流線型形狀阻力之修正模型：計算與實驗分析

Abstract

船舶在航行中所受之總阻力主要可分為摩擦阻力與形狀阻力兩大部分，其中形狀阻力主要由船體幾何所引發之壓力分布差異與流體分離所致，即使對於流線型船體亦不容忽視。為量化船體幾何對黏性壓力阻力的影響，Hughes 方法引入形狀因子（form factor）之概念，並將總阻力係數拆解為平板摩擦係數與形狀因子所放大的黏性壓力阻力項。 在實驗應用上，Prohaska 方法被廣泛用於估算形狀因子，其假設波浪阻力與福勞德數具有多項式關係，常以福勞德數的次方項作為橫軸進行回歸擬合，由低速試驗數據推估出形狀因子（1+K）。為提升線性擬合效果，實務上常根據數據趨勢調整次方項，一般介於 4 至 6 之間，然而近年研究指出，形狀因子實際上會隨雷諾數而變化，挑戰傳統「形狀因子為定值」的假設，並引發尺度外推上的誤差與不確定性。 為改善此問題，本研究提出一套穩定的線性估算方法，透過總阻力係數與平板摩擦係數間之線性關係，取代傳統形狀因子定義。研究結合拖曳水槽實驗與 CFD 模擬，針對球艏油輪與 SUBOFF 模型在多組雷諾數與福勞德數條件下進行分析，並探討壓力與剪應力分布對阻力構成的影響。結果顯示，總阻力與平板摩擦阻力具穩定的線性關係，並可於不同條件下保持一致性，有效降低尺度外推誤差。 進一步從物理角度分析，發現艉部壓力分布受雷諾數影響而產生變化，而剪應力分布則相對穩定，驗證所提模型具備物理依據。該方法不僅能提升阻力預測之準確度，亦簡化傳統流程，具備推廣至多船型與多尺度條件之潛力。雖然目前在實驗條件下尚難以於固定福勞德數下調整流體黏滯度，但於 CFD 模擬環境中，本方法已展現高度應用價值，為船舶水動力性能評估提供嶄新之預測框架。

Total resistance of a ship generally consists of skin friction and form drag. Form drag arises from pressure distribution differences and flow separation induced by hull geometry and remains significant even for streamlined hull forms. To quantify the influence of hull shape on viscous pressure resistance, Hughes method introduced the concept of form factor, which scales flat-plate friction coefficient to account for three-dimensional effects. In experimental applications, Prohaska method is widely used to estimate form factor. It assumes a polynomial relationship between wave-making resistance and Froude number, and commonly uses powers of Froude number as the horizontal axis for regression fitting. To improve linearity, the exponent is often adjusted based on the trend of the data, typically ranging from 4 to 6. However, recent studies have shown that form factor may vary with Reynolds number, challenging the conventional assumption of its constancy and introducing scale-effect-induced uncertainty during extrapolation. To address this issue, this study proposes a stable linear estimation approach that eliminates the need for a predefined form factor by establishing a direct linear relationship between total resistance coefficient and flat-plate friction coefficient. The methodology integrates towing tank experiments and CFD simulations conducted using Star-CCM+ for a bulbous bow tanker and DARPA SUBOFF model under various Reynolds and Froude number conditions. Shear stress and pressure distribution analyses were conducted to examine the physical origin of the observed linearity. Results demonstrate a robust linear relationship that holds consistently across different Reynolds numbers. Stern pressure distribution was found to change with Reynolds number, while shear stress distribution remained relatively stable, supporting the physical validity of the proposed model. The method not only enhances prediction accuracy but also simplifies conventional workflow, offering potential scalability across different hull types and operating conditions. Although adjusting viscosity at a fixed Froude number is currently infeasible in experimental setups, the method proves highly practical in CFD frameworks and provides a novel, physically grounded approach to ship resistance prediction.