# Analysis of influence of duct geometrical parameters on pump jet propulsor hydrodynamic performance

## Abstract

To analyze the influence of duct geometrical parameters on hydrodynamic performance of pump jet propulsor, this paper presents a surface panel method for predicting performance of pump jet propulsor. And, moreover, a meshing method for blade, based on circular conical surface, is proposed. According to the actual situation of the internal flow of the pump jet propulsor, a tip leakage vortex model for the blades with flat top is also proposed. The hydrodynamic performance of pump jet propulsor under different conditions was calculated and compared with CFD results for the verification of the presented method. Then the influence of duct parameters on pump jet performance was analyzed from several aspects including performance index, surface pressure distribution, and flow velocity. The results show that variations of gap size, camber or attack angle of duct result in different hydrodynamic performance. Suitable selection of duct geometry can significantly increase the thrust efficiency of the pump jet propulsor, expand the range of effective work, and improve the loading characteristics of the blade.

## Keywords

Pump jet thrust Duct geometrical parameters Performance prediction Surface panel method Tip leakage vortex model## List of symbols

- \( \vec{V}_{0} \)
Velocity

- \( S \)
Boundary of the fluid

- \( S_{b} \)
Object surface

- \( S_{\text{w}} \)
Wake vortex surface

- \( Q \)
Arbitrary control point on the boundary surface

- \( R_{PQ} \)
Straight line distance between two points

*P*and*Q*- \( \partial \varphi (Q)/\partial n_{Q} \)
Normal derivative of the point velocity potential

*E*Green formula parameter

- \( Q_{1} \)
Point on the wake vortex surface

- \( \overrightarrow {n} \)
Unit normal vector of the corresponding object surface and points to the flow field

- \( \Delta \varphi \)
Velocity potential jump through the wake vortex surface

- \( S_{\text{s}} \)
Stator surface

- \( S_{\text{d}} \)
Duct surface

- \( S_{\text{r}} \)
Rotor surface

- \( S_{\text{h}} \)
Hub surface

- \( S_{\text{ws}} \)
Vortices of the stator surface

- \( S_{\text{wd}} \)
Vortices of the duct surface

- \( S_{\text{wr}} \)
Vortices of the hub surface

- \( \overrightarrow {{\Omega_{\theta } }} \)
Rotational angular velocity of the propeller

- \( k \)
The

*k*th iterative operation- \( \vec{V}_{{{\text{sd}},{\text{rh}}}} \)
Induced velocity generated by the rotor–hub system at the stator and duct surfaces

- \( \vec{V}_{{{\text{rh}},{\text{sd}}}} \)
Induced velocity generated by the rotor–hub system in the opposite direction of the stator and duct surfaces

- \( K_{\text{T}} \)
Thrust coefficient

- \( K_{Q} \)
Torque coefficient

- \( K_{{{\text{T{-}all}}}}\)
Total thrust coefficient

- \( \eta \)
Efficiency of the pump jet propulsor

- \( D_{\text{r}} \)
Maximum diameter of the rotor

- \( J \)
Advance speed coefficient

- \( n \)
Rotor speed

- \( r_{\text{l}} ,r_{\text{t}} \)
Radial positions

- \( x_{\text{l}} ,x_{\text{t}} \)
Axial positions

- \( \alpha \)
The conversion of circular table conical angle

- \( x_{0} \)
Vertex position

- \( c \)
The

*j*th leaf section chord length- \( c_{\text{l}} \)
The leading edge to the generatrix chord distance

- \( x_{\text{r}} \)
Trim value

- \( \theta \)
Side rake angle

- \( d_{{\overline{OP} }} \)
Distance between the arbitrary point

*P*of the leaf section and the vertex*O*of the cone on the plane of the circular table- \( d_{{PB_{1} }} \)
Point

*P*in the circular mesa to*yz*plane arc distance- \( \beta_{0} \)
The initial pitch angle of each vortex line

- \( \beta \)
Pitch angle

- \( \beta_{\text{g}} \)
The geometrical pitch angle of the rotor tip section

- \( x_{T} \)
*T*be the point of the axial coordinate- \( {\text{num}}_{T} \)
The number of cells from the start point to the

*T*point

## Notes

### Acknowledgements

The research was financially supported by the National Natural Science Foundation of China (Grant nos. 51679052, 51639004) and the Defense Industrial Technology Development Program (Grant no. JCKY2016604B001).

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