Sinusoidal Oscillating Flow Through Asymmetrical Bifurcation

Bifurcating vessel is a characteristic feature of biological systems such as arteries in the cardiovascular system and pulmonary airways. In cardiovascular system, the bifurcations are often asymmetric, flow is pulsatile, and the fluid, blood, shows a complex rheology. In this work, we study computationally pulsatile flow in planar symmetric and asymmetric, three-dimensional bifurcating vessels. The fluid is considered to be Newtonian as well as non-Newtonian following Carreau's model, and the results are compared. While the flow divides in the two daughter tubes equally in symmetric bifurcations, the flow distribution is time-dependent during a cardiac cycle in asymmetric bifurcations. The flow pattern changes significantly during a cardiac cycle. The secondary flow caused by a turning streamline is analyzed in terms of secondary velocity, vorticity, and helicity. Significant variation is observed in the secondary flow in a cardiac cycle. The secondary flow is observed to be stronger at the start of the diastole despite reduced flow rate. The separated flow on the outer wall causes a significant reduction in time-averaged wall shear stress, a biomarker to assess the possibility of atherosclerotic plaque development. While no significant difference is observed in the results obtained for Newtonian and non-Newtonian fluids at high shear rates, for example, during systole, significant differences are observed when the shear rate is low, during diastole or in the separation region. The velocity profile for the non-Newtonian fluid is observed to be flatter than that for Newtonian fluid. Further oscillatory shearing index, relative residence time, the parameters used as biomarkers are presented.

Axial gas transport due to the interaction between radial mixing and radially nonuniform axial velocities is responsible for gas transport in thick airways during High-frequency oscillatory ventilation (HFO). Because the airways can be characterized by a bifurcating tube network, the secondary flow in the curved portion of a bifurcating tube contributes to cross-stream mixing. In this study the oscillatory flow and concentration fields through a single symmetrical airway bifurcating tube model were numerically analyzed by solving three-dimensional Navier-Stokes and mass concentration equations with the SIMPLER algorithm. The simulation conditions were for a Womersley number, alpha = 9.1 and Reynolds numbers in the parent tube between 200 and 1000, corresponding to Dn2/alpha 4 in the curved portion between 2 and 80, where Dn is Dean number. For comparison with the results from the bifurcating tube, we calculated the velocity and concentration fields for fully developed oscillatory flow through a curved tube with a curvature rate of 1/10, which is identical to the curved portion of the bifurcating tube. For Dn2/alpha 4 < or = 10 in the curved portion of the bifurcating tube, the flow divider and area changes dominate the axial gas transport, because the effective diffusivity is greater than in either a straight or curved tube, in spite of low secondary velocities. However, for Dn2/alpha 4 > or = 20, the gas transport characteristics in a bifurcation are similar to a curved tube because of the significant effect of secondary flow.

Characterisation of transverse turbulent motion in quasi-two-dimensional aerated flow: Application of four-point air-water flow measurements in hydraulic jump

FLOW STRUCTURE AND VARIATION OF WALL SHEAR STRESS IN ASYMMETRICAL ARTERIAL BRANCH

Color flow mapping has become an important clinical tool, for diagnosing a wide range of vascular diseases. Only the velocity component along the ultrasonic beam is estimated, so to find the actual blood velocity, the beam to flow angle has to be known. Because of the unpredictable nature of vascular hemodynamics, the flow angle cannot easily be found as the angle is temporally and spatially variant. Additionally the precision of traditional methods is severely lowered for high flow angles, and they breakdown for a purely transverse flow. To overcome these problems we propose a new method for estimating the transverse velocity component. The method measures the transverse velocity component by estimating the transit time of the blood between two parallel lines beamformed in receive. The method has been investigated using simulations performed with Field II. Using 15 emissions per estimate, a standard deviation of 1.64% and a bias of 1.13% are obtained for a beam to flow angle of 90 degrees. Using the same setup a standard deviation of 2.21% and a bias of 1.07% are obtained for a beam to flow angle of 75 degrees. Using 20 emissions a standard deviation of 3.4% and a bias of 2.06% are obtained at 45 degrees. The method performs stable down to a signal-to-noise ratio of 0 dB, where a standard deviation of 5.5% and a bias of 1.2% is achieved.

The steady laminar non-isothermal flow of a non-linear viscoelastic fluid in tubes or arbitrary contour is analyzed under constant wall heat flux. Viscous dissipation is taken into account. Non-linear viscoelastic behavior is modeled by means of the Phan-Thien-Tanner model. The equations of motion and energy are solved analytically through a perturbation approach coupled with a one-to-one mapping of the boundary to map the circular shape into various axially symmetric cross-sectional shapes with the Weissenberg number as the perturbation parameter Longitudinal and transversal velocity components are determined for several cross-sectional shapes, for which the temperature field and the Nusselt number variation with the Prandtl, Brinkman and Reynolds numbers are computed.

Channel bifurcations are a fundamental element of a broad variety of flowing freshwater environments worldwide, such as braiding and anabranching rivers, river deltas and alluvial fans. River bifurcations often develop asymmetrical configurations with uneven discharge partition and a bed elevation gap between the downstream anabranches. This has been reproduced by one-dimensional (1-D) analytical theories which, however, rely on the empirical calibration of one or more parameters and cannot provide a clear and detailed physical explanation of the observed dynamics. We propose a novel two-dimensional (2-D) solution for the flow and bed topography in channel bifurcations based on an innovative application to a multi-thread channel configuration of the 2-D steady linear solution developed decades ago to study river bars and meandering in single thread river settings. The resonant value of the upstream channel aspect ratio, corresponding to the theoretical resonance condition of regular river meanders (Blondeaux &amp; Seminara,J. Fluid Mech., vol. 157, 1985, pp. 449–470) is the key parameter discriminating between symmetrical and asymmetrical bifurcations, in quantitative agreement with experimental observations and numerical simulations, and qualitatively matching field observations. Only when the aspect ratio of the upstream channel of the bifurcation exceeds resonance, is the bifurcation node able to trigger the upstream development of a steady alternate bar pattern, thus creating an unbalanced configuration. Ultimately, the work provides an analytical explanation of the intrinsic legacy between bifurcation asymmetry and the phenomenon of 2-D upstream morphodynamic influence discovered by Zolezzi &amp; Seminara (J. Fluid Mech., vol. 438, 2001, pp. 183–211).

Understanding the flow behaviour of synovial fluid is essential for analysing lubrication, nutrient transport, and mechanical functionality within the knee joint. This study presents a mathematical model describing axial and transverse velocity components under pressure driven flow with variable viscosity and porous-like resistance parameters. The governing equations were solved to obtain velocity profiles and volumetric flow rate, enabling a detailed assessment of fluid transport under physiological conditions. The results show that axial velocity follows a smooth parabolic pattern typical of laminar lubrication flow, while transverse velocity is highly sensitive to viscosity ratios and structural resistance, reflecting the influence of synovial membrane permeability. The computed flow rates demonstrate that elevated viscosity and decreased permeability conditions associated with osteoarthritis—significantly reduce fluid transport capacity. The study provides mechanistic insight into synovial fluid dynamics and offers a theoretical basis for improving visco supplementation strategies, developing biomimetic joint lubricants, and informing therapeutic approaches for degenerative knee disorders.

In the formulation of the nonplanar oscillating-surface problem, a complex variable is introduced instead of the two transversal coordinates. Thereby, a compact relation is obtained between the complex transversal velocity, which replaces the two transversal velocity components, and the chordwise integrals, whose integrands are products of the pressure jump and part of the kernel. A particular approach for numerical evaluation of these integrals is also considered. The remaining spanwise integrals are evaluated through interpolation by the aid of Jacobi polynomials. This interpolation, together with the complex representation, leads to a generalization of the Multhopp procedure. Corresponding integration coefficients are determined by Jacobi's functions of the second kind for complex arguments.

In this paper we investigate numerically the periodic, axisymmetric response of a liquid annulus enclosed in a revolving cylinder and subject to a periodic axial excitation within the range of the natural frequencies. We use a description which employs as solution variables the transverse component of the vorticity vector, the scalar stream function and the transverse velocity component, as well as the position of the free surface. The acceleration due to gravity is neglected, whereas friction and surface tension are taken into account. At the fixed walls the no-slip condition is fulfilled except at points on the contact line. At the contact line the slip condition is applied. The solution of this problem is achieved using the spectral method in the time direction and finite differences in the space direction, whereby surface-adapted coordinates are utilized. Far away from the walls the computational results show good agreement with results obtained from a linearized theory assuming an inviscid liquid, while at the walls boundary layers are generated.

Computational fluid dynamics tools are useful for their ability to model patient specific data relevant to the genesis and progression of atherosclerosis, but unavailable to measurement tools. The sensitivity of the physiologically relevant parameters of wall shear stress (WSS) and the oscillatory shear index (OSI) to secondary flow in the inlet velocity profiles was investigated in three realistic models of the carotid bifurcation. Secondary flow profiles were generated using sufficiently long entrance lengths, to which curvature and helical pitch were added. The differences observed were contextualized with respect to effect of the uncertainty of the models' geometry on the same parameters. The effects of secondary velocities in the inlet profile on WSS and OSI break down within a few diameters of the inlet. Overall, the effect of secondary inlet flow on these models was on average more than 3.5 times smaller than the effect of geometric variability, with 13% and 48% WSS variability induced by inlet secondary flow and geometric differences, respectively. The degree of variation is demonstrated to be within the range of the other computational assumptions, and we conclude that given a sufficient entrance length of realistic geometry, simplification to fully developed axial (i.e., Womersley) flow may be made without penalty. Thus, given a choice between measuring three components of inlet velocity or a greater geometric extent, we recommend effort be given to more accurate and detailed geometric reconstructions, as being of primary influence on physiologically significant indicators.

The effect of nonhomogeneous strain caused by two-dimensional objects on single point statistical properties of the turbulent velocity and turbulent scalar (temperature) and their cross moments are investigated experimentally. The heated turbulent flow is produced by means of a biplane array of round rods and a biplane array of heated, thin wires placed downstream of the turbulence producing grid. The experiments are performed for three different ratios of the integral scale, L0, to the object dimension, D, of 0.38, 1.90 and 3.1. Measurements of time resolved temperature and longitudinal and transverse velocity components are obtained using a triple wire probe consisting of a cold wire and two hot wires. Results indicate that, for L0 =1.9 and 3.1, the decay rate of temperature variance is nearly the same in the region of maximum shear stress (mss) and near the centerline. However, the decay rate in these regions is less than the decay rate of the temperature variance outside the cylinder wake. For L0/D = 0.38, the decay rates of temperature variance are the same in the regions of mss, near the centerline and outside the wake. Transverse growth of the wake is found to be either increased or nearly unchanged depending on, respectively, whether the free stream integral scale is larger or less than that of the wake.

The internal motion through porous chambers generated by wall-normal injection has received considerable attention in the second half of the twentieth century. This may be attributed to its relevance to a large number of phenomenological applications. In actuality, the motion of fluids driven by either wall injection or suction can be used to describe a variety of practical problems that encompass a wide range of industries and research areas. To name a few, these include: paper manufacturing (Taylor, 1956), ablation or sweat cooling (Peng & Yuan, 1965; Yuan & Finkelstein, 1958), boundary layer control (Acrivos, 1962; Libby, 1962; Libby & Pierucci, 1964), peristaltic pumping (Fung & Yih, 1968; Uchida & Aoki, 1977), gaseous diffusion or filtration, isotope separation (Berman, 1953; 1958a;b), irrigation, and the mean flow modeling of both solid (Culick, 1966; Zhou & Majdalani, 2002) and hybrid rockets (Majdalani, 2007a). Wall injected flows are initiated by the injection or suction of a fluid across the boundaries of a ducted region having an arbitrary shape and cross-sectional area. This is illustrated in Figure 1 for the special cases of porous channels and tubes. In general, one is required to solve a reduced-order form of the equations of motion for a bounded fluid in order to retrieve a meaningful solution (Terrill & Thomas, 1969). For a general three dimensional setting, this effort leads to a formidable task that is often intractable. However, when simplifying assumptions are invoked, as in the case of an incompressible stream in a channel or tube with uniform injection or suction, Berman (1953) has shown that the Navier-Stokes equations can be reduced to a fourth order nonlinear ODE that may be susceptible to both analytical and numerical treatment. Berman’s approach is based on a spatial similarity that transforms the Navier-Stokes equations to a more manageable ODE by assuming that the transverse velocity component v is axially invariant; this immediately translates into a streamfunction that varies linearly in the streamwise direction, i.e. ψ(x, y) = xF(y) (Berman, 1953; White, 2005). Then by considering the limiting case of a small suction Reynolds number, Re ∼ e, Berman employs a regular perturbation series in Re to obtain an approximate expansion for the mean flow function F(y). Berman’s Reynolds number, Re = Uwa/ν , is based on the injection speed at the wall, Uw, and the channel half height, a. As for the case of large suction, Berman (1953) first remarks that the limit of the reduced ODE cannot be used to obtain a solution owing to the reduction in order of the governing equation. Later, Sellars (1955) and Terrill (1964) invoke a procedure that permits the extraction of a closed-form analytical approximation for the large Re case by implementing a coordinate transformation that takes into account the spatial relocation of the boundary layer to the sidewall region. Internal Flows Driven by Wall-Normal Injection

The split film probe is designed for simultaneous measurements of streamwise and transverse velocity components. However, difficulties in obtaining reliable results have been experienced by many researchers. The problems are attributed mainly to static and dynamic cross talk through the substrate. In this paper, the static cross talk is examined in the first part by deliberately operating the film with different overheats. In the second part, both films are statically balanced, one of the films is subjected to an electrical perturbation, the other film will respond to the dynamic perturbation due to the imperfect insulation of the substrate. At low frequencies, the thermal response can be as high as 37%. At high frequencies, the frequency response is a function of the substrate characteristic frequency and the circuit characteristic frequency. The reasons for the thermal response are examined at the low-frequency limit. The dynamical unbalanced resistance generated by the electrical perturbation will set up an instantaneous temperature gradient across the substrate which produces the cross talk. Furthermore, if azimuthal asymmetry exists, the communication between the two films will also appear due to the azimuthal asymmetric temperature distribution.

Magnetic skyrmions are topologically stable objects that are made with a bunch of spins tightly arranged in a smooth fashion. Their topological nature provides unusual and complex transport properties, such as the skyrmion Hall effect. Extensive Hall data have further revealed asymmetry between skyrmion and antiskyrmion Hall angles, which cannot be accounted by known mechanisms. Here, we explain this asymmetry by utilizing another universal transport coefficient called `Hall viscosity,' extensively studied in quantum Hall systems. Hall viscosity is modeled in steady-state skyrmions motion by generalizing the Thiele equation with a transverse velocity component and is independent of the skyrmion charge. Our analyses, based on available asymmetric Hall angle data, reveal this transverse force amounts 3\% - 5.4\% of the force due to the skyrmion Hall effect. Further clarification of Hall viscosity will be essential for designing next generation storage devices properly, not to mention for our deeper understanding of fundamental properties of nature.