Adiabatic Film Effectiveness Calculation

With the geometry finalised, another set of simulations is carried out in order to determine the adiabatic film effectiveness performance of each design. Due to the high computational requirements involved in carrying out a complete simulation of an entire hole pattern array, this computation is accomplished by splitting the problem up into two parts. First a single passage is simulated using the same domain and mesh definitions as described above. The aim of this simulation is to determine the flow properties through the hole, particularly the velocity distribution. Once the through hole properties are known they are used as inlet boundary conditions for the second part of the computation. This simulation contains the hole pattern array, but only simulates a small region of the flow near the exit of the cooling hole, reducing the number of cells required within each individual hole and allowing more cells to be clustered on the plate surface resulting in better resolution of the coolant film. As a result an array containing multiple rows of coolant holes can be approximated using a much reduced number of grid cells.

These simulations are run with conditions mimicking the experimental adiabatic film effectiveness tests described in section 3.6. In keeping with the experimental film effectiveness methodology, these simulations are resolved using an inert gas scalar mixing based approach where the flow is kept at isothermal conditions throughout. Air is used as the mainstream gas and nitrogen gas is chosen as the coolant simulant. This involves using the multi-component gas model and setting gas properties such as molecular weight, dynamic viscosity and specific heat for each gas component.

4.2.2.1 Single Hole Simulation

The aim of this simulation is to find the flow conditions near the exit of the passage. These conditions will then be used as an inlet boundary for the multi-hole type simulations in order to compare with the results obtained through experimental rig testing (see section 5.1). This is achieved by creating a constrained plane at a distance of 2.4D upstream of the passage exit, as can be seen in Figure 54, and extracting data for the velocity vectors, static temperature,

properties are stored in a table and exported for use in the multi-hole calculation to be applied as an inlet boundary. The location of this extraction plane is selected to be far enough upstream of the exit that it is largely isolated from the influence of any external features such as adjacent jet flows or turbulence.

The domain geometry and mesh used in these simulations share the same design rules and similar controlling parameters as used for the initial discharge coefficient study. The main difference between the two sets of prediction is the switch to isothermal conditions throughout the entire computational domain together with the substitution of a Nitrogen gas as the coolant in line with the experiment. This requires the addition of the coupled species model in order to calculate the interaction of the two gasses.

Figure 54 – Extracted constrained plane section data

4.2.2.2 Multiple Hole Simulation

Once flow conditions near the passage exit have been calculated, they are used as the velocity and species inlet boundary conditions for a calculation on a plate involving multiple hole passages. This reduces the size of the computational domain, allowing a detailed calculation of the flow properties through a single hole and then applying those conditions to form a detailed simulation of the adiabatic flow over the plate surface containing an array of cooling holes.

4.2.2.3 Simulation Topology

The single hole domain is the same as that used in the initial 𝐶𝐶𝑑𝑑 study scaled to the correct effective area. The multi-hole geometry is defined based on that of the experiment as with the single passage case; this is used to define the flow domain parametrically. This flow domain

However, the exit flow region of multiple holes is captured, with typically 8 rows of coolant holes included for all but one of the designs considered based on the hole pattern. As a result this model simulates the interaction between the coolant jets as they exit the cooling holes and mix with each other and the mainstream over the surface. While this approach does not completely capture the more global effects of the array structure on the coolant flow through the holes, in particular the velocity profile, the local effects of the interactions are captured. As a result care must be taken when applying this technique that the effect of the array on the through hole velocity profile is considered.

Inlet and outlet length as well as domain height are kept constant with the single hole model and the domain width is the hole pitch as shown in Figure 55. Periodic repeating boundaries are used for the side walls; as a result flow properties are transferred from one boundary to the other, simulating an infinite width plate with regular cooling passages using an interface. This boundary is shown in yellow in Figure 56. Velocity inlet boundaries are shown in red, these are placed at the same 2.4D distance upstream of the cooling hole exit plane as the extracted plane from the single passage. All other boundaries are the same type as with the single-passage case, in this image the main flow velocity inlet is coloured cream.

4.2.2.4 Meshing

As a result of using the periodic boundary, the mesh generator automatically creates a conformal grid which is exactly the same on both ‘walls’. There are three major differences in the mesh controls between the single- and multi-passage cases. First the surface curvature is reduced from 108 to 72pts/circle with the higher value used to resolve the definition in the sensitive area at the passage entry which is not present in the multi-passage case. The maximum cell size on the plate surface is limited to a target size of 10% of base in order to ensure cells cluster close to this surface and capture the film distribution in the multi hole array. The global target cell size is also reduced to 100% of base; limiting the cell size in the domain and ensuring the exit flow is sufficiently resolved. The resulting multi-hole domains typically contain around 3-5million cells.

4.2.2.5 Physics & Boundary Conditions

Similar physics models are used in both single- and multi-passage cases as described in section 4.2.1.3, the only difference being that the flow is isothermal with the coupled species model used to simulate the mixing of mainstream air with the Nitrogen coolant in order to determine the adiabatic film effectiveness in line with the experimental tests. The main difference between the single- and multi-passage cases is the velocity inlet boundaries used to map the inlet conditions for each passage exit in the multi-hole array; flow properties such as velocity, temperature, and turbulence properties are imported from the data extracted in the single hole simulation for use on these boundaries. The inlet boundary conditions are given in Table 7 below. Two pressure drop conditions are tested similar to the highest and lowest conditions used for the experimental film effectiveness tests as well as high and low freestream turbulence conditions. Other flow properties are kept the same for all simulations in line with the experimental conditions.

𝑻𝑻_{𝟎𝟎𝒄𝒄} 300𝐾𝐾 𝑻𝑻∞ 300𝐾𝐾

∆𝑷𝑷𝒑𝒑𝒑𝒑𝒎𝒎𝒑𝒑𝒑𝒑 2000, 9000𝑃𝑃𝑎𝑎 𝑼𝑼∞ 32.0𝑚𝑚/𝑠𝑠 𝑻𝑻𝒖𝒖∞ 0.05, 0.20 𝜦𝜦𝑳𝑳∞ 16.0, 32.9𝑚𝑚𝑚𝑚 Table 7 – CFD inlet boundary conditions – Adiabatic Film Effectiveness

4.2.2.6 Inlet mapping

Data consisting of velocity components, static temperature, turbulent dissipation rate, turbulent kinetic energy, species mass fraction and position is required to form the inlet

constrained plane in the single-passage case using a table; this table can then be imported into a different simulation to form a boundary condition. In order to map the solution from the single-passage case onto each of the inlets simulated in the multi-passage case, it is necessary to define a local coordinate system for each individual boundary. This ensures that the solver is mapping the profiles correctly, particularly for the side passages which only contain half of the inlet as can be seen in Figure 57. Each boundary has the origin for the associated coordinate system located at the passage centre, equivalent to the centre of the constrained plane section where the origin of the extracted data is located.

Both the extraction plane in the single-hole simulation and the inlet planes on the multi-hole simulation are located 2.4D upstream of the centreline of the coolant passage exit plane in order to capture any upstream flow effects that may be imposed as the coolant leaves the passage and enters the mainstream.

Figure 57 – Inlet condition mapping

4.2.2.7 Stopping Criteria and Post Processing

Simulations are run until the momentum, energy, continuity, turbulence and species residuals have asymptoted to a minimum. Both the discharge coefficient and mass flow balance between the plenum inlet and the constrained plane at the cooling hole exit are monitored for convergence in both simulations. The surface average film effectiveness on the plate is also monitored alongside the mass flow balance in the entire domain for the multi-hole simulation. Comparison with experiments is drawn between both the span-wise averaged surface effectiveness as well as the qualitative surface effectiveness map. In order to make this comparison, the data from the simulation is extracted and imported into a Matlab script which splits the surface effectiveness data into thin slices in the streamwise direction and calculates the area averaged surface effectiveness in each slice. The results are then plotted against

distance from the passage exit plane. Effectiveness for the simulations is visualised by means of a field function and this is defined as;

𝜂𝜂𝑒𝑒𝑦𝑦=

𝐶𝐶𝑎𝑎𝑒𝑒𝑟𝑟_∞− 𝐶𝐶𝑎𝑎𝑒𝑒𝑟𝑟_{𝑥𝑥𝑥𝑥} 𝐶𝐶𝑎𝑎𝑒𝑒𝑟𝑟∞

Equation 85 The subscript ∞ refers to the surface average at the main flow inlet plane.