Flow In Converging Channel Research Articles

Hyper-elastic behavior of soft-tissue like microgels in two-phase converging microchannel flow

Deformation of biological cells, tissues, and similar soft materials is often considered linearly elastic; however, the assumption is only valid in a very limited stress range and often leads to significant errors in mechanical evaluation. We demonstrated the hyper-elastic behavior of ultra-soft poly(N-isopropyl acrylamide) (PNIPAm) microgels (USPNMs) in a converging channel flow, as a representation for biological tissues. The hyper-elasticity of USPNMs in response to a broad range of deformation was characterized at the centerline of the converging flow. We introduced a carrier fluid consisting of baby hydrogels (avg. diameter, 10 μm) and oil that carried the hydrophilic USPNM sample (avg. diameter, 100 μm) on the centerline of oil background fluid. By “baby hydrogel,” we mean small PNIPAm particles obtained during USPNM synthesis, using which, enabled settling-free flow, prevented wall contact, and enhanced carrier fluid viscosity for increased stresses at lower flowrates. Furthermore, drastic reduction of interfacial tension was observed in the converging area due to contact of baby gels with USPNM particles in the carrier fluid. The shear and elongational stresses were balanced with the elastic stress and interfacial Laplace pressure. As a result, we obtained a stress–strain curve from the microscopic images during flow. The non-linear stress–strain curve was characterized by conventional hyper-elastic models. The elastic modulus of the synthesized USPNM was 24 Pa, which is as low as animal brain tissue. This method holds great potential for implementing in similar hyper-elastic systems, enabling accurate mechanical evaluations in the field of soft materials, biology, and medicine.

Investigation of Entropy Production with Thermal Analysis under Soret and Dufour Effects in MHD Flow between Convergent and Divergent Channels.

Hydromagnetic flow and heat transport have sustainable importance in conventional system design along with high-performance thermal equipment and geothermal energy structures. The current computational study investigates the energy transport and entropy production due to the pressure-driven flow of non-Newtonian fluid filled inside the wedge-shaped channel. The nonlinear radiation flux and uniform magnetic field are incorporated into the flow analysis. To be more precise, non-Newtonian fluid initiates from an inlet with the bound of the parabolic profile and leaves at outlet of a convergent/divergent channel. We assume that the channel flow is adiabatic and influenced by the wall friction. The leading flow equations are modeled via the Carreau fluid model using fundamental conservation laws. The thermodynamical aspect of the system is visualized using a two-phase model and analyses of the entropy equation due to fluid friction, ohmic heating, and diffusion of heat and mass fluxes. The modeled system of equations is normalized using a dimensionless variable mechanism. The system was elevated for the significant variation of controlling parameters. The outcomes obtained from the computational investigation are validated with the theoretical results that are available in the literature. An increasing semivertex angle and Reynolds number increase the converging channel flow. In the core flow zone, an increase in the divergent semiangle causes the flow to decelerate, while near and at the channel wall it causes a slight acceleration. Outcomes designate that the main contribution to the irreversibility is due to ohmic loss, frictional loss, and heat loss. The thermal performance and entropy production is dominant for a diverging flow. The outcomes of this research will assist in comprehending the process of entropy minimization in conjunction with the flow of nanomaterials in a nonuniform channel, which is essential in engineering processes such as the creation of micro machines, supersonic Jets, nozzles, and clean energy.

Flow Features of Thermophoretic MHD Viscous Fluid Flow Past a Converging Channel with Heat Source and Chemical Reaction

A boundary layer flow of an electrically conducting viscous fluid past a converging channel in the presence of thermophoresis, heat source, chemical reaction, viscous dissipation and simultaneous heat and mass transfer characteristics is studied in the paper. An external magnetic field of uniform strength is applied transversely to the channel. The similarity solution has been used to transform the partial differential equations that represent the problem into a boundary value problem of coupled ordinary differential equations, which in turn are solved numerically using MATLAB’s built in solver bvp4c. Numerical computations are carried out to solve the problem and graphical illustrations are made to get the physical insight of the same. The convergent channel flow problem of an incompressible electrically conducting viscous fluid in the presence of a magnetic field has a wide range of applicability in different areas of engineering, specially in industrial metal casting and control of molten metal flow.

Experimental investigations on co-rotating vortex pair merger in convergent/divergent channel flow with single-side-wall deflection

The co-rotating vortex pair merger in the convergent and divergent channel flow was investigated in both equal and unequal cases. The crossflow flow phenomenon of vortex pair merger was acquired by applying particle image velocimetry in a series of streamwise locations. The main finding is that the resultant single-side-wall deflection convergent and divergent channel flow can vary the merging rate and merging trajectories of the equal vortex pair. In the unequal vortex merger, distortion and absorption of the weaker vortex by the stronger vortex were observed, which is different from the mutual induction phenomenon in the equal strength vortex pair case. Furthermore, it was found that the flow converging and diverging have common effects on the merging process in both equal and unequal vortex merger. In the convergent channel flow, vortex pair separation experienced early reduction at upper stream locations, and the merger was accelerated. As the vortex pair developed further downstream, the difference in the merger progress among different channel flow environments becomes less significant, which is believed to be due to the combined effect of pressure gradient and developing time variations.

Homotopy analysis method for predicting multiple solutions in the channel flow with stability analysis

The present theoretical investigation covers a study of finding the multiple solutions of a Jeffery–Hamel flow and heat transfer under the influence of magnetic field. An analytical technique (Homotopy Analysis Method) is applied to solve the cylindrical form of governing equations after getting non-dimensional system using suitable transformation. It is noticed that dual solutions exist only for convergent channel case. Critical values of channel angle (αc) are obtained which reveals the existence domain (αc < α < 0) for multiple solutions in convergent channel flow. Stability analysis is also performed by constructing eigenvalue problem to predict the physically stable solution. The minimum positive eigenvalue justifies the fact that the growth of disturbances given to the solution decays with time. The effect of various pertinent physical parameters is shown graphically on velocity, temperature, skin friction coefficient and Nusselt number.

Inhomogeneous vortex tangles in counterflow superfluid turbulence: flow in convergent channels

Abstract We investigate the evolution equation for the average vortex length per unit volume L of superfluid turbulence in inhomogeneous flows. Inhomogeneities in line density L andincounterflowvelocity V may contribute to vortex diffusion, vortex formation and vortex destruction. We explore two different families of contributions: those arising from asecondorder expansionofthe Vinenequationitself, andthose whichare notrelated to the original Vinen equation but must be stated by adding to it second-order terms obtained from dimensional analysis or other physical arguments.

Experimental investigation for optimization of design parameters in a rectangular duct with plate-fins heat exchanger by Taguchi method

This study presents the determination of optimum values of the design parameters in a heat exchanger with a rectangular duct by using Taguchi method. The heat exchanger has plate-fins containing periodically interrupted diverging and converging channel flow domains. The experimental investigation for the established heat exchanger involves short rectangular fins attached in 8 × 8 arrays to a surface having various inclination angles. The effects of the six design parameters such as the ratio of the duct channel width to height, the ratio of the winglets length to the duct channel length, inclination angles of winglets, Reynolds number, flow velocity and pressure drop are investigated. In the Taguchi experimental design method, Nusselt number and friction factor are considered as performance parameters. An L25 (56) orthogonal array is chosen as an experimental plan for the design parameters. The analysis of Taguchi method conducted with an optimization process to reach minimum pressure drop (friction factor) and maximum heat transfer (Nusselt number) for the designed heat exchanger. Experimental results validated the suitability of the proposed approach.

Simulation of geomaterial flow in convergent channels with consideration for internal friction and dilatancy

The closed mathematical model of geomaterial with account for internal friction, dilatancy and anisotropy of the material properties is formulated to solve the problem of geomaterial flow in a convergent radial channel in terms of the general conception of rocks as a medium with internal sources and outflows of energy. The developed finite-element algorithm and software enable solution of deformation boundary-value problems in quasistatic formulation. Numerical solutions to the problem of geomaterial flow in a convergent radial channel are obtained. The stress-strain state patterns of the geomaterial medium under different parameters of the problem are presented.

Tectonic pressure: Theoretical concepts and modelled examples

Pressure variation due to deformation is an intrinsic property of fracture and flow in all materials, including rocks under geological conditions. Strong gradients occur at rheological boundaries (due to inclusions, layers, channels, shear zones, boudin necks, etc) and these gradients are instrumental in driving local pore fluid and/or melt flow during deformation. The pressure distribution in deforming rocks is not static, but changes in space and time. A clear and relevant natural example is the variation during buckle folding of strong layers embedded in a weak matrix. Local pressure gradients and magnitudes can therefore change without any associated change in depth. The magnitude of tectonic pressure is determined by a non-dimensional pressure parameter, reflecting geometry and position, and a scaling factor, with units of stress (Pa), given by the strength of the rock. Brittle fracture places an upper limit on rock strength. For Mohr–Coulomb yield, the tectonic overpressure is equal to the effective vertical load (or “lithostatic pressure”− pore fluid pressure) in the case of plane strain crustal shortening. Deep seismic failure in relatively dry rocks, as recorded by pseudotachylytes developed under lower crustal or even eclogitic conditions, is therefore direct evidence for significant tectonic pressure. For viscous materials, tectonic pressure scales linearly with flow stress, or alternatively with the effective viscosity and strain rate. Typical tectonic pressures related to folds, boudins, or strong inclusions are of order 1–2 times the maximum shear stress that the strong material can support. However, even geologically weak materials (e.g. effective viscosity 10 19–10 20 Pa s) can develop very significant tectonic pressures (on the order of many 100's of MPa to several GPa) when the flow is confined, such as during extrusion or convergent channel flow between strong walls, as has been proposed for active subduction zones. The maximum overpressure in this case is limited by the strength of the confining walls, which do not have to be unrealistically strong (or rigid) for the development of significant tectonic pressures.

Fluid–structure interaction of a splitter plate in a convergent channel

The fluid–structure interaction (FSI) of a splitter plate in a convergent channel flow is studied by measuring both the flow field and the plate vibration. Particle Image Velocimetry (PIV) measurements show that the wake generated by the plate is characterized by cellular vortex shedding. Mean and RMS velocities presented in the plane normal to the main flow direction visualize clearly the cellular structure and related secondary flows. To evaluate the energy and spatial organization of the vortex shedding, spectral and correlation estimation methods are adapted to the PIV data. By presenting the spanwise variation of the streamwise spectra along the trailing edge, the nature of the cellular vortex shedding becomes evident. 2D space-correlation function reveals that the shedding in two neighboring cells occurs in a 180-degree phase shift. The vibration of the plate is studied with Digital Imaging (DI) and Laser Vibrometer (LV). The DI is based on images measured by the PIV system. An image-processing algorithm is used to detect the plate tip location and velocity simultaneously with the estimation of the fluid velocity field. The LV is used for the time-resolved measurement of the plate vibration. The results show that the plate vibrates in a very distinct mode characterized by a spanwise standing wave along the plate-trailing edge. This mode, in turn, causes the cellular vortex shedding.

Numerical simulation in converging channel flow of the fluid M1 using an integral constitutive equation

Numerical simulations have been undertaken for the flow of test fluid M1 passing through the converging channel system designed to measure the extensional viscosity of polymeric liquids. The constitutive equation is an integral-type K-BKZ model with three relaxation times. The simulations have been performed for the full range of experimental measurements in this system, where the extensional deformation is dominant and the deformation rates are very high. Stable solutions have been obtained for the whole range even though the apparent shear rates reach 1300s −1. Results concerning wall pressure difference between two pressure taps are compared with the experimental data measured from the pressure signals. The simulations are in good agreement with the experiments for the low range of flow rates at 21°C and for all flow rates at 30 and 40°C. The discrepancies at high flow rates for the lower temperature are apparently due to the appearance of a stationary bubble in the experiments that may have altered the pressure measurements. The pressure and stress distributions from the simulations show the flow characteristics of the converging channel system, which are difficult to verify by using experimental methods. The specially designed converging channel geometry makes the fluid M1 deform at a constant rate of extensional deformation near the centreline within the constant strainrate section but only at low flow rates, and its normal stresses increase exponentially and then slowly relax in the subsequent cylindrical section. The extensional viscosity of fluid M1 obtained by simulations has been compared with the value from the experimental results. A more appropriate method of measuring extensional viscosity is recommended from the stress analysis in the converging channel flow field.

A computational scheme in generalized coordinates for viscous incompressible flows

This paper presents a computational scheme suitable for analyzing viscous incompressible flows in generalized curvilinear coordinate system. The scheme is based on finite volume algorithm with an overlapping staggered grid. The pseudo-diffusive terms arising from the coordinate transformation are treated as source terms. The system of nonlinear algebraic equations is solved by a semi-implicit procedure based upon line-relaxation and a generalization of Patankar's pressure correction algorithm. Examples of the application of the algorithm to flow in convergent channels, developing flow in a U-bend, and flow past backward facing step, are given. In addition, the case of flow past backward facing step is analyzed in detail, and the computed flowfields are found to be in close agreement with previous experimental and numerical results for expansion ratio (defined as the ratio of step height to channel height) of 0.5. The results are summarized in the form of a correlation relating the primary separation length, Reynolds number and expansion ratio.

A note on the hamel flow of Cosserat fluids

The existence of a radial flow in convergent channels, as is observed in viscous fluids, is studied in the theory of Cosserat fluids. In general, it is observed that such a flow is not possible in a Cosserat fluid.

On Heat Transfer in Laminar Boundary Layers at High Prandtl Number

A study of the asymptotic behavior of the heat transfer in laminary boundary layers for large Prandtl Number is presented. The analysis is based on the observation that, for large Prandtl Number, the conduction term in the energy equation must be important only in a region that is very narrow compared with the velocity boundary layer, but that, in that region, both convection and conduction are essential. A transformation (based on the Prandtl Number) of the coordinate normal to the body surface leads to a form of the energy equation in which the appropriate convection and conduction terms can be balanced with respect to their asymptotic dependence on the Prandtl Number, and the behavior of the local heat-transfer coefficient can be deduced immediately. The general method is applied to the well-known problems of forced convection over a body and of the plate thermometer, where it confirms results previously obtained by other methods. The problems of natural convection over a vertical body, of the flow above a rotating disc, and of the Hamel converging channel flow are then treated; new theoretical results are obtained for these cases.