3. Flows in a Steam Path. Steam Turbine 3. Flow in Steam Path 1 / 112

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1 3. Flows in a Steam Path Steam Trbine 3. Flow in Steam Path /

2 Flid Dynamics Steam Trbine Flow Model 4 Thermodynamics and Flid Dynamics for Steam Trbines 35 Dimensionless Nmbers 49 Implse Trbine and Reaction Trbine 65 Stage Efficiency 0 Blade Profile Enhancement 07 Steam Trbine 3. Flow in Steam Path /

3 Nomenclatre of Trbine Blade Leading edge Blade thickness Camber angle Sction side Pressre side Trailing edge Deflection Stagger angle Pitch Blade inlet angle Blade otlet angle Gas inlet angle Gas otlet angle Direction of gas flow Incidence Deviation Angle Direction of gas flow Steam Trbine 3. Flow in Steam Path 3 /

4 Flid Dynamic Force F = mv = V A m = VA (mass flow rate) Nozzle A, V F R Reaction Action Steam Trbine 3. Flow in Steam Path 4 /

5 Speed of Sond [/] a dv p+dp +d p V = 0 Stationary observer p dp a x Observer travelling with wave front p a dv p+dp +d p dp a a p RT V M a x Steam Trbine 3. Flow in Steam Path 5 /

6 Speed of Sond [/] The effect of compressibility is important in high velocity regimes. Mach nmber is the ratio of velocity to acostic speed of a gas at a given temperatre M V/. Acostic speed is defined as the ratio change in pressre of the gas with respect to its density if the entropy is held constant: a p sc With incompressible flids, the vale of the acostic speed tends toward infinity. For isentropic flow, the relation between pressre and density is as follows: p const. ln p ln const. dp d dp p 0 a p d a p RT Steam Trbine 3. Flow in Steam Path 6 /

7 Flow in a Convergent-Divergent Nozzle [/5] Isentropic Flow with Area Change Consider a one-dimensional isentropic gas flow in a convergent-divergent nozzle. Since the mass flow rate is constant, and taking logarithms and then differentiating gives m VA const. d dv V da A 0 Since the stagnation enthalpy is constant in isentropic flow, differentiating the stagnation enthalpy gives ho h V const. dh VdV From Gibb s eqation Tds dh dp / 0 dh dp / Ths, VdV dp p d a d Elimination of density term sing the continity eqation gives s [ A Convergent-divergent Nozzle ] da A dv M V Steam Trbine 3. Flow in Steam Path 7 /

8 Flow in a Convergent-Divergent Nozzle [/5] da = (M ) dv A V Compressor Blades Blade direction Trbine Blades Axial direction M Convergent Nozzle (Nozzle) M M Convergent Nozzle (Nozzle) M M Divergent Nozzle (Diffser) M M Divergent Nozzle (Diffser) M M Steam Trbine 3. Flow in Steam Path 8 /

9 Flow in a Convergent-Divergent Nozzle [3/5] Convergent-divergent nozzle da = (M ) dv A V M = M [ Convergent-Divergent Nozzle ] M x Blade Overlap [ Spersonic Converging-Diverging Nozzle, GE ] Steam Trbine 3. Flow in Steam Path 9 /

10 Flow in a Convergent-Divergent Nozzle [4/5] 삼천포화력본부 #6 LSB (33.5 /3600 rpm) LSB developed by Siemens (3 /3600 rpm) Steam Trbine 3. Flow in Steam Path 0 /

11 Flow in a Convergent-Divergent Nozzle [5/5] Siemens Steam Trbine 3. Flow in Steam Path /

12 Steam Trbine 3. Flow in Steam Path / Choked Flow [/] V 0 p T A M p const. M T T M M R T Ap m 0 dm m d M RT AM M Aa A V m RT a RT p T p M R A m Choked flow is also called as choking of the flow, or, flow choking, or choke.

13 Choked Flow [/] dm dm 0 M There is a maximm airflow limit that occrs when the Mach nmber is eqal to one. The limiting of the mass flow rate is called choking of the flow. If we sbstitte M =, we can determine the vale of the choked mass flow rate. m Ap T R Steam Trbine 3. Flow in Steam Path 3 /

14 Steam Trbine 3. Flow in Steam Path 4 / V p /p.0 a Sonic velocity (p /p ) critical p p High pressre flid V A T Energy eqation: from dv / d(p /p ) = 0, one can get maximm speed, w z z g V V p p q T T c p p V p p p V a RT p p V critical Choked Flow [3/]

15 Steam Trbine 3. Flow in Steam Path 5 / Mass flow rate: Using isentropic relationship, from dm / d(p /p ) = 0, one can get a critical pressre ratio, A V m critical p p Critical pressre ratio - sperheated steam = (=.3) - satrated steam = (=.35) - air = 0.58 (=.4) (see K.C. Cotton, pp. 5) p p p p p A m p p p A m Choked Flow [4/]

16 HP bypass station Application of Choked Flow to Sparger Main Steam Choked Flow [5/] Stop V/V Crossover Control V/V HP IP LP Gen Cold Reheat Ventilation V/V Reheater Hot Reheat Reheat Stop and Intercept V/V HRH bypass station (HRH: Hot Reheat) Condenser Steam Trbine 3. Flow in Steam Path 6 /

17 Typical Trbine Bypass Dmp to Condenser Choked Flow [6/] [ Typical layot showing dmp tbe diffsers fitted into the condenser inlet dct ] Steam Trbine 3. Flow in Steam Path 7 /

18 Application of Choked Flow to Sparger Choked Flow [7/] Desperheater section of a steam conditioning valve Spargers designed to spray ot to end to eliminate steam impinging pon the condenser tbes Steam Trbine 3. Flow in Steam Path 8 /

19 Application of Choked Flow to Sparger Choked Flow [8/] Pressre redcing valve Sparger Steam Trbine 3. Flow in Steam Path 9 /

20 Choked Flow [9/] Steam Trbine 3. Flow in Steam Path 0 /

21 Choked Flow [0/] PWR System Otline Steam Trbine 3. Flow in Steam Path /

22 Comptational Domain for IRWST Choked Flow [/] 차세대원전에서 비상시원자로냉각재계통 (RSC; Reactor Coolant System) 의압력을낮추어주기위하여 POSRV(Pilot Operated Safety Relief Valve) 를통하여고온고압의증기를 IRWST(In-containment Refeling Water Storage Tank) 내부에잠겨있는 sparger 를통하여방출. <Side View> Steam Trbine 3. Flow in Steam Path /

23 Flid Flow Actal Flow Flow of Flids (CRANE Co.) A 0 A j c c = 0.6 c = 0.98 c c =.00 c = 0.98 c c =.00 c = 0.8 c d = c c c A j = c c A 0 V actal = c V ideal m = V actal A j = c c c V ideal A = c d V ideal A c d = discharge coefficient (or flow coefficient) c c = contraction coefficient c = velocity coefficient Steam Trbine 3. Flow in Steam Path 3 /

24 Flid Dynamics Steam Trbine Flow Model Thermodynamics and Flid Dynamics for Steam Trbines Dimensionless Nmbers Implse Trbine and Reaction Trbine Stage Efficiency Blade Profile Enhancement Steam Trbine 3. Flow in Steam Path 4 /

25 Steam Trbine 3. Flow in Steam Path 5 / Steam Trbine Flow Model p p p p p A c m d p p p p A a c Q d CV SV = Stop Valves CV = Control Valves P = First Stage Shell Pressre L-0 L- Condenser Stage Nmber P Steam SV

26 Steam Trbine Flow Model The flow model is a series of orifices or nozzles in a pipe with a constant pstream pressre and downstream pressre. The pressre between any two of these orifices depends entirely on the qantity of steam and the nozzle area following that point. The first stage is represented as having for orifices to simlate a trbine with for control valves, while all the other stages have only one orifice. If all for control valves are opened, the flow will increase ntil an eqilibrim condition is reached. This steady state flow throgh each orifice in the model will be the same. Therefore, the pressre pstream of each orifice will depend on the area of the downstream orifice. As steam passes from throttle to the condenser, the areas of individal orifices are progressively larger. Therefore, the pressre pstream of each stage is lower than the preceding stage. A nmber of steam trbine stages can be classified into only three grops: 3 The first stage or governing stage Variable flow area by control valve position The last stage (LSB) Flow choking is occrred All the stages between Constant pressre ratio even dring part load operation In view of the specifics of the steam path design, all stages of a condensing steam trbine are divided into for grops, Governing stages Stages with high pressre and low volme discharge of steam (D) 3 Intermediate stages with relatively low pressre and high volme discharge of steam (3D) 4 Last stages in the lowest-pressre range, characterized by a very high volme discharge. Steam Trbine 3. Flow in Steam Path 6 /

27 Throttle press st stage shell nd stage bowl nd stage shell 3 rd stage bowl 3 rd stage shell 4 th stage bowl 4 th stage shell 5 th stage bowl 5 th stage shell 6 th stage bowl Throttle Pressre, psig Steam Trbine Flow Model Factor of 00 Factor of Steam Trbine 3. Flow in Steam Path 7 /

28 Steam Trbine Flow Model Intermediate Stage For a throttle pressre of 400 psig, the first stage pressre with VWO wold be 800 psig and the pressre downstream of the second stage wold be abot 500 psig. In this case, the pressre ratio across the second stage is.. If throttle pressre decreases to 00 psia, the flow wold decrease by a factor of to. this relationship holds tre for all the stages ntil the last stage. That is, the pressre ahead of the last stage will decreases by a factor of to. All other stages, except HP first stage and LP last stage, operate at a constant pressre ratio and therefore a constant efficiency over the load range. Velocity triangles for varios steam trbine loads Steam Trbine 3. Flow in Steam Path 8 /

29 Steam Trbine Flow Model HP st Stage The governing stage has the niqe characteristic of variable area. As control valve opens, the area allowing throttle steam to flow throgh the trbine increase and prodce more power. In addition, the change in flow changes the first stage discharge pressre, reslting in the pressre ratio across the first stage. Therefore, the first stage efficiency changes with control valve position. At valves wide open the first stage is designed for the ideal ratio of wheel velocity and steam velocity. As control valves close, the first stage efficiency decreases. Fll Arc Partial Arc Steam Trbine 3. Flow in Steam Path 9 /

30 Trbine Section Efficiency [%] Steam Trbine Flow Model HP st Stage IP Trbine LP Trbine HP nd Stage to Cold Reheat HP st Stage Throttle Flow Ratio Steam Trbine 3. Flow in Steam Path 30 /

31 Steam Trbine Flow Model LP Last Stage The last low pressre trbine stage is the only other stage that experiences significant changes in pressre ratio as a reslt of normal power plant operation. The pressre of pstream of the last stage changes with control valve position and the downstream pressre changes with condenser pressre. Therefore, the last stage efficiency changes with both control valve position and with condenser pressre. The change in pressre ratio across the first and last stage dictates the change in efficiency of the HP and LP trbines, respectively. Steam Trbine 3. Flow in Steam Path 3 /

32 Stage Pressre Ratio [Sample] Stage Extract Bowl P Shell P Press Remarks (psia) (psia) ratio Throttle HP trbine otlet IV IP trbine otlet X-over pipe LP trbine inlet Exceeding a critical PR Exceeding a critical PR Exceeding a critical PR Connected to condenser Steam Trbine 3. Flow in Steam Path 3 /

33 Pressre ratio Stage Pressre Ratio [Sample] Extraction stage : 5, 7, 0,, 3, 5, 6, 7 Exceeding critical pressre ratio HP IP LP Stage nmber Steam Trbine 3. Flow in Steam Path 33 /

34 Steam Trbine Flow Model Discssion Several LP trbine stages, 3 rd to LSB, have higher than critical pressre ratio. Discss the following isses. ) Possibility of choked flow ) Flow area 3) Steam extraction 4) LSB in terms of degree of reaction Critical pressre ratio - sperheated steam = (=.3) - satrated steam = (=.35) - air = 0.58 (=.4) (see K.C. Cotton, pp. 5) Steam Trbine 3. Flow in Steam Path 34 /

35 Flid Dynamics Steam Trbine Flow Model Thermodynamics and Flid Dynamics for Steam Trbines Dimensionless Nmbers Implse Trbine and Reaction Trbine Stage Efficiency Blade Profile Enhancement Steam Trbine 3. Flow in Steam Path 35 /

36 Flow Behavior in a Trbine Stage r z Nozzle Row Bcket Row The flow behavior is investigated in a tangential plane. Therefore, the flow velocity has two components, one is axial component denoted by sbscript z, and the other is tangential component denoted by sbscript implying a whirl velocity. Pressre E Kinetic E Thermal E Thermal E Mechanical E Steam Trbine 3. Flow in Steam Path 36 /

37 Absolte vs. Relative Velocity Flid velocity is an important variable governing the flow and energy transfer within a trbine. The absolte velocity ( ) is the flid velocity relative to some stationary point and is sally parallel to the nozzle (stationary blade). When considering the flow across a rotating element like a bcket, the relative velocity ( w ) is important and is sally parallel to the rotating element. Vectorially, the relative velocity is defined as: where of the bcket. w c is the tangential velocity c p p w c w 3 3 c 3 3 [ Velocity Triangle in an Axial Trbine ] p 3 c Bcket Row Nozzle Row Steam Trbine 3. Flow in Steam Path 37 /

38 Velocity Triangle at Root Velocity Triangle in a Trbine p c c : absolte velocity of flid : tangential velocity of blade w : relative velocity of flid to blade Tip Nozzle Row p w c Root Bcket Row r Root r Tip Nozzle Row Bcket Row p 3 w 3 3 c 3 3 The absolte velocity increases from c to c across the nozzle. The absolte velocity decreases from c to c 3 across the bcket. This is becase the kinetic energy entering bcket is extracted by the bcket. Ths, bcket attains rotating power. In the case of trbine, the convention chosen is that the angles are positive when measred in the direction of rotation. Therefore,, are positive; 3, 3 are negative. Steam Trbine 3. Flow in Steam Path 38 /

39 Velocity Triangle at Tip Velocity Triangle in a Trbine p c Tip Nozzle Row Root p Bcket Row w c r Root r Tip Nozzle Row Bcket Row p 3 w 3 3 c3 3 Steam Trbine 3. Flow in Steam Path 39 /

40 Expansion Lines A nozzle is sed to provide partial expansion of the gas as well as to gide the flow smoothly into a bcket. If the flow is isentropic in the nozzle, condition s is achieved after passing throgh the nozzle. Practically, however, nozzle expansion occrs along crve - becase of losses occrred in the nozzle path. Change in stagnation pressre (p o, p o, ) is de to the losses, becase there is no work extraction from the flid inside the nozzles. The process along -3 represents the expansion throgh bcket. h o, o, /c /c s o,3ss o,3s 3ss 3s p o, p o, p p o,3 3 p 3 p o3 /c 3 p c p w Bcket Row p 3 w 3 3 Nozzle Row c 3 c 3 If the flow is isentropic only in the bcket, condition o,3s or 3s is achieved. [ Expansion Line in a Trbine Stage ] s Steam Trbine 3. Flow in Steam Path 40 /

41 Trbine Efficiencies Total-to-static Efficiency Total-to-total Efficiency ts h o, h o,3 o, h o,3 ho, ho,3ss ho,3ss h3 ss ho, h3 ss h tt h h o, o, h h o,3 o,3ss In many trbines (especially steam trbines), the kinetic energy at the exit (c 3 /) shold be as small as possible, becase this represents aerodynamic loss. Therefore, the design philosophy is to achieve as low a velocity at the exit as possible. For this reason, active length of LSB of steam trbines is very long. In sch sitations, a total-to-static efficiency is sed. In most aeronatical applications gas trbines, the exhast energy is tilized for thrst generation. Therefore, the exhast energy is sed to prodce sefl power. Therefore, a more appropriate definition to represent the performance of these trbines is the total-to-total efficiency. The total-to-total efficiency is also defined as isentropic efficiency. For a mltistage trbine, total-to-total efficiency shold be sed becase the kinetic energy at the exit of a stage (except the last stage) is not lost. Steam Trbine 3. Flow in Steam Path 4 /

42 Eler Eqation [/7] Notation for Flow in a Bcket Row p c w or c w 3 or c 3 Nozzle Row r r 3 p w c Bcket Row Bcket Row c: absolte velocities (velocities in the reference frame of the nozzles) w: relative velocities (velocities relative to moving srface, the bckets) : tangential velocities of blades (in the positive direction), are positive, and 3, 3 are negative. p 3 w, dc = (c, c,3) c w w w 3 3 c 3 c, B w,3 c 3 c,3 N 3 Steam Trbine 3. Flow in Steam Path 4 /

43 Eler Eqation [/7] The change of momentm between the flow entering and leaving the bcket can be sed to calclate the force acting on the bcket. There are three principal components of this force, axial, radial, and tangential. The axial and radial components are important for the design of bearings and for the analysis of vibration excitations, etc. Bt, these two components cannot contribte to the work transfer between the working flid and the bcket. Only the tangential component of the force can prodce a change in enthalpy throgh a work transfer. Tangential force on rotor from entering flid = Work bcket = force length = Power on bcket per nit time = work on rotor / time = Net power on bcket, W m c m c, r Therefore, Eler s eqation can be derived. m c, m c, r r c r m c c 3,,3 3, 3,3 c c, w W m c 3 3 /, 3,3 c Eler eqation (e.) Trbine has a positive work ot, however, a pmp, fan, and compressor will have negative work ot. Steam Trbine 3. Flow in Steam Path 43 /

44 Eler Eqation [3/7] The first law of thermodynamics is, q3 3 p3 3 p c3 c g q3 h3 h c 3 c gz3 z w3 q h h g z z z3 z w3 o,3 o, w c z q w 3 z 3 c 3 q ho,3 ho, 3 3 w (e.) For an adiabatic bcket row in the absence of external torqes, or large changes in elevation, the first law of thermodynamics gives, w w h h 3 b o, o,3 (e.3) Therefore, following relationship can be obtained from Eler eqation, w w h h 3 b o, o,3, 3,3 c c or dh o d c θ (e.4) It is clear that the stagnation enthalpy and pressre drop in a trbine are directly proportional to the change in tangential velocity and blade speed. This is the most sefl single relation in trbine design. In the preliminary design of axial flow machines, the change of radis of the mean flow can often be ignored, so that a more restricted version of Eler s eqation becomes dh o dc θ (e.5) Steam Trbine 3. Flow in Steam Path 44 /

45 Eler Eqation [4/7] Pressre and Temperatre Drop in a Bcket Row w h h h c T o,3 To, 3c,3 c, o, 3 o, p o,3 w h o, c T h h c c 3 b o,3 o, 3,3, p o, T T o,3 o, cpt o, p p o,3 o, For simple diagram having constant from stage inlet to otlet, c c c cos tan 3c,3 c,,3, tan 3 p p o,3 o, c cos cpto, tan tan 3 p p o,3 o, v a z tan tan 3 T T o,3 o, c cos tan tan cpto, 3 T o,3 T o, vz tan tan a 3 Steam Trbine 3. Flow in Steam Path 45 /

46 Eler Eqation [5/7] Pressre and Temperatre Drop in a Bcket Row p p,3 v T o o,3 z tan tan o, a 3 T o, vz tan tan a 3 The pressre drop and temperatre drop in a trbine are strongly dependent on the blade speed, axial velocity or mass flow, inlet and exit flow angles, and absolte ( 3 ) or relative flow trning angles ( 3 ). Higher trning angles prodce larger pressre and temperatre drops, and ths a higher work otpt. Unlike compressors, large flow trning can be accomplished withot flow separation. The effect of the mass flow (or flow coefficient) is opposite to that of a compressor. A trbine with and 3 fixed and blade speed held constant, higher mass flow prodces larger pressre and temperatre drops. If, 3, and mass flow held constant, higher blade speeds prodce larger pressre or temperatre drops and higher work otpt per stage. Therefore, higher speeds reslt in more compact power plants. (this is why fossil power plants adopt 3600 rpm instead of 800 rpm) Steam Trbine 3. Flow in Steam Path 46 /

47 Eler Eqation [6/7] [Exercise 3.] Use of the Eler s eqation What is the power otpt (kw) of the first stage of an axial flow steam trbine which takes 600 kg/s of steam at 600C and 50 bar stagnation conditions? After passing throgh the nozzle, the flow leaves nozzle at a direction 70 degrees from that of axial, at a velocity of 500 m/s, as given in figre, and discharges it from the bcket (rotor) withot swirl (c,3 = 0). The pitch diameter of the bcket is m, and the shaft speed is 3600 rpm. The trbine has an isentropic stagnation-to-stagnation stage efficiency of 90 percent. =70 Figre Steam Trbine 3. Flow in Steam Path 47 /

48 Eler Eqation [7/7] [Soltion] Power otpt of the stage can be obtained W The first law of thermodynamics is as follows, q The trbine can be treated as adiabatic. Therefore, w From the Eler eqation, h From the given conditions, rn 88.5m / s c, c sin 470m / s 60 h m o, ho,3,566 / 88 s Therefore, kg m W 3 m h m o, o,3 600 s s 40 W m h m 3, o,3 ho,3 ho, 3 3 w h o h W m h o h 3,3 o, h c o, o,3, 3,3, net trbinew MW 3, h o h c c 3, o,3 h h , kw Steam Trbine 3. Flow in Steam Path 48 /

49 Flid Dynamics Steam Trbine Flow Model Thermodynamics and Flid Dynamics for Steam Trbines Dimensionless Nmbers Implse Trbine and Reaction Trbine Stage Efficiency Blade Profile Enhancement Steam Trbine 3. Flow in Steam Path 49 /

50 Generals By means of dimensional analysis, a grop of variables representing some physical state is redced into a small nmber of dimensionless grops. This enables a niqe representation of certain classes of machines based on pressre rise (or drop) and mass flow. Most importantly, it enables redction of laboratory testing effort by redcing the nmber of variables. Specifically, the following can be accomplished: ) Prediction of a prototype performance from tests condcted on a scaled model (similitde). ) Uniqe representation of the performance (e.g., Mach nmber, Reynolds nmber effect). 3) Determination of a best machine on the basis of efficiency for specific head, speed, and flow rate. Most important dimensionless nmbers in axial trbines are degree of reaction, loading coefficient, flow coefficient, etc. Steam Trbine 3. Flow in Steam Path 50 /

51 Loading Coefficient [/] The most important performance variable is the work done on the flid, or delivered by the machines. Its dimensionless form is the loading coefficient, which is also called as work coefficient. That is, the loading coefficient reflects the pressre/temperatre drop across a trbine. For an adiabatic stage, the loading coefficient is defined by the ratio of specific stage work inpt to the sqare of mean bcket speed, that is, w b h o, h o,3 c, c 3,3 where w b is the isentropic work done at bcket row. For simple diagram having constant from stage inlet to otlet, c, c,3 v z tan tan 3 The loading coefficient is positive for trbines, and negative for compressors and pmps. Steam Trbine 3. Flow in Steam Path 5 /

52 Loading Coefficient [/] In trbines having the vale of.5 are called as highly-loaded or high-work trbines (or trbine sections). Vales of.0 mean low-work or lightly-loaded trbine stages. ( =.0, = 0.5, = 0.5) ( =.0, = 0.5, = 0.5) ( = 0.5, = 0.5, = 0.5) (a) high-work trbine (b) medim-work trbine (c) low-work trbine ( = work coefficient, = flow coefficient, = degree of reaction) Normally, last stage blades of steam trbines have very high loadings at the hb, and light loadings at the tip. The vale of the loading coefficient for an implse trbine with a maximm loading coefficient is two when the exit swirl is zero. In a 50% reaction trbine with a maximm loading coefficient is one. c, = c, = c w 3 w 3 c w c 3 c 3 w (a) 0% reaction velocity diagram (b) 50% reaction velocity diagram Steam Trbine 3. Flow in Steam Path 5 /

53 Flow Coefficient The flow coefficient reflects the effect of the mass flow as well as blade speed. The flow coefficient is defined the ratio of the axial velocity entering to the mean bcket speed, that is, v z In a simple velocity diagram, the flow coefficient is constant. The flow coefficient can be different at rotor inlet and at rotor otlet where both c z and vary throgh the stage. It also varies with radis. The relationship between loading coefficient and flow coefficient is tan tan 3 Steam Trbine 3. Flow in Steam Path 53 /

54 Smith Chart A sefl investigation of trbine performance characteristics was compiled by Smith with more than 00 sets of data from 33 trbines. Smith fond that the efficiency of a trbine depends strongly on the loading coefficient and the flow coefficient. The loading coefficient inflences the pressre gradient in the passage, and this increases the losses. The flow coefficient is a direct measre of the mass flow, for a given speed and machine size. Higher flow coefficient, and hence higher mass flow, reslts in a higher pressre drop, and the corresponding losses also increase. Therefore, the highest efficiencies occr at low loading and low flow coefficient. As well as being an excellent comparator for different design options, the chart may be sed to give preliminary jdgment on the efficiency attainable for a given design. The chart gives the highest efficiency. This means that it was prodced nder the assmption that the trbine is designed with large blades, and zero tip clearance. In a practical design which has all the above merits, the highest efficiency attainable wold be 95%. When the lower technology level blades are employed, three points may be redced from the vales obtained from the chart. Steam Trbine 3. Flow in Steam Path 54 /

55 Degree of Reaction [/0] The degree of reaction in the trbine is defined as, In the nozzle path, the first law of thermodynamics is, In the nozzle, adiabatic process occrs, and no work prodces. Therefore, eqation () becomes, From the first law of thermodynamics, The following relationships are valid is a trbine stage. Ths, static enthalpy drop in the bcket = 00 (%) static enthalpy drop in the stage q h q h h h h 3 h h 0. c c w 5 3 h. 5 0 c c h h h h h3 h 0. c 3 c w3 3 5 q c c3 w 3 0 h h 3 h ; adiabatic process ; for a normal stage 3 w w3 w3 o, c 3 ; no work at nozzle row h o,3 c 3 h o, h o,3 w 3 w 3 () () (3) (4) h o, o, /c /c s /c o,3ss o,3s 3ss 3s p o, p o, p p o,3 3 p 3 p o3 /c 3 s [ Expansion Line in a Trbine Stage ] Steam Trbine 3. Flow in Steam Path 55 /

56 Degree of Reaction [/0] Using Eler eqation, h h w c 3 3, 3,3 c (5) Inpt the eqations () and (5) into () gives, c c From the velocity triangle, For a simple velocity triangle, c vz c,,, c vz c v 3,3,3 v z, z,3 c3 c 3,3 Therefore, the degree of reaction becomes, c c,, c,3 c 3,3 For a simple velocity diagram having constant from stage inlet to otlet., c, c,3 vz 3 tan tan 3 (6) p p p 3 c Bcket Row w c w 3 3 c 3 Nozzle Row [ Velocity Triangle in a Trbine Stage ] 3 Steam Trbine 3. Flow in Steam Path 56 /

57 Degree of Reaction [3/0] Eqation (6) becomes, From Eler eqation, v tan tan 3 z tan tan 3 w b c c c tan,,3 z tan 3 (7) (8) Divide eqation (8) by gives, c z w s tan tan 3 ( ) (9) From eqation (7) and (9), an important reslt is obtained. tan 3 tan tan (0) From eqation (9) and (0), the nknown angles of the absolte velocity can be obtained. / tan / tan 3 () Trbomachinery design initiated by experienced designers throgh the choice of the flow and loading coefficients and the degree of reaction and then determine the flow angles sing eq. (). These are tre only for a normal stage. If the axial velocity does not remain constant, the proper eqations need to be redeveloped from the fndamental concepts. Steam Trbine 3. Flow in Steam Path 57 /

58 Degree of Reaction [4/0] Similar expressions can be developed for the flow angles of the relative velocity. The Eler eqation can be written as w s h h3 h h w w v tan,,3 z tan Divide eqation (8) by gives, tan tan 3 3 Since the stagnation enthalpy of the relative motion is constant across the bcket. Ths, h h3 w3 w vz tan 3 tan tan tan 3 Therefore, the nknown angles of the relative velocity can be obtained. 3 w, dc = (c, c,3) c w w c, B w,3 c 3 N c,3 / tan / tan 3 () Steam Trbine 3. Flow in Steam Path 58 /

59 Degree of Reaction [5/0] tan 3 tan tan (0) It shows that the loading increases as the reaction decreases. A small reaction means that the pressre drop across the bcket is small, bt the large loading is the reslt of a large deflection. p c In the nozzle, the flow leaves at high speed at large angle. Nozzle Row The high kinetic energy obtained this way becomes available for doing work on the bckets. p w c The flow is then deflected back toward the axis and beyond to a negative vale of 3, so that the last term in eqation (0) is positive. ( 3 = in most trbine stages) Bcket Row Ths, for a fixed reaction, an increase in the absolte vale of 3, obtained by increasing it in the opposite direction of, leads to a large deflection and a large vale of loading coefficient. p 3 w 3 3 c 3 3 Ths, a fairly low vale of reaction and high trning gives heavily loaded blades and a compact design. Steam Trbine 3. Flow in Steam Path 59 /

60 Degree of Reaction [6/0] c, = (a) 0% reaction velocity diagram c w 3 w c 3 c, = (b) 50% reaction velocity diagram w c w 3 c 3 c,3 c, (c) 00% reaction velocity diagram w 3 w c 3 c Steam Trbine 3. Flow in Steam Path 60 /

61 Degree of Reaction [7/0] 0% Reaction 50% Reaction c, = c w 3 w c 3 c, = w c w 3 c 3 A zero reaction trbine is called an implse trbine becase there is no expansion or acceleration of the flow throgh the rotor blades, and the rotor torqe comes wholly from the implse of the nozzle stream. With no pressre drop across the bcket row, pressre seals are not reqired. A freqently sed implse diagram has axial stage entry and exit flows and the reasonably high loading coefficient of.0. In 50% reaction velocity diagrams, the bisector of the line joining the apexes of the absolte and relative velocity triangles crosses in the middle, which is why the diagrams become symmetric. Sch diagrams are freqently favored for trbines becase they have accelerating flow to an eqal extent in nozzle and bcket passages, which leads to lower losses. The rectanglar trbine stage diagram shown in above has the additional advantage of having axial flow at stage inlet and otlet. Also tests show this gives the highest efficiency for trbine stages. Steam Trbine 3. Flow in Steam Path 6 /

62 Degree of Reaction [8/0] 0% Reaction Stage All of the static enthalpy drops across the nozzle in a 0% reaction stage. For sch a stage, from eq. (), tan tan or It can be assmed that the axial velocity is constant at the inlet and exit of the stage. In this case, w = w If the flow angles are eqal to the blade angles, then the bcket has a symmetric shape. p p c w Bcket Row c w 3 3 c 3 Nozzle Row The blades having low reaction are heavily loaded. For a normal stage with axial entry and with degree of reaction of 0, the relation tan redces to 3 p 3 c, w, dc = (c, c,3) w,3 For an implse stage, the flow angles for absolte and relative velocity are redced to / tan tan / tan 3 tan 3 w c w 3 3 c3 N B Steam Trbine 3. Flow in Steam Path 6 /

63 50% Reaction Stage [/] Degree of Reaction [9/0] A 50% reaction stage has eqal static enthalpy drops across the nozzle and bcket. For sch a stage In order to get a high efficiency, the flow angle at the inlet is kept only slightly negative, bt if some of the efficiency is sacrificed to achieve higher performance, the inlet flow angle may reach = 45. For sch a stage, a flow coefficient may have a vale of = 0.75, which gives =.5. tan tan 3 For a 50% reaction stage, the flow angles for absolte and relative velocity are redced to tan tan 3 tan tan 3 From these it can be seen that tan tan 3 Therefore, the velocity triangles formed at the inlet and exit of the bcket are symmetrical each other. Ths, c w 3 c3 tan 3 tan w Steam Trbine 3. Flow in Steam Path 63 / w, B dc = (c, c,3) c w,3 c,3 c, w [ Velocity Triangle ] p p p 3 c Bcket Row w c w 3 c 3 w 3 Nozzle Row 3 3 c 3 N 3 3

64 Stage Loading Coefficient 50% Reaction Stage [/] Degree of Reaction [0/0] The stage loading coefficient for 50% reaction stage is, tan tan The figre gives the design and off-design performance of 50% reaction stage, based on above eqation. It is clear from the figre that increases linearly with for a given The loading coefficient increases with for a given flow coefficient The present trend in the design of the nozzle is to se as high an as possible. Bt it shold be realized that increasing increases w for a given blade speed, and ths the flow is likely to reach spersonic speeds and limit the mass flow =5 Therefore, the designer has to vary,,, and v z (or ) to get an optimm design for a given trbine inlet temperatre. The crves in this figre are for ideal conditions. That is, viscos losses, shock losses, or three-dimensional effects are not inclded Flow Coefficient [ 50% Reaction Stage ] Steam Trbine 3. Flow in Steam Path 64 /

65 Flid Dynamics Steam Trbine Flow Model Thermodynamics and Flid Dynamics for Steam Trbines Dimensionless Nmbers Implse Trbine and Reaction Trbine Stage Efficiency Blade Profile Enhancement Steam Trbine 3. Flow in Steam Path 65 /

66 터빈동력생산원리 유체유동에의해발생하는힘 V m V Tangential m V sin V sin Axial V m V Steam Trbine 3. Flow in Steam Path 66 /

67 Flow Behaviors arond an Airfoil [/3] Velocity Distribtion arond an Airfoil Velocity distribtion NACA 44 p o p V p V Pressre distribtion Steam Trbine 3. Flow in Steam Path 67 /

68 Flow Behaviors arond an Airfoil [/3] Lift Lift Lift pda p Pressre srface There is an angle of attack that prodces the optimm lift force. If this angle is exceeded, the airfoil stalls and the drag force increases rapidly. (AOA = 5 deg.) Sction srface Steam Trbine 3. Flow in Steam Path 68 / x

69 Flow Behaviors arond an Airfoil [3/3] Lifting Force Acting on a Trbine Blade p p p c ½ c b Direction of rotation P S S P c P: Pressre srface S: Sction srface p ½ c p o Steam Trbine 3. Flow in Steam Path 69 /

70 Degree of Reaction static enthalpy drop in the bcket = 00 (%) static enthalpy drop in the stage h h h h % T T 3 T T 3 p p p p 3 3 dp q dh 00 % 00 % Thermodynamic process occrred in compressor and trbine is adiabatic process. And ignoring density changes. dh dp Steam Trbine 3. Flow in Steam Path 70 /

71 Implse Trbine The pressre and velocity of the gases passing throgh the bcket of the implse trbine remain essentially the same, and the only change thing is the direction of flow. Nozzle Row Therefore, the degree of reaction of the implse trbine is zero. The trbine absorbs the energy by the change of the direction of the high velocity gases. Bcket Row V j U F V j U Bcket U [ LSB (GE) ] [ Implse Trbine, = 0% ] Steam Trbine 3. Flow in Steam Path 7 /

72 Reaction Trbine A reaction trbine changes the velocity and pressre of the gases. The cross-sectional area formed between two adjacent bckets decreases. Ths, gas velocity increases and pressre decreases dring passing throgh the passage. Nozzle Row Therefore, reaction trbine extracts energy by the reaction force prodced by the acceleration of the flow throgh the convergent dct. The degree of reaction of the reaction trbine is 50%. Bcket Row V i F V e U Convergent nozzle [ LSB (Siemens) ] [ Reaction Trbine, = 50% ] Steam Trbine 3. Flow in Steam Path 7 /

73 Evoltion of Trbine Blade Siemens AEG Slzer BBC SCAM Ratea AEI GEC GE USA IMPULSE Siemens-KWU D REACTION W/H USA REACTION BBC CH REACTION Alsthom F IMPULSE GEC UK IMPULSE 970 Ansaldo ASEA STAL Toshiba BHEL F. Tosi CEM Doosan Hitachi N. Piignone Parsons Fji MHI 987 De Pretto ABB LMZ Zamech 989 GEC-Alsthom GE USA IMPULSE 998 Siemens-Westinghose D REACTION MHI J REACTION 999 ABB-Alsthom F REACTION 000 Steam Trbine 3. Flow in Steam Path 73 /

74 Implse vs. Reaction p c Implse Trbine : tangential velocity of blade w : velocity of flid relative to blade c : absolte velocity of flid p Reaction Trbine c Nozzle Row Nozzle Row p w c p w c Bcket Row Bcket Row p 3 w 3 3 c 3 The implse trbine has its entire enthalpy drop in the nozzle. Therefore, it has a very high velocity entering the bcket. Ideally there is no change in the magnitde of the relative velocity w between inlet and exit (which are denoted by sbscripts and 3, respectively). The large inlet velocity c has been redced to a small absolte exit velocity c 3, which ideally is in the axial direction. 3 p 3 w 3 The reaction trbine divides its enthalpy drop in both nozzle and bcket. Therefore, velocities are accelerated when the steam is passing throgh both the nozzle and the bcket. c Steam Trbine 3. Flow in Steam Path 74 /

75 Velocity Diagram Implse Trbine Reaction Trbine Nozzle Bcket Nozzle Bcket c c w w 3 w w w 3 A w A B A 3B A c A 3B c A B w 3 A N 3 c A N w w 3 3 c c 3 p c c 3 3 = 0 p p c w = 0 U 3 = 0 T p p 3 T T p 3 T T 3 T 3 A N A A B = A 3B = 3 w = w 3 c 4c A N A A 3B A B c c w 3 w c c Steam Trbine 3. Flow in Steam Path 75 /

76 Mltistage Implse Trbine The implse trbine has its entire enthalpy drop in the nozzle, therefore, it has a very high velocity entering the bcket. Nozzle Bcket Nozzle Bcket Nozzle Bcket Pressre Absolte Velocity Distance throgh Trbine Steam Trbine 3. Flow in Steam Path 76 /

77 Mltistage Reaction Trbine Nozzle Bcket Nozzle Bcket Nozzle Bcket Pressre Absolte Velocity half of implse trbine Distance throgh Trbine Steam Trbine 3. Flow in Steam Path 77 /

78 Qestion. Compare the implse and reaction trbine in terms of SPE.. Compare the implse and reaction trbine in terms of profile loss. 3. Sggest the eqation to calclate the thrst prodced in a stage. 4. Which type of trbine reqires bigger thrst bearings? 5. Single stage spersonic implse trbine is shown in the figre. ) Discss the shape of nozzle path. ) What is the prpose of the increasing nozzle exiting velocity p to spersonic velocity? T dl p p3 T = Thrst d = mean diameter of blade row l = active length of blade p = pressre at the inlet of stage p 3 = pressre at the exit of stage = degree of reaction at the mean dia. Single Stage Spersonic Implse Trbine Steam Trbine 3. Flow in Steam Path 78 /

79 Comparison of Velocity Triangle Implse Trbine Reaction Trbine w c w c 3 w 3 3 c 3 w 3 3 c 3 = c sin = c sin w sin w 3 sin 3 w 3 sin 3 F = m V = m (c sin + c 3 sin 3 ) = m c sin P = m c sin F = m V = m (c sin + c 3 sin 3 ) = m c sin P = m c sin Steam Trbine 3. Flow in Steam Path 79 /

80 Comparison of the Nmber of Trbine Stages Implse Reaction q FE KE PE in w ot Let s consider a nozzle row only. This is becase there is no heat addition and work ot as well. Neglecting inlet velocity, h c q in h h h c c h h c c c w ot Assme, 90 o c c h h 0.5 h across fixed blades in reaction trbine is only /4 that of implse trbine. Reaction trbines, however, have an additional eqivalent h across the moving blades. Therefore, total h in reaction trbine is a half of implse trbine. This means that reaction trbine needs twice nmber of stages to generate same otpt. Steam Trbine 3. Flow in Steam Path 80 /

81 Design Change of HP Trbine - GE Smaller Rotor and Wheel Diameter Single Flow Control Stage Steam Trbine 3. Flow in Steam Path 8 /

82 Design Change of HP Trbine - GE The length of the rotor shaft is almost same. The reasons for this are ) Pressre drop across the nozzle path in the implse trbine is doble of the reaction trbine. Therefore, the diaphragms of the implse trbine shold be stronger than those of the reaction trbine. ) Trbine bckets of the implse trbine have to work twice of the reaction trbine. Ths, trbine bckets shold be mch stronger than those of the reaction trbine. Another important thing is that the active length of the reaction bcket is longer than that of implse bcket. The longer active length of bckets, the higher the trbine efficiency. Steam Trbine 3. Flow in Steam Path 8 /

83 Newly Designed HP Trbine [GE] ALSTOM HP Trbine Steam Trbine 3. Flow in Steam Path 83 /

84 Steam Trbines for CCPP Application GE D- for Combined Cycle Units 07D-7 Steam Trbine Steam Trbine 3. Flow in Steam Path 84 /

85 Nmber of Trbine Stages Reaction Type HP Trbine 00 MW Steam Trbine for the K-Power. (Hitachi) Implse Type Steam Trbine The nmber of stages of reaction trbine is twice of implse trbine. ) Sggest the method that make the nmber of stages of reaction trbine is eqal to that of implse trbine. ) The answer of the above qestion is not applied in the practical reaction trbine. Discss the reason for that. Steam Trbine 3. Flow in Steam Path 85 /

86 Velocity Diagram Implse Stage Reaction Stage Steam Flow p p Steam Flow 3 = 0.5v 0 p p 0 = 0.65v 0 w = 0.4v 0 c 3 = 0.3v 0 p 3 p 3 c 3 = 0.4v 0 = 0.65v 0 = 0.5V 0 Steam Trbine 3. Flow in Steam Path 86 /

87 Velocity Diagram Implse Stage Reaction Stage The velocity increase abot for times in the nozzle and its direction changes from axial to abot 77 off axial. In a 50% reaction stage, half of the pressre drop is across the nozzle and another half is across the bcket. Vo is the velocity of stream expanded from the pressre pstream of a stage to the downstream pressre withot loss. In a pre implse stage the optimm /c is 0.5. The flow trning in the nozzle of reaction stage is smaller than that of implse stage. The inlet velocity of bcket in the reaction stage is smaller than that in the implse stage. The velocity leaving the stage shold be close to axial to minimize the stage leaving loss. The lower velocity reslts in lower friction loss and lower erosion. The shape of nozzle and bcket is same in a 50% reaction stage. Steam Trbine 3. Flow in Steam Path 87 /

88 Comparison of Leakage Bcket Tip Implse Reaction disc wheels shrnk on to a rotor shaft Diaphragm Root cylindrical drm type rotor Steam Trbine 3. Flow in Steam Path 88 /

89 Comparison of Leakage Trbines have internal sealing systems between the rotating bckets and the stationary casing and between the stationary nozzles and the rotor. The rotating bcket to stationary casing seal is more critical in a reaction trbine than in an implse trbine since the reaction trbine has higher pressre drop across the bckets. The stationary nozzle to rotor seal is more critical in the implse trbine becase of the higher pressre drop across the implse stationary nozzle. However, the implse trbine has a smaller rotor and ths a smaller sealing diameter, offsetting the effects of the higher pressre drop. In addition, the wheel design of the implse trbine rotor allows the installation of rotor seal leakage steam passages (holes) in the wheel, minimizing leakage steam interference with the main steam flow from the stationary nozzle to the rotating bcket. The rotor-monted bcket design of the reaction trbine does not allow the installation of these leakage passages. However, becase of the higher reaction at the root of the bcket, the reaction stage is less affected by reentering leakage from the stationary low. The reaction stage has a higher profile (aerodynamic) efficiency than an implse stage. The implse stage has higher efficiency on stages with small blade heights becase the difference in leakage losses offsets the higher profile of the reaction stage. As the blade height increases, the inflence of leakage losses decreases and a point is reached where the reaction stage is more efficient. Steam Trbine 3. Flow in Steam Path 89 /

90 Implse-Reaction Trbine [/6] Radial Variation of Pressre and Absolte Velocity Velocity and pressre distribtion along radial direction are niform at the inlet and otlet of the stage. Velocity decreases along radial direction between nozzle and bcket. Pressre increases along radial direction between nozzle and bcket. w T c T T c c 3 c p p p 3 w M c M M c R w R R Steam Trbine 3. Flow in Steam Path 90 /

91 Implse-Reaction Trbine [/6] 노즐의역할은작동유체의압력에너지를운동에너지로변환시키는것이다. 따라서노즐을통과한작동유체의속도는크게증가한다. 그러나노즐출구에서의축방향속도는노즐입구에서와동일하기때문에접선방향속도만크게증가한다. 이로인해노즐출구를빠져나온작동유체는큰선회유동으로인해원심력이발생하여유체는버켓팁 (tip) 쪽으로집중되는경향을가진다. 유동이버켓팁쪽으로편중되면버켓과케이싱사이에서누설손실이증가하며, 버켓팁근처에서이차유동손실이증가할뿐만아니라반경방향을따라서버켓에서생산하는동력도균일하지못하게된다. 이런문제를해결하기위해서버켓팁입구쪽의압력을루트 (root, or hb) 입구쪽압력보다높게유지시킨다. 이경우버켓입구의팁부분압력이루트부에비해높기때문에팁쪽에서루트방향으로진행하는유동이형성된다. 즉버켓팁쪽에형성되는높은압력으로인해루트쪽으로진행하려는힘과원심력에의해루트에서팁쪽으로진행하려는두힘은서로방향이반대이기때문에두힘의크기를비슷하게해주면노즐과버켓사이에서유동은축방향으로평행하게흘러가며, 앞서언급된제반문제점들이사라지게된다. 따라서노즐과버켓사이에형성되는유동의특징은반경방향을따라서속도는줄어들고, 압력은증가한다. 한편, 축류형다단터빈은버켓입구에서뿐만이아니라출구에서도압력과속도는반경방향을따라서일정하게유지되어야한다. 따라서버켓은루트에서팁쪽으로가면서반동도가증가하기때문에버켓루트는충동형, 팁은반동형으로설계한다. 이런이유때문에터빈버켓은하나의블레이드에충동형과반동형이혼재된충동 - 반동블레이드 (implsereaction blade) 이다. Steam Trbine 3. Flow in Steam Path 9 /

92 버켓팁으로의유동편중해결방법 Implse-Reaction Trbine [3/6] Free vortex design implse type HP trbine stage 000 psia psia tip 89.7 psia 000 psia 844. psia pitch 89.7 psia 000 psia 88.7 psia root 89.7 psia [ Example of Pressre Variation in Radial Direction ] Steam Trbine 3. Flow in Steam Path 9 /

93 Tre implse stages having 0% reaction and reaction stages that always have 50% reaction do not exist in practical trbine design. In practice, the reaction varies from hb to tip. Normally, reaction trbine stages are designed to operate at 50% reaction at midspan, with oter and inner radii operating at higher and lower reactions, respectively. Implse stages typically have 3% to 5% reaction at the root of bcket in order to avoid zero or negative reaction that reslts in efficiency loss and may lead to flow separation in the bcket. For long reaction stage bckets, the degree of reaction at the mean diameter may be as low as 40%. Implse-Reaction Trbine [4/6] Ths, implse and reaction stages in the classical definition do not exist in practical trbines. Characteristics of flow behaviors in mltistage axial trbine stage: ) Pressre and velocity distribtions along radial direction are niform at the entry of a stage. ) This is same as at the exit of a stage. 3) Centrifgal forces are cased by the tangential component of flow in the nozzle discharge. 4) This is same as in the reaction trbine. 5) The variation of reaction in radial direction is needed to partially cancel the centrifgal forces in the stage. 6) Otherwise, the flow wold migrate to the tip, reslting in a poor stage efficiency de to as followings. Increase of bcket tip leakage loss Increase of secondary flow loss near bcket tips Bcket vibration characteristics becomes worse becase of non-niform load acting on the bcket along radial direction Steam Trbine 3. Flow in Steam Path 93 /

94 Degree of Reaction (%) Degree of Reaction in Fossil Power Implse-Reaction Trbine [5/6] % Reaction Trbine Implse Trbine Tip Root Root Root Root HP IP LP Stage Nmber Tip Steam Trbine 3. Flow in Steam Path 94 /

95 Implse-Reaction Trbine [6/6] Degree of Reaction in Nclear Power Steam Trbine 3. Flow in Steam Path 95 /

96 Stack-Up of Blade (LSB) = tip p = 4.5 psia Tip Root p = 6 psia p 3 = psia p =.5 psia = root Steam Trbine 3. Flow in Steam Path 96 /

97 Comparison of Rotor Shaft The simplest difference between implse and reaction trbines is rotor shaft. Implse design has a little pressre drop across the bckets. Therefore, the bckets can be monted on the periphery of a wheel withot generating significant axial thrst. Implse trbines do not have thrst concern, and the bckets are monted on disk extension of the rotor (wheels), reslting in larger overall diameters, small rotor diameters, and fewer stages than reaction trbines. On the contrary, blades of reaction trbines are monted directly at the shaft srface becase of steam pressre difference between pstream and downstream of blades. This may create a large thrst (axial) force at the shaft cased large bend stress in the discs. In addition, reaction trbines have more stages than implse ones. Wheel and diaphragm constrction for implse blades Drm rotor constrction for reaction blades Steam Trbine 3. Flow in Steam Path 97 /

98 Balance Piston Welding Balance Piston The reaction design has a significant pressre drop across the bckets and high thrst. Therefore, a balance piston, which is normally bilt into the rotor, is installed in highpressre zones of single-flow trbines to offset the thrst. Otherwise, the trbine is designed with doble-flow. Some designers also se a balance piston on implse trbines that have a high thrst. Balance Piston (Siemens) Steam Trbine 3. Flow in Steam Path 98 /

99 Doble Flow T dl p p3 T = Thrst d = mean diameter of blade row l = active length of blade p = pressre at the inlet of stage p 3 = pressre at the exit of stage = degree of reaction at the mean dia. What are the major advantages of doble flow strctre? ) Larger capacity ) Smaller thrst force 3) Shorter LSB Doble flow can be employed to avoid a balance piston in reaction trbines which have a higher thrst than implse trbine Steam Trbine 3. Flow in Steam Path 99 /

100 Reaction Blades Advantages Alstom Higher aerodynamic efficiency Lower trning and accelerating flow in both nozzle and bcket allow design of higher efficient and tolerant profiles Lower acceleration of the flow throgh the nozzle and bcket leads lower profile loss Lower staging loading Many stage can be designed with 50% reaction (all HP and IP stages, and front stages of LP trbine) Symmetric velocity triangle (50% reaction stage) Use of same profile in the nozzle and bcket and it may contribte to cost down Near-zero interstage swirl Becase of the lower pressre drop, there is no need for costly diaphragm constrction It leads larger nmber of stages becase of lower stage loading (roghly twice that of implse stages for 50% reaction stages). Disadvantages Increase of axial thrst which leads higher dmmy balance piston, i.e. increased leakage loss. Drm-type rotor is sitable for reaction trbine and it leads higher leakage area at the hb section. Degree of reaction at the hb and tip section is higher compared with implse stage. Higher hb reaction leads lower leakage loss, however higher tip reaction gives higher leakage loss. Steam Trbine 3. Flow in Steam Path 00 /

101 Flid Dynamics Steam Trbine Flow Model Thermodynamics and Flid Dynamics for Steam Trbines Dimensionless Nmbers Implse Trbine and Reaction Trbine Stage Efficiency Blade Profile Enhancement Steam Trbine 3. Flow in Steam Path 0 /

102 Stage Efficiency Implse Trbine Reaction Trbine st p p actal ideal 버켓에서생산하는실제동력 = 버켓에서생산할수있는이상동력 w c w 3 (a) < sin c w 3 3 c 3 3 w c 3 w c w 3 3 c 3 (b) = sin c w 3 w c 3 st, i 4 sin st, i,max sin c ( = velocity ratio), i (from ) 0 d st sin st, r (c) > sin sin c st, r,max sin sin Steam Trbine 3. Flow in Steam Path 0 /

103 Stage efficiency Stage Efficiency..0 Implse Reaction st, r sin sin st, i 4 sin c Velocity ratio ( ) Steam Trbine 3. Flow in Steam Path 03 /

104 Velocity Wake and Core Flow The wake is a velocity defect generated by the bondary layers of the blade srfaces. If it is ndistrbed by other blades it wold move downstream along the direction of otlet-flow angle while decaying slowly over three or for chord lengths. Reaction stage has better adaptability for core flow of nozzle and higher stage efficiency Implse Bcket Reaction Bcket Nmber of revoltion Steam Trbine 3. Flow in Steam Path 04 /

105 Nmber of Stages [ 연습문제 3.] 증기터빈에유입되는주증기조건 (main steam conditions) 이 30 MPa, 650C 이다. 이증기는 단충동터빈 (one-stage implse trbine) 을등엔트로피팽창 (isentropic expansion) 되어 350C 로빠져나간다. 이때엔탈피강하 (isentropic enthalpy drop) 가 540 kj/kg 이다. 이터빈을 single stage 로설계하는데따른문제점을검토하시오. 단, c 와 가이루는각도는 3, 유량계수 (flow coefficient) 는 0.5, 노즐입구에서의속도 c 은매우작다고가정한다. c c w w 3 c 3 Direction of Rotation Steam Trbine 3. Flow in Steam Path 05 /

106 Nmber of Stages [ 검토결과 ] 노즐에서발생하는일은없다. 아울러노즐통로유동은단열과정이기때문에노즐출구에서의증기속도는열역학제 법칙을이용하여구할수있다. q h h c c gz z w 편의상노즐입구속도는 0 이라가정하면, 열역학제 법칙으로부터다음결과를얻는다. c m/s kj/kg 한편, c 와 가이루는각도가 3 이며, 유량계수 (flow coefficient) 0.5 를이용하여 를계산하면, = c x / h h 540 c = sin3 /0.5 = m/s 증기터빈의회전속도가 3,600 rpm 인경우, 블레이드피치직경은다음식으로구한다. ( d / ) n 60 d =.48 m 따라서, 블레이드회전속도와피치직경이매우크기때문에블레이드는큰응력을받게되며, 큰속도로인해서손실이증가하게된다. 결론적으로이조건에서는증기터빈을다단 (mltiple stages) 으로구성하는것이유리하다. Steam Trbine 3. Flow in Steam Path 06 /

107 Flid Dynamics Steam Trbine Flow Model Thermodynamics and Flid Dynamics for Steam Trbines Dimensionless Nmbers Implse Trbine and Reaction Trbine Stage Efficiency Blade Profile Enhancement Steam Trbine 3. Flow in Steam Path 07 /

108 Implse Blade vs. Reaction Blade Bcket Shape GE Conventional 940 Laminar 950 SCHLICT 965 Sper 980 Siemens T 937 VN 953 T 968 T4 980 TX 995 Steam Trbine 3. Flow in Steam Path 08 /

109 Bcket Profile Enhancement Siemens Steam Trbine 3. Flow in Steam Path 09 /

110 Bcket Profile Enhancement Alstom Steam Trbine 3. Flow in Steam Path 0 /

111 Shroded Blade Shroded blades have redced leakage losses becase they have seal system at the blade tip. Shroded blades have better vibration characteristics becase they are often interlocked to provide mechanical damping. Shroded blades give better efficiency becase they have better aerodynamic characteristics at the blade tip. The tip vortex formed from open tip blade prodce a large distrbed flow when it combined with secondary flow in the blade passage. However, the shrod creates increased stress levels. [ Shroded Blade ] [ Tip Vortex ] [ Free Tip Blade ] Steam Trbine 3. Flow in Steam Path /