In PIV particle image blur is usually observed near fluid optical interfaces, i.e. shock waves, and thin flow structure with large density variations, e.g. shear layers and boundary layers. In such an environment the particle image is not only subject to blur, but is also displaced from its actual position due to refraction, which is denoted as optical displacement. In this study particle image blur near a shock wave is investigated in relation to the auto- and cross-correlation map, measurement accuracy and confidence level. The results from a numerical study are supported by PIV measurements of
a shock wave in a supersonic wind tunnel. It is demonstrated that particle images are blurred in the direction of lower refractive index (directional blurring). The particle images are also skewed. Therefore particle image blur not only causes correlation peak broadening due to the fact that the particle images increase in size, but more importantly can introduce an asymmetry in the correlation peak and in turn introduce a small bias error in the measured velocity. However, experimental results indicate that particle image blur itself is not the main cause for the increase in measurement uncertainty near shock waves, but that the reduced accuracy can be attributed to the optical displacement. The observation of particle image blur can be used as a detection criterion for a qualitative assessment of the optical displacement. Certain combinations of experimental parameters (viewing angle, f/# and interrogation window size) yield significant errors in the measured velocity. Under certain circumstances optical distortion can become so strong to
introduce an unphysical acceleration within the shock wave, visualized as an inflection point with positive slope in the velocity profile across the shock. The study provides some practical suggestions to limit the effect of aero-optical distortion on the velocity measurement.
In compressible flows particle imaging, as done in Particle Image Velocimetry (PIV), is far from trivial. The inhomogeneous refractive index field can cause aero-optical aberrations including blurring of the image, especially near optical interfaces such as shock waves. The understanding of the process causing particle image blur (or blurring of the point spread function of the imaging system) is important in order to assess the measurement accuracy of optical measurement systems, such as PIV. A model for imaging through a shock wave is presented to determine the characteristic shape of blurred particle images when imaged across shock waves. The conjectured model is validated through a PIV experiment, where particle image recordings of the flow across a steady oblique shock wave are obtained in a supersonic wind tunnel. The parametric study focuses on two dominating parameters: 1) the angle between the viewing axis and the shock wave; 2) the numerical aperture of the imaging optics.
This paper describes a quantitative schlieren technique called Calibrated Color Schlieren (CCS) that is capable of measuring the light deflection angle in both spatial directions simultaneously and hence is able to extract the projected density gradient of a two-dimensional flow. CCS makes use of a graded color filter in combination with a square source of size whose size may be varied to change the sensitivity. A calibration polynomial is used to obtain the deflection angle from color ratios at each pixel. The technique’s performance was assessed in terms of repeatability, sensitivity and accuracy using the Prandtl-Meyer expansion fan at the wedge-plate shoulder in a supersonic flow. From the measured deflection angles the density gradient and the density are computed. The density information agrees well with Prandtl-Meyer theory. The technique is also applied to a more complex wake flow, which required the use of a color correction based on a shadowgraph image.