Excercise: Steam superheating

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Dorcas Lyons
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1 Steam superheating Excercise: Steam superheating Calculate the efficiency of thermodynamic cycle in optimum working conditions for: a) the system without repeated steam superheating; b) the system with one degree repeated steam superheating. Processes should be represented in s diagram. For case b) calculate the optimal temperature before repeated superheating (). he expansion thru turbine is assumed to be isentropic. he pressure drop in the boiler with superheater is 0 bar and bar in next superheater. 6a 6b Picture : Scheme of the thermodynamic cycle without repeated superheating and the system with one degree repeated steam superheating. p m h točka bar C kg/s kj/kg a 0,05 6b 0,05 4

2 Steam superheating With repeated steam superheating we achieve increase in the thermodynamic efficiency of the cycle. With regenerative heating of feeding water we increase the average temperature level of the fluid during heat addition in the region of low temperatures, with repeated superheating we increase the average temperature level of the fluid during heat addition in the region of high temperatures. he connection between the average temperature level of the fluid during heat addition and efficiency of steam thermodynamic cycle goes out from the steam cycle carnotization. Carnotization: o the steam cycle the Carnot cycle is ascribed with the same work potential. hat means (picture ) that shaded surface inside steam cycle (---6) that represents the difference between added and taken heat (gain work) is the same like by the ascribed Carnot cycle (-c-c-6). c m, c od Picture : Carnotization of the steam cycle. 6 s If the surfaces are the same it means that the average temperature level of the fluid during heat addition in the case of Carnot cycle is the same value like in the case of steam cycle (m,). he average temperature level of the fluid during heat addition (Picture ) is calculated with m, h h s s It is well known that the Carnot efficiency is: C od So the efficiency of Carnot cycle can be inceased with increasing of the average temperature level of the fluid during heat addition. From comparison with steam cycle it follows that the

3 Steam superheating efficiency of steam cycle can be increased also with increasing the average temperature level of the fluid during heat addition. Both processes can be shown in s diagram. he point is not known that s why the cycle with one degree repeated steam superheating in this point can not be sketched [ C] a 6b Picture : s diagram for the cycle without one degree repeated steam superheating (---6a) and the cycle with one degree repeated steam superheating (-----6b).

4 Steam superheating 4 a) he process without repeated steam superheating he steam cycle efficiency: kp, a Pt Pč Q h h6a h h h h All parameters in all points are relatively simple to establish: h = h(p, ) =, kj/kg h6a = h(p6, s) s = s(p, ) = 6, kj/kgk isentropic expansion h6a = 9,4 kj/kg 6 = s(p6) =,9 C... two-phase region h = h'(p) =,6 kj/kg... boiling water h = h(p, ) p = p + pkotel... we have pressure drop in the boiler p = = 0 bar h = 6, kj/kg he steam cycle efficiency:, 9,4 6,,6 kp, a = 0,44 = 44, %, 6, b) he process with one degree repeated steam superheating he steam cycle efficiency: kp, b Pt Pč Q h h h h h h h 6b h h h he state in point should be defined in the way that the steam cycle efficiency will be maximal. We already figured it out that cycle efficiency is maximal when average temperature level of the fluid during heat addition is maximal. m, h h s s h s h s he state in point and is not changed regarding to example a): we establish h, s, h and s that are constant and equal that those in example a). We need just s: s = s(p, ) = 0,44 kj/kgk

5 Steam superheating 5 he state in point is dependent from state in point. he procedure of determent of state in point is iterative:. We chose the initial value (or p).. We establish h in p, where we take into consideration that s = s (in our case is expansion isentropic).. We establish h and s where we take into consideration that p = p ppp, the temperature after repeated superheating is known. 4. We calculate m, and the value compare with before calculated temperatures. If we found maximum we stop calculating, if not we increase or reduce (or p) and proceed with step. he example in the. step of calculation:. he initial value: = 00 C. State in point : h = h(, s) = 956 kj/kg p = p(, s) = 4,6 bar. State in point : h = h(, p) p = p ppp p = 4,6 = 9,6 bar h = 5, kj/kg s = s(, p) =, kj/kgk 4. he average temperature level of the fluid during heat addition:, 6, 5, 956 m, = 564,5 K = 9,5 C 6, 0,44, 6, he values of m, are marked in the diagram, where the maximum is well seen. In picture 4 values of m, are shown that are calculated with iterations from initial value of = 50 C at step of 0 C. Maximum m, is at = 0 C and is m,,max = 9, C.

6 Steam superheating m,,max m, [K] ,opt Picture 4: he diagram of average temperature level of the fluid during heat addition in dependence of temperature after first expansion. [ C] he steam cycle efficiency in optimal case ( = 0 C): kp, b h h h h h h h 6b h h h = h(, s) = 009 kj/kg h h = h(, p) p = p ppp p = p(, s) = 5 bar p = 5 = 50 bar h = 5,6 kj/kg h6b = h(p6b, s) = 6,5 kj/kg, 009 5,6 6,5 6,,6 kp, b = 0,45 = 45, %, 6, 5,6 009 he efficiency can be calculated with the equation for Carnot process: C od

7 Steam superheating od = 6 = =,9 C = m,,max = 9, C,9 C = 0,45 = 45, % 9, Remarks: C in kp,b are a bit different because of rounding up at calculation and because of IPSE requirements (the efficiency of the pump was set to 0.9, the pressure drop in the condensator 0.00 bar) Questions: How the average temperature level of the fluid during heat addition is defined? Is it demanding isobaric heat addition? he average temperature level of the fluid during heat addition goes out from definition dq ds. Only for isobaric heat addition dq dh ds or dh/ ds is valid. Absolute temperature is guideline coefficient of isobar in h-s diagram. Because we search some middle, average temperature, we take into account m = h/s. What is changed if the real expansion occurs (internal efficiency is 0,9)? he maximal efficiency esn t occur at maximal average temperature level of the fluid during heat. What kind of optimization is in the case of two degree repeated superheating? We change states after first and second expansion, that s why the optimization is twoparametric.

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