Soap Film Channel Research Articles

The wake of a transversely oscillating circular cylinder in a flowing soap film at low Reynolds number

An inclined gravity-driven soap film channel was used to study the wake patterns formed behind a transversely oscillating cylinder at Re=235±14. The natural frequency of vortex shedding from a stationary cylinder, fSt, was used to identify the oscillation frequencies of interest. The (dimensionless) frequency, f∗=f/fSt, and amplitude, A∗=A/D, of the cylinder’s motion was varied over a large portion of the fundamental synchronization region (i.e., for f∗≈1), and a ‘map’ of wake patterns was constructed in (f∗,A∗) space. Lock-on between the frequency of the cylinder’s motion and the dominant frequency of the resulting vortex wake was observed for a large range of this parameter space, predominantly manifested as synchronized ‘2S’ and ‘2P’ wake modes. Synchronized ‘P+S’, ‘2T’, and ‘transitional’ wakes were also found in smaller regions of parameter space. Unsynchronized ‘coalescing’ and ‘perturbed von Kármán’ wakes were observed as the oscillation frequency became sufficiently different from fSt. The wake patterns and vortex formation processes found in this study, particularly the 2P mode wakes, bear a strong resemblance to previous three-dimensional experimental results, despite the physical constraint from the soap film that limits three-dimensional effects in the wake.

Separated rows structure of vortex streets behind triangular objects

We discuss two distinct spatial structures of vortex streets. The ‘conventional mushroom’ structure is commonly discussed in many experimental studies, and the exotic ‘separated rows’ structure is characterized by a thin layer of irrotational fluid between two rows of vortices. In a two-dimensional soap film channel, we generate the exotic vortex arrangement by using triangular objects. This setting allows us to vary the thickness of boundary layers and their separation distance independently. We find that the separated rows structure appears only when the boundary layer is thinner than 40 % of the separation distance. We also discuss two physical mechanisms of the breakdown of vortex structures. The conventional mushroom structure decays due to the mixing, and the separated rows structure decays because its arrangement is hydrodynamically unstable.

Surface tension of flowing soap films

The surface tension of flowing soap films is measured with respect to the film thickness and the concentration of soap solution. We perform this measurement by measuring the curvature of the nylon wires that bound the soap film channel and use the measured curvature to parametrize the relation between the surface tension and the tension of the wire. We find that the surface tension of our soap films increases when the film is relatively thin or is made of soap solution of low concentration; otherwise, it approaches an asymptotic value of $30~\text{mN}~\text{m}^{-1}$. A simple adsorption model with only two parameters describes our observations reasonably well. With our measurements, we are also able to estimate the Gibbs elasticity of our soap film.

Laser Doppler velocimetry using a modified computer mouse

A computer mouse has been modified for use as a low-cost laser Doppler interferometer and used to measure the two-component fluid velocity of a flowing soap film. The mouse sensor contains two vertical cavity surface emitting lasers, photodiodes, and signal processing hardware integrated into a single package, approximately 1 cm2 in size, and interfaces to a host computer via a standard USB port. Using the principle of self-mixing interferometry, whereby laser light re-enters the laser cavity after being scattered from a moving target, the Doppler shift and velocity of scatterers dispersed in the flow are measured. Observations of the boundary layer in a turbulent soap film channel flow demonstrate the capabilities of the sensor.

Scaling of near-wall flows in quasi-two-dimensional turbulent channels.

The law of the wall and the log law rule the near-wall mean velocity profile of three-dimensional turbulent flows. These well-known laws, which are validated by legions of experiments and simulations, may be universal. Here, using a soap-film channel, we report the first experimental test of these laws in quasi-two-dimensional turbulent channel flows under two disparate turbulent spectra. We find that despite the differences with three-dimensional flows, the laws prevail, albeit with notable distinctions: the two parameters of the log law are markedly distinct from their three-dimensional counterpart; further, one parameter (the von Kármán constant) is independent of the spectrum whereas the other (the offset of the log law) depends on the spectrum. Our results suggest that the classical theory of scaling in wall-bounded turbulence is incomplete wherein a key missing element is the link with the turbulent spectrum.

The direct enstrophy cascade of two-dimensional soap film flows

We investigate the direct enstrophy cascade of two-dimensional decaying turbulence in a flowing soap film channel. We use a coarse-graining approach that allows us to resolve the nonlinear dynamics and scale-coupling simultaneously in space and in scale. From our data, we verify an exact relation due to Eyink [“Local energy flux and the refined similarity hypothesis,” J. Stat. Phys. 78, 335–351 (1995); Eyink “Exact results on scaling exponents in the 2D enstrophy cascade,” Phys. Rev. Lett. 74, 3800–3803 (1995)] between traditional 3rd-order structure function and the enstrophy flux obtained by coarse-graining. We also present experimental evidence that enstrophy cascades to smaller (larger) scales with a 60% (40%) probability, in support of theoretical predictions by Merilees and Warn [“On energy and enstrophy exchanges in two-dimensional non-divergent flow,” J. Fluid Mech. 69, 625–630 (1975)] which appear to be valid in our flow owing to the ergodic nature of turbulence. We conjecture that their kinematic arguments break down in quasi-laminar 2D flows. We find some support for these ideas by using an Eulerian coherent structure identification technique, which allows us to determine the effect of flow topology on the enstrophy cascade. A key finding is that “centers” are inefficient at transferring enstrophy between scales, in contrast to “saddle” regions which transfer enstrophy to small scales with high efficiency.

Testing a Missing Spectral Link in Turbulence

Although the cardinal attribute of turbulence is the velocity fluctuations, these fluctuations have been ignored in theories of the frictional drag of turbulent flows. Our goal is to test a new theory that links the frictional drag to the spectral exponent α, a property of the velocity fluctuations in a flow. We use a soap-film channel wherein for the first time the value of α can be switched between 3 and 5/3, the two theoretically possible values in soap-film flows. To induce turbulence with α = 5/3, we make one of the edges of the soap-film channel serrated. Remarkably, the new theory of the frictional drag holds in both soap-film flows (for either value of the spectral exponent α) and ordinary pipe flows (where α = 5/3), even though these types of flow are governed by different equations.

Measurement of pressure distribution from PIV experiments

In this study, a non-staggered grid SIMPLER pressure solution algorithm, which is able to produce correct pressure distribution directly if correct velocities are given, is proposed to solve the pressure distribution for PIV experiments. The cell face pseudo velocity required in the pressure equation is approximated by a simple linear average of the adjacent nodal pseudo velocities so that the velocity and pressure are collocated without causing the checkerboard pressure distribution problem. In addition, the proposed pressure solution algorithm has the features that upwind effects of the convective terms are considered, boundary conditions are not required, and the pressure distribution obtained can be used to correct the velocity field so that the continuity equation is satisfied. These features make the present algorithm a superior method to calculate the pressure distribution for PIV experiments. The pressure field solved is realistic and accurate. The proposed pressure equation solver is first calibrated with a two-dimensional cavity flow. It is found that the results are almost identical to the exact solution of the test flow. The algorithm is then applied to analyze a uniform flow past two side-by-side circular cylinders in a soap film channel. With the velocity and pressure distributions successfully measured, the structures of the complex shedding flow patterns are clearly manifested.

Universal wake structures of Kármán vortex streets in two-dimensional flows

Formation of Kármán vortex streets by circular rods is studied in a flowing soap film channel. The two-dimensional fluid flow in the film allows stable vortex streets to be generated and studied over a broad range of Reynolds numbers, 10<Re<2000. There have been many studies of the Kármán vortex streets. The current study focuses on the universal feature of the near-wake structures generated by circular cylinders in a uniform two-dimensional (2D) flow. The new approach in the investigation is to decompose the street into a series of vortex couples, which defines the outer envelope of the wake, and to study the expansion rate of these couples. Our experiment shows that motion of vortex couples are powered by bursts of transverse jets, and the jet intensity determines the asymptotic width and the expansion rate of the wake. A simple model is constructed that not only allows us to extract the kinetic energy encapsulated in the vortices but also explains the universal appearance of the 2D laminar wakes generated by large and small rods. To the best of our knowledge, this is the first time that the efficiency of energy injected into vortices is estimated and this efficiency turns out to be ∼5%.

Soap film flows: Statistics of two-dimensional turbulence

Soap film flows provide a very convenient laboratory model for studies of two-dimensional (2-D) hydrodynamics including turbulence. For a gravity-driven soap film channel with a grid of equally spaced cylinders inserted in the flow, we have measured the simultaneous velocity and thickness fields in the irregular flow downstream from the cylinders. The velocity field is determined by a modified digital particle image velocimetry method and the thickness from the light scattered by the particles in the film. From these measurements, we compute the decay of mean energy, enstrophy, and thickness fluctuations with downstream distance, and the structure functions of velocity, vorticity, thickness fluctuation, and vorticity flux. From these quantities we determine the microscale Reynolds number of the flow Rλ≈100 and the integral and dissipation scales of 2D turbulence. We also obtain quantitative measures of the degree to which our flow can be considered incompressible and isotropic as a function of downstream distance. We find coarsening of characteristic spatial scales, qualitative correspondence of the decay of energy and enstrophy with the Batchelor model, scaling of energy in k space consistent with the k−3 spectrum of the Kraichnan–Batchelor enstrophy-scaling picture, and power-law scalings of the structure functions of velocity, vorticity, vorticity flux, and thickness. These results are compared with models of 2-D turbulence and with numerical simulations.

Experiments with Turbulent Soap Films.

A vertical soap film channel driven by gravity is used to study two-dimensional turbulence. Velocity differences on different scales and the spectrum of velocity fluctuations show behavior very different from their three-dimensional counterparts. Our findings are consistent with the theoretically predicted enstrophy cascade picture for two-dimensional turbulence. However, significant differences were observed.