# Experimental Investigation in Drag Coefficient of Cubes
## 1 Introduction  
When sand or dust is ingested in the turbine engine, the engine may suffer highly damaging erosion, and the engine life is thus reduced significantly [1]. As a result, sand and dust separation devices are necessary for the turbine engine operating in sandy areas. When the ingested sand or dust particles move in the separation devices, the major interacting force between the air and particles is viscous drag [2]. The degree of turning and acceleration or deceleration achieved by the particles depends on the ratio of the viscous forces to the inertial forces experienced by the particles [3]. Thus, the accurate drag characteristics of sand or dust particles are very important for the separation device's design. Since spherical particles have the simplest geometry to describe, the researchers focused on spherical particles in early studies. Significant work has been performed by various researchers in this field [4, 5, 6, 7, 8]. Many equations have been developed relating the drag coefficient to the Reynolds number for spherical shape particles. A review of theoretical and experimental developments about this issue can be found in [PERSON]'s book [9]. In combination with abundant numerical and experimental results, the so-called standard-drag curve has been presented, which is accurate in the range of 0.1 < \(Re\) < 3 \(\times\) 10\({}^{5}\). [PERSON]'s empirical formula is defined as follows:  
\[C_{D}=\frac{24}{Re}\Big{(}1+0.15 Re^{0.687}\Big{)}+\frac{0.42}{1+4.25\times 10^{4 }Re^{-1.16}}. \tag{1}\]  
[PERSON]'s standard drag curve is used directly to predict the particle motion in many separation device designs. However, the prediction of particle motion characteristics may cause significant error since the feature of particles in nature has more complex geometry, which will result in different drag coefficients [10]. Therefore, accurate drag models for non-spherical particles remain a critical need. Based on the settling experiment and numerical method, some researchers have been brought out the models to predict drag coefficients of non-spherical particles [3; 11; 12; 13; 14; 15; 16; 17]. Table 1 exhibits the widely used prediction model. As can be seen, the form of non-spherical particle's drag coefficient models brought by different researchers show significant differences, and the different models involve different shape factors to describe the particles. This can be attributed to two reasons. Firstly, the geometry feature of non-spherical particles is difficult to describe using a simple uniform factor. Secondly, the secondary motion of the particle leads to variation in the orientation angle as well as the drag coefficient of non-sphere particles during the free-settling process. The secondary motion of the non-spherical particles is inevitable when the Reynolds number is greater than 10 during its free-settling process [18]. These effects lead to the different fitting of drag coefficients. As a result, although the drag models for non-spherical particles greatly improve the prediction of the particle's drag coefficient, the accuracy of them still needs to be improved to satisfy the requirement of practical use. Therefore, in order to improve the accuracy of drag models, the relationship between the drag coefficient and particle orientation angles should be investigated, and the experiment data of non-spherical particles with different fixed orientation angles in a wide Reynolds number range is needed. The cube is a typical non-spherical particle with a regular shape. The drag characteristics of cubic particles are representative of non-spherical particles, and their settling behavior is crucial for establishing drag coefficient prediction models for non-spherical particles [19]. Some researchers have investigated the relationship between the orientation angle and drag coefficient by using the cube. [PERSON] et al. investigated the sedimentation characteristics of cuboids with a square base [20].