MTX221. Session 43. Sessie 43 DRYWINGS-KRINGLOPE (FASE VERANDERING) POWER CYCLES (PHASE CHANGE) Dr. Jaco Dirker. These slides also appear on Click-UP

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1 Ses.43-1 MTX221 Sessie 43 DRYWINGS-KRINGLOPE (FASE VERANDERING) Session 43 POWER CYCLES (PHASE CHANGE) Dr. Jaco Dirker These slides also appear on Click-UP Hierdie skyfies verskyn ook op Click-UP 8 th edition / 8e uitgawe

2 Ses.43-2 Inleiding tot Tema VIII:Drywing-Kringlope Introduction to Theme VIII: Power Cycles Some power plants operate on a TD cycle. Fluid undergoes a full TD cycle These are called CLOSED cycles Geslote kringloop Other power plants operate on a Mech. Cycle, but NOT a TD cycle. Fluid does not undergo a full TD cycle. Examples: Internal Combustion (IC) Engines. Binnebrand-enjins These are called OPEN cycles Oop kringloop Verkoeler Hitte-pomp Similarly, Refrigeration (for cooling) and Heat Pump (for heating) system may also operate on OPEN and CLOSED cycles It is convenient to analyze both OPEN and CLOSED systems using IDEALIZED CLOSED cycles. Example: We use the Otto cycle for a spark ignition engine. Otto-kringloop Vonk-aansteking

3 Ses.43-3 Introduction to Theme VIII: Power Cycles CHAPTER 9 (Ed 8) : Cycles where phase change occurs (evaporation and condensation) Fase-verandering vind plaas Inleiding tot Tema VIII:Drywing-Kringlope CHAPTER 10 (Ed 8): Cycles without phase change. (example: combustion engines etc..) Geen Fase-verandering

4 Ses.43-4 Introduction to Theme VIII: Power Cycles Notation used in these chapters: Notasie van belang: Inleiding tot Tema VIII:Drywing-Kringlope Considering the above-shown heat engine: The following should always be positive by definition: Per definisie altyd positief: W T W P Q H Q L = Amount of work produced by a turbine = Amount of work needed by a pump = Amount of heat received from the high temperature reservoir. = Amount of heat rejected to the low temperature reservoir. Etc Some of these are contrary to the notation we used in the first law.

5 Ses.43-5 Inleiding tot Drywing-Stelsels 9.1 Introduction to Power Systems CYCLIC Heat Engines may be split into two types: Steady state cycles with SHAFT work AS-arbeid Piston/Cylinder cycles with BOUNDARY work. GRENS-arbeid SHAFT WORK: AS-arbeid BOUNDARY WORK: GRENS-arbeid Work Equations (for internally reversible): Shaft work: w vdp (w = 0 if P = const) AS-arbeid Boundary work: w Pdv (w = 0 if v = const) GRENS-arbeid Shaft Work AS-arbeid Boundary Ses. Work 64-5 GRENS-arbeid

6 Ses.43-6 n Tipiese Suid-Afrikaanse Stoomkragstasie A Typical South African Steam Power Plant Kendall-kragstasie in Mpumalanga. Foto s: Loanna Hoffmann (Beeld.com)

7 Ses Introduction to Power Systems Consider the following Power Plant with Shaft work Four steady-state processes gestadigd Internally reversible omkeerbaar Ignore dpe and dke (for simplicity) Turbine & Pump : Adiabatic (for simplicity) Inleiding tot Drywing-Stelsels Adiabaties Difficult to maintain a constant temperature during boiling / avaporation when the pressure changes. T-s diagram AS-arbeid Om Carnot-kringloop te wees moet al vier prosesse in 2-fase gebied lê In order for this to be a Carnot Cycle, all four processes should be within the 2-phase dome. (WHY?) P-v diagram

8 Ses.43-8 Inleiding tot Drywing-Stelsels 9.1 Introduction to Power Systems Consider the net work of the Cycle (shaft work): w net w net 1 2 vdp 3 4 vdp v v vdp vdp w net w T As-arbeid w We notice that: Thus, the net work is positive If the difference between these spec. vol. can be increased, the net work will also increase (GOOD) Thus, condensation and evaporation is good, as it allows for large changes in spec. vol. If this was a piston/cylinder system (boundary work): Grens-arbeid w net 1 2 Pdv 3 2 Pdv 3 4 Pdv 1 4 Pdv P P-v diagram Netto-arbeid =area binne proseslyne Net Work = Area within the process-lines * * For reversible processes PV diagram: [J]. Pv diagram: [J/kg] (spec. net work)

9 Ses.43-9 Rankine-kringloop 9.2 Rankine Cycle Ideale gestadigde vier-proses kringloop Consider an idealized steady state four-process cycle: Ts diagram Rankine-kringloop This is called a Rankine cycle and we use it to model a simple steam power plant. Eenvoudige stoom kragstasie For the remainder of this section we will ignore dke and dpe For simplicity Also valid assumption for real power plants (as a whole)

10 Ses Rankine-kringloop 9.2 Rankine Cycle Ts diagram Ts diagram 1 4 Heat to the fluid is given by area a b-a Heat from the fluid is given by area a-1-4-b-a Net work is given by The thermal efficiency is then described as: Termiese rendement We can also define it in terms of the ave. temp at which heat is received / rejected. Efficiency can be increased by: Increasing the temp. between 2 and 3 Decreasing the temp between 4 and ' a 2 2' 3 b a Verhoog renedement deur: - Hoër temp tussen 2 en 3 - Laer temp tussen 4 en 1

11 Ses Rankine-kringloop 9.2 Rankine Cycle Carnot Efficiency is greater than the Rankine cycle efficiency WHY? Rankine Carnot rendement hoër as Rankine rendement Carnot Un-extracted work Ts diagram Ts diagram 1 4 Why use Rankine then? 1) Difficult to pump a 2-phase mixture from 1 to 2 2) Difficult to maintain a constant temperature during evaporation when in sub-cooled or superheated regions.

12 Ses Rankine-kringloop 9.2 Rankine Cycle Example 9-1 (Ed 8) Determine the thermal efficiency of a Rankine Cycle using steam as working fluid in which the condenser pressure is 10 kpa. The boiler pressure is 2 MPa. The steam leaves the boiler as saturated vapour. Bepaal die termiese rendement van n Rankine Kringloop met stoom as werksvloeier waar die kondensator-druk 10 kpa is. Die ketel-druk is 2 MPa. Die stoom verlaat die ketel as versadigde damp.