Design and optimization of bionic Nautilus volute for a hydrodynamic retarder

Figures & data

Figure 1. Volute structures in the optimization design process of this study.

Figure 2. Cross-sectional view of the hydrodynamic retarder.

Figure 3. Flow channel model of the hydrodynamic retarder with an inlet and outlet.

Table 1. Simulation parameters.

Name	Symbol	Value (unit)
Inlet oil flow	q	200 (L/min)
Inter velocity	v	0.82 (m/s)
Outlet pressure	p	0 (bar)
Rotor speed	n	2000 (rpm)
Density	ρ	820 (kg/m^3)
Dynamic viscosity	μ	0.28 (Pa·s)
Temperature	T	80 (°C)

Table 2. Number of meshes with different sizes.

	Number of grids ×10^5
Size	Inlet volute	Rotor	Stator	Outer ring
1 mm	17.93	73.93	58.19	16.15
2 mm	3.85	34.67	23.04	3.85
3 mm	1.83	28.30	18.33	1.93
4 mm	1.15	23.64	15.86	1.34
5 mm	0.90	21.21	13.24	1.10

Figure 4. Results of grid convergence analysis.

Figure 5. Hydrodynamic retarder mesh model (a) overall, (b) local.

Figure 6. Distribution of y+ values near the wall of inlet volute and rotor blades.

Table 3. Distribution of y+ value.

	Inlet volute	Rotor	Stator	Outer ring
Max y^+	4.669	9.852	4.404	2.794
Ave y^+	0.172	1.121	1.385	0.453

Figure 7. Introduction of the test rig.

Figure 8. Comparison between simulation results and test data.

Figure 9. (a) Volute region division, (b) Typical cross-section oil distribution.

Figure 10. Nautilus cross-sectional shape.

Figure 11. Cross-section profile of bionic nautilus hydrodynamic retarder volute.

Table 4. Design variables and ranges of the volute.

Name	Symbol	Range (mm)
Entry radius	r	[125, 250]
The horizontal distance of the return section	a1	[20, 50]
The vertical distance of return section	a2	[0, 30]
Eccentricity	e	[−10, 10]

Figure 12. Bionic volute optimization design process.

Figure 13. Training set volute cross-section profile.

Figure 14. RBF neural network structure.

Table 5. Settings for NSGA-Ⅱ.

Parameters	Value
Population size	100
Maximum number of generations	200
Crossover fraction	0.9
Mutation fraction	0.1

Figure 15. Correlation between optimization objectives and design variables.

Table 6. Optimization trend of design variables.

	ΔP	vmax	γ
r	Min	Min	Max
a1	Max	Max	Min
a2	Min	Min	Max
e	Max	Max	Min

Figure 16. Regression analysis for the surrogate model.

Table 7. R² analysis results.

Objective function	R^2
Δp	0.94922
vmax	0.93836
γ	0.90963

Figure 17. Computational Pareto frontier.

Figure 18. Comparison of profiles (a) prototype (b) bionic volute.

Table 8. Comparison of the objective function between the prototype and bionic volute.

	Δp (Pa)	γ	vmax (m/s)
Prototype	1766.6	1.134	4.8937
Bionic volute	371.95	1.377	6.8809

Figure 19. Typical section velocity field and streamline diagram comparison.

Figure 20. Flow field vortex identification comparison.

Figure 21. Comparison of outlet flow distribution.

Figure 22. Comparison of pressure and velocity at the outlet of the volute.

Figure 23. Comparison of flow energy loss distribution in the volute.

Figure 24. Emergency braking characteristics of the hydrodynamic retarder.

Table 9. Braking characteristic index of the hydrodynamic retarder.

	Onset time	Max braking torque
Prototype	0.76 s	5960.15 N·m
Bionic volute	0.71 s	6326.49 N·m

Figure 25. Comparison of filling rate changes.

Figure 26. Gas-liquid two-phase distribution during liquid filling.