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The overall heat transfer from a finned-tube heat surface can be obtained using the following equation: C T1 • ' (42) M dt=mP(T1−T1) Here, cp is assumed to be constant, therefore is cancelled out from both sides of the equation. Mc represents the holdup mass in the condenser header and T1' presents pentane inlet temperature to the condenser header and calculated using h1 and saturation pressure. 2.5 The cycle pump It was found for the designed values, the ratio between the total enthalpy of pentane at the cycle pump outlet and the combined heat input at the recuperator and the vaporizer is about 1.03%, which implies that the effect change of pump output pressure (enthalpy) is insignificant compared to the total heat input. Therefore, the pump work can be assumed constant (Wei et al. 2007). The pump outlet pressure has been fixed at 23 bar for the simulation carried for this work. Moreover, the pump is also assumed to have static characteristics same as the turbine because of its fast response. 2.6 The pressure drops in pipes and valves The pressure drops in various valves are assumed negligible. The valves operating in the pentane cycle include the vaporizer pentane-level control valve, situated between the cycle pump and the vaporizer, and the flow control valve situated just after the vaporizer and the turbine inlet. In a typical operation of the plant, the flow control valve is set to its maximum and therefore its effect can be ignored. There are a few other valves attached to the unit, which are not used in normal operation of the plant. Such valves include the bypass valve from the vaporizer to the condenser and the valve for the purge system. The bypass valve is a safety system and only operates in emergencies. The purge systems are actuated when backpressure builds up in the condenser. Although there is an automated purge system working in the unit, its response is very slow and most of the time it is done manually. Therefore, it is beyond the scope of this work. For flow through pipes, there exist major and minor losses (Potter and Wiggert 2002). For simplicity of the model, only major losses are considered: 1A1b1 =R(t)+ +w ++R(36) UC fiAα(A/A)k(A/A)α fo i i i t w nb t 0 Where, Rfi = fouling resistance on the inside surface; Ai = inside surface area; Anb = means the bare surface area; bw = tube wall thickness; Rfo= fouling resistance on the outside surface. The total amount of heat rejected from the condenser is calculated using the following equation: • Q C = U C A t C ∆ t mC (37) Logarithmic mean temperature difference (LMTD) needed in the above equation is calculated as: ∆tmC = To −Tamb ln[(Tw −Tamb)/(Tw −To)] (38) Sohel et al. Where, To and Tamb are outlet and inlet temperatures of cooling air, respectively. Tw is the wall temperature and it is approximated with reasonably good accuracy as: (39) (40) Tw =(9.Tsat +Tamb)/10 The fluid properties are evaluated at an average (bulk) temperature: T1 +T4a Tb= 2 In equation 38, the outlet temperature of air, To is not known and is calculated iteratively. As an initial guess, To is taken to be the same as Tw. From the air side energy balance the heat transfer rate can be calculated: • QC =UCAtC∆tmC =mCp(To −Ti) • (41) The initial LMTD can be calculated using the above mentioned equation. From this value of LMTD a refined value of To can be calculated iteratively, using equation 38. Finally, using the obtained To, a better approximation of LMTD is obtained. Free convection occurs at the headers (where condenser tubes are connected in bundles at the inlet and outlet) of the condenser and pipeline from the condenser to the recuperator. However, it was found that the quantity of heat transfer is very low (approximately 0.05%) compared to that of the condenser itself. Therefore, the effect of heat transfer through headers and pipeline are not taken into consideration. The simplified equation for free convection from a horizontal cylinder surface to air at atmospheric pressure under laminar flow condition was used for the analysis (Holman 1992). The outlet temperature of the header depends on the holdup mass in the header and is calculated from the following equation: h =flv2 loss d 2g (43) However, an easy to use model for pressure drop (Wei et al. 2008) has been adopted for the modelling: • m= ∆p.ρ (44) • ∆pρ 7 ms Here, suffix s stand for standard or observed value. 2.7 The turbine-generator coupling A generator is coupled to the turbines and has heavy rotating parts. However, in normal operations, the generator is maintained at a constant speed so the effect of the inertia of angular velocity does not affect the electrical power output. With a change in thermal power output, the speed of the generator changes and there is a control arrangement to adjust its speed. The target speed for this generator is 1500 rpm. The change in electrical power output is the sum of ssPDF Image | Dynamic Modelling and Simulation of an Organic Rankine Cycle Unit of a Geothermal Power Plant
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