Converging-diverging Channel Research Articles

Mathematical modelling of MHD hybrid nanofluid flow in a convergent and divergent channel under variable thermal conductivity effect

Abstract The aim of this research is to analyse the combined effect of variable thermal conductivity and nonlinear thermal radiation on magnetohydrodynamic (MHD) hybrid nanofluid flow in convergent-divergent channels. The effects of two nanoparticles (i.e. ZrO 2 {\text{ZrO}}_{\text{2}} and SiO 2 {\text{SiO}}_{\text{2}} ) in base fluid (i.e. H 2 O {\text{H}}_{\text{2}}\text{O} ) are considered in this work. The partial differential equations modelling the problem are reduced to ordinary differential equations following the application of the similarity transformations. The system has been solved analytically with the differential transform method and numerically with the Runge–Kutta–Fehlberg 4th–5th order method with the assistance of the shooting technique. Comprehensive analysis and discussion have been conducted regarding the impact of multiple governing parameters on the dimensionless velocity and temperature distributions. These parameters include variable thermal conductivity, nonlinear thermal radiation, Hartman number, and hybrid nanoparticle volume fraction. Finally, this method will provide some insights into the usefulness of MHD hybrid nanofluid flow in convergent-divergent channels, and the results produced by the analytical data have also been strengthened and verified by the use of numerical data as well as data from the literature.

Velocity slip and temperature jump effects on entropy generation of MHD second-grade hybrid nanofluid in Jeffery-Hamel flow

PurposeThis paper aims to model and analyze Jeffery Hamel’s channel flow with the magnetohydrodynamics second-grade hybrid nanofluid. Considering the importance of studying the velocity slip and temperature jump in the boundary conditions of the flow, which leads to results close to reality, this paper intends to analyze the mentioned topic in the convergent and divergent channels that have significant applications.Design/methodology/approachThe examination is conducted on a EG-H_2 O <30%–70%> base fluid that contains hybrid nanoparticles (i.e. SWCNT-MWCNT). To ensure comprehensive results, this study also considers the effects of thermal radiation, thermal sink/source, rotating convergent-divergent channels and magnetic fields. Initially, the governing equations are formulated in cylindrical coordinates and then simplified to ordinary differential equations through appropriate transformations. These equations are solved using the Explicit Runge–Kutta numerical method, and the results are compared with previous studies for validation.FindingsAfter the validation, the effect of the governing parameters on the temperature and velocity of the second-grade hybrid nanofluid has been investigated by means of various and comprehensive contours. In the following, the issue of entropy generation and its related graphical results for this problem is presented. The mentioned contours and graphs accurately display the influence of problem parameters, including velocity slip and temperature jump. Besides, when thermal radiation is introduced (Rd = +0.1 and Rd = +0.2), entropy generation in convergent-divergent channels decreases by 7% and 14%, respectively, compared to conditions without thermal radiation (Rd = 0). Conversely, increasing the thermal sink/source from 0 to 4 leads to an 8% increase in entropy generation at Q = 2 and a 17% increase at Q = 4 in both types of channels. The details of the analysis of contours and the entropy generation results are fully mentioned in the body of the paper.Originality/valueThere are many studies on convergent and divergent channels, but this study comprehensively investigates the effects of velocity slip and temperature jump and certainly, this geometry with the specifications presented in this paper has not been explored before. Among the other distinctive features of this paper compared to previous works, the authors can mention the presentation of velocity and temperature results in the form of contours, which makes the physical analysis of the problem simpler.

MHD nanofluid flow between porous convergent-divergent channel with velocity slip and nanoparticle aggregation

The aggregation of nanoparticles is a major phenomenon having broad consequences in many fields. In order to fully utilize the capabilities of nanoparticles in a variety of applications and to evaluate the effects that they will have on the environment and biological systems, it is crucial to comprehend and manage aggregation. To develop and improve nanoparticle-based technology, researchers are still learning more about the aggregation processes. Thus, the present study investigates the combined effects of velocity slip and nanoparticle aggregation on Heat transfer (HT) analysis of MHD nanofluid (i.e., TiO2-C2H6O2) flow between porous convergent, divergent channel. The modified Krieger–Dougarty and Maxwell–Bruggeman models were utilized for nanoparticle aggregation. The modeling is based on nonlinear PDEs such as continuity, momentum, and heat equations. These equations are transformed into a system of nonlinear ODEs using similarity transformations and then solved numerically and analytically. The analytical solution has been constructed using the ADM method. The present results in particular cases are compared to results obtained by the HAM- package and by the Runge- Kutta Fehlberg 4th–5th order (RKF-45) for validation. The effects of active parameters on the velocity, temperature, concentration, skin friction, and Nusselt numbers are investigated. It is found that nanoparticle aggregation can limit fluid velocity in converging channels by increasing flow resistance through aggregate formation. Individual nanoparticles generate friction and lower velocity, while aggregated nanoparticles boost fluid density and velocity. In addition, it is found that the magnetic field lowers skin friction and increases HT due to Lorentz force, while porosity increases friction and HT. Nanoparticle concentration inversely affects friction, increasing friction without aggregation and decreasing friction with aggregation, with the HT rate rising with increased nanoparticle concentrations.

Physically constrained eigenspace perturbation for turbulence model uncertainty estimation

Aerospace design is increasingly incorporating design under uncertainty-based approaches to lead to more robust and reliable optimal designs. These approaches require dependable estimates of uncertainty in simulations for their success. The key contributor of predictive uncertainty in computational fluid dynamics (CFD) simulations of turbulent flows are the structural limitations of Reynolds-averaged Navier–Stokes models, termed model-form uncertainty. Currently, the common procedure to estimate turbulence model-form uncertainty is the eigenspace perturbation framework (EPF), involving perturbations to the modeled Reynolds stress tensor within physical limits. The EPF has been applied with success in design and analysis tasks in numerous prior works from the industry and academia. Owing to its rapid success and adoption in several commercial and open-source CFD solvers, in-depth verification and validation of the EPF is critical. In this work, we show that under certain conditions, the perturbations in the EPF can lead to Reynolds stress dynamics that are not physically realizable. This analysis enables us to propose a set of necessary physics-based constraints, leading to a realizable EPF. We apply this constrained procedure to the illustrative test case of a converging-diverging channel, and we demonstrate that these constraints limit physically implausible dynamics of the Reynolds stress tensor, while enhancing the accuracy and stability of the uncertainty estimation procedure.

Toward a continuum description of lubrication in highly pressurized nanometer-wide constrictions: The importance of accurate slip laws.

The Reynolds lubrication equation (RLE) is widely used to design sliding contacts in mechanical machinery. While providing an excellent description of hydrodynamic lubrication, friction in boundary lubrication regions is usually considered by empirical laws, because continuum theories are expected to fail for lubricant film heights h0 ≪ 10 nm, especially in highly loaded tribosystems with normal pressures pn ≫ 0.1 GPa. Here, the performance of RLEs is validated by molecular dynamics simulations of pressurized (with pn = 0.2 to 1 GPa) hexadecane in a gold converging-diverging channel with minimum gap heights h0 = 1.4 to 9.7 nm. For pn ≤ 0.4 GPa and h0 ≥ 5 nm, agreement with the RLE requires accurate constitutive laws for pressure-dependent density and viscosity. An additional nonlinear wall slip law relating wall slip velocities to local shear stresses extends the RLE's validity to even the most severe loading condition pn = 1 GPa and h0 = 1.4 nm. Our results demonstrate an innovative route for continuum modeling of highly loaded tribological contacts under boundary lubrication.

Improving material removal rate and surface roughness in macro electrolyte jet machining of TC4 titanium alloy using tools with a converging-diverging Laval-type electrolyte channel

Improving material removal rate and surface roughness in macro electrolyte jet machining of TC4 titanium alloy using tools with a converging-diverging Laval-type electrolyte channel

Flow Rate Augmentation of Valveless Pumping via a Time-Dependent Stenosis: A Novel Device

A novel device of flow rate augmentation is proposed and experimentally examined in a horizontal valveless closed loop pump using a time-dependent stenosis (convergent–divergent channel) in contrast with the commonly used taper tubes of constant opening as flow rectifiers. The stenosis, being a part of the flexible tube of the pump, is formed by a semi-cylindrical surface attached to a compression spring of adjustable pretension compressing the tube against a flat plate. Located at either side of the pump pincher, the shape of the stenosis changes in time, without any external power source, as a function of the fluid pressure and the pretension of the spring. The spring pretension is adjusted by a trial-and-error procedure aiming for net flow rate maximization for each pinching frequency. For the examined pitching frequencies (5 Hz to 11 Hz, for which net flow rate is maximized) and for compression ratios 38% to 75%, the maximum net flow rate was found to be 720% of the non-stenosis case. Important parameters for flow enhancement were found to be the stenosis location along the loop, its opening, the compression ratio at the pincher area and the pinching frequency.

Comparison of different data-assimilation approaches to augment RANS turbulence models

Reynolds-averaged Navier–Stokes (RANS) simulations are the most widespread approach to predict turbulent flows typical of industrial problems. Despite its success, the inherent simplifications and assumptions used to model the unknown Reynolds stresses are sources of inaccuracies. With this in mind, data-assimilation (DA) techniques can be used to minimize errors between the predicted and the exact flow fields by optimizing a space-dependent correction term. This correction term can be subsequently fed into machine learning algorithms to enhance RANS turbulence models. The main objective of this work is to assess the performance of several correction terms to match a full mean-flow velocity field, provided by averaged DNS simulations, and analyze the pros and cons of each when used subsequently in a machine-learning based RANS framework. Three configurations were chosen to perform the analysis: the converging-diverging channel at Re=12600, the flow over periodic hills at Re=2800, and the square cylinder at Re=22000. Six different correction terms were considered and discussed in this paper. Assimilations based on eddy-viscosity corrections, albeit constrained by the Boussinesq hypothesis, were able to correct the velocity field even for flows exhibiting large recirculation regions. However, the precise choice of the correction term employed has a major impact in the optimization process. On the other hand, when correction is applied as source terms in the momentum equations, better fit of the corrected mean-flow field is achieved.

Thermo-hydraulic effect of a convergent-divergent cold channel using MXene nanofluid for thermoelectric-based waste heat recovery system

Thermo-hydraulic effect of a convergent-divergent cold channel using MXene nanofluid for thermoelectric-based waste heat recovery system

The dynamic behavior of a droplet flows through a constricted splitting channel: a lattice Boltzmann study

In this paper, a lattice Boltzmann method is used to simulate the dynamic behavior of a droplet flows through a constricted channel, where an obstacle is placed in the center of the constricted channel to split the droplet. The method is first used to simulate the effect of the capillary number on the volume of the divided daughter droplets. Results show that the volume difference between the daughter droplets above and below the obstacle increases as increases. We also find that reducing the capillary number is conducive to the droplet splitting into two daughter droplets with similar volume. The method is then used to simulate the influence of the viscosity ratio on the droplet flows through a constricted channel. As increases, the volume difference between the daughter droplets above and below the obstacle decreases. Finally, the influence of the confinement ratio on the evolution of the droplet morphology is investigated. With increase in , the volume difference between the daughter droplets above and below the obstacle increases. When , the droplet does not break up and completely enters the bottom channel. Comparing with the converging-diverging and ratchet channels, the constricted splitting channel is more conductive to the breakup of the droplet neck.

Flow reversals of a non-Newtonian fluid in an expanding channel

The flow of an incompressible power-law fluid through convergent–divergent channels is considered where the choice of the viscosity is such that the zero-shear rate viscosity is neither zero nor infinity for any finite value of the power-law exponent. Rather than employing the classical similarity transformation employed by Jeffery and Hamel implying purely radial solutions for the velocity field, we instead consider flow in both the radial and angular directions, under three sets of boundary conditions. This work is in contrast to the earlier study by Mansutti and Rajagopal (1991). wherein the viscosity could be zero or infinity for certain values of the power-law exponent. While seeking solutions to nonlinear differential equations, when seeking similarity solutions, one ought to be cognizant that the equations might have solutions in addition to the similarity solution that is being sought. We observe that the tangential velocity does indeed play a role in the flow regime of the fluid, with flow reversal also present for certain values of α. In the case of traction boundary conditions, we also observe a change in the flow characteristics.

Onset about isothermal flow of Carreau liquid over converging channel with Cattaneo-Christov heat and mass fluxes

In this paper, an innovative mathematical approach is adopted to construct new formulation for exploring thermal characteristics in Jeffery Hamel flow between non-parallel convergent-divergent channels using non-Fourier's law. Due to the occurrence of isothermal flow of non-Newtonian fluids through non-uniform surfaces in many industrial and technological processes, such as film condensation, plastic sheet deformation, crystallization, cooling of metallic sheets, design of nozzles devices, supersonic and various heat exchangers, and glass and polymer industries, the current research is focused on this topic. To modulate this flow, the flow stream is subjected in a non-uniform channel. By incorporating relaxations in Fourier's law, thermal and concentration flux intensities are examined. In the process of mathematically simulating the flow problem, we constructed a set of governing partial differential equations that were embedded with a variety of various parameters. These equations are simplified into order differential equations using the vogue variable conversion approach. By selecting the default tolerance, the MATLAB solver bvp4c completes the numerical simulation. The temperature and concentration profiles were determined to be affected in opposing ways by thermal and concentration relaxations, while thermophoresis improved both fluxes. Inertial forces in a convergent channel accelerate the fluid in a convergent channel, while in the divergent channel the stream is shrink. The temperature distribution of Fourier's law is stronger than that of the non-Fourier's heat flux model. The study has real-world significance in the food business and is pertinent to energy systems, biomedical technology, and contemporary aircraft systems.

Thermal transport and magnetohydrodynamics flow of generalized Newtonian nanofluid with inherent irreversibility between conduit with slip at the walls

This study enlightens the magnetohydrodynamic Jeffery-Hamel flow under an inclined Lorentz force through a non-uniform conduit having slip at walls, which is frequently applied in geothermal applications, electronic cooling devices, and modern energy systems, etc. Therefore, the performance of a two-dimensional purely radial flow inside a converging-diverging channel is explored from the perspective of second law of thermodynamics for Carreau nanofluids. The intersecting walls of conduit are inclined with horizontal plane to construct a converging flow for negative angle (α<0) and a diverging flow for positive angle (α>0). Additionally, second law thermodynamic evaluation offers an effective method for improving thermal performance by reducing entropy production. To accomplish the main objective, rigorous physical theories and assumptions are implemented based on the passive control approach of Buongiorno's model. By applying distinctive modifications, the governing equations are renovated into a system of ordinary differential equations, which are solved numerically by a collocated technique based on finite difference code. Simple shear near the wall influences the flow configurations allow compression in a local flow topology in regions of divergent channel. The temperature profiles increase with sophisticated heat source and Brinkman number. Entropy is minimum and uniform with optimum channel angle and velocity slip.

Fluid Flow Modelling Using Physics-Informed Convolutional Neural Network in Parametrised Domains

We design and implement a physics-informed convolutional neural network (CNN) to solve fluid flow problems on a parametrised domain. The goal is to compare the effectiveness of training based solely on CFD-generated training data with purely physics-informed training and training based on a combination of both. We consider the problem of incompressible fluid flow in a convergent-divergent channel with variable wall shape. A speciality of the designed neural network is the incorporation of the boundary condition directly in the CNN. A physics-informed CNN that uses a non-Cartesian mesh poses a challenge when evaluating partial derivatives. We propose a gradient layer that approximates the first and second partial derivatives by finite differences using Lagrange interpolation. Our analysis shows that the convergence of purely physics-informed training is slow. However, using a small training dataset in combination with physics-informed training can achieve results comparable to physics-uninformed training with a considerably larger training dataset.

MODELING LAMINAR FLOW IN CONVERGING-DIVERGING CHANNELS

Converging-diverging channels have been known to have low net charge (flow parameters) due to associated high frictional flow resistance. Thus, there is a need to optimize frictional flow resistance in these channels. To this end, frictional flow resistance was optimized for a laminar, fully formed flow in a linearly varying cross-sectional converging-diverging channel in this study. To achieve this, an empirical frictional flow resistance model was developed using continuity and momentum equations, and this accurately represents a parabolic axial velocity profile in converging-diverging section. The developed model was solved and parametric investigations carried out on geometrical and fluid flow parameters using MATLAB 6.1. The results show that the frictional flow resistance decreases as radius ratios increases, but increases as Reynolds number and taper angle increase. Radius ratios and Reynolds numbers were found to be more significant than taper angles. Results in comparison to available literature showed that the developed frictional flow model is an accurate model as it predicts axial velocity and the flow resistance with a high degree of precision. The study concludes that, for frictional flow resistance to be kept at barest minimum in a converging diverging channel, radius ratio must be maintained at its highest value and Reynolds number at its lowest possible value.

Dynamics of cavity structures and wall-pressure fluctuations associated with shedding mechanism in unsteady sheet/cloud cavitating flows

The physics and mechanism of sheet/cloud cavitation in a convergent–divergent channel are investigated using synchronized dynamic surface pressure measurement and high-speed imaging in a water tunnel to probe the cavity shedding mechanism. Experiments are conducted at a fixed Reynolds number ofRe = 7.8 × 105for different values of the cavitation numberσbetween 1.20 and 0.65, ranging from intermittent inception cavitation, sheet cavitation to quasi-periodic cloud cavitation. Two distinct cloud cavitation regimes, i.e. the re-entrant jet and shockwave shedding mechanism, are observed, accompanied by complex flow phenomenon and dynamics, and are examined in detail. An increase in pressure fluctuation intensity at the numbers 3 and 4 transducer locations are captured during the transition from re-entrant jet to shockwave shedding mechanism. The spectral content analysis shows that, in cloud cavitation, several frequency peaks are identified with the dominant frequency caused by the large-scale cavity shedding process and the secondary frequency related to re-entrant jet/shockwave dynamics. Statistical analysis based on defined grey level profiles reveals that, in cloud cavitation, the double-peak behaviours of the probability density functions with negative skewness values are found to be owing to the interactions of the re-entrant jet/shockwave with cavities in the region of 0.25 ~ 0.65 mean cavity length (Lc). In addition, multi-scale proper orthogonal decomposition analysis with an emphasis on the flow structures in the region of 0.25 ~ 0.65Lcreveals that, under the shockwave shedding mechanism, both the re-entrant jet and shockwave are captured and their interactions are responsible for the dynamics and statistics of cloud shedding process.

Control of graphene nanoplatelets at the interface of the co-continuous polypropylene/polyamides 6 blend under the elongational flow

Controlling the filler selective distribution at the interface of co-continuous polymer blend is an effective way to fabricate high performance composites. In this work, the graphene nanoplatelets (GNPs) were distributed at the interface of co-continuous polypropylene (PP)/polyamides 6(PA6) blend by melt blending under the elongational flow generated by convergent-divergent channels. And the formation of co-continuous structure and migration mechanism of GNPs in the PP/PA6 blend under the elongational flow were discussed based on the analysis of rheological measurement, scanning electron micrographs, selective etching experiment and thermal conductivity measurement. The results show that both PP and PA6 phase are elongated into fibrous phase structure under the elongational flow. This indeed enlarge the volume ratio range of composites forming co-continuous structure. And GNPs are oriented along the phase interface and stay at the interface during migration under the elongational flow, which can improve its in-plane thermal conductivity. The in-plane thermal conductivity of the PP/PA6/GNPs composites prepared under the elongational flow are all higher than those prepared under the shear flow. Particularly, the composite prepared under the elongational flow with the 65/35 vol ratio of PP/PA6 still kept a co-continuous structure and the GNPs distributed at the interface. Its in-plane thermal conductivity reached a maximum value of 1.13 W/m K.

On low Reynolds number optimization of non‐linear partial differential equations for convergent–divergent engulfment: A numerical result

AbstractThe flow field in a convergent–divergent engulfment along with the installation of infinite cylinders as an obstacle results in non‐linear partial differential equations and the scientific computation in this regard remains a challenging task. The present attempt is the numerical motivation in this direction to evaluate the flowing liquid stream in the convergent–divergent channel at a low Reynolds number. From the left wall, the liquid stream move with the parabolic profile and have interaction with the case‐wise installation of infinite cylinders in the left vicinity of the convergent–divergent throat. The differential system is constructed for the flow field in the channel and hybrid meshed finite element method is utilized to report the numerical solution. A comparative study is enclosed for the hydrodynamic forces faced by obstructions in the left region of the convergent–divergent throat. The drag coefficient for a triangular cylinder acting as an obstruction is higher than that of a circular hitch. In comparison to both triangular and circular hitches, the square‐shaped obstacle suffered the most drag force. Considering drag coefficient one can extend this work to obtain information for the real behavior of the vehicle toward air flow and may conclude findings toward reduction of fuel consumption.

Geometric and thermo hydrodynamic investigation of a 3D converging-diverging channel by Taguchi and ANFIS methods

This paper numerically investigates a three-dimensional channel's thermal and hydrodynamic performance with a convergent-divergent section. The convergent-divergent part of the channel is exposed to constant heat flux, and the other walls of the channel are insulated. In particular, the effect of using the nanofluid and magnetic field on Nusselt values, coefficient of friction, and entropy have been investigated. To improve Nusselt, pressure drop, and dimensionless entropy production rate, the Taguchi and ANFIS techniques have been utilized to optimize Reynolds, Hartmann numbers, nanofluid volume fraction, and geometric parameters of the channel. The sensitivity analysis results depict that Reynolds, Hartmann dimensionless numbers, and nanofluid volume fraction play more significant roles in improving the thermal and hydrodynamic performance of the channel than geometric parameters. The results show that the increase in the nanofluid volume fraction causes the most significant increase in the Nusselt number. In this case, the pressure drop inside the channel has increased slightly, but in total, the entropy production rate decreases due to irreversibility. Compared to the base case with the Reynolds number of 100, and in the absence of a magnetic field (Hartman 0), increasing the nanofluid volume fraction to 7% causes an 80% increase in the Nusselt number and a 65% decrease in the dimensionless entropy production rate. Similarly, by increasing the Reynolds number to 500 compared to the base case, the Nusselt number increases by 60% and the dimensionless entropy production rate decreases by 60%. Also, increasing the Hartmann number to 10 compared to the base case causes a 30% increase in the dimensionless Nusselt number and a 45% decrease in the dimensionless entropy production rate.

Investigation on the flow mechanism of nacelle airframe interaction for podded blended wing body transport

For the flow interaction between the podded engine and the airframe of blended wing body configuration(BWB), taking the 300 seats class BWB civil transport NPU-BWB-300 designed by Northwestern Polytechnical University as the research object, the influence of the podded engines on the BWB airframe at typical high and low speed conditions were investigated by CFD method, and the airframe-nacelle interference mechanism was revealed. The results indicate that the podded engines mainly affect the high speed performance of BWB, but have little effect on the low speed performance. The flow interaction between the airframe and the nacelle at high speed condition is serious when podded the engines, which leads to strong shock wave and flow separation. The flow mechanism of the above-mentioned interaction is as follows: firstly, the large supersonic region and shock wave on the nacelle external surface interferes with airframe surface flow seriously, which induces shock wave and flow separation; secondly, a convergent-divergent channel is formed between the airframe and the nacelle, resulting in the "throat" effect, which produces shock wave and flow separation.