2 results
Dynamical similarity and universality of drop size and velocity spectra in sprays
- K. Dhivyaraja, D. Gaddes, E. Freeman, S. Tadigadapa, M. V. Panchagnula
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- Journal:
- Journal of Fluid Mechanics / Volume 860 / 10 February 2019
- Published online by Cambridge University Press:
- 07 December 2018, pp. 510-543
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Sprays are a class of multiphase flows which exhibit a wide range of drop size and velocity scales spanning several orders of magnitude. The objective of the current work is to experimentally investigate the prospect of dynamical similarity in these flows. We are also motivated to identify a choice of length and time scales which could lead towards a universal description of the drop size and velocity spectra. Towards this end, we have fabricated a cohort of geometrically similar pressure swirl atomizers using micro-electromechanical systems (MEMS) as well as additive manufacturing technology. We have characterized the dynamical characteristics of the sprays as well as the drop size and velocity spectra (in terms of probability density functions, p.d.f.s) over a wide range of Reynolds ($Re$) and Weber numbers ($We$) using high-speed imaging and phase Doppler interferometry, respectively. We show that the dimensionless Sauter mean diameter ($D_{32}$) scaled to the boundary layer thickness in the liquid sheet at the nozzle exit ($\unicode[STIX]{x1D6FF}_{o}$) exhibits self-similarity in the core region of the spray, but not in the outer zone. In addition, we show that global drop size spectra in the sprays show two distinct characteristics. The spectra from varying $Re$ and $We$ collapse onto a universal p.d.f. for drops of size $x$ where $x/\unicode[STIX]{x1D6FF}_{o}>1$. For $x/\unicode[STIX]{x1D6FF}_{o}<1$, a residual effect of $Re$ and $We$ persists in the size spectra. We explain this characteristic by the fact that the physical mechanisms that cause large drops is different from that which is responsible for the small drops. Similarly, with the liquid sheet velocity at the nozzle exit ($u_{s}$) as the choice of velocity scale, we show that drops moving with a velocity $u$ such that $u/u_{s}<1$ collapse onto a universal p.d.f., while drops with $u/u_{s}>1$ exhibit a residual effect of $Re$ and $We$. From these observations, we suggest that physically accurate models for drop size and velocity spectra should rely on piecewise descriptions of the p.d.f. rather than invoking a single mathematical form for the entire distribution. Finally, we show from a dynamical modal analysis that the conical liquid sheet flapping characteristics exhibit a sharp transition in Strouhal number ($St$) at a critical $Re$.
Fabrication of MEMS Tonpilz Transducers
- Q. F. Zhou, L.-P. Wang, G. Gerber, R. Meyer, Jr., D. Van Tol, S. Tadigadapa, W. J. Hughes, S. Trolier-McKinstry
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- Journal:
- MRS Online Proceedings Library Archive / Volume 687 / 2001
- Published online by Cambridge University Press:
- 15 March 2011, B5.22
- Print publication:
- 2001
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Tonpilz transducers consist of a heavy tail mass, a piezoelectric spring, and a light head mass. Miniaturized tonpilz transducers are potentially interesting for the 10 to100 MHz frequency range in imaging transducers due to their high efficiency and output capabilities. Piezoelectric thin films can be used as the active element in the construction of miniaturized tonpilz structures. A 4-10 νm film is necessary for the mass-spring-mass system to resonate at these high frequencies. In this work, fabrication and characterization of lead zirconate titanate (PZT) thick films on conductive oxide LaNiO3 (LNO) coated silicon on insulator (SOI) substrates will be reported for this application. First, conductive LNO thin films, approximately 300 nm in thickness, were grown on SOI substrates by a metal-organic decomposition (MOD) method. The room temperature resistivity of the LNO was 6.5×10-4 ωcm. Randomly oriented PZT (52/48) films up to 7 νm thick were then deposited using a sol-gel process on the LNO coated SOI substrates. 20 mol.% excess lead was added to the solutions to compensate for lead volatilization during film heat treatments. PZT films with LNO bottom electrodes showed good dielectric and ferroelectric properties. The dielectric permittivity (at 1 kHz) was over 1000. The remanent polarization of PZT films was larger than 26 νC/cm2. The e31,f coefficient of PZT thick films was larger than –6.5 C/m2 when poled at -75 kV/cm for 15 minutes. A silver layer approximately 40 νm thick was screen- printed onto the PZT film to form the tail mass of the tonpilz structure. Elements were diced and the bulk silicon was removed by dry and wet-etching methods to leave the p-type silicon layer as tonpilz head mass. Fabrication of MEMS tonpilz microstructures will also be presented.