H. W. Liepmann

Control of laminar-instability waves using a new technique

A new technique using surface-film activators has been developed to induce and control laminar-instability waves by periodic heating. A flat plate was instrumented and installed in the GALCIT High-speed Water Tunnel with flush-mounted surface heaters and probes. Extremely two-dimensional naturally occurring Tolmien-Schlichting (TS) waves were observed along with the subsequent formation of turbulent spots. Laminar-instability waves were then excited in a controlled fashion using the surface-mounted heaters. A preliminary experiment on cancellation of excited laminar-instability waves was carried out. Finally, turbulent spots were produced using amplitude-modulated bursts to form Gaussian TS wave packets. Flow visualization, along with wall shear measurements, was used to infer the velocity and vorticity field near the wall.

Active control of laminar-turbulent transition

Instability waves, commonly called T-S waves, can be introduced in a laminar boundary layer by periodic heating of flush-mounted heating elements. Experiments have demonstrated that nearly complete cancellation of a T-S wave excited in this way can be achieved by using a second downstream heating element with a suitable phase shift. As one application of the technique, a single element together with a feedback loop activated by measured wall shear stress has been used to reduce the amplitude of naturally occurring laminar instability waves. A significant increase in the transition Reynolds number has been achieved.

Structure of a Plane Shock Layer

The structure of a plane shock wave is discussed and the expected range of applicability of the Navier‐Stokes equations within the shock layer is outlined. The shock profiles are computed using the Bhatnagar‐Gross‐Krook model of the Boltzmann equation and a uniformly converging iteration scheme starting from the Navier‐Stokes solution. It is shown that the Navier‐Stokes solution remains a good approximation in the high‐pressure region of the shock layer up to approximately the point of maximum stress for all shock strengths. In the low‐pressure region, the correct profiles deviate with increasing shock strength from the Navier‐Stokes solution. The physical significance of the kinetic model used and the relation of the present study to previous theoretical and experimental work is discussed.

Gaskinetics and gasdynamics of orifice flow

The paper gives the result of a study on the efflux of gases through circular apertures. The problem is considered as an example of a transition from the gasdynamic to the gaskinetic regime.The mass flow of helium, argon and nitrogen was measured for a range of upstream pressures corresponding to (mean free path)/(aperture diameter) from about 50 to 5 × 10−3; within this range the transition from molecular effusion to inviscid, transonic flow takes place. The theory for the two asymptotic limits is discussed and first-order corrections to the free molecular and inviscid limit formulae are given.

Aspects of the turbulence problem

Die Arbeit gibt einen Uberblick uber einige Probleme der neueren Turbulenzforschung. Nach einer allgemeinen Einleitung werden zuerst elementare, fur die Turbulenztheorie wichtige Resultate der Theorie homogener, stochastischer Vorgange diskutiert. Im dritten Teil werden sodann Beispiele linearer Systeme behandelt, bei denen die ausseren Krafte von turbulenten Schwankungen herruhren. Im vierten Teil werden turbulente Transportphanomene gestreift, und im funften Teil wird ein kurzer Uberblick uber Resultate und Fragen der Theorie der isotropen Turbulenz gegeben.

Turbulence Management and Relaminarisation

The last two decades have witnessed an intensifying effort in learning how to manage flow turbulence: it has in fact now become one of the most challenging and prized technological goals in fluid dynamics. The goal itself is of course not new. More than a hundred years ago, Reynolds already listed factors conducive to laminar and to turbulent flow (including among them curvature and acceleration). Furthermore, it is in retrospect clear that there were several early instances of successful turbulence management. Examples are the reduction in drag achieved with a ring-trip placed on the front of a sphere or the insertion of a splitter-plate behind a circular cylinder; by the early 1950s there were numerous exercises at boundary layer control. Although many of these studies were interesting and suggestive, they led to no spectacularly successful practical application, and the effort petered out in the late 1950s.

A simple derivation of Lighthill's heat transfer formula

In the following it will be shown that a simple argument based on the use of the energy integral equation of the laminar boundary layer permits the derivation of a heat transfer formula valid for non-uniform temperature distribution and non-zero pressure gradients. The formula is then shown to be identical in structure with Lighthills (1950) well-known results. Lighthill obtained his formula by solving the boundary layer equations in the von Mises form using operational methods. An elegant way to obtain the same results using exact similarity consideration was given by Lagerstrom (not yet published). The derivation given here is probably the most simple-minded one and the method may be useful for other applications as well. Furthermore, it is shown that the approach can be slightly modified to permit application of the formula to flow near separation. The latter result is applied to the Falkner-Skan solution for just separating flows and is found to be in excellent agreement with the exact solutions.

Local Boiling and Cavitation in Heat‐Induced Counterflow of He II

Local boiling, cavitation, and cavitation collapse have been observed in the heat induced counter‐flow of He II in a convergent‐divergent nozzle. These observations are described and shown to be qualitatively and quantitatively in agreement with the two fluid equations supplemented by the Gorter‐Mellink force.

Shape of shock fronts in shock tubes.

Shock front shape perturbations due to boundary layer effects and shock tube and piston imperfections

Theoretical and experimental aspects of the shock structure problem

There does not yet exist a general, reliable theory of the flow of rarefied gases, bridging the gap between simple free molecular flow methods and the Navier-Stokes theory. It is clear today that an essential improvement of the range of applicability of the Navier-Stokes equations cannot be expected from the higher approximations in the Chapman-Enskog procedure but that different methods of finding approximate solutions of the Boltzmann equation are needed. The shock wave structure problem is one of the best test cases for such attempts because it is realistic, amenable to experimentation, and simple enough to expect that in the future an exact solution of the Boltzmann equation can be obtained.