Design of Radial Turbines & Turbochargers

Transcription

1 RMD50 Design of Radial Turbines & Turbochargers Session delivered by: Prof. Q. H. Nagpurwala M S Ramaiah School of Advanced Studies, Bengaluru

2 Session Objective RMD50 To discuss the design of radial turbines using a procedure based on optimum specific speed To understand the basic construction and working of turbochargers To discuss the design of radial compressor and radial turbine modules of a typical turbocharger M S Ramaiah School of Advanced Studies, Bengaluru

3 RMD50 Design of Radial Turbine (Based on Specific Speed) M S Ramaiah School of Advanced Studies, Bengaluru 3

4 RMD50 Radial Turbine Layout and Expansion Process Nozzle blades At rotor inlet At rotor outlet Expansion process in a radial turbine M S Ramaiah School of Advanced Studies, Bengaluru 4

5 Design Guidelines RMD50 From Euler turbine equation, specific work is given by: A significant contribution comes from the first term. For an axial flow turbine, where U = U, no contribution to the specific work is obtained from this term. A positive contribution to the specific work is obtained from the second term when w 3 > w. In fact, accelerating the relative velocity through the rotor is a most useful aim of the designer as this is conducive to achieving a low loss flow. The third term indicates that the absolute velocity at rotor inlet should be larger than at rotor outlet so as to increase the work input to the rotor. M S Ramaiah School of Advanced Studies, Bengaluru 5

6 Design Guidelines RMD50 The nominal design is defined by relative flow with zero incidence at rotor inlet, i.e. W = r, and axial absolute flow at rotor exit, i.e. 3 = x3 Thus, with w3 = 0 and w = U, the specific work for the nominal design is Spouting Velocity: The term spouting velocity, 0 (originating from hydraulic turbine practice) is defined as that velocity which has an associated kinetic energy equal to the isentropic enthalpy drop from turbine inlet stagnation pressure p 0 to the final exhaust pressure. When no diffuser is used or With complete recovery of the exhaust kinetic energy, and with w = U, At the best efficiency point, generally, 0.68 < U / 0 < 0.7. M S Ramaiah School of Advanced Studies, Bengaluru 6

7 Design Guidelines RMD50 The blades are aligned along the radii for much of their length. Absolute flow angle at rotor inlet = Nozzle outlet angle = ~ 70º. Absolute flow angle at exducer exit = 0º. Inlet relative velocity should be aligned to the blade direction at inlet, which means that it should be radial. However, this may lead to high aerodynamic loading at the tip as the blade tips are open, such high pressure loading can not be maintained Max. efficiency in radial inflow turbines is achieved when inlet flow angle is modified by the concept of slip or deviation as applied to radial compressors. The recommended ddslip correlation lti is that thtgiven by Wiesner w u,, ac cos 0.7 u,, tl Z Z = number of blades (incl. splitter blades) = blade angle w.r.t radial direction M S Ramaiah School of Advanced Studies, Bengaluru 7

8 Variation of Slip Factor with Z RMD50 The slip factor for radial bladed rotor varies with the number of blades: Number of radial blades Slip factor on rotor periphery p u, /u M S Ramaiah School of Advanced Studies, Bengaluru 8

9 Design Data RMD50 Inlet temperature : 00 K Inlet pressure : Pa Rotor-outlet stagnation pressure : Pa Hot-gas inlet mass flow : 0.5 kg/s Fuel/Air ratio : 0.0 Number of rotor blades : 3 (radial) Nozzle outflow angle : 70 to radial direction To find: Rotor diameter Blade axial width at inlet Rotational speed M S Ramaiah School of Advanced Studies, Bengaluru 9

10 Inlet Velocity Triangle RMD50 act c r r, W u, u M S Ramaiah School of Advanced Studies, Bengaluru 0

11 Inlet Flow Parameters RMD50 Guess Stagnation-to-Stagnation polytropic efficiency = 0.9 For 3 blades w = = Then, T T T c 0, 0, p p 0, 0, p Δh Δh 0 0 u, p ψ u ΔT K u r, 8. m/s W R p, c p J/kg K 85, 089 m/s m/s m/s c T 0, = K J/kg m/s c act r, u, M S Ramaiah School of Advanced Studies, Bengaluru u W

12 Optimum Specific Speed RMD50 Distribution of losses along envelope of maximum total-to-static efficiency (Rohlik 968) Typical performance of radial turbine (Rohlik 968) M S Ramaiah School of Advanced Studies, Bengaluru

13 Optimum Specific Speed ( contd.) RMD50 urves for specific speed for radial flow turbine indicate that the max. efficiency should reach at non-dimensional N s of 0.6. N u s,op 0. 6 ωr πn 60 πn 60 V in Δh 3 4 d Vin r, π d b r, g c Δh 0 ω N s ψ u r, π d b 3 4 ψ u πnd 60 π d d b d M S Ramaiah School of Advanced Studies, Bengaluru 3

14 Rotor Inlet Width to Diameter Ratio RMD50 tan b d b d N ψ u N s ψ s u ω d π r, 4π r, ψ u αc, r, N ψ tan α 4π b s c, Inserting appropriate design inputs, we get b /d = 0.07 Both hbb and d can be determined dby calculating l volume flow rate at rotor inlet RT g c 0, M S Ramaiah School of Advanced Studies, Bengaluru 4

15 RMD50 Rotor Inlet Mach Number Mach number can be determined from the following relation or the figure R M R RT g p p c R M M S Ramaiah School of Advanced Studies, Bengaluru 5

16 alculation of Density RMD50 ρ ρ st, 0, p R M p R The stagnation density at rotor inlet can be assumed equal to that at nozzle inlet for this preliminary design 3 RT ρ 0, p 0, 0, 0 ρ st, kg k m 0.87 kg M S Ramaiah School of Advanced Studies, Bengaluru 6 m 3

17 Rotational Speed RMD50 m d b u d r, ρst, π d b r, ρ st, π mm mm N πn d u πd rpm π d b d M S Ramaiah School of Advanced Studies, Bengaluru 7

18 Final Design RMD50 Having found the basic geometric parameters of the rotor (and inlet nozzle vanes), the blade profiles can be generated by using analytic equations using i commercial software, like BLADEGEN The final design has to be arrived at through iteration between structural integrity (considering aerodynamic and thermal loading) and aerodynamic performance. Finally, the mechanical design should be carried out, taking due care of the component manufacturing and assembly requirements. Inlet Nozzle vane Exit Exducer M S Ramaiah School of Advanced Studies, Bengaluru 8

19 RMD50 Design of Turbocharger (Based on Specific Speed) M S Ramaiah School of Advanced Studies, Bengaluru 9

20 Schematic of a Turbocharger RMD50 M S Ramaiah School of Advanced Studies, Bengaluru 0

21 Turbocharger omponents RMD50 M S Ramaiah School of Advanced Studies, Bengaluru

22 Working of Turbocharger RMD50 M S Ramaiah School of Advanced Studies, Bengaluru

23 Turbocharger Design Data RMD50 ompressor Turbine Mass flow rate, kg/s.0.04 Inlet stagnation temperature, K 300 (T 0 0, ) 800 (T 04 0,4 ) Inlet stagnation pressure, N/m *0 5 (P 0, ) Find Engine back pressure (P 0,4 ) Outlet static pressure, N/m * 0 5 (P st,3 ).* 0 5 (P st,7 ) Fluid ud Air ombustion o products 00% theoretical air p J/(kg K ) & ( p /R ) 00 (3.5) 7 (4084) Blade angle at periphery p 30 ( ) 0 ( 5 ) Specific speed, Ns d hb, / d sh, Polytropic oy opcefficiency cy 0.8 ( pts p,ts,-3 3 ) 0.8 ( pts4 p,ts,4-7 7 ) Flow angle at rotor exit, c (deg) 60 0 Flow angle at rotor inlet, c (deg) 0 70 Number of rotor blades, Z 7 3 Polytropic efficiency 0.96 ( p,tt,- ) 0.96 ( p,tt,5-6 ) M S Ramaiah School of Advanced Studies, Bengaluru 3

24 alculations Planes RMD50 M S Ramaiah School of Advanced Studies, Bengaluru 4

25 Wiesner s orrelation RMD50 This correlation, defining slip factor,, can be used to calculate the number of blades, Z, in the radial turbine as well as in the radial compressor. σ w u,,ac u,,tl Z cos β 0. 7 Z M S Ramaiah School of Advanced Studies, Bengaluru 5

26 RMD50 ompressor Design alculations M S Ramaiah School of Advanced Studies, Bengaluru 6

27 ompressor Velocity Triangles RMD50 u u,,tl u, r, W c =60 =30 Outlet Velocity Triangle u sh, xsh x,sh, W w,sh, sh, Inlet Velocity Triangle M S Ramaiah School of Advanced Studies, Bengaluru 7

28 Enthalpy Rise RMD50 T T p 0, 3 p0, 3 0, 0, 3 p p st, 3 0, R p when η p,c,ts η p,c,ts is used T 0, T 0, ΔT, K pc 00 J/kgK Therefore, and Δh 0, 3 87 J/kg 3 4 Δh g c, 3 M S Ramaiah School of Advanced Studies, Bengaluru 8

29 Inlet Volume Flow Rate RMD50 Guess inlet axial velocity First iteration: 0 m/s Second iteration: 7.3 m/s (all second iteration values are in parenthesis) g For ρ ρ 0 st c RT x p 0, R , M M p R p 0. 3 R From slide 5 M S Ramaiah School of Advanced Studies, Bengaluru 9

30 Rotational Speed RMD50 ρ p0, 66. kg/m RT , 0, ρ st, 04. m ρ V st, kg/m ( ) V V. N 3 m /s m /s, 60N s g c Δh π V V V rev/min M S Ramaiah School of Advanced Studies, Bengaluru 30

31 RMD50 ompressor Outlet Velocity Diagram From Wiesner s correlation (slide 5) u,ac u,tl For u u, u d cos σ w β tan β tan αc u u,,tl u, cos β Z r, W cos30,z 7 c =60 =30 g c Δh 0 ψ 60u / N σ 0. 5 w mm 0. 5 ψ m/s M S Ramaiah School of Advanced Studies, Bengaluru 3

32 Inlet Velocity Diagram RMD50 The procedure to select minimum i W sh, is as follows. hoose a valueof dsh,.alculate 3.alculate 4.alculate u A sh, a m Nπ / 60 d πd / RT 0, sh, /A a p 0, sh, m RT0 /gc M M 5. from the relation AP 0 R p calculate M p R 6. alculate pst, /p0, pst, x, Wsh, p R This procedure is given in tabular form in Slide 33, in which the second iteration values are given in brackets. The optimum value of d sh, is found to be 0 mm. M S Ramaiah School of Advanced Studies, Bengaluru 3

33 RMD50 alculation of Optimum Shroud Parameter d sh, (mm) u sh, (m/s) = d sh, (= 575. d sh, ) (57.) (99.64) (9.65) 3 A ( m ) d a sh, m RT , /A p0, M x, ρ st, /ρ (m/s ) W 0, A a. ρ st, u /ρ 0, sh, x, sh, (58.5) (30.9) (30.) M S Ramaiah School of Advanced Studies, Bengaluru 33

34 Impeller-Diffuser Interface RMD50 The minimum value of W sh, is found to be 30. m/s. Hence, the de Haller velocity ratio, W / W sh, = This should not lead to diffusion induced separation. Impeller-Outlet and diffuser-inlet width, b : ψu sin αc, T 0, M ρ st, ρ 0, K g c RT , m/s M S Ramaiah School of Advanced Studies, Bengaluru 34

35 Inducer Hub-Tip Ratio RMD50 Find the rotor-outlet tl t stagnation ti pressure using the rotor efficiency i Therefore, p p p ρ ρ 0, 0, 0, 0, st, r, T T 0, 0, R p kg/m cos 60 kg/m ηp,c,tt, N/m 3 3 πd ρ mm b m st, r, 37. m/s Inducer hub diameter can be determined from hub-tip ratio d hb, d hb, mm d sh, M S Ramaiah School of Advanced Studies, Bengaluru 35

36 Radial Diffuser Stability RMD50 for mean R e, T st, μ d μ 30K st, R e,. 440 b r 6 ρ st, Ns/m From the Stability limits in Jansen s curves b / r (r 3 / r ) mx (by interpolation) 80 percent of.0 is.6 d 3 =.6 x 9. = 350 mm M S Ramaiah School of Advanced Studies, Bengaluru 36

37 Radial Diffuser Stability ( contd.) RMD50 Stable operating range of vaneless diffusers (Jansen, 964) M S Ramaiah School of Advanced Studies, Bengaluru 37

38 RMD50 Turbine Design alculations M S Ramaiah School of Advanced Studies, Bengaluru 38

39 Turbine Design alculations RMD50 Turbine Rotor Diameter: The turbine has slightly increased mass flow, because of fuel addition, and must supply windage and dbearing power in addition to compressor power. 0. Δh0,e 877 J/kg 04. u u u, 5 u, 5,tl u, 5,tl 5 cos 0. 7 Z e u u, 5,ac 5 u 5 β 5 and β * m/s d5 ; Z e u 5 g c u u, 5 5 mm M S Ramaiah School of Advanced Studies, Bengaluru 39

40 Turbine Design alculations RMD50 Turbine Pressure Ratio: m e Δh 0,e. 0 m c Δh 0,c ΔT p p p ,e K 0,in 0,ex 0,ex T T 0,in 0,ex p st,ex R p η p R p,e,ts η p,e,ts p 0,in N/m M S Ramaiah School of Advanced Studies, Bengaluru 40

41 Turbine Design alculations RMD50 Nozzle Outlet Velocity: The following parameters have been calculated: Blade speed = 3.0 m/s ; Work coefficient, = ; Nozzle angle = 70 u, ψu tan 70 φ r, u r, r, r, tan m/s cos70 g c 5 RT 0 r, m/s * 800 with R M p M S Ramaiah School of Advanced Studies, Bengaluru 4

42 Turbine Design alculations RMD50 p R ρ 0 M 37 ρ R. st p ρ , kg/m ρst, kg/m 3 The mass flow rate is.04 kg/s Hence, the volume flow rate is.44 m 3 /s, and the enthalpy drop is 880 J/kg. πn V in Specific speed, N s g Δh π c M S Ramaiah School of Advanced Studies, Bengaluru

43 Velocity Function vs Mach Number for Perfect Gases RMD50 M S Ramaiah School of Advanced Studies, Bengaluru 43

44 Exit Width to Diameter Ratio RMD50 The optimum specific speed for radial-inflow turbine is about The specific speed of this turbine is high. We might expect that there might be a problem arriving at an exducer in which the outlet diameter reduce. Turbine inlet blade width to diameter ratio is calculated using the relation b d b d 5 5 N N s s tan α 4πψ tan α 4π c c5 ψ ψ 3 tan 70 4π N s tan α 4π c ψ 069. M S Ramaiah School of Advanced Studies, Bengaluru 44

45 Optimum Specific Speed RMD50 Distribution of losses along envelope of maximum total-to-static efficiency (Rohlik 968) Typical performance of radial turbine (Rohlik 968) M S Ramaiah School of Advanced Studies, Bengaluru 45

46 Turbine Design alculations RMD50 Outlet Static Density: The outlet static pressure is specified together with the stagnation temperature. The Mach number here is low, and it will be sufficiently accurate to guess the static temperature. 5 p st, 6. 0 N/m T K T 0, 6 st, 6 ρ st, 6 ρ 75 K ρ 57 st, 5 st, 6. guess kg/m M S Ramaiah School of Advanced Studies, Bengaluru 46

47 Results RMD50 The results of the calculations, made for an exducer hub-shroud ratio of 0.3, are tabulated below: W W hb,6 5 d d αw,sh, 6 tan sh, 6 5 x, 6 r, 5 φ Degrees Λ d d φ Degrees tan sh, αw,hb, x, 5 M S Ramaiah School of Advanced Studies, Bengaluru 47

48 Diameter Ratio RMD50 The diameter ratio and the relative flow acceleration are both marginal at 0.8 velocity ratio. Both are satisfactory at a velocity ratio of 0.9. d sh, We select d 5 The flow angles give a guide to the exducer blade angles. The exducer angles should be set to somewhat higher values to allow for flow deviation. An approximate estimate of this deviation would be 3º at the shroud and 5º at the hub. M S Ramaiah School of Advanced Studies, Bengaluru 48

49 Turbine Hub and Tip Dimensions RMD50 d sh, * mm d hb, 6 d d hb,6 sh, π Ψ 3 4 N πφ s mm b d b mm M S Ramaiah School of Advanced Studies, Bengaluru 49

50 Data for Modeling the ompressor RMD50 Inlet Velocity Triangle At Shroud At Hub u hb, x,hb, w,hb, W hb, u sh, =9.65 m/s x,sh, = 7.3 m/s W sh, = 30. w,sh, = 56.4º u hb, = 4.98 m/s x,hb, = 7.3 m/s W hb, = 7.53 w,hb, = 4.º M S Ramaiah School of Advanced Studies, Bengaluru 50

51 Data for Modeling the ompressor RMD50 Outlet Velocity Triangle =350 m/s =7.3 m/s =36.6 m/s =74. m/s =37. m/s m/s M S Ramaiah School of Advanced Studies, Bengaluru 5

52 Data for Modeling Turbine RMD50 Inlet Velocity Triangle act 5 =76.89 m/s c =70 5 w5 w5 =8.68 W 5 =07.95 m/s r,5= U 5 =3.0 m/s M S Ramaiah School of Advanced Studies, Bengaluru 5

53 Modeling Using FX RMD50 reating a Blade: Radial Impeller onfiguration Initial Angle/Thickness Dialog M S Ramaiah School of Advanced Studies, Bengaluru 53

54 Geometric Model - ompressor RMD50 Input Parameters: Blade D sh =4mm D hb = 8.5 mm D =5mm D 3 =30mm Fluid Domain = 30 Z = 0 M S Ramaiah School of Advanced Studies, Bengaluru 54

55 Geometric Model - ompressor RMD50 Blade Fluid Domain Input Parameters: D sh =mm D hb = 5.5 mm D 5 =30mm c5 =70 Z=9 M S Ramaiah School of Advanced Studies, Bengaluru 55

56 3-D AD Models RMD50 ompressor Turbine M S Ramaiah School of Advanced Studies, Bengaluru 56

57 Session Summary RMD50 A procedure for design of radial turbines based on optimum specific speed is discussed. Salient constructional features and working principle of a turbocharger are presented. The design of radial machines is explained through step by step design of compressor and radial turbine modules of a typical turbocharger M S Ramaiah School of Advanced Studies, Bengaluru 57