The interaction of U-shaped rings used for power transmission hardware with a wind-sand field is simulated numerically. A standard

More and more Ultra High Voltage (UHV) transmission lines have been built in recent years [

Wear test on U-shaped ring of PCH under strong wind environment was studied to illustrate the failure mechanism by Yang [

In view of the limitation of the above studies, the standard

Fluid dynamics simulation is a numerical method to solve the governing equations of flow field [

The continuity equation of fluid flow can be derived from the law of conservation of mass.

where a, b and c are the velocity components in the x, y and z directions, respectively.

According to Newton’s second law, the momentum equation of the fluid can be derived:

where

The standard

where

Since the sand grains concentration in the wind-sand environment is less than 10%, the discrete phase model is chosen to simulate the wind-sand flow. The particle trajectories of discrete phases are solved by integrating the differential equation of force balance. Assuming that the sand grains are spherical, the interaction between sand grains is not considered [

where _{p} is the sand grains velocity, _{p} _{D} is drag coefficient, _{x} is the acceleration of gravity in the X direction

U12 PCH were taken as the research object, and NX10.0 was used to conduct three-dimensional model (

The flow field was a cube, 500 mm × 500 mm × 500 mm (

Normal | 0.993 | –0.0307 | 0.000475 | –2.61 e^{–6} |
---|---|---|---|---|

Tangent | 0.998 | –0.029 | 0.000643 | –3.56 e^{–6} |

The sand density is 2650 kg/m, the specific heat capacity is 1230 j/kg k. The sand grain velocity was the same as the wind velocity, and the sand flow rate was 0.1 kg/s [

The flow field was discretized by the tetrahedral mesh. Mesh thinning was performed on the boundary layer via the expansion layer. The expansion layer number was 5 and the growth rate was 1.2. The mesh independence tests were carried out through three different mesh sizes. In this paper, the wind velocity around the U-shaped ring is more concerned. Therefore, the influence sphere with different mesh sizes is used to refine the mesh, as shown in

Conditions | Radius of sphere (mm) | Basic size (mm) | Total number of grids | Velocity (m/s) |
---|---|---|---|---|

Mesh 1 | 50 | 2 | 1094552 | 34.1 |

Mesh 2 | 50 | 1 | 1155049 | 36.3 |

Mesh 3 | 50 | 0.25 | 1268337 | 36.7 |

The accuracy of the numerical simulation is improved with the increasing mesh.

The simulation result of wind pressure is shown in

The wind velocity around U-shaped ring is shown in

where x is the input wind velocity(m/s); y is the maximum wind velocity that can be achieved locally in the U-shaped ring(m/s).

The R value of linear fitting is 1, which indicates that the input wind velocity is completely linearly correlated with the maximum wind velocity around U-shaped ring. The maximum designed wind velocity of 42 m/s was put into the above equation, and the input wind velocity was 23 m/s. Therefore, when the wind velocity exceeds 23 m/s, the local maximum wind velocity near the U-shaped ring has exceeded the maximum design wind velocity. When the U-ring works for a long time with wind velocity greater than 23 m/s, it will cause the U-shaped ring to wear and fail prematurely.

Euler-Lagrange approach was used to simulate the wind-sand field, and the incident velocity of the sand grains was set as 20 m/s.

In order to explore the reason why wind velocity on the leeward side of the U-shaped is zero, observing the

where ^{3} at room temperature;

According to the above formula, Re = 2.8 × 10^{4}, which satisfies the condition of existence of the cylindrical Kármán Vortex Street 47 < Re < 10^{5}. From the above analysis, it indicates that the region with zero wind velocity is caused by the whirl of airflow.

Combined with the above analysis, the reasons for the formation of the wind field around the U-shaped ring are explained in detail by observing

By observing the

The main impacts on the U-shaped ring are the second and third sand trajectories. Stokes numbers in the flow field are often used to describe the follow ability of sand grains to the flow. When the Stokes number is large, the inertia of the sand particles plays a leading role, and the sand particles follow poorly. When the Stokes number is small, the sand particles follow better [

where

It can be seen from the

As the wear progresses, the contact state between the two U-shaped rings would gradually change from point contact to surface contact. The increase in the contact area improve the ability of sand grains to follow the airflow into the contact area of the two U-shaped rings. The sand grains with smaller sizes may follow ‘semi-vortex’ into the contact area of the two U-shaped rings. Therefore, the sand grain sizes were selected to be 0.025 mm, 0.05 mm, 0.1 mm, 0.125 mm and 0.15 mm. The sand grain diameter range that can follow the airflow into the contact area of the two U-shaped rings was determined by the sand streamline diagram (

Under strong wind environment, the windward side of the U-shaped ring is positive pressure zone, and both sides of the U-shaped ring are negative pressure zones.

In the wind-sand field, the sand grains have three movement regimes. Sand grains not only collide with the U-shaped rings directly, but also enter the contact area between the two U-shaped ring to accelerate the wear and failure of the U-shaped rings.

Sand grains size in the range of 0–0.125 mm can follow the airflow into the contact area of the two U-shaped rings, and when the sand size is about 0.1 mm, the number of sand grains entering the contact area of the two U-shaped rings is the largest.