Prandtls Boundary Layer

Ludwig Prandtl's Boundary Layer

In 1904 a little-.known physicist revolutionized fluid dynamics with his notion that the effects of friction are experienced only very near an object moving through a fluid. John D. Anderson Jr.
uring the week of 8 August 1904, a small group of mathematicians and scientists gathered in picturesque Heidelberg, Germany, known for its baroque architecture,cobblestone streets, and castle ruins that looked as if they were still protecting the old city. Home to Germany's oldest university, which was founded in 1386, Heidelberg was a natural venue for the Third International Mathematics Congress. One of the presenters at the congress was Ludwig Prandtl, a 29-year-old professor at the Technische Hochschule (equivalent to a US technical university) in Hanover.Prandtl's presentation was only 10 minutes long, but that was all the time needed to describe a new concept that would revolutionize the understanding and analysis of fluid dynamics. His presentation, and the subsequent paper that was published in the congress's proceedings one year later, introduced the concept of the boundary layer in a fluid flow over a surface. In 2005, concurrent with theWorld Year of Physics celebration of, among other things, Albert Einstein and his famous papers of 1905, we should also celebrate the 100th anniversary of Prandtl's seminal paper. The modern world of aerodynamics and fluid dynamics is still dominated by Prandtl's idea. By every right, his boundary-layer concept was worthy of the Nobel Prize. He never received it, however; some say the Nobel Committeewas reluctant to award the prize for accomplishments in classical physics. tions of Daniel Bernoulli (1700-82), Jean le Rond d'Alembert (1717-83), and Leonhard Euler (1707-83)-all well-known heavy hitters in classical physics. Of the three, Euler was the most instrumental in conceptualizing the mathematical description of a fluid flow. He described flow in terms of spatially varyingthreedimensional pressure and velocity fields and modeled the flow as a continuous collection of infinitesimally small fluid elements. By applying the basic principIes of mass conservation and Newton's second law, Euler obtained two coupled, nonlinear partial differential equations involving the flow fields of pressure and velocity. Although those Euler equations were an intellectual breakthrough intheoretical fluid dynamics, obtaining general solutions of them was quite another matter. Moreover, Euler did not account for the effect of friction acting on the motion of the fluid elements-that is, he ignored viscosity. It was another hundred years before the Euler equations were modified to account for the effect of internal friction within a flow field. The resulting equations, a system of even moreelaborate nonlinear partial differential equations now called the NavierStokes equations, were first derived by Claude-Louis Navier in 1822, and then independently derived by George Stokes in 1845. To this day, those equations are the gold standard in the mathematical description of a fluid flow, and no one has yet obtained a . general analytical solution of them. The inability to solve theNavier-Stokes equations for most practical flow problems was particularly frustrating to those investigators interested in calculating the frictional shear force on a surface immersed in a flow. This difficulty became acute at the beginning of the 20th century, with the invention of the first practical airplane by Orville and Wilbur Wright and with the subsequent need to calculate the lift and drag onairplanes. Consider the flow over the airfoil-shaped body sketched in figure 1. The fluid exerts a net force-the net aerodynamic force-on the airfoil. The figure shows the two sources of that force: the fluid pressure and the shear stress that results from friction between the surface and the flow.1 The pressure and shear-stress distributions are the two hands of Nature by which she grabs hold of...