Streamline Patterns Research Articles

Numerical simulation of electroosmotic force on micropolar pulsatile bloodstream through aneurysm and stenosis of carotid

Smoking and hypertension are significant risk factors for atherosclerotic carotid artery disease, but also for intracranial aneurysms. The medical results suggest incidental intracranial aneurysms in patients with internal carotid artery (ICA) stenosis arteries. Which led to a study of the comparison between stenosis and aneurysm segments through the artery. A mathematical and numerical model for blood solidification and its rupture in a diseased artery is described in this paper. The interaction between the blood flow and a diseased arterial wall was formulated. The blood flow is formulated as a micropolar incompressible fluid with heat and mass transfer under the control of electro-osmotic and electromagnetic forces through an artery that contains stenosis and aneurysms. The approximation of mild stenosis is used to derive the governing flow equation, which is then solved using a method of finite difference. Particular attention is paid to the impact on axial velocity, flow rate, resistance impedance, and wall shear stress of geometrical parameters of the arterial wall and rheological blood parameters. In the instantaneous pattern of streamlines, the global behavior of blood is also investigated. Finally, the effect of all parameters on the blood flow through artery whose stenosis and aneurysm are investigated as a comparison of both segments.

Wake Flow Measurements Behind Rotating Smooth Spheres and Baseballs Near Critical Reynolds Numbers

Abstract The flow field behind spinning baseballs at two different seam orientations was investigated, and compared with a smooth sphere, to isolate effects of seams on the Magnus effect at Reynolds numbers of 5×104 and 1×105. The rotational speed of the three spheres varied from 0 to 2400 rpm, which are typical of spin rates imparted to a thrown baseball. These spin rates are represented nondimensionally as a relative spin rate relating the surface tangential velocity to the freestream velocity, and varied between 0 and 0.94. Mean velocity profiles, streamline patterns, and power spectral density of the velocity signals were taken using hot-wire anemometry and/or stereoscopic particle image velocimetry in the wake region. The sphere wake orientation changed over a range of relative spin rates, indicating an inverse Magnus effect. Vortex shedding at a Strouhal number of 0.25 was present on the sphere at low relative spin rates. However, the seams on the baseball prevented any consequential change in wake orientation and, at most spin rates, suppressed the shedding frequency exhibited by the sphere. Instead, frequencies corresponding to the seam rotation rates were observed in the wake flow. It was concluded that the so-called inverse Magnus effect recorded by previous investigators at specific combinations of Reynolds number and relative spin rate on a sphere exists for a smooth sphere or an axisymmetrically dimpled sphere but not for a baseball near critical Reynolds numbers, where the wake flow pattern is strongly influenced by the raised seams.

On the existence and determination of the incompressible laminar flow located in the polar plane of a porous annular pipe

Despite the extensive research already done on laminar flows with porous boundaries, polar flows bounded by cylinders have not yet been studied. This paper investigates the polar laminar flow for an incompressible fluid located in a porous annular pipe and driven by suction-injection at the walls. The fluid being confined between the cylinders with zero axial velocity, it is proven that the flow takes place in the polar plane with conservation of mass if an incoming flow exists in the same plane to compensate the mass of fluid extorted by suction. So, one of the cylinders undergoes the suction, and the other the injection. Suitable boundary conditions for both cylinders are then found. The problem depends on the Reynolds number, the pipe gap ratio, and the pore density and surface ratios. The method of solution utilizes the shooting technique including the Runge-Kutta and Newton-Raphson algorithms. Radial flows are found as a possible solution. When the flow is not radial, the patterns of the acceptable streamlines highlight a particular zone in which the fluid is at rest, bounded by two singular streamlines and the downstream cylinder. The flow velocity is determined. Physical understandings of the flow are derived.

Investigation and optimization of heat transfer performance of a spirally corrugated tube using the Taguchi method

A three-dimensional numerical model of a spirally corrugated tube is built in this study using ANSYS FLUENT software. The effects of three geometric parameters (i.e., starts number, corrugation depth, and corrugation spacing) on the heat transfer performance are analyzed using the Taguchi method. Based on the influence of the Reynolds number, the optimal structure yielding the best heat transfer performance is obtained. The streamline patterns show that heat transfer is enhanced by the generation of the secondary flow near the spirally corrugated tube wall. Main-effect analysis and analysis of variance both indicate that the contributions of the corrugation depth and corrugation spacing to heat transfer coefficient account for approximately 90%. The mean Heat transfer coefficient improved by 36.3% when corrugation depth increases from 1 mm to 3 mm. While it decreases by 4.8% when corrugation spacing increases from 9 mm to 13 mm. Results show that a larger corrugation depth and smaller corrugation spacing could generate improved heat transfer performance. In addition, the small difference between predicted signal-noise-ratio and signal-noise-ratio implies that the effects of factor interaction on the results for the optimization process can be ignored. The corresponding optimal parameter combinations for the spirally corrugated tube with four starts, corrugation depth e = 3 mm, corrugation spacing P = 9 mm could enhance the heat transfer by 15.0% and 4.9% for Re = 30,000 and 60,000.

Solving steady-state lid-driven square cavity flows at high Reynolds numbers via a coupled improved element-free Galerkin–reduced integration penalty method

Steady-state two-dimensional lid-driven square cavity flows at high Reynolds numbers are solved in this communication using a velocity-based formulation developed in the context of the improved element-free Galerkin–reduced integration penalty method (IEFG–RIPM). The analyses based on the IEFG–RIPM are performed under a standard Galerkin weak-formulation, i.e. without the need of introducing streamline-upwind or pressure stabilizing terms in order to suppress the appearance of non-physical oscillations. Solutions in a wide range of high Reynolds numbers are successfully achieved, and the results obtained have exhibited an excellent agreement with mesh-based solutions reported in the literature. The numerical performance of the proposed IEFG–RIPM in the solution of such benchmark problem has been analysed in terms of velocity distribution, streamline patterns, vorticity and pressure contours, and also in terms of the properties of primary and secondary vortices. The outcomes of this study demonstrate the potential of the IEFG–RIPM as a feasible and reliable numerical technique for the analysis of lid-driven square cavity flows at high Reynolds numbers, allowing the fulfilment of accuracy and stability numerical requirements demanded in the solution of this benchmark problem in a remarkably simple manner.

Computational analysis of nonhomogeneous fluid flow in a two-cylinder-driven rectangular cavity

This paper involves a two-dimensional computational study of flow evolution patterns and the temperature distribution at evolved states of a fluid under compressible conditions contained within a driven rectangular cavity with two symmetrically placed circular cylinders, where one cylinder is heated and the other cooled. Conditions developed by varying the positions of the cylinders within the cavity, by varying the initial conditions of temperature distributions of the fluid as well as temperatures at which the cylinders are held to heat or cool the flow and by varying the orientation of the direction of rotation of the cylinders with respect to each other – either opposing or identical – are studied. The analyses are conducted by observing the temperature distributions over the streamline patterns, the velocity profiles over a line dividing the cavity length in half and the temperature distribution over a line dividing the cavity height in half. Best mixing conditions have been found to be for cavities with cylinders placed close to each other and rotating in identical directions.

Source-like patterns of flow past a circular cylinder of finite span at low Reynolds numbers

This article is to report results of a joint numerical and experimental investigation of vortex structures of flow past a circular cylinder of diameter D and finite span L in a range of low Reynolds numbers. The aspect ratio (AR) (= L/D) of the cylinder varies from 1.5 to 5, and the Reynolds number Re varies from 10 to 150. Given Re = 80, we study the various cases of AR, and given AR = 5, we study the various cases of Reynolds numbers Re. In a regime of parameters, the flow is found to be steady, separated, and doubly symmetric. Beyond this regime, the present study also covers a range of unsteady flow with vortex shedding in the wake behind the cylinder. This study is focused on the streamline patterns on the two planes of symmetry: the middle cross section plane (MCP) of the circular cylinder as well as on the bisectional cross section plane (BCP) on the circular cylinder. The exclusive phenomenon discovered is the occurrence, in a range of flow conditions, of a point-like or line-like source pattern of streamlines in the wake on the MCP. The center of the singular source is denoted by the center of the source (CS). In the cases of steady flow, there is always a pair of recirculating eddies on the BCP, which forms a saddle point (SP) structure at their far end from the cylinder. At the occurrence of source-like flow patterns, CS coincides with SP, signifying that the source-like points concentrate in a small neighborhood of CS (or SP). The SP is characterized by normalizing the location of the source Ds from the cylinder center. It is given a definition of the strength of the source (SS), determined by normalizing the two-dimensional divergence ∇2·v on the MCP. Moreover, the flow patterns with or without a singular source are classified into four categories on the Re–AR parameter plane. In particular, a criterion on SS is found for the occurrence of a source-like pattern. The formation of the source-like wake flow and variations of the source locations and the source strength with Re and AR are given full physical explanations. The interesting trends of the drag coefficients with AR are explained on the relative importance of the surface friction and the pressure (form) drag.

MHD natural convection of a hybrid nanofluid in an enclosure with multiple heat sources

Natural convective flow and heat transfer of a hybrid nanofluid contained in an enclosure with multiple heat sources at the bottom wall are investigated in the presence of magnetic field applied to an angle with the horizontal axis. The system of equations is formulated systematically using dimensionless variables and parameters as well as defining stream function in terms velocity components. Solutions obtained by the finite difference method are then validated with experimental and numerical results which provides a good agreement. A grid independent test is also performed. Results reveal that flow pattern is substantially changed with the change of the magnetic field parameter, angle of magnetic field, number and breadth of heat sources and Rayleigh number. The intensity of the stream function is stronger for higher Rayleigh number and smaller magnetic field parameter. When the volume fraction of Cu nanoparticles is more than 6% the streamlines and isotherms demonstrate distinct pattern from those for its lower value. Moreover, symmetric pattern of streamlines is observed for angle of magnetic field equal to 0 and π/2. Due to the increase of the number of heat sources, angle of magnetic field and Rayleigh number, average Nusselt number is found to increase.

Analisis karakteristik aerodinamika telescopic wing dengan konfigurasi sayap flying wing dan glider menggunakan metode pendekatan simulasi CFD

A telescopic wing is a shape-changing method of the aircraft wing known as the morphing wing system. Wingspan extends capability on telescopic wing increasing the aspect ratio to get a high lift force. The telescopic wing on a flying wing configuration as an external wing and glider wing as an internal wing can be used to increase the coefficient lift (CL) when carrying out special missions. The aerodynamic characteristics using the Computational Fluid Dynamic (CFD) simulation approach is presented. For the 40% internal wingspan, the highest CL increment was 12.9% at a 10o angle of attack. For the 50% internal wingspan, the highest CL increment was 14.9% at a 10o angle of attack. on the 40% internal wing, the highest coefficient drag (CD) increment was 4.7%, and the largest CD increment on 50% internal was 9.5% at the angle of attack of 20o. The pressure distribution along the internal wingspan was uneven from an angle of attack of 15o due to the wing tip vortices of the external wing. Streamline pattern shown a bubble separation from the leading edge at an internal wing root by external wing tip vortices.Keywords: Morphing wing, telescopic wing, flying wing, glider

Large amplitude capillary-gravity solitary waves in a stratified fluid sandwiched between two deep homogeneous layers

The study addresses the propagation of plane capillary gravity solitary waves of permanent form in a three layer formulation. The intermediate fluid is assumed to be stratified, while the upper and lower ones are homogeneous and infinitely deep. One or both interfaces separating these layers are subject to capillarity. The research can be applied to the case of two deep fluids when one of these fluids is stratified near the interface. The latter formulation is relevant to studies of capillary gravity waves in the transitional area between sea water and liquid carbon dioxide in the deep ocean. This has become an issue of importance for the secure storage of carbon dioxide, which is an environmental/technological problem in modern days. Therefore, we address a capillary-gravity wave motion beyond the well-examined cases of a free surface or two fluid flows. It is shown that in the considered formulation, capillary-gravity solitary waves of finite amplitude obey an integro-differential equation. This equation contains both Korteweg-de Vries (KdV) and Benjamin-Ono (BO) dispersion laws and a specific nonlinearity, which depends on the properties of the stratified layer. Capillary (KdV-type) dispersion dominates if the thickness of the stratified layer is d≪d∗. When d≫d∗, the gravitational (BO-type) dispersion determines the flow. The value d∗ depends on the mode number, gravitational acceleration, and capillarity effects. Analytical solutions for the amplitude function and the streamline patterns are presented.

Spiral streamline pattern around a critical point: Its dual directivity and effective characterization by right eigen representation

In recent years, vortex recognition method based on velocity gradient has rapidly become a research hotspot, accompanied by a wide range of applications. As a linear velocity field with the origin as its critical point uniquely corresponds to the velocity gradient, its streamline pattern (SP), especially the spiral streamline structure when the velocity gradient has a couple of complex eigenvalues, is studied using the right eigen representation based on the real Schur form. Compared with the left eigen representation, the right eigen representation of velocity gradient is seldom concerned. In this paper, the right eigen representation is carried out in terms of the spectral representation, and its relation with the left eigen representation is also derived. For two-dimensional case, the SP classification is listed and the typical streamlines are illustrated. After detailed investigation, it is shown that the parameters extracted from the right eigen representation would be more suitable to describe the geometrical features of the spiral streamline pattern around the critical point, and the dual directivity of spiral streamline structure is clarified. Some discussions and an illustrative example from the direct numerical simulation (DNS) data are presented.

Counterflow slip in a two-fluid whirlpool

This experimental study reveals a counterflow slip at the interface of two immiscible fluids filling a sealed vertical cylindrical container whose bottom disk rotates while other walls are stationary. An advanced particle image velocimetry helps us analyze and quantify streamline patterns and velocity profiles of the steady axisymmetric flows of both fluids. As the angular velocity of a disk increases, starting from zero, three changes occur in topology of the upper-fluid flow while topology of the lower-fluid flow remains invariant. These changes result in the counterflow slip at the entire interface, whose nature is speculatively discussed and requires further research.

A Validated Study of a Modified Shallow Water Model for Strong Cyclonic Motions and Their Structures in a Rotating Tank

A joint theoretical and numerical study was carried out to investigate the fluid dynamical aspect of the motion of a vortex generated in a rotating tank with a sloping bottom. This study aims at understanding the evolution of strong cyclonic motions on a β-plane in the Northern Hemisphere. The strong cyclonic vortices were characterized by four nondimensional parameters which were derived through a scale analysis of the depth variations of fluid. By simplifying the model flow field and the prototype flow field, respectively, through the conservation of potential vorticity, two sets of dynamic similarity conditions are derived. This study proposed a sophisticated modified shallow water model (MSWM) to investigate the flow features of such strong vortices. A detailed numerical calculation adopted by multidimensional positive definite advection transport algorithm (MPDATA) was carried out to validate those effects considered in the MSWM model, including sloping bottom, parabolic free surface deformation, and viscous dissipation. Close agreements were found between the experimental and numerical results, including the streamlines patterns and the vortex trajectory. Comprehensive simulations for strong cyclonic vortices over different sloping bottoms were investigated to understand the impact of planetary β effect on vortex. The results calculated by MSWM demonstrate a variety of flow features of interactions between the primary vortex and induced secondary Rossby wave wakes that were essential and prominent in environmental geophysical flows.

Influence of radially magnetic field properties in a peristaltic flow with internal heat generation: Numerical treatment

This article investigates the impact of radially varying magnetic field during the peristaltically flowing nanofluid in a finite flexible tube. The inner surface of axisymmetric tube is filled with metachronal waves of cilia. Flow is provoked as a result of these metachronal waves, which are formed due to wavy or beating motion cilia. The thermal conduction of water base fluid is enhanced by involvement of carbon nanotubes. Moreover, heat transport analysis is performed with heat generation process. Governing problem is simplified under the long wave length and low Reynolds number approximation. Mathematical formulations have been performed which results into nonlinear partial differential equations. The suitable variables have been employed to obtain coupled ordinary differential system. Numerical solution is obtained by using Adams-Bashforth technique. Error analysis for the obtained results have been presented which show the validity in terms of tolerance level. Graphical results are prepared and analyzed for different sundry parameters showing the real insight of the analysis. The peristaltic pumping region is −1.0 < Q < -0.3 for wave amplitude and −1.0 < Q < −0.4 for magnetic parameter. Magnetic parameter reduces the fluid velocity effectively. Streamline pattern and bar charts have been prepared for both single and multiwall CNTs.

Numerical Investigation of Newtonian Fluid Flow around Sharp &amp; Rounded Corner Rectangular Obstruction

In the present study, very stable and converging Least Square finite element method (LSFEM) is employed to calculate the approximate solution of steady state Navier – Stokes equation, consisting continuity and momentum equations in two dimensions. The 2D rectangular domain is considered to study the behavior of linear fluid passing two parallel rectangular obstructions in an open channel. The current numerical analysis is based on two instances, in the first one two rectangular obstructions possesses sharp corners set to face the entering flow while in the other case, obstructions having round corners are analyzed concerning to examine the enhancement in the size of vortex formed due to the flow blockage, intensity of vortex and the recirculation flow rate in the dead zone for Reynolds number from 250 to 2000. The stream line patterns are also presented to monitor the changes appears in the shape of vortex for different Re. The information gather through the analysis suggests the cutoff corner obstruction is congenial in restricting the vortex length and favorable for slow down the flow circulation rate in the lower stream of the channel. The acquired results are compared with established data in past literature which turn out to be in good agreement.

Finite element simulation for free convective flow in an adiabatic enclosure: Study of Lorentz forces and partially thermal walls

This article contains the free convective flow in a rectangular cavity having partially heated vertical wall. Further it is assumed that flow and thermal profiles are influenced by Lorentz forces applied in the perpendicular direction to the flow distribution. This physical setup is translated in mathematical form, which is expressed as differential equation. Finite element method is adopted to get the solution of these partial differential equations, the results against various flow controlling variables are presented in contour plots and line graphs. Results depict that at various heated length streamlines distribution gets stronger due to stronger buoyancy effects. Higher values of Rayleigh number correspond to maximum Nusselt number and temperature profile. Moreover, the streamlines pattern is reduced by increasing Hartman number and resulting the conduction mode of heat transportation.

Computational Study on the Effect of the Staggered Ribs on Heat Transfer Phenomena Between the Horizontal Plates

In terms of multifarious technical applications, various kinds of passive methods are preferred to the active techniques when it comes to increase the amount of convection heat transfer via less energy consumption. As a vortex generator within the scope of the passive method, rib is usually employed to induce the heat transfer enhancement. In this study, the rectangular cross-sectional ribs have been placed to increase the amount of the heat transfer for the staggered arrangement between the horizontal parallel plates. Numerical simulations have been conducted by using k-ω SST turbulence model at Re = 10000. The rib effect has been comparatively investigated in case of thermal and hydraulic performance presented via the numerical results. Time-averaged results for temperature, pressure, streamwise velocity component and streamline patterns have been presented in terms of contour graphics. Furthermore, heat transfer enhancement by using the ribs has been given depending on the increment ratio of Nusselt numbers. Including friction losses due to the ribs mounted on the plates, the values of thermal performance factor for all ducts have been calculated. According to these results for heat transfer augmentation at Re = 10000, h' = 0.1 with S' = 0.5 having η = 1.049 and h' = 0.1 with S' = 0.75 having η = 1.019 have been recommended rather than the smooth duct.

Numerical Simulation of Magnetohydrodynamic Influences on Casson Model for Blood Flow through an Overlapping Stenosed Artery

Magnetohydrodynamic (MHD) effects of unsteady blood flow on Casson fluid through an artery with overlapping stenosis were investigated. The nonlinear governing equations accompanied by the appropriate boundary conditions were discretized and solved based on a finite difference technique, using the pressure correction method with MAC algorithm. Moreover, blood flow characteristics, such as the velocity profile, pressure drop, wall shear stress, and patterns of streamlines, are presented graphically and inspected thoroughly for understanding the blood flow phenomena in the stenosed artery.

Mathematical study on two-fluid model for flow of K\u2013L fluid in a stenosed artery with porous wall

The present communication presents a theoretical study of blood flow through a stenotic artery with a porous wall comprising Brinkman and Darcy layers. The governing equations describing the flow subjected to the boundary conditions have been solved analytically under the low Reynolds number and mild stenosis assumptions. Some special cases of the problem are also presented mathematically. The significant effects of the rheology of blood and porous wall of the artery on physiological flow quantities have been investigated. The results reveal that the wall shear stress at the stenotic throat increases dramatically for the thinner porous wall (i.e. smaller values of the Brinkman and Darcy regions) and the rate of increase is found to be 18.46% while it decreases for the thicker porous wall (i.e. higher values of the Brinkman and Darcy regions) and the rate of decrease is found to be 10.21%. Further, the streamline pattern in the stenotic region has been plotted and discussed.

Altered hemodynamics by 4D flow cardiovascular magnetic resonance predict exercise intolerance in repaired coarctation of the aorta: an in vitro study

BackgroundCoarctation of the aorta (CoA) is associated with decreased exercise capacity despite successful repair. Altered flow patterns have been identified due to abnormal aortic arch geometry. Our previous work demonstrated aorta size mismatch to be associated with exercise intolerance in this population. In this study, we studied aortic flow patterns during simulations of exercise in repaired CoA using 4D flow cardiovascular magnetic resonance (CMR) using aortic replicas connected to an in vitro flow pump and correlated findings with exercise stress test results to identify biomarkers of exercise intolerance.MethodsPatients with CoA repair were retrospectively analyzed after CMR and exercise stress test. Each aorta was manually segmented and 3D printed. Pressure gradient measurements from ascending aorta (AAo) to descending aorta (DAo) and 4D flow CMR were performed during simulations of rest and exercise using a mock circulatory flow loop. Changes in wall shear stress (WSS) and secondary flow formation (vorticity and helicity) from rest to exercise were quantified, as well as estimated DAo Reynolds number. Parameters were correlated with percent predicted peak oxygen consumption (VO2max) and aorta size mismatch (DAAo/DDAo).ResultsFifteen patients were identified (VO2max 47 to 126% predicted). Pressure gradient did not correlate with VO2max at rest or exercise. VO2max correlated positively with the change in peak vorticity (R = 0.55, p = 0.03), peak helicity (R = 0.54, p = 0.04), peak WSS in the AAo (R = 0.68, p = 0.005) and negatively with peak WSS in the DAo (R = − 0.57, p = 0.03) from rest to exercise. DAAo/DDAo correlated strongly with change in vorticity (R = − 0.38, p = 0.01), helicity (R = − 0.66, p = 0.007), and WSS in the AAo (R = − 0.73, p = 0.002) and DAo (R = 0.58, p = 0.02). Estimated DAo Reynolds number negatively correlated with VO2max for exercise (R = − 0.59, p = 0.02), but not rest (R = − 0.28, p = 0.31). Visualization of streamline patterns demonstrated more secondary flow formation in aortic arches with better exercise capacity, larger DAo, and lower Reynolds number.ConclusionsThere are important associations between secondary flow characteristics and exercise capacity in repaired CoA that are not captured by traditional pressure gradient, likely due to increased turbulence and inefficient flow. These 4D flow CMR parameters are a target of investigation to identify optimal aortic arch geometry and improve long term clinical outcomes after CoA repair.