# Feasibility of Optical Flow Field Measurements of the Coolant in a Grinding Machine
## 4 Measurement Results
### Verification of SIV  
To determine how the movement of the characteristic flow structures relates to the flow velocity, SIV and PIV measurements on the MWF supply flow are compared with each other and with the theoretically expected velocities \(v_{\mathrm{sup}}\). For this purpose, the flow rate of 26.6 L/min is used, which sets the MWF supply flow in a laminar to turbulent transient state. Minor characteristic flow structures are present, which allow measurements with SIV, and PIV provides plausible measurement results, since the seeding particles are still detectable. Similar to the analysis in Section 4.2, the 2d velocity fields of PIV and SIV for both views are determined. In Figure 8a the average velocity fields of PIV and SIV from the top view are shown for the range \(x=20\) mm to 120 mm. The velocity fields of both measurements are in agreement and show a homogeneous flow field around 9.5 m/s. It is noticeable that the PIV measurement indicates lower velocities at the lateral edges, which is caused by the refraction of light at the cylindrical geometry. On the other hand, the measurement with SIV in the positions \(x=20\) mm to 50 mm and \(z=0\) mm to \(-10\) mm shows a slightly lower velocity. In Figure 8b, the top view mean velocities and their standard deviations for the area without the cylindrical edge geometries (\(z=-5\) mm to 5 mm) for PIV and SIV are displayed. The velocities are well matched and have a maximum deviation of 0.1 m/s. A slight increase of the velocity in the range of \(x=20\) mm to 80 mm from 9.5 m/s to 9.75 m/s is noticeable, until the velocity remains constant. The increase of the velocity is within the measurement uncertainties caused by random measurement deviations and therefore no statements about a systematic deviation can be made. The standard deviation  
Figure 6: Calculated velocity field for the top view and the side view (**a**) and the corresponding standard deviation (**b**) for a volume flow of 14.9 L/min. Figure 7: Mean flow velocity for the top view (red) and the side view (blue) displayed with their standard deviation (STD) for a volume flow of 14.9 L/min. is almost constant for both measurements and amounts to 0.3 m/s for PIV and 0.6 m/s for SIV, respectively. The measurements for the side view of the MWF supply flow are shown in Figure 8c. The flow field of the PIV measurement is in the range of 9.8 m/s to 9.5 m/s, whereas the SIV measurement is systematically 0.3 m/s lower with velocities in the range of 9.5 m/s to 9.2 m/s. The mean velocities along the \(y\)-direction and their standard deviations are displayed in Figure 8d. Neglecting the offset of 0.3 m/s, the curves of the velocities are almost identical for both measurements, with a standard deviation of 0.3 m/s for PIV and 1.0 m/s for SIV, respectively. It is expected that the offset results from the MWF flow controller of the grinding machine. The flow has to be stopped after each measurement and the flow controller has an estimated flow standard deviation of 0.5 L/min, resulting in a velocity standard deviation of 0.18 m/s. Nevertheless, the higher standard deviation of SIV shows the limitations of the measurements based on the characteristic flow structures. The superposition of characteristic structures from different planes provides a less precise measurement with SIV but still ensures velocity measurements from the MWF supply flow with standard deviations around 10.8% in the side view. To compare the measurement conditions with respect to the feasibility of PIV and SIV, the globally averaged velocities for the MWF supply volume flows of 14.9 L/min and 26.6 L/min are listed in Table 3. The measurements with PIV have an almost constant standard deviation of 3.6%, regardless of the view or the used volume flow. The SIV measurement of the top view has a 0.3 m/s increased standard deviation of 0.6 m/s (6.1%).