Hydrodynamic characteristics of underwater vehicle with X-rudder configuration coupling with incidence and rudder angle

Table 1. Main parameters of SUBOFF submarine model
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Table 1. Main parameters of SUBOFF submarine model
参数数值
垂线间长L_pp/m 4.261
坐标原点距艏纵向距离x/m 2.013
坐标原点距基线垂向距离z/m 0.254
舵轴距舵尾缘纵向距离x_R/m 0.137
舵面积S/m² 0.025
展弦比λ 0.720

Table 2. Comparison of hydrodynamic forces on each part of submarine

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Table 2. Comparison of hydrodynamic forces on each part of submarine

δ₁/(°)	位置力	主体	围壳	舵1	舵2	右下舵	左上舵	合计
−10	1 000Y′	0.194	0.005	0.230	0.011	0.019	−0.032	0.427
10	1 000Y′	−0.145	0.004	−0.216	−0.016	−0.016	0.010	−0.378
−10	1 000Z′	0.402	−0.251	0.223	0.012	−0.022	0.016	0.380
10	1 000Z′	0.069	−0.251	−0.223	−0.007	0.024	−0.017	−0.406

Table 3. Rudder derivatives of rudder-1 and rudder-2 at different attack angles

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Table 3. Rudder derivatives of rudder-1 and rudder-2 at different attack angles

舵	$ Z_\delta ' $					${ {M} }_\delta '$
舵	α = −6°	α = −3°	α = 0°	α = 3°	α = 6°	α = −6°	α = −3°	α = 0°	α = 3°	α = 6°
δ1	−2.528	−2.380	−2.197	−2.021	−1.899	−1.036	−0.979	−0.902	−0.827	−0.777
δ2	−1.905	−2.069	−2.308	−2.373	−2.636	−0.782	−0.850	−0.933	−0.969	−1.064

Table 4. Fitting of hydrodynamic coefficients of single rudder coupling with attack angle

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Table 4. Fitting of hydrodynamic coefficients of single rudder coupling with attack angle

水动力系数	量值
水动力系数	Z′相关	M′相关
$ F_0'$	−0.001×10−3	0.0120×10-3
$ F_w'$	−13.950×10−3	10.880×10−3
$ F_{\delta_1}'$	−2.205×10−3	−0.904×10−3
$ F_{w\delta_1}'$	3.085×10−3	1.280×10−3
$ F_{\delta_2}'$	−2.258×10−3	−0.920×10−3
$ F_{w\delta_2}'$	−3.375×10−3	−1.305×10−3

Table 5. Rudder derivatives of rudder-1 and rudder-2 at different drift angles

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Table 5. Rudder derivatives of rudder-1 and rudder-2 at different drift angles

舵	$Y_\delta '$					${{N} }_\delta '$
舵	β = −6°	β = −3°	β = 0°	β = 3°	β = 6°	β = −6°	β = −3°	β = 0°	β = 3°	β = 6°
δ1	−2.624	−2.319	−2.247	−2.022	−2.058	1.071	0.959	0.922	0.851	0.842
δ2	−2.083	−2.046	−2.225	−2.411	−2.493	0.861	0.863	0.914	0.990	1.025

Table 6. Fitting of hydrodynamic coefficients of single rudder coupling with drift angle

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Table 6. Fitting of hydrodynamic coefficients of single rudder coupling with drift angle

水动力系数	量值
水动力系数	Y′相关	N′相关
$ F_0'$	0	0
$ F_v'$	−29.840×10−3	−14.210×10−3
$ F_{\delta_1}'$	−2.254×10−3	0.929×10−3
$ F_{v\delta_1}'$	−2.727×10−3	1.082×10−3
$ F_{\delta_2}'$	−2.252×10−3	0.930×10−3
$ F_{v\delta_1}'$	2.264×10−3	−0.871×10−3

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Jijun CHEN, Ziying PAN, Wentao ZHENG, Mo CHEN, Xian XIA, Donglin XIAO. Hydrodynamic characteristics of underwater vehicle with X-rudder configuration coupling with incidence and rudder angle[J]. Chinese Journal of Ship Research, 2023, 18(1): 99

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