The photo-physical process governing the operation of a PSP is outlined here. A typical PSP is composed of a luminescent molecule and a polymer binder which must be permeable to oxygen. The molecule is excited by the absorption of a photon. From the excited state the molecule has several competing relaxation paths. The path of interest for PSP involves a forbidden transition to an excited triplet state from which the molecule may simply emit a photon. However, if there is oxygen present the molecule may interact with the oxygen transmitting its energy into a vibrational mode of the oxygen.
This radiationless deactivation, known as oxygen quenching, results in a system where the luminescent intensity from the molecule is a function of the partial pressure of oxygen to which the molecule is exposed. At this point, we have a luminescent paint that is sensitive to the partial pressure of oxygen. The goal is to build an image based pressure measurement system using this paint.
First the surface is coated with the paint using a standard paint gun or airbrush. Typically, surfaces are painted with 20-40 micron thick layers.
Next, the painted surface is illuminated with a light source of the appropriate wavelength to excite the luminescent molecule in the paint.
The surface is imaged through a long pass filter using a scientific grade CCD camera. The filter separates the illumination from the red shifted emission of the luminescent molecule. The luminescent intensity distribution is recorded and stored for conversion to pressure using a previously determined calibration.
Unfortunately the luminescent intensity distribution is not only a function of the partial pressure of oxygen. In fact the luminescence from the painted surface varies with illumination intensity, paint layer thickness, and probe distribution.
If we assume that these parameters don't vary in time however, they can be eliminated by taking the ratio of the image at the test condition or wind-on image to an image taken at a known reference condition or wind-off image. This wind-off to wind-on ratio is often referred to as radiometric PSP.
To determine the intensity versus pressure relationship, a sample of the PSP is placed in a calibration chamber. The sample is exposed to a series of temperatures and pressures and the luminescent intensity of the sample is recorded at each condition. Each intensity is normalized by the intensity at a reference condition and plotted versus pressure. A plot of the calibration of PtTFPP in FIB is shown here. This plot reveals one of the issues of concern for PSP measurements; PSP is sensitive to temperature as well as pressure. This as well as several other sources of error in PSP measurements are addressed using more advanced PSP systems such as Binary PSP or Lifetime PSP, however, Radiometric PSP can provide effective PSP measurements in well controlled experiments.
An example of the utility of PSP is shown in this Figure. Here, a jet is impinging onto a flat surface at an inclined angle. While this is a simple experimental setup, the resulting flow-field can produce a complex series of shock and expansion waves on the impingement surface if the jet is operated in the sonic under-expanded regime. In this under-expanded regime, slight changes in the jet pressure ratio can have a dramatic effect on the magnitude and location of these waves. It would be impractical, and intrusive, to pressure tap the impingement surface. PSP however, can easily be applied to this problem and produce data with the spatial resolution necessary to resolve the pressure field. Examples of the pressure field on the impingement surface are shown in the following Figure. All of this data was acquired in a short time, using a single painted impingement plate.
Originally, PSP systems were operated in the Radiometric wind-off/wind-on mode. These systems demonstrated promising results in lab and bench-top testing. As the systems were evaluated in wind tunnels however, significant disagreement between PSP and pressure taps was discovered. In an effort to identify the source of these errors, Liu modeled the PSP system mathematically and investigated sources of uncertainty for pressure-sensitive paint measurements. A functional relationship between the system components was developed by Liu and the elemental error sources and their sensitivity coefficients in the error propagation were evaluated. These error sources include temperature, illumination, model displacement and deformation, sedimentation, photo-degradation, and camera shot noise. Many of these errors can be minimized in lab testing, for example the inclined impinging jet, but this is not the case in the wind tunnel. Liu’s analysis identified temperature and illumination as the major sources of error for PSP measurements. A brief description of the origin of each error is given here. This will be followed by a description of the Lifetime and Binary PSP systems that are commonly used today to mitigate these errors.
For radiometric PSP, errors in pressure measurements due to temperature are largely the result of changes in the temperature of the model surface between the acquisition of the wind-off and wind-on image. Any temperature gradient on the model surface however, will result in a temperature-induced error in the pressure measurements. These temperature gradients can be the result of model construction, tunnel operation, or fluid dynamics. A rapid prototype model, for example, is constructed using an internal metal structure and a polymer resin. The thermal signature of the internal structure is apparent when the surface of the model is subjected to a heat flux. The model is exposed to a heat flux due to changes in tunnel Mach number for example, this condition is most apparent during tunnel startup, or in any blow-down tunnel.
A PSP experiment was performed in the Ohio State University 22-inch blow-down tunnel which demonstrates several of the temperature issues that must be addressed in wind tunnel testing. Here, the ratio between a pre-run wind-off image and a post-run wind-off image was computed. This tunnel exhausts to atmosphere so the static pressure for each wind-off should be equal to atmospheric pressure and the intensity ratio should be 1. There are two issues that are apparent in the image. First the intensity ratio has increased by 1% between the beginning and the end of a 30-second run. This 1% change would represent an increase in atmospheric pressure of about 6-kPa (0.8-psia) during this interval.
In reality, the model surface cooled down during the run and the 1% increase in signal is the result of temperature sensitivity of the paint. The second issue is the streaks near the leading edge of the airfoil. These streaks are the result of boundary layer transition near the leading edge. The heat transfer coefficient for a turbulent boundary layer is about 5X than that of a laminar boundary layer. In fact, Temperature Sensitive Paint is often used to identify transition in blow-down tunnels.
Even after the model has reached thermal equilibrium the temperature distribution on the model is not necessarily uniform. One example of a temperature gradient generated by the external flow is boundary layer transition. In this case, one must consider the recovery temperature defined above. The recovery factor (r in the above equation) in a laminar boundary layer is 0.81 as opposed to a turbulent boundary layer where it is 0.89. This change in recovery factor will result in a temperature rise of about 1 degree C at Mach 0.5, at Mach 1, this number is closer to 3.5 C. A temperature step at the transition location of this magnitude would appear as a pressure rise of 650-Pa (for the Mach 0.5 case) to 2,250-Pa (for the Mach 1 case) assuming the PSP was UniFIB.
Another example of a flow induced temperature gradient is a shock, which is non-isentropic. The total temperature across a shock is constant, but the velocity is not, and therefore, the static temperature will rise. This rise in static temperature could be several degrees C, and the result will be an apparent change in pressure of a few kPa.
A demonstration of flow-induced temperature gradients is given here. A sonic under-expanded jet impinges on a flat plate at an inclined angel. Measurements of pressure are conducted using PSP and the Adiabatic wall temperature is measured using TSP. The pressure and adiabatic wall temperature distribution along the major axis is plotted in the figure. First note the large temperature dip in the wall jet region, just downstream of the impingement zone of the jet. One would expect the pressure to be relatively flat in this region, in fact, the PSP indicates that the static pressure is below ambient. This false low pressure is a result of the 3-4 degree drop in adiabatic wall temperature in this region, the low temperature appears as low pressure. A more careful experimental setup could be used to minimize this error. A second temperature induced effect is seen in the impingement zone where a series of shocks and expansions are interacting with the surface. Note the way the adiabatic wall temperature is in phase with these shocks and expansions, indicating that these fluid structures do have an impact on model temperature. It is good experimental procedure to minimize these temperature errors by using isothermal models (thick highly conductive materials) and allowing the system (model and tunnel) to reach thermal equilibrium if possible.
The relationship between surface illumination and paint luminescence is linear; and therefore, any change in surface illumination will result in an equal change in paint luminescence. Errors in pressure measurements caused by variations in surface illumination can stem from several sources. Consider utilizing a point source for the illumination of a surface in the Figure. The relationship between illumination intensity at a point on the surface and the distance between the source and the point of interest are an inverse function of the distance squared. Any movement of the painted surface or illumination source will result in a change in the distance between these two points, and thus a change in the illumination intensity at the surface. This movement can result from deformation of the model surface, or physical displacement of the model or illumination source. Another source of illumination errors is the temporal stability of the illumination source. This issue is largely resolved by using well designed LED’s as illumination sources. Any variation of the intensity of the illumination source between the wind-off and wind-on images will register as an error in illumination.
An example of model displacement is shown here using a cylinder in cross flow. The cylinder was painted with Binary FIB and placed in a low speed wind tunnel. The camera and LED were mounted on the building floor, independent of the tunnel. Wind-off and wind-on data was acquired and processed in two ways. First the data was process using only the signal (pressure sensitive) channel. While the result appears reasonable, a careful examination of the data suggests an error as the Cp range is +/- 1.5. The LED was not fixed to the tunnel, and therefore, at wind-on there was some slight movement between the LED and tunnel/model. This demonstrates the impact that minor movement of the model can have on PSP results.