1. Introduction
Speed performance remains crucial for ships, particularly military vessels [
1]. As ships navigate through dual mediums, water and air resistance considerably affect their swiftness, and optimising ship form is vital to mitigating this resistance. Installing energy-saving appendages can enhance resistance performance for vessels with established forms. Currently, the preferred stern appendages for medium- to high-speed ships include wave stern flaps (SFs) [
2] and interceptors [
3]. SF, designed to suppress waves at the stern to reduce wave-making resistance, is increasingly used on planing boats, destroyers, frigates, and other military ships. Interceptors, typically mounted vertically downward on the stern transom plate, occupy less space and offer simpler operation and control than SFs, thereby gaining traction over the past decade.
Research on SF and interceptors can be divided into two. The first is stern appendage mechanism analysis based on simplified modelling. Brizzolara [
4] and Brizzolara and Salian [
5] numerically solved the flow field around a two-dimensional interceptor using a computational fluid dynamics (CFD) solver. The velocity and pressure distributions and other flow field information in the interceptor installation area were analysed to summarise the hydrodynamic mechanism of the interceptor. Deng et al. [
6] studied the interceptor mechanism by simplifying the three-dimensional hull into a two-dimensional flat plate and investigating flow details such as velocity, pressure, and vorticity fields under interceptors of different heights. Using Reynolds-averaged Navier–Stokes (RANS) equations, Mansoori et al. [
7] simulated the flow field around a fixed plate with an interceptor at different heights and angles of attack and compared the numerical results with the experimental data, demonstrating that the thickness of the boundary layer varies by speed, thereby affecting the efficiency of the interceptor. Jacobi et al. [
8] employed particle image velocimetry (PIV) to measure the velocity field in the stern area before and after interceptor installation and reconstructed the pressure load to analyse the blocked flow and high-pressure peak caused by the installation. They reconstructed the three-dimensional flow field by scanning PIV flow field information at multiple sections and analysing the measurement uncertainty and lift change caused by the interceptor.
The second approach involves analysing how appendages such as SFs and interceptors impact resistance and sailing posture in calm waters. Tsai and Hwang [
9] examined the effects of interceptor and SF combinations on planing craft resistance, highlighting that well-designed appendages can diminish trim angle and cut resistance by 2–6%. John et al. [
10] assessed stern energy-saving devices such as stern wedges, flaps, and interceptors. De Luca and Pensa [
11] introduced unconventional SF designs and empirically compared them with conventional designs. Mansoori et al. [
12,
13,
14] extensively explored interceptor use on planing vessels. Using a finite-volume dynamic mesh model, they numerically simulated planing ship models with and without interceptors or combined appendages, demonstrating that the primary purpose of interceptors or combined appendages is to modulate sailing posture and counteract the proposed instability by generating a high-pressure region at the stern. Maki et al. [
15] used the DTMB5415 ship model to experimentally and virtually explore the influence of SFs on ship resistance performance, revealing that resistance reduction primarily arises from SF-induced enhancements in the stern flow field. Avci and Barlas [
16] experimentally assessed the impact of the lateral positioning of the interceptor on its resistance-reducing capabilities and obtained results supporting this theory. Their findings suggested that the SF can be segmented for individualised control to optimise interceptor efficacy. Deng et al. [
17] numerically examined interceptor impact on the viscous flow field of deep-V vessels, focusing on alterations in resistance, lift, and distributions of base pressure and stern velocity. Budiarto et al. [
18] numerically probed the effects of the SF on the resistance components of planing vessels and determined that ship and component resistance can be achieved by adjusting the pitch and heavy value of the ship to decrease its displacement.
CFD technology is increasingly applied in seakeeping simulations [
19,
20]. Sun et al. [
21] simulated SWATH vehicles to assess wavelength- and speed-dependent pitch and heave transfer function alterations. Niklas and Pruszko [
22] simulated how bow profiles modify resistance and wave-induced motion response in full-scale ships. Gong et al. [
23] numerically analysed the added resistance and seakeeping properties of trimarans under various oblique wave circumstances, revealing a motion amplitude trend different from that of monohull ships. Guan et al. [
24] auto-optimised the design of ship types using an Excel/STAR-CCM+ platform, focusing on wave-induced resistance and pitch amplitude.
By further assessing the seakeeping capabilities of stern appendages, Day and Cooper [
25] analysed interceptor influence on sailing yachts in serene waters and minimal wave conditions, demonstrating reduced resistance under minor wave circumstances. Rijkens et al. [
26] modified the interceptor form by adding a substantial circular transition section between the hull’s base and the interceptor and used predictive ship motion software to show that this configuration reduces vertical peak accelerations. Karimi et al. [
27] integrated testing and theoretical approaches to evaluate how auto-controlled interceptors could dampen vertical ship motion. Park et al. [
28] empirically investigated how controllable interceptors impact high-speed planing craft vertical motions and analysed pitch motion variances in regular and irregular waves. Wang et al. [
29] numerically analysed the SF impact on catamaran speedboat single-speed seakeeping traits. Li et al. [
30] numerically analysed a trimaran vessel fitted with a T-foil and SF, focusing on wave steepness variation impact on ship motion and the forces exerted on the T-foil.
Reviewing existing research on interceptors and SF reveals numerous studies relating to their mechanisms or analysing resistance reduction effects in calm waters; however, comprehensive comparative studies addressing the resistance and seakeeping performance of these appendages in wave conditions, particularly in semi-displacement vessels, are limited. Based on previous calm-water work by Song et al. [
31], we employed numerical simulations across diverse wave conditions to contrast resistance reduction effects under wave conditions and calm waters. By examining the variance in pitch and heave transfer functions relative to wavelength and steepness, we sought to discern the underlying mechanisms affecting ship resistance and movement from a hydrodynamical perspective. Our findings offer invaluable insights and practical guidance for designing and applying stern appendages.