Numerical Assessment of an Aerodynamic Probe to Enable Short Focal Length Laser Diagnostics in High Temperature Supersonic Flows Based on Flow Disturbance

High-speed and high-temperature flows have high relevance for engine designers in the aeronautical industry, but gathering experimental data in such conditions poses both mechanical and aerothermal challenges. In high-speed regimes, physical sensors are extensively used for wall measurements (heat flux, skin friction, wall temperature, and near-wall pressure [1–3]). However, when introduced within the freestream, traditional probes are exposed to extreme thermal loads and flow-induced vibrations, and they generate a bow shock that disturbs the flow in the measured point, favoring the application of nonintrusive optical techniques for deep flow field characterization. Molecular tagging velocimetry (MTV) has gained popularity for measurement of velocity in high-speed environments especially due to its minimal intrusion. It consists of a “write” and a “read” lasers that induce fluorescence to tagged species within the flow, and a high-speed camera that captures their motion. Different species have been successfully tagged in supersonic environments for measuring velocity: NO [4], O₂ [5], N₂ [6,7] or OH [8], but despite the suitability of molecular tagging for low and mid-supersonic tests, there are challenges to their application in large-scale, high-supersonic, high-enthalpy facilities [9,10]. MTV techniques require two or even three directions of external optical access for aligning the lasers and the camera, and the compromise in structural integrity makes some of these specific facilities unable to satisfy the optical requirements, and if they do, they are limited in the versatility of their excitation regions, significantly inhibiting the use of MTV.

Another challenge arises as the low-pressure and low-density conditions experienced in high-supersonic regimes reduce the concentration of tagged species and the lifetime of the fluorescence signal used in MTV. This requires maximizing laser power, which is limited by the current development of the technology, as shown by Fisher [6]. Reducing the focal length of the lasers is key to increase the irradiance (energy flux) at the focal point, raising both the intensity and lifetime of the luminescent signal of the tagged species. In a wind tunnel, the minimum focal length is limited by the windows of the test section. Fisher reported a common lower limit of 300 mm, but in high-supersonic large-scale facilities operating in a confined-jet configuration, the lower limit can rise to 500 mm [11]. This is due to a low-pressure enclosure surrounding the jet to sustain high-supersonic conditions, which increases the distance between the jet and the observation windows. In such cases, shorter focal lengths are especially desirable to improve measurement quality. This study presents a novel approach for extending laser velocimetry techniques to high-enthalpy, high-supersonic facilities with reduced optical access.

An optical probe nacelle has been designed that encloses, protects, and cools a set of redirecting optics that can then be introduced within the flow, enabling its placement even at high-enthalpy Mach 6 flow paths [12]. The refrigerated nacelle keeps the optical hardware within their temperature limits and the redirecting optics allow to tune the excitation direction of the lasers, increasing the spatial resolution by adding measurable locations without changing the external structure of the facility. There have been some attempts to redirect laser beams within test sections using submerged optics [4,13], but in both cases noticeable misalignment issues were reported as the optics were freely exposed to the freestream. The use of an aerodynamic nacelle as an optical enclosure protects the optics and the laser path. The introduction of the optical probe in the freestream generates a bow shock, similar to other intrusive probes, but a geometry inspired by high-speed test articles has been used that minimizes the size of the bow shock bringing it closer to the body. The laser exits the probe after passing through the redirecting optics and focuses after crossing the bow shock. The focal point lies in the undisturbed region and even if the probe is intrusive by nature, it measures the unperturbed freestream velocity. Additionally, submerging an optical probe within the flow field brings the focusing optics closer to the measurement point, increasing the irradiance at the focal point. This study demonstrates that the focal length required to place the excitation point upstream the shock is significantly smaller than the ones used in conventional optical configurations with the optics outside the test section.

Three-dimensional steady Reynolds-averaged Navier–Stokes (RANS) simulations are conducted to characterize the flow around the probe and calculate the distance between the bow shock and the optical windows of the nacelle at Mach 6. Due to the open cooling architecture of the nacelle, the interaction between the ejected coolant and the bow shock has been studied, evaluating the sensitivity of the shape of the bow shock to changes in coolant pressure and to hole blocking. Although the beam path transits a boundary layer, a coolant layer, and bow shock to reach the undisturbed flow, deviations in the propagation direction due to refractivity differences across the media remain minimal. Ray-tracing and beam propagation models are used to analyze the effect of the complex flow field in the propagation direction of the laser. Finally, the effusion cooling system of the probe has been characterized experimentally to study the appropriateness of the effusion boundary conditions used in the numerical study. The shape of the coolant jets and possible hole blocking have been studied via Schlieren images; proper orthogonal decomposition (POD) has been applied to the Schlieren images to identify unsteady features in the coolant jets, and total pressure at ejection has been monitored to study pressure differences among holes for the same air-supply pressure.

The body of the probe nacelle was designed to enclose a set of optical components from Thorlabs Inc. that redirect a laser beam and tailor the excitation region in laser velocimetry techniques. From all the MTV techniques, N₂ tagging, also called femtosecond laser electronic excitation tagging (FLEET), is especially relevant as it only requires one laser for both “write” and “read” operations. The laser pulse ionizes the nitrogen molecules in the flow producing a recombination of electrons and ions that leads to the dissociation of nitrogen molecules into nitrogen atoms. Without the need of an additional laser source, these atoms will naturally recombine to reach a lower energy state through a rate-limiting three-body process, producing excited molecules that fluoresce in the visible spectrum and can be tracked with a high-speed camera. FLEET has been demonstrated in a wide variety of wind tunnels and flow conditions [6,7], so its robustness and the simplicity of the optical setup when compared to other MTV techniques motivated the design of an optical assembly for FLEET as the base optical configuration for the probe. The probe has two different windows for providing laser access to the test section, one located in the front and another one in the upper wall, allowing it to be in-line with or below the point of interest. Depending on the window used, the optical components change. For both configurations, the laser is introduced through a port connected to the lower wall, reflected through 90 deg with a mirror and passed through the focusing lens. If the front window is used, the laser will directly exit the probe through the front; if the upper window is used, an additional mirror is placed.

The front of the probe has a “ship's bow” shape to minimize the angle of the bow shock that is formed. Maccoll [14] showed that conical and pyramidal structures in supersonic flows produce weaker and more inclined shocks than wedges due to three-dimensional relieving effects. Additionally, the “ship's bow” shape maintains the top surface parallel to the flow, reducing flow disturbances above the probe. A 30 deg sweepback angle has been given to the front walls to deviate the disturbed streamlines downwards due to Coanda effect, also reducing flow perturbation above the probe. Three-dimensional RANS computational fluid dynamics (CFD) performed by McKelvy [12] showed that the “ship's bow” configuration succeeded in concentrating the disturbances in the lower side.

To operate at conditions as harsh as $T01=1700K$ and Mach 6, the probe was manufactured in Stainless Steel AISI 316 and includes an open cycle gaseous cooling jacket surrounding the optical cavity to keep the surface temperature below 810 K (stainless steel limit) and the optical mounts and cage plates below 315 K (most restrictive limit for Thorlabs Inc. components). A comprehensive description of the internal cooling architecture was done by McKelvy [12]. Dry air is injected through a plenum in the back of the nacelle, routed around the optical cavity, and ejected through a pattern of effusion holes in the front. Effusion cooling is critical as it reduces the average recovery temperature on the probe, but it influences the shape of the bow shock. Most of the cooling holes eject sideways instead of forwards; this was motivated by the work of Lozano and Paniagua [15] that showed a significant increase in bow shock angle due to the momentum of the impinging coolant. Sideways ejection also reduces the risk of inhomogeneous cooling due to Coanda effect, and requires lower coolant pressures to start ejection as the cooling holes are not facing the stagnation pressure of the flow directly. The size of the probe is driven by the optical train. The total volume of the optical cavity is 980 cm³, and the probe has a total length of 400 mm, height of 100 mm, and width of 86 mm, as shown in Fig. 1(a).

The tip diameter of a probe within high-supersonic flow is a tradeoff between drag from shock wave boundary layer interaction (SWBLI) and heat loads from stagnation point heating. A radius of 0.25 in. was employed as it allowed to accommodate six cooling holes of 1 mm diameter. Figure 1(a) shows a cross section of the probe with the optical hardware and schematics of the two possible laser paths. The optical setup in the image is the two-mirror configuration needed to guide the laser to the upper window. A schematic of the flow features around the probe is also shown. Figure 1(b) depicts an external view of a 3D model of the probe, and Fig. 1(c) shows the 3D printed test article with the optical components.

This section describes both the numerical and experimental methodologies used in this study, accompanied by the methods applied for data extraction and processing.

Hypersonic flows are highly energetic flows characterized by internal energy excitation, chemical reactions, or ionization [16]. However, for conditions close to Mach 5, the flow behavior can still be accurately modeled using ideal gas and calorically perfect gas models, as done by South [17] and Krasil’nikov et al. [18]. Due to thermomechanical equilibrium, conventional Navier–Stokes equations can also still be adopted [19]. In this study, numerical simulations have been performed for the probe in a Mach 6 environment assuming an ideal, calorically perfect gas, solving the Navier–Stokes equations. The numerical domain was designed to study the effect that the optical probe and its effusion cooling system have on the flow field around, and it is depicted in Fig. 2.

The freestream flow enters by the left boundary, modeled as a supersonic velocity inlet with uniform flow, giving a Reynolds number per unit length of $Rex=5.95106m−1$ at Mach 6. To avoid unstarting problems, the rest of external boundaries were modeled as supersonic outlets. This model is representative of open jet facilities, in which there are not geometrical constraints to supersonic startability [20]. The cooling holes have been modeled as pressure inlets, where coolant conditions are defined by stagnation pressure and temperature, locating the inlet boundary at a distance of $L/d>2$ from the ejection face. The walls of the probe have been modeled as adiabatic, no-slip walls, as for the results studied (shock wave shape and laser propagation) negligible changes were seen between using adiabatic or isothermal walls. Additionally, adiabatic simulations allow direct computation of the adiabatic cooling effectiveness, which shows the fractional decrease in wall temperature that is produced due to effusion cooling. Parametric studies have been conducted varying the coolant pressure but keeping the total coolant temperature fixed at 315 K, as it is the most restrictive limit for active optical components that could potentially be placed inside the probe, constituting the worst-case thermal scenario. The distance between the upper wall of the probe and the upper boundary is 250 mm, which allows the shape of the bow shock above the probe to be resolved. In an experimental test, the probe will be supported with a diamond-shaped mount that has not been modeled in this study. It will impact the overall drag, but it is located downstream of both optical windows, so it will not affect the flow field near them. Table 1 summarizes the boundary conditions. A low coolant pressure has been used compared to the freestream as downstream of the bow shock formed at the tip of the probe, and the total pressure $P02$ is significantly reduced compared to $P01$⁠.

Lozano and Paniagua [15] showed that for low ejection pressures, the ejected jet turned in one direction and attached to the wall in a non-symmetric manner dominated by Coanda effects. However, the asymmetric effects disappeared when the ejected flow reached Mach 1. Among all the conditions simulated in this study, only for the case of lowest coolant pressure (⁠$P0c=1.33bar$⁠), there are holes that are not choked, but they constitute a minority (4 out of 698 holes). Thus, no asymmetries are expected in the jets in almost all the conditions, supporting the use of a symmetry boundary condition at the middle plain, reducing the computational cost. The simulations solve the RANS equations implementing a k–ω shear stress transport model for turbulence closure.

The domain was spatially discretized with hexahedral cells using the unstructured mesher Hexpress from numeca. The domain was divided into two rectangular regions, one enclosing the probe and another one enclosing the region above it. Both regions were meshed separately and merged with a layer of tetrahedral cells, facilitating the meshing process.

A grid sensitivity analysis was performed monitoring local and integral quantities. Drag from SWBLI was used as an integral grid convergence indicator, and its variation with number of cells is shown in Fig. 3. The error magnitude defined in Eq. (1) quantifies the difference in drag between one mesh and the finest one [15]. A common threshold for a proper mesh is 1%.

In Fig. 3, an asymptotical behavior is observed after the second coarsest grid. The magnitude of the percent error is included and shows that the difference in drag between the third and fourth grids (the two finest meshes studied) becomes lower than 1%, which justifies the selection of the third grid as the mesh for the study. The final grid is shown in Fig. 4, having a total of 15.6 million cells and a minimum of 10 cells per cooling hole diameter. The value of Y+ was lower than 1 at all surface points to capture the behavior in the viscous sublayer.

The simulations have been performed using CFD++, a 3D fully compressible solver from Metacomp [21]. Published results on supersonic flow around canonical geometries can be used to validate the results of this study. Lozano and Paniagua [15] studied the behavior of rounded tips with an ejection hole blowing toward a supersonic freestream and presented numerical results for the distance from the bow shock to the tip for different ejection conditions. Their results have been normalized and are shown in Fig. 5(a), where the shock distance is divided by the diameter of the ejecting hole for different momentum flux ratios. Additionally, the blockage factor (defined as the area used for ejecting coolant over the total cross-sectional area of the tip) has been accounted. In Fig. 5(a), the results from Lozano and Paniagua are compared to the results from the RANS simulations at Mach 6. Due to the complex geometry of the tip of the optical probe, it is considered that only the front 8 cooling holes belong to the tip area, shown in Fig. 5(b). Thus, the effective cooling diameter $deff$ is defined as the diameter of the combined circular area of those eight holes, which is named the effective area $Aeff$⁠. The results of the RANS simulations present the same linear trend noticed by Lozano and Paniagua, with the same slope and agreeing absolute values. For further verification of the results, additional cases at Mach 5 were conducted at coolant pressures yielding chocked ejection.

In the far field, the shape of the bow shock can be compared to the theory of detached shocks developed by Moeckel, which shows that shocks are asymptotic to freestream Mach lines [22]. The bow shock angle has been extracted near the downstream boundary of the computational domain and it is compared to the Mach angle in Table 2. Again, an additional simulation at Mach 5 has been conducted for further verification. For the cases in which no coolant is ejected, the bow shock angle at the end of the domain is less than 1.5 deg higher than the one predicted by Moeckel, further validating the numerical results. The disagreement occurs as the bow shock is still not close enough to the far field asymptote. This fact is even more notorious when coolant starts being ejected, as the shock has to propagate a longer distance to reach the Mach angle.

The validity of the numerical results involving the position and shape of the bow shock depends on the proper specification of the boundary conditions at the ejection holes. The objectives of the experimental study are to confirm that no holes in the manufactured probe are physically blocked due to 3D printing effects and to assess pressure differences and asymmetries in the coolant ejected from different holes. This process allows verification of the validity of the uniform pressure inlet condition and the symmetric ejection assumption used in the numerical simulations. Experimental tests were conducted in the Purdue Experimental Turbine Aerothermal Laboratory [23] in which, to test the effusion cooling system, the probe was secured to an optical table with the effusion holes venting to ambient without external flow. Cooling flow was delivered through the plenum of the probe with an air-supply line capable of providing air at a maximum pressure of 40 bar.

Figure 6(a) shows an overall view of the test setup with the instrumentation used. Pressure taps were placed in specific ejection holes and connected to a ScaniValve MPS unit acquiring at 800 Hz to measure total pressure at ejection and quantify possible differences between holes. A total of 12 taps were installed, blocking less than 2% of the holes to preserve ejection conditions. Most of the pressure taps can be seen in Fig. 6(b). A K-type thermocouple connected to a VTI EX1048A conditioning system and an additional pressure port were located in the air-supply line. Lens-type Schlieren was used for visualizing the ejected flow at the tip using an light-emitting diode as light source and a field of view of 10 cm diameter as shown in Fig. 6(c). A Phantom TMX 5010 high-speed camera was used with an acquisition rate of 50 kHz.

The results from the numerical simulations are presented and analyzed in this section alongside the experimental results.

For a Mach 6 freestream, a detached shock is formed ahead of the probe due to the bluntness of the leading edge. The stagnation streamline in the tip faces a normal shock, while far away from the tip, the detached shock tilts and approaches a terminal angle. Above and below the stagnation streamline in the tip, two different flow structures appear driven by the angle of the walls of the probe. Below the tip, the flow encounters faces at a moderate sweepback angle (30 deg), and the resulting shock wave is attached. Hornung et al. [24] showed this behavior for cones at similar angles and called it the “attached” or “cone behavior.” The shock wave detaches when it encounters the cavity of the front optical window, but soon reattaches below it. Above the tip, a flat surface minimizes the geometric blockage, reducing the strength of the shock and flow distortion. This feature, however, is not able to mitigate the formation of a shock wave and produces a detached shock following what Hornung et al. called the “detached” or “sphere behavior.” Downstream of the probe, the flow structures are driven by the backward facing step in supersonic flow. An expansion fan at the end of the body accelerates the flow until a lip shock is formed that bounds the recirculation region. This region gets thinner until a “neck” is reached at which a recompression shock appears. These features are labeled in the density gradient contour in Fig. 7.

Coolant ejection produces the main distortion to the position and shape of the bow shock. The holes in the tip are facing upstream, so they need to overcome the stagnation pressure downstream of the normal shock to start ejecting (⁠$P0c/P02>1$⁠). Selection of an ejection pressure ratio for the design point requires balancing the increased flow disturbance derived from coolant ejection with improved cooling effectiveness.

Figure 8(a) shows the behavior of the average adiabatic cooling effectiveness with variations in the ejection pressure ratio. The adiabatic cooling effectiveness is defined as the fractional temperature reduction achieved due to effusion cooling when compared to the case at which the walls are at the temperature of the coolant. Even below $P0c/P02=1$⁠, most of the holes have already started ejecting as only the holes in the tip are facing the stagnation pressure downstream of the normal portion of the bow shock, so the figure shows nonzero values of cooling effectiveness. However, the design point requires all holes to be ejecting to ensure proper cooling. Once a pressure ratio of $P0c/P02=1$ is exceeded, the average cooling effectiveness plateaus, so further increases in coolant pressure will widen the shape of the shock wave without having a noticeable return in the cooling performance. Thus, a value of $P0c/P02=1.4$ is set that ensures that all the cooling holes are active, and that the average adiabatic cooling effectiveness has stabilized near its maximum value. Figure 8(b) shows the distribution of cooling effectiveness along the walls for the selected case. Despite the overall high value, two regions of noticeable low effectiveness are seen, which are the tip and the region of the front window, both with values below 0.2. However, these regions are further cooled through convection, with coolant routed through the internal channels, and by diffusion from nearby cooler areas—phenomena that are not captured in adiabatic simulations.

Mach number profiles with and without coolant ejection are compared in Fig. 9(a) (no blowing) and Fig. 9(b) $(P0c/P02=1.4)$⁠, respectively. Arrowed streamlines come from the cooling hole, and non-arrowed streamlines come from the freestream. Many of the same structures present in the uncooled configuration can be seen in the cooled one. However, the variation in Mach number across the bow shock is more prominent in the cooled case. The distance between the bow shock and the upper wall of the probe increases with coolant ejection and the same happens for the distance between the front optical window and the front shock. These distances drive the focal lengths achievable with the laser and are quantified numerically in subsequent sections.

Lasers of different wavelengths can be used for different optical techniques applicable to high-speed testing, typically ranging between 266 and 1064 nm. The contours of the index of refraction at the symmetry plane are shown in Fig. 10(a) for a wavelength of 266 nm and a coolant pressure ratio of $P0c/P02=1.4$⁠. The highest index of refraction appears in the coolant jets due to their high pressure, however, in the vicinity of the optical windows, the main contributor to variations in refractive index is the bow shock. Figure 10(b) illustrates a close-up domain of the refractive index above the upper optical window, where the trajectory of the laser has been computed for a beam initially perpendicular to the window.

Figure 10(c) depicts the trajectory of the beam along the vertical direction for three wavelengths and Fig. 10(d) shows the deviation angle. Continuous lines show the trajectory without blowing (no effect of the coolant film), and dashed lines show the trajectory for a coolant pressure ratio of $P0c/P02=1.4$⁠. All coolant configurations and wavelengths show an increase in angle when crossing the bow shock due to the high gradient in refractive index, but the trajectory of the beam is appreciably different. For the cooled configuration, the initial direction is almost recovered once the shock is crossed, whereas for the case without blowing the final angle of propagation is greater, showing a high dependence of the behavior of the laser on the specific conditions of the coolant and freestream. If different wavelengths are compared, the propagation of the laser also changes, as the deviation angles across the shock are slightly different, and the resulting trajectories separate. However, the maximum predicted deviation is of the order of $10−8m$⁠, and the maximum deviation angle is of the order of 10⁻⁴ deg for all cases, confirming the small refraction effect that occurs when crossing a bow shock almost perpendicularly, agreeing with the results found by Kiefer and Manson [28]. Similar results were obtained for the beam through the front window, where the maximum deviation was of the order of $10−7m$⁠. For both cases, the deviation is small, and the beam can be considered to be propagating straight in the remaining sections of the study.

Different methods can be used to detect shock waves both experimentally and computationally. Experimentally, qualitative data can be extracted with shadowgraph and Schlieren techniques due to their ability to detect density gradients [29], and background oriented Schlieren or calibrated color Schlieren can be used to obtain quantitative results [30]. Numerically, shock waves can be identified plotting iso-surfaces of Mach number, but this method may produce additional surfaces that do not belong to the shock [31]. Gradient identification algorithms can detect shock waves by measuring gradients of different magnitudes, but only gradients in pressure are recommended as they allow shock waves and slip lines to be distinguished [31].

The hyperbolic fit has been used to model the shape of the detached shock above the probe. For the region below the tip, the shock wave is attached to the front face, and a linear fit has been used. Figure 11 shows a graphical representation of the process followed to study the bow shock. It includes a contour of the pressure gradient in the x direction, with the corresponding shock extracted by the gradient identification algorithm, and the different fits used.

The distance between each of the optical windows and the shock above them has been calculated. This is the distance that the laser covers outside the probe to reach the undisturbed flow, but to calculate the minimum focal length achievable, the distance traveled by the laser between the lens and the optical windows must be added. Both the internal and external distances, as well as the resulting minimum focal lengths are shown in Table 3 for the two possible laser paths.

In actual operation, the ejection conditions may deviate from those simulated. Microscope inspection of the probe has shown micropores in the 3D printed cooling holes, and the ejection pressure may also reach a value different to the predicted one due to heating or pressure losses in the cooling lines. It is then necessary to characterize the sensitivity of the position of the shockwave to slight variations in the ejecting conditions. For this purpose, an approach proposed by Moffat [32] based on the analysis of sensitivities has been used. This method allows the sensitivity of a parameter to some variables to be characterized, provided that all the variables are assumed linearly independent. This study only involves the shock wave above the upper optical window, as it features more dramatic variations than the attached shock below the probe tip with changes in cooling conditions. The parameter in this study is the height of the shock wave at the location of the upper optical window, and the independent variables affecting it are the cooling pressure and the number of holes that are active in the region of the tip. The holes in the tip are the most influential ones to the location of the bow shock, so possible blocking of these holes is especially relevant.

For the sensitivity analysis, two different cases have been studied computationally. First, different coolant pressures have been set between $P0c/P02$ of 1.35 and 1.45, keeping all the holes ejecting. Second, the coolant pressure remained unchanged at the nominal value of $P0c/P02=1.4$⁠, and the front holes (66.7% of the holes of the tip) were blocked.

The results of the sensitivity study are summarized in Table 4. The first column indicates the nominal values of the variables and the second column shows the variations studied. The third column lists the “sensitivity coefficient” and indicates the change in the parameter that is produced for a unit change in each variable. To account for the expected range in which each variable will vary, the fourth column lists the “contribution,” which multiplies the sensitivity coefficient by the expected change in the variable $(ΔX)$⁠. Table 4 shows an expected deviation in the shock height lower than 1 mm. This deviation can be accounted for when computing the minimum focal length, but it is significantly lower than the reduction in focal length that can be achieved with the probe, reinforcing the viability of the proposed approach.

High-speed Schlieren images (50 kHz) were used to evaluate the performance of the ejection holes located in the region of the tip. Figure 12 shows the standard deviation of two sets of Schlieren images taken at different ejection pressures yielding subsonic ejection (Fig. 12(a)) and choked ejection (Fig. 12(b)). Whiter zones mean higher standard deviations, representative of the ejected coolant and shear layer. From Fig. 12, it can then be seen that the holes in the leading edge of the probe are all active, with a similar width and depth.

The fact that the ejected coolant is easily identifiable by computing the standard deviation of a set of images implies that there are unsteady modes in the ejected flow. These modes may alter the position of the shock wave from the values computed in the steady numerical simulations. Lozano and Paniagua [15] studied the effect of unsteady blowing on the position of the bow shock ahead of a supersonic airfoil. Unsteadiness were generated with pulsating blowing, and unsteady Reynolds-averaged Navier–Stokes simulations shown that for high frequency unsteadiness in the cooling flow (>1 kHz), the position of the shock wave in time started to stabilize around a value close to the one obtained in the steady simulations.

For identifying the dominant frequencies of the unsteady motion of the coolant jets, a POD technique was applied to the Schlieren images. POD is a modal analysis technique that decomposes a field into a superposition of spatial structures modulated in time ordered by their energy content. Each energy mode captures a flow structure with content at various frequencies. POD is typically applied to velocity fields to find kinetic energy modes but can also be applied to different magnitudes to find flow structures. A POD algorithm presented by Sieber et al. [33] is used that studies a matrix in which each column represents a different Schlieren image whose pixels are rearranged to form the rows. The covariance matrix is then found, and its eigenvalues and eigenvectors are calculated, representing the mode energies and shapes, respectively.

Figure 13 depicts the two highest energy modes with their frequency content. For both cases, density fluctuations occur mainly in the direction of the jets, which resemble the unsteadiness of pulsating blowing. Both modes exhibit frequency peaks around 10 kHz, well above the 1 kHz limit identified by Lozano and Paniagua, beyond which the unsteadiness did not cause noticeable time oscillations in the shock position, supporting the results obtained from steady RANS. Lower energy modes have also been found, but it became difficult to distinguish between the structures in the shear layer of the jets and the ambient air entrained, mainly giving noisy and non-physical results. No noticeable sideways flapping of the jets was found.

The uniformity of the total pressure at ejection was quantified by comparing pressure readings from pressure taps in the cooling holes. Figure 14(a) shows the ejection holes that were instrumented. The internal jacket of the probe is divided into watertight channels, each of them with different geometrical features and different pressure losses, producing differences in ejection pressure between holes. To assess the symmetry of the ejected flow pattern, readings from symmetric ports (1 and 12) were compared. Figure 14(b) shows the coalescence of the total pressure measured at symmetric ejection ports, as assumed in the numerical study. The horizontal axis represents the total pressure measured before entering the plenum of the probe, in the air-supply line.

To assess the differences in ejection pressure among holes fed by different internal channels, different pressure readings are shown in Fig. 14(c). In this case, some differences appear. For a given air-supply pressure, two different trends are seen in the total pressure at ejection depending on the channels that feed each hole, and the difference between both trends becomes higher with increasing pressure. The maximum relative deviation, which occurs between channels 4 and 10, reaches a value of 8% at the highest air-supply pressure represented (2.35 bar). This deviation suggests that the boundary conditions of the numerical simulation could be improved by tailoring the ejection pressure at each cooling hole. However, it was proven with the sensitivity study of Sec. 4.4 that the change in the shock wave shape due to a deviation in the cooling pressure ratio $P0c/P02$ of 0.05 (3.5% change in $P0c$⁠) was less than 1 mm. Thus, an 8% deviation in $P0c$ would yield a change in the height of the shock wave of 2 mm, which does not hinder the use of the probe. Additionally, only some holes will experience that deviation, reducing even more its effect on the shock wave shape.

This article presents a novel optical probe nacelle to enhance laser optical access in high-enthalpy, high-supersonic wind tunnels. Although submerging a probe within the freestream flow generates a bow shock, the aerodynamic shape of the nacelle is designed to reduce the size of the shock, and the focal point of the laser falls upstream of it, allowing measurement of the unperturbed freestream velocity with high versatility in the excitation region. This study also demonstrates that the distance achieved between the bow shock and the probe is small enough to enable the use of shorter focal lengths than the ones used in conventional optical arrangements where the optics are outside the test section, achieving a smaller laser waist and higher irradiance at the excitation point for the same laser power. This facilitates the application of laser velocimetry techniques to rarified flows.

A numerical analysis using a 3D steady RANS model has been conducted to study the flow around the probe in a Mach 6 environment with stagnation conditions of 1700 K and 44.2 bar and coolant being ejected at 1.33–3.99 bar. The laser deviation due to flow refractive effects has been confirmed to be minimal, the edge of the bow shock has been extracted, and the sensitivity of the shock wave shape to variations in cooling pressure and hole clogging has been computed. Additionally, an experimental test has been conducted to characterize possible non-idealities in the effusion system and validate the cooling boundary conditions used in the numerical study.

The focal length achievable with the probe has been found to be less than 200 mm, reducing the value of 300 mm found by Fisher by 33%, and decreasing the 500 mm value observed in large-scale confined-jet supersonic facilities by 150%. A strong dependence of the bow shock shape on cooling pressure was observed, but for the expected variations, the shock wave height changes by less than 1 mm. This low sensitivity ensures the proposed system remains robust to small perturbations in the effusion cooling conditions. Finally, Schlieren images confirmed the proper operation of the front effusion holes and showed that the fluctuations in the jets occur at frequencies high enough not to alter the position of the bow shock. Finally, pressure readings confirmed the symmetry of the effusion pattern, validating the assumptions used in the numerical study.

There are no conflicts of interest.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

d =

cooling hole diameter (m)

n =

refractive index (−)

w =

beam waist (m)

D =

beam diameter (m)

F =

focal length (m)

H =

height (m)

I =

irradiance (W/m²)

L =

length (m)

M =

Mach number (−)

P =

pressure (Pa)

$P¯$ =

total beam power (W)

T =

temperature (K)

W =

width (m)

Fx =

axial force (N)

Re =

Reynolds number (−)

η =

adiabatic cooling effectiveness (−)

$θ$ =

beam angle (deg)

$λ$ =

wavelength (m)

$ρ$ =

density (kg/m³)

σ =

wavenumber (m⁻¹)

0 =

total conditions

1 =

freestream conditions

2 =

conditions downstream of the bow shock

atm =

atmospheric conditions

c =

relative to the coolant

s =

static conditions

shock =

relative to the shock wave

FLEET =

femtosecond laser electronic excitation tagging

MTV =

molecular tagging velocimetry

POD =

proper orthogonal decomposition

RANS =

Reynolds-averaged Navier–Stokes

SST =

shear stress transport

SWBLI =

shock wave boundary layer interaction