Manuscript title: Effect of spanwise groove on the dynamic stall characteristics of an airfoil

Numerical simulations are conducted to investigate the effect of triangular groove on the dynamic stall characteristics of a NACA 0012 airfoil at a Reynolds number of 135,000. The right-angled triangular grooves are placed at either 10%, 25%, or 50% chord locations on the suction and have depths of 0.025c and 0.05c, measured normal to the surface of the airfoil. The solutions that are second order accurate in time and space are obtained using pressure-based finite volume solver and the 4-equation transition SST turbulence model viz. γ- Re θt is used to predict transition and viscous stresses accurately. The airfoil is in harmonic pitch motion about its quarter-chord with a maximum circular frequency of 18.67 rad/s. The results suggest that the presence of a groove, except for the deeper grove at 0.5c, quickens the dynamic stall, but with smaller rise in C l,max and a less severe fall in lift at the stall. The mean C l value during the downstroke is improved by up to 8% for the deeper groove at 0.25c, reducing the hysteresis in lift significantly. The grooves at 0.1c, 0.25c, and 0.5c also reduce the drag by 4%, 7%, and 9% during a complete cycle, with subsequent improvements of 54%, 69%, and 63% in the l/d ratio. The current finding can be thus used to enhance the performance of flapping wing MAVs, helicopter rotors, and wind turbine blades as these applications encounter the dynamic stall phenomena frequently.

Influence of the surface viscous stress on the pinch-off of free surfaces loaded with nearly-inviscid surfactants

We analyze the breakup of a pendant water droplet loaded with SDS. The free surface minimum radius measured in the experiments is compared with that obtained from a numerical solution of the Navier–Stokes equations for different values of the shear and dilatational surface viscosities. This comparison shows the small but measurable effect of the surface viscous stresses for sufficiently small spatiotemporal distances from the breakup point, and allows to establish upper bounds for the values of the shear and dilatational viscosities. We study numerically the distribution of Marangoni and viscous stresses over the free surface as a function of the time to the pinching, and describe how surface viscous stresses grow in the pinching region as the free surface approaches its breakup. When Marangoni and surface viscous stresses are taken into account, the surfactant is not swept away from the thread neck in the time interval analyzed. Surface viscous stresses eventually balance the driving capillary pressure in the pinching region for small enough values of the time to pinching. Based on this result, we propose a scaling law to account for the effect of the surface viscosities on the last stage of temporal evolution of the neck radius.

Towards an analytical description of active microswimmers in clean and in surfactant-covered drops

Geometric confinements are frequently encountered in the biological world and strongly affect the stability, topology, and transport properties of active suspensions in viscous flow. Based on a far-field analytical model, the low-Reynolds-number locomotion of a self-propelled microswimmer moving inside a clean viscous drop or a drop covered with a homogeneously distributed surfactant, is theoretically examined. The interfacial viscous stresses induced by the surfactant are described by the well-established Boussinesq-Scriven constitutive rheological model. Moreover, the active agent is represented by a force dipole and the resulting fluid-mediated hydrodynamic couplings between the swimmer and the confining drop are investigated. We find that the presence of the surfactant significantly alters the dynamics of the encapsulated swimmer by enhancing its reorientation. Exact solutions for the velocity images for the Stokeslet and dipolar flow singularities inside the drop are introduced and expressed in terms of infinite series of harmonic components. Our results offer useful insights into guiding principles for the control of confined active matter systems and support the objective of utilizing synthetic microswimmers to drive drops for targeted drug delivery applications. Graphical abstract

On some model equations for pulsatile flow in viscoelastic vessels

© 2019 Considered here is the derivation of partial differential equations arising in pulsatile flow in pipes with viscoelastic walls. The equations are asymptotic models describing the propagation of long-crested pulses in pipes with cylindrical symmetry. Additional effects due to viscous stresses in bio-fluids are also taken into account. The effects of viscoelasticity of the vessels on the propagation of solitary and periodic waves in a vessel of constant radius are being explored numerically.

On some model equations for pulsatile flow in viscoelastic vessels

© 2019 Considered here is the derivation of partial differential equations arising in pulsatile flow in pipes with viscoelastic walls. The equations are asymptotic models describing the propagation of long-crested pulses in pipes with cylindrical symmetry. Additional effects due to viscous stresses in bio-fluids are also taken into account. The effects of viscoelasticity of the vessels on the propagation of solitary and periodic waves in a vessel of constant radius are being explored numerically.

Relation between dynamic and bulk viscosities

Во многих технических устройствах реализуются течения, при описании которых фигурируют различные виды вязкостей. В работе рассмотрены вопросы возникновения этих вязкостей и связь между ними. Показано, как тензор материальных констант 4C - тензор 4-го ранга, имеющий 81 компоненту, переводит тензор скоростей деформаций в тензор вязких напряжений. При рассмотрении связи между тензорами скоростей деформаций и вязких напряжений после перехода из трехмерного пространства в шестимерное, и использования свойств симметрии среды, можно заметить, что число независимых материальных констант для изотропных жидкостей сводится к двум константам Ламе. Рассмотрение скорости объемного расширения жидкости приводит к появлению объёмной вязкости, которая выражается через эти константы. В случае равенства нулю объёмной вязкости имеет место модель ньютоновской стоксовой жидкости, в которой постоянные Ламе становятся пропорциональными друг другу. Далее записаны уравнения Навье-Стокса при разных выражениях для вязкости жидкости. When describing many real flows in technical systems, different kinds of viscosities are usually used. In the present article, we discuss how these kinds of viscosities occur and what are relations between them. We show how material constants tensor 4C (4th rank tensor containing 81 terms) transforms strain rate tensor into viscous stresses tensor. Considering the relationship between the strain rate tensors and viscous stresses after the transition from three-dimensional to six-dimensional space and using the symmetry properties of the medium, it can be obtained that the number of independent material constants for isotropic fluids decreases to two Lamé constants. Taking into account volume expansion rate leads to volume viscosity, which is expressed with that constants. When bulk viscosity is equal to zero there is a model of Newtonian liquid, where Lamé constants become proportional to each other. Finally Navier-Stocks equations are written for different expressions of fluid viscosity.

Toward the self-consistent model of cold disk accretion

Observations of active galactic nuclei show increasing number of cases when the kinetic luminosity of jets exceeds the bolometric luminosity of disks. We develop a model of so-called cold disk accretion when the majority of the angular momentum is carried out by the wind from the disk rather than by turbulent viscous stresses. In this case the luminosity of the disk can be essentially suppressed and kinetic-to-bolometric luminosity ratio can be consistent with the observations. The method of self-consistent numerical solution of the problem of the outflow and disk accretion is proposed in this work. In this problem the angular momentum carried out by the wind is equal to the angular momentum loss by the Keplerian disk with specified accretion mass rate. Thus, the problem of the wind outflow is consistent with the disk accretion. Example of self-consistent solution of the problem by this method is presented.

Interface Analysis of a Combined Electroosmotic/Pressure Driven Flow of Three Viscoelastic Immiscible Fluids in a Microchannel

This paper presents the analytical solution of a combined electroosmotic/pressure driven flow of three viscoelastic immiscible fluids in a parallel flat plate microchannel. The mathematical model is based in the Poisson-Boltzmann equation and Cauchy momentum conservation equation. In the steady state analysis, we consider that the three fluids are electric conductors and obey to the simplified Phan-Thien-Tanner rheological model; therefore, different conditions at the interface between the fluids as electric slip, surface charge density and electro-viscous stresses balance are discussed in detail. Results show the transport phenomena coupled in the description of the velocity profiles, by the analyzing of the dimensionless parameters obtained, such as: the electric slips, the electric permittivities ratios, the surface charge densities, the zeta potentials at the walls, the interfaces positions, the viscosity ratios, the viscoelastic and electrokinetic parameters, and the term involving the external pressure gradient. Here, the presence of a net electric charges balance at the interface, breaks the continuity of shear viscous stresses, modifying the flow field; hence, for the established electric conditions at the interface through the values of the electric slips and the surface charge densities, play a role like a switch on the flow behavior. This investigation extends the knowledge about the techniques on the control of immiscible non-Newtonian fluids in microescale.