## 2 Experimental Setup  
### Test Rig  
Experimental acquisitions were performed using a test rig that replicates at full scale the geometry of a single filter element in the reference industrial system. The rig operates at ambient temperature but at the same (ambient) pressure encountered in the reference system.  
Figure 1 shows the experimental rig. The supersonic nozzle is mounted at the bottom of a plenum or \"showerhead\" and faces down toward the Venturi. The Venturi sits above the throat of the filter housing.  
As shown in Figure 2, the nozzle throat has the geometry of a 4 mm diameter, 11.4 mm long tube. Upstream of that throat is a cone with a 118\({}^{\circ}\) angle opening. When a solenoidal valve is triggered, high-pressure gas from a 3.9-L reservoir is released into the showerhead, producing a supersonic jet past the nozzle. 12.7 mm (1/2 in) tubing (1 m long) connects the reservoir to the 0.85-L showerhead. The MTV seed gas, chosen as N\({}_{2}\)O, is mixed in low concentration with the compressed air in the reservoir when the reservoir is filled.  
Below the showerhead, a plastic \"seed gas injector\" built through additive manufacturing injects N\({}_{2}\)O through small holes at very low flow rates. This injection ensures that the volume surrounding the jet is also seeded. This is necessary for MTV to resolve the flow entrained and mixed by the jet. This is particularly important for measurements in the far field of the nozzle, i.e., near the Venturi entrance.  
Figure 1: Experimental setup and main components.  
The so-called Venturi is a conical converging channel followed by a straight segment; it is located 94.7 mm downstream of the nozzle exit. The conical angle is 45\({}^{\circ}\). To enable probing the flow inside the Venturi, the latter was fabricated out of thin-wall UV-transparent fused quartz, which guarantees a 70% transmittance for MTV conducted there. A flat plate around the top of the Venturi seals the air path that would bypass the Venturi's entrance. The plate contains a narrow gap needed as a path for lasers used in velocimetry acquisitions.  
Figure 2: Key dimensions (in mm) of flow boundaries in the test rig.  
Downstream of the Venturi, two concentric filter candles are present: an inner stainless steel filter and an outer silicon carbide one. During normal filter operation, gas would flow radially from the outside to the inside and then axially to the downstream plenum, resulting in the accumulation of solid particulate on the outside surface. When regeneration is triggered, the pulse jet is directed axially to the internal cavity of the cylindrical filter from the downstream \"clean side\" plenum, causing reverse mass flux through the filter mesh and filter regeneration. The porous viscous resistance across each of the two filters is available from the manufacturers as indicated below. Respectively, for the inner and outer filter:  
\[\frac{\Delta p}{\rho u}=1.4\times 10^{8}\;\text{m}^{-1}, \tag{1}\]  
\[\frac{\Delta p}{u}=81,434\;\text{kg}\;\text{m}^{-2}\;\text{s}^{-1}. \tag{2}\]  
Both equations include pressure drop \(\Delta p\) and velocity \(u\), and the first one also includes density \(\rho\) and kinematic viscosity \(\
u\).