Showing papers on "Incompressible flow published in 2019"

Solution Properties of a 3D Stochastic Euler Fluid Equation

Abstract: We prove local well-posedness in regular spaces and a Beale–Kato–Majda blow-up criterion for a recently derived stochastic model of the 3D Euler fluid equation for incompressible flow. This model describes incompressible fluid motions whose Lagrangian particle paths follow a stochastic process with cylindrical noise and also satisfy Newton’s second law in every Lagrangian domain.

Droplets in homogeneous shear turbulence

Abstract: We simulate the flow of two immiscible and incompressible fluids separated by an interface in a homogeneous turbulent shear flow at a shear Reynolds number equal to 15 200. The viscosity and density of the two fluids are equal, and various surface tensions and initial droplet diameters are considered in the present study. We show that the two-phase flow reaches a statistically stationary turbulent state sustained by a non-zero mean turbulent production rate due to the presence of the mean shear. Compared to single-phase flow, we find that the resulting steady-state conditions exhibit reduced Taylor-microscale Reynolds numbers owing to the presence of the dispersed phase, which acts as a sink of turbulent kinetic energy for the carrier fluid. At steady state, the mean power of surface tension is zero and the turbulent production rate is in balance with the turbulent dissipation rate, with their values being larger than in the reference single-phase case. The interface modifies the energy spectrum by introducing energy at small scales, with the difference from the single-phase case reducing as the Weber number increases. This is caused by both the number of droplets in the domain and the total surface area increasing monotonically with the Weber number. This reflects also in the droplet size distribution, which changes with the Weber number, with the peak of the distribution moving to smaller sizes as the Weber number increases. We show that the Hinze estimate for the maximum droplet size, obtained considering break-up in homogeneous isotropic turbulence, provides an excellent estimate notwithstanding the action of significant coalescence and the presence of a mean shear.

Flow physics and dynamics of flow-induced pitch oscillations of an airfoil

Abstract: We conduct a computational study of flow-induced pitch oscillations of a rigid airfoil at a chord-based Reynolds number of 1000. A sharp-interface immersed boundary method is used to simulate two-dimensional incompressible flow, and this is coupled with the equations for a rigid foil supported at the elastic axis with a linear torsional spring. We explore the effect of spring stiffness, equilibrium angle-of-attack and elastic-axis location on the onset of flutter, and the analysis of the simulation data provides insights into the time scales and mechanisms that drive the onset and dynamics of flutter. The dynamics of this configuration includes complex phenomena such as bifurcations, non-monotonic saturation amplitudes, hysteresis and non-stationary limit-cycle oscillations. We show the utility of ‘maps’ of energy exchange between the flow and the airfoil system, as a way to understand, and even predict, this complex behaviour.

History and Progress of Boundary-Layer Transition on a Mach-6 Flared Cone

Abstract: Results from experimental, theoretical, and computational efforts are combined in a comprehensive review to summarize the improved understanding of the underlying physical mechanisms causing second...

On high-order pressure-robust space discretisations, their advantages for incompressible high Reynolds number generalised Beltrami flows and beyond

Abstract: An improved understanding of the divergence-free constraint for the incompressible Navier--Stokes equations leads to the observation that a semi-norm and corresponding equivalence classes of forces are fundamental for their nonlinear dynamics. The recent concept of {\em pressure-robustness} allows to distinguish between space discretisations that discretise these equivalence classes appropriately or not. This contribution compares the accuracy of pressure-robust and non-pressure-robust space discretisations for transient high Reynolds number flows, starting from the observation that in generalised Beltrami flows the nonlinear convection term is balanced by a strong pressure gradient. Then, pressure-robust methods are shown to outperform comparable non-pressure-robust space discretisations. Indeed, pressure-robust methods of formal order $k$ are comparably accurate than non-pressure-robust methods of formal order $2k$ on coarse meshes. Investigating the material derivative of incompressible Euler flows, it is conjectured that strong pressure gradients are typical for non-trivial high Reynolds number flows. Connections to vortex-dominated flows are established. Thus, pressure-robustness appears to be a prerequisite for accurate incompressible flow solvers at high Reynolds numbers. The arguments are supported by numerical analysis and numerical experiments.

Heat transport features of magnetic water–graphene oxide nanofluid flow with thermal radiation: Stability Test

Abstract: This paper documents the incompressible hydro-magnetic flow and heat transfer analysis of water–Graphene oxide (GO) nanofluid. More exactly, the nanofluid flow occurs along a thin needle moving axially. Despite the fact that there seems to be various works on the subject in the existing literature, however, very few studies have been carried out to investigate the dual numerical solution for such flow. Consequently, the inspiration here is to look for dual numerical solutions for such a non-linear phenomenon along with the stability analysis of computed solutions. The governing coupled equations representing the mathematical formulation of the current physical problem were obtained from the equation of motion and the mass and the energy conservations by taking steady and incompressible flow. The numerical solution of governing set of simultaneous ordinary differential equations is computed with the assistance of Matlab solver bvp4c. This research aimed at revealing the conceivable impacts of existing fluid interaction parameters on non-dimensional velocity and temperature distributions. These computations exhibits that more than one solution is possible only in case of flow over shrinking needle for certain combinations of the parameters. The result shows that the skin friction coefficient increases in both solutions with higher nanoparticles volume fraction. Furthermore, an enhancement in local Nusselt number is noted as the thermal radiation parameter increases.

Turbulent Micropolar SPH Fluids with Foam

Abstract: In this paper we introduce a novel micropolar material model for the simulation of turbulent inviscid fluids. The governing equations are solved by using the concept of Smoothed Particle Hydrodynamics (SPH). As already investigated in previous works, SPH fluid simulations suffer from numerical diffusion which leads to a lower vorticity, a loss in turbulent details and finally in less realistic results. To solve this problem we propose a micropolar fluid model. The micropolar fluid model is a generalization of the classical Navier-Stokes equations, which are typically used in computer graphics to simulate fluids. In contrast to the classical Navier-Stokes model, micropolar fluids have a microstructure and therefore consider the rotational motion of fluid particles. In addition to the linear velocity field these fluids also have a field of microrotation which represents existing vortices and provides a source for new ones. However, classical micropolar materials are viscous and the translational and the rotational motion are coupled in a dissipative way. Since our goal is to simulate turbulent fluids, we introduce a novel modified micropolar material for inviscid fluids with a non-dissipative coupling. Our model can generate realistic turbulences, is linear and angular momentum conserving, can be easily integrated in existing SPH simulation methods and its computational overhead is negligible. Another important visual feature of turbulent liquids is foam. Therefore, we present a post-processing method which considers microrotation in the foam particle generation. It works completely automatic and requires only one user-defined parameter to control the amount of foam.

Effects of Sidewalls and Leading-Edge Blowing on Flows over Long Rectangular Cavities

Abstract: The present work investigates sidewall effects on the characteristics of three-dimensional (3-D) compressible flows over a rectangular cavity with aspect ratios of L/D=6 and W/D=2 at ReD=104 using ...

Macroscopic model for unsteady flow in porous media

Abstract: The present article reports on a formal derivation of a macroscopic model for unsteady one-phase incompressible flow in rigid and periodic porous media using an upscaling technique. The derivation is carried out in the time domain in the general situation where inertia may have a significant impact. The resulting model is non-local in time and involves two effective coefficients in the macroscopic filtration law, namely a dynamic apparent permeability tensor, H t , and a vector, α, accounting for the time-decaying influence of the flow initial condition. This model generalizes previous non-local macroscale models restricted to creeping flow conditions. Ancillary closure problems are provided, which allow computing the effective coefficients. Symmetry and positiveness analyses of H t are carried out, evidencing that this tensor is symmetric only in the creeping regime. The effective coefficients are functions of time, geometry, macroscopic forcings and the initial flow condition. This is illustrated through numerical solutions of the closure problems. Predictions are made on a simple periodic structure for a wide range of Reynolds numbers smaller than the critical value characterizing the first Hopf bifurcation. Finally, the performance of the macroscopic model for a variety of macroscopic forcing and initial conditions is examined in several case studies. Validation through comparisons with direct numerical simulations is performed. It is shown that the purely heuristic classical model, widely used for unsteady flow, consisting in a Darcy-like model complemented with an accumulation term on the filtration velocity, is inappropriate.

Large data analysis for Kolmogorov’s two-equation model of turbulence

Abstract: Kolmogorov seems to have been the first to recognize that a two-equation model of turbulence might be used as the basis of turbulent flow prediction. Nowadays, a whole hierarchy of phenomenological two-equation models of turbulence is in place. The structure of their governing equations is similar to the Navier–Stokes equations for incompressible fluids, the difference is that the viscosity is not constant but depends on two scalar quantities that measure the effect of turbulence: the average of the kinetic energy of velocity fluctuations (i.e. the turbulent energy) and the measure related to the length scales of turbulence. For these two scalar quantities two additional evolutionary convection–diffusion equations are added to the generalized Navier–Stokes system. Although Kolmogorov’s model has so far been almost unnoticed, it exhibits interesting features. First of all, in contrast to other two-equation models of turbulence, there is no source term in the equation for the frequency. Consequently, nonhomogeneous Dirichlet boundary conditions for the quantities measuring the effect of turbulence are assigned to a part of the boundary. Second, the structure of the governing equations is such that one can find an “equivalent” reformulation of the equation for turbulent energy that eliminates the presence of the energy dissipation acting as the source in the original equation for turbulent energy and which is merely an L 1 quantity. Third, the material coefficients such as the viscosity and turbulent diffusivities may degenerate, and thus the a priori control of the derivatives of the quantities involved is unclear. We establish long-time and large-data existence of a suitable weak solution to three-dimensional internal unsteady flows described by Kolmogorov’s two-equation model of turbulence. The governing system of equations is completed by initial and boundary conditions; concerning the velocity we consider generalized stick–slip boundary conditions. The fact that the admissible class of boundary conditions includes various types of slipping mechanisms on the boundary makes the result robust from the point of view of possible applications.

Direct numerical simulation of backward-facing step flow at and expansion ratio 2

Abstract: Backward-facing step (BFS) constitutes a canonical configuration to study wall-bounded flows subject to massive expansions produced by abrupt changes in geometry. Recirculation flow regions are common in this type of flow, driving the separated flow to its downstream reattachment. Consequently, strong adverse pressure gradients arise through this process, feeding flow instabilities. Therefore, both phenomena are strongly correlated as the recirculation bubble shape defines how the flow is expanded, and how the pressure rises. In an incompressible flow, this shape depends on the Reynolds value and the expansion ratio. The influence of these two variables on the bubble length is widely studied, presenting an asymptotic behaviour when both parameters are beyond a certain threshold. This is the usual operating point of many practical applications, such as in aeronautical and environmental engineering. Several numerical and experimental studies have been carried out regarding this topic. The existing simulations considering cases beyond the above-mentioned threshold have only been achieved through turbulence modelling, whereas direct numerical simulations (DNS) have been performed only at low Reynolds numbers. Hence, despite the great importance of achieving this threshold, there is a lack of reliable numerical data to assess the accuracy of turbulence models. In this context, a DNS of an incompressible flow over a BFS is presented in this paper, considering a friction Reynolds number () of 395 at the inflow and an expansion ratio 2. Finally, the elongation of the Kelvin–Helmholtz instabilities along the shear layer is also studied.

On the classification of incompressible fluids and a mathematical analysis of the equations that govern their motion

Abstract: In the first part of the paper we provide a new classification of incompressible fluids characterized by a continuous monotone relation between the velocity gradient and the Cauchy stress. The considered class includes Euler fluids, Navier-Stokes fluids, classical power-law fluids as well as stress power-law fluids, and their various generalizations including the fluids that we refer to as activated fluids, namely fluids that behave as an Euler fluid prior activation and behave as a viscous fluid once activation takes place. We also present a classification concerning boundary conditions that are viewed as the constitutive relations on the boundary. In the second part of the paper, we develop a robust mathematical theory for activated Euler fluids associated with different types of the boundary conditions ranging from no-slip to freeslip and include Navier's slip as well as stick-slip. Both steady and unsteady flows of such fluids in three-dimensional domains are analyzed.

Droplets in homogeneous shear turbulence

Abstract: We simulate the flow of two immiscible and incompressible fluids separated by an interface in a homogeneous turbulent shear flow at a shear Reynolds number equal to 15200. The viscosity and density of the two fluids are equal, and various surface tensions and initial droplet diameters are considered in the present study. We show that the two-phase flow reaches a statistically stationary turbulent state sustained by a non-zero mean turbulent production rate due to the presence of the mean shear. Compared to single-phase flow, we find that the resulting steady state conditions exhibit reduced Taylor microscale Reynolds numbers owing to the presence of the dispersed phase, which acts as a sink of turbulent kinetic energy for the carrier fluid. At steady state, the mean power of surface tension is zero and the turbulent production rate is in balance with the turbulent dissipation rate, with their values being larger than in the reference single-phase case. The interface modifies the energy spectrum by introducing energy at small-scales, with the difference from the single-phase case reducing as the Weber number increases. This is caused by both the number of droplets in the domain and the total surface area increasing monotonically with the Weber number. This reflects also in the droplets size distribution which changes with the Weber number, with the peak of the distribution moving to smaller sizes as the Weber number increases. We show that the Hinze estimate for the maximum droplet size, obtained considering breakup in homogeneous isotropic turbulence, provides an excellent estimate notwithstanding the action of significant coalescence and the presence of a mean shear.

Laminar–turbulent transition in channel flow with superhydrophobic surfaces modelled as a partial slip wall

Abstract: Superhydrophobic surfaces are capable of trapping gas pockets within the micro-roughnesses on their surfaces when submerged in a liquid, with the overall effect of lubricating the flow on top of them. These bio-inspired surfaces have proven to be capable of dramatically reducing skin friction of the overlying flow in both laminar and turbulent regimes. However, their effect in transitional conditions, in which the flow evolution strongly depends on the initial conditions, has still not been deeply investigated. In this work the influence of superhydrophobic surfaces on several scenarios of laminar–turbulent transition in channel flow is studied by means of direct numerical simulations. A single phase incompressible flow has been considered and the effect of the micro-structured superhydrophobic surfaces has been modelled imposing a slip condition with given slip length at both walls. The evolution from laminar, to transitional, to fully developed turbulent flow has been followed starting from several different initial conditions. When modal disturbances issued from linear stability analyses are used for perturbing the laminar flow, as in supercritical conditions or in the classical K-type transition scenario, superhydrophobic surfaces are able to delay or even avoid the onset of turbulence, leading to a considerable drag reduction. Whereas, when transition is triggered by non-modal mechanisms, as in the optimal or uncontrolled transition scenarios, which are currently observed in noisy environments, these surfaces are totally ineffective for controlling transition. Superhydrophobic surfaces can thus be considered effective for delaying transition only in low-noise environments, where transition is triggered mostly by modal mechanisms.