Multiphase Computational Fluid Dynamics Analysis of Hydro-Abrasive Wear in Slurry Pipelines Using the Oka Erosion Model with Ultrasonic Validation

2.1 From blueprints to Computer-Aided Design: Geometric reconstruction of spool 31

The geometric fidelity of the computational domain is a fundamental requirement for reliable Computational Fluid Dynamics (CFD) predictions [23, 24]. In this study, the discharge assembly, comprising the suction line, the Warman 650 MCR-M200 pump, and the sequence of spools from 26 to 38, was reconstructed from original manufacturer blueprints. The resulting three-dimensional Computer-Aided Design (CAD) model, developed at full scale in SolidWorks, captures the internal flow passages and the bifurcation associated with the emergency discharge system, as shown in Figure 2.

Figure 2. Isometric Computer-Aided Design (CAD) of discharge system: (a) Pump assembly, (b) Spool 31 rectangular lining, and (c) Spool 34 hexagonal lining

This geometric reconstruction enables the identification of localized features that govern hydrodynamic behavior and wear distribution. In particular, Spool 31 exhibits a Y-junction configuration in which the main branch ascends at 45° toward the cyclone cluster, while the secondary horizontal branch functions as an emergency discharge and maintenance outlet. Under normal operating conditions, this lateral branch remains closed, forming a low-velocity region where particulate matter accumulates. This accumulation modifies the local flow structure and must be removed prior to inspection procedures such as UT.

Due to its critical location within the system, Spool 31 incorporates an increased lining thickness. The internal protection is based on rectangular ceramic tiles arranged to minimize interfacial discontinuities and reduce localized erosion at joints. In contrast, Spool 34, an elbow responsible for redirecting the flow toward a vertical trajectory, employs a hexagonal ceramic configuration, which provides improved surface conformity in curved regions and enhances coverage continuity.

The reconstructed geometry explicitly includes the nominal thickness of the multi-material lining system. This ensures that the computational domain accurately represents the effective internal diameter and the fluid–structure interface, allowing for consistent evaluation of flow patterns and erosion mechanisms under representative operating conditions.

2.2 Variable pumping dynamics: Warman pump cycles and flow analysis

The hydraulic behavior of the classification circuit is governed by the performance of the centrifugal pumping system. The Warman 650 MCR-M200 pump, shown in Figure 3, operates with an 8° tangential discharge configuration, while the suction system integrates the manifold corresponding to Spools 21–24.

(a) Operational unit with 8° tangential discharge

(b) Isometric view of the suction manifold (Spools 21–24)

Figure 3. Warman 650 MCR-M200 pump configuration

To establish physically consistent boundary conditions, the relationship between impeller rotational speed N and volumetric flow rate Q was defined using the pump affinity laws, following Visintainer et al. [25]. These relationships can be expressed as:

$\frac{Q_1}{Q_2}=\frac{N_1}{N_2} ; \frac{H_1}{H_2}=\left(\frac{N_1}{N_2}\right)^2 ; \frac{P_1}{P_2}=\left(\frac{N_1}{N_2}\right)^3$                      (1)

Operational data obtained from the Variable Frequency Drive (VFD) system over a six-month period were analyzed to characterize flow variability. The recorded signals showed fluctuations in rotational speed within a defined operating window, which were incorporated into the numerical model as discrete steady-state conditions representative of low, nominal, and high flow regimes. This approach provides a practical approximation of transient behavior while maintaining computational tractability.

Under reduced flow conditions, the capacity of the carrier fluid to maintain coarse particles in suspension decreases significantly. This effect was evaluated using the Archimedes number, defined as [25]:

$A r=\frac{g d_p^3 \rho\left(\rho_p-\rho\right)}{\mu^2}$                      (2)

where, $g$ is gravitational acceleration, $d_p$ is the particle diameter (up to 30 mm for oversized fragments), $\rho_s$ and $\rho_f$ are the solid and fluid densities, and μ is the dynamic viscosity of the slurry. The resulting Archimedes number indicates that gravitational forces dominate over viscous effects during low-velocity regimes, promoting particle settling in regions with reduced flow momentum, particularly within the lateral branch of Spool 31.

The set of components included in the geometric reconstruction is summarized in Table 1, where Spool 31 (Y-junction) is defined as the primary computational domain. This location represents a critical transition zone where the initial 8° discharge inclination evolves into a 45° ascending flow toward the cyclone system, generating complex hydrodynamic conditions that directly influence erosion patterns.

Table 1. Technical specifications of the suction and discharge line components

2.3 Multi-material lining systems: Tribological properties

The internal protection system implemented in Spool 31 is based on a hybrid lining architecture designed to mitigate multiple wear mechanisms associated with hydro-abrasive flow. This configuration combines high-purity alumina ($\mathrm{Al}_2 \mathrm{O}_3$) ceramic tiles, which provide resistance to sliding abrasion, with a natural rubber backing layer that enhances impact energy dissipation from coarse particles.

To assess the integrity of the ceramic–elastomer interface, a qualitative microstructural analysis was conducted using Scanning Electron Microscopy (SEM) [26, 27]. The objective of this characterization was to verify the continuity of the bonding interface and to identify potential discontinuities that could act as stress concentrators under cyclic loading conditions.

Figure 4 shows a representative SEM micrograph of the alumina–rubber interface. The ceramic phase exhibits a dense polycrystalline structure with well-defined grain boundaries and no evidence of interfacial debonding or porosity. The absence of microcracks or voids indicates effective mechanical coupling between the ceramic tiles and the elastomeric substrate. This interfacial continuity is essential to reduce stress localization and delay the onset of ceramic spalling under repeated particle impacts ($d_p$ = 30 mm).

These observations are consistent with established tribological criteria, where dense ceramic phases combined with compliant substrates improve impact resistance by promoting load redistribution and energy absorption rather than brittle fracture [28, 29].

The mechanical and tribological properties of the system components are summarized in Table 2. These properties, particularly density, hardness, and elastic modulus, constitute key inputs for the erosion model, as they influence particle wall interaction mechanics and energy transfer during impact events.

Table 2. Mechanical and tribological properties of the system components

2.4 In-situ thickness monitoring: Ultrasonic Testing

An experimental monitoring campaign was conducted during scheduled maintenance shutdowns to provide a reference dataset for model validation. Although Spool 31 represents the primary hydrodynamic region of interest, its composite ceramic–rubber lining presents high acoustic impedance, which limits the applicability of conventional ultrasonic pulse-echo techniques for internal thickness measurements.

As a result, direct ultrasonic measurements were not feasible for Spool 31. Instead, inspection of this component was based on visual assessment and localized repair interventions. To establish a quantitative validation baseline, UT was performed on Spool 32, a steel-lined component located immediately downstream, where reliable acoustic measurements can be obtained.

Measurements were acquired using a SIUI SMARTOR ultrasonic gauge equipped with a 1 MHz transducer, calibrated for an acoustic velocity of 1587 m/s and a gain of 38.5 dB. The inspection grid consisted of 12 measurement points distributed across three axial stations: upstream (S1), mid-section (S2), and downstream (S3). At each station, four circumferential positions were evaluated (0°, 90°, 180°, and 270°), as illustrated in Figure 5.

Figure 5. Monitoring grid and spatial discretization of spool 32

The results, summarized in Table 3, reveal a clear asymmetry in wear distribution. The minimum thickness was recorded at the S1–90° position (16.27 mm), while visual inspection identified a localized region of complete lining loss near the coupling interface. Direct mechanical measurement in this region indicated a residual wall thickness of 10.7 mm, corresponding to exposure of the base material (see Figure 6).

Table 3. Ultrasonic Testing (UT) thickness measurement data for spool 32 (Baseline)

Figure 6. Field Inspection and In-Situ Wear Evidence

This experimental dataset provides an indirect validation reference for the numerical model. Specifically, it enables the comparison between predicted erosion hotspots in Spool 31 and the observed wear patterns in Spool 32, which are physically linked through the flow field exiting the Y-junction. While this approach does not constitute direct validation of the primary computational domain, it offers a consistent basis for assessing the predictive capability of the model under real operating conditions.

To relate numerical erosion predictions to physical material loss, the simulated mass removal rate is converted into a linear erosion rate. Following the formulation proposed by Blazek [30], the erosion rate at each surface element is defined as:

$R_{\text {erosion }}=\frac{\dot{E}_{\text {mass }}}{\rho_{\text {wall }} \cdot A_{\text {face }}}$                   (3)

where, $\dot{E}_{\text {mass}}$ is the mass loss rate $(\mathrm{kg} / \mathrm{s}), \rho_{\text {wall}}$ is the material density, and $A_{\text {face}}$ is the local surface area. This transformation enables direct comparison with measured thickness loss and supports the statistical validation framework presented in Section 4.

(a) Spool 30–31 velocity profile

(b) Spool 30-31 cross–sectional contour

(c) Spool 31–32 discharge profile

(d) Spool 31–32 cross-sectional contour

Figure 8. Velocity distribution at the Y-junction transition

(c) Spool 34–35 velocity profile (flow recovery)

(d) Spool 34–35 cross-sectional contour

Figure 9. Velocity distribution across the verticalization elbow

4.1.4 Localized pressure peaks and mechanical stress

In addition to velocity effects, the pressure field contributes to material degradation [42, 43]. As shown in Figure 10, the static pressure at the Spool 31 emergency cover reaches 59.4 kPa.

Figure 10. Static pressure distribution at the Spool 31 emergency cover transition

The overlap between high velocity (9.04 m/s, Figure 8(d)) and elevated pressure results in combined tangential and normal stresses, explaining the severe material loss observed at the 90° position (10.7 mm).

4.1.5 Particle trajectories and residence time analysis

To complete the hydrodynamic characterization, the discrete phase behavior was analyzed through Velocity Magnitude Pathlines and Particle Residence Time [44, 45]. While the carrier phase follows the pipeline geometry, coarse particles exhibit significant inertial deviation due to Stk ≫ 1 (Eq. (13)), particularly at the Y-junction transition. As shown in Figure 11, the pathlines near the Spool 31 emergency cover reveal a recirculating vortex structure [11, 12].

(a) Lateral view of the assembly

(b) Rear view focus on the Spool 31 emergency cover transition

Figure 11. Velocity magnitude pathlines for the solid phase

The velocity magnitude within these trajectories remains high, indicating that particles do not exit the junction in a streamlined manner but are instead subjected to rotational motion. This behavior increases impact frequency and produces a localized “sandblasting” effect, which is consistent with the wear patterns observed during field inspections.

The Particle Residence Time distribution (Figure 12) further identifies stagnation regions near the junction boundaries, where particles remain for extended periods, reaching values up to $4.08 \times 10^2 s$ in critical zones [46, 47]. This prolonged exposure significantly amplifies cumulative erosion.

Figure 16. Erosion regime map based on Oka scaling

At the characteristic operating condition of the system (impact velocity approximately 9 m/s), the elastomeric lining (SBR rubber, $H_v=0.03$) is located within a high-erosion domain, whereas alumina ceramic ($H_v=1550$) lies in a region where erosion rates are several orders of magnitude lower. This separation confirms that the difference in predicted service life observed in Figure 15 is primarily governed by intrinsic material properties rather than operational variability.

The combined interpretation of Figures 15 and 16 demonstrates that the premature failure of the rubber lining is not a consequence of localized anomalies but a direct result of its limited hardness under high-energy particle impacts. Consequently, the transition to an alumina-based lining in Spool 32 is supported not only by numerical prediction and field validation, but also by the fundamental scaling behavior of erosion.

The combined interpretation of Figures 15 and 16 demonstrates that the premature failure of the rubber lining is not a consequence of localized anomalies but an inherent limitation of its mechanical resistance under high-energy particle impacts. Consequently, the transition to an alumina-based lining in Spool 32 is supported not only by numerical prediction and field validation, but also by the fundamental scaling behavior of erosion.

We thank the Universidad Nacional de San Agustín de Arequipa for their support and knowledge.