⚡ electrical engineering

Uncertainty Analysis of Corrosion-Induced Surface Roughness Transfer From Ra to Equivalent Sand-Grain Roughness in Centrifugal Pumps

This study proposes an uncertainty-aware framework to convert corrosion-induced surface arithmetic roughness (Ra) into equivalent sand-grain roughness (ks) for centrifugal pump CFD modeling, utilizing experimental data to quantify transfer model uncertainty and prevent the misattribution of performance degradation solely to surface roughness.

Original authors: Nsini Udo

Published 2026-09-30

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Nsini Udo

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a centrifugal pump as the heart of an industrial system, tirelessly pushing fluids through pipes to keep everything running. When these pumps move corrosive liquids like seawater, their internal metal surfaces slowly degrade. This degradation isn't just a cosmetic issue; it changes the texture of the metal, making it rougher. In the world of fluid mechanics, this roughness matters immensely. A smooth surface allows water to glide with minimal resistance, while a rough surface creates friction, slowing the flow and forcing the pump to work harder. Engineers have long known that to predict how a pump will perform, they need to know exactly how rough the inside walls have become. However, there is a significant gap between what they can easily measure and what their computer models actually need.

The problem lies in the difference between two ways of describing a surface. One method, called arithmetic roughness, is a standard measurement that gives a single number representing the average height of the tiny bumps and valleys on a metal surface. It is easy to measure with a probe. The other method, known as equivalent sand-grain roughness, is a specific value used by computer simulations to calculate how that roughness will slow down the flow of water. The challenge is that these two numbers are not the same thing. A surface might have a certain average height but a shape that creates much more or much less friction than expected. Without a clear, proven rule to translate the easy measurement into the simulation value, engineers are forced to guess. If they guess wrong, their computer models might predict a pump that works perfectly when, in reality, it is struggling.

A researcher named Nsini Udo tackled this uncertainty by looking at real-world data from a pump that had been running in synthetic seawater for 200 hours. Instead of trying to force a single, perfect answer, the study focused on mapping out the range of possibilities. The pump, made of a corrosion-resistant steel, was monitored at five different points in time. Over those 200 hours, the surface roughness increased steadily, and the pump's performance declined in a matching pattern. The water pressure it could generate dropped, the amount of water it moved decreased, and its energy efficiency fell significantly. At the same time, the vibration of the machine increased, suggesting that the internal damage was affecting the mechanical balance as well.

The core of the research was to see what happens when you try to convert the measured surface roughness into the value needed for computer models. The researcher tested three different conversion scenarios, essentially asking: "If the surface roughness is this high, how much roughness would the computer model need to see if we assumed a specific, uncalibrated relationship?" By applying these different conversion factors without performing any calibration against solver results, the study revealed a wide spread in the results. At the end of the 200-hour test, the estimated roughness value for the computer model could be anywhere from a very low number to a value four times higher, depending on which conversion rule was used. This finding is crucial because it shows that simply measuring the surface is not enough; without a specific calibration for that particular pump and fluid, the number fed into the computer is highly uncertain.

The study also highlighted that the drop in the pump's performance was not caused by surface roughness alone. While the roughness increased, other factors were changing simultaneously. The metal developed pits, which are small, deep craters, and the clearances between moving parts likely grew larger due to wear. These changes, along with the roughness, all contributed to the pump's struggle. The research introduced a new way of thinking about this problem: instead of blaming the entire drop in performance on the rough surface, engineers should acknowledge that some of the loss comes from other mechanical changes. This approach prevents the computer model from being tricked into thinking that a single number can explain every problem.

To move forward, the paper proposes a checklist of evidence that engineers must gather before they can trust a computer model of a corroded pump. First, they need to preserve the history of how the surface changed over time. Second, they must look at the three-dimensional shape of the corrosion, not just the average height, because the shape of the pits matters. Third, they need to test how the pump actually performs at different speeds to see how the roughness affects the flow. Finally, they must measure the physical dimensions of the pump after the test to see if the gaps between parts have changed. Until all these pieces of evidence are collected, the computer model should be treated as a tool for exploring possibilities rather than a definitive prediction.

This work does not claim to have solved the problem of predicting pump failure. Instead, it provides a clear, honest framework for understanding the limits of current knowledge. It shows that while we can measure the surface of a pump, the path from that measurement to a reliable computer simulation is filled with uncertainty. By making this uncertainty visible and defining the steps needed to reduce it, the research offers a more realistic path for engineers. It suggests that the future of pump modeling lies not in finding a single magic number, but in building a complete picture that accounts for the complex, messy reality of corrosion, geometry, and fluid flow.

Technical Summary: Uncertainty Analysis of Corrosion-Induced Surface Roughness Transfer in Centrifugal Pumps

Problem Statement
The paper addresses a critical disconnect in the computational fluid dynamics (CFD) modeling of centrifugal pumps: the inability to directly translate measured arithmetic surface roughness ( $R_a$ ) into the equivalent sand-grain roughness ( $k_s$ ) required for hydraulic rough-wall flow models. While $R_a$ is a standard statistical descriptor of surface height variation, $k_s$ is a hydraulic parameter governing momentum transfer. The author argues that treating a corrosion-induced $R_a$ trajectory as a deterministic input for $k_s$ without calibration introduces significant, often hidden, model-form uncertainty. Furthermore, in real-world corrosion scenarios, performance degradation (e.g., head loss) is rarely caused by surface roughness alone; it is often coupled with clearance growth, leakage, pitting morphology, and mechanical imbalance. Attributing all observed hydraulic losses solely to an increased $k_s$ risks creating numerically accurate but physically flawed models.

Methodology
This study is a secondary analysis of experimental data from a previously reported 200-hour corrosion exposure test on a 316L stainless-steel centrifugal pump operating in 30-ppt synthetic seawater (Udo, 2026). The methodology avoids new experimental measurements or CFD solver runs, focusing instead on an uncertainty-aware framework to analyze the transition from corrosion data to hydraulic parameters.

Key methodological components include:

Exposure-Indexed Trajectory: The study utilizes five sequential exposure states (0, 50, 100, 150, and 200 hours) rather than independent samples, preserving the degradation path of $R_a$ , head, flow, efficiency, vibration, and pit density.
Deterministic Sensitivity Scenarios: Instead of a single conversion factor, the transfer from $R_a$ to $k_s$ is modeled as $k_s = \alpha R_a$ . Three deterministic scenarios are evaluated with $\alpha = 0.5, 1.0,$ and $2.0$ to represent model-form uncertainty.
Uncertainty Separation: The framework explicitly separates measurement uncertainty (in $R_a$ ) from transfer-model uncertainty (in $\alpha$ ). It introduces an "attribution residual" concept ( $\Delta H_{res}$ ) to account for head loss components not attributable to roughness.
Derived Metrics: The study calculates an envelope ratio ( $U_\alpha$ ), absolute envelope width ( $W_{k_s}$ ), and a midpoint-normalized half-width ( $C_{k_s}$ ) to quantify the spread of potential $k_s$ values without assuming probability distributions.
Pre-CFD Readiness Gates: A six-stage framework is proposed to define the minimum evidence required before a corrosion-aware CFD model can be considered validated.

Key Results

Degradation Envelope: Over 200 hours, $R_a$ increased monotonically from 0.8 to 3.4 $\mu$ m. Concurrently, pump head dropped from 12.0 to 10.7 m, flow decreased from 1.50 to 1.38 L/s, efficiency fell from 70.6% to 58.0%, and RMS vibration rose from 0.20 to 0.75 mm/s.
Transfer Uncertainty: Applying the transfer scenarios ( $\alpha = 0.5, 1.0, 2.0$ ) to the final $R_a$ of 3.4 $\mu$ m yields a $k_s$ envelope ranging from 1.7 to 6.8 $\mu$ m. This represents a four-fold variation (high-to-low ratio of 4.0) solely due to the choice of the transfer factor.
Growth of Uncertainty: The absolute width of the uncertainty envelope ( $W_{k_s}$ ) increases with corrosion exposure, growing from 1.2 $\mu$ m at 0 hours to 5.1 $\mu$ m at 200 hours. This indicates that uncertainty in the inferred hydraulic roughness becomes more consequential as the surface degrades.
Correlation vs. Causation: While Pearson correlation coefficients between $R_a$ and performance variables (head, flow, efficiency, vibration) are extremely high (approx. $\pm 0.99$ ), the author cautions that these represent coupled exposure-indexed associations, not causal proof that roughness alone drove the hydraulic losses.
Attribution Residual: The study establishes that the observed 1.30 m head drop cannot be fully attributed to roughness without further calibration. A residual term ( $\Delta H_{res}$ ) is necessary to account for geometry changes, leakage, and mechanical effects.

Key Contributions
The paper introduces three primary methodological innovations:

Exposure-Indexed Roughness Envelope: It preserves the measured $R_a$ path as a time-indexed evidence envelope rather than reducing it to a single representative value.
Explicit Uncertainty Separation: It distinguishes between the uncertainty of the surface measurement and the uncertainty of the $R_a$ -to- $k_s$ transfer model, preventing the former from being contaminated by the latter.
Attribution Residual Concept: It formalizes a method to prevent the misattribution of total hydraulic degradation to surface roughness alone, reserving a residual term for unmeasured mechanisms (e.g., clearance growth, pitting morphology).

Additionally, the work proposes a Pre-CFD Readiness Framework consisting of six gates (Exposure Trajectory, Surface Morphology, Hydraulic Transfer, Local Regime, Geometry Integrity, and Pump Validation) to guide the transition from corrosion testing to solver-based modeling.

Significance and Claims
The author claims this work provides a "transparent start" to the transition from corrosion testing to CFD modeling without replacing unknown calibration with fictitious numerical values. The significance lies in shifting the engineering perspective from seeking a single "accurate" $k_s$ value to acknowledging a "transparent uncertainty envelope."

The paper asserts that:

Current practices of arbitrarily assigning a $k_s$ value based on $R_a$ mask significant model-form uncertainty.
A deterministic $k_s$ input is insufficient for predictive modeling of corroded pumps; an uncertainty-aware approach is required.
The proposed framework serves as a "rule of cessation," ensuring that if specific evidence gates (such as 3D topography or local flow data) are not met, the resulting CFD output should be treated as sensitivity analysis rather than validation.
The methodology is portable, though the specific numerical trends are limited to the tested material (316L), fluid (synthetic seawater), and duration (200 hours).

Ultimately, the paper argues that until sufficient evidence (morphology, geometry, local flow, and multi-point validation) is accumulated, the uncertainty envelope constructed here remains the most honest representation of the corrosion-to-CFD transfer problem.

Technical Summary: Uncertainty Analysis of Corrosion-Induced Surface Roughness Transfer in Centrifugal Pumps

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