# Application of EDEM Simulation for Calculating and Optimizing a Closed Coal Fly Ash Screw Conveyor
## 2 Materials and Methods
### Methods for Calculating Screw Conveyors  
**Screw pumps capacity**  
The capacity of the pipe screw is contingent upon the rotational speed of the screw, the material being transported, and the filling level or filling factor of the screw. The screw capacity is determined by the following expression [3]:  
\[Q=Q_{t}\eta_{V}\;(\text{m}^{3}/\text{s}) \tag{1}\] \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Material Property Parameters**} & **Value** & **EDEM Material** \\  & **(for Calculation and EDEM Simulation)** & **Library** \\  & **GEMM\_Particle 8454** \\ \hline Angle of repose (degree) & 47.5 & 47.51 \\ Bulk density (kg/m\({}^{3}\)) & 883 & 724.54 \\ Solid density (kg/m\({}^{3}\)) & 2200 & 1500 \\ The coefficient of static friction & 0.55 & 0.56 \\ The coefficient of rolling friction & 0.08 & 0.1 \\ The coefficient of restitution & 0.5 & 0.55 \\ The coefficient of static friction with steel surface & 0.6 & – \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Material property parameters of coal fly ash in Vietnam. where, \(Q_{t}\)--maximum capacity that can be transported; \(\eta_{V}\)--volume coefficient. The maximum capacity can be written as  
\[Q_{t}=\Gamma\omega D^{3}(\text{m}^{3}/\text{s}) \tag{2}\]  
With  
\[\Gamma=\frac{1}{8}\Bigg{[}\left(1+2\frac{C}{D}\right)^{2}-\left(\frac{D_{c}}{D} \right)^{2}\Bigg{]}\left[\frac{p}{D}-\frac{t_{s}}{D}\right] \tag{3}\]  
where \(D\)--diameter of conveyor screw (m); \(p\)--screw pitch (m); C--radial clearance (m); \(D_{c}\)--screw diameter (m); \(\omega\)--rotational speed of the screw (rad/s); \(t_{s}\)--thickness of screw blade (m). The dimensions of the screw conveyor are shown in detail in the design drawing of the screw conveyor that the authors designed, optimized, manufactured, and are currently using stably at the Vinh Tan thermal power plant. The specifications of the actual screw conveyor are shown in Figure 3.  
The magnitude of the relative velocity is primarily influenced by the frictional resistance between the material and the screw housing. This force hinges on the coefficient of friction existing between the material and the screw housing, as well as the centrifugal pressure exerted by the material on the screw housing [29]. The force acting on the screw conveyor is illustrated in Figure 4.  
Figure 4: Force acting in a screw conveyor [3]. (**a**) Forces acting on the bulk material during conveying; (**b**) A cross section showing the forces acting on a screw conveyor. Figure 3: Specifications of the actual screw conveyor. The connection between the rotational speed Ns and the incline angle of the screw conveyor is defined as follows:  
\[N_{s}=\frac{r\omega^{2}}{g}=\frac{N^{2}D}{1789}=\left[1+\frac{\tan\lambda}{\tan \alpha}\right]^{2}\left[\frac{k_{F}\sin(\alpha+\phi_{s})}{\mu_{g}\cos(\alpha+ \phi_{s}+\lambda)}-k_{s}\right] \tag{4}\]  
where \(g\) is gravitational acceleration; \(k_{F}=(1-\mu_{g}k_{s})\); \(k_{s}=2k;\eta_{F}(p/D)\); \(k_{j}=0.4\); \(\eta_{F}\) is filling ratio; and \(\phi_{S}\) is friction angle for screw surface. Based on the theoretical framework presented, a calculation application was developed to determine essential parameters when designing a screw conveyor for fly ash. This application was implemented using Excel VBA programming, enabling rapid and efficient calculations to optimize conveyor capacity [16]. The dimensions of the coal fly ash screw conveyor for calculation and simulation are shown in Table 3.  
The result of the VBA program calculation is shown in the line graph. The capacity and motor power of the coal fly ash screw conveyor in range of speed by [PERSON] and tool VBA Excel is illustrated in Figure 5. Indeed, it is evident that the maximum capacity of the screw conveyor reaches approximately 65.7 tons per hour, achieved at a speed of around 500 revolutions per minute (rpm). When applying the [PERSON] method, it was noted that the motor power curve bore a relatively similar shape to the power curve of the screw conveyor.