**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Publication# All you need is time to generalise the Goman-Khrabrov dynamic stall model

Abstract

Dynamic stall on airfoils negatively impacts their aerodynamic performance and can lead to structural damage. Accurate prediction and modelling of the dynamic stall loads are crucial for a more robust design of wings and blades that operate under unsteady conditions susceptible to dynamic stall and for widening the range of operation of these lifting surfaces. Many dynamic stall models rely on empirical parameters that need to be obtained from experimental or numerical data which limits their generalisability. Mere, we introduce physically derived time scales to replace the empirical parameters in the Goman-Khrabrov dynamic stall model. The physics-based time constants correspond to the dynamic stall delay and the decay of post-stall load fluctuations. The dynamic stall delay is largely independent of the type of motion, the Reynolds number and the airfoil geometry, and is described as a function of a normalised instantaneous pitch rate. The post-stall decay is independent of the motion kinematics and is related to the Strouhal number of the post-stall vortex shedding. The general validity of our physics-based time constants is demonstrated using three sets of experimental dynamic stall data covering various airfoil profiles, Reynolds numbers varying from 75 000 to 1 000 000, and sinusoidal and ramp-up pitching motions. The use of physics-based time constants generalises the Goman-Khrabrov dynamic stall model and extends its range of application.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (1)

Related MOOCs (8)

Related concepts (10)

Plasma Physics: Introduction

Learn the basics of plasma, one of the fundamental states of matter, and the different types of models used to describe it, including fluid and kinetic.

Plasma Physics: Introduction

Learn the basics of plasma, one of the fundamental states of matter, and the different types of models used to describe it, including fluid and kinetic.

Plasma Physics: Applications

Learn about plasma applications from nuclear fusion powering the sun, to making integrated circuits, to generating electricity.

Strouhal number

In dimensional analysis, the Strouhal number (St, or sometimes Sr to avoid the conflict with the Stanton number) is a dimensionless number describing oscillating flow mechanisms. The parameter is named after Vincenc Strouhal, a Czech physicist who experimented in 1878 with wires experiencing vortex shedding and singing in the wind. The Strouhal number is an integral part of the fundamentals of fluid mechanics.

Airfoil

An airfoil (American English) or aerofoil (British English) is a streamlined body that is capable of generating significantly more lift than drag. Wings, sails and propeller blades are examples of airfoils. Foils of similar function designed with water as the working fluid are called hydrofoils. When oriented at a suitable angle, a solid body moving through a fluid deflects the oncoming fluid (for fixed-wing aircraft, a downward force), resulting in a force on the airfoil in the direction opposite to the deflection.

Reynolds number

In fluid mechanics, the Reynolds number (Re) is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers, flows tend to be turbulent. The turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow (eddy currents).

The presence of aerodynamic vortices is widespread in nature. They can be found at small scales near the wing tip of flying insects or at bigger scale in the form of hurricanes, cyclones or even galaxies. They are identified as coherent regions of high vorticity where the flow is locally dominated by rotation over strain. A better comprehension of vortex dynamics has a great potential to increase aerodynamic performances of moving vehicles, such as drones or autonomous underwater vehicles. An accelerated flat plate, a pitching airfoil or a jet flow ejected from a nozzle give rise to the formation of a primary vortex, followed by the shedding of smaller secondary vortices. We experimentally study the growth, timing and trajectory of primary and secondary vortices generated from a rectangular flat plate that is rotated around its centre location in a quiescent fluid. We systematically vary the rotational speed of the plate to get a chord based Reynolds number \Rey that ranges from 800 to 12000. We identify the critical \Rey for the occurrence of secondary vortices to be at 2500. The timing of the formation of the primary vortex is \Rey independent but is affected by the plate's dimensions. The circulation of the primary vortex increases with the angular position $\alpha$ of the plate, until the plate reaches 30°. Increasing the thickness and decreasing the chord lead to a longer growth of the primary vortex. Therefore, the primary vortex reaches a higher dimensionless limit strength. We define a new dimensionless time $T^*$ based on the thickness of the plate to scale the age of the primary vortex. The primary vortex stops growing when $T^* \approx 10$, regardless of the dimensions of the plate. We consider this value to be the vortex formation number of the primary vortex generated from a rotating rectangular flat plate in a Reynolds number range that goes from 800 to 12000. When $\alpha$ > 30°, the circulation released in the flow is entrained into secondary vortices for $\Rey > 2500$. The circulation of all secondary vortices is approximately 4 to 5 times smaller than the circulation of the primary vortex. We present a modified version of the Kaden spiral that accurately predicts the shear layer evolution and the trajectory of primary and secondary vortices during the entire rotation of the plate.We model the timing dynamics of secondary vortices with a power law equation that depends on two distinct parameter: $\chi$ and $\alpha_{0}$.The parameter $\chi$ indicates the relative increase in the time interval between the release of successive secondary vortices.The parameter $\alpha_{0}$ indicates the angular position at which the primary vortex stops growing and pinches-off from the plate.We also observe that the total circulation released in the flow is proportional to $\alpha^{1/3}$, as predicted by the inviscid theory.The combination of the power law equation with the total circulation computed from inviscid theory predict the strength of primary and secondary vortices, based purely on the plate's geometry and kinematics.The strength prediction is confirmed by experimental measurements.In this thesis we provided a valuable insight into the growth, timing and trajectory of primary and secondary vortices generated by a rotating flat plate. Future work should be directed towards more complex object geometries and kinematics, to confirm the validity of the modified Kaden spiral and explore the influence on the formation number.