Development of ${\rm N}_2{\rm O}$-MTV for low-speed flow and in-situ deployment to an integral effect test facility

Abstract

A molecular tagging velocity (MTV) technique is developed to non-intrusively measure velocity in an integral effect test (IET) facility simulating a high-temperature helium-cooled nuclear reactor in accident scenarios. In these scenarios, the velocities are expected to be low, on the order of 1 m/s or less, which forces special requirements on the MTV tracer selection. Nitrous oxide $({\rm N}_2{\rm O})$ is identified as a suitable seed gas to generate NO tracers capable of probing the flow over a large range of pressure, temperature, and flow velocity. The performance of ${\rm N}_2{\rm O}$-MTV is assessed in the laboratory at temperature and pressure ranging from 295 to 781 K and 1 to 3 atm. MTV signal improves with a temperature increase, but decreases with a pressure increase. Velocity precision down to 0.004 m/s is achieved with a probe time of 40 ms at ambient pressure and temperature. Measurement precision is limited by tracer diffusion, and absorption of the tag laser beam by the seed gas. Processing by cross-correlation of single-shot images with high signal-to-noise ratio reference images improves the precision by about 10% compared to traditional single-shot image correlations. The instrument is then deployed to the IET facility. Challenges associated with heat, vibrations, safety, beam delivery, and imaging are addressed in order to successfully operate this sensitive instrument in-situ. Data are presented for an isothermal depressurized conduction cooldown. Velocity profiles from MTV reveal a complex flow transient driven by buoyancy, diffusion, and instability taking place over short $(<1\, {\rm s})$ and long ($>30$ min) time scales at sub-meter per second speed. The precision of the in-situ results is estimated at 0.027, 0.0095, and 0.006 m/s for a probe time of 5, 15, and 35 ms, respectively.

Appendices

Appendix A1: MTV processing algorithm

The pair of single-shot images recorded at t and $t+\Delta t$ and shown in Fig. 14a, b have low SNR in the N₂ region, as discussed in Sect. 4.1. Cross-correlating these two single-shot images, referred to as $x_{t}$ and $x_{t + \Delta t}$, results in weak correlation peaks, producing many outliers. Furthermore, there also exists differences between the two images in term of read pulse intensity and tracer line width (due to diffusion), which are detrimental to cross-correlation.

An attempt at mitigating these effects is performed here by including time-averaged reference images in the processing, as detailed below:

• Prior to the beginning of a run, reference images are recorded at zero velocity (no flow) for the first and second read pulses, and averaged over 300 consecutive samples. These images are recorded with circulators turned off; thus, vibrations are negligible. This acquisition takes 30 s, time over which the beam drift is negligible (drift < 1 pixel/h, Sect. 4.4). Figure 14c, d shows such reference images for the first and second read pulses, respectively. This provides high SNR images of the undisplaced tracer for each read pulse, $X_0$ and $X_{\Delta t}$. This step is performed for each value of $\Delta t$ used in the experiment. Note that diffusion has visibly increased the line width between Fig. 14c, d.

• In order to reduce noise and improve the cross-correlation, each image is binned in the tag line direction using with a 160 pixel-wide window (with an overlap of $75\%$).

• Every binned row in each single-shot image is cross-correlated with its respective reference image, i.e., $X_0 \otimes x_{t}$ and $X_{\Delta t} \otimes x_{t + \Delta t}$. Such correlation performs particularly well when diffusion is important because the two correlated images are for the same probe time delay. Furthermore, it is also unaffected by difference in intensity and spatial profile between first and second read pulses.

• The width of the binning window is iteratively refined based on the unscaled cross-correlation value. For instance, a high value indicates a strong signal and well-defined tag line, enabling to decrease the binning window size and improve the spatial resolution. The binning window size is bounded between 40 and 160 pixels.

• Once the window size has converged, the correlation peak is curve fitted to a Gaussian function to extract the displacement (cross-correlation lag) to a sub-pixel level between the single-shot image and its reference location for the first and second read pulses. The corresponding lag results for the first and second pulses, $X_0 \otimes x_{t}$ and $X_{\Delta t} \otimes x_{t + \Delta t}$, are displayed in Fig. 15a, b, respectively. Note that Fig. 15a is a direct measurement of the single-shot write beam wandering with respect the initial reference location, while Fig. 15b is a measurement of the single-shot tracer displacement with respect to the initial reference location.

• The lag of $X_{\Delta t} \otimes X_0$ is negligible, even at $\Delta t=35$ ms, thus the reference location ($X_0$ or $X_{\Delta t}$) can be assumed identical for first and second read pulses. Therefore, the final tracer instantaneous displacement between the two single-shot images is obtained by taking the difference between the two displacements obtained by cross-correlation as done in Fig. 15c. This requires interpolation because data from the two images are on a different grid as a consequence of the adaptive windowing.

As a dual-pulse technique, this method still accounts for beam wandering as shown in Fig. 15a. A drawback of this method would be that in some experiments, it is not possible to record reference images at zero velocity.

Using the data of Sect. 4, and performing an estimation of the precision as done in Sect. 4.3, the improvement in precision with this method is between 5 and $15\%$ (for $\Delta t=5$ and 35 ms) compared to the usual cross-correlation of single-shot image pairs ($x_{t} \otimes x_{t + \Delta t}$). As expected, the gain is more significant at longer $\Delta t$ due to the effect of diffusion.

Fig. 14

${\rm N}_2{\rm O}$-MTV images of the first [(a),(c)] and second read pulse [(b), (d)] with $\Delta t=5$ ms. Images a, b are single-shot frames recorded during the run at $t=12.5$ s and $t=12.5+\Delta t$ s, respectively. Images c, d are time-averaged over 300 frames recorded prior to a run, at zero flow velocity. The exit of the pipe is visible to the left of the tag line on each image. Image brightness and contrast have been adjusted to show low SNR regions, while avoiding saturation of high SNR regions

Fig. 15

Main steps of the cross-correlation scheme. Single-shot tracer displacement (lag of maximum cross-correlation peak) relative to reference location for first and second read pulses (a, b), respectively. Tracer displacement between the two single-shot images is recovered by taking the difference between the relative displacements (c)

Appendix A2

The number density of ${\rm N}_2{\rm O}$ molecules dissociated in a control volume of length dL located at a distance L is obtained by combining Eqs. 2 and  3, and setting the beam energy entering the control volume to be $E_0 {\rm e}^{-\sigma n_i L}$:

$$\begin{aligned} n_{\rm d} =\frac{E_0 {\rm e}^{-\sigma n_i L}}{h \nu A dL} ( 1-{\rm e}^{-\sigma n_i dL} ) . \end{aligned}$$

(9)

The maximum value of $n_{\rm d}$ is found by solving $\partial n_{\rm d} / \partial n_i=0$ for $n_i$:

$$\begin{aligned} n_i =\frac{1}{\sigma dL} \ln \bigg ( 1+\frac{dL}{L} \bigg ), \end{aligned}$$

(10)

dL can be set arbitrarily small such as $dL \ll L$, in which case Eq. 10 becomes:

$$\begin{aligned} n_i =\frac{1}{\sigma L} \end{aligned}$$

(11)

Appendix A3

The adaptive interrogation window size algorithm refined the window size in the region of high SNR characterized by a high correlation peak. The window size for the second read pulse as a function of time and spatial location is shown in Fig. 16. The window size is larger near the top and bottom of the frame than near the center for the following reasons: image vignetting, reduced overlap of the read and write beams, larger diameter of the write pulse beam, and depth of field limited by the camera angle. The window size reaches the minimum of 40 pixels in the ${\rm N}_2{\rm O}$-rich helium stream from the hot leg pipe after $t=10$ s. After $t\sim 80$ s, the ${\rm N}_2{\rm O}$ concentration of the helium/N₂ mixture from the RPV is lower, and the window size increases to a minimum of 100 pixels for the rest of the run, with the exception of the interval where $\Delta t$ was set to 35 ms between $t=1055$ and 1095 s.

Fig. 16

Time-space color plot of the interrogation window size for the second read pulse images, indicated in pixels on the chart. Missing data are in black