## 1 Introduction
Based on experimental data, they proposed design improvements such as passive pressure balance and active pressure balance to optimize brush seal performance. However, conducting experiments on brush seals under high-temperature and high-pressure conditions to replicate realistic gas turbine environments poses significant challenges. Consequently, computational fluid dynamics (CFD) is being actively considered as a viable approach for evaluating the performance of brush seals in actual turbine environments [14]. Figure 1: (**a**) Cross-section and geometric parameters of brush seal used in turbine rotor. (**b**) Lay angle of brush seal applied to rotor. The bristle pack of a brush seal comprises fine wires, thus, performing detailed 3D computer simulations that include each of these wires requires substantial time and resources. Therefore, 2D CFD simulations, in which the bristle pack is modeled as a porous medium, have been widely adopted [15; 16]. Due to the axisymmetric structure of the brush seal, its geometry can be simplified to a 2D axisymmetric configuration, which enables efficient computation; in this regard, studies have presented results that closely match experimental leakage flow rates [17]. Specifically, 2D CFD is effective at reducing time and cost during early design stages, which involve numerous design degrees of freedom and variables. However, to capture the 3D effects of actual brush seals and the influence of various components during the analysis process, empirical correlations remain essential. Clearance is a key geometric parameter that must be carefully considered when designing brush seals. Based on the presence or absence of clearance, brush seals are generally categorized into two types, namely contact seals without clearance and seals with an initial clearance, depending on the requirements for the gas turbine. Most brush seals are designed in a contact configuration, where the bristles interfere with the rotor surface to minimize fluid leakage [18]. Brush seals with an initial clearance are also designed to regulate cooling and leakage flows [19]. This design considers the blow-down effect, where a pressure differential causes the bristles to move radially toward the rotor, thereby gradually reducing the clearance [20]. The blow-down effect occurs when a pressure load is applied to the brush seal, causing the bristles to deflect axially downstream, pivot around the bristle root, and compact against the backing plate surface. Additionally, the incoming flow exerts a bending moment on the bristles due to their lay angle, causing them to bend toward the rotor surface and close the clearance [21]. The clearance between the bristle pack tip and the rotor must be sufficiently large to avoid collision, but an excessive clearance will lead to increased leakage flow [22]. In cases without clearance, the leakage flow rate has been accurately predicted using the Flo-master commercial 1D code, closely matching experimental results [23; 24]. However, since most brush seal models in 1D codes, including Flo-master, assume a contact state without clearance, predicting the performance of brush seals with clearance is challenging [24]. In this study, a three-step 2D CFD analysis was conducted to design brush seals with clearance. In the first step, a 2D CFD simulation was conducted for brush seals without clearance, and the resulting leakage flow rate was compared with experimental data. The simulations were performed for two geometries: those used by [PERSON] et al. [25] and [PERSON] et al. [26]. As in previous studies [4; 5], the bristle pack was modeled as a porous medium in the CFD calculations, and the porosity and flow resistance values were calibrated to match the experimentally measured leakage flow rates. Through this approach, a porosity correction factor model was developed based on the experimental data. In the second step, the performance of brush seals with clearances was predicted via 2D CFD simulations. The simulations were conducted based on the geometry presented by [PERSON] et al.