Chapter 7 Steam Turbines MEE 325 Power Plants Engineering

Transcription

1 Chapter 7 Steam Turbines MEE 325 Power Plants Engineering Atikorn W. Mechanical Engineering Department King Mongkut s University of Technology Thonburi

2 Introduction Steam turbine is an energy conversion device which compose of two steps; 1. The high pressure and high temperature steam flow through the nozzle leaving out very high velocity. 2. Steam jet impacts the turbine blades to transfer momentum to the wheel directed shaft work. Applications Electrical generator prime mover Sea-trans propel Large compressors, pumps, fans Hero of Alexandria (120 BC)

3 Steam turbine classifications 1. Straight-flow without reheat/ Condensing or Noncondensing 2. HP-LP without reheat/ Condensing 3. Single reheat (HP-IP)-Double flow LP /Condensing 4. Double reheat (HP-IP)-Reheat turbine-(multi) flow-lp/ Condensing 5. Controlled or Uncontrolled extraction with automatic valve ( for load variation or process ) 6. Tandem-Compound shaft orientation (60Hz/3600rpm only) 7. Cross-Compound shaft orientation (60Hz/3600 rpm, 50Hz/3000rpm) Named Shaft oriented: No. of LP flow:last stage blade length Ex. TC4F30 = Tandem: 4 Flow (2x2) : 30 inch

4 Steam turbine classifications

5 Steam turbine classifications

6 Steam turbine classifications

7 Steam turbine classifications

8 Fundamental Thermo-Fluid review Velocity of pressure pulse in a fluid ( reversible isentropic) c = p ρ s for liquid c = (γrt) (assume ideal gas) when c = sonic velocity produced by pressure pulse and depends on density; for common liquids c = 1650 m/s ; air at 300K, c = m/s consider M = θ/c if M<1 called subsonic, M>1 called supersonic

9 Fundamental Thermo-Fluid review Stagnation properties (isentropic stagnation state)

10 Fundamental Thermo-Fluid review Stagnation properties (isentropic stagnation state) stagnation properties use subscript o (Oh) not 0 (zero) h o = h + θ2 2 For ideal gas h=c p.t ; hence p 0 = T 0 p T γ γ 1 = 1 + γ 1 γ M2 γ γ 1

11 Fundamental Thermo-Fluid review Subsonic and Supersonic Nozzles For isentropic flow da A = (M2 1) dθ θ when M<1 at inlet; if A= conv, outlet = Nozz ; div-diff when M>1 at inlet; if A= conv, outlet = Diff, div-nozz

12 Fundamental Thermo-Fluid review Subsonic and Supersonic Nozzles

13 Fundamental Thermo-Fluid review Critical Pressure ratio and Choked Flow ω A = γ R p 0 M T γ 1 (γ+1)/[2 γ 1 ] M2 2

14 Fundamental Thermo-Fluid review Critical P-T ratio and Choked Flow T T 0 = 2 γ + 1 p p 0 = 2 γ + 1 γ γ 1 = Specific heat ratio for an ideal gas p 0, T 0 = inlet pressure and temperature p *, T * = sonic pressure and temperature however, it is related to polytropic exponents constant (k) such as air; k=1.4 sat. steam; k = ; initially superheated steam; k = 1.3 or calculate from Zeuner s relation for wet steam x = steam quality k = (x)

15 Fundamental Thermo-Fluid review Flow in Steam Nozzle when θ 0 is small h 0 + θ = h 1 + θ θ 1 = h 0 h 1 1/2 m/s G.Thu

16 Fundamental Thermo-Fluid review Flow in Steam Nozzle (derived from conv-div nozzle) θ1 = 2k k 1 p 0ν 0 1 p 1 p 0 (k 1)/k 1/2 ω A = 2k k 1 p 0 ν 0 p 1 p 0 2/k p 1 p 0 (k 1)/k 1/2 when applies maximum discharge at throat p p 0 = 2 k + 1 k k 1

17 Fundamental Thermo-Fluid review Nozzle Efficiency η n = h 0 h 1 h 0 h 1s For an ideal gas η n = T 0 T 1 T 0 T 1s also or η n = θ 1 2 θ 0 2 θ 1s 2 θ 0 2 η n = θ 1 2 θ 1s 2 when θ 0 comparable small

18 Fundamental Thermo-Fluid review Nozzle Efficiency new defined velocity coefficient ; φ = θ 1 θ 1s = η s 1/2 and discharge coefficient; C d C d = ω ω s The angle should not be too large to prevent flow separation, normally, varies from 5 to 8.

19 Fundamental Thermo-Fluid review Nozzle Types There are two types: 1. Reamed or round nozzles, easily made, low cost, greater in length, good for high pressure impulse, but low efficiency. 2. Foil nozzles made of curved airfoil sections, good issuing jet, high efficiency with more expensive.

20 Supersaturated Flow Expansion in a nozzle การขยายต วของความด นและการกล นต วของไอเป ยกใน nozzle เก ดข นอย าง รวดเร วซ งแม ว าจะอ างอ งกระบวนการขยายต วแบบ isentropic แต ในความจร งแล ว การกล นต วของไอน าจะเร มเก ดข นหล งจากความด นลดต าลงอย างรวดเร วท ไหลผ าน nozzle โดยเร มกล นต วหล งจากผ านค า dryness (x) = ไปแล ว ด งน นการไหลหล งจากเส น sat. vapor จนถ งช วง x= น เร ยกว า Supersaturated flow โดยม เส นท แสดงค า x= เร ยกว า Wilson line

21 Expansion in a nozzle Supersaturated Flow (p )

22 7.3 Turbine Blading Impulse turbines Constant pressure flow through the blade passage Wheel rotates only due to the impulsive effect of the jets Momentum conservation Inlet jet Outlet jet = Angular momentum of wheel

23 V 0 = inlet to the nozzles V 1 = outlet of the nozzles = inlet to the blades V 2 = outlet of the blades V b = πd mn = mean blade velocity 60 A b = π 4 D2 2 D 2 1 = πd m h b

24 7.3.1 Impulse turbines 1 Velocity diagrams, diagram work and diagram efficiency

25 7.3.1 Impulse turbines 1 Velocity diagrams, diagram work and diagram efficiency V 0 = inlet to the nozzles V 1 = outlet of the nozzles = inlet to the blades V r1 = relative inlet velocity to the blades V 2 = outlet of the blades V r2 = relative outlet velocity to the blades V b = πd mn = mean blade velocity 60 α = nozzle angle or steam inlet to the blades β 1 = inlet blade angle subtended to the rotation direction β 2 = outlet blade angle subtended to the rotation direction γ, δ = relative and absolute exit blade angle measured Clockwise V ω = change in the velocity of whirl, to make tangential thrust V a = change in the velocity of axial, to make axial thrust

26 7.3.1 Impulse turbines 1. Velocity diagrams, diagram work and diagram efficiency V ω = V ω1 V ω2 = V 1 cosα V 2 cosδ tanβ 1 = V 1sinα V 1 cosα V b blade friction factor = k b = V r2 V r1 Tangential thrust = P t = ω s V ω Axial thrust = P a = ω s V a Blading work = W D = P t V b = V ω V b Blading efficiency = η D = 2 V ωv b V 2 1

27 2. Optimum velocity ratio Impulse turbines velocity ratio = ρ = V b V 1 3. Graphical method η D max = 1 + k b 2 cos 2 α

28 7.3.1 Impulse turbines 4. Alternative way of drawing Example case of symmetrical blade with blade friction

29 7.3.1 Impulse turbines 4. Alternative way of drawing Example case of symmetrical blade with frictionless

30 7.3.1 Impulse turbines 6. Pressure compounding or Rateau staging Fixed nozzle with multistage impulse turbines Equal enthalpy drops at each turbine stage isentropically All nozzles increase velocity at the same speed due to equal expansion A four stage turbine V 1 = h 0 h 4 1/2 the require n stage of expansion is calculated by n = Δh s total Δh s stage

31 6. Pressure compounding or Rateau staging

32 6. Pressure compounding or Rateau staging

33 7.3.1 Impulse turbines 7. Velocity compounding or Curtis staging All the pressure and enthalpy drop take place in first stage The pressure remains constant thereafter the first stage The only velocity decreases gradually flow through moving stage blades A 2-row Curtis stage P t = ω s Σ V ω P a = ω s Σ V a η D = 2Σ V ωv b V 2 1

34 7.3.1 Impulse turbines 7. Velocity compounding or Curtis staging

35 7.3.1 Impulse turbines 7. Velocity compounding or Curtis staging

36 7.3.1 Impulse turbines 9. Optimum velocity ratio for a Curtis staging Let s consider symetrical two-row, frictionless Curtis stage

37 7.3.1 Impulse turbines 9. Optimum velocity ratio for a Curtis staging Let s consider symmetrical two-row, frictionless Curtis stage Rate ofenergy transfer from fluid to rotor = W D = ω s V ω V b For any Z-rows moving blades Curtis optimum velocity ratio = ρ opt = cosα 2Z η D max = cos 2 α

38 Chapter 7 (to be continued)

39 7.3.2 Reaction turbines Reaction turbines Pressure drop occurs both in the nozzles and or the fixed blades (fb), as well as the moving row of blades (mb) All blades channels are also of the nozzle shape Blades rotates due to both the impulse effect of the jets and the reaction force of the exiting jets, so-called in short impulse turbines degree of reaction = R = h mb h fb + h mb 50% reaction turbines are called Parsons turbines

40 7.3.2 Reaction turbines

41 7.3.2 Reaction turbines

42 7.3.3 Variation of blade velocity along blade height For the LP turbine stage, the blade heights are quite large, the a big different acts on the root and tip speed For good efficiency, the blade angles should vary with the diameter twisted blades are used in the later stages of the turbine Since V b is proportional to the radius, angle 1 will varies accordingly to maintain blade work; V b V constant

43 7.3.3 Variation of blade velocity along blade height

44 7.3.3 Variation of blade velocity along blade height

45 Last stage blade height As the pressure decreases during the expansion, the specific volume increase The volume flow of steam needs to be increase with inceasing flow area At the last stage h b and D m should have maximum values Limitation of materials stress are normally limited the maximum blade velocity to m/s For straight Blade height is normally 20% of Dm which maximum h b is about m For twisted and tapered blade height could reach to 30% of Dm which maximum h b is about 0.67 m

46 End of Chapter 7