High Reynolds number turbulence in small apparatus

Liquid helium at 4.2 K has a viscosity that is about 40 times smaller than that of water at room temperature, and about 600 times smaller than that of air at atmospheric pressure. It is therefore a convenient fluid for generating in a table-top apparatus turbulent flows at high Reynolds numbers that would otherwise require large air and water facilities. In this thesis, we take advantage of the low kinematic viscosity of liquid helium ν ≈ 2.5 × 10−4 cm2 s−1 and liquid nitrogen ν ≈ 1.8 × 10−3 cm2s −1 to generate high-Reynolds number turbulence behind towed grids in a square channel 5 cm on the side at mesh Reynolds numbers up to 7 × 105 in liquid helium and about 2 × 10 4 in liquid nitrogen. In both instances, we map two-dimensional fields of velocity vectors using particle image velocimetry (PIV), and compare the data with those in water and air.; When high Reynolds numbers are produced in a small apparatus, the smallest turbulent scales become correspondingly smaller. Resolving these scales proved difficult for two reasons, both principally related to finding appropriate tracer particles. First, the low kinematic viscosity and low density of liquid helium required that the particle density nearly match that of liquid helium as to prevent the particle from rapidly settling out of the liquid (smallness alone produces added complications). This required using hollow glass spheres that are about 1 μm in diameter. Second, in PIV it is required that about 10 particles be present per interrogation area (smallest scale resolved in PIV) and that the particle population be less than about 10−5 . This means that to resolve length scales micron in size (which is typically the smallest turbulent length scales generated) requires using tracer particles that are submicron in size. The inability to resolve the smallest scales provided the major source of noise in the measurements. We correct for the noise by comparing the measured second-order structure function to well-established results.; We measure the temporal decay of the mean-squared velocity fluctuation, the growth rate of the longitudinal integral length-scale L, the temporal development of the Taylor microscale λ and the normalized turbulent dissipation rate ε L/u′3 , where ε is the dissipation rate and u ′ is the rms velocity fluctuation. We compare these results to those obtained in air and water and show that towed grid turbulence in liquid helium and liquid nitrogen is very similar to towed grid and wind tunnel generated turbulence in water and air. This work demonstrates that detailed spatial measurements of turbulence can be made in cryogenic helium for turbulence studies, and provides strong evidence that helium turbulence indeed obeys Navier-Stokes equations. We believe that the work of this thesis enhances the likelihood of making major advances in understanding turbulence phenomena.