Chris J. Swanson

Friction factors for smooth pipe flow

Friction factor data from two recent pipe flow experiments are combined to provide a comprehensive picture of the friction factor variation for Reynolds numbers from 10 to 36,000,000.

Pipe flow measurements over a wide range of Reynolds numbers using liquid helium and various gases

We demonstrate that an unusually small pipe flow apparatus using both liquid helium and room temperature gases can span an enormous range of Reynolds numbers. This paper describes the construction and operation of the apparatus in some detail. A wide range of Reynolds numbers is an advantage in any experiment seeking to establish scaling laws. This experiment also adds to evidence already in hand that the normal phase of liquid helium is a Navier–Stokes fluid. Finally, we explore recent questions concerning the influence of molecular motions on the transition to turbulence (Muriel 1998) and are unable to observe any influence.

Emerging issues in helium turbulence

It has been appreciated recently that because helium has the lowest viscosity of any known material, it can be used in reaching the very highest Reynolds numbers and Rayleigh numbers. Critical helium gas, helium I and helium II are all candidates for such uses. Helium gas and helium I are classical fluids and the advantage stems solely from their low kinematic viscosity. Helium II obeys two-fluid equations and their use in turbulence investigations is under study. This article provides a brief introduction and review of this topic, outlining some of the progress already made and questions which need to be resolved as this relatively new field of investigation evolves. A summary of instrumentation available is included.

Experimental investigation of periodic flow in curved pipes

We have studied oscillatory flow through a 180° curved tube with the ratio of tube radius to radius of curvature equal to 1/7. The flow rate is constrained to vary sinusoidally about a non-zero mean at a specified period T , and mean flow rate Q . At a certain parameter range of interest Hamakiotes & Berger (1990) predict that fully developed flow undergoes a period-tripling bifurcation. Our measurements using laser-Doppler velocimetry found no bifurcation. An additional experiment was done to ensure that the flow was fully developed.

Turbulent pipe flow of He I and He II

Abstract Turbulent pipe flow of liquid 4 He has been investigated for Reynolds numbers from Re=3×10 3 to Re=3×10 6 to examine He I and He II turbulence in the presence of shear. The extremely low kinematic viscosity of liquid helium allows us to achieve high Reynolds numbers in small laboratory apparatus. Our results agree with those using classical fluids, showing the utility of helium as a fluid for turbulence research.

Onset of vorticity in a rotating annulus of helium II

We present measurements of the critical angular velocity for the onset of vorticity in a rotating annulus. The measurements of the critical velocity were made over a temperature range from 1.5 to 2.165 K, and are consistently lower than theoretical predictions by about 20%. Nor do our results agree within experimental uncertainty with previous measurements of the critical velocity in an annulus. It appears that the discrepancies can be explained by the presence and growth of high concentrations of residual vorticity which prevent the system from achieving the lowest free energy state. We find that vorticity perpendicular to the axis of rotation grows as the angular velocity is increased and that the axial mutual friction coefficientB″ is 0.

Measurement devices for cryogenic turbulence research

Recent interest in the study of turbulence using liquid and gaseous helium has prompted the need for high-quality fluid dynamical measurements in a cryogenic environment. To meet this need we have been developing two measurement tools specifically designed to operate below 10 K. The first is a high-accuracy pressure transducer capable of resolving over five orders of magnitude in pressure at both room temperature and at low temperatures. The second is a 1 MHz cryogenic thermal sensor that can be used as a hot film anemometer to measure velocity fluctuations. In this paper we report on the design features of the devices and measurement results.

Taylor–Couette flow of helium II

Abstract The wealth of experience and information available about the classical Taylor–Couette system makes it an ideal candidate for studies of the flow of helium II. In particular, the stability of Couette flow of helium II has proven to be an excellent test bed for the equations of motion. As early as 1957 Chandrasekhar and Donnelly began examining the stability of flowing helium II. Progress, however, has been slow due to the quantum ‘two-fluid’ nature of helium II. In helium II the Navier–Stokes equation is transformed into a pair of coupled non-linear equations significantly complicating any analysis. Furthermore, there has been some debate over which terms are to be included in the equations. Recent efforts by Barenghi and Jones have produced a computational linear stability program which is based upon the modern ‘HVBK’ equations. For rotation of the inner cylinder only, they have made predictions of the critical Taylor number as a function of temperature. Data from experiments performed by two different groups corroborate the computed temperature dependence putting the modern equations of motion on a firm footing. In addition to the determination of the onset of instability, studies have been made of flow beyond the instability, of flow between counter-rotating cylinders, and of high Reynolds number flow. With the inner cylinder rotating at a Reynolds number just above the instability, the flow exhibits Taylor rolls. In counter-rotating flow, the appearance of instability has been correctly computed by linear stability analysis. Finally, at high Reynolds number, flow visualization shows Taylor rolls very similar in size to classical rolls.

Quantized vortices between counter-rotating cylinders

We report the results of both experimental and theoretical studies on the stability of the flow of helium II between concentric counter-rotating cylinders. The agreement between theory and measurements confirms the validity of the HVBK equations which generalize Landaus original two fluid model to take into account the presence of quantised vortex lines and extends the dynamic range over which theory and experiments can be compared.

Instrument Development for High Reynolds Number Pipe Flow in Liquid Helium

We have developed a flowmeter and pressure transducer for use in studying turbulent pipe flow in liquid helium. The flowmeter measures the average velocity of flow in a pipe by determining the variations of the time of flight of an ultrasonic sound burst. It is capable of measuring velocities from 0.1 cm/sec to over 1 m/s without introducing any heat losses into the flow. Future developments promise to extend the accuracy and range of this flowmeter. The pressure transducer is a parallel plate capacitance manometer using a flexible plastic membrane as one of the plates. The transducer is capable of resolving pressures from 0.05 Pa up to 50 Pa using current calibrations and could be calibrated up to 500 Pa without permanently deforming the membrane. The transducer has the potential to measure both pressure differences and local velocities if used with a Pitot tube. Both of these instruments have been tested initially in a half inch diameter flow tube in which we were able to achieve a maximum Reynolds number of 1.5 million.