Question 9.4: Characteristic curve of a boiler Construct the characteristi......
Characteristic curve of a boiler
Construct the characteristic curve of the condensing boiler in Fig. E.9.10, which is part of the experimental installation of the LCCE.
The Type chosen in the TRNSYS v17 library to build the characteristic curve is Type 700, which corresponds to a boiler. We will assume that it works at high temperature (60-80°C) so that it behaves like a conventional high-performance boiler. The energy efficiency of the boiler is
\eta_{C}=\frac{\dot{E}_{1}-\dot{E}_{2}}{\dot{E}_{20}}and the specific exergy consumption is
k_{C}={\frac{{\dot{B}}_{20}}{{\dot{B}}_{1}-{\dot{B}}_{2}}}The exergy for the water flows i = 1, 2 is calculated by Eq. (3.44), while the exergy of the natural gas is obtained from Eq. (3.136), that is, \dot{B}_{20}=\dot{m}_{N G}{\phi}I C V_{N G} where \phi is the correlation coefficient that for natural gas takes the average value of 1.04.
{\dot{B}}=\dot m c\left(T-T_{0}-T_{0}l n{\frac{T}{T_{0}}}\right)\qquad\qquad(3.44) \\ b_{{\rm C}_{a}{\rm H}_{b}}^{c h,0}=H H V_{{\rm C}_{a}{\rm H}_{b}}-T^{0}\left[s_{{\rm C}_{a}{\rm H}_{b}}^{0}+\left(a+\frac{b}{4}\right)s_{{\rm O}_{2}}^{0}-a s_{{\rm C}{\rm O}_{2}}^{0}-\frac{b}{2}s_{{\rm H}_{2}{\rm O}}^{0}\right]\\ +\left[a b_{\mathrm{CO_{2}}}^{c h,0}+{\frac{b}{2}}b_{\mathrm{H}_{2}0}^{c h,0}-\left(a+{\frac{b}{4}}\right)b_{\mathrm{O_{2}}}^{c h,0}\right]\qquad\qquad(3.136)The independent variables (\tau_{C}) chosen for the boiler are the inlet temperature (T_{1}), the mass flow rate of the water to be heated ({\dot{m}}_{1}={\dot{m}}_{2}={\dot{m}}) and the ambient temper-ature (T_{0}). Also, known parameters are defined as the maximum power ({\dot{E}}_{M A X}), the set temperature at which hot water is produced (T_{set}), the energy efficiency curve (\eta_{C}(\Delta T,{\dot{m}}_{1})) and the minimum power at which it can work. The boiler outlet temper-ature (T_{2}) and the required fuel (\dot{E}_{20}) depend on these variables.
There are two main states for the boiler: there is no mass flow rate (boiler off), or there is circulating flow (boiler on). In the first case, the model establishes the outlet temperature equal to that of the inlet (T_{2}=T_{1}) and the consumption is zero ({\dot{E}}_{20}\,=0). In the second state, the model first calculates the required energy ({\dot{E}}_{r e q}) to raise the water temperature to the set temperature.
If {\dot{E}}_{r e q} is negative, it means that the inlet temperature is higher than the set temper-ature; therefore, the boiler behaves as if it is switched off. If (\dot{E}_{req}) is between 0 and the maximum power, the energy transferred to the water \left({\dot{E}}_{2}-{\dot{E}}_{1}\right) will be {\dot{E}}_{r e q}. The boiler is internally controlled, in such a way that it adapts the consumption to obtain the hot water at T_{2}=T_{s e t}, operating at partial load (PLR), so that the consumption will be \dot{E}_{r e q}\,=\,P L R\,\dot{E}_{M AX}.
If {\dot{E}}_{r e q} is greater than {\dot{E}}_{MAX}, it means that the energy input would exceed the power of the boiler. In this case, the energy transferred to the water \left({\dot{E}}_{2}-{\dot{E}}_{1}\right) is {\dot{E}}_{MAX}, so that the partial load coefficient will be the unit (PLR = 1) and the outlet temperature is T_{2}={T_1}+\dot{E}_{M A X}/\dot{m}c_{p}. Once the energy transferred to the water is known in all cases, the fuel consumption is {\dot{E}}_{20}=\left({\dot{E}}_{2}-{\dot{E}}_{1}\right)/\eta_{c} and in this way k_{\mathit{C}} is obtained as a function of the independent variables.
Fig. E.9.11 shows the values of k_{\mathit{c}} when one of the independent variables T_{1} varies, and the others remain constant for the following values: \dot{m}=\;1.062\:\mathrm{kg/s}\:,T_{0}=15^{\circ}{\rm C},\dot{E}_{M A X}=28\;\mathrm{kW~and~}T_{s e t}=75^{\circ}\mathrm{C}.
