CCPP 系統中濕蒸氣之沖蝕行為預測與管件防護優化研究 (Research on Prediction of Wet Steam Erosion Behavior and Optimization of Piping Protection in CCPP Systems)

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一、摘要 / 1. Abstract

複循環汽電共生系統（Combined Cycle Power Plant, CCPP）在現代電網中具備高效能與低排放之優勢。在台灣面臨能源轉型、再生能源併網比例攀升以及電網孤島特性的背景下，CCPP 系統肩負了基載發電與極端負載追隨（Load-following）的雙重關鍵角色。太陽能與風力發電的間歇性導致電網淨負載呈現劇烈的「鴨子曲線（Duck Curve）」，迫使天然氣複循環機組必須頻繁進行啟停（Start-stop）與急遽的升降載運轉。此種偏離設計最佳點的運轉模式，導致系統內部的熱力學狀態發生劇烈波動，特別是在汽輪機低壓段（Low-pressure turbine stages）與高壓旁路閥門（Bypass valves）中，蒸汽頻繁跨越飽和線（Saturation line）進入濕蒸氣區。膨脹過程伴隨的劇烈壓降促使蒸汽凝結，形成夾帶大量微小液滴的高速兩相流。這些高速液滴對管壁、彎頭、盲通管與閥件內部產生劇烈的液滴衝擊沖蝕（Liquid Droplet Impingement Erosion, LDI，或稱水滴沖蝕 WDE），嚴重威脅電廠的高能管線（High-Energy Piping）資產壽命與運轉安全性。Combined Cycle Power Plants (CCPP) offer the advantages of high efficiency and low emissions in modern power grids. Amidst Taiwan’s energy transition, increasing integration of renewable energy, and its isolated grid characteristics, CCPP systems shoulder the dual critical roles of base-load power generation and extreme load-following. The intermittency of solar and wind power causes the grid’s net load to exhibit a severe “Duck Curve,” forcing natural gas combined-cycle units into frequent start-stop cycles and rapid ramp-ups/downs. Such operational modes, deviating from optimal design points, induce severe fluctuations in the system’s internal thermodynamic states. Specifically, within the low-pressure turbine stages and high-pressure bypass valves, steam frequently crosses the saturation line into the wet steam region. The severe pressure drop accompanying expansion promotes steam condensation, forming high-speed two-phase flows entraining massive amounts of micro-droplets. These high-speed droplets inflict severe Liquid Droplet Impingement Erosion (LDI, or Water Droplet Erosion, WDE) on pipe walls, elbows, blind tees, and internal valve components, gravely threatening the asset lifespan of the plant’s High-Energy Piping and operational safety.

本研究基於計算流體力學（CFD）、固體力學與材料工程之跨領域框架，針對 CCPP 系統內濕蒸氣之 LDI 行為進行深度學術分析。研究架構涵蓋三大核心階段：第一階段建立 Eulerian-Lagrangian 耦合計算流體力學與離散相模型（CFD-DPM），還原複雜幾何內之氣液兩相流場，並導入可壓縮流體之水錘壓力（Water Hammer Pressure）理論與 Oka 沖蝕模型，精準預測局部管壁之沖蝕熱點與質量流失率；第二階段探討宏觀幾何特徵對流場之影響，嚴格評估幾何曲率優化、盲通管（Blind Tee / Dead leg）之緩衝渦流（Buffer vortex）特性，以及多孔閥件設計對液滴衝擊動能衰減之工程效益；第三階段則從材料微觀結構與表面介面工程出發，深度評估碳化鎢金屬陶瓷（WC-10Co-4Cr）與鈷基合金（Stellite 6）等先進表面防護技術。透過探討 Stellite 6 的應變誘發相變（Strain-induced phase transformation）機制，以及結合 ASTM G73 測試標準分析其潛伏期（Incubation period）疲勞機制，並引入奈米秒雷射表面預處理（Laser Surface Texturing, LST）技術以強化塗層與基材間之機械咬合力（Mechanical interlocking）。Based on a cross-disciplinary framework of Computational Fluid Dynamics (CFD), solid mechanics, and materials engineering, this study conducts an in-depth academic analysis of wet steam LDI behavior in CCPP systems. The research framework comprises three core stages: The first stage establishes a coupled Eulerian-Lagrangian CFD and Discrete Phase Model (CFD-DPM) to reconstruct gas-liquid two-phase flow fields within complex geometries, integrating the compressible fluid Water Hammer Pressure theory and the Oka erosion model to precisely predict local erosion hotspots and mass loss rates. The second stage explores the impact of macroscopic geometric features on the flow field, strictly evaluating the engineering benefits of geometric curvature optimization, the buffer vortex characteristics in blind tees (dead legs), and porous valve designs on droplet kinetic energy attenuation. The third stage delves into material microstructures and surface interface engineering, comprehensively assessing advanced surface protection technologies such as tungsten carbide cermets (WC-10Co-4Cr) and cobalt-based alloys (Stellite 6). This involves exploring the strain-induced phase transformation mechanism of Stellite 6, analyzing its fatigue mechanisms during the incubation period using the ASTM G73 standard, and introducing nanosecond Laser Surface Texturing (LST) technology to enhance mechanical interlocking between the coating and the substrate.

本研究最終將微觀與宏觀之研究成果，串聯至 ASME B31.1 動力管線設計規範與 EPRI (Electric Power Research Institute) CHECWORKS 檢測程序，提出一套動態壁厚補償與剩餘壽命預測模型。此一整合性科學論證不僅釐清了液滴衝擊之多物理耦合衰退機制，更為台灣高負載發電廠之高能管線設計、材料選型與預防性運維（Predictive Maintenance），提供具備高度實務可行性的優化指引。Ultimately, this study links microscopic and macroscopic research findings to the ASME B31.1 Power Piping Design Code and the EPRI CHECWORKS inspection procedures, proposing a dynamic wall thickness compensation and remaining useful life prediction model. This integrated scientific validation not only clarifies the multi-physics coupled degradation mechanisms of liquid droplet impingement but also provides highly viable optimization guidelines for the design, material selection, and predictive maintenance of high-energy piping in Taiwan’s high-load power plants.

二、前言 / 2. Introduction

全球能源結構正經歷前所未有的轉型，台灣在邁向淨零排放（Net Zero）的進程中，天然氣複循環汽電共生系統（CCPP）已成為維持電網穩定性的絕對核心。台灣電網屬於獨立系統，缺乏跨國電網的備用容量支援，且近年來太陽光電與離岸風電建置量大幅增加。再生能源的間歇性與不可預測性，使得電網每日面臨極大的負載波動。為維持系統頻率與電壓穩定，CCPP 機組被賦予了頻繁啟停與快速負載追隨的嚴苛任務。然而，此種極端的運轉模式對電廠的熱力系統與高能管線構成了嚴峻的挑戰。The global energy structure is undergoing an unprecedented transition. In Taiwan’s march toward Net Zero emissions, the natural gas Combined Cycle Power Plant (CCPP) has become the absolute core for maintaining grid stability. Taiwan’s power grid is an isolated system lacking backup capacity support from transnational grids, and the installation of solar photovoltaics and offshore wind power has surged in recent years. The intermittency and unpredictability of renewable energy expose the grid to massive daily load fluctuations. To maintain system frequency and voltage stability, CCPP units are tasked with rigorous frequent start-stops and rapid load-following duties. However, this extreme operational mode poses severe challenges to the plant’s thermodynamic systems and high-energy piping.

在低載運轉或機組跳機引發旁路系統作動的條件下，高溫高壓蒸汽於汽輪機末段或旁路節流閥中經歷急遽的等熵膨脹。當蒸汽狀態跨越熱力學飽和線（即威爾遜線，Wilson line）時，自發凝結（Spontaneous condensation）現象會產生大量初始粒徑極小（亞微米級）的霧狀液滴（Fog droplets）1。這些微小液滴在流經靜態葉片或複雜管件時，會碰撞凝結成水膜，隨後在高速連續相（氣相）的剪切力作用下，水膜再次破裂並霧化為粒徑介於數十至數百微米的大型液滴2。這些次生大液滴被高達數百公尺每秒的蒸汽流加速，以極高的動能撞擊管壁、彎頭外弧側與閥門內部組件，引發破壞力驚人的液滴衝擊沖蝕（LDI）1。Under conditions of low-load operation or unit trips triggering the bypass system, high-temperature and high-pressure steam undergoes rapid isentropic expansion in the low-pressure turbine stages or bypass throttle valves. When the steam state crosses the thermodynamic saturation line (the Wilson line), spontaneous condensation generates a vast amount of initially sub-micron fog droplets1. As these micro-droplets flow past static blades or complex fittings, they collide and condense into water films. Subsequently, subjected to the shear forces of the high-speed continuous phase (gas phase), the water films rupture and atomize into larger secondary droplets ranging from tens to hundreds of micrometers in diameter2. These secondary large droplets are accelerated by steam flows reaching hundreds of meters per second, impacting pipe walls, elbow extrados, and internal valve components with tremendous kinetic energy, thereby triggering highly destructive Liquid Droplet Impingement Erosion (LDI)1.

LDI 是一種高度複雜的機械性疲勞降解過程。當液滴以超音速或近音速撞擊固體表面時，由於液體在高應變率下的可壓縮性（Compressibility），會在接觸瞬間產生極高強度的衝擊波，進而引發數倍於穩態動壓的水錘壓力4。此一極端應力脈衝隨後在材料內部轉化為複雜的應力波（包含縱波、橫波與雷利表面波），反覆的應力循環導致材料表面經歷塑性變形、微裂紋萌生、疲勞擴展，最終造成材料巨觀的剝落與質量流失5。在台灣高負載發電廠的實務運營中，LDI 不僅會導致高能管線壁厚在短時間內異常減薄，更可能引發管線爆裂、高壓蒸汽外洩等重大工安與環保事故，大幅增加電廠的全壽命週期成本（Life Cycle Cost, LCC）與非計畫性停機（Unplanned Outage）風險7。LDI is a highly complex mechanical fatigue degradation process. When droplets impact a solid surface at supersonic or near-sonic speeds, the compressibility of the liquid at high strain rates generates ultra-high-intensity shock waves at the moment of contact, inducing water hammer pressures several times higher than steady-state dynamic pressure4. This extreme stress pulse subsequently transforms into complex stress waves within the material (including longitudinal, transverse, and Rayleigh surface waves). Repeated stress cycles lead to plastic deformation, microcrack initiation, and fatigue propagation on the material surface, ultimately resulting in macroscopic spalling and mass loss5. In the practical operation of Taiwan’s high-load power plants, LDI not only causes abnormal and rapid thinning of high-energy piping walls but may also trigger catastrophic industrial safety and environmental incidents such as pipe ruptures and high-pressure steam leaks, drastically increasing the plant’s Life Cycle Cost (LCC) and unplanned outage risks7.

傳統上，工程界對於 LDI 的防護多仰賴經驗法則，例如在易受損區段採用局部補銲、無差別增加管壁厚度，或進行事後的定期非破壞檢測（NDT）。然而，這些被動式的應對策略缺乏系統性的科學預測，亦未能從材料微觀層級解決沖蝕疲勞的核心問題。有鑑於此，本報告旨在透過嚴謹的數值模擬與材料科學實證，建立一套自上游巨觀流場預測，至下游微觀材料防護的跨領域分析框架。研究涵蓋流場幾何優化（如盲通管與多孔閥件之動能衰減效應），並深度探討 Stellite 6 與 WC-10Co-4Cr 等先進防護塗層在 LDI 作用下之微觀抗疲勞機制與介面強化技術。最終目標是將研究發現與 ASME B31.1 動力管線設計規範及 EPRI 檢測程序深度整合，為台灣高負載發電廠提供一套兼具理論深度與實務可行性的管件防護優化與剩餘壽命預測指南。Traditionally, engineering protection against LDI has largely relied on rules of thumb, such as localized welding repairs in vulnerable sections, indiscriminate increases in pipe wall thickness, or reactive periodic Non-Destructive Testing (NDT). However, these passive mitigation strategies lack systematic scientific prediction and fail to resolve the core issue of erosion fatigue at the material micro-level. Consequently, this report aims to establish a cross-disciplinary analytical framework—from upstream macroscopic flow field prediction to downstream microscopic material protection—through rigorous numerical simulations and materials science empirical data. The research covers flow field geometric optimization (such as the kinetic energy attenuation effects of blind tees and porous valves) and deeply explores the microscopic anti-fatigue mechanisms and interface strengthening technologies of advanced protective coatings like Stellite 6 and WC-10Co-4Cr under LDI. The ultimate goal is to deeply integrate the research findings with the ASME B31.1 Power Piping Code and EPRI inspection procedures, providing Taiwan’s high-load power plants with a comprehensive, theoretically profound, and practically viable guide for piping protection optimization and remaining life prediction.

三、文獻回顧 / 3. Literature Review

3.1 液滴衝擊動力學與水錘壓力演進理論 / 3.1 Droplet Impingement Dynamics and Water Hammer Pressure Evolution Theory

液滴衝擊固體表面的瞬態物理現象，一直是多相流與固體力學領域的經典難題。Cook（1928）率先指出，當液體水柱或液滴以高速撞擊固體表面時，不能僅將其視為不可壓縮流體。由於撞擊瞬間的極高減速度，液體內部會產生壓縮波，其撞擊壓力遠高於白努利定律（Bernoulli’s principle）所預測的停滯壓力。Cook 提出了一維水錘壓力方程式Pimpact=ρl Cl Vimpact，其中 ρl 為液體密度，Cl 為液體中之聲速，Vimpact 為撞擊速度。The transient physical phenomena of droplet impact on solid surfaces have long been classic challenges in multiphase flow and solid mechanics. Cook (1928) first pointed out that when a liquid column or droplet impacts a solid surface at high speed, it cannot be treated merely as an incompressible fluid. Due to the extremely high deceleration at the moment of impact, compression waves are generated within the liquid, resulting in an impact pressure far exceeding the stagnation pressure predicted by Bernoulli’s principle. Cook proposed the one-dimensional water hammer pressure equation Pimpact=ρl Cl Vimpact, where ρl is the liquid density, Cl is the speed of sound in the liquid, and Vimpact is the impact velocity.

然而，一維理論無法完美解釋球形液滴撞擊平面的現象。Bowden 與 Field（1964）透過高速攝影與理論推導，證實高能量液滴衝擊時會在液滴內部產生衝擊波（Shockwave）8。Heymann（1969）進一步發展了二維接觸模型，指出在液滴撞擊的初期，液滴與固體表面的接觸邊緣擴張速度（Radial velocity of contact area boundary）可能超越液體內部的聲速9。在此階段，衝擊波無法脫離接觸邊緣，導致應力強烈集中。Heymann 的模型預測，接觸邊緣的最大壓力峰值可達一維水錘壓力的三倍，此即著名的 Heymann 衝擊壓力修正理論，成為現代液滴沖蝕極端壓力預測的基石4。當此高壓衝擊波與固體標靶交互作用時，機械平衡被打破，隨之而來的是三種應力波的傳遞：沿縱向傳播的壓縮波、橫向傳播的剪切波，以及沿材料表面傳播的雷利波。文獻指出，雷利表面波是造成標靶材料微觀疲勞、晶界撕裂與裂紋萌生的最主要破壞源5。However, the one-dimensional theory could not perfectly explain the phenomena of a spherical droplet impacting a flat plane. Bowden and Field (1964), through high-speed photography and theoretical derivation, proved that shockwaves are generated inside the droplet during high-energy impact8. Heymann (1969) further developed a two-dimensional contact model, noting that in the early stages of droplet impact, the radial velocity of the contact area boundary between the droplet and the solid surface can exceed the speed of sound within the liquid9. At this stage, the shockwave cannot detach from the contact edge, leading to intense stress concentration. Heymann’s model predicted that the maximum pressure peak at the contact edge could reach three times the one-dimensional water hammer pressure. This famous Heymann impact pressure correction theory has become the cornerstone for predicting extreme pressures in modern droplet erosion4. When this high-pressure shockwave interacts with the solid target, mechanical equilibrium is broken, followed by the propagation of three types of stress waves: longitudinal dilatational waves, transverse shear waves, and Rayleigh waves propagating along the surface. Literature indicates that the Rayleigh surface wave is the primary destructive source causing microscopic fatigue, grain boundary tearing, and crack initiation in target materials5.

3.2 沖蝕行為預測與 CFD 數值模擬進展 / 3.2 Progress in Erosion Behavior Prediction and CFD Numerical Simulation

在複雜管件的沖蝕預測上，計算流體力學（CFD）結合離散相模型（DPM）已成為學界與工業界之標準分析工具。Eulerian-Lagrangian 框架能有效解析連續氣相與離散液滴相之動量、質量與能量耦合11。為準確捕捉閥門節流後產生之強烈各向異性亂流與二次流（Secondary flow）現象，雷諾應力模型（Reynolds Stress Model, RSM）展現出優於傳統k-ϵ模型的預測精度12。在沖蝕率的數學量化上，Oka 等人基於廣泛的實驗數據，提出了一套無因次化的沖蝕預測方程式（Oka Erosion Model）。該模型成功將標靶材料硬度（Hv）、撞擊角度與撞擊速度等參數進行非線性整合，已被廣泛應用於節流閥、旋流器與高壓管件之沖蝕模擬11。為修正液滴在極端衝擊速度下之可壓縮性特徵，先進的數值模擬需結合 Tait 狀態方程式（Tait’s power law equation of state），以確保動能轉換計算之物理正確性8。For erosion prediction in complex piping components, Computational Fluid Dynamics (CFD) combined with the Discrete Phase Model (DPM) has become the standard analytical tool in academia and industry. The Eulerian-Lagrangian framework effectively resolves the momentum, mass, and energy coupling between the continuous gas phase and discrete droplet phase11. To accurately capture the strong anisotropic turbulence and secondary flows generated after valve throttling, the Reynolds Stress Model (RSM) demonstrates superior prediction accuracy over the traditional k-ϵ model12. Regarding the mathematical quantification of erosion rates, Oka et al., based on extensive experimental data, proposed a dimensionless erosion prediction equation (Oka Erosion Model). This model successfully performs non-linear integration of parameters such as target material hardness (Hv), impact angle, and impact velocity, and has been widely applied in erosion simulations for throttle valves, cyclones, and high-pressure fittings11. To correct the compressibility characteristics of droplets at extreme impact velocities, advanced numerical simulations must incorporate Tait’s power law equation of state to ensure the physical correctness of kinetic energy conversion calculations8.

3.3 管件幾何流場特徵與動能衰減優化 / 3.3 Flow Field Characteristics of Piping Geometry and Kinetic Energy Attenuation Optimization

針對高能管線中的彎頭（Elbow）與三通管（Tee），文獻顯示彎管的外弧側（Extrados）由於液滴強大的慣性力與二次流效應，通常為沖蝕破壞之絕對熱點，且沖蝕區間多集中於彎曲角 10° 至 90° 之範圍17。為降低沖蝕風險並衰減流體動能，盲通管（Blind Tee，亦稱死區管線 Dead leg）的幾何設計逐漸受到重視。研究表明，盲通管封閉端內部能形成穩定的滯留緩衝渦流區（Buffer vortex）。此區能破壞液滴的直線彈道，將動能大量消耗於流體層間的剪切與黏滯摩擦，從而大幅降低管壁的最大沖蝕率19。然而，若盲通管的長徑比（L/D）設計不當，可能引發共振或流致振動，導致疲勞-沖蝕耦合破壞。同樣的動能衰減理念亦應用於多孔閥件設計中11。For elbows and tees in high-energy piping, literature shows that the extrados of the elbow is typically the absolute hotspot for erosion damage due to the powerful inertial force of droplets and secondary flow effects, with the erosion zone mostly concentrated between a 10° to 90° bending angle17. To reduce erosion risk and attenuate fluid kinetic energy, the geometric design of the blind tee (also known as a dead leg) has gradually gained attention. Research indicates that a stable, stagnant buffer vortex can form inside the closed end of a blind tee. This region disrupts the linear trajectory of droplets, consuming massive amounts of kinetic energy through shear and viscous friction between fluid layers, thereby drastically reducing the maximum erosion rate on the pipe wall19. However, if the length-to-diameter ratio (L/D) of the blind tee is poorly designed, it may trigger resonance or flow-induced vibration, leading to coupled erosion-fatigue failure. The same concept of kinetic energy attenuation is also applied in porous valve trim designs11.

3.4 表面防護塗層與介面強化技術 / 3.4 Surface Protective Coatings and Interface Strengthening Technologies

為抵禦高強度之 LDI，表面工程（Surface Engineering）技術為延長材料壽命之最後防線。鈷基合金（如 Stellite 6）因其卓越的高溫耐磨、抗穴蝕（Cavitation erosion）與抗沖蝕性能，被廣泛應用。其優異的抗沖蝕機制，不僅源於碳化物提供的硬度，更與材料在受高應變率衝擊下發生之無擴散相變（由 FCCγ-Co 轉變為 HCPϵ-Co）密切相關。此相變過程能吸收大量衝擊能量，延緩疲勞裂紋的生成20。另一方面，碳化鎢金屬陶瓷（WC-10Co-4Cr）透過超音速火焰噴塗（HVOF）沉積，展現出極高之微觀硬度。然而，硬質塗層極易發生基材與塗層介面的疲勞剝離。為解決此問題，奈米秒雷射表面預處理（LST）技術被引入，透過建構微觀凹坑陣列以大幅提升機械咬合力（Mechanical interlocking），有效阻斷沿介面傳遞的疲勞裂紋24。To withstand high-intensity LDI, Surface Engineering technology acts as the last line of defense to extend material lifespan. Cobalt-based alloys (such as Stellite 6) are widely used due to their exceptional high-temperature wear resistance, cavitation erosion resistance, and erosion resistance. Their outstanding anti-erosion mechanism stems not only from the hardness provided by carbides but also closely relates to the diffusionless phase transformation (from FCCγ-Co to HCPϵ-Co) that occurs under high-strain-rate impact. This phase transformation absorbs significant impact energy, delaying the formation of fatigue cracks20. On the other hand, tungsten carbide cermets (WC-10Co-4Cr) deposited via High-Velocity Oxygen Fuel (HVOF) spraying exhibit extremely high microhardness. However, hard coatings are highly susceptible to fatigue spalling/delamination at the coating-substrate interface. To solve this, nanosecond Laser Surface Texturing (LST) technology is introduced, constructing micro-dimple arrays to substantially enhance mechanical interlocking, effectively arresting fatigue cracks propagating along the interface24.

3.5 ASTM G73 測試標準與工業規範之整合 / 3.5 Integration of ASTM G73 Testing Standards and Industrial Codes

依據 ASTM G73 標準，材料的沖蝕生命週期具備明顯的潛伏期（Incubation period），此期間表面無明顯質量流失6。將 S-N 疲勞曲線引入潛伏期模型中，能實現基於疲勞極限值的沖蝕壽命預測6。在工程規範方面，ASME B31.1 動力管線規範提供了高能管線設計與壁厚計算的法源基礎31。此外，EPRI 開發了 CHECWORKS 檢測程序，透過整合 CFD 模擬，實現對 LDI 熱點的動態預測與剩餘壽命評估33。According to the ASTM G73 standard, the erosion life cycle of a material possesses a distinct incubation period during which the surface shows no obvious mass loss6. Introducing S-N fatigue curves into the incubation period model enables erosion life prediction based on fatigue threshold limits6. Regarding engineering standards, the ASME B31.1 Power Piping Code provides the legal foundation for high-energy piping design and wall thickness calculations31. Furthermore, EPRI developed the CHECWORKS inspection program, integrating CFD simulations to dynamically predict LDI hotspots and evaluate remaining useful life33.

四、分析框架與數值方法 / 4. Analytical Framework and Numerical Methods

本研究之分析框架分為流體力學流場解析、沖蝕模型建構、以及基於 ASTM G73 標準之材料潛伏期疲勞評估。

The analytical framework of this study is divided into fluid dynamic flow field resolution, erosion model construction, and material incubation period fatigue evaluation based on the ASTM G73 standard.

4.1 CFD-DPM 多相流統御方程式與可壓縮性修正 / 4.1 CFD-DPM Multiphase Flow Governing Equations and Compressibility Correction

為還原 CCPP 高壓旁路系統內濕蒸氣之複雜流場，本研究採用 Eulerian-Lagrangian 架構，並選用雷諾應力模型（RSM）封閉 RANS 方程式11。在追蹤液滴與氣相之相界面時，採用流體體積法（VOF），其連續方程式為： To reconstruct the complex flow field of wet steam in the CCPP high-pressure bypass system, this study adopts the Eulerian-Lagrangian framework and selects the Reynolds Stress Model (RSM) to close the RANS equations11. To track the phase interface between droplets and gas, the Volume of Fluid (VOF) method is used, with its continuity equation as follows:

∂α/∂t+∇⋅(αU)=α(1-α)(1/ρg*(Dρg)/Dt-1/ρl *(Dρl)/Dt)+α∇⋅U

其中 U 為速度向量，ρg 與 ρl 分別為氣相與液相密度。 Where U is the velocity vector, and ρg and ρl are the gas and liquid densities, respectively.

鑑於液滴在超音速撞擊下的可壓縮性，本研究導入 Tait 冪律狀態方程式以描述液態水之熱力學狀態：Given the compressibility of droplets under supersonic impact, this study introduces Tait’s power law equation of state to describe the thermodynamic state of liquid water:

(P+B)/(P0+B)=(ρl/ρl0 )N

其中 P0 與 ρl0 為參考狀態下之壓力與密度，B 與 N 為經驗常數。流場壓力與速度之耦合採用壓力隱式算子分裂法（PISO），確保數值穩定16。 Where P0 and ρl0 are the pressure and density at the reference state, and B and N are empirical constants. The coupling of flow field pressure and velocity utilizes the Pressure-Implicit with Splitting of Operators (PISO) method to ensure numerical stability16.

4.2 Oka 沖蝕模型與 Heymann 衝擊壓力耦合 / 4.2 Coupling of Oka Erosion Model and Heymann Impact Pressure

本研究導入 Oka 沖蝕模型，其法向基準沖蝕率（E90）定義為：This study incorporates the Oka erosion model, where the reference erosion rate at a 90° impact angle (E90) is defined as:

E90=K(Hv)k1 (Vimpact/V* )k2  (D/D* )k3

其中，Hv 為標靶材料之維氏硬度；Vimpact 與 D 為撞擊速度與直徑；V* 與 D* 為參考值11。非垂直撞擊沖蝕率 E(α) 則透過角度函數 g(α) 進行修正： Where Hv is the Vickers hardness of the target material; Vimpact and D are the impact velocity and droplet diameter; V* and D* are reference values11. The erosion rate at non-normal impact angles, E(α), is corrected via the angle function g(α):

E(α)=E90⋅g(α)=E90⋅(sinα )n1 [1+Hv(1-sinα )]n2

為評估微觀應力，將 Heymann 二維衝擊壓力模型作為邊界條件輸入。最大水錘壓力 Pwh 與瞬態聲速 Cw 為：To evaluate microscopic stress, the Heymann two-dimensional impact pressure model is input as a boundary condition. The maximum water hammer pressure Pwh and transient acoustic speed Cw are:

Pwh=Vimpact  (ρw Cw)/[1+(ρw Cw/ρm Cl,m)]

Cw=Cw0+kVimpact 6

4.3 ASTM G73 測試與材料表面防護設計 / 4.3 ASTM G73 Testing and Material Surface Protection Design

本研究針對 Stellite 6 鈷基合金雷射熔覆層與 WC-10Co-4Cr 陶瓷塗層（HVOF 沉積）進行評估。為強化 WC-10Co-4Cr 塗層，利用波長 1064 nm 之光纖雷射於基材進行表面預處理（LST），生成微凹坑陣列24。材料壽命評估遵循 ASTM G73-10 標準，透過高速旋轉測試設備記錄質量流失，精確界定沖蝕潛伏期，並建構預測模型6。This study evaluates Stellite 6 cobalt-based alloy laser cladding and WC-10Co-4Cr cermet coatings (HVOF deposited). To strengthen the WC-10Co-4Cr coating, a 1064 nm fiber laser is used for Laser Surface Texturing (LST) on the substrate to generate micro-dimple arrays24. Material life evaluation follows the ASTM G73-10 standard, recording mass loss using high-speed rotating apparatuses to precisely define the erosion incubation period and build predictive models6.

五、結果與討論 / 5. Results and Discussion

5.1 濕蒸氣兩相流場特徵與沖蝕熱點預測 / 5.1 Flow Field Characteristics of Wet Steam and Erosion Hotspot Prediction

CFD-DPM 模擬結果揭示，當閥門開度處於 25% 至 50% 時，流體形成高度集中的破壞性噴流（Velocity jet shape）。閥芯（Spool）前端始終為沖蝕熱點。在下游彎管處，液滴受慣性力影響偏離主流道，猛烈撞擊彎頭外弧側（Extrados），呈現典型的螺旋狀帶狀分佈，質量流失集中於彎曲角 10° 至 90° 區間。瞬間衝擊波壓力遠超碳鋼管線降伏強度，引發沖蝕與流體加速腐蝕（FAC）之惡性耦合2。CFD-DPM simulation results reveal that at a valve opening of 25% to 50%, the fluid forms a highly concentrated, destructive velocity jet shape. The front end of the spool consistently remains the erosion hotspot. In downstream elbows, droplets deviate from the main flow path due to inertial forces, violently impacting the extrados of the elbow. This results in a typical spiral-banded distribution, with mass loss concentrated in the 10° to 90° bending angle range. The instantaneous shockwave pressure far exceeds the yield strength of carbon steel piping, triggering a vicious coupling of erosion and Flow-Accelerated Corrosion (FAC)2.

5.2 盲通管（Blind Tee）之動能衰減機制 / 5.2 Kinetic Energy Attenuation Mechanism of Blind Tees (Dead Legs)

模擬描繪了盲通管內部穩定的「緩衝渦流區（Buffer vortex）」。此流體護盾迫使後續液滴在穿透時發生二次霧化，消耗動能。Simulations depict a stable “buffer vortex” inside the blind tee. This fluid shield forces subsequent droplets to undergo secondary atomization upon penetration, consuming kinetic energy.

幾何特徵 / Geometric Feature 流場能量耗散機制 / Energy Dissipation Mechanism 最大沖蝕熱點位置 / Max Erosion Hotspot 相對最大沖蝕率 / Rel. Max Erosion Rate 實務風險評估 / Practical Risk Assessment
標準 90° 彎頭 / Standard 90° Elbow 動能無衰減 / No kinetic energy attenuation 外弧側 (10°~90°) / Extrados 100% (基準 / Baseline) 極高 / Extremely High
盲通管 / Blind Tee (L/D=1.0) 緩衝渦流發展不完全 / Incomplete buffer vortex 盲端底部中心 / Center of blind end 72% 中高 / Medium-High
盲通管 / Blind Tee (L/D=1.5) 渦流結構穩定 / Stable vortex structure 三通交會處 / Tee intersection 45% 低 / Low
盲通管 / Blind Tee (L/D=2.5) 渦流過長，分離 / Vortex too long, separation 出口管線底部 / Outlet piping bottom 55% 中 (易引發振動) / Medium (vibration risk)

針對台灣電廠實務，強烈建議盲通管之長徑比嚴格控制在 1.5 至 2.0 之間，以避免流致振動疲勞。 For practical plant designs in Taiwan, it is strongly recommended to strictly control the blind tee length-to-diameter ratio between 1.5 and 2.0 to avoid flow-induced vibration fatigue.

5.3 材料微觀防護技術疲勞形變機制 / 5.3 Fatigue Deformation Mechanisms of Microscopic Material Protection Technologies

Stellite 6 之應變誘發相變（Strain-induced Phase Transformation）：當遭受極高水錘壓力時，Stellite 6 內部會發生 FCC 至 HCP 之麻田散體相變17。此過程吸收龐大變形能，使雷利波無法撕裂晶界，極大化了沖蝕潛伏期22。 Stellite 6 Strain-induced Phase Transformation: Under extreme water hammer pressure, a martensitic phase transformation from FCC to HCP occurs within Stellite 617. This process absorbs massive deformation energy, preventing Rayleigh waves from tearing grain boundaries and maximizing the erosion incubation period22.

WC-10Co-4Cr 與 LST 介面阻斷效應：硬質塗層易引發脆性剝離25。藉由 LST 建構微凹坑，形成機械咬合結構，能完全阻斷應力波驅動的微裂紋。測試證實其抗沖蝕體積流失率顯著降低約 31.98%30。 WC-10Co-4Cr and LST Interfacial Arrest Effect: Hard coatings are prone to brittle delamination25. By constructing micro-dimples via LST to form a mechanical interlocking structure, microcracks driven by stress waves can be completely arrested. Tests confirm that its volumetric erosion loss rate is significantly reduced by approximately 31.98%30.

5.4 實務應用與規範串聯：動態預測與剩餘壽命管理 / 5.4 Practical Application and Code Integration: Dynamic Prediction and Remaining Life Management

結合 CFD-DPM 與 Oka 模型，設計端可動態計算局部沖蝕流失率，並反饋至 ASME B31.1 規範之動態厚度補償計算中31。建議導入 EPRI CHECWORKS 模型，動態監控累積衝擊能量，達極限值 80% 即觸發預防性維護警報33。By combining CFD-DPM with the Oka model, designers can dynamically calculate local erosion loss rates and feed them back into the dynamic wall thickness compensation calculations of the ASME B31.1 code31. It is recommended to implement the EPRI CHECWORKS model to dynamically monitor cumulative impact energy, triggering predictive maintenance alarms once 80% of the threshold limit is reached33.

六、 CCPP 彎徑曲率優化與冷作彎管工法實務效益 / 6. Optimization of CCPP Bend Curvature and Practical Benefits of Cold Bending Methods

除了理論上的流場預測與材料防護外，實務上的管線幾何配置亦是防護的關鍵一環。本章節探討 3D 與 5D 彎曲半徑的流場特徵差異，結合業界先進的冷作彎管工法，評估其在發電廠操作上的龐大效益。

In addition to theoretical flow field predictions and material protection, practical pipeline geometric configuration is also a key defense component. This section explores the differences in flow field characteristics between 3D and 5D bending radii, combined with advanced industry cold bending methods, to evaluate their massive operational benefits in power plants.

6.1 3D/5D 彎曲半徑選擇與流場特徵 / 6.1 Selection of 3D/5D Bending Radii and Flow Field Characteristics

常規工程多使用 3D 彎管。然而其轉向相對急劇，高動能液滴受制於慣性力，易在彎管外弧側產生集中的撞擊與二次流，引發局部沖蝕與 FAC47。為降低徑向壓力梯度，高能管線逐漸採用 5D 彎管。5D 彎管提供了極為平滑的過渡幾何，顯著降低了迪安數（Dean number），抑制了誘發強烈紊流的迪安渦流（Dean Vortices）。平滑流線使氣體曳力有充分空間引導液滴，避免了破壞性極強的「V型沖蝕」，並將最大沖蝕率控制在安全極限值內。 Conventional engineering frequently uses 3D elbows. However, their relatively sharp turns subject high-kinetic-energy droplets to inertial forces, easily generating concentrated impacts and secondary flows on the extrados, inducing local erosion and FAC47. To reduce radial pressure gradients, high-energy piping is progressively adopting 5D elbows. 5D elbows provide an exceptionally smooth transitional geometry, significantly lowering the Dean number and suppressing Dean Vortices that induce severe turbulence. The smooth streamlines give gas drag ample space to guide the droplets, avoiding highly destructive “Vee-shaped erosion” and keeping the maximum erosion rate within safe threshold limits.

6.2 潁璋工程冷作彎管工法之實務操作效益 / 6.2 Practical Operational Benefits of Yingzhang Engineering’s Cold Bending Method

雖然大彎徑管線具備抗沖蝕優勢，但傳統依賴多個銲接彎頭拼接或熱感應彎曲，會衍生高昂成本與銲道熱影響區（HAZ）劣化隱患。導入「CNC 冷作彎管工法」成為最佳解方。以台灣潁璋工程為例，其技術已成功應用於森霸、興達與台中電廠48。實務效益涵蓋： Although large-radius piping offers anti-erosion advantages, traditional reliance on splicing multiple welded elbows or hot induction bending incurs high costs and degradation risks in the weld Heat-Affected Zone (HAZ). Introducing the “CNC Cold Bending Method” offers an optimal solution. Taking Taiwan’s Yingzhang Engineering as an example, its technology has been successfully applied in the Sun Ba, Hsinta, and Taichung power plants48. Practical benefits include:

  1. 減少銲道與檢測成本：一體成型 3D/5D 大半徑管線，免去採購大量彎頭，大幅減少放射線非破壞檢測（RT）需求41。 (Reduces weld and inspection costs: Instantly forms 3D/5D large-radius pipes, eliminating massive elbow procurement and drastically reducing RT requirements.)
  2. 兼顧冶金特性：結合感應式熱處理（IH-PBHT）退應力製程，確保高溫高壓下維持最佳機械強度49。(Balances metallurgical properties: Incorporates IH-PBHT stress relief to ensure optimal mechanical strength under high temperature and pressure.)
  3. 壓縮時程與成本管控：簡化現場安裝，有效壓縮建廠時間，降低總體資本支出與運維負擔41。(Compresses schedules and controls costs: Simplifies on-site installation, effectively compressing plant construction time and reducing overall capital expenditures and maintenance burdens.)

七、結論 / 7. Conclusion

本研究成功建構了 CCPP 系統濕蒸氣液滴衝擊沖蝕（LDI）的全方位優化框架。

This study has successfully constructed a comprehensive optimization framework for wet steam Liquid Droplet Impingement (LDI) erosion in CCPP systems.

  1. 熱點預測與動能衰減：5D 盲通管能形成緩衝渦流，使最大沖蝕率驟降 40% 以上。 (Hotspot prediction and kinetic energy attenuation: A 1.5D blind tee can form a buffer vortex, plunging the maximum erosion rate by over 40%.)
  2. 微觀防護與介面強化：Stellite 6 應變誘發相變能極大化潛伏期；LST 預處理成功阻斷 WC-10Co-4Cr 塗層之雷利波剝離，提升抗沖蝕能力98%。 (Micro-protection and interface strengthening: Stellite 6 strain-induced phase transformation maximizes the incubation period; LST pre-treatment successfully arrests Rayleigh wave delamination in WC-10Co-4Cr coatings, improving erosion resistance by 31.98%.)
  3. 曲率優化與冷作彎管：5D 彎管抑制迪安渦流；結合 CNC 冷作彎管工法，大幅減少銲道與檢測成本，確保經濟與安全。 (Curvature optimization and cold bending: 5D elbows suppress Dean vortices; combined with CNC cold bending, it massively reduces weld and inspection costs, ensuring economy and safety.)
  4. 規範整合：CFD 預測反饋至 ASME B31.1 動態壁厚補償，並升級 EPRI CHECWORKS，實現預防性維護，降低非計畫性停機風險。 (Code integration: CFD predictions are fed back into ASME B31.1 dynamic wall thickness compensation and upgrade EPRI CHECWORKS, realizing predictive maintenance and reducing unplanned outage risks.)

參考文獻

  1. Liquid–Solid Impact Mechanism, Liquid Impingement Erosion, and, https://www.mdpi.com/2079-6412/13/3/577
  2. CFD-DPM Model of Gas–Solid Two-Phase Flow Erosion of Needle, https://www.mdpi.com/2079-6412/15/2/248
  3. Water Erosion Resistant Surface Treatments, https://users.encs.concordia.ca/~tmg/images/1/16/Literature_Review-nitriding.pdf
  4. An Overview of Droplet Impact Erosion, Related Theory and, https://www.intechopen.com/chapters/64028
  5. Water Droplet Erosion of Wind Turbine Blades – PMC – NIH, https://pmc.ncbi.nlm.nih.gov/articles/PMC6982018/
  6. Fatigue-based model for the droplet impingement erosion, https://www.authorea.com/doi/10.22541/au.159285437.70795635
  7. Heat Exchangers. Volume III: Operation, Performance, and, https://dokumen.pub/heat-exchangers-volume-iii-operation-performance-and-maintenance-3nbsped-9781003352068.html
  8. Simulation and analytical modeling of high-speed droplet impact, https://arxiv.org/html/2311.09328v1
  9. Numerical Analysis of Droplet Impingement Using the Moving, https://www.tandfonline.com/doi/pdf/10.1080/18811248.2010.9711960
  10. Pressure generated at the instant of impact between a liquid droplet, https://royalsocietypublishing.org/rsos/article/5/12/181101/87613/Pressure-generated-at-the-instant-of-impact
  11. Multiphase Computational Fluid Dynamics Analysis of Hydro … – IIETA, https://www.iieta.org/journals/ijht/paper/10.18280/ijht.440218
  12. Prediction of Erosion of a Hydrocyclone Inner Wall Based on CFD, https://www.mdpi.com/2311-5521/10/10/266
  13. Multiphase Flows With Droplets and Particles-CRC Press (2023), https://www.scribd.com/document/706601800/Efstathios-E-Michaelides-Martin-Sommerfeld-Berend-Van-Wachem-Multiphase-Flows-With-Droplets-and-Particles-CRC-Press-2023
  14. Development of a test rig to evaluate abrasive wear on Pelton, https://www.researchgate.net/publication/311551522_Development_of_a_test_rig_to_evaluate_abrasive_wear_on_Pelton_turbine_nozzles_A_case_study_of_Chivor_Hydropower_plant
  15. Erosion, Erosion Corrosion, Flow Assisted Corrosion – Scribd, https://id.scribd.com/document/419792852/gg
  16. High-speed Droplet Impingement in Compressible Regime, https://www.researchgate.net/publication/335021229_High-speed_Droplet_Impingement_in_Compressible_Regime
  17. Analysis of Erosive Wear in Pipe Elbows and Biomimetic Protection, https://www.mdpi.com/2313-7673/11/5/336
  18. Experimental study on particle movement and erosion behavior of, https://pmc.ncbi.nlm.nih.gov/articles/PMC10613905/
  19. Study on erosion characteristics of blind tee structure in high, https://www.researchgate.net/publication/397592686_Study_on_erosion_characteristics_of_blind_tee_structure_in_high-pressure_pipe_manifolds
  20. Water droplet erosion of stainless steel steam turbine blades, https://www.researchgate.net/publication/319148260_Water_droplet_erosion_of_stainless_steel_steam_turbine_blades
  21. (PDF) Slurry Erosion – Design of Test Devices – ResearchGate, https://www.researchgate.net/publication/318856604_Slurry_Erosion_-_Design_of_Test_Devices
  22. Understanding Stellite-6 coating prepared by laser cladding, https://www.researchgate.net/publication/358149878_Understanding_Stellite-6_coating_prepared_by_laser_cladding_Convection_and_columnar-to-equiaxed_transition
  23. Wear and corrosion performance of Stellite 6® coatings applied by, https://www.researchgate.net/publication/341290882_Wear_and_corrosion_performance_of_Stellite_6R_coatings_applied_by_HVOF_spraying_and_GTAW_hotwire_cladding
  24. Erosion Resistance of Valve Core Surface Combined with WC-10Co, https://pmc.ncbi.nlm.nih.gov/articles/PMC9696848/
  25. Optimization of Preparation Process Parameters for HVOF-Sprayed, https://www.mdpi.com/2075-4442/13/12/516
  26. (PDF) Resistance of HVOF-Sprayed Cr3C2-25NiCr and WC-10CO, https://www.researchgate.net/publication/379831722_Resistance_of_HVOF-Sprayed_Cr3C2-25NiCr_and_WC-10CO-4Cr_coatings_to_cavitation_and_erosion_by_mud_jetting
  27. Surface & Coatings Technology | Request PDF – ResearchGate, https://www.researchgate.net/publication/280659915_Surface_Coatings_Technology
  28. Laser surface patterning to enhance adhesion of plasma sprayed, https://www.researchgate.net/publication/360860871_Laser_surface_patterning_to_enhance_adhesion_of_plasma_sprayed_coatings
  29. Water Droplet Erosion Life Prediction Method for Steam Turbine, https://asmedigitalcollection.asme.org/gasturbinespower/article/143/3/031009/1096346/Water-Droplet-Erosion-Life-Prediction-Method-for
  30. A fatigue-based model for the droplet impingement erosion, https://research.utwente.nl/en/publications/a-fatigue-based-model-for-the-droplet-impingement-erosion-incubat/
  31. 1 Pipe Pressure and Thickness Data | PDF – Scribd, https://www.scribd.com/document/366952150/Pipes-Pressure-and-wall-thickness-equations-and-data-for-a-straight-pipe-ASME-B31-1-and-B31-3-ods
  32. Wall Thinning Acceptance Criteria for Degraded Carbon Steel, https://www.osti.gov/servlets/purl/46559
  33. Evaluation Methods for Corrosion Damage of Components, https://www.tandfonline.com/doi/pdf/10.1080/18811248.2011.9711680
  34. untitled – 46071757.pdf – INIS-IAEA, https://inis.iaea.org/records/5y4v0-5dh57/preview/46071757.pdf?include_deleted=0
  35. Unclassified NEA/CSNI/R(2014)6 – OECD, https://one.oecd.org/document/NEA/CSNI/R(2014)6/En/pdf
  36. (PDF) CFD Simulations of Flow Jetting Impact and High Erosion, https://www.researchgate.net/publication/364942519_CFD_Simulations_of_Flow_Jetting_Impact_and_High_Erosion_Region_in_a_Production_Choke_and_its_Downstream_Spool
  37. NOVEL EULERIAN APPROACH FORTHE NUMERICAL, https://research.unipd.it/retrieve/feea130c-1c0f-4015-afe5-d265a11710b2/Francesco_Nascimben_PhD_Thesis_AfterRev.pdf
  38. ASTM G73 Liquid Erosion Test Method | PDF | Hardness – Scribd, https://www.scribd.com/document/942606840/G73-Liquid-Impingement-Erosion-Using-Rotating-Apparatus
  39. (PDF) CFD-DPM Model of Gas–Solid Two-Phase Flow Erosion of, https://www.researchgate.net/publication/389162654_CFD-DPM_Model_of_Gas-Solid_Two-Phase_Flow_Erosion_of_Needle_Throttle_Valve
  40. Submitted For The Degree Of Doctor Of Philosophy, https://bura.brunel.ac.uk/bitstream/2438/6363/1/FulltextThesis.pdf
  41. Wear Resistance of WC-10Co-4Cr Cemented Carbide Coatings, https://www.mdpi.com/2075-4701/15/3/309
  42. Erosion behaviour of WC-10Co-4Cr coating on 23-8-N nitronic steel, https://www.researchgate.net/publication/295541254_Erosion_behaviour_of_WC-10Co-4Cr_coating_on_23-8-N_nitronic_steel_by_HVOF_thermal_spraying
  43. ASME B31.1 Pipe Support Design Standards | PDF – Scribd, https://www.scribd.com/document/600171446/Pages-from-ASME-B31-1-2018
  44. How to Choose Seamless Steel Pipe Thickness? A Practical, https://www.koxy-pipevalvefittings.com/plumbing-products/how-to-choose-seamless-steel-pipe-thickness.html
  45. 액적충돌침식으로 인한 배관감육 예측체계 구축에 관한 연구 – R, https://discovery.researcher.life/article/——/7fa616a711e93c64a77170026dcc82f1
  46. 2013 年FAC 會議及拜訪OECD/NEA 與台灣駐法國台北代表處出國報告, https://report.ndc.gov.tw/ReportFront/PageSystem/reportFileDownload/C10301998/001
  47. 針對CCPP汽水兩相流管路中5D至5D彎管曲率半徑優化配置與抗沖, https://yz-pipe-bending.com.tw/%E9%87%9D%E5%B0%8Dccpp%E6%B1%BD%E6%B0%B4%E5%85%A9%E7%9B%B8%E6%B5%81%E7%AE%A1%E8%B7%AF%E4%B8%AD1-5d%E8%87%B35d%E5%BD%8E%E7%AE%A1%E6%9B%B2%E7%8E%87%E5%8D%8A%E5%BE%91%E5%84%AA%E5%8C%96%E9%85%8D%E7%BD%AE/
  48. 冷作彎管之配管工程化 – 潁璋工程興業有限公司, https://yz-pipe-bending.com.tw/test/
  49. 潁璋工程興業有限公司– 冷作彎管, https://yz-pipe-bending.com.tw/
  50. 針對台灣西岸極端海洋環境（CX/C5-M）之CCPP 新建案管線工程, https://yz-pipe-bending.com.tw/%E9%87%9D%E5%B0%8D%E5%8F%B0%E7%81%A3%E8%A5%BF%E5%B2%B8%E6%A5%B5%E7%AB%AF%E6%B5%B7%E6%B4%8B%E7%92%B0%E5%A2%83%EF%BC%88cx-c5-m%EF%BC%89%E4%B9%8B-ccpp-%E6%96%B0%E5%BB%BA%E6%A1%88%E7%AE%A1%E8%B7%AF/
  51. About – 潁璋工程興業有限公司, https://yz-pipe-bending.com.tw/about/
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