Measurement of Near-Bed Velocity and Bottom Shear Stress by Ferrofluids
In physical modelling of hydraulic processes, the knowledge of wall shear stress is fundamental to evaluate the energy dissipation of the flow and to assess the flow interaction with the bottom. Furthermore, the interaction between flow and solid walls influences to a great extent the characteristic of the flow itself. For such reasons measurements of wall shear stresses are extremely important.
In the past, several instruments have been developed and used to measure the shear stresses generated at the bottom in the presence of waves and currents.
Simple instruments, such as Preston tubes and Stanton tubes, have been used to measure bed shear stresses . Advantages of such instruments are the robustness. However, because their application is restricted to flows where the normal law of the wall is valid, they are affected by several limits as, for example, the tube dimensions must be smaller than wall layer and the difference between total (dynamic+static) and static pressure must be large.
Nowadays, velocity measurements are often carried out using system based on the acoustic and optic methodologies, such as ADV (Acoustic Doppler Velocimetry), LDA (Laser Doppler Anemometry), PIV (Particle image velocimetry) and PTV (Particle tracking Velocimetry). Some application of such instruments can be found in    end . Bottom shear stresses are derived from such instruments adopting theoretical approaches (e.g. log-fit, momentum integral method, etc). The advantage of such instruments is their reliability. However, such instruments have the following disadvantages: both acoustic and optical techniques cannot measure very close to the bottom, either due to the size of the sampling volume of the acoustic probe or to undesired reflection and disturbances from the bottom itself; the use of optical instruments is limited in large flumes; and measurements with such instruments are extremely difficult in the presence of sediments. Furthermore, for example at the bottom of sea waves, the velocity profiles are not logarithmic which is an underlying assumption of some instrument.
Direct measurements of bed shear stresses can be performed also by means of flush-mounted shear plates, which integrate the force over a relatively large area    . The system allows to resolve shear stress of O(1 mNm−2). However, one of the main problems while using shear plates is the tradeoff between sensor spatial resolution and the sensor capability to measure small forces.
Another class of instruments is the one of thermal sensors, to which hot film anemometers belong  . The system allows to measure turbulent fluctuations. Unfortunately, besides the well-known fragility of the sensors, hot film techniques are traditionally limited by difficulties in obtaining a unique calibration relationship between heat transfer and wall shear-stresses, from the reduction in sensitivity and complications in the dynamic response due to frequency-dependent conductive heat transfer into the substrate, and by measurement errors associated with mean temperature drift.
To overcome some of the above mentioned limits, recent studies     demonstrated the possibility to use ferrofluids sensors to measure near-bed velocity. Another promising method has been presented recently by  using sensor films with arrays of flexible micro-pillars sensing the wall shear stress by their bending in the flow. Ferrofluids sensors can be applied in the presence of sandy bottoms, over which state-of-the-art-instruments usually fail, and are characterized by a high robustness and a low cost.
- M. R. Head and I. Rechenberg, “The Preston tube as a means of measuring skin friction,” J. Fluid Mech., vol. 14, no. 1, pp. 1–17, 1962.
- D. T. Cox, N. Kobayashi, and A. Okayasu, “Bottom shear stress in the surf zone,” J. Geophys. Res. Ocean., vol. 101, no. C6, pp. 14337–14348, 1996.
- W. N. Smith, P. Atsavapranee, J. Katz, and T. Osborn, “PIV measurements in the bottom boundary layer of the coastal ocean,” Exp. Fluids, vol. 33, no. 6, pp. 962–971, 2002.
- R. E. Musumeci, L. Cavallaro, E. Foti, P. Scandura, and P. Blondeaux, “Waves plus currents crossing at a right angle: Experimental investigation,” J. Geophys. Res. Ocean., vol. 111, no. C7, 2006.
- S.-J. Lee and H.-B. Kim, “Laboratory measurements of velocity and turbulence field behind porous fences,” J. Wind Eng. Ind. Aerodyn., vol. 80, no. 3, pp. 311–326, 1999.
- M. P. Barnes and T. E. Baldock, “Direct bed shear stress measurements in laboratory swash,” in Journal of Coastal Research, 2007, vol. 50, no. Special issue, pp. 641–645.
- K. L. Rankin and R. I. Hires, “Laboratory measurement of bottom shear stress on a movable bed,” J. Geophys. Res. Ocean., vol. 105, no. C7, pp. 17011–17019, 2000.
- Z. You, B. Yin, and G. Huo, “Direct Measurement of Wave-Induced Bottom Shear Stress Under Irregular Waves,” in Advances in Water Resources and Hydraulic Engineering, Springer, 2009, pp. 1213–1218.
- B. M. Sumer, M. M. Arnskov, N. Christiansen, and F. E. Jørgensen, “Two-component hot-film probe for measurements of wall shear stress,” Exp. Fluids, vol. 15, no. 6, pp. 380–384, 1993.
- G. Gust, “Skin friction probes for field applications,” J. Geophys. Res. Ocean., vol. 93, no. C11, pp. 14121–14132, 1988.
- B. Andò, S. Baglio, V. Marletta, E. Foti, and R. E. Musumeci, “Measurement of bottom velocities and shear stresses by ferrofluids at the sea bottom,” in Instrumentation and Measurement Technology Conference (I2MTC) Proceedings, 2014 IEEE International, 2014, pp. 728–731.
- R. E. Musumeci, V. MARLETTA, A. Bruno, S. BAGLIO, and F. Enrico, “Ferrofluid measurements of bottom velocities and shear stresses,” J. Hydrodyn. Ser. B, vol. 27, no. 1, pp. 150–158, 2015.
- R. E. Musumeci, V. Marletta, B. Andò, S. Baglio, and E. Foti, “Measurement of wave near-bed velocity and bottom shear stress by ferrofluids,” IEEE Trans. Instrum. Meas., vol. 64, no. 5, pp. 1224–1231, 2015.
- R. E. Musumeci, V. Marletta, A. Sanchez-Arcilla, and E. Foti, “A ferrofluid-based sensor to measure bottom shear stresses under currents and waves,” J. Hydraul. Res., pp. 1–18, 2018.
- C. Brücker, J. Spatz, and W. Schröder, “Feasability study of wall shear stress imaging using microstructured surfaces with flexible micropillars,” Exp. Fluids, vol. 39, no. 2, pp. 464–474, 2005.
- S. Odenbach, “Ferrofluids: Magnetically Controllable Fluids and Their Applications,” Appl. Rheol., vol. 14, no. 4, p. 179, 2004.
- M. D. Cowley and R. E. Rosensweig, “The interfacial stability of a ferromagnetic fluid,” J. Fluid Mech., vol. 30, no. 4, pp. 671–688, 1967.
- B. Andò, S. Baglio, C. Trigona, and C. Faraci, “Ferrofluids for a novel approach to the measurement of velocity profiles and shear stresses in boundary layers,” in Sensors, 2009 IEEE, 2009, pp. 1069–1071.