⚡ electrical engineering

Multi-objective optimization of adjustable orifice valve insulation lining based on thermal-solid coupling and improved whale algorithm

This paper presents a multi-objective optimization framework combining finite element analysis, surrogate modeling, and an improved whale algorithm to determine the optimal geometric parameters for an adjustable orifice valve's insulation lining, successfully balancing thermal insulation performance with structural reliability and reducing maximum equivalent stress by approximately 36.3%.

Original authors: Shuxun Li, Jian Zhang, Xinhao Liu, Yu Zhao, Jianlong Zhu

Published 2026-08-14

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Shuxun Li, Jian Zhang, Xinhao Liu, Yu Zhao, Jianlong Zhu

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

The Heat-Proof Puzzle: Keeping Valves Cool Without Breaking

Imagine a high-pressure valve in a chemical factory as the heart of a massive, fiery engine. Inside, scorching hot gas rushes through at temperatures that would melt ordinary metal. To protect the valve's metal body from melting, engineers wrap it in a thick, heat-resistant blanket called "insulation lining." But here's the tricky part: this blanket is made of a brittle, ceramic-like material, while the valve body is tough metal. When things get hot, metal expands quickly, but the ceramic blanket expands slowly. It's like trying to wear a wool sweater over a balloon that's inflating; the mismatch creates stress, leading to cracks or even the blanket falling off entirely.

To stop this, engineers use metal "anchors"—little hooks or spikes that pin the blanket to the metal wall, holding it tight. However, these metal hooks act like tiny bridges for heat, letting the fire sneak through and creating hot spots that weaken the structure. The goal is to find the perfect balance: a lining thick enough to keep the heat out, anchors spaced just right to hold it together without letting too much heat through, and a design that doesn't cost a fortune. This paper tackles that exact puzzle, using computer simulations to figure out how to build a valve lining that stays cool, stays strong, and stays affordable, even in the most extreme heat.

The Paper's Story: Tuning the Perfect Thermal Shield

The researchers at Lanzhou University of Technology set out to solve the "Goldilocks problem" of high-temperature valve linings. They wanted to find the exact recipe for a lining that keeps the metal valve body safe from the 770°C (1,418°F) flue gas inside, without cracking under pressure or costing too much.

The Simulation Game
Instead of building and breaking dozens of real valves (which would be expensive and slow), the team built a virtual version in a computer. They used a method called "thermal-solid coupling," which is like running a video game where the physics engine calculates both the heat moving through the materials and the stress pushing on them at the same time. They tested two main scenarios: a lining with no anchors (which is safe from heat bridges but might fall off) and a lining with "Ω-type" anchors (which hold the lining tight but create tiny heat bridges).

Their simulations showed a clear trade-off. Adding a special thermal insulation coating on the inside of the lining was a huge win, dropping the temperature of the lining by about 33.8% and reducing stress on the metal valve by 36%. However, the anchors themselves were a double-edged sword. While they kept the lining from peeling off, the metal anchors acted as "heat bridges," conducting heat into the lining and creating intense stress points where the metal hook met the ceramic material. In fact, the anchors themselves faced a theoretical stress peak of 517.55 MPa, making them a potential weak link.

The Smart Algorithm Hunt
To find the perfect design, the team didn't just guess. They used a clever computer trick. First, they created a "surrogate model"—a fast, simplified prediction tool trained on data from their heavy-duty simulations. To make this tool super accurate, they improved a standard AI brain (a BP neural network) using a "Whale Optimization Algorithm."

Think of the Whale Optimization Algorithm like a school of humpback whales hunting fish. In nature, whales use a "bubble net" strategy to trap prey. In the computer, each "whale" represents a possible design (a specific spacing of anchors, a specific thickness of lining). The algorithm makes these virtual whales swim around, searching for the best design. The researchers improved this by adding a "chaotic map" to help the whales start in better positions and a "sine factor" to help them stop wandering and focus on the best spot. This helped the computer avoid getting stuck in a "local optimum" (a good solution that isn't the best one) and find the true global champion.

The Winning Recipe
After running thousands of virtual tests, the improved algorithm spit out the optimal combination of parameters. The "champion" design features:

Anchor spacing: 196.5 mm (about 77 inches)
Anchor diameter: 9.6 mm
Lining thickness: 119.1 mm
Coating thickness: 3.0 mm

When the researchers tested this specific "champion" design in their detailed computer simulation, the results were impressive. The maximum stress on the lining dropped by about 36.3% compared to the original, unoptimized design. The computer predicted the stress values with high accuracy, showing only a 2.70% difference between the prediction and the final detailed simulation.

What This Means
The paper concludes that you can't just make the lining thicker or add more anchors to fix the problem. Instead, you need a collaborative approach. The thermal coating handles the global job of blocking heat, while the anchors handle the mechanical job of holding things together. By using this smart, whale-inspired algorithm to fine-tune the spacing and size of the anchors, engineers can create a valve lining that is lighter, lasts longer, and survives the extreme heat of industrial chemical processes without cracking or falling apart. The study suggests that this method of using advanced AI to optimize physical structures is a reliable way to design safer, more efficient high-temperature equipment.

Technical Summary: Multi-objective Optimization of Adjustable Orifice Valve Insulation Lining

Problem Statement
Adjustable orifice valves in catalytic cracking units operate in extreme environments, requiring internal flow channels to withstand flue gas temperatures exceeding 770°C. To protect the metal valve body, a composite lining structure consisting of refractory castable and metal anchorage is employed. However, this design faces a critical trade-off: the significant difference in thermal expansion coefficients between refractory materials and metals, combined with the high thermal conductivity of metal anchors, creates local hot spots and thermal stress cracks. Existing research often lacks quantitative analysis of the anchor-lining interaction mechanism and fails to simultaneously optimize thermal insulation performance, structural strength, and economic factors.

Methodology
The study employs a comprehensive approach combining finite element analysis (FEA), surrogate modeling, and advanced optimization algorithms:

Thermal-Solid Coupling Analysis:
- Modeling: Finite element models were developed for adjustable orifice valve lining structures with and without anchoring parts, including a new thermal insulation coating. The models utilized a local refined meshing strategy to capture stress concentrations at the anchor-lining interface.
- Simulation: Steady-state thermal-solid coupling simulations were conducted to analyze temperature and stress field distributions. Boundary conditions included convective heat transfer from high-temperature flue gas and ambient cooling.
- Verification: Mesh independence tests confirmed that a specific mesh density (Scheme C) provided results within 1% variation of finer meshes, balancing accuracy and computational cost.
Surrogate Model Construction:
- Experimental Design: An optimal Latin hypercube design was used to generate 50 sample design schemes varying four key parameters: anchorage spacing ( $X$ ), lining thickness ( $L_1$ ), anchorage diameter ( $D$ ), and coating thickness ( $L_2$ ).
- Algorithm Improvement: To overcome the limitations of standard BP neural networks (slow convergence, local optima), the authors developed an L-TIWOA-BP model. This integrates:
  - Logistic-Tent (L-T) Chaotic Map: To initialize the population with better uniformity.
  - Improved Whale Optimization Algorithm (IWOA): Incorporating adaptive weights and sine factors to update whale positions, enhancing global search capabilities.
  - BP Neural Network: Optimized by the L-TIWOA to serve as a high-precision surrogate model for predicting lining stress, anchor stress, and material cost.
Multi-objective Optimization:
- Objectives: Minimize lining stress ( $y_1$ ), minimize average anchor stress ( $y_2$ ), and minimize material cost ( $y_3$ ).
- Algorithm: An improved NSGA-II (Non-dominated Sorting Genetic Algorithm II) with an adaptive mutation operator was applied to the L-TIWOA-BP surrogate model to generate the Pareto optimal solution set.

Key Results

Mechanism Analysis: The study clarified the distinct roles of the lining components. The thermal insulation coating provides global thermal attenuation, significantly reducing valve body and lining temperatures (by ~33-36%) and relieving thermal stress. Conversely, the $\Omega$ -type anchorage ensures mechanical integrity but acts as a thermal bridge and a source of local stress concentration, with peak anchor stresses reaching theoretical values of 517.55 MPa in unoptimized configurations.
Optimization Performance: The L-TIWOA-BP surrogate model demonstrated superior accuracy compared to standard BP networks, with significantly lower mean absolute and root mean square errors.
Optimal Parameters: The multi-objective optimization yielded the following optimal structural parameters:
- Anchorage spacing: 196.5 mm
- Anchorage diameter: 9.6 mm
- Lining thickness: 119.1 mm
- Coating thickness: 3.0 mm
Validation: Numerical simulation using the optimized parameters showed a maximum stress error of 2.70% and an average anchor stress error of 1.19% compared to the surrogate model predictions. These errors are notably lower than the 7.00% average relative error reported in comparable literature [33].
Performance Gains: The optimized design reduced the maximum equivalent stress of the lining by approximately 36.3% compared to initial configurations, while maintaining economic viability.

Significance and Claims
The paper claims to provide a theoretical basis for the lightweight and long-life design of high-temperature valve insulation structures. By integrating thermal-solid coupling analysis with a hybrid optimization algorithm (L-TIWOA-BP combined with NSGA-II), the study offers a method to quantitatively balance thermal insulation efficiency, structural reliability, and cost. The research addresses a gap in the specific optimization of catalytic cracking adjustable orifice valves, demonstrating that a synergistic design approach—combining global thermal attenuation via coatings with fine-tuned local force regulation via anchorage layout—can effectively mitigate stress concentration and extend service life under extreme thermal-mechanical loads.

The Heat-Proof Puzzle: Keeping Valves Cool Without Breaking

The Paper's Story: Tuning the Perfect Thermal Shield

Technical Summary: Multi-objective Optimization of Adjustable Orifice Valve Insulation Lining

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