Journal Of Applied Fluid Mechanics
Volume:11 Issue: 6, Nov-Dec 2018

A bulk of a liquid dispersed into single droplets using the kinetic energy of a high-velocity gas in an air-blast atomizer is frequently employed in technical atomization processes. The atomized liquid is primary situated on a surface (prefilming surface) to form a thin liquid film before being exposed to high-velocity air flow. Moreover, the performance of spray processes is affected by the variation in the atomizer geometry, liquid physical properties and operational conditions. The purpose of this study is to examine and describe the influence of the nozzle geometry and a wide range of test conditions on the spray performance of prefilming air-blast atomizers. In order to evade the commonly complicated internal flow, an important but simple geometry was selected. Liquid break up mechanisms close to the atomizer exit were investigated using shadowgraphy associated with particle tracking. Furthermore, high-resolution local velocity and droplet size measurements were performed using phase Doppler anemometry (PDA). On the whole, the break up mechanism is considerably influenced by either air pressure and liquid flowrates or atomization edge size. Droplet size distribution profile of the different spray parameters in axial and radial directions are studied. The location of the maximum droplet mean velocity and the minimum Sauter mean diameter (SMD) within the spray are determined. The prefilming surface area and atomization edge size were observed to influence the liquid sheet breakup, droplet velocity and droplet size. With an atomization edge length increase of 5.7 mm, the global SMD increased to a maximum of 70% within different operation conditions.

Natural or industrial flows of a fluid often involve droplets or bubbles of another fluid, pinned by physical or chemical impurities or by the roughness of the bounding walls. Here we study numerically one drop pinned on a circular hydrophilic patch, on an oscillating incline whose angle is proportional to sin(ωt). The resulting deformation of the drop is measured by the displacement of its center of mass, which behaves similarly to a driven over-damped linear oscillator with amplitude A(ω) and phase lag φ(ω). The phase lag is O(ω) at small ω like a linear oscillator, but the amplitude is O(ω−1) in a wide range of large ω instead of O(ω−2) for a linear oscillator. A heuristic explanation is given for this behaviour. The simulations were performed with the software Comsol in mode Laminar Two-Phase Flow, Level Set, with fluid 1 as engine oil and fluid 2 as water.

Numerical investigations using Scale-Adaptive Simulation (SAS) turbulence model are carried out to study the flow around a circular cylinder near to a plane boundary at Reynolds numbers between 8.6x104 and 2.77x105 with two different boundary layer thickness (δ) on the plane. The effects of gap (G) between the cylinder and the plane, the Reynolds number and the thickness of the plane boundary layer are analyzed through the drag and the lift coefficients, the Strouhal number, as well as through the wake flow structures behind the cylinder. Two and three-dimensional simulations are performed to examine the significance of the flow three-dimensionality when the cylinder is located near a plane. The SAS model results are compared with published experimental data and numerical results for similar flow conditions. The characteristics of the wake structures and force acting on the cylinder are in good agreement with previous studies. In general, the 3D-SAS model performed better than 2D-SAS. Based on the numerical results here obtained, the SAS turbulence model can be applied to study this flow configuration.

This paper presents the study of the overall aerodynamic performance of road vehicles and suggests a method to reduce the drag force and also to find the optimum location for placing basebleed in a car using aerodynamic principle. The overall aerodynamic drag force is reduced by eliminating wake region at the rear side of the car and reducing pressure in the front region of the car by delaying the flow separation. This improves the overall aerodynamic performance of the car thereby reducing fuel consumption, as well as improving stability and comfort by the attachment of basebleed. The wind tunnel tests are conducted for a subscale model of car with the basebleed at various locations along the front and rear side of the car in both X and Y directions. The coefficient of drag (CD), the coefficient of lift (CL) and coefficient of side force (CS) for the car is measured to interpret the effect of flow conditions on the car model. The experimental result reveals that the attachment of base bleed at an optimum position in the front and rear side of the car improves its performance and decreases drag coefficient by 6.188 %.

A variety of wall shear stress (WSS) based hemodynamic descriptors have been defined over the years to study hemodynamic flow instabilities as potential indicators or prognosticators of endothelial wall dysfunction. Generally, these hemodynamic indicators have been calculated numerically using ‘single phase’ approach. In single phase models, the flow-dependent cell interactions and their transport are usually neglected by treating blood as a single phase non- Newtonian fluid. In the present investigation, a multiphase mixture-theory model is used to define the motion of red blood cells (RBCs) in blood plasma and interactions between these two-components. The multiphase mixture theory model exhibited good agreement with the experimental results and performed better than non-Newtonian single phase model. The mixture-theory model is then applied to simulate pulsatile blood flow through four idealized coronary artery models having different degrees of stenosis (DOS) severities viz., 30, 50, 70 and 85% diameter reduction stenosis. The maximum WSS is seen at the stenosis throat in all the cases and maximum oscillatory shear index (OSI) is seen in downstream region of the stenosis. Our findings suggest that for degree of coronary stenosis more than 50%, a more disturbed fluid dynamics is observed downstream of stenosis. This could lead to further progression of stenosis and may promote a higher risk of atherogenesis and plaque buildup in the flow-disturbed area. The potential atherosclerotic lesion sites were identified based on clinically relevant values of WSS, timeaveraged WSS gradient (TAWSSG), time-averaged WSS (TAWSS), and OSI. Finally, the change in potential atherosclerotic lesion sites with respect to DOS has been quantified.

A unique approach of analyzing jet exhaust nozzle integrated to aircraft and propulsion system is presented in this paper. Engine exhaust nozzle is usually omitted in Wind Tunnel Testing and numerical analysis of aircraft due to complexities involved in integration of nozzle and presence of high pressure / temperature inside exhaust nozzle. Also, the flow properties are non-uniform and highly turbulent in the vicinity of nozzle. Therefore, exhaust nozzle is usually analyzed in isolation and these results often lead to inaccuracies from actual scenario where nozzle is integrated with aircraft and its propulsion system. This research aims to integrate engine exhaust nozzle on a supersonic fighter aircraft and analyze its flow characteristics and variation in performance parameters due to its integration. Engine propulsion characteristics and parameters such as nozzle inlet temperature and total pressure have been analyzed through an in-house validated engine analytical model developed by some of the authors of this study. In the first part of paper, exhaust plume structure has been analyzed to study the flow behaviour (flow turbulence and flow distortion etc) at nozzle exit. Later, nozzle performance parameters such as Exit Velocity, Nozzle Pressure Ratio (NPR), Engine Pressure Ratio (EPR), and Engine Temperature Ratio (ETR) have been calculated when exhaust nozzle is integrated with the aircraft. Finally, the results are compared and validated with analytical calculations to compare the performance of nozzle when it is in isolation and when it is integrated on aircraft. It is observed that nozzle flow has no significant effect on aircraft major surfaces such as fuselage, wing upper and lower surfaces, and nose section. However, there is a prominent effect of exhaust nozzle flow on horizontal stabilizers, vertical tail and rear fuselage area of the aircraft. An average difference of 18% in NPR, 12% in EPR, and 9% in ETR is observed between integrated nozzle and isolated nozzle which further signifies the importance of integrating exhaust nozzle in aircraft analysis. This proposed methodology will allow more accurate analysis of the effects of exhaust nozzle on the overall performance of aircraft. The methodology can further be used for proposing design changes in existing nozzle configurations.

In order to investigate the effect of air flow rate distribution on plate flow field characteristics, an experiment of plate with air injection was conducted in a high speed towing tank. The influence of air flow rate distribution at longitudinal and transverse on drag reduction and the morphology of air layer were investigated. The result show that the air-water mixed flow under the plate surface is mainly affected by the velocity of flow and air flow rate. When the non-dimensionalzed air flow rate coefficient is less than 1.554 (Cq≤1.554), the mixed flow mainly has a bubbly flow; when the non-dimensionalized air flow rate coefficient is greater than 2.331 (Cq≥2.331), the mixed flow has an air-water stratified flow; Otherwise, there is a transitional flow that is both bubbly and stratified. The local friction drag reduction at the lower surface of the plate near the injection is 100%. The drag reduction rate of total resistance for the lower surface of flat plate will reach 60.65% when improves the strategies of air injection and the air ratio is 1:4:1 in the header air injection device. The joint air injection of header and central device has no contribution to the drag reduction rate of total resistance.

This paper reports enhancement of mixing process via electroosmotic phenomenon using a microelectrode system, which is structured by aligning a number of electrodes placed on the walls of a mixing chamber integrated within a T-Shape micromixer. A number of electrodes are dispositioned on the inner and outer loops of the annular mixing chamber, and different design patterns based on a variety of arrangements for these electrodes are investigated using numerical methods. The electric potentials on the microelectrodes are time-dependent, and this is found to be a key element for chaotic mixing. Also, it is deduced that due to the impact of the applied AC electric field and the induced surface charge on the fluid particles, a number of vortices are generated in the aqueous solution. These vortices significantly enhance the mixing of the species in the mixing chamber. In order to find an optimum pattern based on electrode dispositioning and the number of electrodes, effects of the geometric configuration of the microelectrodes are analyzed and the mixing effects for different design patterns are investigated via comparing the associated flow structure, concentration transport mechanism, and the mixing performance. Analyzing different designs, an optimum pattern based on the electrode arrangement and the number of electrodes is found to be the case for which the electrodes are placed on the inner and outer loops of the mixing chamber in a cross-like pattern.

In this paper, a numerical solver is developed for the computation of one and two dimensional dam break problems. The considered equations are the 2D shallow water equations written in conservative form. The algorithm uses a finite volume method which is based on Roe’s approximate Riemann solver. It is of second order in space and time, and can be used on complicated geometries with unstructured meshes. The stiffness coming from discontinuity propagation due to the dam is taken into account by the introduction of a dynamical mesh refinement-unrefinement procedure. The results presented on some benchmark dam break situations including wet/dry beds, and comparisons with analytical solutions, show the accuracy of the used methods and the efficiency of the adaptation technique in the simulation of such phenomena.

In this paper, the hydrodynamic lubrication of finite porous self-lubricating journal bearings is investigated taking into account the rheological lubricant behavior effect. The modified Reynolds equation is derived by considering both the fluid flow in the porous matrix and the lubricant rheological behavior where Darcy’s law and power- law model were used. Governing differential equations were solved numerically using the finite difference method. Static characteristics are obtained by considering three types of lubricants: pseudo-plastic, dilatant and Newtonian fluids. Obtained results showed that the power law index, n, has important effects on the performance of porous and non-porous bearings. An improvement in the fluid bearing characteristics (load capacity, pressure) is observed for dilatant fluids (n>1) while these characteristics decreased for pseudoplastic fluids (n<1). The permeability of the porous structure has significant effects on the performance of porous journal bearings of finite length, particularly at higher eccentricity ratios. Good agreement is observed between the results obtained in this study and those of literature revue.

In this paper, the effect of mesh topology on the numerical predictions of the immediate near wake region of a horizontal axis wind turbine is investigated. The present work focuses on the nacelle anemometry measurements. Steady Reynolds Averaged Navier-Stokes (RANS) equations are applied to describe the airflow around the wind turbine nacelle. The k-ε turbulence model is used. To model the turbine rotor, the approach based on the actuator disc concept is considered. The computational domain has been meshed with five different configurations of grid; namely, quasi-structured, unstructured and three different hybrid grids constituted of blending of quasi-structured and unstructured grids. The obtained results are compared to the available experimental data. The hybrid mesh with quasi-structured grid in the boundary layer region and unstructured grid in the vicinity of the nacelle is found to be more promising to simulate the near wake generated downstream of the wind turbine nacelle and to predict accurately the nacelle anemometry measurements.

Evaluation of store separation experimentally is expensive; time consuming and dangerous as human risks are involved. This results in development of computational methods to simulate the store separation. Store separation studies include store separation simulation and determination of linear and angular displacements of store under the influence of complex and non-uniform flow field of parent aircraft. In order to validate the methodology, the unsteady CFD results, obtained by coupling six degrees of freedom (6-DOF) with flow solver, are compared with experimental results. Major trends are captured which are consistent with experimental results. Variation in store trajectory has been evaluated with different combinations of forward and rearward ejection forces. By increasing the magnitude of forward ejection force vertical displacement increases and store separates more safely from the wing. Moreover, effects of varying parent wing configuration on store trajectory has also been analyzed by incorporation of leading-edge flaps (LEFs). Store always separates in nose down condition due to LEFs which increases vertical displacement of store and thus safety related to store separation is enhanced.

It is known that rotating cavitation (RC) characteristic of an inducer can greatly influence the safe and stable operation of a liquid rocket. In this paper, the possibility of geometrically optimizing an inducer with respect to RC generated radial forces was discussed. The characteristics of the inducer was firstly evaluated through computational fluid dynamics (CFD), which was validated against experimental results. Then by employing an orthogonal experiment combined with CFD, influences of geometric parametric combinations on RC were investigated. Primary influencing factors and the best parametric combination have been obtained through a variance analysis. Comparing with the original inducer, a significant improvement in the cavitation performance, as well as the radial force characteristic of the optimized inducer has been achieved. Pressure distribution on the blades have been analyzed to reveal the related flow mechanism. This work provides a feasible and effective route in engineering practice to optimize the characteristic of RC generated radial forces for an inducer.

To date, the Smoothed Particle Hydrodynamics (SPH) method has been successfully applied to reproduce the hydrodynamics behind three-dimensional flow-structure interactions. However, as soon as the effect of flow resistance becomes significant, the results obtained are not consistent with observations. This is the case for open channel flows (OCF), in which the water surface is largely influenced by the boundary friction. The roughness generated by the current boundary condition methodologies is solely numerical and cannot be associated to physical values of friction. In light of this challenge, the authors present a novel formulation for the friction boundary condition. The new implementation includes an additional shear stress at the boundaries to reproduce roughness effects, allowing for the adequate three-dimensional simulation of open channel flows using the SPH method. Finally, in order to reduce the high computational cost, typical of the Lagrangian models, without interfering in the representativeness of the SPH simulations, a criterion to define the adequate fluid particle size is proposed.

In this paper, 2-D numerical solution scheme is used to study the performance of semi-passive flapping foil flow energy harvester at Reynolds numbers ranging from 5000 to 50,000. The energy harvester comprises of NACA0015 airfoil which is supported on a translational spring and damper. An external sinosoidal pitch excitation is provided to the airfoil. Energy is extracted from the flow induced vibration of airfoil in translational mode. Movement of airfoil is accommodated in fluid domain by using a hybrid meshfreeCartesian fluid grid. A body conformal meshfree nodal cloud forms the near field domain, encompassing the airfoil. During the simulation, the solid boundary causes the motion of the meshfree nodal cloud, without necessitating re-meshing. In the far field, the static Cartesian grid encloses and partly overlaps the meshfree nodal cloud. A coupled mesh based and meshfree solution scheme is utilized to solve laminar flow, viscous, incompressible equations, in Arbitrary-Lagrangian-Eulerian (ALE) formulation, over a hybrid grid. Spatial discretization of flow equations is carried out using radial basis function in finite difference mode (RBF-FD) over meshfree nodes and conventional finite differencing over Cartesian grid. Stabilized flow momentum equations are used to avoid spurious fluctuations at high Reynolds numbers. A closely coupled, partitioned, sub iteration method is used for fluid structure interaction. The study is focused to analyse the behaviour of flow energy harvesters at various Reynolds numbers. Effects of changing the translational spring stiffness and pitch activation frequency are also investigated. Instantaneous flow structures around the airfoil have been compared at different Reynolds numbers and pitch amplitudes. It is found that net power extracted by the system increases at high Reynolds numbers. Moreover, re-attachment of leading edge separation vortex plays an important role in ther overall system performance.

In this work, we investigate the the problem of an unsteady tank drainage while considering an isothermal and incompressible Ellis fluid. Exact solution is gotten for a resulting non-linear PDE (partial differential equation)subject to proper boundary conditions-. The special cases such as Newtonian, Power law, and as well as Bingham solution are retrieved from this suggested model of Ellis fluid. Expressions for velocity profile, shear stress on the pipe, volume flux, average velocity, and the relationship between the time vary with the depth of a tank and the time required for complete drainage are obtained. Impacts of different developing parameters on velocity profile vz and depth H(t) are illustrated graphically. The analogy of the Ellis, power law, Newtonian, and Bingham Plastic fluids for the relation of depth with respect to time, unfold that the tank can be empty faster for Ellis fluid as compared to its special cases.

In order to accurately and reliably analyze in details the cavitation mechanism and their impact on flow structures, a three-dimensional unsteady .cavitating .turbulent .flow .around .the .three-dimension .Clark-y .hydrofoil .is .investigated .be .using .a Partially-Average Navier Stokes (PANS) model based on Shear Stress Transport (SST). To track the interface of the liquid and the vapor, a Volume of Fluid (VOF) model is employed based on homogeneous mixture approach. To capture the interaction between the cavitation and the flow structure, a bridging method (PANS) between RANS and DNS have been chosen. This technique is able to resolve the unsteady turbulent structures by employing a more consistent methodology. The present numerical .results .are .validated .with .experimental .data. .The .interaction .between .the .cavitation .and .the .fluid .vortex .is .analyzed .and discussed. The numerical results show the capability of the presented model to predict the re-entrant jet and cavitation cloud shedding accurately.

In this study, numerical investigations on the energy extraction performance of a flapping foil device are carried out by using a modified foil shape. The new foil shape is designed by combining the thick leading edge of NACA0012 foil and the thin trailing edge of NACA0006 foil. The numerical simulations are based on the solution of the unsteady and incompressible Navier-Stokes equations that govern the fluid flow around the flapping foil. These equations are resolved in a two-dimensional domain with a dynamic mesh technique using the CFD software ANSYS Fluent 16. A User Define Function (UDF) controls the imposed sinusoidal heaving and pitching motions. First, for a validation study, numerical simulations are performed for a NACA0012 foil undergoing imposed heaving and pitching motions at a low Reynolds number. The obtained results are in good agreement with numerical and experimental data available in the literature. Thereafter, the computations are applied for the new foil shape. The influences of the connecting area location between the leading and trailing segments, the Strouhal number and the effective angle of attack on the energy extraction performance are investigated at low Reynolds number (Re = 10 000). Then, the new foil shape performance was compared to those of both NACA0006 and NACA0012 baseline foils. The results have shown that the proposed foil shape achieves higher performance compared to the baseline NACA foils. Moreover, the energy extraction efficiency was improved by 30.60% compared to NACA0006 and by 17.32% compared to NACA0012. The analysis of the flow field around the flapping foils indicates a change of the vortex structure and the pressure distribution near the trailing edge of the combined foil compared to the baseline foils.

The coefficient adaptation problem is often encountered in CFD simulations. The accuracy of simulation results depends much on the empirical coefficients of mathematical models. Cavitation simulation is a typical application of CFD. Researchers have proposed methods to optimize the empirical coefficients of the cavitation model. However, these methods can only acquire constant values which aren’t adaptive to all the operating conditions. This paper focused on the condensation and the evaporation coefficients of the Zwart model and considered quasi-steady cavitating flows around a 2-D NACA66(MOD) hydrofoil. For the first time, we gave a formal description of the coefficient adaptation problem, and put forward a method to model the relationship between the best coefficient values and the operating conditions. We designed and implemented the coefficient adaptation platform combining OpenFOAM, and validated the best coefficient values predicted by our method. The overall results show the predicted coefficient values result in an increase of accuracy by 12% in average, compared with the default values and the tuned values by Morgut, thus indicating our method can effectively solve the coefficient adaptation problem for the Zwart model. We believe the proposed method can be extended to other mathematical models in practical uses.

The joint effect of pulsating throughflow and external electric field on the outset of convective instability in a horizontal porous medium layer saturated by a dielectric nanofluid is investigated. Pulsating throughflow alters the basic profiles for temperature and the volumetric fraction of nanoparticle from linear to nonlinear with layer height, which marks the stability expressively. To treat this problem, the Buongiorno’s two-phase mathematical model is used taking the flux of volumetric fraction of nanoparticle is vanish on the horizontal boundaries. Using the framework of linear stability theory and frozen profile approach, the stability equations are derived and solved analytically applying the Galerkin weighted residuals method with thermal RayleighDarcy number D R as the eigenvalue. The effect of increasing the external AC electric Rayleigh-Darcy numberRe, the modified diffusivity ratio A N and the nanoparticle Rayleigh number N R is to favorable for the convective motion, while the Lewis number e L and porosity parameter  have dual influence on the stability scheme in the existence of pulsating throughflow. The frozen profile method shows that the result of pulsating throughflow in both directions is stabilizing. An enlarged amplitude of throughflow fluctuations offers to increased stability by an amount that vary on frequency. It is also found that the oscillatory mode of convection is not favorable for nanofluids if the vertical nanoparticle flux is vanish on the boundaries.

When a vertical liquid jet impinges on a horizontal flat plate, at a certain distance from the location of impingement, the depth and velocity of the liquid change and a circular hydraulic jump is formed. The importance of this phenomenon in certain industries has motivated continued quest for more thorough knowledge of the parameters affecting it. Previous research has shown that physical parameters, such as flow rate, jet diameter and geometry of target plate, significantly affect the size and shape of hydraulic jumps. In this study, the effect of target plate roughness on the parameters of circular hydraulic jumps is experimentally investigated. The results show that adding roughness to the target plate leads to an increase in hydraulic jump radius. Furthermore, utilizing the results obtained from the experiments, an empirical law is proposed which determines the hydraulic jump radius and fluid height downstream of the jump position for a given surface roughness of target plate. One of the best-known models for the characterization of the behavior of circular hydraulic jumps is the Bush and Aristoff’s model, which is presented as a curve for smooth surfaces. Since the effect of roughness of target plate surface is ignored in the Bush and Arisstof’s model, the results obtained in this investigation are further used, for the first time, to improve this model for different degrees of surface roughness.

In order to improve the performance of a transonic centrifugal compressor stage, non-axisymmetric endwall profiling optimization was conducted for the diffuser under design condition, Artificial Neural Network (ANN) and Genetic Algorithm (GA) were used to execute the optimization with the objective of maximizing the isentropic efficiency of the compressor stage. The influence mechanism of non-axisymmetric endwall profiling on flow field and performance was discussed. Results show non-axisymmetric endwall profiling is an effective way to significantly reduce the flow loss in the diffuser. The total pressure loss of the diffuser decreases by 9.31% and 20.29% for NA0.70 and NA1.40 respectively. The profiled endwall suppresses the flow separation through accelerating the low-energy flow and reducing lateral pressure gradient. The corresponding high vorticity within the flow separation zone is reduced, which delays the formation and development of the flow separation. The diffuser becomes more fore-loaded, the overall blade loading is not affected, and the pressure ratio of the compressor stage is improved as well. At the outlet of the diffuser, the more uniform flow angle and much lower total pressure loss along spanwise are obtained. However, the backflow with high velocity gathering near the shroud of the diffuser makes the mass flow rate decrease and easily induce the stall, which results in the smaller operating range for both profiled endwall.

A theoretical model for strong converging cylindrical and spherical shock waves in non-ideal gas characterized by the equation of state (EOS) of the Mie-Gruneisen type is investigated. The governing equations of unsteady one dimensional compressible flow including monochromatic radiation in Eulerian hydrodynamics are considered. These equations are reduced to a system of ordinary differential equations (ODEs) using similarity transformations. Shock is assumed to be strong and propagating into a medium according to a power law. In the present work, two different equations of state (EOS) of Mie-Gruneisen type have been considered and the cylindrical and spherical cases are worked out in detail. The complete set of governing equations is formulated as finite difference problem and solved numerically using MATLAB. The numerical technique applied in this paper provides a global solution to the problem for the flow variables, the similarity exponent for different Gruneisen parameters. It is observed that increase in measure of shock strength has effect on the shock front. The velocity and pressure behind the shock front increases quickly in the presence of the monochromatic radiation and decreases gradually. A comparison between the results obtained for non-ideal and perfect gas in the presence of monochromatic radiation has been illustrated graphically.

In the last two decades much research works have been performed in order to model the dynamics of highspeed supercavitating projectiles. In the present study, the high speed supercavitating projectiles have been investigated analytically. In this context, the equations of motion were developed for the projectile inside the supercavity. To achieve this purpose, the projectile is described by its mass, geometry and moment of inertia relative to a body-fixed coordinates system. Two experimental based models were used for simulation of supercavity dynamics and the planing force. Furthermore, a detailed parametric study was performed to investigate effect of three main parameters including the mass, cavitator diameter and length of projectile, on the flight performance of a high speed supercavitating projectile. Results obtained in this parametric study can provide some physical insights into high-speed supercavitating projectile design.

Three dimensional flows of complex non-Newtonian fluids in sudden expending pipes are numerically investigated in this paper. The distribution channels have one or multiple inlet pipes and one outlet pipe. The working fluids have a shear thinning behavior modeled by the Ostwald De Waele law. The effects of different parameters on the flow fields and pressure drop are explored. It concerns the effect of Reynolds number Re (from 0.1 to 600), power law index n (from 0.4 to 1), number of branching channels (nb = 1, 2, 3 and 4), spacing between the branching channels (l/D = 0.1, 0.2, 0.3 and 0.4) and the expansion ratio (d/D = 0.2, 0.35, 0.5, 0.6 and 0.8). Three-dimensional complex flows were observed in the downstream expansion for such multiple branching systems, especially when the spacing l/D is small, where an asymmetry of flows is observed and a third recirculation loop is formed. A considerable increase in pressure drop is found with the rise of Reynolds number, with increased power law index and decreased expansion ratio. However, only a slight increase is observed with decreased spacing ratio and it remained almost the same with increased number of branching channels.

Magnetorheological (MR) fluid finishing process is an application of MR technology in which controllability of the MR fluid is used advantageously to finish the workpiece surface. MR finishing fluid changes its stiffness in accordance with the applied magnetic field and hence it behaves like a flexible finishing tool. A relative motion between this tool and workpiece removes the material from the machining surface. The quality of the final finished surface depends on the constituents of the finishing fluid and the applied magnetic field strength as these parameters affect the rheological properties of the fluid. A study on the rheological properties of the fluid at high shear rates is carried out through Taguchi Design of Experiments to characterize its flow behaviour to be used in continuous flow finishing process. Constitutive modeling of the fluid sample is done using Bingham Plastic, Casson Fluid and Herschel Bulkley fluid models to characterize their rheological behavior. The Hershel–Bulkley model is found to be the best suited model for the finishing fluid. Analysis of Variance has revealed that volume percentage of iron particles is the most significant parameter with a contribution of 91.68% on the yield stress and viscosity on the finishing fluid. The highest yield stress of the fluid is observed between magnetic flux density ranges from 0.3 to 0.5 Tesla. An optimised combination is then synthesized to confirm the theoretical results. The effect of temperature is also studied on the optimised fluid which has shown that temperature shares an inverse relation with the yield stress of the finishing fluid.