# Feasibility of Optical Flow Field Measurements of the Coolant in a Grinding Machine
## 4 Measurement Results
### Flow Field with Rotating Grinding Wheel  
For the flow field measurements with the fluid-tool interaction, the MWF flow was generated with volume flows of 16.0 L/min, 26.6 L/min and 37.2 L/min with a nozzle outlet height of \(h=0.9\) mm. With SIV, a velocity field calculation of the flow before, with and after interaction is achieved based on the visualised flow structures. As a measure for the supply condition of the grinding process, the velocity ratio \(R=\frac{v_{\text{sup}}}{v_{\text{g}}}\) of the MWF supply flow \(v_{\text{sup}}\) to the circumferential velocity of the grinding wheel \(v_{\text{g}}=25\) m/s is used. Currently, a range of \(R\approx 0.8-1.0\) is assumed to be adequate for a sufficient MWF supply condition [7]. To obtain the quantitative MWF supply velocity \(v_{\text{sup}}\) from the SIV measurements, the flow structures in the homogeneous area of \(x=80\) mm to 110 mm are used (see Figure 9a). The velocity ratios \(R\) range from 0.496 to 1.04 and are listed in Table 4 together with the measured and theoretical MWF supply flow velocities. To depict the results, the calculated average velocities are plotted in Figure 9 as colour-coded vectors in the corresponding shadowgram image. To present the capabilities of SIV regarding the flow field of a grinding process, the determined flow fields are discussed qualitatively and quantitatively in relation to the MWF supply conditions. With the impact of the MWF on the grinding wheel at \(x=120\) mm, the flow splits in two parts. One part of the flow adheres to the surface of the grinding wheel and the other gets deflected. The adherent flow gets accelerated to the circumferential velocity of the grinding wheel until it loses adherence due to centripetal forces. This results in differences in velocity between the adherent and deflected flows, which can be seen in a sheared flow in the area of \(x=180\) mm to 280 mm and \(y=-20\) mm to 0 mm. An increase in the velocity field in this area is observed for the volume flows of 16.0 L/min (\(R=0.50\)) and 26.6 L/min (\(R=0.76\)). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(Q\) in L/min & **View** & \(v_{\text{sup}}\) (PIV) & \(v_{\text{sup}}\) (SIV) & \(v_{\text{sup,theo}}\) \\ \hline \multirow{3}{*}{14.9} & top & \((5.56\pm 0.20)\) m/s & & 5.40 \\  & side & \((5.54\pm 0.17)\) m/s & - & m/s \\  & rel. error & 3.1–3.6\% & & \\ \hline \multirow{3}{*}{26.6} & top & \((9.57\pm 0.33)\) m/s & \((9.62\pm 0.59)\) m/s & \\  & side & \((9.63\pm 0.33)\) m/s & \((9.33\pm 1.01)\) m/s & 9.60 \\  & rel. error & 3.6\% & 6.1–10.8\% & m/s \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Calculated and theoretical free jet velocities with standard deviations for PIV and SIV measurements of the MWF free jet. For the volume flow of \(37.2\,\mathrm{L/min}\) (\(R=1.04\)), the jet velocity is higher than the circumferential velocity of the grinding wheel, which leads to a different characteristic in the visualised flow field and its velocity field. In the region of \(x=180\,\mathrm{mm}\) to \(280\,\mathrm{mm}\) and \(y=-30\,\mathrm{mm}\) to \(-10\,\mathrm{mm}\), a droplet structure is observable, which appears to be the deflected supply flow. Despite the interaction with the grinding wheel, the MWF is largely coherent and moves with a velocity above the circumferential velocity. The investigations indicate that for a velocity ratio \(R=1.04>1\), most of the MWF gets deflected instead of entrained into the grinding process. This observation matches the fact that above a certain flow rate, no further increase in heat dissipation can be achieved [7]. A fluid dynamical change, which might describe this phenomenon, is explained by the qualitative visualisation of the flow, as well as the calculated quantitative flow field. It is noticeable that the theoretically expected velocities \(v_{\mathrm{sup,theo}}\) are significantly higher than the measured \(v_{\mathrm{sup}}\). The reason for this cannot be clearly traced back. It is assumed that the 3D-printed resin nozzle expands with respect to the volume flows.