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Register a new userThe effect of entrance flow development on vortex formation and wall shear stress in a curved artery model
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We numerically investigate the effect of entrance condition on the spatial and temporal evolution of multiple three-dimensional vortex pairs and wall shear stress distribution in a curved artery model. We perform this study using a Newtonian blood-analog fluid subjected to a pulsatile flow with two inflow conditions. The first flow condition is fully developed while the second condition is undeveloped (i.e. uniform). We discuss the connection along the axial direction between regions of organized vorticity observed at various cross-sections of the model and compare results between the different entrance conditions. We model a human artery with a simple, rigid $180^circ$ curved pipe with circular cross-section and constant curvature, neglecting effects of taper, torsion and elasticity. Numerical results are computed from a discontinuous high-order spectral element flow solver. The flow rate used in this study is physiological. We observe differences in secondary flow patterns, especially during the deceleration phase of the physiological waveform where multiple vortical structures of both Dean-type and Lyne-type coexist. We highlight the effect of the entrance condition on the formation of these structures and subsequent appearance of abnormal inner wall shear stresses - a potentially significant correlation since cardiovascular disease is known to progress along the inner wall of curved arteries under varying degrees of flow development.
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The seminal Batchelor-Greens (BG) theory on the hydrodynamic interaction of two spherical particles of radii a suspended in a viscous shear flow neglects the effect of the boundaries. In the present paper we study how a plane wall modifies this interaction. Using an integral equation for the surface traction we derive the expression for the particles relative velocity as a sum of the BGs velocity and the term due to the presence of a wall at finite distance, z_0. Our calculation is not the perturbation theory of the BG solution, so the contribution due to the wall is not necessarily small. The distance at which the wall significantly alters the particles interaction scales as z_0^{3/5}. The phase portrait of the particles relative motion is different from the BG theory, where there are two singly-connected regions of open and closed trajectories both of infinite volume. For finite z_0, there is a new domain of closed (dancing) and open (swapping) trajectories. The width of this region behaves as 1/z_0. Along the swapping trajectories, that have been previously observed numerically, the incoming particle is turning back after the encounter with the reference particle, rather than passing it by, as in the BG theory. The region of dancing trajectories has infinite volume. We found a one-parameter family of equilibrium states, overlooked previously, whereas the pair of spheres flows as a whole without changing its configuration. These states are marginally stable and their perturbation yields a two-parameter family of the dancing trajectories, where the particle is orbiting around a fixed point in a frame co-moving with the reference particle. We suggest that the phase portrait obtained at z_0>>a is topologically stable and can be extended down to rather small z_0 of several particle diameters. We confirm this by direct numerical simulations of the Navier-Stokes equations with z_0=5a.
A comprehensive study of the effect of wall heating or cooling on the linear, transient and secondary growth of instability in channel flow is conducted. The effect of viscosity stratification, heat diffusivity and of buoyancy are estimated separately, with some unexpected results. From linear stability results, it has been accepted that heat diffusivity does not affect stability. However, we show that realistic Prandtl numbers cause a transient growth of disturbances that is an order of magnitude higher than at zero Prandtl number. Buoyancy, even at fairly low levels, gives rise to high levels of subcritical energy growth. Unusually for transient growth, both of these are spanwise-independent and not in the form of streamwise vortices. At moderate Grashof numbers, exponential growth dominates, with distinct Rayleigh-Benard and Poiseuille modes for Grashof numbers upto $sim 25000$, which merge thereafter. Wall heating has a converse effect on the secondary instability compared to the primary, destabilising significantly when viscosity decreases towards the wall. It is hoped that the work will motivate experimental and numerical efforts to understand the role of wall heating in the control of channel and pipe flows.
This paper presents a method for calculating the wall shear rate in pipe turbulent flow. It collapses adequately the data measured in laminar flow and turbulent flow into a single flow curve and gives the basis for the design of turbulent flow viscometers. Key words: non-Newtonian, wall shear rate, turbulent, rheometer
We simulated two particle-based fluid models, namely multiparticle collision dynamics and dissipative particle dynamics, under shear using reverse nonequilibrium simulations (RNES). In cubic periodic simulation boxes, the expected shear flow profile for a Newtonian fluid developed, consistent with the fluid viscosities. However, unexpected secondary flows along the shear gradient formed when the simulation box was elongated in the flow direction. The standard shear flow profile was obtained when the simulation box was longer in the shear-gradient dimension than the flow dimension, while the secondary flows were always present when the flow dimension was at least 25% larger than the shear-gradient dimension. The secondary flows satisfy the boundary conditions imposed by the RNES and have a lower rate of viscous dissipation in the fluid than the corresponding unidirectional flows. This work highlights a previously unappreciated limitation of RNES for generating shear flow in simulation boxes that are elongated in the flow dimension, an important consideration when applying RNES to complex fluids like polymer solutions.
The direct measurement of wall shear stress in turbulent boundary layers (TBL) is challenging, therefore requiring it to be indirectly determined from mean profile measurements. Most popular methods assume the mean streamwise velocity to satisfy either a logarithmic law in the inner layer or a composite velocity profile with many tuned constants for the entire TBL, and require reliable data from the noise-prone inner layer. A simple method is proposed to determine the wall shear stress in zero pressure gradient TBL from measured mean profiles, without requiring noise-prone near-wall data. The method requires a single point measurement of mean streamwise velocity and mean shear stress in the outer layer, preferably between $20$ to $50$ $%$ of the TBL, and an estimate of boundary layer thickness and shape factor. The friction velocities obtained using the proposed method agree with reference values, to within $3$ $%$ over a range of Reynolds number.
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