# Numerical and Experimental Analysis of Labyrinth Seals with Rhomboidal Cells
## 2 Numerical Analysis
### Thermalase Models Predictions  
The third phase of the numerical analysis was performed using the two numerical models representing the phenomena taking place within the TA used to carry out the experiments (Figure 13). These two models are used, one for fluid network analysis (Flowmaster) and the second for thermal analysis (Patran/P-Thermal). The fluid network is reproduced in Patran/P-Thermal using 1D element with two nodes (advection bars). Using this method and simply assigning the airflow and direction to each of the bars in the network, it is possible to reproduce in the P-Thermal model the elements used in Flowmaster. During the calculation, the mass flow rates and the temperatures information are shared between the two models until the fluid and thermal balance is reached. Figure 11: Test Article (TA), boundary conditions. Figure 12: Mass flow split for the CFD model. The two described numerical models allow reproducing the fluid dynamic and thermal fields inside the TA. For this reason, these models can be used to further investigate the impact of rhomboidal cells and, in particular, to verify the reduction of the leakage flow and to predict the impact of the new seal on the temperature distribution in the surrounding area. Initially, some adjustments to the fluid network and to the 2D thermal model described in [25, 26] were necessary to adequately model the innovative cell features. In particular, in the fluid network, the elements representing the honeycomb cells were replaced with rhombi. The purpose of this third numerical investigation is to provide an overview that is representative of the real operating conditions. For this reason, the numerical model includes all the typical mass flow rates that can be observed within an AGTE (Aircraft Gas Turbine Engine) and which are also modeled within the TA, unlike the CFD simulations that model only the FP mass flow rate. In standard operating conditions, two other flows are active within the TA with engine thermal control functions [18]. The first one is the Cooling mass flow rate (Coo), which flows in the casing upper cavities and prevents hot gas ingestion through the gaps among the different components. The second one is the Active Clearance Control (ACC) mass flow rate used, as well known, to control the clearance height during the different flight phases. A first part of the analysis was performed simply using the fluid network and considering only the mass flow rates of FP and Coo because, as explained in [14], the ACC stream, which flows in a separate channel, does not interact with the other two flows from the fluid dynamic point of view. Two numerical simulations were performed by setting the temperature of the FP equal to 873 K and \(\beta=1.1\). To highlight the possible presence of effects on the split of the FP between the restrictor and the tip of the fin, due to the temperature of the Coo, in the simulations, two different Coo temperatures are used. Table 7 shows the used set-up values and the resulting FP split, which allows us to state that the Coo temperature does not significantly influence the behavior of the labyrinth seal. Figure 14, which reproduces the zone in which the restrictor, the blade tip, and the labyrinth seal are positioned, shows the split of mass flow rates obtained numerically for the two examined cases. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Case** & **T\({}_{\text{FP}}\) (K)** & \(\beta\) (\(\downarrow\)) & **T\({}_{\text{Coo}}\) (K)** & \(\dot{m}_{\text{restr}}\) (\%) & \(\dot{m}_{\text{leak}}\) (\%)** \\ \hline A & 873 & 1.1 & 473 & 72.8 & 27.5 \\ B & 873 & 1.1 & 573 & 72.9 & 27.4 \\ \end{tabular}
\end{table} 
Table 7: Set up values and Flow Path (FP) mass flow rate split. Figure 13: Fluid network (**left**) and thermal network (**right**). The results obtained with the Thermalcase fluid network are in good agreement with those provided by the CFD analyses.