Numerical investigations on dynamic stall of low Reynolds number flow around oscillating airfoils

This paper presents a 2D computational investigation on the dynamic stall phenomenon associated with unsteady flow around the NACA0012 airfoil at low Reynolds number (Re_c ≈ 10⁵). Two sets of oscillating patterns with different frequencies, mean oscillating angles and amplitudes are numerically simulated using Computational Fluid Dynamics (CFD), and the results obtained are validated against the corresponding published experimental data. It is concluded that the CFD prediction captures well the vortex-shedding predominated flow structure which is experimentally obtained and the results quantitatively agree well with the experimental data, except when the blade is at a very high angle of attack.     

Large eddy simulation of pulsating flow over a circular cylinder at subcritical Reynolds number

The pulsating cross-flow over a single circular cylinder at the subcritical Reynolds number Re_D = 2580 is studied with the large eddy simulation (LES) technique using the standard Smagorinsky model as well as a dynamic model in which the test filtered quantities are evaluated through a truncated Taylor series expansion. The filtered equations are discretised using the finite volume method in an unstructured, collocated grid arrangement with a second-order accurate method, in both space and time. The predictions are compared against very detailed experiments for mean velocities and Reynolds stresses that were performed in a duct of cross-section 72 mm × 72 mm using the PIV technique. The effects of mesh refinement close to the cylinder as well as of subgrid scale model are also examined. The numerical predictions are in very good agreement with the measurements in terms of mean as well as turbulence quantities. The instantaneous flow patterns of the flow field are examined and the effect of the external flow pulsation on the wake characteristics such as vortex formation length, vortex strength, Strouhal number as well as the lift and drag coefficients is quantified. The vortex formation length is decreased while the mean drag, as well as the rms values of the drag and lift coefficients increase significantly under pulsating flow conditions. The performance of the LES technique is analysed in the light of the wake characteristics.     

Numerical investigation on the efficient mixing of overbridged split-and-recombine micromixer at low Reynolds number

It is promising to design a novel structured micromixer that can be easily processed but also exhibit high mixing efficiency as well as low pressure drop at a wide range of Reynolds numbers. The overbridged structure was introduced into the planner E-shape micromixers for the first time to construct a novel kind of bridge-street structure micromixer, in order to improve the mixing efficiency in the wide range of Reynolds number. We investigated numerically the mixing performance of six overbridged E-shape split-and-recombine micromixers via solving 3D Navier–Stokes equations and adopting species transfer model. It is indicated that at lower Reynolds number the tilted interface in the overbridged channel increases the interfacial area and improves the mass transfer efficiency, while at higher Reynolds number the overbridged channels tend to induce vortices and promote the convective diffusion. The results show that the optimal overbridged micromixer DBEM-3 has excellent mixing efficiency exceeding 95% in the range of Re = 0.5–100. The optimal structure of overbridged micromixer was studied further with different viscosity ratio and power law fluid. In addition, the pressure drop under various Reynolds number was calculated, and the pressure drop of the power law fluid was represented by Euler number to reflect the magnitude of the momentum loss rate. It is illustrated that DBEM-3 has excellent mixing efficiency in wide Reynolds number for three different fluid systems, which has promising applications in the biochemistry analysis or mixing systems.

     

Numerical simulation of flow over three circular cylinders in equilateral arrangements at low Reynolds number by a second-order characteristic-based split finite element method

In this paper, two versions of a second-order characteristic-based split scheme are developed in the framework of incremental projection method for the solution of incompressible flow problem. After the demonstration of the good accuracy and effectiveness of the developed schemes, a flow over three equal circular cylinders arranged in equilateral-triangle arrangement is numerically investigated on unstructured mesh systems. The examined Reynolds number is 100 and the flow is supposed to be laminar. Computations by the developed algorithm are then performed for six gap spacings, s, ranging from 0.5 to 4.0, and for three incidence angles, α = 0°, 30° and 60°. Numerical results show that, at sufficiently small and large s, the range of which is different for different α, the flow interference is dominated by proximity and wake effect, respectively. And in the intermediate range of the spacing, the flow pattern is influenced by both of them. The mean force results are compared with the existing experimental measurements and that shows a similar trend in the variation of mean force with the spacing for different Reynolds number. It is also observed that the interference effect transitions plays an important role in the variation of the fluctuating forces and Strouhal number.     

Efficient mixing of viscoelastic fluids in a microchannel at low Reynolds number

In this paper, we examined mixing of various two-fluid flows in a silicon/glass microchannel based on the competition of dominant forces in a flow field, namely viscous/elastic, viscous/viscous and viscous/inertial. Experiments were performed over a range of Deborah and Reynolds numbers (0.36 < De < 278, 0.005 < Re < 24.2). Fluorescent dye and microshperes were used to characterize the flow kinematics. Employing abrupt convergent/divergent channel geometry, we achieved efficient mixing of two-dissimilar viscoelastic fluids at very low Reynolds number. Enhanced mixing was achieved through elastically induced flow instability at negligible diffusion and inertial effects (i.e. enormous Peclet and Elasticity numbers). This viscoelastic mixing was achieved over a short effective mixing length and relatively fast flow velocities.     

Steady and unsteady flow past a rotating circular cylinder at low Reynolds numbers

Results of calculations of the steady and unsteady flows past a circular cylinder which is rotating with constant angular velocity and translating with constant linear velocity are presented. The motion is assumed to be two-dimensional and to be governed by the Navier-Stokes equations for incompressible fluids. For the unsteady flow, the cylinder is started impulsively from rest and it is found that for low Reynolds numbers the flow approaches a steady state after a large enough time. Detailed results are given for the development of the flow with time for Reynolds numbers 5 and 20 based on the diameter of the cylinder. For comparison purposes the corresponding steady flow problem has been solved. The calculated values of the steady-state lift, drag and moment coefficients from the two methods are found to be in good agreement. Notable, however, are the discrepancies between these results and other recent numerical solutions to the steady-state Navier-Stokes equations. Some unsteady results are also given for the higher Reynolds numbers of 60, 100 and 200. In these cases the flow does not tend to be a steady state but develops a periodic pattern of vortex shedding.     

Comparative study of finite difference approaches in simulation of magnetohydrodynamic turbulence at low magnetic Reynolds number

Two approaches to finite difference approximation of turbulent flows of electrically conducting incompressible fluids in the presence of a steady magnetic field are analyzed. One is based on high-order approximations and upwind-biased discretization of the nonlinear term. Another is consistently of the second order and nearly fully conservative in regard of mass, momentum, kinetic energy, and electric charge conservation principles. The analysis is conducted using comparison with high-accuracy spectral direct numerical simulations of channel flows with wall-normal and spanwise magnetic fields. Focus of the analysis is on the quality of finite difference approximation in the situation when the magnetic field leads to significant transformation of the flow structure. In the case of turbulent flows at moderate magnetic fields, the conservative scheme approach offers better stability and equal or higher accuracy than the approach based on the upwind discretization. The conservation property is expected to become increasingly important and even indispensable at stronger magnetic fields.     

Formation of vortices in long microcavities at low Reynolds number

Microcavities are a central feature of many microflow systems ranging from sprouting capillaries during angiogenesis to various microfluidic devices. Recently, the flow and transport phenomena in microcavities have been subject of a number of studies, yet a physical picture of the flow properties at low Reynolds number, which is the relevant regime in many biological applications, has not been fully brought out. We have therefore systematically investigated, experimentally and by modeling, the flow in a long microcavity and found that the flow properties depend decisively on the depth/width ratio of the cavity. Notably, if this cavity aspect ratio is higher than approximately 0.51, counter-flow vortices emerge in the cavity even at vanishing Reynolds number. The distance of the first vortex from the cavity entrance decreases with an increasing aspect ratio as an inverse power law. In the vortex-free regime below the threshold aspect ratio, the flow velocity decays exponentially away from the cavity entrance, with a decay length that scales with the width of the cavity and depends also on the aspect ratio of its cross section. The results of our numerical simulations are supported by a theoretical analysis and are in good agreement with experimental data, acquired by optical velocimetry with optical tweezers.     

Numerical simulation of oscillations and rotations of a free liquid droplet using the level set method

Three-dimensional oscillations and rotations of a free liquid droplet are simulated numerically using the level set method. The oscillations of order 2, 3 and 4 are simulated, and the frequency and the damping for small-amplitude oscillations are shown to agree well with those by the linear theory. Flow fields in the inside and outside of the droplet are visualized, and three-dimensional vortex structures are found to appear around the droplet. It is also found that the number of vortices is the same as the order of oscillation. The effects of initial amplitude and rotation on the oscillation frequency are studied, and it is shown that the oscillation frequency decreases as the initial amplitude increases, while it increases as the rotation rate increases. These effects are found to be overestimated by theoretical predictions.     

Variational multiscale large-eddy simulations of the flow past a circular cylinder: Reynolds number effects

Variational multiscale large-eddy simulations (VMS–LES) of the flow around a circular cylinder are carried out at different Reynolds numbers in the subcritical regime, viz. Re = 3900, 10,000 and 20,000, based on the cylinder diameter. A mixed finite-element/finite-volume discretization on unstructured grids is used. The separation between the largest and the smallest resolved scales is obtained through a variational projection operator and finite-volume cell agglomeration. The WALE subgrid scale model is used to account for the effects of the unresolved scales; in the VMS approach, it is only added to the smallest resolved ones. The capability of this methodology to accurately predict the aerodynamic forces acting on the cylinder and in capturing the flow features are evaluated for the different Reynolds numbers considered. The sensitivity of the results to different simulation parameters, viz. agglomeration level and numerical viscosity, is also investigated at Re = 20,000.     

Numerical simulation of the regularized driven cavity flows at high Reynolds numbers

We present a numerical simulation of the unsteady incompressible flows in the unit cavity as well as in the rectangular cavity of aspect ratio 2 by using a second order projection scheme in time and a Chebyshev-Tau approximation for the space variables. The time-accurate discretization and the high accuracy of the spectral methods enable us to observe dynamical features not apparent in previous studies.     

Numerical solutions of Burgers’ equation with a large Reynolds number

In this article the exact solution of Burgers’ equation represented as an infinite series is transformed into a simpler form involving the elliptic function? ₃(υ, q). To evaluate? ₃(υ, q), we use the Jacobi Imaginary Transformation. It is made clear that the solutions obtained by the proposed approach are numerically stable and precise.     

Numerical simulation of fluid oscillations in fuel tanks

Fluid oscillations (sloshing) in a closed vessel have been numerically simulated. The statement of the problem corresponds to the situations that arise in the fuel tanks of ice-breaking ships in collisions with ice barriers and movement on the waves. The results are obtained using the regularized shallow-water equations.     

Effect of the Reynolds number on streamline bifurcations in a double-lid-driven cavity with free surfaces

The two-dimensional Navier-Stokes equations for a Newtonian fluid in the absence of body forces are considered in a rectangular double-lid-driven cavity with free surface side walls, the cavity aspect ratio A and three cases of the ratio (S=0,−1,1) of the upper to the lower lid speed. Using a finite element formulation with a mesh which is adaptively refined to facilitate the location of stagnation points, the effect of Reynolds numbers (Re) in the range [0,100] on the streamline patterns and their bifurcations is investigated as A is varied for each S. For Re→0 and each S as A is decreased, a sequence of pitchfork bifurcations at a stagnation point on x=0 is identified as seen in the work of Gaskell et al. [Proc Instn Mech Engrs Sci Part C 212 (1998) 387]. As Re increases for S=0 and decreasing A the stagnation point on x=0 disappears and away from x=0 cusp (saddle-node) bifurcations arise rather than the pitchfork bifurcation whereas for S=−1 and Re∈[0,100] the origin is always a stagnation point at which the same type of bifurcations arises.     

Numerical simulation of flow-induced cavity noise in self-sustained oscillations

The generation and near-field radiation of aerodynamic sound from a low-speed unsteady flow over a two-dimensional automobile door cavity is simulated by using a source-extraction-based coupling method. In the coupling procedure, the unsteady cavity flow field is first computed solving the Reynolds- averaged Navier–Stokes (RANS) equations. The radiated sound is then calculated by using a set of acoustic perturbation equations with acoustic source terms which are extracted from the time-dependent solutions of the unsteady flow. The aerodynamic and its resulting acoustic field are computed for the Reynolds number of 53,266 based on the base length of the cavity. The free stream flow velocity is taken to be 50.9 m/s. As first stage of the numerical investigation of flow-induced cavity noise, laminar flow is assumed. The CFD solver is based on a cell-centered finite volume method. A dispersion-relation-preserving (DRP), optimized, fourth-order finite difference scheme with fully staggered-grid implementation is used in the acoustic solver.     

Numerical simulation of novel gas separation effect in microchannel with a series of oscillating barriers

A free-molecular gas flow through the microchannel with a series of oscillating microbarriers is studied. Barriers are oscillating with high frequency in the plane, perpendicular to the axis of the channel. It is shown that probability of passing through the channel for gas molecules significantly depends on relation of oscillations frequency, molecules thermal speed and distance between barriers. Presented effect can be used for separation of gases with different molecular masses due to discrepancy of their thermal speeds. The nature of this phenomenon is studied for different values of frequencies, characteristic sizes and number of barriers. Special attention is paid to comparison of different laws of gas–surface interactions.     

Numerical simulation of free surface flows on a fish bypass

A computational fluid dynamics (CFD) model is developed to better understand the complex flow field inside a free surface fish bypass constructed at Rocky Reach Dam. This facility consists of two identical parallel channels, with fish screens on the side walls of each channel, and a pump station recirculating 96% of incoming flows into the forebay. The model is based on the Reynolds-averaged Navier-Stokes (RANS) equations, with a standard κ-ε turbulence model. The volume of fluid (VOF) method is used to predict free surface elevations. A proportional controller is implemented in the model to achieve a target flow rate at the pump exits. The pressure drop in the fish screens is modeled using porous media. Quantitative validation and visualization of the flow field characteristics indicate that CFD modeling may be a useful tool for fish passage design.     

Suppression of vortex-induced vibration of a circular cylinder at subcritical Reynolds numbers using shape optimization

Structural and Multidisciplinary Optimization - In this paper, shape optimization is employed to improve the stability of the flow past an elastically mounted circular cylinder at subcritical...