2.1 Oxford combustor turbine interactions rig

The Oxford Combustor-Turbine Interaction (CTI) rig (Fig. 1) generates engine-representative flow at its large-scale, two-passage, nozzle guide vane (NGV) cascade by employing a combustor simulator with opposed dilution ports and endwall film cooling. The NGV cascade geometry is a linear extrusion of the midspan cross section of a modern civil engine NGV design. Tailboards downstream of the vanes are adjusted in order to obtain a periodic pressure distribution^{(Reference Cresci10)}. The mainstream flow is drawn by a suction fan and heated by approximately 40 K using an electric mesh upstream of the simulator, as measured by a thermocouple downstream. The combustor inlet mass flow rate is measured by a pitot tube upstream of the heater mesh. The dilution port, endwall, and NGV coolant are supplied by a separate blower fan.

Figure 1. Features of the Oxford Combustor-Turbine Interaction rig.

Butterfly valves and orifice flow meters permit control and measurement of the coolant mass flow rate to the feed plenum of each cooling feature, where the coolant temperature is also measured by a thermocouple. The endwall film cooling is unused in this study, but dilution port and NGV leading edge (LE) film coolant mass flow rates are varied. Only the central vane LE is film-cooled, with the rig being designed to allow this LE to be replaced with various test pieces to allow experiments of different types and on different film hole geometries. The LE film coolant mass flow rate ${\dot{{\rm m}}}_{{\rm c}}$ is non-dimensionalised as an average blowing ratio based upon the bulk velocity approaching the vane $v_{\infty }$ :

(4) $$M = \frac{{\skew3\dot{m}}_c}{{\rho }_{\infty }v_{\infty }A_h} \label{eqn4}$$

where A_h is the combined area of the leading edge film cooling holes and ρ_∞ and $v_{\infty }$ are the mainstream flow density and velocity, respectively. The dilution port coolant mass flow rate is reported as a momentum flux ratio between the coolant and the mainstream:

(5) $$J_D=\frac{{\rho }_c{v_c}^2}{{\rho }_{\infty }{v_{\infty }}^2} \label{eqn5}$$

The combustor-turbine interface plane temperature, turbulence, and velocity profiles at fixed J_D = 9 were experimentally measured by Cresci et al.^{(Reference Cresci, Ireland, Bacic, Tibbott and Rawlinson11,Reference Cresci, Ireland, Bacic, Tibbott and Rawlinson12)} . Turbulence intensities were approximately 18% near the midspan and 25% just downstream of the outer endwall film injection. Infrared temperature measurements of the central leading edge are recorded through two Germanium windows positioned to allow observation of both the pressure side (PS) and the suction side (SS). While the coolant-to-mainstream density ratio is not engine-realistic, the leading edge film cooling results are intended for comparison rather than use in engine overall effectiveness calculations etc. Previous research on film cooling density ratio has found that higher density ratios reduce coolant momentum at a given blowing ratio, which tends to reduce jet lift off and thus enhance film effectiveness^{(Reference Drost and Bölcs13,Reference Pietrzyk, Bogard and Crawford14)} . The film effectiveness measurements in this study are therefore expected to be slightly lower than those for equivalent engine condition results. The suction fan speed was kept constant across tests, such that changes to the dilution port and leading edge coolant mass flow rates resulted in a range of Reynolds numbers (based on the vane throat flow properties and chord length) of $8.54\times {10}^5$ to $1.02\times {10}^6$ . Varying the fan speed while the coolant parameters were fixed at J_D = 0 and M = 1.5 showed that across this Reynolds number range the film effectiveness and HTC distributions vary by less than 0.02 and 5%, respectively.

2.2 Leading edge test pieces

Three film-cooled, Rohacell foam leading edge test pieces have been investigated in terms of the changes to their film cooling performance across a range of blowing ratios and dilution port mass flow rates. The three models all feature the same cross-sectional profile and identical PS3 and SS3-SS6 hole rows, inclined purely in the streamwise direction. They vary only in terms of the spanwise distribution of radial showerhead hole surface angle, as shown in Fig. 2 (rows PS2-SS2 i.e. the four rows surrounding the geometric stagnation line, which expel coolant in the radial direction of the turbomachine). The position of the geometric stagnation line is also indicated. A fourth foam test piece used in this study features no film cooling holes, but instead includes an array of 42 foil thermocouples distributed over both the PS and SS surfaces. Experiments performed with this ‘calibration test piece’ provided an IR calibration which considered the variation in the magnitude of IR reflections from different locations on the test piece. All test pieces were uniformly spray-painted the same matte black colour in order to minimise the intensity of the reflected radiation originating from the wind tunnel walls.

Figure 2. (a) Three film-cooled NGV leading edge geometries and (b) the streamwise inclinations of their hole rows.

2.3 Infrared thermography

Leading edge surface temperatures are acquired simultaneously by two FLIR A655sc infrared cameras at 12.5 frames-per-second throughout the approximately 50 second duration of each heated experiment. This duration is sufficient for the temperatures of both the wind tunnel interior surfaces and the observed test surface to asymptote such that any further changes are less than 1% of the overall local temperature change. For each frame, the surface temperature distribution T_s(x) is calculated according to Equation (6):

(6) $$T_s({\mathbf x})=\sqrt[4]{\frac{\sigma {T_{bb}({\mathbf x})}^4-(1-\tau )q^*({\mathbf x})}{\sigma \tau \varepsilon }} \label{eqn6}$$

where σ is the Stefan-Boltzmann constant. The black-body temperature $T_{bb}({\mathbf x})$ is the temperature distribution recorded by the camera on the assumption that all the IR radiation it receives is due to ideal black-body thermal emission from the NGV. In fact, the transmissivity τ of the optical pathway (through the air and Germanium window), the emissivity of the painted vane surface ε, and the extraneous radiation reflecting from the test piece $q^*({\mathbf x})$ must all be accounted for. The product $\tau \varepsilon = \frac{{T_{bb}}^4-{T_{amb}}^4}{{T_w}^4-{T_{amb}}^4}$ was calculated by simultaneously measuring the through-window camera $T_{bb}$ and the observed surface thermocouple temperature $T_w$ on a heated aluminium block painted with the same black paint as the Rohacell test pieces, and can be treated as a constant under CTI rig experimental conditions^{(Reference Holgate, Ireland and Self15)}. For each heated film cooling experiment performed, a heated experiment with the same rig conditions is also carried out with the calibration test piece. The spatially variant reflection quantity $q^*({\mathbf x})$ can then be determined uniquely for each experiment (necessary since it is a function of the rig wall temperatures). It is calculated as the normalised difference between the vane surface radiosity perceived by the IR camera $\sigma {T_{bb}({\mathbf x})}^{4}$ and the amount of that radiosity which is due to the thermal emissions of the surface $\sigma \tau \varepsilon {T_w({\mathbf x})}^{4}$ :

(7) $$q^*({\mathbf C}) = \frac{\sigma {T_{bb}}^{4}\left({\mathbf C}\right) - \sigma \tau \varepsilon {T_w}^{4}\left({\mathbf C}\right)}{1-\tau \varepsilon } \label{eqn7}$$

This quantity is calculated separately for each thermocouple location ${\mathbf C}$ on the calibration test piece using its temperature reading $T_w({\mathbf C})$ and the mean $T_{bb}$ value for pixels near to it $T_{bb}({\mathbf C})$ . Thermocouple and IR video data are recorded at the same frequency, permitting transient $q^*({\mathbf C})$ measurements. For calculating pixel-wise surface temperatures T_s(x), a pixel-wise $q^*({\mathbf x})$ is interpolated from the at-thermocouple values $q^*({\mathbf C})$ .

3.1 Film effectiveness

A test’s final three seconds of surface temperature data are averaged for calculation of the film effectiveness. By this time, the rig walls and test piece temperatures are essentially steady. Rohacell foam is used for the leading edge test pieces due to its combination of stability under machining and low thermal conductivity ( $k = 0.032\ {\rm W\ }{{\rm m}}^{-1}{{\rm K}}^{-1}$ ). Despite this, the wall thickness between the vane leading edge external surface and the film coolant supply passage is low enough (9 mm) for conduction to produce an appreciable discrepancy between the measured external surface temperature distribution and the corresponding adiabatic wall temperature distribution. Images of the surface temperature on the no-films calibration test piece are used to correct film-cooled surface temperature results for these conduction effects, as detailed by Holgate et al.^{(Reference Holgate, Ireland and Romero16)}. The same authors also describe a technique by which the temperature profile generated by the upstream injection of dilution port coolant is removed from the image to yield the true additional cooling effect of the leading edge films.

3.2 Heat transfer coefficients

HTCs are determined from the transient phase of the same test used to determine the corresponding film effectiveness at steady-state. They are calculated via a transient, one-dimensional (1D) finite element (FE) conduction model of the test piece wall, implemented in MATLAB. Convective heat transfer boundary conditions are used for both the internal surface (coolant plenum) and the external surface (hot mainstream). The internal driving gas temperature is the NGV coolant temperature $T_c$ , which is essentially constant everywhere and throughout an entire test. The internal HTC is estimated as a constant attained with the Dittus-Boelter equation. The results for external HTC were found to have very low sensitivity to the internal HTC, justifying this estimation.

The external driving gas temperature history throughout the transient phase $T_g({\mathbf x},t)$ can be calculated for each pixel with Equation (8). Since the blowing ratio and coolant-to-mainstream density ratio variations are small throughout the transient (approximately 6% and 10%, respectively), the leading edge coolant jet physics remain essentially unchanged. Therefore, the film effectiveness distribution as determined during the steady-state phase closely approximates the driving gas temperature distribution throughout the transient mainstream temperature rise generated by the heater mesh $T_{\infty }({\textit{t}})$ .

(8) $$T_g({\mathbf x},t) = T_{\infty }(t) - \eta ({\mathbf x}){\mathbf \times }\left(T_{\infty }(t) - T_c\right) \label{eqn8}$$

$T_{\infty }(t)$ is the mass-averaged temperature of the combustor simulator inlet flow (heated by the heater mesh) and the flow from the dilution ports. When the dilution ports are unused, $T_{\infty }(t)$ is just the measured combustor inlet transient temperature. The temperature as measured across the combustor inlet was found to be highly uniform, however the dilution ports create momentum flux ratio-dependent temperature profiles at the cascade inlet. A typical driving gas temperature transient for a single pixel is shown in Fig. 3. The departure from an ideal step rise is caused by initial heat conduction from the mesh into its brass electrical connectors and from the heated flow into the initially ambient temperature rig walls.

Figure 3. Iterative progress of the HTC-finding algorithm, showing convergence of FE-predicted surface temperature histories towards the measured history for a single pixel. To reduce the computational requirements of the transient FE calculations, only a reduced, initial portion of the entire heated experiment is considered.

An iterative algorithm was devised to refine an initial pair of HTC guesses ${(h_1,h_2)}_0$ at a single pixel for N iterations until the pair of improved guesses ${(h_1,h_2)}_{{\rm N}}$ converges to within a small tolerance. The initial guesses are chosen to span the full range of expected HTC values in the domain, since the algorithm assumes that the true HTC lies somewhere in between. Each HTC guess is applied to the FE model external surface to produce an external surface temperature history prediction $T_{s,p}(t)$ intended to resemble the true history $T_{s,t}(t)$ captured by the camera. A simple error metric E is used to evaluate the closeness of each fit: $E{\mkern 1mu} = {\mkern 1mu} {\sum _r}\left( {{T_{s,p}} - {T_{s,t}}} \right)$ , where $\Gamma$ is the set of infrared temperature data points within the time period considered. A positive error metric indicates that $T_{s,p}(t)$ lies entirely or primarily above $T_{s,t}(t)$ and that the associated HTC guess is too high (and vice-versa). The algorithm proceeds as follows at each iteration, and an example of the convergence towards an answer for a single pixel is presented in Fig. 3. The symbols $\cap \ $ and $\cup $ refer to logical ‘and’ and ‘or’, respectively.

1. 1) For each of the current guesses ${(h_1,h_2)}_n$ perform the FE calculation leading to the predicted surface temperature history.

2. 2) Get the error metrics ${(E_1,E_2)}_n$ for the current guesses.

3. 3) Determine new guesses ${(h_1,h_2)}_{n+1}$ according to ${(E_1,E_2)}_n$ :

   1. a) If $(E_{1} > 0\cap E_{2} \lt {\rm{0}})\cup (E_{1} \lt {\rm{0}}\cap E_{2} \gt {\rm{0}})$

   i.e. one predicted history lies primarily above and the other primarily below the true history:

   $h_{1,n+1}$ - mean of guesses ${(h_1,h_2)}_{{\rm n}}$

   $h_{2,n+1}$ - guess ${(h_1,h_2)}_{{\rm n}}$ with the lowest error metric (absolute value)

   1. b) If $(E_{1} > 0\cap E_{2} > 0)$

   i.e. both predicted histories lie primarily above the true history:

   $h_{{1},n +1 }$ - minimum of guesses ${(h_{1},h_{2})}_n$

   $h_{{2},n +1 }$ - minimum of guesses ${(h_{1},h_{2})}_{n-{1}}$

   1. c) If $(E_{1} \lt 0\cap E_{2} \lt 0)$

i.e. both predicted histories lie primarily below the true history:

${h}_{{1},n +1 }$ - maximum of guesses ${(h_{1},h_{2})}_n$

$h_{{2},n +1 }$ - maximum of guesses ${\left(h_{1},h_{2}\right)}_{n-{1}}$

1. 4) If $(h_{1,n+1}-h_{2,n+1})$ is less than the tolerance value, the solution is the mean of guesses ${(h_1,h_2)}_{n+1}$ , otherwise return to step 1 with the updated guesses. A tolerance of 0.5 is used, which is small compared to the overall HTC uncertainty.

This process resembles that used by Coletti et al.^{(Reference Coletti, Scialanga and Arts17)} and later Ryley et al.^{(Reference Ryley, Mcgilvray and Gillespie18)} to determine HTC distributions on ribbed internal cooling geometries. They used a commercial, transient FE code and full-surface temperature data (obtained by IR and TLC, respectively) on their complex, three-dimensional (3D) geometries to iteratively refine initial guesses for full-surface HTC distributions. This was intended to improve upon the constraint of 1D geometry imposed by the common analytical solution in Equation (3), while the present technique employs FE to avoid the analytical solution’s initial temperature and semi-infinite substrate assumptions. It also differs from these past FE applications by being simple to implement without a commercial FE code, and in the technique by which the distribution of transient gas driving temperature is determined from the steady-state film effectiveness measurement, as per Equation (8).

The blower fan used in this experiment to supply coolant increases the temperature of the coolant above atmospheric. Before the heater mesh is turned on, the leading edge test pieces are therefore initially exposed to warmed air inside the coolant plenum and predominantly atmospheric air on the external, film-cooled surface. This creates initial depth-wise temperature gradients inside the leading edge test piece which are modelled at each pixel in the FE HTC calculation as a linear temperature gradient between the two sides. In the present experiment, using the FE model and assuming that the temperature throughout the thickness at each pixel is uniformly equal to that pixel’s initial surface temperature results in HTC over-predictions of up to 7%. Increasing the test surface thickness in the FE model to be essentially semi-infinite further increases this maximum error to over 30%. This illustrates the importance in the present experiment of accounting for the initial temperature gradient and the true thickness of the test pieces.

For the present study, a single workstation was used to run the explicit method, 1D FE calculations in a serial MATLAB implementation. Under these conditions, each full surface pressure side HTC solution takes approximately 30 minutes (around 0.01 seconds per converged pixel solution). While acceptable for most experimental purposes, this duration could be significantly improved upon by optimisation of the finite element method and parallelisation, as well as the choice of computer hardware and software.

3.3 Uncertainty analysis

The combustor inlet velocity uncertainty is calculated according to the uncertainties in the pitot tube velocity equation measurands. The coolant mass flow rate uncertainties are calculated in accordance with the orifice meter uncertainty procedures detailed in European Standard ISO 5167-2. The facility is designed for easy removal and replacement of the central vane’s leading edge, and some leakage from the film coolant plenum around the leading edge test pieces into the mainstream is unavoidable. The leading-edge coolant mass flow rate is therefore assigned an additional 2% uncertainty on the basis of an estimation of the leakage area as a proportion of the total cooling hole area. Coolant mass flow rates are reported as dimensionless quantities dependent on the mainstream velocities near the injection points, and uncertainty is propagated from both coolant and mainstream flow velocities and densities. Since the coolant mass flow rates are controlled with hand-operated valves, there is always a small deviation of the measured nominal quantity from its target value, and these deviations were included in the uncertainty estimates. The resulting maximum percentage uncertainties are approximately 12% for M and 5% for $J_D$ .

Conduction-corrected film effectiveness uncertainties vary slightly over the PS (0.033 to 0.043) and SS (0.029 to 0.034) and are calculated on the basis of the underlying temperature and mass flow rate measurands. HTC uncertainties were estimated using the perturbation method described by Moffat^{(Reference Moffat19)}. The variables driving uncertainty in the HTC calculation procedure were surface temperature, material thermal diffusivity, and surface-gas temperature time error, as well as the film effectiveness, coolant temperature and mainstream temperature used in the calculation of the driving gas temperatures. By far the largest contributors to HTC uncertainty are the surface temperature and the film effectiveness. This is apparent in the maps of uncertainty %δ_HTC in Fig. 4 for both the PS and SS since they resemble the corresponding maps of effectiveness shown in Figs. 5(a) and 6(a). This leads to uncertainties of approximately 9% to 18% on the PS 10% to 60% on the SS. The lower uncertainties occur near PS and upstream SS film rows and are broadly consistent with uncertainties reported in previous, single-row HTC studies. Regions of high film cooling effectiveness (within and after the final SS rows) exhibit greatly elevated HTC uncertainty because they experience a relatively insignificant temperature rise after the mainstream becomes heated. The HTC uncertainties in these regions could be reduced with a greater mainstream-to-coolant temperature difference. Alternatively, conducting a second test in which the coolant is heated rather than the mainstream would create a longer temperature transient in these regions. The HTC results from this test could then be blended with the existing HTC results farther upstream as per Chambers et al.^{(Reference Chambers, Gillespie, Ireland and Dailey20)} (though the experimental technique would essentially become two-test).

Figure 4. Percentage HTC uncertainties on the PS and SS (model C, M = 3.5, J_D = 9). Geometric stagnation line indicated.

Figure 5. (a) Film effectiveness (b) Nusselt number (c) Frossling number and (d) predicted net heat flux reduction on the suction side (model C, M = 3.5, J_D = 9). Geometric stagnation line indicated.

Figure 6. (a) Film effectiveness (b) Nusselt number (c) Frossling number and (d) predicted net heat flux reduction on the pressure side (model C, M = 3.5, J_D = 9). Geometric stagnation line indicated.

The 1D FE code was extended to a reduced-domain 3D code in order to assess the influence on HTC results of the 1D conduction assumption. The domains were rectangular prisms comprised of the same number of nodes in the wall thickness direction as in the 1D case, but additional nodes in the surface directions to correspond to the additional surface temperature pixel data available. The pixel for which HTC was calculated remained as the central external surface node, and the unique pixel-wise gas temperature histories calculated according to Equation (8) were applied to their appropriate nodes. The coolant plenum nodes were all subject to the aforementioned convective boundary condition, while the remaining sides of the domain were adiabatic. Regardless of the size of the domain, the results indicated HTC variations consistently less than 2% from the 1D model, justifying the use of the latter. So long as convergence is achieved, the choice of time step makes a negligible difference to results, while the nodal distance used produces results consistently less than 1% different from those produced with smaller distances.