Magnus effekten undersøgt ved dimensionsanalyse og empiri: Investigation of the Magnus effect using dimensional analysis and empirical measurements

Cathrine Christiansen, Jonatan Køhler, Lars Arildskov Sørensen & Mikkel Topsøe

Studenteropgave: Semesterprojekt

Abstrakt

This project investigates the deflective force observed on a spinning sphere moving through a liquid. This force is due to the Magnus effect and is given as: F_M=½πC_M ρr^2 v^2. Many attempts has previously been made to describe the Magnus coefficient, C_M, however, none have reached a clear and general description. This project investigates the behavior of C_M theoretically by dimensional analysis and empirically by wind tunnel experiments. C_M is deterimed to be a function of the Reynolds number, Re, and the spinparameter, S, by use of dimensional analysis. A number of relations between C_M and the relative velocity between the sphere and liquid, v, the characteristic length of the sphere, r, and Re respectively is hypothesized. A specially designed experimental set-up was used to measure the Magnus effect directly on a spinning sphere. Measurements in the range of 1-16 m⁄s of windspeed, 0,0146-0,0273 m of sphere radii and 30-145 Hz of rotational speed were carried out. It is shown from the experimental results, that C_M depends on v, however, vaguely. Furthermore, it is shown that F_M depends linearly of v^n where n is a number between 1 and 2, corresponding to a linear dependence of v^m on C_M where m is a number between 0 and -1. It could not be determined whether C_M was dependent on r due to limitations in the experimental set-up. It appeared that C_M is independent on Re and thus dependent on S and implicitly r. However, by further analysis of the results, it is shown that C_M is vaguely dependent on Re for Re

UddannelserFysik, (Bachelor/kandidatuddannelse) Bachelor el. kandidat
SprogDansk
Udgivelsesdato16 jan. 2015
VejledereJens Højgaard Jensen

Emneord

  • Magnus effekt
  • Dimensionsanalyse