# Feasibility of Optical Flow Field Measurements of the Coolant in a Grinding Machine
### State of the Art  
A general approach to investigate liquid jet shapes is shadowgraphy imaging [9], which is based on the influence of light refraction by the observed object (e.g., MWF jet) on a homogeneous background illumination. The difference in the refractive index numbers of the two phases (air and liquid) in the flow generally leads to a deflection of light at their interface. Inhomogeneities in the surface of the liquid become visible, as the evenly distributed illuminating light gets deflected differently, leading to the observation of areas with lower or higher light intensity [10; 11]. The resulting camera image of the illuminated flow is called a shadowgram. Exemplarily, a shadowgram from the present study is shown in Figure 1, depicting the investigated MWF supply flow qualitatively. The image contains the entire MWF supply flow from the jet-generating nozzle to the interaction of the fluid with the rotating grinding wheel and beyond. Shadowgram-based flow investigations have already been conducted in a grinding machine. For example, [PERSON] et al. [12] visualised the qualitative MWF inflow field for different nozzles and volume flows but did not derive quantitative flow field information. A quantitative velocity field measurement based on visualised turbulent structures in air flows was reported by [PERSON] et al. [13] and improved by [PERSON] et al. [14]. Turbulent structures were used as natural flow tracers and evaluated regarding their movement during a defined period of time. For this measurement approach, the term shadowgram image velocimetry (SIV) is used here, which means tracking characteristic flow structures that are visualised with a shadowgram. However, it has to be examined if the visualisation in a grinding machine is sufficient for a quantitative velocity measurement of the MWF flow. Furthermore, it has to be checked if the correlation of the shadowgram reflects the actual MWF flow velocity. Therefore, a comparative measurement is necessary for the MWF supply flow. As an alternative to SIV, different flow velocity measurement techniques such as Doppler-based methods or in particular the particle image velocimetry (PIV) can be taken into account. Although Doppler techniques seem to be more robust against light refractions [15], PIV is preferred here due to its less specific laser requirements. With PIV, a 2d velocity flow field is obtained by seeding the fluid with tracer particles and observing their motion with one camera. The measurement plane is defined by a light sheet illumination obtained with a double-pulse laser. Particles in the measuring plane are illuminated by the double pulse and the defined time gap between the pulses enables the determination of particle position changes (by means of cross-correlating interrogation windows in the image pairs) as well as a corresponding velocity measurement [16]. The impact of light deflection on the PIV measurement in two-phase flows depends on the surface geometry of the phase transition. For stationary liquid-air phase transitions, the systematic measurement error can be corrected by ray-tracing and mapping algorithms [17; 18]. Consequently, PIV measurements in laminar two-phase flows are feasible in principle. However, the jet flow in the grinding machine typically has a randomly  
Figure 1: Edited shadowgram image of the MWF flow hitting a rotating grinding wheel without workpiece. The liquid gets projected as a continuous free jet onto the grinding wheel until the liquid-surface interaction divides the liquid into droplets. fluctuating liquid-air phase due to the inflow conditions with velocities up to 60 m/s. This leads to an increase of disturbances in the light paths of illumination and observation, resulting in an increased measurement uncertainty [19]. For PIV measurements in fluctuating refractive index fields in air, the systematic measurement error has been determined and partially corrected [20; 21].