of a spindle-provided ejector operated with R290 on the performance of the refrigeration system. The analysis has been carried out using an integrated lumped parameter/CFD approach, thus linking the local flow properties and global performances. Different spindle positions have been tested to assess how the different nozzle area ratios affect both the entrainment ratio and the critical pressure. Results showed that increasing primary nozzle area ratio the system can effectively reduce the thermal input, increasing the average COP at the expanse of a lower critical pressure. In conclusion, using a moving spindle control system might ensure an improvement of the ejector performance.

Lagrangian stochastic modelling of liquid flow in a mechanically agitated vessel

Deterministic models of complex flows are challenging and computationally expensive. We propose here, for the first time, a computationally efficient data-driven Lagrangian stochastic approach to predict liquid flow inside a mechanically agitated vessel. The model relies on the input of a short driver data set to predict the full flow field. We investigate the capability of zeroth, first and second order models over a wide range of flow conditions including different impeller configurations and rotational speeds. The first and second order models provide good predictions of local flow properties, with the first order model being slightly superior. The technique is also capable of predicting flow well outside the range of experimental conditions.

Computational fluid dynamic modelling of supersonic ejectors: comparison between 2D and 3D modelling

It is known that the global performances of ejector-based systems (viz., at the “global-scale”) depend on the local flow properties within the ejector (viz., at the “local-scale”). For this reason, reliable computational fluid-dynamics (CFD) approaches, to obtain a precise and an a-priori knowledge of the local flow phenomena, are of fundamental importance to support the deployment of innovative ejector-based systems. This communication contributes to the existing discussion by presenting a numerical study of the turbulent compressible flow in a supersonic ejector. In particular, this communication focuses on a precise knowledge gap: the comparison between 2D and 3D modelling approaches as well as density-based and pressure-based solvers. The different approaches have been compared and validated against literature data consisting in entrainment ratio and wall static pressure measurements. In conclusion, this paper is intended to provide guidelines for researchers dealing with the numerical simulation of ejectors.

Hypersonic nozzle for laser-spectroscopy studies at 17 K characterized by resonance-ionization-spectroscopy-based flow mapping

The in-gas-jet laser spectroscopy method relies on the production of uniform and low-temperature gas jets to fully resolve the atomic hyperfine structure and efficiently determine fundamental nuclear properties of short-lived isotopes from, e.g., the hardly accessible actinide and transactinide elements. In this article we present the studies devoted to designing, producing, and characterizing the flow properties of a convergent-divergent (de Laval) hypersonic nozzle with a superior performance for laser spectroscopy applications. A novel flow mapping technique, based on resonance ionization spectroscopy (RIS), has been employed to characterize the local flow properties of an argon gas jet formed by this nozzle, revealing a 61.5-mm long, highly collimated atomic jet at a uniform low temperature of 16.6(5) K [Mach 8.11(12)] that will enable laser spectroscopy experiments on heavy-exotic nuclei with an unprecedented spectral resolution and a high efficiency. These results have been compared with those obtained by planar laser induced fluorescence spectroscopy (PLIFS) studies and show a good agreement between the two techniques and a significant improvement in efficiency of the RIS mapping method with respect to PLIFS. The data are compared to state-of-the-art fluid-dynamics calculations that were carried out to obtain the nozzle contour and simulate its performance, as well as to explain the observation of a possible onset of argon nucleation.

Local flame and flow properties of propagating premixed turbulent flames during light-round process in a MICCA-type annular combustor

In this paper, local flame and flow properties of propagating premixed turbulent propane/air flames were derived by two-dimensional time-resolved Mie scattering and PIV methodology in a MICCA-type annular combustor. The curvature of flame front, local flame speed and the evolution of leading points during the light-round process were analyzed in detail. All experiments were performed under a constant equivalence ratio of 0.67, with the bulk flow velocity set from 1.95 to 5.85 m/s in five cases to achieve different turbulent intensities. The instantaneous flame fronts and velocity fields of unburned gases were measured to investigate the flame-flow interactions corresponding to four regions of the annular combustor. The results indicate that the slight asymmetry of the propagation in two flame branches is mainly due to the competition between the local swirling injection and the overall circumferential flow along the inner or outer parts of the combustor. Based on the statistical analysis of the local radius of flame curvature, the whole flame front tends to be convex to the unburned mixture. As a characteristic length scale, the inner-cutoff scale εi of the flame front is about 2–3 times the flame thickness δL, which decreases with the increase of turbulent intensity. The value of fractal dimension increases with the increase of turbulence intensity, and its value is about 2.15–2.25 for all cases. Besides, in order to analyze the flame properties during the ignition process, the local flame speed wn was calculated using statistical method as well as the velocity of unburned mixture gas. Moreover, the experimental results (Ub=3.90 m/s) of the leading points’ trajectory were consistent with the large-eddy simulations at the height of h =25 mm, and the leading points of the flame fronts were generally concentrated near (about 5 mm away) the inner tube for both flame branches. The researches of ignition mechanisms in annular combustors have been carried out for almost ten years, but the quantitative measurements of flow and flame fronts are barely reported. Motivated by this, it will provide new insights into the ignition process in annular combustors from this work.

DES법을 이용한 SUBOFF 잠수함 모델 주위 유동 수치해석 연구

In this study, the numerical investigation of the flow around the SUBOFF submarine model is performed by using the Detached Eddy Simulation (DES) method which is developed based on the SST k-ω turbulence model. At the DES analysis level, complex vortical flows around the submarine model are caused mainly by the vortices due to the appendages and their interactions with the flows from the hull boundary layer and other appendages. The complexity and scale of the vortical flow obtained from the numerical simulations are highly dependent on the grid. The computed local flow properties of the submarine model are compared with the available experimental data showing a good agreement. The DES analysis more reasonably estimates the physical phenomena inherent in the experimental result in a low radius of the propeller plane where vortical flows smaller than the RANS scale are dominant.

Modifications of Heat Transfer and Induced Flow Rate of a Solar Chimney by an Obstacle in the Air Channel

Using renewable energy resources in buildings has been increasing for saving energy. Among widely used methods, solar chimneys absorb solar radiation and induce an airflow for ventilation, heating, or cooling buildings. The performance of a solar chimney depends on the heat transfer in its air channel, which can be modified by changing the shape of the heat exchange surface. In this study, we examine the effects of a rectangular obstacle placed on the heated surface of the air channel of a solar chimney. A numerical model was built with the Computational Fluid Dynamics (CFD) technique. By changing the geometries of the chimney and of the obstacle, and location of the obstacle, it was found that the obstacle had strong effects on the local flow and heat transfer properties close to the object, particularly the Nusselt number and the temperature field. However, average quantities of the whole air channel flow, such as the averaged Nusselt number and the induced flow rate, were modified insignificantly, except for the temperature rise through the chimney and the thermal efficiency. The change of the flow rate and the average Nusselt number was 5.0% while the temperature rises and the thermal efficiency was up to 13.0%. The height of the obstacle had more influence than the length. This study suggests more investigations to achieve the objective of enhancing the induced flow rate for ventilation of buildings with an obstacle in the air channel of a solar chimney.

Data-assisted combustion simulations with dynamic submodel assignment using random forests

In this investigation, we outline a data-assisted approach that employs random forest classifiers for local and dynamic combustion submodel assignment in turbulent-combustion simulations. This method is applied in simulations of a single-element GOX/GCH4 rocket combustor; a priori as well as a posteriori assessments are conducted to (i) evaluate the accuracy and adjustability of the classifier for targeting different quantities-of-interest (QoIs), and (ii) assess improvements, resulting from the data-assisted combustion model assignment, in predicting target QoIs during simulation runtime. Results from the a priori study show that random forests, trained with local flow properties as input variables and combustion model errors as training labels, assign three different combustion models - finite-rate chemistry (FRC), flamelet progress variable (FPV) model, and inert mixing (IM) - with reasonable classification performance even when targeting multiple QoIs. Applications in a posteriori studies demonstrate improved predictions from data-assisted simulations, in temperature and CO mass fraction, when compared with monolithic FPV calculations. These results demonstrate that this data-driven framework holds promise for the dynamic combustion submodel assignment in reacting flow simulations.

Bubble column fluid dynamics: A novel perspective for flow regimes and comprehensive experimental investigations

When a gas phase is injected into a liquid phase, it gives rise to a rich, fascinating and mysterious fluid dynamic phenomenology. The lack of knowledge regarding this phenomenology, a shortcoming in the design and operation of multi-phase reactors, is related to the absence of an unique definition of the flow regimes. To date, different studies gave different definitions of the flow patterns and, subsequently they experimentally obtained some global and local flow properties, with no physical-based description of the flow patterns. Is there a theory able to determine a-priori the boundaries of different flow regimes (and, thus, the flow regime for a given set of boundary conditions, given the phases and the system design)? Answering this question requires changing the present point of view in defining and describing the flow regimes and it is the primary motivation of this paper. To achieve this goal, a new theory has been formulated, which changes the present way of approaching bubble columns and which is based on the following statement: the fluid dynamics in gas-liquid bubble columns is interpreted by means of a general relationship―built upon five flow regime transitions―between two global fluid dynamic parameters. The strategic path to formulate this theory is, first, to go back to the pioneering studies and formulate basic relationships on the basis of a general principle. Subsequently, in order to support and verify the theory a comprehensive and multi-scale experimental investigation has been performed and coupled with previous experimental studies. The different experimental studies have been conducted in a gas-liquid large-scale bubble column (height of 5.3 m; inner diameter of 0.24 m) operated in the batch and in counter-current modes; to study all flow regimes, the bubble column was tested with five gas spargers (viz., pipe sparger in open tube and annular gap configuration, spider sparger, two different perforated plates and needle spargers) with different values of the aspect ratios and different liquid phases. It was found that, in an air-water bubble column, the gas velocity is approximately 0.03 m/s either in the case of the destabilization of the mono-dispersed homogeneous flow regimes or in the case of the destabilization of the pseudo-homogeneous flow regimes. Increasing the gas sparger opening induces a narrowing of the boundaries between the transitional flow regimes; conversely, increasing the bubble column aspect ratio destabilizes the existing flow regimes up to some critical values. Also, increasing the superficial liquid velocity in the counter-current mode destabilizes the homogeneous flow regime. Finally, it has been observed that the prevailing effect of the liquid phase, in a bubble column operated with a “coarse” gas sparger, is to change the boundary of the homogenous flow regime. It has also been discussed how the change in coordinates of the flow regime transition between the homogeneous and the heterogeneous flow regimes is caused by the changes in the size distribution. This study is intended to outline a precise definition of the flow regimes in bubble columns and it poses a rational basis for future studies.

Continuum Modeling of Pressure‐Balanced and Fluidized Granular Flows in 2‐D: Comparison With Glass Bead Experiments and Implications for Concentrated Pyroclastic Density Currents

AbstractGranular flows are found across multiple geophysical environments and include pyroclastic density currents, debris flows, and avalanches, among others. The key to describing transport of these hazardous flows is the rheology of these complex multiphase mixtures. Here we use the multiphase model MFIX in 2‐D for concentrated currents to examine the implications of rheological assumptions and validate this approach through comparison to experiments of both frictional and fluidized flows made of glass beads (Sauter mean grain‐size of 75 μm). Because the rheology of highly polydisperse, highly angular, polydensity granular mixtures is poorly known, we focus on simplified monodisperse or bidisperse mixtures described by the frictional flow theory of Schaeffer (1987, https://doi.org/10.1016/0022‐0396(87)90038‐6) and Srivastava‐Sundaresan, often referred to as the Princeton model (Srivastava & Sundaresan, 2003, https://doi.org/10.1016/S0032‐5910(02)00132‐8). We show that simulations including the latter model replicate well the flow shape, kinematics, and pore fluid pressure that match well‐constrained dam‐break experiments of initially fluidized or pressure‐balanced granular flows. Simulations reveal that pore fluid pressure is intrinsically modulated by dilation and compaction of the flow and hence can be generated in concentrated pyroclastic density currents. We use these simulations to interpret basal pore pressure signals from local flow properties (mixture density, solid velocity, and pore fluid pressure). Rheological changes retard these simulated flows considerably near the predicted runout, but most continuum models cannot inherently predict a zero velocity. We suggest an inertial number parameter that can be used to approximate deposition, and this approach could be a valuable tool used to validate simulations against natural pyroclastic current examples.

Flow-dependent DDES[formula omitted] coupling model for the simulation of separated transitional flow

A new DDES and γ−Re‾θt coupling model for separated transitional flow is proposed. The studies in this paper indicate that the activation of the LES branch in the free stream may lead to an inappropriate decrease in the inflow turbulence intensity and a delayed transition. To address this problem, a new flow-dependent RANS/LES switch function based on identification functions for the boundary layer and wake regions is designed. In this new model, the adoption of the RANS or LES branch is decided by both the local grid density and local flow properties, and the LES branch is only allowed to be active in the wake region. Therefore, the inflow turbulence intensity uncertainties caused by grid dependence of the LES branch in the free stream are largely eliminated. Separated transitional cases including flows over an A-Airfoil (small separation), a DBLN-526 airfoil (moderate separation), and a circular cylinder in subcritical and critical regimes (massive separation) are studied. The performance of two commonly employed boundary layer shielding functions is examined. Good agreements are achieved between the numerical and experimental results, and the accuracy and reliability of the new model are demonstrated.