## Abstract

In this paper we investigate the impact of lean-burn-representative swirl and temperature distortion on the aerothermal performance of fully-cooled high-pressure nozzle guide vanes (NGVs) from a modern aero-engine. Experiments were carried out in the Engine Component AeroThermal (ECAT) facility at the University of Oxford. This is a fully-annular warm-flow engine parts facility, designed to operate at engine-representative conditions of Reynolds and Mach number. Inlet profiles of swirl, turbulence, and non-dimensional total temperature were generated using a non-reacting combustor simulator. The NGV outlet flow was experimentally characterized at three downstream planes in experiments with and without lean-burn-representative inlet conditions. Area-survey measurements included distributions of whirl angle, kinetic energy (KE) loss, and non-dimensional total temperature. Experimental data is compared to computational fluid dynamics (CFD) simulations. Fully-featured NGV geometry (including film cooling holes and internal passages) was used, to account for internal cooling flow redistribution resulting from altered external loading. We show that lean-burn inlet conditions result in significant surface flow redistribution, relatively high levels of residual swirl in the downstream flow, and a small increase of integrated KE loss.

## Introduction

Nitrogen oxide (NO_{x}) emissions have been linked to increased mortality from respiratory conditions and have been identified as a potential forcing agent for global climate change [1]. Lean-burn combustion architectures promise to reduce aero-engine NO_{x} emissions by reducing peak combustion temperature. As demonstrated by both prototype [2] and in-service systems [3], this is achieved by increasing the proportion of engine core-flow that passes through the fuel injector. The intended result is lower peak temperature, but with the consequence of greater residual swirl. In addition to combustion-related challenges (flashback, altitude relight, instability; see Ref. [4]) there are considerations relating to the performance of the high-pressure turbine. This has been extensively studied using computational fluid dynamics (CFD) and in a number of experiments using non-reacting combustor simulators.

The literature on lean-burn combustor–turbine interaction highlights the high-pressure stage performance sensitivity to: circumferential alignment of fuel injectors relative to the nozzle guide vanes (NGVs); the swirl sense (co-rotating or counter-rotating with respect to the NGV flow); the injector-NGV count ratio; and the resulting temperature profile shape. Here we refer to co-rotating flow as that in which the direction of the angular momentum vector of the swirler vortices is the same as that of the NGV outlet flow, and where in counter-rotating flow they are opposed. Thus, in co-rotating flow, the vortex could—loosely—be considered to augment the turning at the casing (also off-loading the vane) and lessen the turning at the hub (also increasing loading of the vane). In counter-rotating flow the effects at case and hub are reversed. As a natural development of trying to understand interactions, the question of optimum circumferential clocking of the fuel injectors (and associated vortices) *relative* to the NGV arises. Both *passage-clocked* and *leading-edge-clocked* (LE-clocked) vortex alignment has been studied, often in experiments or simulations with an NGV-to-injector count of two. Integer NGV-to-injector count has the advantage of being efficient for CFD, and suitable for experiments in which *stage* performance is to be studied (capacity; efficiency; inter-stage pressure ratio; etc.).

Some of the first investigators of lean-burn combustor–turbine interactions examined the effect of inlet swirl alone; that is, without temperature distortion. Qureshi et al. [5,6] and Beard et al. [7] experimentally tested LE-clocked configurations with co-rotating swirl, making comparisons to a baseline case with uniform inflow. They found that with the introduction of lean-burn swirl there was 1.2% decrease in turbine stage efficiency, a 2.0% reduction in stage capacity, and increased NGV and rotor heat transfer. The reduced stage efficiency and capacity were attributed to additional losses arising from off-design incidence operation of the NGV. Qureshi et al. [5] suggested that enhanced rotor heat transfer might be related to the greater inlet turbulence intensity (TI). In the NGV, combustor swirl significantly altered the surface streamline pattern. One consequence was amplified secondary flow intensity at the hub, which was attributed to increased loading, caused by positive incidence in this region. The altered secondary flow structure affected NGV endwall heat transfer, with circumferentially-averaged Nusselt number increasing by up to 26% at the hub, and decreasing as much as 7% at the casing [6].

Efforts in finding an optimum combination of swirl clocking and direction were pioneered by Khanal et al. [8], who reported that passage-clocking of a combined co-rotating swirl-core with hot-streak was preferable to LE-clocking in terms of the combined heat load of NGV and rotor. This marked what might be called the *second wave* of lean-burn-interaction studies, and the authors argued that swirl and temperature distortion effects must be studied together because the individual effects superposed poorly. Griffini et al. [9] studied the effects of swirl (counter-rotating only) and hot-streak clocking on the overall cooling effectiveness of NGV using conjugate CFD, and found that a passage-clocked-swirl configuration had reduced average metal temperature and reduced peak metal temperature when compared to a LE-clocked configuration. This was largely in line with Ref. [8]. Li et al. [10] performed a computational study in which both heat load and stage efficiency were considered, and concluded that LE-clocking with counter-rotating swirl was an optimum arrangement for their stage design. It is apparent that the development of the flow field within the high-pressure stage is sensitive to both the turbine geometry and the shape of the upstream swirl and temperature profiles. This highlights the importance of validating design tools with high quality experimental data.

Effects of lean-burn on the thermal performance of *film-cooled* NGV were examined by Griffini et al. [9], Bacci et al. [11], and Werschnik et al. [12]. For LE-clocked-swirl the greatest influence was around the showerhead of the vortex-aligned vane, where a low-pressure region at the vortex center had the effect of increasing coolant flow at the location where it impinged on the vane. This had the effect of improving film coverage locally, at the expense of greater coolant flow [11]. The swirl-induced change in airfoil loading caused greater mass efflux from film cooling holes in regions with reduced external pressure [9]. Externally, the coolant films migrated according to the streamline pattern set up by the swirling flow. As the vanes had been designed for uniform flow, this generally resulted in less uniform coolant coverage, especially on the pressure side (PS). Platform cooling performance also deteriorated: when lean-burn flow was introduced the mean Nusselt number increased, and the mean film cooling effectiveness decreased [12]. Importantly, these studies emphasize that coolant migration effects can only be accurately predicted by models which consider both the internal and external geometry.

As understanding of turbomachinery has advanced, there has been increasing interest in turbulence and unsteady phenomena. For example, Folk et al. [13] demonstrated a strong sensitivity of NGV loss to the inlet turbulence intensity. Likewise, elevated turbulence is known to enhance heat transfer and accelerate film coolant decay [12], both of which have detrimental effects on thermal performance. Although the effects of turbulence are now reasonably well documented under experimental conditions, uncertainty surrounding real-world turbine performance persists because measuring combustor turbulence under *reacting conditions* is extremely difficult, and therefore combustor turbulence characteristics are poorly characterized. Schroll et al. [14] overcame this difficulty using particle image velocimetry, measuring turbulence intensities between 8% and 20% at the outlet of a single-sector reacting lean-burn combustor. In the related numerical study of Adoua and Page [15] the authors argued that turbulence intensity was *reduced* under reacting conditions, primarily because of volume-dilation-induced axial acceleration. Scarcity of data means there is still uncertainty about the nature of turbulence in many real-engines environments. Notwithstanding this limitation, high quality experimental data from non-reacting combustor simulators is important for numerical model *validation*.

A recent example of CFD model validation is the study of Thomas et al. [16], which compared experimental data from a fully-cooled turbine stage with combustor simulator (the FACTOR consortium project) to a large eddy simulation of the same. The simulation results were *qualitatively* similar to experiments, but with significant discrepancies in terms of the thermal field downstream of the NGVs. The authors attributed this to the modeling method for film cooling holes, which used patch inlets. This demonstrates the importance of resolving internal cooling passages. Scale resolving simulations of this kind show great promise in improving predictions of large-scale unsteadiness and free shear mixing, but currently remain too resource-intensive for design work, which continues to rely heavily on Reynolds-averaged Navier–Stokes (RANS) methods. In this vein, Adams et al. [17] compared experimental data from a combustor simulator and cooled 1.5-stage turbine (the Oxford Turbine Research Facility) with unsteady RANS (URANS). Downstream of the rotor, URANS solutions were undermixed, showing greater persistence of the radial temperature distortion than measured experimentally. Importantly, the study demonstrates that changes in NGV aerodynamics are primarily impacted by combustor swirl, whereas changes in rotor aerodynamics are primarily driven by temperature distortion.

In this study we present high-fidelity experimental data of fully-cooled NGVs subject to inlet swirl and temperature distortion. Cascade inlet conditions of total pressure, flow angles, temperature distortion, and turbulence were characterized using an upstream traverse system. We present detailed surveys of the aerodynamic and thermal fields downstream of the NGV at three axial planes, allowing us to analyze the development of residual swirl, kinetic energy (KE) loss, and hot-streak migration. Comparisons are made to corresponding measurements with uniform inflow. We compare this data to CFD simulations using fully-resolved NGV geometry. The unusually high-fidelity data allow detailed investigation of the impact of lean-burn flows on the first-stage nozzle aerothermal performance, and benchmarking of the CFD method.

## Experimental Methods

Experiments were conducted in the Engine Component AeroThermal (ECAT) facility at the University of Oxford (see Ref. [18]). The ECAT facility is a fully-annular NGV test facility used to test in-service and prototype engine hardware at engine-matched conditions of Reynolds number, Mach number, and coolant-to-mainstream mass flow ratio. The facility can operate in warm-flow (used for these tests) or hot-flow [19] mode, and for the experiments we report was configured *with* and *without* a lean-burn simulator [20]. The simulator reproduced target conditions of swirl, temperature distortion, and turbulence.

### Test Section Overview.

Meridional views of the ECAT facility working section, configured for both *uniform* and *lean-burn* testing, are shown in Fig. 1. For the uniform test case (top of Fig. 1), the upstream flow passes through a turbulence grid into a contracting inlet duct, which has a similar design to the annulus line of the engine. The NGVs are supplied with coolant from plena at the hub and casing. The NGV exit flow exhausts to ambient conditions through a parallel annular exit duct, which extends approximately three axial chords downstream of the NGV trailing edge (TE).

*Lean-burn-representative* inlet conditions are generated using a non-reacting combustor simulator (see Ref. [20]). This is illustrated in the bottom half of Fig. 1. The 20 counter-clockwise (CCW) oriented (when viewed from upstream) swirlers have the same sense of rotation as the NGV (co-rotating). The nominal swirl number (intensity) of the flow was estimated to be 0.26 using correlations based on the geometric design. This number was later confirmed using CFD simulations. The vane count was 40, giving a count ratio of 2:1 with the swirler. The *swirler* centerline is geometrically clocked onto the leading edges (LEs) of alternating vanes. Vanes are manufactured in pairs, and (inheriting language from the design process) we refer to the swirler-aligned vane as the trailing vane (TV) and the other mis-aligned vane as the leading vane (LV). Leading and trailing vanes are aerodynamically identical, but have slightly different cooling systems designed to account for combustor non-uniformity (caused by indexing between burners and vanes) in the real engine. Combustor temperature distortion is simulated by injecting cold air into the swirling hot stream from annular slots at the hub and casing walls.

The ECAT facility combustor simulator [20] is closely related to the combustor simulator recently used by Adams et al. [17,21] to investigate the effect of lean-burn on the performance of a 1.5-stage turbine. Both simulators were developed in parallel from the prototype of Hall and Povey [22]. We draw comparisons with the results of Adams et al. [17] to add depth to the analysis.

### Instrumentation and Measurements.

A schematic of the working section in the lean-burn configuration is shown in Fig. 2, with the key measurement planes marked. Cascade inlet conditions of total pressure and total temperature at plane 1 were monitored using spanwise rakes, totaling 32 Pitot and 32 thermocouple probes split across 8 circumferential, and 8 radial locations (see example of rake in Fig. 2). Additionally, detailed area surveys of total pressure, total temperature, flow angles, and turbulence were acquired at plane 1 using an upstream traverse system [23]. Slightly further downstream, at plane 1b, Amend et al. [20] characterized the combustor simulator flow (but not the turbulence grid) at low back pressure (i.e., without NGV installed). This data is used in the analysis of thermal field development. Stagnation pressure and temperature were measured in the temperature distortion module plena, and the vane coolant plena.

Downstream static pressure was measured along the circumference of two vane pairs, which were instrumented with 16 tappings on each of the platform overhangs at the hub and casing. Exit planes 2, 3, and 4 were located 0.25, 0.50, and 0.75 *C _{x}* axially downstream of the midspan TE, respectively. The aerodynamic and thermal field at planes 2, 3, and 4 was surveyed over the full span radially, and across two vane pitches circumferentially using an aerodynamic five-hole probe (reporting flow angle, Mach number, and total pressure), Pitot probe (near-wall region only), and dual-sensor thermocouple probe. To eliminate bias from hardware variations, the uniform and lean-burn test cases considered the same physical parts, and followed the same wakes when moving between planes (i.e., the traverse was clocked to follow the flow). Details of probe design, traverse resolution, and measurement uncertainty are summarized by Amend et al. [24].

### Experimental Operating Conditions.

Cascade operating conditions for the uniform and lean-burn experiments are summarized in Table 1. The thermal field measurements were performed with a mainstream-to-coolant temperature ratio of approximately 1.2, whereas the aerodynamic field was surveyed without temperature distortion. Reynolds number, Mach number, and coolant-to-mainstream mass flow ratio were well-matched between the uniform and lean-burn test cases.

Uniform | Lean-burn | |
---|---|---|

Swirl number, S (–) | 0.0 | 0.26 |

Vane Reynolds number, $Re$ (–) | 7.7 × 10^{5} | 7.6 × 10^{5} |

Vane Mach number, $M2$ (–) | 0.91–0.93 | 0.91–0.93 |

Vane coolant-to-mainstream mass flow ratio, $m\u02d9c/m\u02d91$ (–) | 0.14 | 0.13 |

Mainstream total temperature, $T01$ (K) | 325–355 | 320–350 |

Combustor coolant total temperature, $T0b$ (K) | N/A | 290–300 |

Vane coolant total temperature, $T0c$ (K) | 284–292 | 290–300 |

Plane 1 total pressure uniformity (–) | ±0.1% | ±1.1% |

Plane 1 turbulence intensity, TI (–) | 13% | 15% |

Uniform | Lean-burn | |
---|---|---|

Swirl number, S (–) | 0.0 | 0.26 |

Vane Reynolds number, $Re$ (–) | 7.7 × 10^{5} | 7.6 × 10^{5} |

Vane Mach number, $M2$ (–) | 0.91–0.93 | 0.91–0.93 |

Vane coolant-to-mainstream mass flow ratio, $m\u02d9c/m\u02d91$ (–) | 0.14 | 0.13 |

Mainstream total temperature, $T01$ (K) | 325–355 | 320–350 |

Combustor coolant total temperature, $T0b$ (K) | N/A | 290–300 |

Vane coolant total temperature, $T0c$ (K) | 284–292 | 290–300 |

Plane 1 total pressure uniformity (–) | ±0.1% | ±1.1% |

Plane 1 turbulence intensity, TI (–) | 13% | 15% |

## Performance Metrics

This section summarizes the performance metrics used for the inlet flow survey (plane 1), and in the analysis of the aerodynamic and thermal fields downstream of the NGV (planes 2, 3, and 4).

### Flow Angle Definitions.

### Upstream Normalized Total Pressure.

*upstream*normalized total pressure, $p01,norm(r,\theta )$, is defined as

*r*, and circumferential position $\theta $; 0.75 s sampling period), and $p01,rake$ is the ensemble average of the 32 stationary Pitot pressures at the same axial plane over the same time period. Normalization allows us to differentiate between spatial non-uniformities, and temporal variations of the inlet flow (these are low-frequency and very small in magnitude). We use $p01,norm$ to estimate the instantaneous mass-flux-weighted total pressure at plane 1 from the instantaneous total pressure reported by the rake.

### Upstream Non-Dimensional Total Temperature.

*upstream*total temperature, $\Theta 1$, by

*T*

_{0b}= 293.15 K (i.e., the ambient temperature during testing).

### Upstream Turbulence Intensity and Integral Length Scale.

*k*is turbulence kinetic energy,

*V*is absolute velocity, and $\tau $ is the integral timescale (average of three components). Turbulence kinetic energy, velocity, and timescales were measured using a pair of split-fiber (hotwire) probes (see Ref. [23] for details of setup). The components of the integral time scale (in

*x*,

*r*, and $\theta $) were defined as the integral of the normalized autocorrelation function of the corresponding velocity component from zero time shift to the first zero crossing.

### Kinetic Energy Loss Coefficients.

The aerodynamic efficiency of the NGV was quantified using a number of KE loss coefficients. We adopt the definitions used during a prior analysis of the uniform test case [24], which made use of a *local* KE loss coefficient ($\zeta 1$); a *circumferentially-averaged* KE loss coefficient ($\zeta 3$); a *plane*-*averaged* KE loss coefficient ($\zeta 4$); and a *mixed-out* KE loss coefficient ($\zeta 5$). *Local* and *circumferentially-averaged* KE loss coefficients correspond to the definitions of Burdett and Povey [25]; the *plane-averaged* KE loss coefficient was defined following Lawaczeck [26]; and *mixed-out* conditions were calculated according to the Dzung method [27,28]. For brevity, we do not rehearse the definitions here.

### Non-Dimensional Downstream/Surface Total Temperature.

*excluding*thermocouples immersed in the coolant layer). $\Theta 2$ ranges between 0 and 1; higher values indicate higher temperature. The definitions of $\Theta 1$ and $\Theta 2$ are equivalent when $T0b=T0c$. When presenting adiabatic wall temperatures, we use the symbol $\Theta w$ for clarity but follow the same definition as that in Eq. (6).

## Combustor Simulator Outlet Profiles

An upstream traverse system [23] was used to survey the inlet flow at plane 1 (see Fig. 2) over a 34.4-deg circumferential sector, and across the full span radially. The mean-flow and the turbulence at inlet were fully characterized using a combination of total pressure, thermocouple, and split-fiber (hotwire) probes. The intention was to use this data as reference conditions for experimental measurements downstream of the NGV, and as inlet boundary conditions for complementary CFD simulations. Due to a probe size limitation, a small region at the hub could not be traversed. The approach taken to estimate values of missing data is explained later in this section. Details relating to the spatial resolution, sampling period, and data reduction method can be found in Ref. [23]. Amend et al. [24] previously presented the inlet profiles for the *uniform* inlet condition (plane 1). For brevity, we only present the lean-burn profiles in this paper.

Experimentally-measured combustor simulator outlet profiles (plane 1) of normalized total pressure ($p01,norm$), non-dimensional total temperature ($\Theta 1$), turbulence intensity (TI), and normalized integral length scale ($\u2113/Cx$) are shown in Fig. 3. The distributions were obtained by mapping the surveyed 34.4-deg sector onto a single swirler sector (18 deg). Regions of duplicate data were averaged, with slight smoothing across circumferential boundaries to ensure periodicity (required for suitability as a CFD boundary condition). The *x*-axis ($\theta norm$) is the vane-pitch-normalized circumferential coordinate, where $\theta norm=0$ is the swirler centerline, which is clocked onto the leading edges of alternating NGVs (recall that the NGVs have a 2:1 count ratio with the swirlers). The axially-projected locations of NGV LE are indicated by the vertical dashed lines. Of note, the *x*-axis is inverted (i.e., descending toward the right) because the $+\theta $ direction was defined as the turning direction of the NGV, which is CCW (left) when viewed from upstream. The *y*-axis ($rnorm$) is the normalized span fraction. The superimposed vector field represents the in-plane flow direction and magnitude for an equivalent horizontal duct. The inclination of the duct (around 15 deg) is accounted for by plotting the *deviatory* radial vector component (see transformation method of Bacci et al. [29]).

First consider the in-plane flow field in upstream plane 1, shown by the vector field superimposed on all subplots of Fig. 3. The swirl direction is CCW when viewed from upstream. Maximum and minimum whirl angles at plane 1 were approximately +30 deg and −38 deg respectively. By plane 1b (0.5 axial chords upstream of vane LE) these were shown to be attenuated to +20 deg and −22 deg (see five-hole probe measurements of Amend et al. [20]). The attenuation arises because of the axial acceleration due to the converging duct. The center of circulation—indicated by a white cross—is located approximately 2 deg to the left of the geometric center of the swirler ($\theta norm=0)$. This type of circumferential vortex core migration has previously been reported by Bacci et al. [29] and Schmid et al. [30]. The mechanism is that as individual vortices mix-out through inter-vortex free shear, conservation of angular momentum causes bulk-turning of the flow (see discussion in Ref. [20]). In the study of Bacci et al. [29], the vortex was slightly PS-biased, leading to NGV flows more typical of passage-clocked swirl. For the current study, the center of circulation is also slightly PS-biased, but the migration effect had minimal impact, because the whirl angle is relatively circumferentially-uniform at a particular radial height, and therefore affects the flow in alternating vane passages similarly regardless of clocking (i.e., the swirl is less localized; see distributions from Ref. [20]). This is consistent with recent observations from the similar combustor simulator of Adams et al. [17] (also derived from the prototype of Hall and Povey [22]), for which NGV inlet profiles were likened to a *circumferentially-shearing* flow.

Now consider the distribution of normalized total pressure ($p01,norm$; see Eq. (2)), which is shown in the top left subplot of Fig. 3. Between 4% and 91% span, normalized total pressure is approximately uniform. Here the maximum variation is ±0.2% of the rake average, with a local minimum of 0.998 at the vortex center. Toward the casing the normalized total pressure increases steeply, reaching a maximum of 1.017 near the wall. Normalized total pressures higher than unity are associated with coolant ejection from the annular temperature profile generator slots, and is a consequence of the particular design decisions taken (matched total pressure is also possible). Mild excess near-wall total pressure may be a characteristic of lean-burn combustor designs in which there is significant combustor liner coolant. Indeed, a similar near-wall total pressure excess of approximately 1.0% was observed in the lean-burn combustor outlet profiles used by Shahpar and Caloni [31] in a turbine optimization study. These originated from a high-fidelity simulation of a lean-burn combustor prototype. It was not possible to perform measurements in the 0–3% span region (near hub flow) and this region was *patched* with data from CFD simulations of the combustor simulator. The maximum normalized total pressure in the patched data was 1.020. This is slightly higher than the maximum value at the casing (1.017), but this is explained by the fact that the exit of the hub coolant feed is closer to plane 1 than the exit of the casing coolant feed slot. Thus the hub coolant flow is less mixed-out at the measurement plane.

It is worth noting that the pressure surpluses in the hub and case coolant flows mix-out fairly rapidly downstream of the injection slots, with the non-uniformity approximately halving by plane 1b (non-uniformity of ±0.4%; see measurements in Ref. [20]).

Now consider the distribution of the non-dimensional total temperature ($\Theta 1$; see Eq. (3)), which is shown in the top right subplot of Fig. 3. The profile is broadly radial in nature (i.e., low circumferential distortion), with approximately uniform temperature ($\Theta 1\u22481$) over the wide region between 6% and 89% span. Near the casing, the temperature decreases steeply due to coolant injected from the temperature distortion module (emulating the effect of combustor liner cooling). The patched region at the hub (0–3% span) was linearly interpolated between the last measured point (3% span) and an assumed value of $\Theta 1=0$ at the wall. The assumed value is justified on the basis that this point is just downstream of the hub slot exit, and therefore should be fully covered by unmixed hub coolant flow. This total temperature profile mixes rapidly between plane 1 and plane 1b, leading to a more rounded radial distribution at the NGV inlet (see measurements in Ref. [20]).

Now consider the distribution of the $turbulenceintensity$ (TI; see Eq. (4)), which is shown in the lower left subplot of Fig. 3. The average turbulence intensity is approximately 15%, but with a large region of elevated intensity approximately downstream of the swirler geometric center. Here the peak value of turbulence intensity was 22%. In the hub and case coolant jets, the turbulence intensity reduces: values of TI = 10% were measured near the casing wall; values of 8% were estimated at the hub wall based on a CFD-predicted profile linearly scaled to match the last measured value in the near hub flow (at 5% span).

Finally, consider the profiles of normalized integral length scale ($\u2113/Cx$; see Eq. (5)), shown in the lower right subplot of Fig. 3. Experimentally-measured length scales had relatively high precision uncertainty because the sampling period (0.75 s) had to be optimized for the relatively short (approximately 60 s) facility run duration. As CFD simulations of the combustor simulator showed that $\u2113$ varied primarily as a function of the radius, the measured distribution was circumferentially-averaged. Though a relatively crude approach, this ensures that the profile is suitable for use as a CFD inlet condition. In the resulting profile, the circumferentially-averaged length scale was approximately constant between 20% and 75% span (average of $0.88Cx$), with slightly higher values in the free shear layers between the hub and case cooling flows and the main-flow. These elevated values might be related to unsteadiness of the shear layer. Near the casing, $\u2113/Cx$ decreased on approach to the wall, with the lowest measured value being 0.34. This is consistent with the commonly-observed linear variation of length scale in the near-wall region (see, e.g., Ref. [32]). In principle, we would expect $\u2113/Cx=0$ at the wall. The non-zero value in current measurements is likely explained by an interaction with the probe access port at the casing, resulting in a disturbed cavity flow (instead of a boundary layer flow). For compatibility with the numerical model, $\u2113/Cx=0$ was enforced at both the hub and casing walls, interpolating linearly with the last measured values of $\u2113/Cx=0.80$ and 0.58 at 5% and 98% span, respectively.

## Numerical Methods

Steady RANS simulations of the fully-featured NGV were performed for uniform and lean-burn-representative inlet conditions. The purpose of these simulations was twofold: insight into the effects of inlet swirl and inlet temperature distortion on the flow in regions which were difficult to measure; assessment of the accuracy of CFD methods for lean-burn inlet conditions. In this section we describe the domain, boundary conditions, and models.

### Computational Domain and Grid.

The mesh used in the current study has previously been described by Amend et al. [24], and is therefore summarized only briefly. The mainstream inlet is located at plane 1 (see Fig. 2), and the outlet is located approximately three axial chords downstream of the vane TE at the outlet of the vane exit duct. The internals of the vanes are fully-resolved, with coolant introduced from inlets inside the hub and casing plena. Resolving the vane internals ensures that coupling effects arising from the impact of the altered external loading (due to inlet swirl) on the internal flow redistribution are correctly accounted for. The mesh contains roughly 312 million cells, approximately half of which were internal. A second mesh *excluding airfoil film cooling* (no internals; same refinement level; 151 million cells) is used to investigate the effect of inlet swirl on the surface streamlines, which would otherwise be interrupted by the presence of cooling holes.

### Boundary Conditions.

We now consider the domain boundary conditions for the uniform and the lean-burn-representative test cases. In each case, the aim was to replicate the respective experimental boundary conditions.

For the *uniform test case*, the inlet boundary conditions at plane 1 were specified as the experimentally-measured radial profiles of total pressure, total temperature, turbulence intensity, and turbulence length scale. For further detail see Ref. [24]. The average turbulence intensity at plane 1 was 13%, and the turbulence length scale was on the order of one axial chord ($\u2113/Cx\u22481$). The flow direction was in the meridional plane, with a pitch angle distribution bounded by the hade angles at the hub and casing walls.

For the *lean-burn test case*, the inlet profiles of total pressure, total temperature, flow angles, turbulence intensity, and turbulence length scale were specified as the pre-conditioned (periodic; missing data patched) experimentally-measured area maps at plane 1 (see Fig. 3). The inlet values of turbulence dissipation rate, $\u03f5$, were estimated using the CFX definition of the turbulence length scale ($\u03f5=k1.5/\u2113$; see CFX solver theory guide), where the turbulence length scale, $\u2113$, was assumed to be equal to the integral length scale (see discussion on the choice of scaling constant [33]). A comparison between CFD-predicted turbulence dissipation rates at plane 1 with those estimated from experimentally-measured integral length scales suggests that this is a good approximation for the present combustor simulator flow.

For both uniform and lean-burn test cases, coolant plena inlets were specified with boundary conditions of constant mass flow rate and total temperature (average across experimental dataset), and with a turbulence intensity of 5% and a viscosity ratio of 10. The domain outlet had a radial equilibrium condition specified. Exit static pressure was allowed to vary in the circumferential direction to ensure the solution was not over-constrained. Periodic interfaces were conformal (one-to-one node mapping). All wetted surfaces were modeled as hydraulically smooth. For simulations using the mesh that *excluded airfoil film cooling*, boundary conditions were the same as for the cooled simulations.

### Model and Solver Settings.

Simulations were performed using ansys cfx (version 22.1). The working fluid was dry air, which was treated as an ideal gas with constant transport properties. The mean-flow energy equation included the viscous-work term, and turbulent fluxes were modeled with eddy diffusivity using a turbulent Prandtl number of 0.50 (optimized for free shear mixing of coolant; see Ref. [34]). Turbulence was modeled using the baseline explicit algebraic Reynolds stress model (BSL-ARSM; see Ref. [35]), with the turbulence production limiter disabled. These settings were shown to offer a good compromise between predictions of integral loss, and aerodynamic wake mixing for the uniform test case, but were found to result in slight overmixing of the thermal field. Choice of turbulence model for this problem is discussed by Amend and Povey [33]. The mean-flow and turbulence equation systems were discretized with a second-order upwind-biased numerical scheme.

## Nozzle Guide Vane Loading and Streamline Pattern

The effects of inlet swirl on the NGV surface static pressure distribution and surface streamline pattern were investigated using CFD. This allows analysis of the cooling system response, which is affected both in terms of internal flow redistribution due to altered external pressure, and in terms of the external migration of film coolant on the vane surface. The NGV static pressure distribution is also relevant from an external-aerodynamic standpoint because changes in loading and flow pattern alter the KE loss distributions and secondary flow intensity.

### Nozzle Guide Vane Loading Distribution.

The *change* in normalized static pressure ($\Delta p2/p01$) due to swirl is shown in Fig. 4. Normalized static pressure is defined as the surface static pressure ($p2$) normalized by the mass-flux-weighted total pressure at plane 1 ($p01$). The distributions are shown for the PS and SS of both the TV and LV. Looked at in terms of *changes* in static pressure on the PS and SS, local loading is reduced when the pressure on the PS decreases *relative* to that on the SS (i.e., when $\Delta p2,PS<\Delta p2,SS$).

We first note that the changes on the TV and LV are extremely similar to each other. We recall that the yaw angle of the incoming flow is relatively uniform circumferentially, resulting in comparable incidence onto both vanes. This behavior has been seen in other studies with these *circumferentially*-*shearing* swirl profiles at inlet [17,31]. For lean-burn combustors with flow patterns of this type, design integration with the NGV may be simpler (same airfoil for TV and LV).

The sense of swirl in this study was co-rotating, such that it caused negative incidence in the (approximately) upper half of the span range (reduced loading) and positive incidence in the lower half of the span range (increased loading). Accordingly (see Fig. 4), in the upper half of the span range we see an increase in SS pressure and a decrease in PS pressure (reduced loading); the effect is reversed in the lower half of the span range. The changes are fairly uniform with chord along the PS of the vane (slight changes in the entire vane exit flow field), but concentrated toward the LE on the SS of the vane (change in SS peak only). Therefore, the LE region is much more affected than the TE region in terms of loading, with limited changes beyond 40% axial chord.

### Surface Streamlines.

CFD-predicted surface streamlines for uniform and lean-burn-representative (swirling) inlet conditions are shown in Fig. 5. The surface streamlines are based on simulation of the vanes *excluding* film cooling. Although film cooling locally enhances momentum flux and could—in principle—alter the streamline pattern, similar uncooled simulations have been shown to be a good predictor of surface streamline pattern (see Ref. [17]). An advantage of uncooled simulations is that the surface flow is uninterrupted and therefore easier to interpret *visually*.

First consider the surface streamlines for the uniform test case, which are shown on the left side of Fig. 5. The streamline pattern is effectively identical for both vanes. On both the PS and SS, surface streamlines between 15% and 80% span are approximately parallel to each other, with mild upwash near the stagnation line (combined effect of radially-inclined inlet duct and a backwards-swept LE). From mid-chord onwards on both the PS and SS there is mild downwash over most of the surface, caused by low momentum fluid migrating radially-inwards in the radial pressure gradient set up by the mainstream flow. The effect is less pronounced on the SS than the PS because the ratio of local momentum to radial static pressure gradient is lower. Near the hub and casing endwalls, the streamlines are disturbed by low-intensity secondary flows.

Now consider the surface streamline pattern for the case with lean-burn-representative (swirling) inlet flow, shown on the right side of Fig. 5. The streamline pattern is relatively similar for both vanes. This is a result of the incoming flow pattern, which is relatively circumferentially-uniform at a particular radial height. The introduction of swirling flow causes significant upwash on the lower span sections of the PS, and significant downwash on the upper span sections. This causes the streamlines to coalesce toward the midspan: coolant concentration in this region is therefore expected. The SS is much less affected by the introduction of inlet swirl, but the very mild downwash we see in the uniform case is slightly enhanced by inlet swirl. This is consistent with the fact that the dominant pressure disturbance associated with inlet swirl is one that enhances the radially-inwards pressure field on the early SS (see Fig. 4). The introduction of inlet swirl seems also to slightly suppress the casing secondary flow, which remains confined closer to the endwall under swirling inlet conditions. Similar surface streamlines were reported by Adams et al. [17].

Finally, consider the leading edge stagnation lines for the uniform and lean-burn-representative test cases. For uniform inflow, the stagnation line is almost straight, aligning with the SS crown and—more significantly—the film cooling hole pattern. With the introduction of swirl, the stagnation line migrates toward the PS in the lower half of the span, and toward the SS in the upper half of the span, creating a mild sinusoidal shape in the stagnation line (relative to the stagnation line from the uniform test case, which is shown superimposed in Fig. 5). This causes some LE film trajectories to move from one side of the vane to the other (from PS to SS and vice versa). This has implications for the cooling budget of the two surfaces, but also makes the affected holes susceptible to separation because their lay-orientation (with respect to the local surface) opposes the external flow direction. Clearly the vane aerodynamics and cooling system would need to be designed for a specific lean-burn inlet condition, considering both swirl and temperature distortion.

## Effect on Cooling System

Inlet swirl significantly alters both the vane surface pressure distribution and surface streamline pattern, leading to changes in individual film mass flow rates (internal redistribution) and external coolant migration. We study these effects in this section.

### Description of Film Cooling Configuration.

The PS and SS of the vane airfoil each feature five rows of film cooling holes. The TE is cooled by a letterbox-style slot with PS-ejection (i.e., with SS overhang), extending along the full span. The hub and casing endwalls are cooled by two staggered rows of film cooling holes. Vane airfoil coolant (PS, SS, and TE slot) and hub endwall coolant are supplied from a shared plenum at the hub. The casing endwall coolant is fed from a separate plenum. Both plena are shown schematically in Fig. 2 (proprietary details are omitted, but the cooling system is approximately as shown).

### Internal Flow Redistribution.

We now consider the redistribution of the internal cooling flows by looking at the impact of lean-burn swirl on the row-wise and spanwise cooling mass flow rates.

Consider first the effect of swirl on row-wise coolant redistribution. Row-wise normalized mass flow rates ($m\u02d9/m\u02d9c$) for uniform and lean-burn-representative inlet conditions are shown in Fig. 6, considering the TV and the LV separately.

We see from Fig. 6 that *row-wise* redistribution of coolant with the introduction of lean-burn swirl is relatively subtle. The normalized mass flow through the TE slot increases by 1.9% for the TV and by 1.7% for the LV under lean-burn conditions. The increase in TE slot mass fraction is caused by an increase in the total-to-static pressure ratio at the TE slot exit, caused by a reduction in the base pressure. For the vane surface cooling rows (excluding TE slots), the maximum percentage increase in mass flow was for PS row 5 of the TV (+1.1%), and the maximum decrease was for PS row 2 of the TV (−3.4%). The reason for the limited sensitivity of row-wise mass flows is that the change in external static pressure is approximately antisymmetric about the midspan (see Fig. 4). A reduction in the mass flow at one end of the cooling row is therefore compensated for by a proportionate rise in mass flow at the other end. We explore this effect further now.

Mass flow rates of individual film cooling holes are now investigated to consider *spanwise* redistribution effects. Intuitively, we expect that mass flows will depend primarily on the static pressure at the exit of the film cooling hole. In Fig. 7, for each cooling hole we plot the *actual ratio* of coolant mass flow rates for lean-burn and uniform conditions, $m\u02d92/m\u02d91$ (where $m\u02d91$ is the uniform coolant hole mass flow rate, and $m\u02d92$ is the lean-burn mass flow rate) against an *estimated ratio* based on isentropic mass flow function and area-averaged static pressure across the film cooling hole exit (and mass-flux-weighted total temperature and pressure entering the hub coolant plenum). Presented in this way, the spread on the *y*-axis shows the actual distribution of mass flow ratio changes with swirl, and the goodness of correlation (with a linear trend of slope unity) shows the degree to which the change is purely explained by external static pressure changes. Scatter points are colored to distinguish PS, SS, and TE (each TE slot is treated as a single hole).

Looking first at the changes in actual mass flow rate ratios, we see that the introduction of swirl causes changes of +19.1% and −14.2% for individual SS holes, and +8.9% and −11.4% for PS holes. The mass flow of the TE slots increased by 1.7% and 1.9%. The change for SS holes is significantly greater than for PS holes, in line with the greater change in static pressure on the SS than on the PS (see Fig. 4).

Now consider the comparison of the actual and estimated mass flow rate ratios. There is reasonably good agreement with a linear trend of slope unity, showing that to first order the mass flow rate changes can be explained by changes in external static pressure. With reference to the static pressure *change* distributions in Fig. 4, this implies that the PS experiences internal coolant redistribution from hub (increased static pressure) to casing (decreased static pressure), while the opposite is true for the SS. Deviations from the linear trend are explained by the fact that internal duct pressure losses, and cross flow effects on both the inlet and outlet of the hole are not captured by the low-order model.

### Adiabatic Wall Temperature.

We now consider the effect of lean-burn swirl and inlet temperature distortion (see Fig. 3) on CFD-predicted adiabatic wall temperatures of the vane airfoil. The three primary mechanisms are: a change in the inlet external driving temperature (see discussion of Qureshi et al. [36]); a swirl-induced change in surface streamline pattern which causes change in coolant flow migration and temperature field migration (see discussion of Khanal et al. [8]); a change in freestream turbulence which affects both the lateral spreading and streamwise decay rates of coolant films (see discussion of Schmidt and Bogard [37]). To separate the effect of local coolant concentration and local driving temperature (which are easily conflated) we perform additional uniform and lean-burn-swirl simulations with *constant total temperature* at inlet specifically with the purpose of investigating the effects of swirl and turbulence on a like-for-like basis with the uniform test case. Separation of effects in this way is justified by the Munk and Prim [38] principle, according to which the streamline pattern remains unchanged for a changing inlet temperature profile.

Airfoil surface distributions of normalized adiabatic wall temperature, $\Theta w$ (see Eq. (6)), from simulations with constant inlet total temperature but with uniform and lean-burn-representative inlet conditions for swirl and turbulence are shown in Fig. 8. Corresponding surface-averaged values are reported in Table 2. Here we are interested in qualitative comparison of overall trends and note that absolute values are unlikely to be highly accurate due to the choice of turbulent Prandtl number, which was optimized for free shear thermal mixing, in favor of wall heat transfer.

Uniform | Lean-burn | |
---|---|---|

TV PS | 0.335 | 0.400 |

TV SS | 0.241 | 0.295 |

LV PS | 0.363 | 0.408 |

LV SS | 0.237 | 0.284 |

PS average | 0.349 | 0.404 |

SS average | 0.239 | 0.290 |

Uniform | Lean-burn | |
---|---|---|

TV PS | 0.335 | 0.400 |

TV SS | 0.241 | 0.295 |

LV PS | 0.363 | 0.408 |

LV SS | 0.237 | 0.284 |

PS average | 0.349 | 0.404 |

SS average | 0.239 | 0.290 |

First, consider the CFD-predicted distributions of $\Theta w$ under uniform flow conditions. In the upstream view (top row), both airfoils exhibit an elongated hotspot along the stagnation line. For reasons relating to the combustor hot-streak clocking in the real engine, the TV and LV feature different film cooling designs. This leads to slightly different adiabatic wall temperature distributions, even under uniform inlet conditions. Notably, the TV PS is on average slightly colder ($\Theta w=0.335$) than the LV PS ($\Theta w=0.363$; see Table 2), indicating better film coverage. The LV PS $\Theta w$ distribution is also slightly less radially uniform, with a colder region between approximately 10% and 40% span. On the SS (bottom row) the TV and LV have more similar $\Theta w$ distributions, the predominant feature being increasing adiabatic wall temperature toward the TE as the films mix-out with the freestream (lower film effectiveness). Near the casing (80–100% span) there is a notably cold region of secondary flow with entrained endwall coolant.

Now consider the impact of lean-burn-representative inlet conditions for swirl and turbulence. Looking first at the upstream view (top row) of the PS and early SS, the most striking difference compared to the uniform flow case is the reduced intensity of the stagnation line hotspot. With reference to the surface streamline pattern in Fig. 5, this is explained by coolant migration, which is locally redirected toward the spanwise (as opposed to the chordwise) direction, thus improving the coverage uniformity in the LE region. This effect is likely reinforced by the elevated turbulence intensity, which promotes lateral spreading of films (see Ref. [37]). Despite a reduced *maximum* adiabatic wall temperature, the *area-average* adiabatic wall temperature on the PS increases significantly (from 0.349 on average across both vanes to 0.404; see Table 2). This appears to be associated with poor film coverage and possibly the accelerated decay of films under high turbulence conditions [37]. Poor film coverage is especially apparent on the mid-to-late TV PS, where the upper half of the film-cooled region is significantly colder than the lower half. This is caused by two effects. First, by variation of cooling hole mass flow rates on account of swirl-induced changes in static pressure (see Fig. 4), which results in a net internal redistribution of coolant from hub to casing on the PS. Second, by changes in the external streamline pattern, which causes the flow to concentrate around 60% span. Because the streamline pattern redistributes coolant away from the near-wall regions, the adiabatic wall temperature on the aft PS near both the hub and casing increases. We recall that here we are concerned with the effect of swirl and turbulence only, and that for an engine-realistic inlet temperature distribution the radial adiabatic wall temperature variation would be less severe.

Finally, consider the downstream view (bottom row) of the adiabatic wall temperature distribution on the mid-to-late SS. The area-averaged adiabatic wall temperature increased with lean-burn conditions (from 0.239 to 0.290 on average across both vanes; see Table 2); i.e., there is lower film performance with lean-burn conditions. We recall that the internal flow redistribution effect on the SS is such that the lower half of the span is slightly colder than the upper half. This effect is evident in Fig. 8. Swirl-induced secondary flows cause downwash in the lower half of the span, and seem to confine the casing secondary flow closer to the wall.

## Effect on Downstream Flow

In this section, we consider the effect of inlet swirl and temperature distortion on experimentally-measured and CFD-predicted distributions of vane exit whirl angle ($\alpha $), local KE loss ($\zeta 1$), and non-dimensional total temperature ($\Theta 2$) at three downstream planes. We also characterize integral KE loss using plane-averaged and mixed-out KE loss coefficients. Experimental measurements are compared with CFD predictions using the BSL-ARSM turbulence model.

### Whirl Angle and Residual Combustor Swirl.

Experimentally-measured and CFD-predicted whirl angle ($\alpha $) distributions for the uniform and lean-burn-representative test cases are shown in Fig. 9. Data are viewed from downstream, and cover two vane pitches, equivalent to one swirler pitch. We consider the effect of inlet swirl on the flow field at downstream planes 2, 3, and 4 (located at 0.25 *C _{x}*, 0.50

*C*, and 0.75

_{x}*C*downstream of the midspan TE, respectively; see Fig. 2). As we move between planes, the analysis regions move to track the same wakes in both the experimental and CFD results (method uses the mass-flux-weighted whirl angle). Thus, the abscissa, $\theta norm$, represents the vane-pitch-normalized circumferential location in the wake-following coordinate frame. The ordinate, $rnorm$, is the normalized span datumed to the radius at the hub. The wakes of the TV and LV are centered around $\theta norm=0$ and 1, respectively. Whirl angles are presented in terms of the deviation from the midspan TE metal angle ($\alpha TE$), where a positive value ($\alpha \u2212\alpha TE>0$) corresponds to overturning. A contour of the normalized local KE loss coefficient corresponding to $\zeta 1/\zeta ref=0.5$ is superimposed to outline the aerodynamic wakes. Here, the

_{x}*reference*KE loss coefficient, $\zeta ref$, is defined as the experimentally-measured mixed-out KE loss coefficient at plane 4 for the uniform test case (i.e., a single value for all normalizations). For the test case with inlet swirl, the wakes of NGV aligned with the swirler/vortex are marked with a circular arrow indicating the direction of swirl.

The flow field for the uniform test case was previously analyzed in detail using experimental measurements (first column), and CFD simulations (second column) [24]. We briefly review the key observations, starting with the experimentally-measured whirl angle distribution at plane 2 (first row and column). For uniform inlet conditions, the radial variation of whirl angle generally follows the spanwise metal angle distribution of the NGV, which has slightly higher turning in the upper half of the span. Circumferential non-uniformities are associated with the potential field of the TE, which *locally* reduces the whirl angle of the downstream flow in regions circumferentially aligned with the *axially-projected* location of the TE. For a discussion of this effect see Ref. [24]. Outlines of the aerodynamic wakes at plane 2 are slightly bowed toward higher $\theta norm$ at midspan, approximately following the shape of the compound-leaned TE as viewed on an axial cross section. At downstream planes 3 and 4 (see rows two and three) the radial variation in whirl angle is similar to plane 2, but there is a reduction in circumferential non-uniformities due to decreasing potential field intensity and turbulent mixing of the flow. Aerodynamic wakes become increasingly distorted at planes 3 and 4, due to radial variations in the progression rate of the wake (i.e., angular versus axial displacement; $d\theta /dx\u2248tan(\alpha )/r$). CFD predictions of whirl angle (second column) are in generally good agreement with the experimentally-measured distributions.

Now consider the experimentally-measured distributions of whirl angle under lean-burn-representative inlet conditions (third column of Fig. 9). Visually, the whirl angle distributions appear periodic according to the vane pitch and not the swirler pitch; this is expected because the potential field is dominated by the vane, with only a secondary influence of inlet swirl. The area map at plane 2 (first row) broadly resembles that of the uniform test case, but with superimposed distortion from upstream swirl. In accordance with the direction of upstream swirl (see circular arrow), whirl angle increases between 35% and 80% span and is reduced below 35%. Above 80% span, wedge-shaped regions of underturned fluid appear toward the casing. Here, the change in whirl angle *opposes* the anticipated distortion based on the upstream direction of swirl. The underturning is caused by a radial band of elevated total pressure (combined influence of inlet pressure profile and casing endwall cooling), which renders the affected streamlines less responsive to the static pressure field set up by the bulk flow. The effect is of the same mechanism as, but opposite in sign to, the commonly-observed overturning of endwall boundary layer fluid (which has a deficit of total pressure). Similar trends were observed by Adams et al. [17], who also had elevated near-endwall upstream total pressure and associated underturning. In our test case we also have *mildly* elevated total pressure near the hub, and expect associated underturning: there is no obviously-distinguishable effect in the data, but the expected location is in a larger region of underturned flow due to upstream swirl. At downstream planes 3 and 4, the flow field becomes increasingly uniform in the circumferential direction, while the radial distribution remains largely unaffected. The CFD (see fourth column) and experimental data are in very good agreement at all axial planes.

Consider now the locations of the aerodynamic wakes under lean-burn-representative inlet conditions. With inlet swirl, the wakes experience significantly greater circumferential stretching between planes 2 and 4 than for the uniform test case. Amplified wake stretching is explained by the effect of whirl angle distortion on wake progression rates ($d\theta /dx\u2248tan(\alpha )/r$): the combination of raised whirl angles around the midspan (35–80% span), and reduced whirl angles near the walls (0–35% and 80–100% span) gives rise to a lead–lag effect, whereby the overturned flow near the midspan migrates toward higher $\theta norm$ at a faster rate than the underturned near-wall flow. Similarly, the plane-to-plane *streamwise* distance, *s*, is also extremely sensitive to whirl angle distortion, increasing with the *secant* of the whirl angle; i.e., $ds/dx\u2248sec\alpha $. For a representative exit angle of 75 deg, this corresponds to a 7% increase of streamwise distance for every degree increase in turning (locally linear assumption). We discuss the influence of streamwise development distance on perceived mixing rates in a later section on aerodynamic losses.

Now consider the experimentally-measured and CFD-predicted radial profiles of the circumferentially mass-flux-weighted absolute whirl angle, $\alpha $, which are shown in Fig. 10 for the uniform and the lean-burn-representative test cases. We consider the profiles at plane 4 (0.75 *C _{x}*; see Fig. 2), which corresponds to the approximate location of the high-pressure rotor LE.

Under uniform inlet conditions, the experimentally-measured trend is approximately linear from hub to casing (*y*-axis), which reflects the radial variation of the metal angle (lower turning at the hub). Slightly negative deviation angles at midspan (i.e., flow angles *exceeding* the midspan metal angle $\alpha TE$) are explained by an expansion of the passage area between the true TE and the measurement plane (flared endwalls).

Under lean-burn-representative inlet conditions the experimentally-measured radial distribution of whirl angle deviates from the uniform trend according to the direction of the upstream swirl (see arrows). In the previously-identified region of overturning (35–80% span), the maximum increase of whirl angle was 2.7 deg relative to uniform inlet conditions, while the maximum reduction in the 0–35% span range was 2.3 deg. In the region of total-pressure-driven underturning toward the casing (80–100% span), the maximum reduction was 2.6 deg.

CFD predictions for both test cases match the experimental measurements reasonably well. The CFD-to-experiment root-mean-square/maximum errors were 0.5/1.8 and 0.7/2.5 deg for uniform and swirling inlet conditions, respectively. For the lean-burn-representative test case, CFD underpredicts peak whirl angle by 0.9 deg, and exhibits lower sensitivity to the pressure-driven underturning effect toward the casing (80–100% span) than was measured experimentally.

Plane-averaged whirl angles (mass-flux-weighted) were only slightly affected by inlet swirl: experimentally-measured plane-averaged deviation angles were +0.59 deg for the uniform test case and +0.27 deg with inlet swirl; CFD-predicted plane-averaged deviation angles were +0.63 deg for the uniform test case and +0.40 deg with inlet swirl. That is, experiments and CFD both show a small, but systematic decrease of the plane-averaged whirl angle of around 0.2 deg under swirling inlet conditions (within uncertainty limits in the case of experiments).

### Kinetic Energy Loss Coefficient.

Experimentally-measured and CFD-predicted distributions of the normalized local KE loss coefficient ($\zeta 1/\zeta ref$) for the uniform and lean-burn-representative test cases are shown in Fig. 11. The local KE loss coefficient quantifies the fractional KE deficit of the flow, relative to and normalized by an ideal expansion from the mass-flux-weighted total pressure at plane 1 to the local downstream static pressure. We recall that the normalizing reference KE loss coefficient ($\zeta ref$) is defined as the experimentally-measured mixed-out KE loss coefficient at plane 4 for the uniform test case. The effect of lean-burn inlet conditions on aerodynamic wake development is studied using area maps at downstream planes 2, 3, and 4. A wake-tracking method is used (previously described).

Before investigating the effect of lean-burn on local KE loss, we briefly review the key features of the aerodynamic wakes under uniform inlet conditions, starting with the experimentally-measured distribution at plane 2 (0.25 *C _{x}*; first row and column of Fig. 11). The data are viewed from downstream. The wakes of the TV (marked W1) and LV (W2) are centered about $\theta norm=0$ and 1 (respectively) in the wake-tracking reference frame. Both wakes are gently bowed so that at midspan they are at higher $\theta norm$, following the compound-leaned shape of the TE on an axial cross section. The region between 10% and 90% span is dominated by profile loss, which is relatively uniform in the spanwise direction. Secondary flow loss cores located around 12% and 79% span cause a slight broadening of the wake, accompanied by local maxima of KE loss. The steep rise of the local KE loss coefficient near the walls is driven by the endwall boundary layers. As expected, the aerodynamic wakes gradually mix-out at downstream planes 3 and 4 (second and third row of first column), leading to progressive broadening of the wake, and an attendant decrease in peak KE loss. Simultaneously, the endwall boundary layers at the hub and casing grow in thickness. The CFD simulation of the uniform test case (second column) captures the KE loss distribution in the profile region reasonably well, but underpredicts radial spreading of endwall boundary layers slightly.

Let us now examine the experimentally-measured distributions of normalized local KE loss coefficient under lean-burn-representative inlet conditions, which are shown in the third column of Fig. 11. Aerodynamic wakes W1 and W2 appear to respond similarly to lean-burn inlet conditions, and we therefore analyze the wakes together, but for completeness mark the swirler-clocked vane wake with circular arrows. We begin by examining the aerodynamic wakes at plane 2 (0.25 *C _{x}*; first row and third column). The wakes are more circumferentially stretched than for uniform inlet conditions, an effect that is explained by the difference in wake progression rates (i.e., whirl angles) between the TE and plane 2. Around the midspan, the wakes are broader and have lower peak KE loss than was the case for uniform inlet conditions. This behavior is likely driven by the elevated midspan turbulence intensity at inlet (TI ≈ 13% for uniform flow; TI ≈ 20% for lean-burn inlet) which promotes diffusion.

Secondary flow structures respond according to the local change in aerodynamic loading due to inlet swirl. At the hub, incidence and loading increase, which causes the hub secondary flow to grow in size. Conversely, swirl-induced off-loading of the casing causes the corresponding loss cores to shrink. The casing secondary flow also migrates radially-outwards from around 79% span under uniform inlet conditions to approximately 90% span with inlet swirl. This is in accord with the change in SS surface streamline pattern (Fig. 5). Curiously, despite an increase in near-wall *upstream* total pressure with lean-burn inlet conditions, the endwall distribution of KE loss downstream of the vanes remains effectively unchanged. The low sensitivity is explained by the high *absolute* KE loss in the endwall boundary layers, which is large in comparison to the change in upstream total pressure.

Consider now the development of the experimentally-measured aerodynamic wakes at downstream plane 3 (0.50 *C _{x}*; second row) and plane 4 (0.75

*C*; third row). Strikingly, the plane-to-plane mixing rate is significantly greater than for uniform inlet conditions, especially around the midspan. One might assume that this is attributed solely to the elevated upstream turbulence intensity (lean-burn profile peaking around at midspan). Noting however the strong correlation between wake width/depth and

_{x}*streamwise distance*(as opposed to

*axial distance*; see Ref. [25]), we believe that the enhanced mixing is reinforced by whirl angle distortion (i.e., residual swirl) via its effect on streamwise distance ($ds/dx\u2248sec(\alpha )$). With reference to the whirl angle distribution at plane 4 (see Fig. 10), whirl angle between 35% and 80% span is increased by 1.6 deg on average (2.7 deg maximum) relative to uniform conditions, which corresponds to plane-to-plane increases of the

*streamwise distance*around 12% (average) and 24% (maximum). Under the assumption that the wake grows approximately linearly with

*streamwise distance*(see discussion in Refs. [24,25]), this would account for proportionally wider wakes (the rest being attributed to increased turbulence).

Finally, consider the CFD-predicted distributions of normalized local KE loss coefficient, which are shown in the fourth column of Fig. 11. CFD captures the wake shape, secondary flow footprint, and profile region mixing rates very well. The relatively high accuracy of these predictions of wake mixing is perhaps surprising, considering that unsteady vortex shedding was not modeled (steady RANS simulations). The good agreement with experimental data is because the BSL-ARSM model is observed to have higher SS diffusion and free shear mixing (for certain inlet conditions) than other models (see discussion in Ref. [33]), for example the more popular shear stress transport model. This may be an argument for using the BSL-ARSM model in certain cases.

Consider now the experimentally-measured and CFD-predicted *radial profiles* of normalized circumferentially-averaged KE loss ($\zeta 3/\zeta ref$) at plane 4, which are shown in Fig. 12. The circumferentially-averaged KE loss coefficient quantifies the mass-flux-weighted KE deficit in a radial band, relative to and normalized by the KE of an ideal expansion from the mass-flux-weighted total pressure at plane 1 to the circumferentially-averaged downstream static pressure of the radial band in question.

First, consider the experimentally-measured circumferentially-averaged KE loss coefficient under uniform inlet conditions. The radial distribution is relatively uniform between 20% and 65% span. The casing secondary flow manifests as a local maximum of KE loss around 75% span. Approaching the casing wall, KE loss reaches a minimum at 89% span, before steeply rising in the endwall boundary layer (95–100% span). The minimum appears to be associated with high total pressure casing platform coolant advected from upstream of the NGV, with the effect possibly being enhanced by radially-inward migration of the high-loss secondary flow core (away from the location of this minimum in loss). The hub secondary flow (in the range 10–15% span)—relatively mixed-out at plane 4—merges with the hub endwall boundary layer and is manifest as a weak peak in the profile in this span range.

Now consider the experimentally-measured circumferentially-averaged KE loss coefficient under simulated lean-burn inlet conditions. Relative to the uniform test case, KE loss increases between 15% and 70% span, whilst reducing below 15%, and above 70% span. This trend loosely corresponds to the total pressure non-uniformity at vane inlet. Indeed, noting that $\zeta 3$ is defined relative to an ideal expansion from the *average* total pressure upstream of the vanes—given the same *absolute* total pressure loss as for the uniform test case—we would expect the circumferentially-averaged KE loss coefficient to decrease near the walls (elevated upstream $p0$) and to increase around the midspan (lower-than average upstream $p0$). In line with the analysis of Fig. 11, we see that the hub secondary flow is amplified with lean-burn inlet conditions, and the casing secondary flow is suppressed. This was explained by changes in spanwise loading distribution. The global minimum in loss at 89% span becomes deeper with lean-burn inlet conditions, likely enhanced (in our definition of loss) due to slightly higher local upstream total pressure. Similarly, a local minimum develops around 10% span, likely caused by the hub peak in upstream total pressure. Endwall boundary layers were not significantly affected by lean-burn, except for a very subtle thinning at the hub.

Finally, consider the CFD predictions of circumferentially-averaged KE loss coefficient. In both cases, CFD predictions are in excellent agreement with experimental measurements in the region between 20% and 85% span. The CFD-predicted secondary flows at the hub appear somewhat over-mixed, and the depth of the minimum in loss at 89% span is overpredicted. Endwall boundary layers are also somewhat thinner than in experiments (i.e., undermixed). We conclude that BSL-ARSM predicts KE loss in the profile region very well, but is less accurate in high-gradient regions of secondary or endwall flow.

### Axial Development of Integral Kinetic Energy Loss.

We conclude our analysis of NGV aerodynamic performance by investigating the effect of lean-burn inlet conditions on the integrated KE loss. Specifically, we examine the axial trends of the plane-averaged KE loss coefficient ($\zeta 4$; definition of Lawaczeck [26]), and the mixed-out KE loss coefficient ($\zeta 5$; Dzung mixing model [27,28]). This data is shown in Fig. 13. A profile–endwall decomposition of KE loss was not performed, considering possible ambiguity in mapping of upstream and downstream total pressures. Experimental data is reported at downstream planes 2, 3, and 4, and CFD trends were generated by sampling results at axial intervals of 0.014 *C _{x}*. All data were normalized by the reference KE loss coefficient, $\zeta ref$. Summary results are reported in Table 3.

Plane 2 | Plane 3 | Plane 4 | |
---|---|---|---|

Uniform experiment | 0.823/0.921 | 0.901/0.943 | 0.977/1.000 |

Lean-burn experiment | 0.855/0.986 | 0.987/1.081 | 1.035/1.091 |

Uniform CFD | 0.798/0.883 | 0.905/0.949 | 0.966/0.970 |

Lean-burn CFD | 0.887/0.990 | 1.006/1.059 | 1.079/1.087 |

Hybrid case 1 CFD | 0.873/0.975 | 0.985/1.038 | 1.059/1.067 |

Hybrid case 2 CFD | 0.819/0.903 | 0.935/0.976 | 0.994/0.995 |

Plane 2 | Plane 3 | Plane 4 | |
---|---|---|---|

Uniform experiment | 0.823/0.921 | 0.901/0.943 | 0.977/1.000 |

Lean-burn experiment | 0.855/0.986 | 0.987/1.081 | 1.035/1.091 |

Uniform CFD | 0.798/0.883 | 0.905/0.949 | 0.966/0.970 |

Lean-burn CFD | 0.887/0.990 | 1.006/1.059 | 1.079/1.087 |

Hybrid case 1 CFD | 0.873/0.975 | 0.985/1.038 | 1.059/1.067 |

Hybrid case 2 CFD | 0.819/0.903 | 0.935/0.976 | 0.994/0.995 |

First, consider the experimentally-measured axial development of integral KE loss under uniform inlet conditions. The normalized *plane-averaged* KE loss coefficient is shown using circular markers and increases approximately linearly with axial distance. The plane-to-plane increase is caused by endwall boundary layer growth, and wake mixing losses. Consider also, the *mixed-out* KE loss coefficient, which is a measure of the KE loss associated with a flow that is hypothetically-mixed to a prescribed equilibrium state according to one-dimensional conservation laws. This offers a more rational comparison between two flows of differing states of local mixing. We see (as expected) that the mixed-out KE loss coefficient (triangular markers) is consistently greater than the corresponding plane-averaged KE loss for the uniform test case. With increasing axial distance, the plane-averaged trend approaches the mixed-out trend quasi-asymptotically indicating *realization* of mixing losses and reduction of flow secondary kinetic energy.

Now consider the experimentally-measured trends of plane-averaged and mixed-out KE loss coefficient under simulated lean-burn conditions. The trends are similar in shape to those for uniform flow, but with both the plane-averaged and mixed-out KE loss coefficients vertically offset from the trends of the uniform test case. Plane-averaged and mixed-out KE loss increased by 6.5% and 10.3%, respectively, on average across planes 2–4 (see summary in Table 3). The additional loss might be attributed to off-design flow incidence and greater turbulence intensity.

Now consider the CFD-predicted trends for the uniform and the lean-burn test cases. The CFD trends are in very good agreement with the experimental data, with plane-averaged and mixed-out KE loss increasing by 11.4% and 11.9%, respectively, under simulated lean-burn conditions. The CFD predictions were in good absolute agreement with experimental data, with average differences for plane-averaged KE loss of −1.2% and +3.3% for the uniform and the lean-burn test case, respectively.

### Separating Mean-Flow and Turbulence Effects.

It is unclear from the simulations presented what proportion of the increase in overall KE loss is attributable to turbulence effects or mean-flow effects (swirl and total pressure non-uniformity). Two additional simulations were performed in an attempt to decouple these effects.

The additional simulations used hybrid boundary conditions, with the turbulence conditions at inlet swapped between the uniform and lean-burn test cases. Hybrid case 1 used the combustor simulator swirl, pressure, and temperature profiles, but with turbulence representative of the uniform inlet condition. Hybrid case 2 used uniform flow, but with turbulence representative of the lean-burn condition. The results are reported in Table 3, and show that between 74% and 82% of the additional losses are caused by mean-flow effects (swirl and total pressure distortion), with only 18% to 26% being related to turbulence. Critically, approximately 23% (or $0.026\xd7\zeta ref$) of the additional losses occur *upstream of the vanes* due to the mixing-out of the non-uniform inlet profile. If these are accounted for as combustion losses (noting that the secondary kinetic energy that ultimately manifests as loss is associated with the combustor), then the rise of the *experimentally-measured* plane-averaged and mixed-out KE loss coefficients due to lean-burn falls to 3.6% and 7.8%, respectively.

The conclusion is that losses *attributable to interaction of the swirl and pressure profiles with the NGV* (as opposed to with the combustion profile mixing out) are relatively minor; an outcome supported by the results of Adams et al. [17]. This, of course, is for an NGV that was optimized for uniform inlet flow. It is likely that there would be no (or very little) decrease in NGV performance for a vane optimized for lean-burn inlet conditions (see, e.g., Ref. [31]).

### Downstream Thermal Field.

The effect of combined inlet swirl and temperature distortion on the downstream thermal field is now examined. The thermal field affects rotor-relative incidence angles, the thermal loading of the rotor, and unsteady temperature segregation effects. Experimentally-measured and CFD-predicted distributions of normalized downstream total temperature ($\Theta 2$) for the uniform and lean-burn-representative test cases are presented in Fig. 14.

First consider the experimentally-measured distributions of $\Theta 2$ for the uniform test case, shown in the first column of Fig. 14. At plane 2 (first row), airfoil and TE slot coolant has developed into a *thermal wake* which follows the approximate shape of the corresponding aerodynamic wake. Cold layers at the hub and case endwalls correspond to platform coolant advected from upstream of the airfoils. Endwall coolant is rolled-up by secondary flows, which causes an accumulation of cold fluid around the junctions of the wakes with the wall. There are slight differences between the two wakes, related to differences in the cooling design (discussed previously): for example, W1 has slightly greater depth around the midspan, when compared to W2. By the same mechanisms as for the aerodynamic field, the thermal wakes distort and mix-out as they progress from plane 2 to planes 3 and 4. We also see radial spreading of the endwall coolant.

CFD simulation results for the uniform test case are shown in the second column. These are generally in excellent agreement with the experimental data (reproducing the W1–W2 variations reasonably well) but with a tendency to be overmixed, as evidenced by the wider thermal wakes, and the overpenetration of endwall coolant into the hot freestream. A notable limitation of the current adiabatic CFD simulations is that they do not capture the heat *gain* of internal coolant via the through-wall heat flux. If this heat flux is accounted for, it is estimated that the average non-dimensional total temperature, $\Theta $, of fluid exiting the film cooling holes and the TE slot are 0.03 and 0.09, respectively. If this effect were modeled, the circumferential variation at an axial plane immediately downstream of the TE would be smaller than in an adiabatic simulation. In particular, the minimum values of $\Theta $ would likely increase slightly. Based on arguments of bulk enthalpy conservation, we would also expect the thermal wake width to increase slightly. The effect would become smaller in the partially mixed-out downstream flow.

Now consider the experimentally-measured distributions of $\Theta 2$ with lean-burn-representative inlet conditions of swirl and inlet temperature distortion, shown in the third column of Fig. 14. As discussed previously, we anticipate that the thermal field will be affected by internal and external coolant redistribution, enhanced mixing due to turbulence, and migration of the inlet temperature profile. At plane 2, the wakes have lower depth at midspan, but gradually broaden and increase in depth toward the endwalls. This combination is suggestive of superimposed *radial gradients* of total temperature, which are most likely the radially mixed-out inlet temperature profile. Freestream regions midway between wakes are noticeably colder across the full range of span. This is likely caused by partially mixed-out combustor coolant transported into the freestream by the swirl pattern.

Consider now the experimentally-measured distributions of $\Theta 2$ at planes 3 and 4 for lean-burn inlet conditions. The plane-to-plane circumferential migration and distortion pattern are determined by the mean-flow and were similar to that of the *aerodynamic* wakes with lean-burn inlet conditions. Apparently colder endwalls at planes 3 and 4 is an artifact of the plane 2 data not being traversed so close to the wall. Another interesting difference is that W1 is more washed out around 40% span than W2, whereas the opposite was true with uniform inflow. This appears to be due to external migration of coolant, noting that W1 is narrower and shallower than W2 even at plane 2. The result is perhaps surprising, because the external surface streamline pattern was similar for both vanes (see Fig. 5), but the effect on the downstream profile is clearly seen in both experimental and CFD results (considered now).

CFD simulations with simulated lean-burn are shown in the fourth column of Fig. 14. They are generally in good agreement with the experimental data, but with a tendency to be overmixed. In the CFX solver, turbulent fluxes of the BSL-ARSM equations are modeled using the standard eddy viscosity instead of the effective eddy viscosity (see CFX solver theory guide). It remains unclear, however, whether this simplification extends to the turbulent enthalpy flux of the energy equation. Since the standard eddy viscosity is generally greater than the effective eddy viscosity, this could explain why the thermal wake was overmixed while the aerodynamic wake was not.

Thermal field development is now examined by considering the radial profiles of circumferentially mass-flux-weighted normalized total temperature. These are shown in Fig. 15. Profiles are shown for uniform and lean-burn conditions at plane 4 alongside the corresponding inlet profiles at plane 1, and—for the lean-burn test case only—a profile taken at plane 1b (0.50 *C _{x}* upstream of LE; see Fig. 2; from the study of Amend et al. [20]). A direct comparison of inlet and outlet profiles requires equivalence of $\Theta 1$ and $\Theta 2$ definitions, which is satisfied when $T0b=T0c$ (i.e., when combustor and vane coolant temperatures are equal). For the purpose of discussion, this is assumed to hold true for the lean-burn case, noting however that in practice the cold-stream temperatures can differ by up to 2 K. For the uniform test case, $T0b$ is undefined, and a normalization is performed assuming $T0b$ is equal to 293.15 K (approximate ambient conditions). Although this is a crude method, it helps illustrate the relative magnitude of the thermal deficits due to convective heat losses (uniform case) and explicit temperature distortion (lean-burn case).

First consider the thermal field development under uniform inlet conditions. At inlet plane 1, the experimentally-measured total temperature (also used as a CFD inlet condition) is approximately constant between 5% and 95% span, with thermal boundary layers developing near the walls on account of heat losses to the test section walls. At downstream plane 4, experimentally-measured normalized total temperature is approximately constant between 20% and 65% span, but with a reduced value of $\Theta \u22480.91$ (cf. $\Theta \u22481.00$ at inlet). As previously discussed, this region is dominated by coolant ejected onto the vane surfaces and from TE slots. The cold regions approaching the endwalls (0–20%; 65–100% span) are caused by platform coolant. There is evidence of radial spreading caused by diffusion and coolant wash-up local to secondary flows (see area maps in Fig. 14). The integrated enthalpy deficit and spanwise penetration depth of the temperature deficit are greater at the casing, because the casing platform coolant mass flow is greater than that at the hub. CFD captures the spanwise temperature distribution reasonably well, but with small differences in high-gradient near-wall regions (differences in mixing rate).

Now consider the radial profiles of normalized total temperature under lean-burn inlet conditions. In the experimentally-measured inlet temperature profiles significant radial mixing occurs upstream of the NGV between plane 1 (dotted line) and plane 1b (dashed line). This leads to radial spreading of the hub and case coolant layers. This is accompanied by an increase in the near-wall temperature (expected based on energy conservation argument). The *temperature deficit* between the profiles and a hypothetical line of $\Theta =1$ increases, however, especially at the hub. Although on first inspection this seems to not satisfy energy conservation, the explanation is a simultaneous *reduction* of the near-wall mass-flux (coolant jets mixing-out *kinematically*). Because plane 1b has significantly greater mass flux uniformity than plane 1, downstream profiles are more easily compared to plane 1b.

Finally, consider the experimentally-measured plane 4 profile of $\Theta $ with lean-burn inlet conditions (circular markers). Compared to the uniform test case, normalized total temperature is globally lower, particularly in proximity to the endwalls. This is consistent with expectation based on superimposed inlet temperature distortion. A significant reduction of $\Theta $ between 25% and 70% span (i.e., where $\Theta \u22481.00$ at plane 1b) indicates that the inlet temperature profile continues to mix radially throughout the vane passage. This effect is conflated with the coolant redistribution effect discussed earlier.

### Separating Effects on Downstream Thermal Field Due to Inlet Temperature Profile Migration and Coolant Migration.

We attempt to decouple effects (on the downstream thermal field) associated with inlet temperature profile migration and swirl-induced coolant migration using additional uniform and lean-burn simulations with *constant inlet total temperature* (at plane 1) but otherwise nominal boundary conditions and coolant flows.

Here, we treat the non-dimensional total temperature field, $\Theta 2$, as a hot gas ($\Theta 2=1$) with superposed effects due to two cold streams ($\Theta 2=0$). The cold streams represent the combustor coolant flow and vane coolant flow. We define their mass fractions as $\lambda b$ and $\lambda c$, respectively. In flows dominated by advection and mixing (as opposed to molecular conduction), it can be shown that $\Theta 2\u22481\u2212\lambda b\u2212\lambda c$. For *constant inlet total temperature* (hot stream only), $\lambda b$ is everywhere zero, meaning that thermal field non-uniformities arise from vane coolant migration/mixing alone (i.e., $\Theta c=1\u2212\lambda c$). The value of $\lambda b$ can then be obtained by substitution, i.e., $\lambda b=\Theta c\u2212\Theta 2$. This approach is justified by the Munk and Prim [38] principle, according to which the streamline pattern is unaffected by a change in inlet temperature profile alone. The values of $\lambda c$ and $\lambda b$ are presented in Fig. 16, where they are cast as equivalent non-dimensional total temperatures, $\Theta =1\u2212\lambda $.

First consider the radial profiles of $\Theta c$ obtained directly from the additional uniform and lean-burn CFD cases with *constant total temperature* at inlet, which are shown in the left subplot of Fig. 16. We study these together to analyze swirl-induced coolant migration. With lean-burn, coolant migration leads to colder flow (higher coolant concentration) in the 35–65% span range, and warmer flow in the 20–35% and 65–95% span ranges (lower coolant concentration). These effects are associated with streamline convergence and divergence in the area profile.

Using the Munk and Prim superposition principle, we isolate the effect of combustor coolant ($\lambda b$) by subtracting the temperature field under *nominal conditions* from that of the case with *constant inlet total temperature*: $\lambda b=\Theta c\u2212\Theta 2$. The corresponding non-dimensional thermal field ($\Theta b=1\u2212\lambda b$) is that which would hypothetically arise from *inlet temperature profile migration* alone, but accounting for *aerodynamic* interactions with the vane coolant flow.

Plane 4 radial distributions of $\Theta b$ are shown in the right subplot of Fig. 16. For the uniform test case, the influence of the inlet profile is very subtle, with $\Theta b$ decreasing slightly (by no more than 3.7%) toward the endwalls and reaching minima of 0.963 and 0.971 at 1% and 96% span, respectively. The effect occurs due to radial mixing of the upstream thermal boundary layers (see Fig. 15). For lean-burn, the effect is more pronounced, with $\Theta b$ decreasing at every spanwise location, compared to the uniform test case. This indicates that the influence of combustor coolant is felt across the entire span. As expected, the general distribution is for decreasing $\Theta b$ in the near-wall regions. The slight increase in $\Theta b$ in the very-near-wall region might be explained by the *aerodynamic* mass-displacement effect of platform cooling flow, which reduces interaction of near-wall inlet flow with the very-near-wall region (some interaction occurs through mixing). $\Theta b$ reaches minima of 0.836 and 0.797 at 2% and 89% span, respectively.

We conclude that changes in the downstream thermal field are primarily driven by mixing-out of the inlet temperature profile, with only a secondary influence of coolant redistribution.

## Conclusions

The effect of lean-burn combustor outlet flow on the aerothermal field development downstream of fully-cooled NGVs was investigated. Experiments were performed using real engine hardware. CFD simulations used fully-featured NGV geometry.

In some combustor–turbine interaction studies, there is significant sensitivity to vortex clocking, leading to adjacent passages having significantly different flow patterns. This is a characteristic of well-defined vortex formations of relatively small scale. In the current study, based on a lean-burn engine architecture, we found that the swirl pattern had primarily radial variation (individual vortices relatively mixed-out) in swirl, and observed that both passages responded similarly (swirler-to-vane ratio of 1:2). This behavior has been seen in other studies (e.g., [17,31]).

The effects of lean-burn inlet conditions on airfoil loading, coolant migration, and adiabatic film effectiveness were studied using CFD. Results were as follows:

The swirl-induced change of incidence caused normalized static pressure on both airfoils to rise on the lower PS and the upper SS. The upper PS and lower SS experienced a reduction in pressure. This corresponds to increased loading in the lower half of the span, and decreased loading in the upper half.

Individual cooling hole mass flow rates changed by as much as +19.1% and −14.2% with one standard deviation being ±5.4%.

Row-wise coolant mass flow rates changed relatively little because the redistribution effect between holes was approximately antisymmetric about the midspan.

Compared to uniform inflow, the surface streamline pattern exhibited significantly greater radial flow component in the LE region, had significantly converging flow (to around the 60% span region) on the PS, and mildly downwashing flow on the SS. This improved film coverage around the stagnation line, reducing the peak adiabatic wall temperature around the LE. In the aft region of the vane, changes in individual film cooling mass flow rates and changes in surface coolant migration combined to give rise to significant spanwise variations in film coverage. Overall there was significant degradation of cooling performance with lean-burn inlet conditions, partly due to poor film coverage (consequence of the vane being optimized for uniform inlet conditions), and possibly exacerbated by elevated freestream turbulence, which is known to increase the streamwise decay rates of cooling films.

The effects of lean-burn inlet conditions on downstream distributions of whirl angle, KE loss, and non-dimensional total temperature were studied experimentally and computationally. Results were as follows:

Experimentally-measured downstream whirl angle distributions were distorted in the direction of upstream swirl at a particular radial location. In general, this led to higher whirl angle in the upper half of the span and lower whirl angle in lower half. A small radial band of underturned fluid near the casing opposed the expected trend due to swirl, and was linked to a local excess in the upstream total pressure (consistent with results of Adams et al. [17]). In the radial profiles, peak whirl angle increased by 2.7 deg, and the minimum decreased by 2.6 deg.

Experimentally-measured distributions of KE loss showed significant circumferential stretching of the wakes due to the introduction of inlet swirl. The wakes also mixed-out more rapidly, due to the greater freestream turbulence and—in areas of overturning due to swirl—due to an increase in the plane-to-plane streamwise distance. Changes in aerodynamic loading amplified the hub secondary flow of both airfoils. Casing secondary flows were suppressed. Integral KE loss was quantified using plane-averaged and mixed-out KE loss coefficients, which were on average 3.6% and 7.8% greater with simulated lean-burn, after adjusting for differences in mixing losses that occur

*upstream of the vanes.*If the loss that occurs in the inlet field is not accounted for, the increase in loss with lean-burn increases to 6.5% and 10.3%, respectively.The analysis of the experimentally-measured thermal field revealed significant mixing of the inlet temperature profile, both upstream of the vanes, and throughout the vane passage. The thermal field also showed evidence of vane coolant redistribution, but this effect was small in comparison to the influence of the inlet temperature profile.

In terms of the performance of the CFD method we observe the following:

The BSL-ARSM turbulence model predicted downstream distributions of residual swirl, and KE loss very well. Despite using a steady turbulence modeling approach, aerodynamic wake mixing rates were surprisingly well-matched to experiments. This is an artifact of the BSL-ARSM model, whereby wake decay is accelerated for large length scales and high turbulence intensity (see Ref. [33]). This happens for non-physical reasons, meaning it is unlikely to work

*reliably*for a wide range of inlet boundary conditions.Predictions of the thermal field were qualitatively in good agreement with the experimental data but showed signs of overmixing. This contrasts with significant undermixing that is typical of simulations using the more common

*k*–*ω*shear stress transport model. It seems that accurate prediction of the thermal field remains a significant challenge. From a practical standpoint, this might be addressed by carefully tuning the turbulent Prandtl number.

This study represents a comprehensive analysis of the impact of lean-burn combustor flow on NGV performance, gives insight into the robustness of typical engine parts to inlet profile changes, and highlights areas for redesign to optimize for lean-burn profiles.

## Acknowledgment

The financial support of Innovate UK, the Aerospace Technology Institute, the Engineering and Physical Sciences Research Council, and Rolls-Royce plc is gratefully acknowledged.

## Conflict of Interest

There are no conflicts of interest.

## Data Availability Statement

The authors attest that all data for this study are included in the paper.

## Nomenclature

### Romans

- $Cx$ =
axial chord length (m)

- $k$ =
turbulence kinetic energy (m

^{2}s^{−2})- $\u2113$ =
turbulence/integral length scale (m)

- $m\u02d9$ =
mass flow rate (kg s

^{−1})- M =
Mach number (–)

- $p$ =
pressure (Pa)

- $r$ =
radius (m)

- $Re$ =
Reynolds number (–)

- $s$ =
streamwise distance (m)

- $S$ =
swirl number (–)

- $T$ =
temperature (K)

- $V$ =
velocity magnitude (m s

^{−1})- $Vx$ =
axial velocity (m s

^{−1})- $Vr$ =
radial velocity (m s

^{−1})- $V\theta $ =
circumferential velocity (m s

^{−1})*x*=axial coordinate (m)

### Greeks

- $\alpha $ =
absolute whirl angle (deg)

- $\beta $ =
absolute pitch angle (deg)

- $\u03f5$ =
turbulence dissipation rate (m

^{2}s^{−3})- $\zeta 1$ =
local KE loss coefficient (–)

- $\zeta 3$ =
circumferentially-averaged KE loss coefficient (–)

- $\zeta 4$ =
plane-averaged KE loss coefficient (–)

- $\zeta 5$ =
mixed-out KE loss coefficient (Dzung method) (–)

- $\theta $ =
circumferential coordinate (deg)

- $\Theta $ =
non-dimensional total temperature (–)

- $\lambda $ =
cold gas mass fraction (–)

- $\tau $ =
integral time scale (average) (s)

### Subscripts

## References

^{st}Century