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PEMP RMD510 Design of Radial Turbines & Turbochargers Session delivered by: Prof Q. Prof. Q H. H Nagpurwala 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 1 Session Objective PEMP RMD510 • To discuss the design of radial turbines using a • • 14 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 2 PEMP RMD510 Design of Radial Turbine (Based on Specific Speed) 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 3 PEMP RMD510 Radial Turbine Layout and Expansion Process Nozzle blades At rotor t iinlet l t Expansion process in a radial turbine At rotor outlet 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 4 Design Guidelines PEMP RMD510 From Euler turbine equation, specific work is given by: A significant contribution comes from the first term. For an axial flow turbine, where U2 = U1, 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 w3 > w2. 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 y at rotor inlet should be larger g than at rotor outlet so as to increase the work input to the rotor. 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 5 Design Guidelines The Th PEMP RMD510 nominall design d i defined is d fi d by b relative flow with zero incidence at rotor inlet, i.e. W2 = Cr2, and axial absolute flow at rotor exit,, i.e. C3 = Cx3 Thus, with Cw3 = 0 and Cw2 = U2, the specific work for the nominal design is Spouting Velocity: The term spouting velocity, C0 (originating from hydraulic turbine practice) is ddefined fi d as that h velocity l i which hi h hhas an associated i d ki i energy equall to the h kinetic isentropic enthalpy drop from turbine inlet stagnation pressure p01 to the final exhaust pressure. When no diffuser is used or With complete recovery of the exhaust kinetic energy, and with Cw2 = U2, At the best efficiency point, generally, 0.68 < U2 / C0 < 0.71. 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 6 Design Guidelines The PEMP RMD510 blades are aligned along the radii for much of their length. Absolute flow angle at rotor inlet = Nozzle outlet angle = ~ 70º. Absolute Ab l flow fl angle l at exducer d exit i = 0º. 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 Th recommended d d slip li correlation l ti is i that th t given i by b Wiesner Wi Cu ,1,ac cos 1 w 1 0.7 C Z u ,1,tl 14 Z = number of blades (incl. splitter blades) 1 = blade angle w.r.t w r t radial direction @ M S Ramaiah School of Advanced Studies, Bengaluru 7 Variation of Slip Factor with Z PEMP RMD510 The slip factor for radial bladed rotor varies with the number of blades: 14 Number of radial blades on rotor pperiphery p y Slip factor Cu,11/u1 9 11 13 15 17 19 0.785 0 813 0.813 0.834 0.850 0.862 0.873 @ M S Ramaiah School of Advanced Studies, Bengaluru 8 Design Data Inlet temperature : 1200 K Inlet pressure : 300 000 Pa PEMP RMD510 Rotor-outlet stagnation pressure : 110 000 Pa Hot-gas inlet mass flow : 0.5 kg/s Fuel/Air ratio : 0.02 Number of rotor blades : 13 (radial) Nozzle outflow angle : 70° to radial direction To find: Rotor diameter Blade axial width at inlet Rotational speed 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 9 Inlet Velocity Triangle act c1 C1 1 PEMP RMD510 W1 Cr,1 r1 Cu,1 u1 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 10 PEMP RMD510 Inlet Flow Parameters • G Guess S Stagnation-to-Stagnation i S i polytropic l i efficiency ffi i = 0.92 0 92 • For 13 blades w= = 0.834 T0, 2 T0,1 p0 , 2 p0,1 R cp p ,c T0,2 = 961.36 K Then, T 1080.68 K c p 1194.64 J/kg K Δh 0 C p ΔT 0 285,089 J/kg act C1 c1 1 W1 Cr,1 Δh 0 ψ u12 u1 584.7 m/s Cu,1 487.6 m/s C1 518.9 m/s Cr,1 181.1 m/s W1 206.4 m/s 14 Cu,1 u1 @ M S Ramaiah School of Advanced Studies, Bengaluru 11 Optimum Specific Speed Distribution of losses along envelope of maximum total total-to-static to static efficiency (Rohlik 1968) 14 PEMP RMD510 Typical performance of radial turbine (Rohlik 1968) @ M S Ramaiah School of Advanced Studies, Bengaluru 12 Optimum Specific Speed (… contd.) PEMP RMD510 Curves for specific speed for radial flow turbine indicate that the max. efficiency should reach at non-dimensional Ns of 0.6. N s,op 0.6 2πN Vin 60 Δh 2πN d1 πNd1 u1 ω r1 60 2 60 2 b1 Vin Cr,1 π d1 b1 Cr,1 π d1 d1 g c Δh0 ψ u1 34 2 ω Cr,1 π d1 b1 d1 2 Ns ψ u 2 34 1 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 13 Rotor Inlet Width to Diameter Ratio PEMP RMD510 N s2ψ 3 2u13 N s2ψ 3 2 u1 b1 2 2 d1 ω d1 π C r,1 4π C r,1 tan αc,1 ψ u1 C r,1 2 12 b1 N s ψ tan αc,1 d1 4π Inserting appropriate design inputs, inputs we get b1/d1 = 0.072 Bothh b1 andd d1 can be B b determined d i d by b calculating l l i volume l flow fl rate at rotor inlet. C1 0.8843 g c RT0 ,1 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 14 Rotor Inlet Mach Number PEMP RMD510 Mach number can be determined from the following relation or the figure g 0.8843 1 2 Cp M C 2 1 1 R Cp g c RT 0 2 1 R M 1 0.815 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 15 Calculation of Density ρ st,1 ρ0 ,1 1 2 M1 Cp 1 2 R C p R PEMP RMD510 1 0.729 The stagnation density at rotor inlet can be assumed equal to that at nozzle inlet for this preliminary design ρ0 ,1 p 0 ,1 RT0 ,1 300 10 3 286 .96 120 0 .8712 kg m 3 ρ st,1 0. 0 6353 kg k m3 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 16 Rotational Speed PEMP RMD510 m C r,1 ρ st,1π d1 b1 C r,1 ρ st,1 π d12 b1 d 1 0 .5 d 181.11 0 .6353 π 0 .072 2 1 d 1 138 .6 mm b1 9 .98 mm 2 πN d 1 u1 60 2 60 u1 N 80 560 rpm πd 1 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 17 PEMP RMD510 Final Design Having found the basic geometric parameters of the rotor (and inlet nozzle vanes), the blade profiles can be generated by Inlet Exit using analytic equations using i commercial i l software, f like lik 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 g and assemblyy requirements. q 14 Nozzle vane @ M S Ramaiah School of Advanced Studies, Bengaluru Exducer 18 PEMP RMD510 Design of Turbocharger (Based on Specific Speed) 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 19 Schematic of a Turbocharger 14 @ M S Ramaiah School of Advanced Studies, Bengaluru PEMP RMD510 20 Turbocharger Components 14 @ M S Ramaiah School of Advanced Studies, Bengaluru PEMP RMD510 21 Working of Turbocharger 14 @ M S Ramaiah School of Advanced Studies, Bengaluru PEMP RMD510 22 PEMP RMD510 Turbocharger Design Data Compressor Turbine 1.0 1.04 Inlet stagnation g temperature, p ,K 300 ((T0,1 0 1) 800 ((T0,4 0 4) Inlet stagnation pressure, N/m2 1*105 (P0,1) Find Engine back pressure (P0,4) Outlet static pressure, N/m2 2* 105(Pst,3) 1.2* 105 (Pst,7) Air Combustion Co bust o products p oducts 100% 00% theoretical air Cp J/(kg K ) & ( Cp /R ) 1010 (3.52) 1172 (4084) Blade angle g at periphery p p y 30° (2) 0 ° (5) Specific speed, Ns 0.628 -- dhb,1/ dsh,1 0.60 -- 0.82 (p,ts,1-3 0.8 p ts 1 3) 0.82 (p,ts,4-7 0.8 p ts 4 7) Flow angle at rotor exit, c2 (deg) 60 0 Flow angle at rotor inlet, c1 (deg) 0 70 Number of rotor blades, blades Z 17 13 0.96 (p,tt,1-2) 0.96 (p,tt,5-6) Mass flow rate, kg/s Fluid ud Polytropic o y op c efficiency e c e cy Polytropic efficiency 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 23 Calculations Planes 14 @ M S Ramaiah School of Advanced Studies, Bengaluru PEMP RMD510 24 Wiesner’s Correlation PEMP RMD510 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 di l compressor. cos β Cu,1,ac 1 σw 1 0 . 7 C u u, 1 ,tl tl Z 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 25 PEMP RMD510 Compressor Design Calculations 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 26 Compressor Velocity Triangles PEMP RMD510 u2 CCu,2,tl u,2,tl Cu,2 Outlet Velocity Triangle Cr,2 W2 c2=60 60 2=30 30 ush,1 Cx,sh,1 x sh 1 14 h1 w,sh,1 Wsh,1 Inlet Velocity Triangle @ M S Ramaiah School of Advanced Studies, Bengaluru 27 Enthalpy Rise R C p 1 η p,c,ts PEMP RMD510 T0 ,3 p 0 ,3 T0 ,1 p 0 ,1 p 0 ,3 p st,3 when η p,c,ts is used T0 ,3 2 0 .3484 1.2732 T0 ,1 ΔT 0 ,1 3 0 .2732 300 81.95 K C pc 1010 J/kgK Therefore, and 14 Δh 0 ,1 3 82722 J/kg g c Δh0 ,13 3 4 4879 .9 @ M S Ramaiah School of Advanced Studies, Bengaluru 28 Inlet Volume Flow Rate PEMP RMD510 Guess inlet axial velocity First iteration: 110 m/s Second iteration: 127.3 m/s (all second iteration values are in parenthesis) Cx 110 0 .375 0 .434 293 .41 g c RT 0 ,1 For C p R 3 .52 , M 1 0 .32 0 .371 C p R 1 2 ρ0 M 1 ρ st Cp 1 2 R 1.0520 1.0703 14 @ M S Ramaiah School of Advanced Studies, Bengaluru From slide 15 29 Rotational Speed PEMP RMD510 p0 ,1 105 1.1616 kg/m3 ρ0 ,1 R T0 ,1 286.96 300 ρst,1 1.1042 kg/m3 ( 1.0853 ) m ρ V st,1 1 V1 0.9056 m 3 /s V1 0.9516 V 0.9214 m /s, V1 0.9599 60 N s g c Δh0 N 2π V 30767 rev/min 30500 3 1 34 1 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 30 Compressor Outlet Velocity Diagram PEMP RMD510 u2 From Wiesner’s correlation (slide 25) CCu,2,tl u,2,tl Cu,2 cos β2 Cu,ac σw 1 0.872 0 .7 Cu,tl Z Cr,2 W2 c2=60 2=30 For cos β2 cos 30 , Z 17 1 1 Cu,2 tan β2 1 0.676 ψ u2 tan αc 2 σ w 0 .5 g c Δh0 82772 u2 0.676 ψ d 2 60 u2 /N 219.2 mm 14 0 .5 350.0 m/s / @ M S Ramaiah School of Advanced Studies, Bengaluru 31 PEMP RMD510 Inlet Velocity Diagram Th procedure The d to t select l t minimum i i Wsh,1 is i as follows f ll 1. Choose a value of d sh,1 2 Calculate u sh,1 Nπ / 60d sh,1 2. 2 2 3. Calculate Aa πd sh, 1 / 4 1 0.6 4 Calculate m RT0 ,1 /Aa p0 ,1 4. 2 m RT0 /g / c M M 1 5. from the relation AP0 Cp R 1 1 2 calculate M1 Cp R 6. Calculate pst,1 /p0 ,1 pst,1 C x,1 Wsh,1 Cp 1 R This pprocedure is given g in tabular form in Slide 33,, in which the second iteration values are given in brackets. The optimum value of dsh,1 is found to be 120 mm. 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 32 PEMP RMD510 Calculation of Optimum Shroud Parameter dsh,1 (mm) 100 125 120 ush,1(m/s) = 1610.97 dsh,1 (= 1575.22 dsh,1) 161.10 (157.22) 201.37 (199.64) 193.32 (191.65) Aa (m2 ) 0.5027dsh2 ,1 103 5 026 5.026 7 854 7.854 7 2389 7.2389 0.5838 0.3736 0.4053 0.61 0.34 0.37 0.836 0.944 0.934 204 93 204.93 116 06 116.06 127 31 127.31 260.7 (258.5) 232.4 (230.9) 231.5 (230.1) m RT0 ,1 /A p0 ,1 M1 ρ st, 1 /ρ 0 ,1 C x,1 ( m/s ) 0 .86088 Aa ρ st,1 /ρ 0 ,1 Wsh,1 Cx2,1 ush2 ,1 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 33 Impeller-Diffuser Interface PEMP RMD510 The minimum value of Wsh,1 is found to be 230.1 m/s. Hence, the de Haller velocity ratio, W2 / Wsh,1= 0.83. This should not lead to diffusion induced separation. Impeller-Outlet and diffuser-inlet width, b2: C2 ψu 2 sin αc,2 274.1 m/s T0 ,2 381.95 K C2 g c RT0 ,2 0.8281 M 2 0.740 ρst,2 0.771 ρ0 ,2 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 34 Inducer Hub-Tip Ratio PEMP RMD510 Find Fi d the th rotor-outlet t tl t stagnation t ti pressure using i the th rotor t efficiency ffi i C p R η p,c,tt,1 2 p0 ,2 T0 ,2 p0 ,1 T0 ,1 5 2 Therefore,, p0 ,2 2.262 10 N/m ρ0 ,2 2.0635 kg/m 3 3 . ρ st, 1 5909 kg/m g st 2 C r,2 C 2 cos 60 137 .1 m/s b2 m πd 2 ρst,2C r,2 6.69 mm Inducer hub diameter can be determined from hub-tip ratio d hb, hb 1 0.60 d hb,1 0.60 120 72 mm d sh,1 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 35 Radial Diffuser Stability PEMP RMD510 C2 d 2 2 ρst,2 Re,2 μst,2 for mean Tst,2 320 K μ 2.020 10 5 Ns/m 2 Re,2 2.44 106 b2 r2 0.061 From the Stability limits in Jansen’s curves b 2 / r2 0.125 0 08 0.08 0.061 14 (r3 / r2)mx 4.0 29 2.9 2.0 (by interpolation) 80 percent of 2.0 is 1.6 d3 =11.6 6 x 219 219.22 = 350 mm @ M S Ramaiah School of Advanced Studies, Bengaluru 36 Radial Diffuser Stability (… contd.) PEMP RMD510 Stable operating range of vaneless diffusers (Jansen, 1964) 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 37 PEMP RMD510 Turbine Design Calculations 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 38 Turbine Design Calculations Turbine Rotor Diameter: Δh0 ,e The turbine has slightly increased mass flow, flow because of fuel addition, and must supply windage and d bearing b i power in i addition to compressor power. PEMP RMD510 2 u 1 02 . 5 Cu,5 82772 J/kg g c u5 1.04 cos β5 Cu,5 1 Z e0 .7 Cu,u 5 ,tltl Cu,5 ,tl u5 and β5 0 ; Z e 13 C u,5 ,ac 0 .834 u5 1.02 82772 .4 u * 1.04 0 .834 u 5 312 .0 m/s / d 5 198 .1 mm 2 5 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 39 Turbine Design Calculations PEMP RMD510 Turbine Pressure Ratio: m e Δh 0 ,e 1.02 m c Δh 0 ,c ΔT 0 ,e 1010 1 . 02 1 . 0 81 .953 69 .27 K 1.04 1172 p 0 ,in T0 ,in p 0 ,,ex T0 ,,ex p 0 ,ex C p R 800 730 .73 p st,ex 1 η p,e,ts C p R 1 η p,e,ts 1.570 p 0 ,in 1.570 1.2 10 5 1.884 10 5 N/m 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 2 40 Turbine Design Calculations PEMP RMD510 N l Outlet Nozzle O l Velocity: Vl i The following parameters have been calculated: Blade speed = 312.0 m/s ; Work coefficient, = 0.834 ; Nozzle angle = 70° Cu,1 ψu1 tan 70 Cr,1 Cr,1 Cr,1 0.834 φ 0.3035 u1 tan 70 Cr,1 94.70 m/s Cr,5 cos 70 C5 276.89 m/s C5 C5 276.89 0.5779 g c RT0 286.96*800 with C p R 4 .084 M 0 .513 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 41 Turbine Design Calculations PEMP RMD510 C p R 1 ρ0 M 1.137 1 ρ st 2 C p R 1 1.884 10 5 0 .8207 kg/m 3 ρ st,5 0 .7215 kg/m 3 ρ0 ,5 286 .96 800 2 The mass flow rate is 1.04 kg/s Hence, the volume flow rate is 1.441 m3/s, and the enthalpy drop is 81180 J/kg. Vin 2 πN Specific speed, N s 60 g c Δh 0 3 4 14 2π 30500 1441 0.797 0 797 3 4 60 81180 @ M S Ramaiah School of Advanced Studies, Bengaluru 42 Velocity Function vs Mach Number for Perfect Gases 14 @ M S Ramaiah School of Advanced Studies, Bengaluru PEMP RMD510 43 Exit Width to Diameter Ratio PEMP RMD510 The optimum specific speed for radial-inflow turbine is about 0.65. 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 b1 N s2 tan αc1ψ 3 2 N s2 tan αc1ψ 1 2 4πψ 4π d1 b5 N s2 tan αc 5ψ 1 2 d5 4π 0.797 2 tan 70 0.834 0.1269 4π 1 7.9 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 44 Optimum Specific Speed Distribution of losses along envelope of maximum total total-to-static to static efficiency (Rohlik 1968) 14 PEMP RMD510 Typical performance of radial turbine (Rohlik 1968) @ M S Ramaiah School of Advanced Studies, Bengaluru 45 Turbine Design Calculations PEMP RMD510 Outlet Static Density: The outlet static pressure is specified together with the stagnation temperature temperature. The Mach number here is low, and it will be sufficiently accurate to guess the static temperature. pst,6 1.2 105 N/m 2 T0 ,6 730.73 K Tst,6 725 K guess 1.2 105 ρst,6 0.577 kg/m 3 286.96 725 ρst,5 ρst,6 1.257 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 46 PEMP RMD510 Results The results of the calculations, made for an exducer hub-shroud ratio of 0.3, are tabulated below: --- 0.8 0.9 1.0 --- 0.935 0.881 0.836 --- 1.15 1.208 1.314 αw,sh,6 tan1 d sh,6 d5 Cx,6 Cr,5 φ Degrees 75.44 72.77 70.05 αw,hb,6 tan t 1 Λdsh,6 d5 Cx,6 C5 φ Degrees 49 12 49.12 44 06 44.06 39 51 39.51 Whb,,6 W5 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 47 Diameter Ratio PEMP RMD510 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. We select d sh,6 0.881 d5 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 33º at the shroud and 5º at the hub. 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 48 Turbine Hub and Tip Dimensions PEMP RMD510 d sh,6 0.881*198.1 174.5 mm 2 34 d hb , 6 Ψ N s1 2 1 1 πφ φ d sh , 6 0.8343 4 0.797 0.712 π 0.3035 2 1.0.506944 0.702 d hb,6 0.702 174.5 122.49 mm b5 0.1269 d5 b5 0.1269 198.1 25.138 mm 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 49 Data for Modeling the Compressor PEMP RMD510 Inlet Velocity Triangle At Shroud At Hub uhb,1 Cx,hb,1 Whb,1 ush,1 =191.65 m/s uhb,1 = 114.98 m/s Cx,sh,1 = 127.3 127 3 m/s Cx,hb,1 = 127.3 m/s Wsh,1= 230.1 Whb,1 = 171.53 w,sh,1 = 56.4º 14 w,hb,1 w,hb,1 = 42.1º @ M S Ramaiah School of Advanced Studies, Bengaluru 50 Data for Modeling the Compressor Outlet Velocity Triangle PEMP RMD510 =350 m/s =271 271.3 3 m/s =236.6 m/s C2=274.1 m/s =137.1 m/s 158.08 m/s 137.1 78.7 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 51 Data for Modeling Turbine PEMP RMD510 Inlet Velocity Triangle act C5=276.89 m/s c1=70° w5=28.68° Cr,5=94.7 W5=107.95 m/s 260.19 U5 =312.0 m/s 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 52 Modeling Using CFX PEMP RMD510 Creating a Blade: Radial Impeller Configuration 14 Initial Angle/Thickness Dialog @ M S Ramaiah School of Advanced Studies, Bengaluru 53 Geometric Model - Compressor PEMP RMD510 Input Parameters: Blade Fluid Domain 14 Dsh = 14 mm Dhb = 8.5 mm D2 = 25 mm D3 = 30 mm 2 = 30 Z = 10 @ M S Ramaiah School of Advanced Studies, Bengaluru 54 Geometric Model - Compressor Blade Fluid Domain 14 PEMP RMD510 Input Parameters: Dsh = 21 mm Dhb = 5.25 mm D5 = 30 mm c5 = 70 Z=9 @ M S Ramaiah School of Advanced Studies, Bengaluru 55 3-D CAD Models PEMP RMD510 Compressor Turbine 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 56 Session Summary PEMP RMD510 • A procedure for design of radial turbines based on optimum specific ifi speedd is i discussed. di d • Salient constructional features and working principle of a turbocharger are presented. presented • The design of radial machines is explained through step by step design of compressor and radial turbine modules of a typical turbocharger 14 @ M S Ramaiah School of Advanced Studies, Bengaluru 57