Due to the requirement to extract engine equivalent metal temperatures from the data obtained on this rig, it has to be correctly aero-thermally scaled. The Reynolds number must be matched to ensure the flow field is correct. Nusselt number is matched to scale the boundary between the fluid and the wall and Biot number reproduces the conduction of heat away from the surface and into the wall. Therefore, both the fluid properties, in order to match engine Nusselt number, and hence convective heat transfer, as well as the solid properties, to match engine Biot number and hence conductive heat transfer, must be scaled.
𝑀𝑀𝑅𝑅 =𝜌𝜌𝑈𝑈𝐿𝐿𝜇𝜇 , 𝑁𝑁𝑇𝑇 =𝑘𝑘ℎ𝐿𝐿 𝑔𝑔𝑎𝑎𝑚𝑚, 𝐵𝐵𝐵𝐵 = ℎ𝐿𝐿 𝑘𝑘𝑎𝑎𝑎𝑎𝑤𝑤𝑤𝑤 Equation 46a,b,c As a result, both fluid properties, as in conventional adiabatic cooling flow experiments (i.e. 𝑀𝑀𝑅𝑅, 𝑀𝑀, 𝐼𝐼 and 𝑘𝑘𝑐𝑐), as well as the wall conductivity 𝑘𝑘𝑎𝑎 must be considered. As such, the conductivity ratio 𝑘𝑘𝑎𝑎/𝑘𝑘𝑐𝑐 must be matched correctly by choosing an appropriate material from which to manufacture the test plates. The ‘Biot Scale’ test rig was conceived and developed by Steve Thorpe and Damian Martin alongside this scaling methodology. Martiny et al. (58) show the importance of Biot number on heat transfer in effusion cooling problems through the development of a mathematical model.
Figure 35 shows the influence changing Biot number has on the normalised metal temperature distribution around a single cylindrical hole through a wall. It shows that in order to correctly capture the thermal gradients within the metal, the conductivity ratio between metal and air at test conditions must be matched to those at engine conditions. A computational study was carried out as a preliminary part of this study to ensure the material choice for the test plates is appropriate by scaling the calculated overall effectiveness taken on a line through the centre of the test plate back up to engine scale conditions and subtracting the resultant metal temperature from those obtained from a simulation carried out at engine conditions, the result of which is illustrated in Figure 36. From this plot it can be seen that using the correct material is important to get the correct temperature field, particularly in the area around the cooling hole. Figure 37 shows typical engine running conditions and properties for an example engine cycle, along with equivalent test conditions once scaling to rig appropriate conditions has been applied.
Figure 36 – Comparison of experimental scale results to engine scale temperature
Figure 35 – Biot number effect on normalised metal temperature 𝑩𝑩𝑩𝑩 ≫ 𝟏𝟏
𝑩𝑩𝑩𝑩 ≪ 𝟏𝟏
KR=500
KR=520
Figure 37 –Aero and thermal scaling for an example engine cycle
However, the scaling process is constrained by the operating limitations of the test rig; the coolant delivery temperature is limited to a near ambient condition due to the lack of any pre- cooling of the coolant flow. The freestream temperature is limited to roughly 550K due to the occurrence of thermal degradation of the zinc-selenide window coating above this temperature. Fan power limits the freestream velocity to around 38m/s. Nitrogen feed pressure limits the maximum coolant mass flow rate to around 1000l/min restricting the maximum coolant pressure drop to around 10,000Pa and the rig is not pressurised limiting the freestream pressure to ambient.
A scale factor of 4.2 is chosen for these tests as it allows for a sufficient number of cooling holes to be placed in the test plate area available whilst allowing the rig to be run at atmospheric pressure conditions when scaling is applied. As outlined earlier, the experiment must first be scaled aerodynamically, the first step of which is to match the flow Reynolds number, in particular in relation to the coolant hole flow. This is constrained by the pressure drop available to drive the cooling air through the hole as the coolant temperature is limited to near- atmospheric conditions. Once this flow rate is determined, the freestream conditions are set to match the momentum flux ratio. Due to the limited freestream velocity and temperature available it is not possible to match both momentum flux and density ratios, but as noted in section 2.2.6 density ratio has only a second order effect on the cooling film. Momentum ratio
possible to match density ratio as shown by Martin (57). Momentum ratio describes how the jet is deflected by the mainstream flow where blowing ratio describes the relative mass of air in each stream, therefore by scaling on momentum ratio the shape of the cooling patch is better captured, this is important as in the geometries tested all rely on the coolant stream remaining attached to the wall. The shape of this coolant patch will have a larger impact on the cooling performance than the mass of coolant used, particularly as this is a single skin problem where the blowing ratio is high. The maximum running speed of the fan dictates the freestream velocity and matching the momentum flux ratio then determines the freestream temperature completing the selection of running conditions. The thermal conductivity must then be considered; this is characterised by the Nusselt and Biot numbers. As the thermal conductivity of the gas is known, the only remaining variable is the conductivity of the material the test plate is made from. In order to match the conductivity ratio between air and wall as closely as possible to engine conditions, the test plates are manufactured from Inconel718. Running conditions and the equivalent engine conditions for the experiments described here are given in Table 4.