scholarly journals Why the Coriolis force turns a wind farm wake clockwise in the Northern Hemisphere

2016 ◽  
Author(s):  
Maarten Paul van der Laan ◽  
Niels Nørmark Sørensen
Keyword(s):  
Coriolis Force ◽  
Turbulent Mixing ◽  
Wind Farm ◽  
Flow Direction ◽  
Cross Flow ◽  
Momentum Balance ◽  
Navier Stokes ◽  
Strong Wind ◽  
High Roughness ◽  
Turbine Wake

Abstract. The interaction between the Coriolis force and a wind farm wake is investigated by Reynolds-Averaged Navier-Stokes simulations, using two different wind farm representations: a high roughness and alternatively by 5 × 5 actuator disks. Surprisingly, the calculated wind farm wake deflection is opposite in the two simulations. A momentum balance in the cross flow direction shows that the interaction between the Coriolis force and the 5 × 5 actuator disks is complex due to turbulent mixing of veered momentum from above into the wind farm, which is not observed for the interaction between the Coriolis force and a roughness change. An additional simulation of a single actuator disk, operating in a shallow atmospheric boundary layer, confirms that the Coriolis force indirectly turns a wind turbine wake clockwise, as observed from above, due to the presence of a strong wind veer.

scholarly journals Why the Coriolis force turns a wind farm wake clockwise in the Northern Hemisphere

2017 ◽  
Vol 2 (1) ◽  
pp. 285-294 ◽  
Author(s):  
Maarten Paul van der Laan ◽  
Niels Nørmark Sørensen
Keyword(s):  
Coriolis Force ◽  
Turbulent Mixing ◽  
Wind Farm ◽  
Flow Direction ◽  
Cross Flow ◽  
Momentum Balance ◽  
Navier Stokes ◽  
Strong Wind ◽  
High Roughness ◽  
Turbine Wake

Abstract. The interaction between the Coriolis force and a wind farm wake is investigated by Reynolds-averaged Navier–Stokes simulations, using two different wind farm representations: a high roughness and 5 × 5 actuator disks. Surprisingly, the calculated wind farm wake deflection is the opposite in the two simulations. A momentum balance in the cross flow direction shows that the interaction between the Coriolis force and the 5 × 5 actuator disks is complex due to turbulent mixing of veered momentum from above into the wind farm, which is not observed for the interaction between the Coriolis force and a roughness change. When the wind farm simulations are performed with a horizontally constant Coriolis force in order to isolate the effect of the wind veer, the wind farm wake deflection of the 5 × 5 actuator disks simulation remains unchanged. This proves that the present wind veer deflects the wind farm wake and not the local changes in the Coriolis force in the wake deficit region. An additional simulation of a single actuator disk, operating in a shallow atmospheric boundary layer, confirms that the Coriolis force indirectly turns a wind turbine wake clockwise, as observed from above, due to the presence of a strong wind veer.

Numerical investigation of vortex-induced vibration of an elastically mounted circular cylinder with One-degree of freedom at high Reynolds number using different turbulent models

2018 ◽  
Vol 233 (2) ◽  
pp. 443-453 ◽  
Author(s):  
Niaz Bahadur Khan ◽  
Zainah Ibrahim
Keyword(s):  
Reynolds Number ◽  
Flow Direction ◽  
Cross Flow ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Detached Eddy Simulation ◽  
Eddy Simulation ◽  
Flow Around Cylinder ◽  
Reynolds Averaged Navier Stokes ◽  
Turbulent Models

This study presents numerical investigation for flow around cylinder at Reynolds number = 104 using different turbulent models. Numerical simulations have been conducted for fixed cylinder case at Reynolds number = 104 and for cylinder free to oscillate in cross-flow direction, at Reynolds number O (104), mass–damping ratio = 0.011 and range of frequency ratio wt = 0.4–1.4 using two-dimensional Reynolds-averaged Navier–Stokes equations. In the literature, the study has been conducted using detached eddy simulation, large eddy simulation and direct numerical simulation which are comparatively expensive in terms of computational cost. This study utilizes the Reynolds-averaged Navier–Stokes shear stress transport k-ω and realizable k-ε models to investigate the flow around fixed cylinder and flow around cylinder constrained to oscillate in cross-flow direction only. Hydrodynamic coefficients, vortex mode shape and maximum amplitude ( Ay/ D) extracted from this study are compared with detached eddy simulation, large eddy simulation and direct numerical simulation results. Results obtained using two-dimensional Reynolds-averaged Navier–Stokes shear stress transport k-ω model are encouraging, while realizable k-ε model is unable to capture the entire response branches. In addition, broad range of “lock-in” region is observed due to delay in capturing the transition from upper to lower branch during two-dimensional realizable k-ε analyses.

Thermally Developing 3D Cross Flow Between Cross Corrugated Parallel Plates in Evaporative Coolers

2010 ◽  
Author(s):  
Ehsan Tavakoli ◽  
Reza Hosseini
Keyword(s):  
Pressure Drop ◽  
Flow Direction ◽  
Cross Flow ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Main Emphasis ◽  
Saturation Efficiency ◽  
Finite Difference Discretization ◽  
Corrugated Plates ◽  
Energy Equations

The 3D cross flow between parallel corrugated plates with perpendicular directions of corrugation is numerically modeled as a laminar, incompressible, steady flow. The present work tries to investigate the thermally developing characteristics of the flow in this type of geometry, in the case of constant temperature on walls. The main emphasis is on introducing correlations for saturation efficiency and simply modeling the evaporation process within evaporative coolers with such geometries. The applied numerical method is the Chorin’s artificial incompressibility method and finite difference discretization is used to model the Navier-Stokes and energy equations in a structured mesh. The results show that saturation efficiency decreases with increase in Reynolds number. This also depends on the depth of evaporative media along the flow direction. Increasing the number of waves along the flow direction, results higher saturation efficiencies and also more pressure drop. For a specific saturation efficiency, the overall pressure drop decreases at higher amplitude to wavelength ratios. Also the overall pressure drop grows as the depth of the domain increases. The same trend is observed for experimental data of commercial evaporative pads.

Vortex-Induced Vibration of Two Side-by-Side Cylinders With a Small Gap in Uniform Flow

2017 ◽  
Author(s):  
Adnan Munir ◽  
Ming Zhao ◽  
Helen Wu
Keyword(s):  
Stokes Equations ◽  
Flow Direction ◽  
Three Dimensional ◽  
Cross Flow ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Gap Ratio ◽  
Vortex Induced Vibrations ◽  
Lock In

Vortex-induced vibrations of two elastically mounted and rigidly coupled circular cylinders in side-by-side arrangement in steady flow are investigated numerically. The vibration of the cylinders is limited to the cross-flow direction only. The three-dimensional Navier-Stokes equations are solved using the Petrov-Galerkin Finite element method and the equation of motion is solved using the fourth order Runge Kutta method. It is well known that when the gap between two stationary side-by-side cylinders is very small, the flow between the two cylinders is biased towards one cylinder and the lift force on each cylinder is significantly smaller than that of an isolated single cylinder. The aim of this study is to investigate the effect of a small gap ratio of 0.5 between the two cylinders on the lock-in regime and the amplitude of the vibration of two side-by-side cylinders in a fluid flow. Simulations are carried out for a constant mass ratio of 2, a constant Reynolds number of 1000 and a range of reduced velocities. It is found that in the lock-in range of the reduced velocity, the two cylinders vibrate about their balance position with high amplitudes. Outside the lock-in regime the flow from the gap becomes biased towards one cylinder, which is similar to that from the gap between stationary cylinders.

Numerical Investigation of Vortex-Induced Vibration (VIV) of a Circular Cylinder in Oscillatory Flow

2011 ◽  
Author(s):  
Ming Zhao ◽  
Liang Cheng ◽  
Tongming Zhou
Keyword(s):  
Circular Cylinder ◽  
Oscillatory Flow ◽  
Stokes Equations ◽  
Flow Direction ◽  
Cross Flow ◽  
Frequency Component ◽  
Degree Of Freedom ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Vortex Induced Vibration

Vortex-induced vibration (VIV) of a circular cylinder in oscillatory flow is investigated numerically in this study. The incompressible Reynolds-Averaged Navier-Stokes equations governing fluid flow around a circular cylinder are solved using Arbitrary Langrangian-Eulerian (ALE) scheme and Petrov-Galerkin finite element method. The equation of motion is solved for the displacements of the cylinder both in the inline and cross-flow directions. The numerical model is firstly validated against the experimental results of one-degree-of-freedom VIV in cross-flow direction. It is found that both VIV frequency and amplitude vary with reduced velocity for a fixed KC number. In most of the simulated cases the vibration comprises of multiple frequencies of different amplitudes. Each frequency component is multiple times of the frequency of the oscillatory flow. Two-degree-of-freedom VIV is investigated with the same parameters used in the one-degree-of-freedom case. By examining the XY-trajectory of the vibration, it if found that the vibration follows different trajectory for different KC numbers or reduced velocities.

scholarly journals Advanced Constitutive Modeling of the Thixotropic Elasto-Visco-Plastic Behavior of Blood: Steady-State Blood Flow in Microtubes

Materials ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 367
Author(s):  
Konstantinos Giannokostas ◽  
Yannis Dimakopoulos ◽  
Andreas Anayiotos ◽  
John Tsamopoulos
Keyword(s):  
Blood Flow ◽  
Steady State ◽  
Constitutive Model ◽  
Blood Plasma ◽  
Constitutive Modeling ◽  
Flow Direction ◽  
Momentum Balance ◽  
Plastic Behavior ◽  
Flow Investigation ◽  
The Impact

The present work focuses on the in-silico investigation of the steady-state blood flow in straight microtubes, incorporating advanced constitutive modeling for human blood and blood plasma. The blood constitutive model accounts for the interplay between thixotropy and elasto-visco-plasticity via a scalar variable that describes the level of the local blood structure at any instance. The constitutive model is enhanced by the non-Newtonian modeling of the plasma phase, which features bulk viscoelasticity. Incorporating microcirculation phenomena such as the cell-free layer (CFL) formation or the Fåhraeus and the Fåhraeus-Lindqvist effects is an indispensable part of the blood flow investigation. The coupling between them and the momentum balance is achieved through correlations based on experimental observations. Notably, we propose a new simplified form for the dependence of the apparent viscosity on the hematocrit that predicts the CFL thickness correctly. Our investigation focuses on the impact of the microtube diameter and the pressure-gradient on velocity profiles, normal and shear viscoelastic stresses, and thixotropic properties. We demonstrate the microstructural configuration of blood in steady-state conditions, revealing that blood is highly aggregated in narrow tubes, promoting a flat velocity profile. Additionally, the proper accounting of the CFL thickness shows that for narrow microtubes, the reduction of discharged hematocrit is significant, which in some cases is up to 70%. At high pressure-gradients, the plasmatic proteins in both regions are extended in the flow direction, developing large axial normal stresses, which are more significant in the core region. We also provide normal stress predictions at both the blood/plasma interface (INS) and the tube wall (WNS), which are difficult to measure experimentally. Both decrease with the tube radius; however, they exhibit significant differences in magnitude and type of variation. INS varies linearly from 4.5 to 2 Pa, while WNS exhibits an exponential decrease taking values from 50 mPa to zero.

Exact Navier-Stokes Solutions Including Swirl and Cross Flow

1967 ◽  
Vol 10 (7) ◽  
pp. 1438 ◽  
Author(s):  
Sheldon Weinbaum
Keyword(s):  
Cross Flow ◽  
Navier Stokes

Computed Effects of Rotor-Induced Swirl on Brush Seal Performance—Part 2: Bristle Force Analysis

1996 ◽  
Vol 118 (4) ◽  
pp. 920-926 ◽  
Author(s):  
M. C. Sharatchandra ◽  
D. L. Rhode
Keyword(s):  
Inclination Angle ◽  
Flow Direction ◽  
Flow Simulation ◽  
Companion Paper ◽  
Navier Stokes ◽  
Brush Seal ◽  
Swirl Flows ◽  
Lift Off ◽  
Square Configuration ◽  
Periodic Module

This paper analytically investigates the aerodynamic bristle force distributions in brush seals used in aircraft gas turbine engines. These forces are responsible for the onset of bristle tip lift-off from the rotor surface which significantly affects brush seal performance. In order to provide an enhanced understanding of the mechanisms governing the bristle force distributions, a full Navier-Stokes flow simulation is performed in a streamwise periodic module of bristles corresponding to the staggered square configuration. As is the case with a companion paper (Sharatchandra and Rhode, 1996), this study has the novel feature of considering the combined effects of axial (leakage) and tangential (swirl) flows. Specifically, the effects of intra-bristle spacing and bristle inclination angle are explored. The results indicate that the lifting bristle force increases with reduced intra-bristle spacing and increased inclination angle. It was also observed that increases in the axial or tangential flow rates increased the force component in the normal as well as the flow direction.

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