# Analysis of the Impact of Forces in Hanger Rods on Power Boiler Operation
## 3 Boundary Conditions for the Boiler Model under Analysis  
The model of the analysed boiler is shown in Figure 3. It is a biomass-fired 447 MWth CFB (circulating fluidized bed) boiler operating in a Polish power plant. The proposed boiler is made of a furnace chamber (1), which is permanently connected to a return leg (3). The separator (2) is separated from the furnace chamber by bellow expansion joints (4). The cross-over duct (5) is connected to the separator by welding. All these elements are suspended on hanger rods (6). A diagram of the arrangement of the rods and their numbering is presented in Figure 4. The rod numbering was adopted according to the design documentation. Figure 3: A model of the analysed boiler: view of the furnace chamber rear (**left**) and front wall (**right**). 1—furnace chamber, 2—separators, 3—return legs, 4—expansion joints, 5—cross-over ducts, 6—hanger rods. Although operating independently in the horizontal direction, the separators and the furnace chamber interact with each other when carrying vertical loads because they are connected by means of horizontal reinforcements, such as buckstays. The boiler walls were modelled using an equivalent orthotropic model. The shrouds were modelled as simplified elements using the remote point function with the selection of the degrees of freedom as displacements in horizontal directions. The hanger rods were modelled as 1D elements. The other elements were modelled according to the real model. A model built in this way provides good grounds for presenting boiler behaviour that assumes that the forces measured in the hanger rods are on site, which is called global analysis. The rods are made of 13 CrMo4-5 steel. Their material properties [16] are listed in Table 1.  
The weight of the boiler was measured by a system of pumps and actuators during the boiler downtime. A schematic diagram of the applied measurement system is shown in Figure 5. The system makes it possible to lift the rod (1) using hydraulic cylinders (6) through the flange system (4) and a special nut (5). Lifting the rod (1) in Step 1 makes it possible to loosen the rod nut (3), thereby enabling it to be tightened or loosened to achieve the required tension in the rod (in Step 2). The force measurement itself is conducted by lifting the rod until the operator detects the moment the nut (3) loosens, at which point the pressure on the pump is read, thus enabling the recording of the force that balances the force in the rod. The precision of such measurements is debatable and depends on the operator's disposition and the conditions on the boiler. Sometimes, the measurements are performed using strain gauges, which is also very labour-intensive and time-consuming, as well as inaccurate due to the conditions during the measurements. The conditions on the boiler are characterized by high dust levels and high temperatures (also caused by the operation of neighbouring units). The time for the measurement and appropriate adjustments is short due to the need to distribute energy to the central grid as soon as possible, which is required because each day of delay in the supply of energy involves penalties. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Temperature**} & **Yield Point Rp\({}_{0.2}\)** & **Tensile Strength Rm** & **Young’s Modulus** \\  & **[MPa]** & **[MPa]** & **[GPa]** \\ \hline
20 \({}^{\circ}\)C & 275 & 400 & 211.8 \\ \hline
100 \({}^{\circ}\)C & 256 & No data & 206.1 \\ \hline
400 \({}^{\circ}\)C & 168 & No data & 182.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Steel 13 CrMo4-5 material properties. Figure 4: A diagram and numbering of the rods. The measurement system presented in Figure 5 was calibrated on the purpose-built stand that is shown in Figure 6.  
The measurements on the calibration stand were performed in the same way as on the real boiler facility, except that the additional mass (6) and the rod (5) were weighed in advance using a precision balance.