Abstract Image-based computational fluid dynamics (CFD) has become a new capability for determining wall stresses of pulsatile flows. However, a computational platform that directly connects image information to pulsatile wall stresses is lacking. Prevailing methods rely on manual crafting of a hodgepodge of multidisciplinary software packages, which is usually laborious and error-prone. We present a new computational platform, to compute wall stresses in image-based pulsatile flows using the volumetric lattice Boltzmann method (VLBM). The novelty includes: (1) a unique image processing to extract flow domain and local wall normality, (2) a seamless connection between image extraction and VLBM, (3) an en-route calculation of strain-rate tensor, and (4) GPU acceleration (not included here). We first generalize the streaming operation in the VLBM and then conduct application studies to demonstrate its reliability and applicability. A benchmark study is for laminar and turbulent pulsatile flows in an image-based pipe (Reynolds number: 10 to 5000). The computed pulsatile velocity and shear stress are in good agreements with Womersley's analytical solutions for laminar pulsatile flows and concurrent laboratory measurements for turbulent pulsatile flows. An application study is to quantify the pulsatile hemodynamics in image-based human vertebral and carotid arteries including velocity vector, pressure, and wall-shear stress. The computed velocity vector fields are in reasonably well agreement with MRA (magnetic resonance angiography) measured ones. This computational platform is good for image-based CFD with medical applications and pore-scale porous media flows in various natural and engineering systems.
more »
« less
Incompressible active phases at an interface. Part 1. Formulation and axisymmetric odd flows
Inspired by the recent realization of a two-dimensional (2-D) chiral fluid as an active monolayer droplet moving atop a 3-D Stokesian fluid, we formulate mathematically its free-boundary dynamics. The surface droplet is described as a general 2-D linear, incompressible and isotropic fluid, having a viscous shear stress, an active chiral driving stress and a Hall stress allowed by the lack of time-reversal symmetry. The droplet interacts with itself through its driven internal mechanics and by driving flows in the underlying 3-D Stokes phase. We pose the dynamics as the solution to a singular integral–differential equation, over the droplet surface, using the mapping from surface stress to surface velocity for the 3-D Stokes equations. Specializing to the case of axisymmetric droplets, exact representations for the chiral surface flow are given in terms of solutions to a singular integral equation, solved using both analytical and numerical techniques. For a disc-shaped monolayer, we additionally employ a semi-analytical solution that hinges on an orthogonal basis of Bessel functions and allows for efficient computation of the monolayer velocity field, which ranges from a nearly solid-body rotation to a unidirectional edge current, depending on the subphase depth and the Saffman–Delbrück length. Except in the near-wall limit, these solutions have divergent surface shear stresses at droplet boundaries, a signature of systems with codimension-one domains embedded in a 3-D medium. We further investigate the effect of a Hall viscosity, which couples radial and transverse surface velocity components, on the dynamics of a closing cavity. Hall stresses are seen to drive inward radial motion, even in the absence of edge tension.
more »
« less
- NSF-PAR ID:
- 10400882
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 951
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
The interplay between viscoelasticity and inertia in dilute polymer solutions at high deformation rates can result in inertioelastic instabilities. The nonlinear evolution of these instabilities generates a state of turbulence with significantly different spatiotemporal features compared to Newtonian turbulence, termed elastoinertial turbulence (EIT). We ex- plore EIT by studying the dynamics of a submerged planar jet of a dilute aqueous polymer solution injected into a quiescent tank of water using a combination of schlieren imaging and laser Doppler velocimetry (LDV). We show how fluid elasticity has a nonmonotonic effect on the jet stability depending on its magnitude, creating two distinct regimes in which elastic effects can either destabilize or stabilize the jet. In agreement with linear stability analyses of viscoelastic jets, an inertioelastic shear-layer instability emerges near the edge of the jet for small levels of elasticity, independent of bulk undulations in the fluid column. The growth of this disturbance mode destabilizes the flow, resulting in a turbulence transition at lower Reynolds numbers and closer to the nozzle compared to the conditions required for the transition to turbulence in a Newtonian jet. Increasing the fluid elasticity merges the shear-layer instability into a bulk instability of the jet column. In this regime, elastic tensile stresses generated in the shear layer act as an “elastic membrane” that partially stabilizes the flow, retarding the transition to turbulence to higher levels of inertia and greater distances from the nozzle. In the fully turbulent state far from the nozzle, planar viscoelastic jets exhibit unique spatiotemporal features associated with EIT. The time-averaged angle of jet spreading, an Eulerian measure of the degree of entrainment, and the centerline velocity of the jets both evolve self-similarly with distance from the nozzle. The autocovariance of the schlieren images in the fully turbulent region of the jets shows coherent structures that are elongated in the streamwise direction, consistent with the suppression of streamwise vortices by elastic stresses. These coherent structures give a higher spectral energy to small frequency modes in EIT characterized by LDV measurements of the velocity fluctuations at the jet centerline. Finally, our LDV measurements reveal a frequency spectrum characterized by a −3 power-law exponent, different from the well-known −5/3 power-law exponent characteristic of Newtonian turbulence.more » « less
-
The relative velocities and positions of monodisperse high-inertia particle pairs in isotropic turbulence are studied using direct numerical simulations (DNS), as well as Langevin simulations (LS) based on a probability density function (PDF) kinetic model for pair relative motion. In a prior study (Rani et al. , J. Fluid Mech. , vol. 756, 2014, pp. 870–902), the authors developed a stochastic theory that involved deriving closures in the limit of high Stokes number for the diffusivity tensor in the PDF equation for monodisperse particle pairs. The diffusivity contained the time integral of the Eulerian two-time correlation of fluid relative velocities seen by pairs that are nearly stationary. The two-time correlation was analytically resolved through the approximation that the temporal change in the fluid relative velocities seen by a pair occurs principally due to the advection of smaller eddies past the pair by large-scale eddies. Accordingly, two diffusivity expressions were obtained based on whether the pair centre of mass remained fixed during flow time scales, or moved in response to integral-scale eddies. In the current study, a quantitative analysis of the (Rani et al. 2014) stochastic theory is performed through a comparison of the pair statistics obtained using LS with those from DNS. LS consist of evolving the Langevin equations for pair separation and relative velocity, which is statistically equivalent to solving the classical Fokker–Planck form of the pair PDF equation. Langevin simulations of particle-pair dispersion were performed using three closure forms of the diffusivity – i.e. the one containing the time integral of the Eulerian two-time correlation of the seen fluid relative velocities and the two analytical diffusivity expressions. In the first closure form, the two-time correlation was computed using DNS of forced isotropic turbulence laden with stationary particles. The two analytical closure forms have the advantage that they can be evaluated using a model for the turbulence energy spectrum that closely matched the DNS spectrum. The three diffusivities are analysed to quantify the effects of the approximations made in deriving them. Pair relative-motion statistics obtained from the three sets of Langevin simulations are compared with the results from the DNS of (moving) particle-laden forced isotropic turbulence for $St_{\unicode[STIX]{x1D702}}=10,20,40,80$ and $Re_{\unicode[STIX]{x1D706}}=76,131$ . Here, $St_{\unicode[STIX]{x1D702}}$ is the particle Stokes number based on the Kolmogorov time scale and $Re_{\unicode[STIX]{x1D706}}$ is the Taylor micro-scale Reynolds number. Statistics such as the radial distribution function (RDF), the variance and kurtosis of particle-pair relative velocities and the particle collision kernel were computed using both Langevin and DNS runs, and compared. The RDFs from the stochastic runs were in good agreement with those from the DNS. Also computed were the PDFs $\unicode[STIX]{x1D6FA}(U|r)$ and $\unicode[STIX]{x1D6FA}(U_{r}|r)$ of relative velocity $U$ and of the radial component of relative velocity $U_{r}$ respectively, both PDFs conditioned on separation $r$ . The first closure form, involving the Eulerian two-time correlation of fluid relative velocities, showed the best agreement with the DNS results for the PDFs.more » « less
-
We analyse the pressure-driven flow of the Oldroyd-B fluid in slowly varying arbitrarily shaped, narrow channels and present a theoretical framework for calculating the relationship between the flow rate $q$ and pressure drop $\Delta p$ . We first identify the characteristic scales and dimensionless parameters governing the flow in the lubrication limit. Employing a perturbation expansion in powers of the Deborah number ( $De$ ), we provide analytical expressions for the velocity, stress and the $q$ – $\Delta p$ relation in the weakly viscoelastic limit up to $O(De^2)$ . Furthermore, we exploit the reciprocal theorem derived by Boyko $\&$ Stone ( Phys. Rev. Fluids , vol. 6, 2021, L081301) to obtain the $q$ – $\Delta p$ relation at the next order, $O(De^3)$ , using only the velocity and stress fields at the previous orders. We validate our analytical results with two-dimensional numerical simulations in the case of a hyperbolic, symmetric contracting channel and find excellent agreement. While the velocity remains approximately Newtonian in the weakly viscoelastic limit (i.e. the theorem of Tanner and Pipkin), we reveal that the pressure drop strongly depends on the viscoelastic effects and decreases with $De$ . We elucidate the relative importance of different terms in the momentum equation contributing to the pressure drop along the symmetry line and identify that a pressure drop reduction for narrow contracting geometries is primarily due to gradients in the viscoelastic shear stresses. We further show that, although for narrow geometries the viscoelastic axial stresses are negligible along the symmetry line, they are comparable or larger than shear stresses in the rest of the domain.more » « less
-
null (Ed.)Abstract This study investigates the dynamics of velocity shear and Reynolds stress in the ocean surface boundary layer for idealized misaligned wind and wave fields using a large-eddy simulation (LES) model based on the Craik–Leibovich equations, which captures Langmuir turbulence (LT). To focus on the role of LT, the LES experiments omit the Coriolis force, which obscures a stress–current-relation analysis. Furthermore, a vertically uniform body force is imposed so that the volume-averaged Eulerian flow does not accelerate but is steady. All simulations are first spun-up without wind-wave misalignment to reach a fully developed stationary turbulent state. Then, a crosswind Stokes drift profile is abruptly imposed, which drives crosswind stresses and associated crosswind currents without generating volume-averaged crosswind currents. The flow evolves to a new stationary state, in which the crosswind Reynolds stress vanishes while the crosswind Eulerian shear and Stokes drift shear are still present, yielding a misalignment between Reynolds stress and Lagrangian shear (sum of Eulerian current and Stokes drift). A Reynolds stress budgets analysis reveals a balance between stress production and velocity–pressure gradient terms (VPG) that encloses crosswind Eulerian shear, demonstrating a complex relation between shear and stress. In addition, the misalignment between Reynolds stress and Eulerian shear generates a horizontal turbulent momentum flux (due to correlations of along-wind and crosswind turbulent velocities) that can be important in producing Reynolds stress (due to correlations of horizontal and vertical turbulent velocities). Thus, details of the Reynolds stress production by Eulerian and Stokes drift shear may be critical for driving upper-ocean currents and for accurate turbulence parameterizations in misaligned wind-wave conditions.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2022.856
