Research on shipping energy-saving technology: Hydrofoil amphibious vehicle driven by waterjet propulsion
船舶节能技术研究--喷水推进水翼两栖艇

Bolong Liu, Xiaojun Xu, Dibo Pan *, Xiaocong Wang
刘博龙，徐晓军，潘迪波 *，王晓聪College of Intelligence Science and Technology, National University of Defense Technology, Changsha, 410073, China
国防科学技术大学智能科学与技术学院，长沙，410073

ARTICLE INFO 产品信息

Keywords: 保留字：

Carbon emissions 碳排放
Energy saving technology 节能技术
Amphibious vehicle 两栖车辆
Hydrofoil 水翼
Waterjet propulsion 喷水推进
Hydrodynamic characteristics
水动力特性

Abstract 摘要

The shipping industry is one of the crucial sources of carbon emissions. With carrying capacity both on land and water, the hydrodynamic characteristics of amphibious vehicles are essential indicators of energy saving and emission reduction. The hydrodynamic characteristics of an amphibious vehicle driven by a single waterjet propulsion are investigated in this study, together with the impact of the NACA0012 hydrofoil mounted at the bow and stern. Based on the RANS and body force methods, the hydrodynamic calculation models of the bare hull and waterjet-driven hull are established. All CFD calculations are based on STAR-CCM+. Based on the towing experiment, an uncertainty analysis is conducted to confirm the precision and legitimacy of the numerical calculation approach. The thrust deduction characteristics of vehicle hulls with different hydrofoil models are analyzed respectively. Small or negative thrust deductions always occur at medium and high speeds. Combined with the analysis of vehicle attitude, flow field, and pressure distribution, the inherent thrust deduction characteristics of the amphibious vehicle and the influence of hydrofoils are studied. Then, the hydrodynamic characteristics of different configurations are compared. The lift characteristics of hydrofoils and their influence on the vehicle’s attitude and resistance are studied. The change in the performance of the stern hydrofoil caused by the waterjet propulsion is analyzed. Results show that the hull with two hydrofoils has the best drag-reduction effect when $Fr < 1.43$ , and the highest drag-reduction rate is $25.7 %$ .
航运业是碳排放的重要来源之一。水陆两栖车辆兼具水陆两种运载能力，其水动力特性是其节能减排的重要指标。研究了单喷水推进两栖车辆的水动力特性，以及安装在船头和船尾的NACA 0012水翼的冲击。基于RANS法和体积力法建立了裸船体和喷水推进船体的水动力计算模型。所有CFD计算均基于STAR-CCM+。基于拖航试验，对数值计算方法进行了不确定度分析，验证了数值计算方法的准确性和合理性。分析了不同水翼模型的船体推力减力特性。小的或负的推力扣除总是发生在中速和高速。结合对两栖车辆姿态、流场和压力分布的分析，研究了两栖车辆固有推力的减小特性及水翼的影响。比较了不同构型的水动力特性。研究了水翼的升力特性及其对航行器姿态和阻力的影响。分析了喷水推进对尾水翼性能的影响。结果表明，带双翼的船体在 $Fr < 1.43$ 时减阻效果最好，在 $25.7 %$ 时减阻率最高。

1. Introduction 1.介绍

With the growing attention on energy conservation and environmental protection, a series of policies to promote energy saving and pollution emissions reduction has been issued. The shipping industry is one of the crucial sources of carbon emissions. Reducing energy consumption and carbon emissions during the transportation is an effective means to promote carbon neutrality. With walking mechanisms on land, the additional resistance per unit displacement of amphibious vehicles is more significant than that of traditional ships. In order to increase sailing speed, engines with higher power are often adopted to get greater thrust, resulting in a decline in energy efficiency and higher energy loss. Therefore, the research on the drag reduction and energy-saving technology of amphibious vehicles is significant in reducing carbon emissions and protecting the environment.
随着节能环保的日益重视，一系列促进节能减排的政策相继出台。航运业是碳排放的重要来源之一。减少运输过程中的能源消耗和碳排放是促进碳中和的有效手段。两栖车辆在陆地上使用行走机构，单位排水量的附加阻力比传统船舶更显著。为了提高航速，往往采用功率更大的发动机来获得更大的推力，导致能效下降，能量损失更大。因此，研究两栖车辆减阻节能技术对减少碳排放、保护环境具有重要意义。

Unlike traditional ships and vehicles, an amphibious vehicle’s walking mechanisms on land and water need to compromise with each other. In order to ensure the moving and obstacle-crossing ability on the road, the overall hull size and the walking mechanism position are
与传统的船舶和车辆不同，两栖车辆的陆地和水上行走机构需要相互妥协。为保证在道路上的移动和越障能力，对船体总体尺寸和行走机构位置进行了设计，
limited, resulting in added energy consumption on water. On the other hand, to reduce energy consumption on water, its propulsion system, transmission mechanism, and lifting walking mechanism all need to be specially designed, which have a specific impact on the weight and stiffness of the chassis. The waterjets and propellers are widely used for moving on water, and wheels and tracks are mainly used on land (Ehrlich et al., 1970). Waterjet propulsions are often used to provide high power for high-speed amphibious vehicles (Nenashev et al., 2020). As for moving on land, the wheels are conducive to flexibility (Xie et al., 2017), and the crawler is conducive to obstacle-crossing ability (Marquardt et al., 2014). This study aims to explore a larger optimization space for hydrodynamic performance and energy consumption of amphibious vehicles with the limit of land-moving performance.
有限，导致水的能源消耗增加。另一方面，为了减少水上能耗，其推进系统、传动机构、升降行走机构都需要专门设计，这对底盘的重量和刚度有特定的影响。喷水推进器和螺旋桨广泛用于水上移动，而轮子和履带主要用于陆地上（埃利希等人，1970年）。喷水推进器通常用于为高速两栖车辆提供高功率（Nenashev等人，2020年）。至于在陆地上移动，轮子有利于灵活性（Xie等人，2017年），并且履带车有利于跨越障碍物的能力（马夸特等人，2014年）。本研究旨在探索水陆两栖车辆在陆地行驶性能受限的情况下，其水动力性能和能耗有更大的优化空间。

The small aspect ratio of amphibious vehicles and their nonstreamlined shapes are essential sources of additional resistance. At present, the drag reduction methods adopted on amphibious vehicles mainly include the walking mechanism lifting technology, the bow and stern planing plate, and the planing hulls (Behara et al., 2020; Helvacioglu et al., 2011; Kemp, 2001; Latorre and Arana, 2011; Lee et al.,
两栖车辆的小展弦比和非流线型外形是附加阻力的重要来源。目前，两栖车辆上采用的减阻方法主要有行走机构升降技术、艏艉滑行板、滑行船体（Behara et al. 2020; Helvacioglu等人，2011;肯普，2001;拉托雷和阿拉纳，2011;李等人，

2017). Gibbs has developed a single-seat light amphibious vehicle (Behara et al., 2020), which has good hydrodynamic characteristics through a retraction technology of the walking mechanism. However, the structure of the retraction mechanism is complex and more sensitive to weight, so it is often used in small and light amphibious vehicles. The lifting mechanism is more common in amphibious vehicles (Bratan et al., 2018). The amphibious vehicle’s hull can be given extra lifting force by installing bow and stern planing plates, which can lower the displacement volume and resistance. In addition, the bow planing plate can suppress the bow wave, and the stern plate can increase the virtual length of the hull and suppress excessive ‘rooster flow’, thereby improving the flow field and sailing attitude of the vehicle (Latorre and Arana, 2011; Lee et al., 2017). In addition to the bow and stern plates, flanks installed on the concave grooves can also play a noticeable drag reduction effect (Pan et al., 2021). Since the resistance increase is caused by a lot of prominent sites of the vehicle surface, optimized designs of the shape and structure can also play a significant role in reducing resistance and increasing speed (Duan et al., 2015; Liu et al., 2022; Marquardt et al., 2014).
2017年）的报告。吉布斯已经开发了一种单座轻型两栖车辆（Behara等人，2020），其通过行走机构的缩回技术而具有良好的流体动力学特性。但伸缩机构结构复杂，对重量较敏感，因此常用于小型、轻型两栖车辆。提升机构在两栖车辆中更为常见（Bratan等人，2018年）。两栖车辆船体通过安装艏、艉滑行板，可以获得额外的升力，降低排水量和阻力。此外，船首滑行板可以抑制船首波浪，船尾板可以增加船体的虚拟长度，抑制过度的“公鸡流”，从而改善车辆的流场和航行姿态（Latorre和Arana，2011; Lee等人，2017年）的报告。除了船头和船尾板，安装在凹槽上的侧翼也能起到明显的减阻效果（Pan等人，2021年）。由于阻力增加是由车辆表面的许多突出部位引起的，因此形状和结构的优化设计也可以在降低阻力和提高速度方面发挥重要作用（Duan等人，2015年; Liu等人，2022;马夸特等人，2014年）。

The above researches list various resistance-reduction methods for amphibious vehicles. However, limited by the lack of published research, there are still many aspects to be studied in the field of amphibious vehicle hydrodynamics. The research on the characteristics of hydrofoils and waterjet propulsions on amphibious vehicles helps provide solutions for more efficient water sailing.
上述研究列出了各种两栖车辆的减阻方法。但受限于发表的研究较少，两栖车辆流体动力学领域仍有许多方面有待研究。对两栖车辆的水翼和喷水推进特性的研究有助于为更有效的水上航行提供解决方案。

The hydrofoil has the same principle as airfoils; they all use the dynamic lift generated on the foil to lift the body. For amphibious vehicles, the dynamic lift can help to reduce displacement and resistance. At present, much research has been carried out on hydrofoils (Ismail et al.). analyzed the effect of different hydrofoil types and shapes on the lift and resistance of ships. Results show that rectangular fully submerged foil has the best drag reduction effect, and the best rate can reach 17.822% (Bi et al., 2019). conducted a study on the hydrodynamic characteristics of planning craft in regular waves with hydrofoils. The parameters such as hydrofoil attack angle, installation height, and craft sailing speed were studied. The results show that an appropriate negative attack angle and lower installation height can improve the seakeeping performance of the boat, and the effect becomes more significant with the increase in speed (Bøckmann and Steen, 2016). installed two fixed bow-mounted foils on the bow, which can provide a drag reduction effect of

9 % -

17 %

in head seas and has a certain mitigation effect on both heave and trim. Compared with the extensive research on hydrofoil boats, in the current public reports, there is still a lack of research on hydrofoils installed on amphibious vehicles. One of the main reasons is the concern about the impact of hydrofoils on the land performance of amphibious vehicles.
水翼与机翼具有相同的原理;它们都使用在翼上产生的动态升力来提升身体。对于两栖车辆，动态升力可以帮助减少位移和阻力。目前，许多研究已经进行了水翼（伊斯梅尔等人）。分析了不同的水翼型式和形状对船舶升力和阻力的影响。结果表明，矩形全淹没翼型的减阻效果最好，最大减阻率可达17.822%（Bi et al.，2019年）。研究了带水翼滑行艇在规则波中的水动力特性。研究了水翼攻角、安装高度、艇速等参数对水翼性能的影响。结果表明，适当的负攻角和较低的安装高度可以提高艇的耐波性，并且随着航速的增加，效果变得更加显著（Bøckmann and Steen，2016）。在船首安装了两个固定的船首安装翼片，可以在头浪中提供

9 % -

1#的减阻效果，并且对垂荡和纵倾都有一定的缓解效果。与对水翼艇的广泛研究相比，在目前的公开报道中，对安装在两栖车辆上的水翼的研究还比较缺乏。其中一个主要原因是担心水翼对两栖车辆陆地性能的影响。

Waterjet propulsions also significantly affect the analysis of hull resistance, which can be evaluated by thrust deduction (Eslamdoost et al., 2018). In all of the studies on waterjet propulsions, there are two standard numerical simulation methods for the pump system: modeling real pump geometry and using body force models (Eslamdoost and Vikström, 2019). Compared with the former method, the latter, with the advantage of low calculating cost, is more suitable for research only interested in the import and export flow (Takai et al., 2011). analyzed the influence of waterjet propulsion on a ship using simplified body force models, and the results show that this model can accurately predict the self-propulsion performance (Rhee and Coleman, 2009). studied the flow field of waterjet propulsion based on the RANS method, and the actuator disk based on the body force method was used to simulate the real pump. The research shows that this method can effectively estimate the capture area by tracking the streamline into and out of the control volume (Delaney et al., 2009). adopted the RANS method with momentum and energy flux method to analyze the waterjet system of a High-Speed Sealift Concept Vessel. Compared with the experimental data, the error of full scale powering prediction is less than

2 %

.
喷水推进器还显著影响船体阻力的分析，其可以通过推力扣除来评估（Eslamdoost等人，2018年）。在所有关于喷水推进的研究中，泵系统有两种标准的数值模拟方法：建模真实的泵几何形状和使用体积力模型（Eslamdoost和Vikström，2019）。与前一种方法相比，后一种方法具有计算成本低的优点，更适合于只对进出口流感兴趣的研究（Takai et al.，2011年）的报告。使用简化的体积力模型分析喷水推进对船舶的影响，结果表明该模型可以准确预测自航性能（Rhee and科尔曼，2009）。基于RANS方法对喷水推进器的流场进行了研究，并采用基于体积力法的作动盘对真实的泵进行了模拟。研究表明，该方法通过跟踪流线进出控制体积，可以有效地估计捕获面积（Delaney等，2009年）。采用动量和能量通量法结合的RANS方法，对高速海运概念船喷水推进系统进行了分析。与实验数据相比，满量程功率预测误差小于0#。

Although there are many studies on the independent characteristics
虽然有很多关于独立性的研究
of waterjet propulsion and hydrofoils, their coupling has not been publicly studied. Hydrofoils will change the hull attitude and flow field, affecting the power and efficiency of the waterjet, and the waterjet’s suction will change the flow field around the hydrofoil. The study of the interaction between them helps tap their potential more deeply.
喷水推进和水翼，他们的耦合还没有公开研究。水翼会改变船体的姿态和流场，从而影响喷水推进器的功率和效率，而喷水推进器的吸力又会改变水翼周围的流场。研究他们之间的互动关系有助于更深入地挖掘他们的潜力。

This study focuses primarily on a high-speed amphibious vehicle’s hydrodynamic properties. The hydrofoil controlling mechanism based on a double rocker is creatively designed. With the combination of hydrofoil controlling mechanisms and lifting walking mechanisms, the interference of hydrofoils on the land motion is solved, providing feasibility for applying hydrofoils on the amphibious vehicle. A type of shallowly submerged hydrofoil installed at the vehicle bow and stern is designed based on NACA0012, and the drag reduction principle of the hydrofoil is analyzed. To solve the matching problem of hydrofoils and waterjet propulsion in amphibious vehicles, these two are studied together in this paper for the first time. The body force method is adopted to analyze the effect of the waterjet propulsion on hull resistance, and the thrust deduction at different speeds is calculated and explained by flow field and pressure distribution. Combined with the study of thrust deduction, different combination models of hull and hydrofoils are studied, and the effects of hydrofoils installation on amphibious vehicle hydrodynamics are analyzed and evaluated. The process and conclusions of this study can provide a reference for drag reduction and energy saving in the shipping field.
本文主要研究高速两栖车辆的水动力特性。创新性地设计了基于双摇杆的水翼操纵机构。将水翼控制机构与升降行走机构相结合，解决了水翼对陆地运动的干扰，为将水翼应用于水陆两栖车辆提供了可行性。基于NACA0012设计了一种安装在航行器首尾的浅潜式水翼，分析了该水翼的减阻原理。为解决两栖车辆中水翼与喷水推进的匹配问题，本文首次将两者结合起来进行研究。采用体积力法分析了喷水推进对船体阻力的影响，计算了不同航速下的推力减额，并从流场和压力分布上进行了解释。结合推力扣除的研究，研究了船体与水翼的不同组合模型，分析评价了安装水翼对两栖车辆水动力的影响。本文的研究过程和结论可为船舶减阻节能提供参考。

2. Research model 2.研究模型

2.1. Amphibious vehicle model
2.1.两栖车辆模型

The vehicle model studied in this paper is a scaled-down model of a high-speed amphibious vehicle, which is equipped with four retractable track wheels. The height of the track wheels can be adjusted by lifting mechanisms, and the groove shape is designed according to the track wheel’s shape. When the amphibious vehicle moves on land, the wheels are put down as the primary movement mechanism. While sailing on the water, the track wheels are lifted in the groove. The vehicle’s overall structure is shown in Fig. 1. The amphibious vehicle is driven by a single waterjet propellor located at the stern when sailing on the water. The waterjet model used in this study is self-designed. The reverse and steering of the vehicle are realized by a reversing device (not shown in the figure) located at the nozzle. The waterjet system’s flow channel arrangement is not the main subject of this study; hence its precise specifications are not given. The main geometry parameters of the amphibious vehicle model are shown in Table 1.
本文研究的车辆模型是高速两栖车辆的缩小模型，配备了四个可伸缩的履带轮。履带轮的高度可通过升降机构调节，槽形根据履带轮的形状设计。当两栖车辆在陆地上移动时，车轮被放下作为主要的移动机构。当在水上航行时，履带轮在凹槽中升起。车辆的整体结构如图1所示。水陆两用车辆在水上航行时由位于船尾的单个喷水推进器驱动。本研究所用的水射流模型是自行设计的。车辆的倒车和转向通过位于喷嘴处的倒车装置（图中未示出）来实现。水射流系统的流道布置不是本研究的主要内容，因此没有给出其精确的技术指标。水陆两栖车辆模型的主要几何参数如表1所示。

2.2. Hydrofoil model 2.2.水翼模型

The hydrofoil mechanisms are installed at the front and rear wheels of the amphibious vehicle. A double rocker mechanism connected to both sides of the hydrofoil is used to rotate and release the foil. The schematic diagram of the control mechanism is shown in Fig. 2(b). When the amphibious vehicle is sailing on the water, the wheels are lifted and the hydrofoil is lowered; when the amphibious vehicle needs to move on land, the hydrofoil can be retracted above the body. The NACA0012 hydrofoil model with a large lift-drag ratio (Bi et al., 2019) is selected. The chord length is 0.254 m , and the span length is 0.91 m . In normal working conditions, the submergence depth is less than the chord length, so the hydrofoil is a shallowly submerged hydrofoil. When the linkage mechanism turns to the working position, the hydrofoil angle relative to the hull is also fixed. The attack angle is passively adjusted according to the vehicle’s attitude. In this study, considering that the hull has a positive trim angle, the installation angle of the hydrofoil is set to 0 deg. The hydrofoil structure is shown in Fig. 2.
水翼机构安装在两栖车辆的前轮和后轮上。连接到水翼两侧的双摇杆机构用于旋转和释放水翼。控制机构的示意图如图2（B）所示。当水陆两用车在水上航行时，车轮升起，水翼下降;当水陆两用车需要在陆地上移动时，水翼可以缩回到车身上方。具有大升阻比的NACA 0012水翼模型（Bi等人，2019年，被选中。弦长0.254 m，跨度0.91 m。在正常工作状态下，淹没深度小于弦长，所以该水翼是一种浅淹没的水翼。当连杆机构转动到工作位置时，相对于船体的水翼角度也是固定的。攻角根据飞行器的姿态被动调整。在本研究中，考虑到船体具有正纵倾角，将水翼的安装角设置为0度。图2中示出了水翼结构。

The pressure difference occurs when the water flows through the upper and lower surfaces of the hydrofoil. Usually, the pressure on the lower surface is more significant than on the upper side, thereby
当水流过水翼的上表面和下表面时，就会产生压力差。通常，下表面上的压力比上侧上的压力更大，从而

Fig. 1. Geometry model of the amphibious vehicle.
图1.水陆两栖车辆的几何模型。

Table 1 表1
Main parameters of the amphibious model.
两栖模型主要参数。

Main parameters 主要参数	Symbol 符号	Value 值
Length between perpendiculars 望远镜之间的长度	$L_{P P}$	2.6 m
Length of waterline 水线长度	$L_{W L}$	2.22 m
Beam at waterline 水线处的横梁	$B$	0.9 m
Draught 吃水	$T$	0.212 m 0.212米
Displacement 位移	$\nabla$	$0.256 m^{3}$
Longitudinal center of gravity from the aft peak 纵向重心从船尾顶点	LCG	1.023 m 1.023米
Vertical center of gravity from the keel 垂直重心距龙骨	KG	0.283 m 0.283米

generating a lift force. The amphibious vehicle is lifted by the hydrofoil, and the draft is reduced, thus reducing the resistance and power consumption. The lift of the hydrofoil can be expressed as:
产生升力。水陆两用车通过水翼提升，吃水减小，从而减少阻力和动力消耗。水翼的升力可以表示为：

F_{l} = 1 / 2 S_{i} ρ U^{2} C_{l}

where

S_{i}

is the projected area of the hydrofoil; for a standard airfoil,

S_{i} =

l_{i} \cdot b_{i}; l_{i}

and

b_{i}

represents the span and chord length of the hydrofoil respectively, their values are 0.91 m and

0.254 m; ρ

is the density of the fluid, the value is

997.561 kg / m^{3}

for water and

1.18415 kg / m^{3}

for air;

U

is the flow speed;

C_{l}

represents the lift coefficient, which is related to the configuration, attack angle and submergence depth. The lift coefficient can be calculated according to the formula proposed by Wadlin and Christopher (1958):
式中，

S_{i}

为水翼投影面积;对于标准翼型，

S_{i} =

、

l_{i} \cdot b_{i}; l_{i}

、

b_{i}

分别为水翼翼展和弦长，取值为0.91 m;

0.254 m; ρ

为流体密度，水为

997.561 kg / m^{3}

，空气为

1.18415 kg / m^{3}

;

U

为流速;

C_{l}

表示升力系数，它与外形、攻角和淹没深度有关。升力系数可根据Wadlin和Christopher（1958）提出的公式计算：

C_{l} = \frac{2 K_{2 i} π λ_{i} α_{i}}{λ_{i} + 2 K_{2 i} + 1} + \frac{8}{3} (1 - \frac{λ_{i}}{10}) \sin^{2} α_{i} \cos α_{i}

where

λ_{i}

is the span-chord ratio, which is the inherent parameter of a hydrofoil;

α_{i}

represents the hydrodynamic attack angle; when the wave response is not considered,

α_{i} = α_{i n s} + θ - α_{0 i}; α_{i n s}

is the installation angle of the hydrofoil;

θ

is the hull trim angle;

α_{0 i}

represents the zero-lift attack angle of the hydrofoil, which is 0 for the NACA0012 hydrofoil studied;

K_{2 i}

is the depth correction factor of the lifting surface, which varies with the submerged depth of the hydrofoil.
式中：

λ_{i}

为展弦比，为翼型的固有参数;

α_{i}

为水动力攻角;不考虑波浪响应时，

α_{i} = α_{i n s} + θ - α_{0 i}; α_{i n s}

为翼型安装角;

θ

为船体纵倾角;

α_{0 i}

为翼型零升力攻角，所研究的NACA 0012翼型为0;

K_{2 i}

是升力面的深度修正系数，它随水翼的浸没深度而变化。

Since the hydrofoil support plate’s inflow surface is small and
由于水翼支撑板的流入表面小，

positioned vertically in this study, the resistance and lift it generates can be disregarded. Therefore, the model is simplified to a combination of hull and hydrofoils, as shown in Fig. 3. The installation position parameters of the hydrofoil are shown in Table 2:
在本研究中垂直放置，其产生的阻力和升力可以忽略。因此，将模型简化为船体和水翼的组合，如图3所示。水翼安装位置参数见表2：

2.3. Hydrodynamic model of waterjet propulsion
2.3.喷水推进水动力模型

The influence of waterjet propulsion on amphibious vehicle resistance is usually expressed by thrust deduction

Δ T

, defined as the additional resistance caused by the action of waterjet propulsion. In order to obtain a more general representation, the thrust deduction fraction is defined as:
喷水推进对两栖车辆阻力的影响通常用推力扣除

Δ T

来表示，定义为喷水推进作用引起的附加阻力。为了获得更一般的表示，推力扣除分数定义为：

t = \frac{Δ T}{T} = 1 - \frac{R_{t}}{T}

where

T

is the thrust of the waterjet;

R_{t}

is the resistance of the hull without waterjet driven, and

R_{t} = T - Δ T

. Since the studies were all carried out at the model scale, the effect of scale effects on thrust deduction was not considered.
其中，

T

为喷水推进器的推力;

R_{t}

为无喷水推进器驱动时船体的阻力;

R_{t} = T - Δ T

。由于研究都是在模型尺度下进行的，因此没有考虑尺度效应对推力扣除的影响。

Due to the complex shape of the flow channel, it is not easy to measure the net thrust of the waterjet propulsion directly. According to the ITTC recommendation, the momentum and energy flux method is used to analyze the performance of the waterjet (Procedures, T.S.C.o.V. o.W.j.T., 2002). The control volume model of the waterjet propulsion is expressed in Fig. 4. To avoid the flow distortions by the intake geometry, the capture area of the water flow inlet is set to surface 1 , as recommended by ITTC, at an impeller diameter in front of the oblique tangent point A of the waterjet propulsion inlet (Procedures, T.S.C.o.V.o.W.j.T., 2005). Surface 2 is an imaginary surface, with no matter transfer occurring on this surface. Surface 3 neither belongs to the waterjet control volume nor the vehicle body. It is generated by the stagnation line on the intake lip, as well as the merged line of the channel and the flat bottom (Eslamdoost et al., 2018). Surface 4 is the inner surface of the waterjet, surface 5 represents the area of the pump, surface 6 is the outlet area of the nozzle, and surface 7 represents the contraction section of the flow.
由于喷水推进器流道形状复杂，直接测量喷水推进器的净推力并不容易。根据ITTC的建议，使用动量和能量通量方法来分析水射流的性能（Procedures，T.S.C.o.V. o.W.j.T.，2002年）。喷水推进的控制容积模型如图4所示。为了避免进气口几何形状造成的气流畸变，按照ITTC的建议，将水流入口的捕获区域设置为表面1，位于喷水推进器入口斜切点A前方的叶轮直径处（程序，T.S.C.o.V.o.W.j.T.，2005年）。表面2是假想的表面，在该表面上不发生物质转移。表面3既不属于水射流控制容积，也不属于车身。它是由进气唇上的滞流线以及通道和平底的合并线产生的（Eslamdoost等人，2018年）。表面4是水射流的内表面，表面5表示泵的区域，表面6是喷嘴的出口区域，表面7表示流的收缩部分。

Fig. 2. Geometry model of hydrofoil (a) and diagram of the controlling mechanism (b).
图2.水翼的几何模型（a）和控制机构图（B）。

- Corresponding author. 通讯作者。
E-mail address: pan_db150265@163.com (D. Pan).
电子邮件地址：pan_db150265@163.com（D. Pan）。

Research on shipping energy-saving technology: Hydrofoil amphibious vehicle driven by waterjet propulsion 船舶节能技术研究--喷水推进水翼两栖艇

ARTICLE INFO 产品信息

Keywords: 保留字：

Abstract 摘要

1. Introduction 1.介绍

2. Research model 2.研究模型

2.1. Amphibious vehicle model2.1.两栖车辆模型

2.2. Hydrofoil model 2.2.水翼模型

2.3. Hydrodynamic model of waterjet propulsion2.3.喷水推进水动力模型

Research on shipping energy-saving technology: Hydrofoil amphibious vehicle driven by waterjet propulsion
船舶节能技术研究--喷水推进水翼两栖艇

2.1. Amphibious vehicle model
2.1.两栖车辆模型

2.3. Hydrodynamic model of waterjet propulsion
2.3.喷水推进水动力模型