# Numerical and Experimental Analysis of Labyrinth Seals with Rhomboidal Cells
## 1 Introduction  
Decreasing the leakage flow in turbomachinery is one of the goals researchers have tried to achieve in the last decades in order to improve efficiency. With this aim, many different studies have been carried out to enhance the effect of the sealing systems, applied to partially prevent flow losses through the unavoidable gaps between the static and rotating parts. Different typologies of labyrinth seals, lots of which are made of abradable materials, have been both numerically analyzed and experimentally tested: Straight-through, stepped, and staggered labyrinth seals, coupled with different tooth geometries (standard teeth, rounded-edge teeth, slanted teeth, etc.). Regardless of the chosen configuration, the efforts have been mainly devoted to understanding how the different parts (abradable land and teeth) contribute to the dissipation of the kinetic energy of the flow. For this reason, and in order to perform an optimization of the shape that allows reducing the discharge coefficient, the behavior of the flow along these tortuous paths has been studied through an in-depth characterization of both the flow separation mechanisms and the different recirculation phenomena. Several authors investigated the flow features in labyrinth seals using both numerical and experimental methods [1, 2, 3, 4, 5, 6]. [PERSON] et al. [7] reported the numerical and experimental analyses carried out to examine the flow patterns through honeycomb lands. [PERSON] et al. [8] performed numerical analyses on straight and stepped seals, evaluating both the discharge coefficient at different clearances and pressure ratios and the dissipative effects produced thanks to the vortices that occur in the sealing cavities. [PERSON] et al. [9], based on parametric studies performed on tooth height and thickness and on cell shape, proposed an innovative low leakage labyrinth seal with staggered honeycomb cells. Recently [PERSON] et al. [10] showed, through Computational Fluid Dynamics (CFD) simulations, that the radial clearance affects the sealing effect in labyrinth seals to a greater extent than positioning the teeth on the stator or the rotor. The literature also reports thermal analyses on labyrinth seals, even if, compared to the large amount of fluid dynamic studies, and despite the importance of leakages in determining the thermal behavior of turbomachinery, only a small number of papers deal with the thermal aspects [11; 12; 13]. [PERSON] et al. [11] analyzed, for labyrinth seals, the effects of rotation on the heat transfer coefficients, highlighting that the highest values are recorded near the tips of the teeth and inside the cells, on the wall facing the stator shroud. [PERSON] et al. [12] performed CFD simulations on stepped labyrinth seals, with honeycomb, in order to evaluate the effects of cell geometry and clearance variations on stator temperature. [PERSON] et al. [13] carried out experimental tests on smooth labyrinth seals to analyze the influence of the Reynolds number on the Nusselt number. Although many different solutions have been highlighted over the years, research on this topic continues to be of great interest, also due to the new construction techniques recently developed (e.g., direct metal laser sintering). In fact, although the impact of these losses on overall efficiency is very small, considering that modern gas turbines can generate power in the order of megawatts, any improvement in efficiency becomes cost-effective. In this paper, a previously validated CFD methodology [14] was used to point out a configuration, alternative to honeycomb cells, capable of guaranteeing a reduction in leakage flow. Several configurations, partly similar to those reported in [15; 16], were examined, and among these, the rhomboid pattern, previously proposed in the literature by [PERSON] et al. [17], has proved to be the most promising.