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Before the energy balance is described, we first introduce the notion of enthalpy of formation hf. It can be explained as the enthalpy of a substance at a specified state due to its chemical composition. A reference state is used, T = 298.15 K and p = 1 atm. At this state, all stable elements have a value of hf = 0 and with a stable element we mean chemical stable elements like N2, H2 and O2 in their naturally occurring form, not the atomic versions of N, H and O. Using this reference we state: The enthalpy of formation of a component, at the reference state, is the value of energy released or absorbed, when it is created from its primary stable forms (O2 etc) at the same reference state, Cengel (1998). A negative enthalpy of formation means that energy is released during the creation of the component and vice versa. An example is liquid propane, that has an enthalpy of formation of -118 910 kJ/kmol. For each kmol of propane that is burned and reacts to carbon dioxide and water, 118 910 kJ of energy is released. If the products or reactants are not in the reference state, the enthalpy of formation will vary. We introduce the notion of total enthalpy, which is the sum of enthalpy of formation at the reference state and the normal (sensible) enthalpy at the current state relative to the enthalpy at the reference state: Enthalpy=h0 +(h−h0) f (5.8.8) where the superscript 0 indicates the value at the reference state (T = 298.15 K and p = 1 atm). Now we can state the energy balance equation from Cengel (1998). (5.8.9) where the subscripts p and r denotes products and reactants. The changes in kinetic energy in the combustion chamber can be neglected together with the changes in potential energy. We also know that the volume is constant, which gives zero work done. The released energy is then used to heat the products of the combustion. The combustion chamber is well insulated but still has some heat losses. The heat losses and a possible incomplete combustion can be modelled with an efficiency of combustion, ηcc. The energy balance will then be: (5.8.10) 5.9 The temperature sensor The temperatures in the model are given by evaluations in the control volumes. If we want to know the exact temperature at some other locations, e.g. after the compressor (a flow model), we (5.8.10) need an independent temperature sensor. As mentioned earlier the temperature in the outlet flow connector of the flow model is the following control volume’s temperature, which can be very different. Instead we can use the flow variables energy flow qconv and the mass flow m& to get the correct enthalpy: (5.9.1) Using equation (4.4.1), which gives the enthalpy as a function of temperature, we can state an equation for Dymola to solve for temperature: (5.9.2) Dymola solves the high-order non-linear equation and we get the correct temperature. The computations are fast and do not increase the simulation time significantly. In some cases as e.g. in the heat exchanger the true temperature does not differ much from the temperature in the following control volume, since the temperature drop depends on the pressure loss over the flow model, which is usually small. In other cases as e.g. right before the finishing gas reservoir the && ∑ ∑ Q+W+dPE+dKE= m& (h0 +(h−h0)) − m& (h0 +(h−h0)) pf rf pr ∑m& (h0 +(h−h0)) =η ⋅∑m& (h0 +(h−h0)) pf cc pr rf h(T) = qconv m& T2T3T4T5q R−a1T−1+a2lnT+a3T+a4 +a5 +a6 +a7 +b1− conv =0 2 3 4 5 m& 40PDF Image | Modelling of Microturbine Systems
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