Flow Bifurcation Research Articles

Directional dark-field implicit x-ray speckle tracking using an anisotropic-diffusion Fokker-Planck equation

When a macroscopic-sized non-crystalline sample is illuminated using coherent x-ray radiation, a bifurcation of photon energy flow may occur. The coarse-grained complex refractive index of the sample may be considered to attenuate and refract the incident coherent beam, leading to a coherent component of the transmitted beam. Spatially-unresolved sample microstructure, associated with the fine-grained components of the complex refractive index, introduces a diffuse component to the transmitted beam. This diffuse photon-scattering channel may be viewed in terms of position-dependent fans of ultra-small-angle x-ray scatter. These position-dependent fans, at the exit surface of the object, may under certain circumstances be approximated as having a locally-elliptical shape. By using an anisotropic-diffusion Fokker-Planck approach to model this bifurcated x-ray energy flow, we show how all three components (attenuation, refraction and locally-elliptical diffuse scatter) may be recovered. This is done via x-ray speckle tracking, in which the sample is illuminated with spatially-random x-ray fields generated by coherent illumination of a spatially-random membrane. The theory is developed, and then successfully applied to experimental x-ray data.

Modeling the Air Flow Cooling Process and Determining the Geometric Dimensions of the GASK Model

The article is devoted to the calculation of the parameters of the air flow cooling process and the determination of the geometrical dimensions of a model of a gas-jet apparatus of a special design with a gas flow bifurcation (GASK). The article discusses the device and the principle of operation of the GASK, calculates the dependences of temperature on the pressure drop, gas flow rate on the gas pressure ratio. The calculated parameters of the process under consideration and the geometric dimensions of the GASK are given.

Subcritical and supercritical bifurcations in axisymmetric viscoelastic pipe flows

Axisymmetric viscoelastic pipe flow of Oldroyd-B fluids has been recently found to be linearly unstable by Garget al.(Phys. Rev. Lett., vol. 121, 2018, 024502). From a nonlinear point of view, this means that the flow can transition to turbulence supercritically, in contrast to the subcritical Newtonian pipe flows. Experimental evidence of subcritical and supercritical bifurcations of viscoelastic pipe flows have been reported, but these nonlinear phenomena have not been examined theoretically. In this work, we study the weakly nonlinear stability of this flow by performing a multiple-scale expansion of the disturbance around linear critical conditions. The perturbed parameter is the Reynolds number with the others being unperturbed. A third-order Ginzburg–Landau equation is derived with its coefficient indicating the bifurcation type of the flow. After exploring a large parameter space, we found that polymer concentration plays an important role: at high polymer concentrations (or small solvent-to-solution viscosity ratio$\beta \lessapprox 0.785$), the nonlinearity stabilizes the flow, indicating that the flow will bifurcate supercritically, while at low polymer concentrations ($\beta \gtrapprox 0.785$), the flow bifurcation is subcritical. The results agree qualitatively with experimental observations where critical$\beta \approx 0.855$. The pipe flow of upper convected Maxwell fluids can be linearly unstable and its bifurcation type is also supercritical. At a fixed value of$\beta$, the Landau coefficient scales with the inverse of the Weissenberg number ($Wi$) when$Wi$is sufficiently large. The present analysis provides a theoretical understanding of the recent studies on the supercritical and subcritical routes to the elasto-inertial turbulence in viscoelastic pipe flows.

Bifurcations of a plane parallel flow with Kolmogorov forcing

We study the primary bifurcations of a plane parallel flow in a channel with Kolmogorov forcing. We find a new type of bifurcation with both the oscillation frequency and the amplitude of the growing mode being zero at the threshold. We call this a stationary drift bifurcation. The laminar steady flow can display different types of bifurcation depending on the forcing wave number of the base flow. This is in contrast to the case of doubly periodic boundary conditions for which the primary bifurcation is stationary.

Investigation of boundary stresses on MHD flow in a convergent/divergent channel: An analytical and numerical study

This study investigates the boundary stresses prescribed by the traction boundary condition on an incompressible magnetohydrodynamic Jeffery-Hamel flow of viscous fluid. The governing partial differential equations are transformed to a nonlinear ordinary differential equation (ODE) by the transformation obtained from continuity equation. We have modeled traction boundary conditions to solve the problem. We have not imposed flow symmetry condition and applied prescribed flow rate condition. We have computed analytical and numerical solutions of the problem. We have developed modified Adomian decomposition method based on Daun-Rach Approach (DRA) for general nonlinear third order ODE subject to Robin’s and integral boundary conditions. The governing equation is solved using the developed scheme. The Mathematica routine, NDSolve, is used to obtain numerical solution by first approximating the constant flow rate condition by Gauss-Lobatto integration formula of four and five points as well as by trapezoidal rule. Analytical and numerical results are compared and found in good agreement. The slip and no-slip scenarios are observed both for inertial and non-inertial flows. The back flow occurs both for convergent and divergent channel geometries. Flow bifurcations and boundary layer get strengthened due to presence of boundary stresses. The symmetric and asymmetric natures of flow are also captured due to presence of boundary stresses.

Stability effect of an axial magnetic field on fluid flow bifurcation between coaxial cylinders

Numerical simulations aim to investigate the bifurcation caused by swirling flow between two coaxial vertical cylinders, and the fluid layers produced by the thermal gradient. The stability of both bifurcation and fluid layers by an axial magnetic field is analyzed. The finite-volume method is used to solve the governing Navier–Stokes, temperature and potential equations. A conducting viscous fluid characterized by a small Prandtl number [Formula: see text] is placed in the gap between two coaxial cylinders. The combination of aspect ratio, [Formula: see text] and Reynolds number, [Formula: see text] for three annular gaps ([Formula: see text] and [Formula: see text]) is compared in terms of flow stability, and heat transfer rates. Without a magnetic field, the vortex breakdown takes place near the inner cylinder due to the increased pumping action of the Ekman boundary layer. Fluid layered structures are developed by the competition between buoyancy and viscous forces. The increase in the magnitude of the magnetic field retarders the onset of the oscillatory instability caused by the disappearance of the vortex breakdown and reduces the number of fluid layers. The limits in which a vortex breakdown bubble manifests and the limits of transition from the multiple fluid layers to the single fluid layer are established.

Steady-State Bifurcation of a Non-parallel Flow Involving Energy Dissipation over a Hartmann Boundary Layer

A plane non-parallel vortex flow in a square fluid domain is examined. The energy dissipation of the flow is dominated by viscosity and linear friction effect of a Hartmann layer. This is a traditional Navier-Stokes flow when the linear friction effect is not involved, whereas it is a magnetohydrodynamic flow when the energy dissipation is fundamentally dominated by the friction. It is proved that linear critical values of a spectral problem are nonlinear thresholds leading to the onset of secondary steady-state flows, the nonlinear phenomenon observed in laboratory experiments.

Secondary flow in bifurcations – Important effects of curvature, bifurcation angle and stents

Coronary bifurcations have complex flow patterns including secondary flow zones and helical flow, which directly affect pathophysiological mechanisms such as the development of atherosclerosis. The objective of this study was to generate insights into the effects of curvature, bifurcation angle and the presence of stents on flow patterns and resulting haemodynamics in coronary left main bifurcations. The blood flow and associated metrics were modelled in both idealised and patient-specific bifurcations with varying curvature and bifurcation angles with and without stents, resulting in a total of 128 geometries considered. The results showed that larger curvature of bifurcating vessels has a significant influence on secondary flow, especially with distance to the bifurcation region, causing a skew, spin and asymmetry of Dean vortices, an increase in helical flow intensity with symmetry loss, and a decrease in adversely low time-average wall shear stress (TAWSS). Generally, asymmetric flow patterns coincided with adversely low TAWSS regions. In identical stented geometries, the presence of the stents induced local recirculation immediately adjacent to the stent struts, thus generating adversely low TAWSS in these areas, with some effect on the overall secondary flow. Overall, the effect of stents outweighed the effect of curvature and BA. This new knowledge contributes to a better understanding of the joint effects of curvature, bifurcation angle, and stents on flow patterns and haemodynamics in coronary bifurcations.

The effects of plaque morphological characteristics on the post-stenotic flow in left main coronary artery bifurcation

Local post-stenotic hemodynamics has critical influence in the atherosclerotic plaque progression occurring in susceptible arterial sites, in particular the left main coronary artery (LMCA) bifurcation. Understanding the effects of plaque morphological characteristics: stenosis severity (SS), eccentricity index (EI) and lesion length (LL) on the post-stenotic flow behavior can significantly improve treatment planning. In order to investigate these effects, we have employed computational fluid dynamics (CFD) simulations in twenty computer-generated and five patient-specific LMCA models and the hemodynamic parameters: velocity, pressure (P), wall pressure gradient (WPG), wall shear stress (WSS), time averaged wall shear stress (TAWSS), oscillatory shear index (OSI), relative residence time (RRT) and helicity intensity (h2) were analyzed. Our results revealed that the effect of stenosis eccentricity varied significantly for different values of stenosis severity and lesion length. Regions with low WSS, low TAWSS and high RRT were more prominent in models having higher stenosis severity. For smaller lesion length, at low and moderate stenosis severity, surface area with low TAWSS and high RRT decreased with increasing eccentricity index, whereas for high stenosis severity models, low TAWSS region and average RRT values increased with eccentricity. However, for models with longer lesion length, regions with high OSI and RRT overall increased gradually with eccentricity. The helicity intensity (h2) of all models remained very low except at the most eccentric model with longer lesion length. The presence of very high helical flow in this model suggests the possibility of atheroprotective flow. It can be concluded that all plaque morphological characteristics covered under this investigation play an important role in plaque progression.

Symmetry-breaking bifurcations in two-dimensional square vortex flows

We present a theoretical study of spatial symmetries and bifurcations in a laterally bounded two-dimensional flow composed of approximately square vortices. The numerical setting simulates a laboratory experiment wherein a shallow electrolyte layer is driven by a plane-parallel force that is nearly sinusoidal in both extended directions. Choosing an integer or half-integer number of forcing wavelengths along each direction, we generate square vortex flows invariant under different spatial symmetries. We then map out the sequence of symmetry-breaking bifurcations leading to the formation of fully asymmetric flows. Our analysis reveals a gallery of pitchfork and Hopf bifurcations, both supercritical and subcritical in nature, resulting in either steady or time-dependent asymmetric flows. Furthermore, we demonstrate that different types of flows (steady, periodic, pre-periodic, or quasi-periodic), at times with twofold multiplicity, emerge as a result of symmetry-breaking bifurcations. Our results also provide new theoretical insights into previous experimental observations in quasi-two-dimensional square vortex flows.

Use of Geospatial Tools in Morphometric Analysis and Prioritisation of Sub-catchments of the Soungrougrou (Casamance Basin)

Abstract The prioritisation of catchments, particularly in the context of catchment plans and management programmes, is part of water resources development. In fact, morphometric analysis assisted by geospatial technology is carried out by prioritising sub-catchments according to their natural resource availability characteristics. Information on the geomorphology and erosion factors of the study area is used in the area in the preparation of local models of ungauged sub-catchments, which otherwise lack an adequate hydrological database. The objective of this paper is to use geographic information systems (GISs) in morphometric analysis to prioritise sub-catchments of the Soungrougrou (a tributary of the Casamance River). In this respect, the integrated methodology involving morphometric aspects from geospatial technology is used. To carry out the geospatial research, basic mathematical equations used in a GIS environment were used to measure a series of aspects of hydrology such as flow length, flow length ratio, bifurcation ratio, drainage density, drainage texture, flow frequency, elongation rate, circularity ratio, form factor, relief and relief ratio. The results divided the whole catchment into three priority areas, namely high, medium and low. The results are relevant for establishing soil and water conservation plans in the Soungrougrou basin, as well as adequate groundwater production and management. The high category (sub-basins 6, 8, 14, 17 and 18) is subject to maximum soil erosion, which requires immediate intervention to avoid possible natural hazards.

A Numerical Study on the Exact Onset of Flow Instabilities in Thermo-Solutal Marangoni Convection Driven by Opposing Forces in a Half-Zone Liquid Bridge under Zero Gravity

The theoretical onset of the Marangoni convection instability occurring in a half-zone liquid bridge of the floating zone (FZ) growth of SixGe1–x has been investigated by numerical simulations. A half-zone model of the liquid bridge between a cold (bottom plane) and a hot (top plane) disk is considered. The highest Si concentration is on the top of the liquid bridge. Therefore, the driving forces for thermal and solutal Marangoni flows are in opposite directions in this configuration. The nonlinear equilibria and periodic orbits are obtained using the Newton–Krylov method, and their stability is analyzed with global linear stability analysis. A flow bifurcation analysis is conducted. The results show that when the solutal Marangoni number, MaC, ≤360, the primary flow bifurcation is from 2D axisymmetric to 3D steady flow. When MaC>360, the 2D axisymmetric flow becomes weakly periodic 2D axisymmetric, and eventually becomes chaotic. The critical thermal Marangoni number is monotonically increasing as MaC increases, and the flow is 2D axisymmetric when the solutal Marangoni forceis dominant. The stability evaluation for various thermal Marangoni number values at MaC=893 reveals that the onset of transition is from steady to periodic. However, the reverse transition does not occur at the same Marangoni number value. The simulation results show that the hysteresis behavior of the flow field exhibits an approximately 1% difference between two critical thermal Marangoni numbers. The present study suggests that the control parameters of FZ crystal growth should be smaller than the calculated critical values to avoid any flow-induced disturbances.

Electro-thermo-convection in power-law fluids within a square enclosure with an inner cylinder

This paper investigates the electro-thermo-convection of power-law non-Newtonian fluids between a square enclosure and inner cylinder subjected to the simultaneous actions of external thermal and electric fields via lattice Boltzmann method. We concentrate on the flow structure transition, heat transfer efficiency as well as the bifurcation criteria concerning the electric Rayleigh number T for various power index 0.6≤n≤1.4. In addition, in order to comprehensively examine the impacts of buoyancy, two different Rayleigh numbers (Ra=103,105) are considered, corresponding to the weak and strong buoyancy. The cases for Newtonian fluids are used as the basic result to compare with the non-Newtonian cases. Based on the simulations, it is found that the flow motion and bifurcation criteria depend strongly on the power-law index. Specifically, the shear-shinning characteristic decreases the bifurcation threshold and exhibits a smaller hysteresis loop compared with Newtonian fluid, and the opposite effect and more evolution details about the transformation of charge void region with different shapes can be captured for shear-thickening characteristic. Additionally, the flow motions with stronger thermal convection illustrate more complex bifurcation diagrams and hysteresis loops due to the cooperation and competition between the buoyant and Coulomb forces, while it is not obvious for shear-thickening fluids.

Deterministic and stochastic bifurcations in two-dimensional electroconvective flows

Abstract

Flow Bifurcation Phenomena of Shear-Thinning and Newtonian Fluids in a Rectangular Channel in Presence of Intermediate Steps: using Carreau-Yasuda Model

Flow bifurcation transitions of shear-thinning fluid and Newtonian fluid, flow through a two-dimensional rectangular channel in presence of intermediate steps have been considered in this manuscript. Employing SIMPLE algorithm, the governing equations have been solved numerically and using FLUENT software to visualize the simulation results for convenience. The Rheological properties of shear-thinning and Newtonian fluids are described in the light of Carreau-Yasuda model. The result of this formulation has been validated with those of an earlier work. The motivation of this work is to study the bifurcation characteristics for different values of Reynolds numbers in presence of multiple steps in a rectangular channel. Pressure drop characteristic has also been studied for different values of expansion ratio and intermediate steps. For some particular value of expansion ratio (ER), a linear relation between 〖Re〗_crit and the value of n of Carreau-Yasuda model has been shown.

Bifurcation analysis of coupling thermosolutal convection induced by a thermal and solutal source in a horizontal cavity

In this study, the bifurcation phenomenon and the existence of dual asymmetry solutions of double-diffusive convection driven by an internal thermal and solutal source in a horizontal cavity have been investigated systematically. The problem is solved by the SIMPLE algorithm with the QUICK scheme in a non-uniform staggered grid system. The Rayleigh numbers, 200 ≤ Ra ≤ 106, buoyancy ratios, −20 ≤ Nc ≤ 20, Soret numbers, 0 ≤ Sr ≤ 0.8, and Dufour numbers, 0 ≤ Df ≤ 0.8, are considered in this study. Different streamlines for the onset and evolution of static bifurcation are tracked. The paper aims to determine the critical Rayleigh numbers and buoyancy ratios for the onset of symmetry-breaking through bifurcation diagrams based on the vortex length. The results indicate that increasing buoyancy can destabilize the symmetric system. The strong couple diffusion effect delays the onset of bifurcation flow. A pair of asymmetric modes can be obtained under different initial conditions.

A numerical analysis on multi-stage Tesla valve based cold plate for cooling of pouch type Li-ion batteries

The operating temperature can significantly influence the performance, cycle life, and safety of Li-ion batteries used in electric vehicles. One of the critical factors is to assess the temperature distribution within the battery pack when operated under extreme conditions and choosing an appropriate cooling method. Concerning this, a liquid cooling plate comprising Tesla valve configuration with high recognition in microfluidic applications is proposed to provide a safer temperature range for pouch type Li-ion batteries. A multi-stage Tesla valve with forward and reverse flow configuration is designed and analysed to improve a conventional rectangular channel's intrinsic temperature gradient issues for turbulent flow conditions. Moreover, the influence of various parameters such as channel number, the distance between two consecutive valves, coolant temperature, and heat flux applied on the cold plate's top and bottom surfaces are numerically investigated for varying Reynold's number using COMSOL Multiphysics software. An enhancement in heat transfer with the reverse flow in multi-stage Tesla valve is seen, mainly caused by flow bifurcation and mixing mechanisms, at the cost of pressure drop. A cold plate with 4 channels and valve to valve distance of 8.82 mm exhibits the most effective cooling performance.

Onset of vortex structures in rotating plane Couette flow

Abstract

Flow topology and bifurcations of buoyancy and mixed convection in an elongated channel with an abrupt section variation

A forward-facing step (FFS) located half-way in an elongated duct subjected to a horizontal pressure gradient and a vertical temperature difference is considered as a simplified geometrical model to investigate numerically typical problems of internal non-isothermal flow in the presence of blunt obstacles. The sensitivity of this system to thermal buoyancy for each considered rate of fluid injection (measured through the related Richardson number, Ri) is explored by varying parametrically the corresponding Rayleigh number (Ra) over a large interval of orders of magnitude (up to the onset of chaos) and assuming two alternate paradigms for the bottom of the considered channel, namely an adiabatic or kept-at-constant temperature (hot) boundary. Through this conceptual framework, a kaleidoscope of situations are revealed in the (Ri, Ra) space, differing in terms of flow patterning behavior, thermal plume generation phenomena, intensity of heat exchange at the walls and bifurcation scenario. In particular, while for the isothermal floor case a higher Ri leads to an increase in the value of the Rayleigh number needed for transition to time-dependent flow, the corresponding trend becomes non-monotonic if the same boundary is thermally insulated. In such a case the Nusselt number (Nu) calculated for the horizontal surface of the step is always smaller than the equivalent Nu evaluated for the vertical side. The latter is significantly lowered when the hot-floor condition is assumed.

Tapered Vector Doppler for Improved Quantification of Low Velocity Blood Flow.

A new vector velocity estimation scheme is developed, termed tapered vector Doppler (TVD), aiming to improve the accuracy of low velocity flow estimation. This is done by assessing the effects of singular value decomposition (SVD) and finite impulse response (FIR) filters and designing an estimator which accounts for signal loss due to filtering. Synthetic data created using a combination of in vivo recordings and flow simulations were used to investigate scenarios with low blood flow, in combination with true clutter motion. Using this approach, the accuracy and precision of TVD was investigated for a range of clutter-to-blood and signal-to-noise ratios. The results indicated that for the investigated carotid application and setup, the SVD filter performed as a frequency-based filter. For both SVD and FIR filters, suppression of the clutter signal resulted in large bias and variance in the estimated blood velocity magnitude and direction close to the vessel walls. Application of the proposed tapering technique yielded significant improvement in the accuracy and precision of near-wall vector velocity measurements, compared to non-TVD and weighted least squares approaches. In synthetic data, for a blood SNR of 5 dB, and in a near-wall region where the average blood velocity was 9 cm/s, the use of tapering reduced the average velocity magnitude bias from 26.3 to 1.4 cm/s. Complex flow in a carotid bifurcation was used to demonstrate the in vivo performance of TVD, and it was shown that tapering enables vector velocity estimation less affected by clutter and clutter filtering than what could be obtained by adaptive filter design only.