Lecture 8 Turbocharger Modeling

Lecture 8 Turbocharger Modeling System Modeling Institute for Dynamic Systems and Control (IDSC) Camillo Balerna Dr. Guillaume Ducard Camillo Balerna 07/11/2017 1

Lecture Overview Turbocharger modeling Turbine & Compressor Causality diagram Inputs, outputs Maps and operation Source: https://auto.howstuffworks.com/turbo2.htm Turbocharged internal combustion engines Engine power modeling Naturally aspirated (NA) Vs turbocharged (TC) engines Benefits of turbocharging F1 electrified turbocharger Camillo Balerna 07/11/2017 2

Turbocharger Θ tc dω tc dt = T t T c + T ext Source: https://auto.howstuffworks.com/turbo2.htm Camillo Balerna 07/11/2017 3

Turbine Power pressure T position Source: https://auto.howstuffworks.com/turbo2.htm Camillo Balerna 07/11/2017 4

Turbine Causality Diagram Inputs Outputs Inputs θ 3 : Temperature before the turbine [K] p 3 : pressure before the turbine [Pa] p 4 : pressure after the turbine [Pa] ω t : Turbine speed [rad/s] u vng : Variable nozzle geometry control input [ ] Π t = p 3 p 4 = p bef,t p aft,t Camillo Balerna 07/11/2017 5

Turbine Causality Diagram Inputs Outputs Outputs θ 4 : Temperature of the flow exiting the turbine [K] t : Mass flow through the turbine [Kg/s] T t : Torque generated by the turbine [Nm] Camillo Balerna 07/11/2017 6

Turbine Outputs o Temperature ofthe flow exiting the turbine θ 4 = θ 3 1 κ κ 1 η t 1 Π t o Mass Flow through the turbine Π t = p 3 p 4 = p bef,t p aft,t t = p 3 p ref,0 θ ref,0 θ 3 μሶ t o Torque produced by the turbine T t = P t ω t = t c p θ 3 ω t 1 Π t 1 κ κ η t Camillo Balerna 07/11/2017 7

Turbine Outputs derivation Open system de dt = ሶ H in ሶ H out ሶ W t + ሶ Q o Turbine does not store energy over time de dt = 0 o Turbine is assumed to be adiabatic no heat transfer ሶ Q = 0 P t = ሶ W t = ሶ H in ሶ H out = t c p θ 3 θ 4 Isentropic relation θ 3 θ 4,is = p 3 p 4 κ 1 κ κ 1 κ = Π t Turbine exit temperature θ 4 = θ 3 1 κ κ 1 η t 1 Π t Isentropic efficiency η t = θ 3 θ 4 θ 3 θ 4,is Turbine power produced P t = 1 κ κ t c p θ 3 1 Π t η t Camillo Balerna 07/11/2017 8

Turbine Outputs o Temperature ofthe flow exiting the turbine θ t = θ 3 1 κ κ 1 η t 1 Π t o Mass Flow through the turbine Π t = p 3 p 4 = p bef,t p aft,t t = p 3 p ref,0 θ ref,0 θ 3 μሶ t o Torque produced by the turbine T t = P t ω t = t c p θ 3 ω t 1 Π t 1 κ κ η t Camillo Balerna 07/11/2017 9

Turbine Efficiency Map Input Output c us = 2 c p θ 3 1 Π t (1 κ)/κ c us ǁ = r t ω t c us Since the turbine efficiency mainly depends on the angle of incidence of the inflowing gas, the turbine blade speed ratio c us ǁ is used as variable. Camillo Balerna 07/11/2017 10

Turbine Efficiency Map Variable Geometry Source: https://www.dieselnet.com/tech/air_turbo_vgt.php Camillo Balerna 07/11/2017 11

Turbine Outputs o Temperature ofthe flow exiting the turbine θ t = θ 3 1 κ κ 1 η t 1 Π t o Mass Flow through the turbine Π t = p 3 p 4 = p bef,t p aft,t t = p 3 p ref,0 θ ref,0 θ 3 μሶ t o Torque produced by the turbine T t = P t ω t = t c p θ 3 ω t 1 Π t 1 κ κ η t Camillo Balerna 07/11/2017 12

Turbine Mass Flow Map Input Output For control purposes, the mass flow behaviour of fluid-dynamic turbines can be modeled quite well as orifice compressible flow through a valve. If the turbine is a Variable Nozzle Turbine (VNT) or Variable Geometry Turbine (VGT), the mass flow and its maximum value depend on the nozzle position (as it is for the compressible flow through a valve). Camillo Balerna 07/11/2017 13

Turbine Mass Flow Map Fixed Geometry Source: https://www.dieselnet.com/tech/air_turbo_vgt.php Camillo Balerna 07/11/2017 14

Turbine Mass Flow Map Variable Geometry Source: https://www.dieselnet.com/tech/air_turbo_vgt.php Camillo Balerna 07/11/2017 15

Turbine Variable Geometry Turbine (VGT) At Low Engine Speed low mass flow low pressure low turbine power Narrow inlet area Better incidence Increased efficiency Increased power At High Engine Speed high mass flow high pressure Wide inlet area Avoid choke! Source: https://www.intmarketing.org/en/automotive/113-variable-turbine-geometry.html Camillo Balerna 07/11/2017 16

Compressor Source: https://auto.howstuffworks.com/turbo2.htm Camillo Balerna 07/11/2017 17

Compressor pressure C Power position Source: https://auto.howstuffworks.com/turbo2.htm Camillo Balerna 07/11/2017 18

Compressor Causality Diagram Inputs Outputs Inputs p 1 : Pressure before the compressor [Pa] p 2 : Pressure after the compressor [Pa] θ 1 : Temperature before the compressor [K] ω c : Compressor speed [rad/s] Π c = p 2 p 1 = p aft,c p bef,c Camillo Balerna 07/11/2017 19

Compressor Causality Diagram Inputs Outputs Outputs θ c : Temperature of the flow exiting the compressor [K] c : Mass flow through the compressor [Kg/s] T c : Torque absorbed by the compressor [Nm] Camillo Balerna 07/11/2017 20

Compressor Outputs o Temperature ofthe flow exiting the compressor θ c = θ 1 + Π c κ 1 κ 1 θ 1 η c o Mass Flow through the compressor Π c = p 2 p 1 = p aft,c p bef,c c = p 1 p ref,0 θ ref,0 θ 1 μሶ c o Torque absorbed by the compressor T c = P c ω c = c c p θ 1 ω c Π c κ 1 κ 1 1 η c Camillo Balerna 07/11/2017 21

Compressor Outputs derivation Open system de dt = ሶ H in ሶ H out ሶ W c + ሶ Q o Compressor does not store energy over time de dt = 0 o Compressor is assumed to be adiabatic no heat transfer ሶ Q = 0 P c = ሶ W c = Hሶ out Hሶ in = c c p θ 2 θ 1 Isentropic relation θ 2,is θ 1 = p 2 p 1 κ 1 κ Isentropic efficiency η c = θ 2,is θ 1 θ 2 θ 1 κ 1 κ = Π c Compressor exit temperature θ 2 = θ 1 + Π c κ 1 κ 1 θ 1 η c Compressor power absorbed P c = κ 1 c c p θ 1 Π κ c 1 1 η c Camillo Balerna 07/11/2017 22

Compressor Outputs o Temperature ofthe flow exiting the compressor θ c = θ 1 + Π c κ 1 κ 1 θ 1 η c o Mass Flow through the compressor Π c = p 2 p 1 = p aft,c p bef,c c = p 1 p ref,0 θ ref,0 θ 1 μሶ c o Torque absorbed by the compressor T c = P c ω c = c c p θ 1 ω c Π c κ 1 κ 1 1 η c Camillo Balerna 07/11/2017 23

Compressor Mass Flow & Efficiency Map Input Output Camillo Balerna 07/11/2017 24

Compressor Mass Flow & Efficiency Map Source: http://www.enginelabs.com/engine-tech/poweradders/understanding-compressor-maps-sizing-a-turbocharger/ Camillo Balerna 07/11/2017 25

Compressor Operational Limits Fluid-dynamic instabilities destroy the regular flow pattern possible back-flow Maximum speed allowed to avoid mechanical damages centrifugal forces Behaviour at zero (or very low) speed blocking orifice Flow reaches sonics conditions choked orifice Camillo Balerna 07/11/2017 26

Formula 1 Turbocharged Engine Source: https://sport.sky.it/formula1/2017/03/21/formula-1--il-dizionario--power-unit-ed-elettronica.html Camillo Balerna 07/11/2017 27

Internal Combustion Engine Engine Power can be approximated as following: P engine = P comb,fuel + P fric + P pump Assume constant engine speed ω e o Engine Power coming from the fuel combustion: P comb,fuel = e comb P f = e comb H l fuel k 1 fuel o Engine Power coming from the pistons mechanical friction: P fric k 2 o Engine Power coming from the gas exchange: P pump = p intake p exhaust V d ω e 4π k 3 p intake p exhaust Camillo Balerna 07/11/2017 28

Internal Combustion Engine o Engine Power, neglecting the friction and assuming p intake = p exhaust : P engine k 1 fuel + k 3 p intake p exhaust k 1 fuel o Air to Fuel Ratio is defined as following: λ AF = air 1 fuel σ 0 λ AF = 1 fuel = air σ 0 o Engine Air Mass Flow isapproximated as following: air = p intake R air θ intake ω e 4π V d λ vol k 4 p intake P engine fuel air p intake NA 1 bar 100 kw TC 4 bar 400 kw Camillo Balerna 07/11/2017 29

Turbocharged Engine o Engine Power, neglecting the friction and for a specific P engine k 1 fuel : fuel + k 3 p intake p exhaust NA 1 bar TC 4 bar NA 1 bar TC 2 bar C intake exhaust T ω e = 10 000 rpm V d = 1. 6 L P pump,na 0 kw P pump,tc 26 kw Camillo Balerna 07/11/2017 30

Engine Response P engine P engine,req Naturally Aspirated Slower increase time Camillo Balerna 07/11/2017 31

Formula 1 Engine Response How and how fast is the engine power response of a conventional turbocharger compared to an electrified turbocharger (e.g. F1)? Turbocharger 1) Press throttle pedal 2) More fuel injected 3) Exhaust temperature increases 4) More power extracted by the turbine 5) Turbocharger speed increases 6) Compressor mass flow increases 7) More air more fuel can be injected 8) More Engine power Electrified Turbocharger 1) Press throttle pedal 2) More fuel injected & MGU-H positive 3) Turbocharger speed increases faster ( MGU-H & exhaust temperature) 4) Compressor mass flow increases 5) More air more fuel can be injected 6) More Engine power Camillo Balerna 07/11/2017 32

Formula 1 Engine Response P engine P engine,req Steeper increase time Camillo Balerna 07/11/2017 33

IDSC Open Lab 2017 Camillo Balerna 07/11/2017 34

IDSC Open Lab 2017 Formula 1 Power Unit Efficient control algorithms are designed for the hybrid electric propulsion system of the Formula 1 car, in order to achieve the fastest possible lap-time. (Presentations in English or German) Mauro Salazar, maurosalazar@idsc.mavt.ethz.ch Camillo Balerna, balernac@idsc.mavt.ethz.ch ML K37.1 http://www.idsc.ethz.ch/research-guzzellaonder/research-projects/formula1.html Camillo Balerna 07/11/2017 35