Direct Numerical Simulation of Transitional and Turbulent Flows Over Multi-Scale Surface Roughness—Part II: The Effect of Roughness on the Performance of a High-Pressure Turbine Blade

Gas turbines are still the most widely used technology for power generation and aircraft propulsion. Even small percentage improvements to their overall efficiency can save billions of dollars of fuel every year, with the additional benefit of significantly reducing CO₂ emissions. During their operational life, gas turbine components are subjected to different kinds of in-service degradation such as fouling and metal erosion, which can quickly produce levels of surface roughness that are no longer negligible from an aero-thermal perspective. Experimental studies have shown that roughness-related effects have detrimental consequences on the performance of gas turbines and they can lead to a reduction in efficiency of the order of $10%$ for both compressors and turbines [1]. This is particularly relevant for the high-pressure turbine (HPT), which is located downstream of the combustion chamber and experiences high levels of unsteadiness and turbulence. It is also subjected to the highest temperatures, pressures and velocities in the engine. These extreme operational conditions can increase the blade surface roughness by promoting and accelerating surface erosion [1]. In addition, HPT blades can also present certain degrees of surface roughness introduced by the additive manufacturing process [2]. Hence, the importance of understanding and quantifying the effect of surface roughness on the aero-thermal performance of the HPT blade.

Since the pioneering works of Nikuradse [3] and Schlichting [4], decades of research efforts have been spent trying to produce models that can link roughness topological parameters to performance-critical quantities such as skin friction and heat flux for numerous engineering applications. A comprehensive review of the challenges related to understanding the effects of surface roughness is outside the scope of this work and the reader is referred to the publications of Jimenez [5], Bons [1], and Chung et al. [6]. Despite the efforts, finding general relationships or correlations that can be applied to different types of flows is still an elusive goal due to the highly complex and nonlinear mechanisms governing the interactions between roughness and fluid dynamics. This is particularly true in gas turbines: it is well known, in fact, that HPT flows present a broad array of complex multi-scale flow and thermal features, often interacting with each other in nonlinear ways. This includes multiple laminar-turbulent transition mechanisms, strong pressure gradients, shock waves, and vortical wakes [7]. Dissecting the interactions between the flow dynamics and roughness and, consequently, understanding their implications on the blade performance poses significant challenges.

To date, the majority of research on surface roughness effects in turbomachinery have been carried out by means of experiments [8–14]. Apart from being costly, physical tests often do not provide the necessary level of detail required to carefully understanding the physics of HPT flows and their implications on the design of more efficient blades. One example is represented by the overall heat transfer and skin friction—although there is general consensus that surface roughness increases both quantities with respect to the values measured on an equivalent smooth surface, the detailed underlying physical mechanisms are still poorly understood [13].

Thanks to recent performance improvements offered by modern supercomputers, computational fluid dynamics can provide new insights into the physics of flows over HPT rough blades at engine-relevant conditions. Reynolds-averaged Navier–Stokes (RANS) simulations, although being a well-established industrial tool in the design of HPTs due to their computational efficiency, are known to suffer from accuracy issues in the presence of the complex flow mixing processes [15–17] present in gas turbine aerodynamics. These effects are amplified by the presence of surface roughness, which is known to promote boundary layer transition and turbulent mixing. Dassler et al. [18] accounted for roughness effects on boundary layer transition in RANS simulations by introducing an artificial roughness amplification variable A_r governed by a scalar transport equation. This variable, directly linked to the surface roughness topology, modifies the boundary layer momentum thickness and, consequently, the turbulence production term of the solver. This approach has been validated against the experimental results of Fiendt [19] for roughness-induced transition on a flat plate, showing good agreement. The method has also been applied to a low-pressure turbine cascade with and without roughness and the results in terms of on-blade pressure coefficient and wake loss have been compared to the experiments of Montis et al. [12]. The model showed good agreement for the pressure coefficient at low and moderate Reynolds numbers, but it was unable to account for roughness-induced separation effects at high Reynolds number. In terms of wake predictions, the wake width, its location, and the overall loss were not accurately captured by the solver. No results were shown for the wall shear stress and the heat flux, two quantities that are more sensitive to boundary layer changes than the pressure coefficient.

Accurate predictions of on-blade aerodynamic variables are pivotal in gas turbines, especially in HPTs. It is in fact estimated that a $2%$ error in the predicted surface metal temperature can halve the effective blade life [20]. For this reason, there is a need for numerical tools that exceed the level of fidelity provided by RANS. High-fidelity simulations such as large eddy simulation and, in particular, direct numerical simulation (DNS), have been shown to be very accurate in simulating turbomachinery flows [7,21–23], as well as canonical flows such as channels, pipes, and flat plates in the presence of different kinds of surface roughness [24–27]. The main advantage of DNS lies in its capability of resolving all turbulent scales in the unsteady flow, hence allowing to capture with great detail their interaction with the small-scale and complex topology of the surface roughness. Achieving this level of detail requires large grids that exceed the billion-point count, hence requiring much higher computational resources with respect to simulations performed on smooth geometries under equivalent conditions.

The aim of this work is to provide a high-fidelity framework to accurately predict roughness-induced aero-thermal effects on HPTs at engine-relevant conditions, establishing a benchmark for future studies. By employing a well-validated DNS solver and an immersed boundary method, the present framework overcomes the accuracy limitations offered by lower-fidelity numerical methods, also offering a strong advantage over experiments in terms of data capturing and data processing capabilities, in particular with regard to engineering relevant on-surface quantities. To this end, a simulation campaign to investigate the aero-thermal performance of an HPT blade with different levels of surface roughness is carried out. Following the preliminary work of Jelly et al. [28], a new efficient computational setup is employed, offering a much higher numerical resolution localized in the blade near-wall region and hence conveniently limiting the consequent increase in computational effort of the simulations. Three cases with homogeneous roughness distributions and an additional case with surface-varying roughness are simulated. This numerical investigation is carried out using an immersed boundary method, which directly enforces wall boundary conditions from arbitrary geometries on a non-conforming mesh, thus allowing the simulation of realistic multi-scale roughness distributions. The results are compared with respect to a reference smooth blade and discussed.

Numerical simulations are carried out using HiPSTAR, a well-validated, high-performance in-house numerical solver for compressible flow. In HiPSTAR, the compressible Navier–Stokes equations are solved on curvilinear structured grids by employing a fourth-order accurate finite difference scheme to compute the spatial derivatives and a five-step, fourth-order accurate, low-storage Runge–Kutta method for the time integration [22]. We refer to Part I [29] for a detailed introduction of the computational setup and of the main flow parameters, here only providing a summary of the relevant information. Simulations are carried out at engine-relevant conditions, with an inlet Mach number M_in = 0.2 and a Reynolds number based on the axial chord C_ax of Re = 110,000 resulting in M = 0.9 and Re = 590,000 at the outlet. The computational domain is periodic in the pitchwise and spanwise directions and the length of the span is L_z = 0.4. Unless otherwise specified, all quantities are presented in non-dimensional form, with lengths normalized by C_ax and flow quantities such as velocities, density, and temperature normalized by reference inlet conditions. Isotropic turbulence with an intensity $Tk/Uin=8%$ with respect to the inlet velocity and an integral length scale $Lx/Cax=8%$ with respect to the axial chord is prescribed at the inlet using a compressible variant of the digital filter technique [30].

The blade geometry is obtained from an LS89 HPT blade and it is represented using a novel three-dimensional immersed boundary method, here referred to as 3D boundary data immersion method (BDIM), introduced in Part I [29]. The advantage of the BDIM lies in the possibility to simulate complex three-dimensional surfaces without the need for computational grids that conform to the geometry of the solid boundary, hence retaining high computational efficiency. The numerical solver and the surface data-capturing method have been validated in Part I on two cases relevant to this work—a channel flow with egg-carton roughness and a smooth HPT blade, showing excellent agreement with previous studies.

The type of roughness considered in this work is irregular and three-dimensional, with a spatial statistical distribution that is near-Gaussian, which has been shown to well represent the surface characteristics of real-life blades subjected to operational metal erosion [9]. A generic surface roughness distribution can be characterized by an equivalent value of Nikuradse sand grain roughness k_s, which is related to the root mean square roughness height k_rms such that k_s = 5.0k_rms. In the present work, a total of five blade configurations are investigated, differing in the level and the characteristics of their surface roughness. The first case is a perfectly smooth LS89 blade, indicated as $k0s$⁠, and it serves as the baseline. Three blades with homogeneous roughness of increasing amplitude are then considered, with nominal roughness values of k_s = 0.001, k_s = 0.002, and k_s = 0.003. For a blade with an axial chord of 50 mm, this corresponds to a surface roughness distribution with k_s = 50 μm (and k_rms = 10 μm), k_s = 100 μm (and k_rms = 20 μm), and k_s = 200 μm (and k_rms = 30 μm), respectively. They will be indicated by the following abbreviated expressions: $k1s$⁠, $k2s$⁠, and $k3s$⁠, respectively. A summary of the main topological parameters of each roughness distribution, including skewness, kurtosis, streamwise effective slope ES_s, and spanwise effective slope ES_z (see Part I for more details), can be found in Table 1.

Finally, an additional blade geometry with varying surface roughness (⁠$kvs$⁠) is investigated. The characteristics of this blade are shown in Fig. 1. At the leading edge, the blade geometry is identical to $k3s$⁠, but its roughness progressively decreases for 0.36 < x < 0.71 until the surface becomes perfectly smooth on the suction side for x > 0.71. On the pressure side, the roughness distribution gradually reduces to k_s = 0.001 in a region between x = −0.49 and x = −0.72. The purpose of this geometry is to provide a more realistic model that mimics the operational surface wear observed in HPT blades, with the leading edge and the pressure side being more subjected to metal erosion due to their direct exposure to the incident flow.

The domain is discretized using a three-block mesh setup composed of one H-type grid for the background (Block 1) and two layers, an outer (Block 2) and an inner one (Block 3), of O-type grids wrapped around the turbine blade. The main purpose of the inner O-grid, labeled as Block 3, is to provide enhanced localized resolution in the thin region around the blade surface where the roughness is located. The three grids are connected by means of overlapping regions using an overset method [31]. The grid characteristics are summarized in Table 2. Block 1 and Block 2 are the same for all the cases, while Block 3 differs for the number of points in the wall-normal direction, which increases with the roughness height. However, the wall-normal grid spacing Δy in the roughness region is constant and it is the same for all the cases. A preliminary convergence study suggested that a spanwise resolution of N_z = 576 in Block 3 is sufficient to adequately resolve the flow around the reference HPT smooth blade. Information on the grid spacing with respect to the boundary layer quantities is provided in Part I.

An on-blade analysis is presented, first introducing a qualitative overview of the flow around the HPT blade and then discussing the relationship between the surface roughness and quantities of interest such as blade boundary layers, skin friction coefficient, and heat transfer at the wall. A discussion on the performance of the different HPT blades follows, focusing on the wake loss and on the wake turbulent kinetic energy (TKE).

A qualitative comparison of the flow behavior for the different HPT blades is provided in Fig. 2 by showing side-by-side snapshots of the instantaneous spanwise velocity field w collected at mid span in the axial-pitchwise plane. The flow field snapshots are accompanied by a representation of the three-dimensional blade surface, in order to provide a visual comparison of the different roughness topology. The blade surface is colored by the magnitude of the spanwise vorticity ω_z at the wall. From the velocity field, it can be observed that the large blade curvature on the suction side produces a strong acceleration in the flow, altering the structure of the incident turbulent eddies, which are subjected to stretching in the streamwise direction. On the blade surface, the roughness features of each blade have a strong impact on the characteristics of the boundary layer, in particular on the suction side. Both the reference smooth blade $k0s$ and the smallest amplitude roughness $k1s$ present boundary layers that are predominantly laminar and undergo a bypass-type transition only in the proximity of the trailing edge. Larger roughness amplitudes introduce larger perturbations in the boundary layers and promote an early transition, moving the transition region upstream and closer to the leading edge, as shown in Fig. 2. As a result, the surface area subjected to fully turbulent boundary layers is much larger for $k2s$ and $k3s$ with respect to the smooth blade. This is also true for $kvs$⁠, which undergoes an almost identical transition mechanism as $k3s$⁠, having the same roughness characteristics in the leading edge region. However, the geometry of $kvs$ differs from $k3s$ as it gradually becomes smooth on the suction side. As a result, this particular case presents a fully turbulent boundary layer convecting over a smooth region on the suction side, allowing for an interesting comparison of the blade performance with respect to the reference $k0s$⁠. The insets at the bottom of Fig. 2 provide a close-up view of the blade trailing edge: here the boundary layers separate and the turbulent eddies are shed in a strong vortical wake. We will see that the width of the wake and its energy content are directly linked to the boundary layer state.

A boundary layer analysis is performed on the blade suction side by computing and comparing the boundary layer thickness δ, the displacement thickness δ*, the momentum thickness θ, and the shape factor H = δ*/θ. The results are summarized in Fig. 3. All boundary layer quantities are extracted from the time-averaged and spanwise-averaged flow field. For the rough cases, the reference geometry that defines the location of the wall and from which the boundary layer quantities are integrated is assumed to be the smooth blade profile, which allows for a rigorous comparison between the different cases. This assumption is justified by the fact that the mean profile of any of the rough blades coincides with the smooth blade. In other words, the mean roughness height of each surface distribution is zero. The boundary layer thickness is computed using a vorticity threshold condition and it is defined as the wall-normal distance between the blade surface (the reference smooth blade, in this case) and a point along the normal in which the magnitude of the spanwise vorticity |ω_z| drops below a certain threshold $ωz*$⁠. For this work, a value of $ωz*=10$ has been chosen after a sensitivity study (i.e., doubling or halving the threshold has a negligible effect on the resulting boundary layer thickness). The results obtained using this method are comparable to the values that result from other boundary layer identification methods, such as the $99%$ of the vorticity integral in the wall-normal direction. However, the threshold method yields more accurate results in the leading edge region, where the boundary layer is very thin, especially in the presence of roughness. By observing Fig. 3, it is clear that the smooth blade $k0s$ and the case with the smallest roughness $k1s$ have comparable boundary layer thickness. This indicates that the blade surface roughness for $k1s$ is small enough that its effect on the boundary layers is negligible. This can also be inferred by looking at the shape factor H: its sharp increase and subsequent drop toward the trailing edge, in a region between x = 0.8 and x = 0.9, reveals the boundary layer location region, which is the same for both $k0s$ and $k1s$⁠. The value of the shape factor in the trailing-edge region H ≈ 3 indicates that the laminar boundary layer is subjected to some level of separation before transitioning to turbulent. This is not surprising, since the trailing-edge region is characterized by a strong adverse pressure gradient. Larger values of the nominal roughness height produce thicker boundary layers, as can be observed for cases $k2s$ and $k3s$⁠, with values that are 1.5–2 times larger than the reference smooth blade at the trailing edge. In these cases, the transition is caused by the roughness itself and not by the disturbances in the boundary layer introduced by the freestream turbulence. From x = 0.5 toward the trailing edge, the flow is fully turbulent, as indicated by values of the shape factor that are between 1.4 and 1.6, which is considered typical for fully developed boundary layers [32]. The lower values of H with respect to $k0s$ and $k1s$ indicate that the early onset of transition prevents the occurrence of on-blade separation mechanisms in the trailing-edge region. This behavior can have beneficial effects on the overall blade performance if the loss reduction due to the suppression of the separation exceeds the loss increase due to a larger turbulent wetted area caused by the earlier roughness-induced transition. This is more commonly observed in low-pressure turbines, where separation effects are more relevant compared to HPTs [1]. For the present study, we will see that the earlier roughness-induced transition onset always results in a larger overall blade loss with respect to the reference. For case $kvs$⁠, the boundary layer behaves as $k3s$ up to mid-chord, indicating that the transition is driven by the leading edge roughness, which in the two blades has the same amplitude and distribution. As the blade surface transitions from rough to smooth, the boundary layer thickness of $kvs$ grows at a slower rate compared to $k2s$ and $k3s$⁠. This suggests that the roughness amplitude and its distribution do not only have an impact on the boundary layer transition, but also on its subsequent development on the blade surface.

Figure 6 shows a comparison of the time and spanwise-averaged skin friction coefficient $C¯f$ and $C¯f*$ and heat flux $Q¯$ between the smooth blade and the rough cases. Positive values of x refer to the suction side, while negative values indicate the pressure side, with x = 0.0 being the leading edge coordinate. From the skin friction coefficient profiles, it is evident how the contribution of the wall shear stress only accounts for a fraction of the overall tangential force coefficient, particularly on the suction side. The laminar to turbulent transition of the boundary layer is indicated by a sharp increase in both the skin friction and the heat flux. For $k0s$ and $k1s$⁠, the boundary layer transitions in the trailing-edge region on the suction side, as already discussed previously. For $k2s$ the suction side transition is located between x = 0.45 and x = 0.55, while $k3s$ and $kvs$ show a similar increase of $C¯f*$ and $Q¯$ between x = 0.4 and x = 0.5. More importantly, $kvs$ shows lower values of both the skin friction and the heat flux in the smooth region with respect to $k2s$ and $k3s$⁠, indicating a favorable effect on the smooth surface on both quantities. Further studies are needed to understand the effect of varying roughness on transitional and turbulent boundary layers on the suction side of the blade. As an additional remark, it is worth noticing that for case $kvs$ the value of $C¯f$ becomes equal to $C¯f*$ as the blade transitions from rough to smooth on the suction side. Interestingly, for cases $k2s$⁠, $k3s$⁠, and $kvs$ the boundary layer turbulent transition occurs on the pressure side as well, albeit this is limited to the trailing-edge region.

It is worth mentioning that although case $k1s$ shows an excellent agreement with $k0s$⁠, both $C¯f*$ and $Q¯$ are locally slightly under-predicted. This is probably an indicator that this geometry requires a larger number of points to perfectly resolve the complex interactions between the flow and the small-scale roughness elements. This is compatible with the observation that this case not only has the smallest roughness amplitude, but also the smallest roughness length-scale, as it can also be inferred by looking at the surface visualization in Fig. 5. However, for the scope of this paper, the trends of both surface variables are captured correctly and the present grid resolution can be considered adequate.

The right column plots in Fig. 6 show the ratio between heat flux and skin friction coefficient. If the thermal and hydrodynamic boundary layers are comparable, the two quantities are related by a coefficient of proportionality. This is known as Reynolds analogy. Bons [33] postulated that this analogy does not hold for rough surfaces, since the roughness-induced skin friction increase exceeds the increase in heat flux. From our analysis, we can conclude that the Reynolds analogy still holds for the viscous component of the skin friction coefficient $C¯f$ on rough surfaces. In fact, roughness causes an increase in $Q¯f$ that is proportional to the increase in $C¯f$⁠. However, the additional contribution of the form drag invalidates the analogy, since it increases the overall skin friction $C¯f*$ without affecting the heat flux. From the analysis conducted so far, we can conclude that surface roughness can have a strong impact on both the tangential force at the wall and the heat flux, with strong implications for the design of the HPT blade. From the analysis of the case with varying roughness $kvs$⁠, we have shown the importance of the surface state in the leading edge region, because large values of roughness can trigger the boundary layer transition, significantly promoting viscous stress and heat exchange on the suction side even if the blade becomes perfectly smooth.

As discussed by Chung et al. [6], first-order predictive tools or correlation relationships for aero-thermal performance-critical quantities with respect to roughness topological parameters are not reliable for most engineering applications. Several attempts have been made to identify a threshold value of k_s under which a surface distribution can be considered aerodynamically smooth [1], in order, for example, to provide guidance for manufacturers or maintenance operators. A threshold value that is frequently accepted in engineering is related to experiments on rough plates carried out by Feindt [19] and it is expressed in terms of $Reks=ksUrefν$⁠. Feindt found that roughness with a k_s value such that in Re_ks < 120 did not have any effect on the boundary layer transition location. As we have seen, the suction side of a gas turbine is subjected to very strong favorable pressure gradients and complex flow dynamics and it is very different from the controlled experiment of Feindt. Bons [1] highlighted some of the limitations of this approach, indicating that others have suggested a higher threshold value, as high as 600. In terms of viscous units, $ks+<19$ has been suggested in the literature [1].

The computation of $ks+$ and Re_ks as a function of the blade axial chord for the roughness distributions investigated in this work is presented in Fig. 7. For the computation of Re_ks, the local maximum streamwise velocity in the throat has been used as the reference (hence the dependency of Re_ks on x even for the constant amplitude roughness distributions). From what we have seen, the aero-thermal performance of $k1s$ is almost identical to the reference smooth blade and, unlike the other cases, it can be considered hydro-dynamically smooth. It seems therefore that both thresholds Re_ks < 600 and $ks+<19$ hold in this context. All the other roughness distributions have values of Re_ks and $ks+$ that exceed the thresholds. For $kvs$⁠, the boundary layer transition is triggered by the above-threshold values of Re_ks and k_s in the leading edge region. A more systematic study with streamwise varying roughness would help refine the limits of applicability of these simple but useful correlations between k_s and hydrodynamic behavior.

After carefully considering the effect of the different levels of surface roughness on the blade near-wall region, with a particular focus on the skin friction and the heat flux, we now discuss the overall performance of the different HPT blades and their efficiency by considering the wake loss and the wake turbulent kinetic energy.

The analysis of the wake turbulent kinetic energy, defined as $TKE=12ui′ui′¯$ with i = 1, 3 and u′_i being the turbulent velocity component, is shown in Fig. 8(b). For cases $k1s$⁠, $k2s$⁠, $k3s$⁠, and $kvs$⁠, larger roughness amplitudes are associated with a larger turbulent kinetic energy in the wake. This is not surprising, as the blades with larger roughness have thicker turbulent boundary layers. In addition, for cases $k3s$ and $kvs$ the TKE profile presents an asymmetry, with a peak toward the pressure side. However, it is interesting to notice that the wake TKE level of the smooth blade is higher than in case $k1s$⁠. Since for these two cases the boundary layers have similar characteristics, differences in the wake TKE are probably related to the shedding dynamics that occur at the trailing edge. Here, the surface roughness of $k1s$ can accelerate and promote the breakdown of the near-wake vortical structures, reducing their overall coherence and hence reducing the level of unsteadiness with respect to the smooth blade, where the trailing edge structures might present larger coherence. An analogous behavior has been observed by Leggett et al. [35] in an HPT stage for the total temperature: in that case, higher levels of freestream turbulence resulted in a reduction in the occurrence of temperature hot spots, and hence a reduction of the average total temperature in the stator near-wake, due to enhanced breakdown of the strong coherent vortex structures. Further studies are required to carefully understand the near-wake dynamics and their implications on the far-wake characteristics. Despite minor differences in the wake TKE levels, the blade with a surface roughness distribution with k_s = 0.001 has aero-thermal performance that is very close to the smooth blade, despite its k_s being above the threshold k_s,adm introduced in Sec. 2. The main reason is that k_s,adm refers to a flat plate under zero-pressure gradient conditions, while a turbine blade presents large curvature values and strong pressure gradients. It is possible that the favorable pressure gradient reduces the sensitivity of the boundary layers to disturbances such as those introduced by a rough surface, hence increasing the value of k_s,adm.

High-pressure turbine blades with different amplitudes and distributions of roughness have been simulated at engine-relevant conditions by means of direct numerical simulation. Such a computationally expensive investigation has been achieved thanks to a newly developed computational framework that employs three overset grids with different topologies and resolutions in combination with a three-dimensional immersed boundary method for surface roughness. Simulations have shown that a uniform roughness distribution with k_s = 0.001 has negligible effects on the blade aero-thermal behavior, with overall performance that is comparable to the smooth reference. This is in agreement with roughness threshold values of k_s present in the literature. Cases with a nominal roughness of k_s = 0.002 and k_s = 0.003 have been shown to promote boundary layer transition on the blade suction side, increasing the surface area wetted by turbulent flow and producing thicker boundary layers. As a consequence, roughness increases the acceleration of the flow in the blade passage, promoting the formation of normal shockwaves. The flow acceleration has implications on the mass flow and on the overall engine performance. Roughness also enhances the wall shear stress and the heat flux at the wall, affecting the blade surface temperature and, consequently, its operational life. Surface data capturing allowed us to demonstrate that the Reynolds analogy does not hold for rough surfaces, since the viscous component of the skin friction coefficient is augmented by the contribution of the additional pressure drag due to the morphology of the roughness elements. The higher levels of turbulence triggered by roughness translate into higher total pressure losses in the HPT blade, as shown by a wake loss and wake turbulent kinetic energy analysis. An additional case with chordwise varying amplitude roughness—from k_s = 0.003 at the leading edge to smooth at the trailing edge on the suction side—presented a transition behavior similar to $k3s$⁠, but smaller skin friction and heat flux in the smooth region and reduced overall losses. This suggests that the roughness distribution not only governs the laminar-to-turbulent transition, but also affects the turbulent flow development, with consequences on the overall blade performance.

We are grateful for the permission of GE Aerospace to publish results from this study. Support from the ARC is acknowledged. This research used data generated on the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC05-00OR22725.

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.