**1. Introduction**

In the hydrocarbon industries, erosion is a common problem that leads to pipeline leakage, component damage, and even overall pipeline system failure. Erosive wear takes place when a fluid-carrying erodent consistently impacts the target surface [1]. This consistent impact force applied by the erodent causes gradual material loss from the target material [2]. The angle of impaction between carrier fluid and target surface plays a crucial role in defining the erosion rate [3]. Therefore, flow-changing devices, like elbows, valves, chokes, tees, U-bends, and offset elbows are comparatively more prone to erosive wear and tear [4].

The standard 90◦ elbow is widely used in the hydrocarbon industry as a flow-changing device [5]. Erosive wear in the 90◦ elbows has been the central focus of various experimental and numerical investigations [6]. Erosion in elbows is quite large compared to straight pipes [7]. Though erosion is inevitable and cannot be avoided fully, engineers and scientists have utilized a diverse range of erosion mitigation techniques to minimize devastating damages to elbows due to erosive wear and tear [8].

Design modification is a popular technique for mitigating erosive wear and tear in elbows. A vertex chamber was examined in comparison to a standard 90◦ elbow [9]. The basic geometric parameters, such as pipe diameter, domain size, and curvature radius, were not modified. A semi-sphere was constructed at the upstream section. The research work concluded that the erosion rate in the vertex chamber was considerably reduced, and in the worst-case scenario it was half of the 90◦ elbow.

This research study presents a numerical approach to predict the erosion rate and mechanism in a standard 90◦ elbow. The key focus of this research work aims at analyzing the influence of two-phase, air-solid flow on the erosion of the elbow at different locations.

**Citation:** Khan, N.; Khan, M.R.; Ullah, S.; Talha, T.; Khan, M.A.; Sajid, Z. Numerical Study of Gas-Sand Two-Phase Flow Erosion in a Standard 90◦ Elbow. *Eng. Proc.* **2023**, *45*, 28. https://doi.org/10.3390/ engproc2023045028

Academic Editors: Mohammad Javed Hyder, Muhammad Mahabat Khan, Muhammad Irfan and Manzar Masud

Published: 12 September 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

7

To decouple the effect of two-phase, air-sand flow on erosion in a standard 90◦ elbow, it is subjected to a range of flow velocities and mass flow rates.

This research work numerically validates the experimental and computational claims made by Viera et al. [10].

#### **2. Methods**

The 3D model displayed in Figure 1 was created in SOLIDWORKS. To compare and analyze the results, the geometry of Viera et al. [10] was utilized for the simulations. Flow enters the pipe through a straight section that is 1000 mm in length. This section contains a 90◦ elbow with r/D equal to 1.5 followed by another straight segment that is a 600 mm flow outlet. The geometry and other details are shown in Figure 1. The inside diameter (D) of the pipe is equal to 76.2 mm. In this study, a grid with 2.7 million cells was used for all the simulation cases due to its optimal computational cost and accuracy.

**Figure 1.** Geometry dimensions.

The experimental results of Viera et al. [10] were validated using CFD simulations. In Viera et al.'s experiment, various tests were performed at different air velocities and different sand flow rates. The experimental results were then validated by CFD simulations. For the vertical horizontal (V-H) configuration tests, sand sizes of 150 and 300 μm were used.

#### **3. Results and Discussion**

This research work presents a numerical approach to verify the experimental findings of Viera et al. [10]. Six cases with different velocities and particle sizes were carried out. The operating conditions were consistent with those used in the experiments. The numerical results, which are displayed in Table 1, were in close agreement with the experimental results.


**Table 1.** Comparison of numerical and experimental results.

A literature study reveals that elliptical and V-shape erosion scars appear on the largest inner surface bend (extrados) of the elbow due to erosive wear. In this research work, both elliptical and V-shape scars were developed, as shown in Figure 2a. The erosion rate is negligible from 0◦ to 20◦ and increases gradually from 20◦ to 55◦ of the 90◦ elbow, with severe erosion observed at 45◦ to 55◦. Figure 2b shows the erosion rate at different curvature angles of the standard 90◦ elbow.

**Figure 2.** (**a**) Elliptical and V-shaped erosion scar; (**b**) erosion at various curvature angles.

It was observed that the erosive wear rate increased with erodent size diameter, as shown in Figure 3. Erodents of 150 and 300 μm size were used in this case study, and carrier fluid velocity was kept at 23 m/s for both particle sizes.

**Figure 3.** Erosion rate for different particle sizes: (**a**) 150 μm (**b**) 300 μm.

The influence of fluid velocity on erosion rate was analyzed. Two flow velocities, 11 and 23 m/s were considered in this case. The particle size of 300 μm was used for both velocities. It was concluded that the erosion rate increases with the fluid velocity.

It is evident from the numerical results that the highest pressure is observed at the outer surface, and the lowest pressure is achieved at the inner surface of the elbow. Gradual pressure drop is observed from outer surface towards inner surface. The pressure distribution across the entire elbow is presented in Figure 4.

Particle trajectory shows that particles enter through the inlet and follow a straight path and then move in an irregular pattern after hitting the elbow. The majority of the erodent impacts the outer wall, which produces maximum wear. The inner wall of the pipe is a no-erodent zone with minimum erosion, as shown in Figure 5.

**Figure 4.** Pressure variation.

**Figure 5.** Particle track.

#### **4. Conclusions**

A CFD-based numerical approach was utilized to validate previous experimental and numerical results of erosion in a 90◦ elbow bend. The influence of different parameters on erosive wear rate and future recommendations are extensively discussed below.


The influence of non-spherical sand particles could be studied in future for a better understanding of sand erosion, as sand particles are non-spherical in nature.

**Author Contributions:** Conceptualization, writing—original draft, formal analysis, software, and validation: N.K.; supervision, investigation, and methodology: M.R.K., S.U. and T.T.; writing review and editing: M.A.K. and Z.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research work did not receive any funding from external sources.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding authors.

**Acknowledgments:** The authors acknowledge the College of Electrical and Mechanical Engineering (CEME), NUST, for providing the high-performance computing system.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

