基於 ASME B31J 規範之高能管線紊流與沖蝕腐蝕對比研究——內突銲道與冷作彎管之探討 (Comparative Study on Flow Turbulence and Erosion-Corrosion in High-Energy Piping based on ASME B31J: Investigating Weld Root Protrusions and Cold Bends)

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摘要 / Abstract

現代複循環發電廠（Combined Cycle Power Plant, CCPP）透過整合燃氣渦輪機與熱回收蒸汽產生器（HRSG），將發電效率推升至極致，然而其高壓蒸汽與給水管線系統亦因此暴露於極端的高溫、高壓與高速流場環境中。在此嚴苛條件下，管線系統的局部幾何特徵，特別是管線對接處產生的「內突銲道」（Weld Root Protrusion）與為適應工廠空間配置而常溫成型的「冷作彎管」（Cold Bend），成為流動加速腐蝕（Flow-Accelerated Corrosion, FAC）與沖蝕腐蝕（Erosion-Corrosion）的兩大高風險區域。本研究以深度學術論文之形式，針對這兩種幾何特徵在惡劣流場下的流體動力學與材料電化學劣化機制進行 Exhaustive 的對比分析。Modern Combined Cycle Power Plants (CCPP) maximize power generation efficiency by integrating gas turbines with heat recovery steam generators (HRSG); however, their high-pressure steam and feedwater piping systems are consequently exposed to extreme environments of high temperature, high pressure, and high-velocity flow fields. Under such severe conditions, local geometric features of the piping systems—specifically the “weld root protrusion” generated at pipe butt joints and the “cold bend” formed at room temperature to accommodate plant spatial layouts—become two major high-risk areas for Flow-Accelerated Corrosion (FAC) and erosion-corrosion. Through the format of an in-depth academic paper, this study conducts an exhaustive comparative analysis of the fluid dynamics and material electrochemical degradation mechanisms of these two geometric features under severe flow fields.

研究結果表明，流場在行經內突銲道時，會產生劇烈的幾何分離（Flow Separation），並於下游再附著點（Reattachment Point）激發出極高強度的紊流動能（Turbulent Kinetic Energy, TKE）與壁面剪應力（Wall Shear Stress, WSS），進而突破質傳極限值，造成局部保護性磁鐵礦（Magnetite）膜的溶解與微電偶腐蝕（Micro-galvanic Corrosion）。相對於內突銲道的局部點狀破壞，冷作彎管則透過離心力誘發迪恩渦流（Dean Vortices），形成大尺度的二次流（Secondary Flow）洗刷效應；同時，冷作過程所引發的應變硬化（Strain Hardening）導致材料內部差排密度劇增，造成局部的腐蝕電位（Corrosion Potential, Ecorr）顯著下降，從熱力學根源上提升了材料的電化學反應活性。The results indicate that when the flow field passes over a weld root protrusion, severe flow separation occurs, triggering extremely high turbulent kinetic energy (TKE) and wall shear stress (WSS) at the downstream reattachment point. This breaches the mass transfer limit, leading to the dissolution of the localized protective magnetite film and subsequent micro-galvanic corrosion. In contrast to the localized pitting damage caused by weld root protrusions, cold bends induce Dean vortices via centrifugal forces, creating a large-scale secondary flow washing effect. Simultaneously, the strain hardening induced by the cold working process causes a dramatic surge in internal dislocation density, leading to a significant drop in the local corrosion potential (Ecorr) and thereby elevating the material’s electrochemical reactivity from its thermodynamic roots.

本研究整合了計算流體力學（CFD）的k-ω SST 紊流模型、Kastner與Sanchez-Caldera質傳腐蝕模型，以及 ASME B31.1 動力管線規範中的減薄餘裕與熱處理要求，建立了一個綜合性的力學-電化學（Mechano-electrochemical）評估框架。此外，研究更進一步前瞻 2026 版 ASME B31J 規範強制導入後的實務決策，以及 AI 與數位孿生（Digital Twin）技術在未來高能管線完整性管理中的前沿應用，為電廠管線的預測性維護提供深層次的科學洞見。This study integrates the k-ω SST turbulence model of Computational Fluid Dynamics (CFD), the Kastner and Sanchez-Caldera mass transfer corrosion models, and the thinning allowance and heat treatment requirements in the ASME B31.1 Power Piping Code to establish a comprehensive mechano-electrochemical evaluation framework. Furthermore, the research looks ahead to the practical engineering decisions following the mandatory implementation of the 2026 ASME B31J code, as well as the cutting-edge application of AI and Digital Twin technologies in the future integrity management of high-energy piping, providing profound scientific insights for the predictive maintenance of power plant piping.

一、 緒論與複循環發電廠高壓系統背景 / 1. Introduction and Background of CCPP High-Pressure Systems

複循環發電廠（CCPP）作為當前全球能源結構中兼具高效率與低碳排特性的核心基載與尖峰負載電力來源，其運作原理在於回收燃氣渦輪機（Gas Turbine）排出的高溫廢氣，並將此廢熱導入熱回收蒸汽產生器（HRSG）中產生高壓蒸汽，進而推動蒸汽渦輪機（Steam Turbine）發電1。透過這種熱力學循環的疊加，整體電廠的熱轉換效率可大幅躍升至 60% 以上，相較於傳統燃煤或單循環電廠具有無可比擬的經濟與環保優勢1。為了達成最佳的可用能（Exergy）利用率，現代的 HRSG 多採用三壓（Triple-pressure）循環設計，涵蓋高壓（HP）、中壓（IP）與低壓（LP）系統，並伴隨複雜的再熱（Reheat）機制1。 As a core base-load and peak-load power source featuring both high efficiency and low carbon emissions in the current global energy structure, the Combined Cycle Power Plant (CCPP) operates by recovering the high-temperature exhaust gas discharged from the gas turbine. This waste heat is directed into the Heat Recovery Steam Generator (HRSG) to produce high-pressure steam, which in turn drives the steam turbine to generate electricity1. Through the superimposition of these thermodynamic cycles, the overall thermal conversion efficiency of the plant can leap to over 60%, offering unparalleled economic and environmental advantages compared to traditional coal-fired or single-cycle power plants1. To achieve optimal exergy utilization, modern HRSGs mostly adopt a triple-pressure cycle design, covering high-pressure (HP), intermediate-pressure (IP), and low-pressure (LP) systems, accompanied by complex reheat mechanisms1.

在如此複雜的熱力循環中，高壓主蒸汽管線與高壓飼水（Feedwater）管線承受著最為極端的操作條件。這些管線系統不僅需要在高溫高壓下維持絕對的結構完整性，還必須承受啟停機（Startup and Shutdown）頻繁帶來的熱應力與壓力波動，以及高速流體對管壁的持續性沖刷6。在管線的製造與現場施工過程中，無論是管與管對接銲接所殘留的「內突銲道」，或是將直管彎曲以改變走向的「冷作彎管」，都會打破原本直管內部平滑的流場邊界條件8。這兩種看似微小的幾何不連續性，實際上是誘發流動加速腐蝕（FAC）與沖蝕腐蝕的核心元兇。 In such complex thermodynamic cycles, the high-pressure main steam piping and high-pressure feedwater piping endure the most extreme operating conditions. These piping systems must not only maintain absolute structural integrity under high temperatures and high pressures but also with stand the thermal stress and pressure fluctuations brought by frequent startups and shutdowns, as well as the continuous scouring of the pipe walls by high-velocity fluids6. During the manufacturing and on-site construction of the piping, both the “weld root protrusion” left by pipe-to-pipe butt welding and the “cold bend” formed by bending straight pipes to alter routing disrupt the otherwise smooth internal flow boundary conditions of the straight pipe8. These two seemingly minor geometric discontinuities are, in fact, the primary culprits inducing Flow-Accelerated Corrosion (FAC) and erosion-corrosion.

流動加速腐蝕（FAC）是一個高度複雜的材料劣化過程，其本質是金屬管壁表面的保護性氧化層（主要為磁鐵礦 Fe3O4）在高速流體的高質傳效應下發生異常快速的電化學溶解，暴露出活潑的底層碳鋼，隨後碳鋼再次氧化並反覆被流體剝離，最終導致管壁急遽減薄甚至發生無預警的延性破裂（Ductile fracture）9。沖蝕腐蝕則進一步涵蓋了流體中可能存在的微小液滴或顆粒對管壁的純機械性衝擊剝離（Mechanical wear），兩者常以協同作用（Synergistic effect）的形式存在於電廠管線中8。因此，深入剖析內突銲道與冷作彎管在流體力學與材料劣化機制上的根本差異，不僅是學術界致力突破的課題，更是工程界落實 ASME B31.1 等國際規範以確保電廠安全運轉的必要基石。 Flow-Accelerated Corrosion (FAC) is a highly complex material degradation process. Its essence is the abnormally rapid electrochemical dissolution of the protective oxide layer (primarily magnetite, Fe3O4) on the metal pipe wall under the high mass transfer effect of high-velocity fluids. This exposes the active underlying carbon steel, which is subsequently re-oxidized and repeatedly stripped by the fluid, ultimately leading to a sharp thinning of the pipe wall and even unpredictable ductile fracture2. Erosion-corrosion further encompasses the pure mechanical impact and stripping (mechanical wear) of the pipe wall by tiny droplets or particles that may be present in the fluid. The two often exist in a synergistic effect within power plant piping9. Therefore, deeply analyzing the fundamental differences in fluid dynamics and material degradation mechanisms between weld root protrusions and cold bends is not only a breakthrough target for academia but also a necessary cornerstone for the engineering sector to implement international codes such as ASME B31.1 to ensure the safe operation of power plants.

二、 系統操作環境與熱力學參數解析 / 2. Analysis of System Operating Environments and Thermodynamic Parameters

要精確評估管線的劣化機制，首先必須量化 CCPP 高壓系統的物理與熱力學環境。現代大型 CCPP 通常配備如西門子（Siemens Energy）SST-5000 或 SST-6000 系列的先進蒸汽渦輪機，其單一機組的發電量可達數百至上千兆瓦（MW）3。這些大型機組的高壓主蒸汽管線的設計與操作條件已達到了材料科學的極限。 To accurately evaluate the degradation mechanisms of piping, the physical and thermodynamic environments of the CCPP high-pressure systems must first be quantified. Modern large-scale CCPPs are typically equipped with advanced steam turbines such as the Siemens Energy SST-5000 or SST-6000 series, whose single-unit power generation capacity can reach hundreds to over a thousand megawatts (MW) 3. The design and operating conditions of the high-pressure main steam piping for these massive units have pushed the limits of materials science.

2.1 高壓蒸汽與飼水系統之流體條件 / 2.1 Fluid Conditions of High-Pressure Steam and Feedwater Systems

根據主流設備製造商與現場量測數據顯示，在 200 MW 至 700 MW 級別的 CCPP 中，高壓主蒸汽的入口壓力可高達 177 bar（約 2,567 psi），在超臨界（Supercritical）蒸汽電廠甚至可達 260 bar 至 330 bar，而蒸汽溫度則維持在 565°C 至 610°C 之間2。在如此高溫高壓下，流體呈現高度可壓縮與極低黏滯度的特性，流速常高達數十公尺每秒，管線內部的雷諾數（Reynolds Number, Re）輕易突破 106，屬於充分發展的高度紊流（Fully turbulent flow）狀態15。 According to mainstream equipment manufacturers and field measurement data, in 200 MW to 700 MW-class CCPPs, the inlet pressure of high-pressure main steam can reach up to 177 bar (approx. 2,567 psi), and even 260 bar to 330 bar in supercritical steam power plants, while the steam temperature is maintained between 565°C and 610°C 2. Under such high temperatures and pressures, the fluid exhibits highly compressible and extremely low-viscosity characteristics. The flow velocity often reaches tens of meters per second, and the internal Reynolds Number (Re) easily exceeds 106, classifying it as a fully developed turbulent flow state15.

在飼水系統方面，高壓飼水泵浦將來自凝結水系統的水加壓後送入 HRSG，其操作條件同樣嚴苛。根據超音波流量計的量測規格，HP 飼水系統的最大體積流率可達 600 m3/h，設計壓力高達 230 bar（約 3,336 psi），而最高溫度則達 375°C 2。如此巨大的質量流率與動量，使得流體在遇到管線幾何突變時，會產生極大的動壓變化與剪切力。 Regarding the feedwater system, the high-pressure feedwater pump pressurizes the water from the condensate system and feeds it into the HRSG under equally stringent operating conditions. According to ultrasonic flowmeter measurement specifications, the maximum volumetric flow rate of the HP feedwater system can reach 600 m3/h, with a design pressure up to 230 bar (approx. 3,336 psi) and a maximum temperature of 375°C 2. Such immense mass flow rates and momentum result in drastic dynamic pressure changes and shear forces when the fluid encounters sudden geometric variations in the piping.

為提供更直觀的設備操作邊界參考，下表統整了先進蒸汽渦輪機在 CCPP 與傳統汽力電廠（SPP）中的核心操作參數：To provide a more intuitive reference for equipment operating boundaries, the table below summarizes the core operating parameters of advanced steam turbines in CCPPs and conventional steam power plants (SPP):

設備型號與應用領域 Equipment Model & Application 輸出功率 Power Output (MW) 頻率 Frequency (Hz) 最大入口蒸汽壓力 Max Inlet Steam Pressure 最高入口蒸汽溫度 Max Inlet Steam Temp 最高再熱蒸汽溫度 Max Reheat Steam Temp
SST-3000 90 – 275 50 / 60 177 bar / 2,567 psi 600 °C / 1,112 °F 610 °C / 1,130 °F
SST-4000 100 – 500 50 / 60 105 bar / 1,523 psi 600 °C / 1,112 °F N/A
SST-5000 (CCPP) 120 – 700 50 / 60 177 bar / 2,567 psi 600 °C / 1,112 °F 610 °C / 1,130 °F
SST-5000 (SPP) 200 – 500 50 / 60 260 bar / 3,771 psi 600 °C / 1,112 °F 610 °C / 1,130 °F
SST-6000 300 – 1,200 50 / 60 330 bar / 4,786 psi 610 °C / 1,130 °F 630 °C / 1,166 °F

2.2 熱力學不可逆性與可用能（Exergy）損失 / 2.2 Thermodynamic Irreversibility and Exergy Loss

流體在經過內突銲道或冷作彎管時，流場的劇烈擾動與分離不僅帶來材料磨損的問題，從熱力學第二定律的角度來看，這些幾何特徵也是系統可用能（Exergy）損失與熵產（Entropy production）的重要來源。高壓管線中的摩擦壓降、紊流耗散與流場分離造成的總壓損失，會直接導致流體機械可用能的不可逆消耗。研究文獻中的可用能平衡（Exergy balance）分析指出，蒸汽渦輪機與高壓蒸汽管線中的高質量流率會顯著放大這些不可逆性，導致電廠的熱力成本流率（Cost flow rate）上升5。雖然單一銲道或彎管的壓降微乎其微，但在綿延數公里的電廠管網中，這些局部阻力的累積將對系統總效率產生不可忽視的負面效應，迫使飼水泵浦與氣渦輪機需消耗額外功以克服系統背壓。 When fluid passes through weld root protrusions or cold bends, the intense flow disturbance and separation not only cause material wear but also act as significant sources of exergy loss and entropy production from the perspective of the Second Law of Thermodynamics. Total pressure losses caused by frictional pressure drops, turbulent dissipation, and flow separation in high-pressure pipelines directly lead to the irreversible consumption of the fluid’s mechanical exergy. Exergy balance analyses in the research literature indicate that the high mass flow rates in steam turbines and high-pressure steam piping significantly amplify these irreversibilities, leading to an increase in the plant’s cost flow rate5. Although the pressure drop of a single weld bead or bend is negligible, the accumulation of these local resistances across kilometers of plant piping networks exerts an undeniable negative impact on the overall system efficiency, forcing feedwater pumps and gas turbines to consume additional work to overcome system backpressure.

三、 管線材料特性與合金元素之抗腐蝕機制 / 3. Piping Material Properties and Anti-Corrosion Mechanisms of Alloy Elements

面對高溫、高壓且充滿擾動的流場，CCPP 高壓管線的材料選擇極為講究。業界最廣泛使用的是符合 ASTM A335 規範的無縫鐵素體（Ferritic）合金鋼管，俗稱鉻鉬鋼（Chrome-Moly pipes）。其中，ASTM A335 P22（含有 2.25% 鉻與 1% 鉬）與 ASTM A335 P91（含有 9% 鉻與 1% 鉬，並微調添加釩與鈮）是高壓系統的兩大主力材料16。 Facing high temperatures, high pressures, and highly disturbed flow fields, the material selection for CCPP high-pressure piping is extremely meticulous. The industry most widely utilizes seamless ferritic alloy steel pipes complying with ASTM A335 specifications, commonly known as Chrome-Moly pipes. Among them, ASTM A335 P22 (containing 2.25% chromium and 1% molybdenum) and ASTM A335 P91 (containing 9% chromium and 1% molybdenum, with fine-tuned additions of vanadium and niobium) are the two mainstays for high-pressure systems16.

3.1 鉻含量（Chromium Content）對 FAC 的抑制作用 / 3.1 Inhibitory Effect of Chromium Content on FAC

材料中的鉻含量是決定其抵抗流動加速腐蝕（FAC）能力的絕對關鍵。FAC 是一個由化學溶解與物理質傳共同控制的過程，當純碳鋼暴露於高溫流動的水中時，其表面會生成一層多孔且附著力不佳的磁鐵礦（Fe3O4）氧化層。這層氧化層容易被高速流體帶走，造成底層金屬持續流失。然而，當管材中添加了適當比例的鉻元素後，其腐蝕行為將發生本質上的改變。The chromium content in the material is the absolute key determining its resistance to Flow-Accelerated Corrosion (FAC). FAC is a process jointly controlled by chemical dissolution and physical mass transfer. When plain carbon steel is exposed to high-temperature flowing water, a porous and poorly adherent magnetite (Fe3O4) oxide layer forms on its surface. This oxide layer is easily swept away by high-velocity fluids, causing continuous loss of the underlying metal. However, when an appropriate proportion of chromium is added to the piping material, its corrosion behavior undergoes a fundamental change.

研究與電廠運行數據表明，微量的鉻（即使僅 0.1%）即可使 FAC 速率顯著下降20。當材料如 P22 鋼管含有 2.25% 的鉻時，在腐蝕進行的初期，鉻離子會向氧化膜的最外層富集，並與鐵、氧形成極度緻密、難溶且附著力極強的鐵鉻尖晶石（Iron-Chromium Spinel）結構薄膜11。這種富鉻的氧化膜如同為管壁穿上了一層奈米級的防護裝甲，大幅阻斷了金屬基體內鐵離子向流體邊界層擴散的路徑，從而在大範圍內近乎完全抑制了宏觀的 FAC 發生。然而，必須強調的是，即便是 P22 或 P91 這種高合金鋼管，在遭遇內突銲道或極端冷作彎管所引發的局部異常剪應力與微電偶效應時，這層保護膜仍有被局部突破的風險。 Research and power plant operational data show that even trace amounts of chromium (as little as 0.1%) can cause a significant drop in the FAC rate20. When a material like P22 steel pipe contains 2.25% chromium, during the early stages of corrosion, chromium ions will enrich the outermost layer of the oxide film, reacting with iron and oxygen to form an extremely dense11, highly insoluble, and strongly adherent Iron-Chromium Spinel structural film2. This chromium-rich oxide film acts like nano-scale armor for the pipe wall, vastly blocking the diffusion path of iron ions from the metal matrix to the fluid boundary layer, thereby almost completely suppressing macroscopic FAC over large areas. However, it must be emphasized that even with high-alloy steel pipes like P22 or P91, this protective film still risks being locally breached when encountering abnormal local shear stresses and micro-galvanic effects induced by weld root protrusions or extreme cold bends.

3.2 磁鐵礦層的半導體特性與微電偶效應 / 3.2 Semiconductor Properties of Magnetite Layers and Micro-Galvanic Effects

在管壁表面生成的磁鐵礦層（Fe3O4）並非單純的絕緣阻擋層，其本質上是一種具有一定導電能力的半導體礦物。從電化學熱力學的角度來看，磁鐵礦的自然腐蝕電位相較於裸露的鐵素體碳鋼具有更高的貴電位（Nobler potential）22。 The magnetite layer (Fe3O4) formed on the pipe wall surface is not merely an insulating barrier layer; essentially, it is a semiconductor mineral possessing a certain degree of electrical conductivity. From the perspective of electrochemical thermodynamics, the natural corrosion potential of magnetite has a higher nobler potential compared to bare ferritic carbon steel22.

當高壓流體行經管線內部時，若流場平穩，這層磁鐵礦能穩定存在；但在流場發生劇烈擾動的區域（如內突銲道下游或彎管外弧側），高強度的壁面剪應力與極端質傳會將局部的磁鐵礦保護層無情剝離，暴露出新鮮的裸鋼基體9。此時，大面積未被剝離的磁鐵礦層與微小面積的裸露鋼基體，便構成了一個經典的「大陰極（磁鐵礦）－小陽極（裸鋼）」的微電偶腐蝕（Micro-galvanic corrosion）電池系統22。這個微電偶效應會將原本廣泛分佈的腐蝕電流集中於極小的裸鋼區域，導致陽極發生毀滅性的加速溶解。這種機械力與電化學耦合的協同破壞，是解釋為何管線減薄往往在極短距離內形成深坑或扇貝狀（Scallop pattern）缺陷的核心機制。 When high-pressure fluid flows through the pipeline, this magnetite layer remains stable if the flow field is steady; however, in regions of severe flow disturbance (such as downstream of a weld root protrusion or at the extrados of a bend), high-intensity wall shear stress and extreme mass transfer mercilessly strip away the localized magnetite protective layer, exposing the fresh bare steel matrix9. At this point, the large area of unstripped magnetite layer and the minuscule area of bare steel matrix constitute a classic “large cathode (magnetite) – small anode (bare steel)” micro-galvanic corrosion cell system22. This micro-galvanic effect concentrates the initially widely distributed corrosion current onto the tiny bare steel area, leading to devastatingly accelerated dissolution of the anode. This synergistic destruction coupling mechanical forces and electrochemistry is the core mechanism explaining why pipe wall thinning often forms deep pits or scallop patterns over very short distances.

四、 預測 FAC 的理論模型與水化學控制 / 4. Theoretical Models for FAC Prediction and Water Chemistry Control

為了在工程設計階段與日常營運中預測並控制 FAC 帶來的威脅，學術界與產業界發展出多種預測模型。這些模型整合了流體動力學、材料科學與水化學（Water Chemistry）參數，為電廠的運作邊界提供了量化依據。To predict and control the threats posed by FAC during the engineering design phase and daily operations, academia and industry have developed various predictive models. These models integrate parameters of fluid dynamics, materials science, and water chemistry, providing a quantitative basis for the operating boundaries of power plants.

4.1 Kastner 經驗模型與水化學參數敏感度 / 4.1 Kastner Empirical Model and Water Chemistry Parameter Sensitivity

Kastner 模型是業界公認且廣泛應用的 FAC 預測體系之一，該模型認定 FAC 的速率是由流速、溫度、pH 值、溶氧量（Dissolved Oxygen, DO）以及材料合金含量等五大變數交織控制的函數20。 The Kastner model is one of the industry’s universally recognized and widely applied FAC prediction frameworks. This model establishes that the FAC rate is a function interwoven and controlled by five major variables: flow velocity, temperature, pH value, dissolved oxygen (DO), and material alloy content20.

在水化學控制策略中，溫度與 pH 值展現出強烈的協同效應。在單相液體流動中，FAC 的破壞速率並非隨溫度單調上升，而是在 140°C 至 160°C 的區間內達到峰值；而在雙相流（如濕蒸汽）中，峰值溫度則落於約 180°C 9。這個鐘形曲線（Bell-shape curve）的成因在於：低溫下雖然水的黏度較大、溶氧度較高，但離子擴散速率緩慢；而當溫度超過 200°C 甚至 260°C 以上時，儘管離子活躍度極高，但金屬表面能極為快速地自發生成緻密穩定的磁鐵礦層，從而扼殺了進一步的溶解反應。 In water chemistry control strategies, temperature and pH demonstrate a strong synergistic effect. In single-phase liquid flow, the FAC destruction rate does not rise monotonically with temperature but peaks within the range of 140°C to 160°C; whereas in two-phase flow (e.g., wet steam), the peak temperature lands at around 180°C 9. The cause of this bell-shaped curve is that at lower temperatures, although water viscosity is higher and dissolved oxygen is greater, the ion diffusion rate is slow. Conversely, when the temperature exceeds 200°C or even 260°C, despite extremely high ion activity, the metal surface can spontaneously and very rapidly generate a dense and stable magnetite layer, thereby stifling further dissolution reactions.

控制水質的 pH 值是電廠抑制 FAC 最直接且有效的手段。人工神經網路（ANN）與 Kastner 模型的敏感度分析證實，在中性水質（pH 7）下，FAC 速率極高；當透過添加氨水等化學劑將系統操作在鹼性環境（pH 值維持在 9.2 至 9.8 之間）時，磁鐵礦的溶解度會急遽下降，FAC 速率可降低超過一個數量級（即減少 90% 以上的腐蝕量）25。此外，微量的溶氧量（DO）控制也至關重要。研究指出，在 180°C 與 pH 9.8 的鹼性條件下，即便是在 20 m/s 的極高流速下，僅需維持 1 至 5 ppb 的微量溶氧，即可促使氧化膜維持穩定，進而大幅壓抑 FAC26。 Controlling the water’s pH value is the most direct and effective means for power plants to suppress FAC. Sensitivity analyses using Artificial Neural Networks (ANN) and the Kastner model confirm that the FAC rate is extremely high in neutral water (pH 7). When chemical agents such as ammonia are added to operate the system in an alkaline environment (maintaining the pH between 9.2 and 9.8), the solubility of magnetite drops sharply, and the FAC rate can be reduced by more than an order of magnitude (i.e., a reduction in corrosion amount by over 90%)25. In addition, controlling trace amounts of dissolved oxygen (DO) is also crucial. Studies indicate that under alkaline conditions of 180°C and pH 9.8, even at an extremely high flow velocity of 20 m/s, maintaining just 1 to 5 ppb of trace dissolved oxygen is sufficient to keep the oxide film stable, thereby drastically suppressing FAC26.

4.2 Sanchez-Caldera 理論質傳模型 / 4.2 Sanchez-Caldera Theoretical Mass Transfer Model

有別於 Kastner 的純經驗擬合，Sanchez-Caldera 模型從非平衡熱力學與電化學溶解的物理機制出發，將壁面減薄率與邊界層的質量傳輸係數建立了嚴謹的數學連結12。 Unlike the purely empirical fitting of the Kastner model, the Sanchez-Caldera model originates from the physical mechanisms of non-equilibrium thermodynamics and electrochemical dissolution, establishing a rigorous mathematical link between the wall thinning rate and the mass transfer coefficient of the boundary layer12.

該模型將管壁減薄率（tc）視為化學腐蝕（ Wc）與機械沖蝕（We）的疊加。在 FAC 佔主導的穩態條件下，其材料減薄速率的理論推導公式為：This model treats the pipe wall thinning rate (tc) as a superimposition of chemical corrosion (Wc) and mechanical erosion (We). Under steady-state conditions where FAC is dominant, the theoretically derived formula for the material thinning rate is:

JFAC=(1-θ)⋅Kd⋅(Cs-Cb)

其中，JFAC 代表壁面的溶解通量；θ 為氧化膜的孔隙率（在150°C 以下的高壓水中常假設為 0.03）；Kd 為對流質傳係數（Mass Transfer Coefficient），代表流場將離子帶離壁面的能力；Cs 為氧化物與流體介面處鐵離子的平衡濃度（即局部溶解度）；Cb 則為遠離壁面的主流區鐵離子濃度12。 Where JFAC represents the dissolution flux at the wall; θ is the porosity of the oxide film (commonly assumed to be 0.03 in high-pressure water below 150°C); Kd is the convective mass transfer coefficient, representing the flow field’s ability to transport ions away from the wall; Cs is the equilibrium concentration of iron ions (i.e., local solubility) at the oxide-fluid interface; and Cb is the iron ion concentration in the mainstream region away from the wall12.

這個公式深刻地揭示了流體力學與 FAC 的交集點：當流體流經內突銲道或彎管時，流場產生的極端紊流與剪應力會直接導致局部的質傳係數（Kd）飆升，這使得該區域的 (Cs-Cb) 濃度梯度驅動力被無限放大，鐵離子被高速抽離，迫使基體必須不斷進行新的氧化反應以試圖達到平衡，最終釀成管壁的快速減薄。This formula profoundly reveals the intersection between fluid mechanics and FAC: when fluid flows through a weld root protrusion or a bend, the extreme turbulence and shear stress generated by the flow field directly cause the local mass transfer coefficient (Kd) to spike. This infinitely magnifies the driving force of the (Cs-Cb) concentration gradient in that region, extracting iron ions at high speeds and forcing the matrix to continuously undergo new oxidation reactions in an attempt to reach equilibrium, ultimately resulting in rapid thinning of the pipe wall.

五、 流體動力學與紊流模型分析 / 5. Fluid Dynamics and Turbulence Model Analysis

為了精確捕捉內突銲道與冷作彎管如何影響上述的質傳係數與剪應力，計算流體力學（CFD）成為不可或缺的分析工具。流體在高壓管線中的運動遵循質量與動量守恆的雷諾平均納維-斯托克斯（Reynolds-averaged Navier-Stokes, RANS）方程式，而如何封閉這些方程式以模擬真實的紊流，是數值模擬的核心挑戰15。 To accurately capture how weld root protrusions and cold bends affect the aforementioned mass transfer coefficient and shear stress, Computational Fluid Dynamics (CFD) has become an indispensable analytical tool. Fluid motion in high-pressure pipelines complies with the mass and momentum conservation principles of the Reynolds-averaged Navier-Stokes (RANS) equations, and how to close these equations to simulate true turbulence remains a core challenge in numerical simulation15.

5.1 k-ω 剪切應力傳輸 (SST) 紊流模型 / 5.1 The k-ω Shear Stress Transport (SST) Turbulence Model

在歷史上，工程界常使用標準的k-ε 兩方程式模型來模擬自由流場，但在處理邊界層分離（如內突銲道引發的逆壓梯度）以及強烈曲率流動（如彎管的二次流）時，k-ε 模型因為無法準確解析黏滯底層（Viscous sublayer）內的行為，常會嚴重過度預測壁面剪應力，並給出錯誤的流動分離點31。另一方面，Wilcox 提出的標準k-ω 模型雖在近壁區表現優異，但對自由流場的邊界條件卻極為敏感，容易導致數值發散33。 Historically, the engineering community frequently used the standard k-ε two-equation model to simulate free-stream flows. However, when handling boundary layer separation (such as the adverse pressure gradient induced by a weld root protrusion) and strong curvature flows (such as secondary flows in bends), the k-ε model—unable to accurately resolve behavior within the viscous sublayer—often severely over-predicts wall shear stress and yields incorrect flow separation points31. On the other hand, while the standard k-ω model proposed by Wilcox performs excellently in the near-wall region, it is extremely sensitive to free-stream boundary conditions, easily leading to numerical divergence33.

為了解決這個兩難，Menter 提出了結合兩者優勢的 k-ω SST（Shear Stress Transport）模型，現已成為工業 CFD 分析的黃金標準31。SST 模型的精髓在於引入了一個混合函數（Blending function, F1），該函數在極接近固體壁面的區域值為 1，使方程式完全以 k-ω 的形式運作，無須添加人為的阻尼函數即可精準解析邊界層；而當逐漸遠離壁面進入主流區時，F1 平滑地過渡為 0，方程式則自動切換為抗干擾性佳的 k-ε 形式31。 To resolve this dilemma, Menter proposed the k-ω SST (Shear Stress Transport) model, which combines the strengths of both and has now become the gold standard in industrial CFD analysis31. The essence of the SST model lies in the introduction of a blending function (F1), which equals 1 in the region extremely close to solid walls, allowing the equations to operate entirely in the k-ω format to accurately resolve the boundary layer without adding artificial damping functions. As it moves progressively away from the wall into the mainstream region, F1 smoothly transitions to 0, automatically switching the equations into the more interference-resistant k-ε format31.

其紊流動能（k）與比耗散率（ω）的守恆方程式可表達為：Its conservation equations for turbulent kinetic energy (k) and specific dissipation rate (ω) can be expressed as:

∂(ρk)/∂t+∇⋅(ρVk)=P ̃k–β* ρkω+∇⋅((μ+σkμt )∇k)

∂(ρω)/∂t+∇⋅(ρVω)=α ω/k Pk–βρω2+∇⋅((μ+σωμt )∇ω)+2(1-F1 )ρσω21/ω ∇k⋅∇ω

透過引入渦黏性限制器（Eddy-viscosity limiter），SST 模型確保了在強烈逆壓梯度下（如流體越過銲道時）剪切應力的傳輸不會被高估，從而能極其準確地預測流場的再附著距離（Reattachment length）與分離泡的尺寸31。 By incorporating an eddy-viscosity limiter, the SST model ensures that shear stress transport is not overestimated under strong adverse pressure gradients (such as when fluid passes over a weld bead), thereby enabling highly accurate predictions of the reattachment length and separation bubble size31.

5.2 壁面剪應力 (WSS) 與紊流動能 (TKE) 的推導與意義 / 5.2 Derivation and Significance of Wall Shear Stress (WSS) and Turbulent Kinetic Energy (TKE)

在 CFD 分析中，評估管壁劣化風險的兩個最直接物理量為壁面剪應力（WSS, τw）與紊流動能（TKE, k）。In CFD analysis, the two most direct physical quantities for evaluating pipe wall degradation risks are Wall Shear Stress (WSS, τw) and Turbulent Kinetic Energy (TKE, k).

壁面剪應力是由流體黏滯性與近壁面極大的速度梯度所產生，其定義為： Wall shear stress is generated by fluid viscosity and the immense velocity gradient near the wall, defined as:

τw=μ(∂u/∂y)y=0

其中 μ 為流體的動態黏滯度，∂u/∂y 為垂直於壁面的速度梯度38。在計算時，為確保能捕捉到黏滯底層內的劇烈變化，近壁面的第一層網格高度必須極其細微，通常要求無因次壁面距離y+ 值約等於或小於 1 34。WSS 的物理意義不僅在於它對表面氧化膜施加了直接的機械撕裂力，根據 Chilton-Colburn 類比公式，WSS 更與質傳係數成正比：Where μ is the dynamic viscosity of the fluid, and ∂u/∂y is the velocity gradient perpendicular to the wall38. During computation, to ensure the capture of drastic changes within the viscous sublayer, the height of the first grid layer near the wall must be extremely fine, typically requiring a dimensionless wall distance y+ value of approximately equal to or less than 1 34. The physical significance of WSS lies not only in its direct mechanical tearing force exerted on the surface oxide film, but according to the Chilton-Colburn analogy, WSS is also directly proportional to the mass transfer coefficient:

Kd=τw/ρUb Sc-2/3

這意味著，流場中 WSS 出現極大值（Peaks）的區域，正是質傳最為劇烈、保護膜溶解最快、FAC 發生機率最高的死亡熱點24。 This implies that regions in the flow field exhibiting maximum WSS peaks are precisely the deadly hot spots where mass transfer is most intense, protective film dissolution is fastest, and FAC occurrence probability is highest24.

同時，紊流動能（TKE）代表了流體脈動速度所包含的能量：Simultaneously, Turbulent Kinetic Energy (TKE) represents the energy contained in fluid velocity fluctuations:

k=1/2 (¯(u’2 )+¯(v’2 )+¯(w’2 ))

高 TKE 意味著流體微團在邊界層內進行著極為暴力的動量與質量交換。在分離流場中，高 TKE 的區域如同無數微觀的攪拌器，將管壁附近溶出的鐵離子瞬間拋射至主流區，使得局部濃度永遠無法達到飽和，強迫腐蝕反應無限循環15。 High TKE indicates that fluid parcels within the boundary layer are engaged in violently aggressive momentum and mass exchanges. In separated flow fields, high TKE regions act like countless microscopic agitators, instantly ejecting dissolved iron ions near the pipe wall into the mainstream region. This prevents the local concentration from ever reaching saturation, forcing the corrosion reaction into an endless cycle15.

六、 內突銲道與冷作彎管之劣化行為深度對比 / 6. In-Depth Comparison of Degradation Behaviors between Weld Root Protrusions and Cold Bends

基於上述的流體力學模型與電化學理論框架，我們得以對管線中最脆弱的兩個特徵——「內突銲道」與「冷作彎管」進行細緻的對比剖析。兩者雖皆會引發 FAC 與沖蝕腐蝕，但其誘發機制在時間與空間尺度上存在本質的差異。Based on the aforementioned fluid dynamics models and electrochemical theoretical framework, we can conduct a meticulous comparative analysis of the two most vulnerable features in pipelines: “weld root protrusions” and “cold bends.” While both induce FAC and erosion-corrosion, their triggering mechanisms possess fundamental differences across temporal and spatial scales.

6.1 內突銲道：點狀爆發的流動分離與極端衝擊 / 6.1 Weld Root Protrusion: Punctiform Eruptions of Flow Separation and Extreme Impact

在管線安裝進行全滲透對接銲時，若未能徹底磨平內部，銲根（Weld root）會向管內突出形成所謂的內突銲道8。雖然這個突出物的高度可能僅為管徑的 1% 至 5%，但其對邊界層的破壞堪稱災難級。 During pipeline installation for full-penetration butt welding, if the interior is not thoroughly ground flat, the weld root will protrude inward to form what is known as a weld root protrusion8. Although the height of this protrusion may be merely 1% to 5% of the pipe diameter, its destruction to the boundary layer is catastrophic.

  1. 流動分離與自由剪切層（Free Shear Layer）：當高壓流體以極高速度行經銲道頂部時，流體因慣性作用無法貼合銲道後方的管壁，產生了陡峭的流動分離8。分離點後方形成了一個強烈的自由剪切層，流體在極短的空間內發生劇烈減速並產生強大的逆壓梯度，導致該區域的紊流動能（TKE）產生極端的尖峰值38。Flow Separation and Free Shear Layer: When high-pressure fluid travels over the top of the weld bead at extreme velocities, the fluid’s inertia prevents it from adhering to the pipe wall behind the bead, creating steep flow separation8. A strong free shear layer forms behind the separation point, where the fluid undergoes violent deceleration in a very short space and generates a powerful adverse pressure gradient, causing extreme peak values in the turbulent kinetic energy (TKE) of that region38.
  2. 下游再循環尾流區與再附著點（Reattachment Point）：在銲道正後方，分離的邊界層下方形成一個充滿渦漩的再循環區，流體在此甚至出現逆向回流。最致命的破壞發生在距離銲道下游約 3 至 5 倍銲道高度的位置，此時分離的剪切層動能耗盡，重新向管壁撞擊並「附著」於管壁上，這被稱為再附著點43。Downstream Recirculating Wake Zone and Reattachment Point: Directly behind the weld bead, a vortex-filled recirculating zone forms beneath the separated boundary layer, where the fluid even exhibits reverse flow. The most fatal damage occurs at a distance approximately 3 to 5 times the weld bead height downstream; at this location, the separated shear layer’s kinetic energy depletes, impacting and “reattaching” itself back onto the pipe wall—known as the reattachment point43.
  3. 衝擊點的微電偶腐蝕與扇貝狀穿孔：在再附著點，流體幾乎是以垂直或大角度直接衝擊管壁，造成壁面剪應力（WSS）與質傳係數的局部極大化23。強大的撕裂力與質傳將該點的磁鐵礦保護層瞬間瓦解，露出底層鋼材。此時，微電偶效應啟動，周圍未剝落的高貴電位磁鐵礦將這微小的裸鋼區域作為陽極猛烈攻擊，使其快速溶解9。這種機制精確解釋了為何電廠的銲道失效案例中，穿孔往往不是發生在銲道正上方，而是發生在銲道下游幾公分處的局部深坑或扇貝狀（Scallops）蝕孔9。Micro-Galvanic Corrosion and Scalloped Perforation at the Impact Point: At the reattachment point, the fluid impacts the pipe wall almost vertically or at a sharp angle, causing localized maximization of wall shear stress (WSS) and mass transfer coefficients23. The immense tearing force and mass transfer instantly disintegrate the magnetite protective layer at this point, exposing the underlying steel. Concurrently, the micro-galvanic effect activates, where the surrounding intact, nobler-potential magnetite fiercely attacks this minuscule bare steel area acting as the anode, causing its rapid dissolution9. This mechanism precisely explains why in power plant weld failure cases, perforations often do not occur directly atop the weld bead but manifest as localized deep pits or scalloped holes a few centimeters downstream9.

 

6.2 冷作彎管：廣域離心洗刷與材料內能崩潰 / 6.2 Cold Bends: Wide-Area Centrifugal Washing and Material Internal Energy Collapse

相對於銲道的局部擾動，冷作彎管（特別是半徑小於 5D 的短半徑彎管）引發的是跨越數個管徑的大尺度全域流場重整，並伴隨著嚴重的材料機械降解。In contrast to the localized disturbance of weld beads, cold bends (especially short-radius bends with a radius smaller than 5D) induce a large-scale, global flow field reorganization spanning several pipe diameters, accompanied by severe material mechanical degradation.

  1. 離心力與迪恩二次渦流（Dean Vortices）：流體進入彎管後受到離心力的強烈牽引，最高流速的核心流體（Core flow）被迫向彎管的外弧側（Extrados）偏移24。這不僅導致外弧側的靜壓與 WSS 遠高於內弧側，更因壓差驅動形成了一對對稱的二次旋渦，即迪恩渦流46。Centrifugal Forces and Dean Vortices: Upon entering the bend, the fluid is strongly drawn by centrifugal forces, forcing the highest-velocity core flow to shift toward the bend’s extrados24. This not only results in the static pressure and WSS at the extrados being far higher than those at the intrados, but the pressure differential also drives the formation of a pair of symmetrical secondary vortices, known as Dean vortices46.
  2. 三維螺旋式沖刷網路：與直管內的單向流動不同，迪恩渦流使得流體在沿軸向推進的同時，還帶有強烈的切線方向旋轉。這種螺旋式的二次流會持續洗刷彎管的外弧側與側壁（特別是在 45° 與 90° 彎角處），導致整個外弧側形成大面積的 WSS 高值區，並將擾動一路延續至彎管下游的直管過渡段26。3D Spiral Scouring Network: Unlike the unidirectional flow in straight pipes, Dean vortices impart a strong tangential rotation to the fluid while it advances axially. This spiral secondary flow continuously washes the extrados and sidewalls of the bend (especially around 45° and 90° angles), creating a large area of high WSS across the entire extrados and extending the disturbance all the way into the downstream straight pipe transition segment26.
  3. 應變硬化（Strain Hardening）與腐蝕電位（Ecorr）崩潰：除了流場的肆虐，冷作彎管的致命弱點更在於其成型工法。常溫下的塑性彎曲（Cold working）使得外弧側承受了極大的拉伸應變。這導致金屬內部的差排密度（Dislocation density）呈指數級增長，發生強烈的應變硬化50。在材料熱力學上，巨量差排與殘留應力的積累意味著內部自由能（Internal energy）大幅躍升，金屬處於極度不穩定的活性狀態，其腐蝕電位（Corrosion Potential, Ecorr）會發生顯著負移（Drop/Decrease）52。Strain Hardening and Corrosion Potential (Ecorr) Collapse: Beyond the ravages of the flow field, the fatal weakness of cold bends lies in their forming methodology. Plastic bending at room temperature (cold working) subjects the extrados to massive tensile strain. This triggers an exponential increase in the metal’s internal dislocation density, resulting in intense strain hardening50. In material thermodynamics, the accumulation of massive dislocations and residual stresses signifies a massive leap in internal free energy. The metal enters a highly unstable, active state, causing its corrosion potential (Ecorr) to undergo a significant negative shift (drop/decrease) 52.
  4. 機-電化學的終極協同：外部迪恩渦流的高效質傳洗刷，遭遇內部已經因為應變硬化而極度活躍、極易釋放電子的金屬基體，兩者一拍即合。這使得冷作彎管外弧側的 FAC 破壞呈現大面積、溝槽狀的整體減薄，其破壞量級遠甚於直管，是電廠中最需重點監控的區域。Ultimate Mechano-Electrochemical Synergy: The highly efficient mass-transfer washing from the external Dean vortices encounters a metal matrix that is already extremely active and eager to release electrons due to strain hardening—the two converge perfectly. This causes the FAC destruction on the extrados of cold bends to manifest as wide-area, trench-like overall wall thinning, far exceeding the magnitude of damage in straight pipes, making it a critical area requiring rigorous monitoring in power plants.
分析特徵維度 Analytical Feature Dimension 內突銲道 Weld Root Protrusion 冷作彎管 Cold Bend
流場擾動尺度 Flow Disturbance Scale 局部微觀至中等尺度，侷限於下游短距離。 Local micro to meso-scale, confined to short downstream distances. 宏觀大尺度，影響涵蓋彎曲段並延伸至下游直管。 Macro large-scale, impacting the bend and extending into downstream straight pipes.
核心流體動力學 Core Fluid Dynamics 流動幾何分離、逆壓梯度、自由剪切層。 Flow geometric separation, adverse pressure gradients, free shear layers. 離心力驅動、速度核外移、迪恩二次渦流（Dean Vortices）。 Centrifugal force-driven, outward shift of velocity core, Dean secondary vortices.
壁面剪應力最大處 Max WSS Location 銲道下游再附著點（Reattachment point）極端尖峰。 Extreme peaks at the downstream reattachment point. 外弧側（Extrados）及受二次流影響之側壁，呈廣泛高值。 Widespread high values on the extrados and sidewalls affected by secondary flow.
電化學劣化協同機制 Electrochemical Synergy 高質傳剝離氧化膜，引發「大陰極-小陽極」微電偶腐蝕。 High mass transfer strips oxide film, triggering “large cathode-small anode” micro-galvanic corrosion. 應變硬化致差排激增，內部能量升高，材料腐蝕電位驟降。 Strain hardening surges dislocations, raising internal energy and plummeting material corrosion potential.
損傷外觀形貌 Damage Morphology 局部深坑、密集連續的扇貝狀（Scallop）凹槽。 Localized deep pits, dense continuous scallop grooves. 大面積的厚度漸進流失、拉長的溝槽或大片魚鱗狀剝落。 Wide-area progressive thickness loss, elongated trenches, or large scale-like spalling.

七、 規範準則與防護策略：ASME B31.1 之工程實踐 / 7. Code Standards and Protection Strategies: Engineering Practice of ASME B31.1

針對上述深刻的流體與材料耦合破壞機制，國際公認的權威規範《ASME B31.1 動力管線規範》（Power Piping Code）提供了嚴謹的設計與製造框架，旨在透過物理裕度與熱處理手腕，將管線失效的風險降至最低54。 In response to the profound fluid-material coupled destruction mechanisms described above, the internationally recognized authoritative code, “ASME B31.1 Power Piping Code,” provides a rigorous design and manufacturing framework aimed at minimizing pipeline failure risks through physical margins and heat treatment techniques54.

7.1 管線厚度設計與彎管減薄餘裕（Bend Thinning Allowance） / 7.1 Pipe Wall Thickness Design and Bend Thinning Allowance

為了抵抗高壓與潛在的管壁減薄，B31.1 規範第 104.1.2 節明確定義了承受內壓直管的最小厚度方程式：To resist high pressure and potential wall thinning, Section 104.1.2 of the B31.1 Code explicitly defines the minimum thickness equations for straight pipes under internal pressure:

t=(PDo)/2(SEW+Py)

tm=t+A

在此公式中，P 為內部設計壓力； Do為管線外徑； SE為材料在設計溫度下的最大許用應力（包含接頭效率）；W 為銲縫強度折減係數（Weld strength reduction factor）；y 為溫度修正係數，用於補償溫度升高導致的應力重分配；A 則為額外的厚度補償裕度（如腐蝕裕度）。計算出最小厚度後，還必須考量鋼廠在製造管線時允許的「負公差」（Mill under-tolerance，通常為 12.5%），方能推導出實際的採購厚度55。 In this formula, P is the internal design pressure; Do is the outside diameter of the pipe; SE is the maximum allowable stress of the material at design temperature (including joint efficiency); W is the weld strength reduction factor; y is the temperature coefficient used to compensate for stress redistribution due to rising temperatures; and A is the additional thickness allowance (e.g., corrosion allowance). After calculating the minimum thickness, the “mill under-tolerance” (typically 12.5%) permitted for steel mills during pipe manufacturing must also be factored in to derive the actual ordering thickness55.

然而，針對冷作彎管，純粹的直管公式已不足以應對。由於彎管成型過程必然導致外弧側變薄，B31.1 第 102.4.5 段落強制規定，成型後彎管的任何一處最小壁厚，皆不得小於直管的計算要求58。這意味著工程師在設計彎管時，必須基於彎曲半徑與管徑比（R/D），在原始直管厚度上預加一層「彎管減薄餘裕」（Bend Thinning Allowance，見規範 Table 102.4.5）。彎曲半徑越短，離心力與塑性變形越大，所需的預留厚度補償比例就越高57。這個厚度餘裕不僅是用來彌補物理成型的消耗，更是為日後迪恩渦流引發的二次流 FAC 預留了保命的緩衝空間。 However, for cold bends, pure straight pipe formulas are insufficient. Because the bend forming process inevitably thins the extrados, Paragraph 102.4.5 of B31.1 mandates that the minimum wall thickness at any point on a completed bend shall not be less than the calculated requirement for straight pipes58. This means that when designing bends, engineers must add a “Bend Thinning Allowance” (see Code Table 102.4.5) to the original straight pipe thickness based on the bend radius to pipe diameter ratio (R/D). The shorter the bend radius, the greater the centrifugal force and plastic deformation, and therefore the higher the required thickness compensation percentage57. This thickness allowance compensates not only for physical forming losses but also acts as a crucial safety buffer against future secondary flow FAC induced by Dean vortices.

參數代號 Parameter 參數物理意義與來源 Physical Meaning & Source 備註說明 Remarks
P 內部設計錶壓 Internal design gauge pressure 依據管線所處之高壓或中低壓系統而定 Depends on the high or low-pressure system
Do 管線外徑 Outside diameter 決定受力面積的關鍵幾何參數 Key geometric parameter determining load area
SE 許用應力 Allowable stress (incl. joint efficiency) 依材料及溫度自規範附錄 A 取得 Acquired from Appendix A based on material/temp
W 銲縫強度折減係數 Weld strength reduction factor 評估銲道高溫潛變強度弱化（預設 1.0） Evaluates weld creep strength reduction (default 1.0)
y 溫度係數 Temperature coefficient 反映高溫下厚度應力重分配 Reflects stress redistribution at high temps (Table 104.1.2-1)
Mill Tol. 製造負公差 Mill under-tolerance fraction 通常無縫鋼管製造公差為 12.5% Seamless pipe tolerance is typically 12.5%

7.2 彎管後熱處理（PBHT / SRHT）之微觀修復機制 / 7.2 Micro-Restoration Mechanisms of Post-Bend Heat Treatment (PBHT / SRHT)

針對冷作彎管引發的應變硬化與電化學活性升高問題，B31.1 規範提出了強而有力的反制措施：彎管後熱處理（Post-Bend Heat Treatment, PBHT 或退應力熱處理 SRHT）。To combat the strain hardening and elevated electrochemical reactivity caused by cold bending, the B31.1 Code proposes a robust countermeasure: Post-Bend Heat Treatment (PBHT) or Stress Relief Heat Treatment (SRHT).

根據 B31.1 相關修訂與 Code Case（如 Code Case 183 等），當 P-No. 15E（如 P91 合金鋼）或特定的低合金鋼在冷成型過程中，若其冷應變量超過 20%（或在設計溫度超過 1115°F/600°C 且應變超過 5% 時），強制要求必須進行退火（Normalize and Temper）或回火熱處理54。從金屬物理學角度分析，將冷作彎管加熱至亞臨界溫度範圍（約 1350°F 至 1425°F）並持溫一段時間，能夠賦予金屬原子足夠的熱動能進行擴散、回復（Recovery）與再結晶（Recrystallization）。這一過程不僅能徹底消除巨觀的殘留應力，最關鍵的是它能將冷加工累積的巨量差排（Dislocations）消滅，使金屬的內部晶格恢復至能量最低的穩定態50。伴隨差排密度的下降，材料的腐蝕電位（Ecorr）將穩定回升，徹底關閉了冷作彎管因化學活性異常升高而遭 FAC 快速吞噬的後門53。 According to relevant B31.1 revisions and Code Cases (such as Code Case 183), when P-No. 15E (e.g., P91 alloy steel) or specific low-alloy steels undergo cold forming resulting in cold strains exceeding 20% (or exceeding 5% when the design temperature surpasses 1115°F/600°C), normalizing and tempering or tempering heat treatments are mandatorily required54. Analyzed from a metallurgical physics perspective, heating the cold bend to a subcritical temperature range (approx. 1350°F to 1425°F) and holding it gives metal atoms sufficient thermal kinetic energy for diffusion, recovery, and recrystallization. This process not only entirely eliminates macroscopic residual stresses but, most crucially, annihilates the massive accumulation of dislocations from cold working, restoring the metal’s internal lattice to a stable state with minimum energy50. Concomitant with the reduction in dislocation density, the material’s corrosion potential (Ecorr) steadily rebounds, firmly shutting the back door for FAC to rapidly devour cold bends due to abnormally elevated chemical reactivity53.

八、 基於 2026 版 ASME B31J 強制導入之實務工程與決策深度解析 / 8. In-Depth Analysis of Practical Engineering and Decisions Based on the Mandatory Implementation of 2026 ASME B31J

隨著美國機械工程師學會（ASME）在最新版規範中進行了典範轉移，工程界對於管線設計、分析與製造策略產生了根本性的改變。本章節將針對 2026 版 ASME B31J 的強制導入，深度解析 1.5D 電銲彎頭與 3D/5D 冷作彎管在實務工程上的優劣與決策邏輯。With the paradigm shift introduced by the American Society of Mechanical Engineers (ASME) in their latest code editions, the engineering community has undergone fundamental changes in pipeline design, analysis, and manufacturing strategies. This chapter delves into the mandatory implementation of the 2026 ASME B31J, providing an in-depth analysis of the practical engineering pros, cons, and decision logic between 1.5D welded elbows and 3D/5D cold bends.

8.1 2026 版 ASME B31J 強制導入與應力解耦機制 / 8.1 Mandatory Implementation of 2026 ASME B31J and Stress Decoupling Mechanisms

ASME B31 管線規範體系在近年的版本更新（特別是 2024 至 2026 年版）中，正式淘汰了沿用七十餘年的 B31.3 Appendix D 舊有經驗公式，並全面強制導入 ASME B31J 作為應力強化因子（Stress Intensification Factor, SIF, i）與柔性因子（Flexibility Factor, k）的唯一法定計算標準63。 In recent version updates (particularly the 2024 to 2026 editions), the ASME B31 piping code system has officially phased out the old empirical formulas of B31.3 Appendix D used for over seventy years. It has fully mandated the adoption of ASME B31J as the sole statutory calculation standard for Stress Intensification Factors (SIF, i) and Flexibility Factors (k) 63.

B31J 的核心突破在於應力解耦（Stress Decoupling）：The core breakthrough of B31J lies in Stress Decoupling:

  1. SIF 之方向性獨立分解：摒棄了過去單一 SIF 套用所有方向的做法，B31J 基於有限元素分析（FEA），將 SIF 精準解構為平面內（iin）、平面外（ iout）與扭轉（it）三大獨立方向因子65。Directional Independent Decomposition of SIF: Discarding the old practice of applying a single SIF to all directions, B31J utilizes Finite Element Analysis (FEA) to accurately deconstruct SIF into three independent directional factors: in-plane (iin), out-of-plane (iout), and torsional (it) 65.
  2. 持續應力指數（SSI）與 SIF 解耦：過去常將動態疲勞的 SIF 乘以0.75 直接套用於靜態預測（即 0.75i）。B31J 則引入了獨立的持續應力指數（Sustained Stress Index, SSI），其值設定為max(0.75i,1.0) ，避免了厚壁彎管在高溫持續負載下對靜態塑性崩塌風險的誤判64。 這項法規變革，使得 3D/5D 大半徑冷作彎管在應力計算上獲得了極大的柔性紅利，大幅降低了系統的理論應力峰值。Decoupling of Sustained Stress Index (SSI) and SIF: Previously, dynamic fatigue SIFs were often simply multiplied by 0.75 for static predictions (i.e., 0.75i). B31J introduces an independent Sustained Stress Index (SSI), defined as max(0.75i,1.0), avoiding misjudgments regarding the static plastic collapse risks of thick-walled bends under sustained high-temperature loads64. This regulatory evolution grants 3D/5D large-radius cold bends immense flexibility dividends in stress calculations, drastically reducing theoretical stress peaks in the system.

8.2 多維度利害關係人對管線實務之考量與決策 / 8.2 Multi-Dimensional Stakeholder Considerations and Decisions on Piping Practices

在強制落實 B31J 的框架下，電廠專案中的各方利害關係人對「1.5D 電銲彎頭」與「3D/5D 冷作彎管」的選擇，展現出不同的實務考量：Under the framework of mandatory B31J implementation, various stakeholders in power plant projects exhibit differing practical considerations when choosing between “1.5D welded elbows” and “3D/5D cold bends”:

  • 業主（維護管理及營運決策）：傳統1.5D 電銲彎頭具有環向對銲銲道，極易引發第四型潛變破裂（Type IV Creep Cracking）68。此外，銲道處是 FAC 沖蝕熱點，需耗費鉅資進行檢測。冷作彎管消除了銲縫，徹底排除了潛變破裂風險與銲道檢驗成本。Owners (Maintenance Management & Operational Decisions): Traditional 1.5D welded elbows feature girth welds, which are highly susceptible to Type IV Creep Cracking68. Furthermore, welds are FAC hot spots requiring costly inspections. Cold bends eliminate welds, thoroughly removing creep rupture risks and weld inspection costs.
  • EPC 統包商與設計單位（空間佈置與應力配置）：1.5D 彎頭具備佔地極小的幾何優勢，但剛性極高，會將膨脹應力傳導至敏感設備65。採用 3D/5D 冷作彎管可透過其優異的柔性，巨幅降低管線應力與管口荷重，減少昂貴彈簧吊架配置69。EPC Contractors and Design Units (Spatial Layout & Stress Configuration): 1.5D elbows offer geometric advantages with minimal footprint, but their extreme rigidity transfers expansion stress to sensitive equipment65. Adopting 3D/5D cold bends utilizes their superior flexibility to drastically reduce piping stress and nozzle loads, minimizing the need for expensive spring hangers69.
  • 廠務管理者（安全與流體動態要求）：高壓流體通過1.5D 短半徑彎頭時會產生劇烈壓降與高頻振動41。改用 3D/5D 冷作彎管能顯著平滑流場邊界，降低流體擾動，提供更寧靜安全的運作環境68。Plant Operations Managers (Safety & Fluid Dynamic Requirements): High-pressure fluid passing through 1.5D short-radius elbows generates severe pressure drops and high-frequency vibrations41. Switching to 3D/5D cold bends significantly smooths flow boundaries, lowers fluid disturbance, and provides a quieter, safer operational environment68.
  • 冷作彎管協力廠商（因應策略與工法升級）：製造 3D/5D 彎管需要克服厚壁合金鋼極高降伏強度。協力廠必須導入高階 CNC 數控彎管設備以符合嚴格公差極限值70。Cold Bending Subcontractors (Coping Strategies & Method Upgrades): Manufacturing 3D/5D bends requires overcoming the extreme yield strength of thick-walled alloy steels. Subcontractors must integrate advanced CNC pipe bending equipment to meet strict tolerance limits70.

8.3 潁璋工程「能彎不銲」三合一工法之核心價值與合規落實 / 8.3 Core Value and Compliance Execution of Ying-Zhang Engineering’s “Bend-No-Weld” Three-in-One Method

針對上述產業痛點，導入潁璋工程（Ying-Zhang Engineering）所提倡的「三合一工法」（3D/5D CNC 大半徑冷作彎管 + IH-PBHT 單管感應亞臨界彎後熱處理 + QR Code 雲端數位履歷），是發揮大半徑優勢的唯一解方70。此工法管理的核心價值在於徹底落實「能彎不銲」的設計理念，從源頭將易受流體沖刷與疲勞破壞的銲縫轉化為連續平滑的母材彎曲段。針對高能管線，此工法的執行不僅是製造手段的升級，更是嚴格對接 ASME B31.1 與 B31J 規範的合規性展現。 Addressing the aforementioned industry pain points, introducing the “Three-in-One Method” (3D/5D CNC Large-Radius Cold Bends + IH-PBHT Induction Subcritical Post-Bend Heat Treatment + QR Code Cloud Digital Traceability) advocated by Ying-Zhang Engineering is the sole solution for unleashing the advantages of large radii70. The core value of this method management lies in thoroughly implementing the “bend-no-weld” design philosophy, transforming welds—which are highly susceptible to fluid scouring and fatigue damage—into continuous, smooth base metal curved sections straight from the source. For high-energy piping, executing this method is not merely an upgrade in manufacturing techniques but a rigorous demonstration of compliance with ASME B31.1 and B31J standards.

該工法的具體執行涵蓋三個層面：The specific execution of this method encompasses three layers:

  1. CNC 高精密度冷彎：以連續冷作彎管取代傳統的1.5D 對銲彎頭，從微觀層面完全消除了銲接熱影響區（HAZ），解決高階銲工短缺問題，並直接根除銲道 FAC 與氫脆化威脅。High-Precision CNC Cold Bending: Replaces traditional 1.5D welded elbows with continuous cold bends, completely eliminating the weld Heat-Affected Zone (HAZ) at the microscopic level, resolving shortages of advanced welders, and directly eradicating the threats of weld FAC and hydrogen embrittlement.
  2. IH-PBHT 感應熱處理：針對冷彎造成的塑性應變進行即時冶金修復（詳見4 節）。IH-PBHT Induction Heat Treatment: Conducts immediate metallurgical restoration on the plastic strain caused by cold bending (detailed in Section 8.4).
  3. MES 數位履歷與 PSFR 報告：將材料試驗報告（MTR）、冷彎幾何參數與熱處理動態溫度曲線無縫綁定至製造執行系統（MES），並透過 QR Code 生成不可竄改的「管線系統最終報告（PSFR）」。此數位化品質迴圈確保了工法在 ASME B31J 下的絕對合規，更協助 EPC 順利向業主提交規範合規證明。MES Digital Traceability and PSFR Reports: Seamlessly binds Material Test Reports (MTR), cold bending geometric parameters, and dynamic heat treatment temperature curves to the Manufacturing Execution System (MES), generating tamper-proof “Piping System Final Reports (PSFR)” via QR Codes. This digital quality loop ensures absolute compliance under ASME B31J and assists EPCs in smoothly submitting code compliance certifications to owners.

8.4 應變率 (5%~20%) 放寬與 IH-PBHT 冶金修復解析 / 8.4 Strain Rate (5%~20%) Relaxation and IH-PBHT Metallurgical Restoration Analysis

在採用 3D/5D 冷作彎管時，材料的成型應變率（Forming Strain Rate, ϵ）是決定後續熱處理規範的關鍵參數。彎管最外緣的理論彎曲應變公式定義為：When adopting 3D/5D cold bends, the material’s forming strain rate (ϵ) is the key parameter determining subsequent heat treatment requirements. The theoretical bending strain formula for the outermost edge of the bend is defined as:

ϵ=Do/2R1×100%

傳統 1.5D 彎頭理論應變率高達約 33.3%（大於 20%）；而現代的 5D 彎管，其理論彎曲應變率則降至 10.0% 69。The theoretical strain rate of traditional 1.5D elbows is as high as approx. 33.3% (greater than 20%); in contrast, modern 5D bends drop to a theoretical bending strain rate of 10.0% 69.

對於 P-No. 15E 麻田散鐵耐熱鋼，ASME 規範極為嚴格。原本應變率超過 20% 時強制要求進行「正常化與回火（N&T）」60。然而，正因為 5D 彎管應變率落於 5% 至 20% 區間，ASME B31.1 Code Case 183-2 給予了放寬，授權可實施次臨界局部回火（Subcritical Tempering）60。此時潁璋工程的 IH-PBHT 成為最佳解方，將彎曲段加熱並持溫於 730°C 至 775°C 之間60。這避免了超越相變點引發的「鮮韌未回火麻田散鐵」脆化風險，成功將差排歸零，使材料拉森-米勒參數（LMP）完全恢復至安全標準70。 For P-No. 15E martensitic heat-resistant steels, ASME codes are exceedingly strict. Originally, strain rates exceeding 20% mandatorily required “Normalizing and Tempering (N&T)” 60. However, precisely because the 5D bend strain rate falls within the 5% to 20% range, ASME B31.1 Code Case 183-2 grants a relaxation, authorizing the implementation of subcritical localized tempering60. Here, Ying-Zhang Engineering’s IH-PBHT becomes the optimal solution, heating and holding the bent section between 730°C and 775°C 60. This avoids the risk of embrittlement from “untempered martensite” triggered by exceeding the phase transformation point, successfully zeroes out dislocations, and completely restores the material’s Larson-Miller Parameter (LMP) to safety standards70.

九、 ASME B31J 規範之未來演進：全數位化、AI 與前沿製造技術之整合 / 9. Future Evolution of ASME B31J Code: Integration of Full Digitalization, AI, and Frontier Manufacturing Technologies

在 2026 年 ASME B31J 強制適用與全面導入之後，管線應力設計的準則將邁入基於演算法優化與雲端數據驅動的新紀元。未來 B31J 及其相關標準的演進，主要聚焦於全數位化分析、人工智慧（AI）決策輔助，以及與前沿製造技術（如積層製造）的高度整合。Following the mandatory application and comprehensive rollout of ASME B31J in 2026, pipeline stress design guidelines will enter a new era based on algorithmic optimization and cloud data-driven systems. The future evolution of B31J and its related standards will primarily focus on fully digitalized analysis, Artificial Intelligence (AI) decision support, and deep integration with cutting-edge manufacturing technologies (such as additive manufacturing).

  1. 全數位化與 AI 驅動之高精度應力分析：未來的管線應力軟體將深度內建 ASME B31J 的多維度 SIF 計算。透過 AI 輔助優化器，應力工程師能在幾秒鐘內對管線支撐配置進行快速迭代演算，自動尋找出應力最低、成本最優的方案73。Fully Digitalized and AI-Driven High-Precision Stress Analysis: Future piping stress software will deeply integrate the multi-dimensional SIF calculations of ASME B31J. Using AI-assisted optimizers, stress engineers can rapidly iterate pipeline support configurations in seconds, automatically pinpointing the lowest-stress and most cost-effective solutions73.
  2. 數位孿生（Digital Twin）與即時物聯網（IoT）疲勞監測：B31J 的 FEA 基準為建立管線系統的「數位孿生」奠定了基礎68。透過佈署 IoT 感測器並結合 AI 大數據分析，系統能連續監控管線潛變，精準計算剩餘疲勞壽命，實現預測性維護。Digital Twins and Real-Time IoT Fatigue Monitoring: The FEA baselines of B31J establish a foundation for creating “Digital Twins” of piping systems68. By deploying IoT sensors combined with AI big data analysis, systems can continuously monitor pipeline creep, accurately calculating remaining fatigue life and realizing predictive maintenance.
  3. 前沿積層製造（Additive Manufacturing）之標準化整合：3D 列印管件有著不同於傳統鍛造管件的微觀結構。ASME B31J 的標準化實驗程序為這些積層製造元件提供了合規的審驗路徑75。透過高階非線性 FEA 與疲勞測試，設計師能為 3D 列印零件推導專屬 SIF。Standardized Integration of Additive Manufacturing: 3D-printed piping components possess microstructures different from traditional forged parts. The standardized experimental procedures of ASME B31J provide a compliant vetting pathway for these additively manufactured elements75. Through advanced non-linear FEA and fatigue testing, designers can derive dedicated SIFs for 3D-printed parts.

十、 結論與預防性檢測建議 / 10. Conclusions and Preventive Inspection Recommendations

本研究結合熱力學條件、CFD 紊流力學與材料電化學分析，揭示內突銲道主要透過「點狀幾何分離與極端衝擊」，結合微電偶腐蝕撕裂管壁；而冷作彎管則透過「巨觀二次流洗刷」與「應變硬化」進行協同破壞。透過 2026 版 ASME B31J 規範探討，確立了 3D/5D 冷作彎管在應力解耦上的工程優勢。This study combines thermodynamic conditions, CFD turbulence mechanics, and material electrochemical analysis to reveal that weld root protrusions primarily tear pipe walls through “punctiform geometric separation and extreme impact” coupled with micro-galvanic corrosion; whereas cold bends execute synergistic destruction through “macroscopic secondary flow washing” and “strain hardening.” Discussions on the 2026 ASME B31J code established the engineering advantages of 3D/5D cold bends in stress decoupling.

為確保長期安全營運，建議遵循以下策略：To ensure long-term safe operation, the following strategies are recommended:

  1. 銲接工法與檢測擴展：嚴格控制銲根突出量。UT 檢測不可僅侷限於銲縫上方，必須向下游延伸至少 3 至 5 倍管徑，以捕捉再附著點蝕孔。Welding Method and Inspection Expansion: Strictly control weld root protrusion. UT inspections must not be confined just above the weld but extend at least 3 to 5 pipe diameters downstream to capture reattachment point pitting.
  2. 落實冷作彎管之後處理：導入「能彎不銲」三合一工法。絕不可省略彎管後熱處理，善用 Code Case 183-2 的應變率放寬條件，實施 IH-PBHT 重置材料腐蝕電位。Execute Post-Bend Treatments: Introduce the “bend-no-weld” Three-in-One Method. Post-bend heat treatments must never be skipped; leverage the strain rate relaxations of Code Case 183-2 to perform IH-PBHT, resetting material corrosion potentials.
  3. 推進 AI 輔助完整性管理：積極導入基於 B31J 的數位孿生技術與即時 IoT 平台，制定最優化的預測性維護計畫。Advance AI-Assisted Integrity Management: Actively implement B31J-based Digital Twin technologies and real-time IoT platforms to formulate optimized predictive maintenance plans.
  4. 優化水化學邊界：維持高鹼性環境（pH 9.2-9.8）並控制極低溶氧量（DO），壓抑溶解度梯度驅動力。Optimize Water Chemistry Boundaries: Maintain a highly alkaline environment (pH 9.2-9.8) and strictly control trace dissolved oxygen (DO) to suppress the driving forces of solubility gradients.

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