REYNOLDS NUMBER

Thermofluids module Reynolds Number

Thermofluids module Reynolds Number

Introduction

As an object moves through the atmosphere, the gas molecules of the atmosphere near the object are disturbed and move around the object. Aerodynamic forces are generated between the gas and the object. The magnitude of these forces depend on the shape of the object, the speed of the object, the mass of the gas going by the object and on two other important properties of the gas; the viscosity, or stickiness, of the gas and the compressibility, or springiness, of the gas. To properly model these effects, aerodynamicists use similarity parameters which are ratios of these effects to other forces present in the problem (Zagarola, 1996, 15-18). If two experiments have the same values for the similarity parameters, then the relative importance of the forces are being correctly modeled. Representative values for the properties of air are given on another page, but the actual value of the parameter depends on the state of the gas and on the altitude.

Discussion

Aerodynamic forces depend in a complex way on the viscosity of the gas. As an object moves through a gas, the gas molecules stick to the surface. This creates a layer of air near the surface, called a boundary layer, which, in effect, changes the shape of the object. The flow of gas reacts to the edge of the boundary layer as if it was the physical surface of the object (Zagarola, 1996, 15-18). To make things more confusing, the boundary layer may separate from the body and create an effective shape much different from the physical shape. And to make it even more confusing, the flow conditions in and near the boundary layer are often unsteady (changing in time). The boundary layer is very important in determining the drag of an object. To determine and predict these conditions, aerodynamicists rely on wind tunnel testing and very sophisticated computer analysis.

History and Origin of Reynolds Number

In 1908, Arnold Sommerfeldp resented a paper on hydrodynamics tability at the 4th International Congress of Mathematicians in Rome (Sommerfeld 1908). In the equation known today as the Orr-Sommerfeld equation, he introduced a number R as "R is a pure number; we will call it the Reynolds number." The terminology introduced by Sommerfeld has not changed ever since, and the use of the expression "Reynolds number" has spread into all branches of fluid mechanics. Actually Sommerfeld's work is not foremost in one's mind when one thinks of the direct continuation of the ideas set forth by Osborne Reynolds in 1883 (Reynolds 1883). This is probably the reason that Sommerfeld's use of the expression "Reynolds number" was generally forgotten before von Kfirmfin (1954) drew attention to it in his book Aerodynamics. Selected Topics in the Light of Their Historical Development. He referred there to work by Sommerfeld from the year 1908 but did not mention the title and the place of publication. Von Kfirmfin returned to this subject in his paper published in the Albert Betz anniversary issue of the Zeitschriftfiir ...