Dual-plane stereo particle image velocimetry (DSPIV) for measuring velocity gradient fields at intermediate and small scales of turbulent flows John A. Mullin, Werner J. A. Dahm Abstract A two-frequency dual-plane stereo particle im- age velocimetry (DSPIV) technique is described for highly resolved measurements of the complete nine-component velocity gradient tensor field ¶u i /¶x j on the quasi-universal intermediate and small scales of turbulent flows. The method is based on two simultaneous, independent stereo particle image velocimetry (PIV) measurements in two differentially spaced light sheet planes, with light sheet characterization measurements demonstrating the re- quired sheet thicknesses, separation, and two-axis paral- lelism that determine the measurement resolution and accuracy. The present approach uses an asymmetric for- ward–forward scatter configuration with two different la- ser frequencies in conjunction with filters to separate the scattered light onto the individual stereo camera pairs, allowing solid metal oxide particles to be used as seed particles to permit measurements in nonreacting as well as exothermic reacting turbulent flows. 1 Introduction Much of the experimental research in turbulence is aimed at developing models for the quasi-universal intermediate and small scales of both nonreacting and highly exother- mic reacting turbulent flows. This requires information on the structure and dynamics at these scales in various gradient fields, such as the strain rate and vorticity fields and the kinetic energy dissipation rate field, obtained from the velocity derivatives ¶u i /¶x j . Owing to the difficulty in experimentally measuring all nine simultaneous compo- nents of these velocity gradients at the intermediate and small scales of turbulent flows, these gradient fields have, to date, been studied primarily by direct numerical sim- ulations of comparatively simple turbulent flows. Experimental measurements of velocity gradients in turbulent flows originated with Batchelor and Townsend (1949), who used single-point time-series data from hot- wire measurements with Taylor’s hypothesis to approxi- mate a single component of the velocity gradient tensor. Numerous subsequent studies have developed increasingly capable multiple-wire probes to simultaneously measure several components of the velocity gradient tensor (e.g., Kovasznay 1950; Kistler 1952; Foss 1976; Antonia et al. 1998). A few studies have used probes with up to 20 hot- wires to measure all nine components of the velocity gradient tensor at a single point (Antonia et al. 1987; Brown et al. 1987; Balint et al. 1989; Tsinober et al. 1992; Kit et al. 1993). Particle image velocimetry (PIV) allows the simulta- neous nonintrusive measurement of two in-plane velocity components, here denoted u(x, y) and v(x, y). These provide four of the nine velocity gradient tensor components ¶u i /¶x j , which, in turn, give access to three of the six components of the strain rate tensor and a single vorticity component. Stereo PIV, dual-plane PIV (Raffel et al. 1998), and scanning PIV (Bru ¨ckner 1997) additionally provide the out-of-plane velocity component w(x, y) and, thereby, provide two fur- ther velocity gradient components ¶w/¶x and ¶w/¶y. How- ever, these do not give access to any additional components of either the strain rate tensor or the vorticity vector. Particle tracking velocimetry (PTV) provides three- component velocity fields throughout a three-dimensional volume (e.g., Kasagi and Nishino 1991; Malik et al. 1993). However, the comparatively low spatial resolution im- posed by the large particle separations needed to allow accurate particle tracking prevents velocity gradient mea- surements at comparatively small scales of turbulence. The most extensive velocity gradient measurements in turbu- lent flows to date have come from holographic particle image velocimetry (HPIV) (Zhang et al. 1997), though the resolution in those measurements is significantly larger than the smallest scales in the turbulent flow. Indirect measurements of ¶u i /¶x j via scalar imaging velocimetry (SIV) are based on three-dimensional laser- induced fluorescence imaging of a scalar field and inver- sion of the conserved scalar transport equation from the measured scalar field data to obtain the underlying three-component velocity field. This has allowed the first noninvasive measurements of all nine simultaneous components of the velocity gradients at the intermediate and small scales of a turbulent flow (Dahm et al. 1992; Su and Dahm 1996a, 1996b). However, the results are obtained indirectly from measured scalar field data and require additional smoothness and continuity constraints in the inversion to obtain the velocity field data. Experiments in Fluids 38 (2005) 185–196 DOI 10.1007/s00348-004-0898-8 185 Received: 18 February 2004 / Revised: 24 September 2004 Accepted: 7 October 2004 Published online: 22 December 2004 Ó Springer-Verlag 2004 J. A. Mullin, W. J. A. Dahm (&) Laboratory for Turbulence and Combustion (LTC), Department of Aerospace Engineering, The University of Michigan, Ann Arbor MI, 48109-2140, USA E-mail: wdahm@umich.edu