Optimization Design of Mining Tri-cone Bit Air Nozzle by CFD

Performance of the air nozzle of the mine tri-cone bit directly affects life of bit and rock breaking efficiency. The shape of air nozzle influences performance of mine tri-cone bit. It is necessary to optimize the shape of the air nozzle of tri-cone drill bits. The general specifications of gas mine tri-cone bit were analysed. Working condition and parameters of the air nozzle of the mine tri-cone bit were determined. A three-dimensional model of the air nozzle of the mine tri-cone bit was established. The characteristic geometry and range of air nozzle were determined. The performance index of air nozzle was proposed. An orthogonal experiment table of characteristic geometry of air nozzle was established. The ranking of influence weights of characteristic geometry was obtained. Key characteristic geometry which affects the performance of air nozzle was also obtained. This thesis work helps to improve the working performance of the gas nozzle of the three-cone bit. It can provide some reference ideas for the optimized design of the cone bit


Introduction
Tri-con bit is mostly widely used drill tool for coal and metallic mining.Compared with the top hammer drilling method, fixed and rotary bits are popular while fixed bits are preliminarily used for percussion drilling and consist of drag bits and button bits [1].The main function of gas nozzle is to clear rock fragmentation in the hole bottom, cooling hole bottom temperature [2] and prevent repeated breaking of rock cutting by tri-cone bit.Performance of air nozzle directly affects drilling efficiency.Therefore, it is necessary to optimize key feature geometry value of the air nozzle.
Drill pipe vibration would reduce drill bits life [3][4][5].Rafezi and Hassani [6] established bit health monitoring system to achieve fully autonomous blast hole drilling.Cao et al. [7] investigated the effect of the structural parameters of the drill bit used in the Casing-while-Drilling technology on its rock cuttings carrying capacity and reverse circulation performance.He et al. [8] verified effect of multinozzle bit on sandstone by numerical simulation and indoor experiment, however, nozzle fluid medium is water.Luo et al. [9] designed a specially structured drill bit for a reverse circulation down-the-hole air hammer.It can reduce dust production in the local vicinity of the drilling site during operation.This study adopted computational fluid dynamics and experimental methods.However, numerical simulation model of air hammer and air nozzle has no specific optimization.Afzal et al. [10] analysed the effect of submergence depth has been analysed on the thermal characteristics of steam plume issuing into water tank from two geometrically different steam spray nozzles.Jiang et al. [11] machined and measured 40 nozzles of different profiles, converging angle and the throat section length of nozzle were optimized.To summarize, the tri-cone bit has been widely used in the mining and petroleum fields, the nozzle has been investigated for a long time and the structure has been optimized for different applications as the key part of jetting.However, key geometry parameters of the tri-cone bit air nozzle are less studied and optimized.

The Structure of Air Nozzle of Mining Tri-cone Drill Bits
This section introduces the working conditions of mining tri-cone bit and the structure of air nozzle.It concludes that the working parameters of the mining tri-cone bit and the original geometry of the air nozzle.

Working Condition of the Tri-cone Bit
The mining tri-cone bit are mainly used in drilling hole of the open-pit metal mines and underground coal mines.The tri-cone bits consist of bearing structure, cutting structure, flow system and connections [12].The main components of flow system are nozzles.Typically, a tri-cone bit has three air nozzles.The function of the air nozzles is to clean the cutting of the hole bottom.In the figure 1, the drilling rig are presented.The air compressor of drilling rig provides circulating air of tri-cone bits.The tri-cone bits are mainly composed of cones and lug.The nozzles are installed in the lug.

Geometry of the Air Nozzle
Geometry of air nozzle directly affect performance of mining tri-cone bit.Typical structure of air nozzle concludes length of parallel section, inner diameter of parallel section, inlet inner diameter of converging section and length of converging section, which are presented in the figure 2.

Geometric Model
The air nozzle is a solid of revolution.This kind of model can be simplified as an asymmetric plane model.To eliminate influence of boundary condition on simulated fluid zone, a reasonable inlet and outlet zone are added at the upstream and downstream of air nozzle, which are presented in the figure 3. and In these equations, ~k G represents the generation of turbulence kinetic energy due to mean velocity gradients; G  represents the generation of  ; k  and   represent the effective diffusivity of k and omega, respectively.D  represents the cross-diffusion term, calculated as described below.k S and S  are user-defined source terms.Due to compressibility of air, the physical model adopts a density-based solver.The model also considers energy equations.Materials of model is ideal air, whose viscosity satisfies Sutherland gas viscosity formula.The solution method of model is implicit and second-order precision.All numerical simulations in this paper use ANSYS software.

Boundary Condition
Inlet of the fluid computed zone set as mass flow.Outlet of the model set as pressure outlet.Wall of the model set as thermal insulation.The circulating fluid in the hole is powered by an air compressor.The flow rate of air compressor can be artificially regulated.In this paper, instead of a pressure boundary [14,15], the inlet adopts a mass flow boundary condition.This boundary condition of the inlet is better aligned with the field condition.The parameters of boundary conditions are presented in the table 1.

Meshing
The model adopts quadrilateral grid to mesh the fluid computational zone.Nozzle zone has greater velocity and pressure gradient.It resized with smaller mesh size, which are presented in the figure 4. It can be better capture air flow characteristic around nozzle and higher precision.Grid size independent analysis is adopted to find optimal grid size considering accuracy and efficiency.Original nozzle geometry is adopted to simulate air flow behaviour with four types of grid sizes.The location of the velocity profile is selected around the mouth of the air nozzle.According to simulation result, velocity profile with four types of grid size are close to each other, as presented in the figure 5. Considering the balance of precision and computing consumption, the second grid size is adopted to mesh the flow zone.

Geometric Characteristic Parameters of Air Nozzles
There are four characteristic parameters to describe air nozzle geometry.They are respectively length of the parallel section, length of convergence section, inner diameter of parallel section and inner diameter of nozzle inlet, which are presented in the figure 6.

Performance Evaluation Index
To evaluate the performance of the air nozzle of tri-cone bits, we define the maximum velocity in the radial direction of nozzle mouth as an evaluation index.

Orthogonal Experimental Design and Range Analysis
The range of value of four characteristic parameters of the air nozzle geometry are determined.The range of the parallel section length(L1) is between 12mm to 18mm.The range of converging section length(L2) is between 8mm to 12mm.The range of parallel section inner diameter(D1) is between 16mm to 24mm.The range of convergence section inlet diameter(D2) is from 26mm to 30mm.We set up threelevel and four-factor orthogonal experimental tables, which are presented in the table 2.  7.According to the simulation results, the D1 (inner diameter of parallel section) has the maximum value of extremum different.The L1 (length of parallel section) has the minimum value of extremum different.Changing the value of the D1 will significantly affect the performance of the air nozzle.Three other characteristic parameters of the air nozzle geometry do not affect the index much.According to the results of the orthogonal experiment, the optimization result is L1=12mm, L2=8mm, D1=16mm, D2=26mm.

Conclusion
This paper establishes a computational fluid dynamics model of a mining tri-cone bit air nozzle.Reasonable boundary conditions and grid-independent analysis are carried out.Characteristic parameters of the air nozzle are determined.Value ranges of geometry parameters are also determined.An orthogonal experimental table of characteristic parameters is established.According to the results of the range analysis, the inner diameter of the parallel section has the greatest influence on the performance of air nozzle.The smaller the inner diameter, the greater the nozzle flow rate.According to orthogonal experimental table, the optimum value of characteristic geometry parameters is determined.The research ideas in this paper provide a certain reference value for the optimization of the nozzle of drill bits.

Figure 1 .
Figure 1.Working condition and structure of mining tri-cone bit.

Figure 2 .
Figure 2. The original size of the gas nozzle.(unit: mm)
3.2.Physical ModelComputational fluid dynamics numerical simulation of gas nozzles generally adopts Shear-Stress Transport (SST) Model.The SST model was developed by Menter to effectively blend the robust and accurate formulation of the k-omega model in the near-wall region with the free-stream independence of the k-epsilon model in the far field[13].The SST k-omega model has a similar form to the standard k-omega model:

Figure 5 .
Figure 5. Analysis independent of the grid size.

Figure 6 .
Figure 6.Characteristic parameter of air nozzle geometry and original value.

Figure 7 .
Figure 7. Velocity contour of the simulated zone.

Table 2 .
Orthogonal design of experiments and range analysis.