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A holistic consideration of turbocharger heat transfer analysis and advanced turbocharging modeling methodology in a 1D engine process simulation context

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Abstract

The focus on transient engine operation will increase to fulfill future emission requirements in the commercial vehicle sector. Accordingly, the transient turbocharger matching process is becoming increasingly important. The one-dimensional fluid dynamics (1D-CFD) simulation is established as an important development tool for matching the exhaust gas turbocharger to a combustion engine. The optimization of the modeling methodology of the combustion process and the turbocharger modeling are two key parameters to improve the reliability of the dynamic engine process simulation. In this paper, the advanced turbocharger (TC) methodology is described. This includes the determination of the adiabatic turbocharger performance from conventional hot gas test stand (HGS) measurement data, the derivation of an one-dimensional (1D) turbocharger heat transfer model and a method to physically extend the turbine map range. The adiabatic efficiencies of the turbocharger are determined with a model-based heat transfer correction of the conventional measured efficiencies from HGS measurement data. These adiabatic efficiency maps were used as a baseline to extend the conventional TC model with a heat transfer model taking into account of the engine boundary conditions in terms of temperature, pressure and mass flow rate. To assess the temperature distribution and the thermal inertia of the TC main components, in both stationary and transient engine operations, the variable geometry turbine (VGT) turbocharger hardware, installed on a medium-duty diesel engine, was equipped with several thermocouples on all accessible surfaces to make comprehensive surface temperature surveys. A 1D lumped capacitance heat transfer model (HTM) of the VGT TC was developed and validated against the experimental data from the engine test bench. To complete the advanced TC modeling, the turbine map is extended using experimental measurement data, based on extended HGS measurements, in combination with mathematically supported extrapolation. The results from the advanced turbocharger simulation methodology significantly improves the prediction of the temperature drop over the turbine in comparison to the conventional adiabatic TC simulation methodology. The validated heat transfer model also allows the analysis of the heat flow breakdown of the turbocharger. Based on the advanced turbocharger model, a tool for the improved transient turbocharger-engine matching process is given.

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Abbreviations

1D:

One-dimensional

1D-CFD:

One-dimensional computational fluid dynamics

BMEP:

Brake mean effective pressure

BH:

Bearing housing

BP:

Back plate

BSR:

Blade speed ratio

CAD:

Computer-aided design

CARB:

California air resources board

CH:

Compressor housing

\(\hbox {CO}_{2}\) :

Carbon dioxide

CV:

Commercial vehicle

EGR:

Exhaust gas recirculation

EGT:

Exhaust gas aftertreatment

EPA:

Environment Protection Agency

EPS:

Engine process simulation

EU:

European Union

GHG:

Greenhouse gas

HGS:

Hot gas test stand

HTM:

Lumped capacitance heat transfer model

MCE:

Multi-cylinder engine

\(\hbox {NO}_{{x}}\) :

Nitrogen oxides

TC:

Turbocharger

TH:

Turbine housing

VGT:

Variable geometry turbine

WPR:

Windage pressure ratio

\(\alpha\) :

Convection heat transfer coefficient

\(\beta _\text {2,b}\) :

Geometrical impeller blade outlet angle

\(\delta _i\) :

Distance from mass center to the contact area

\(\varDelta h^{\star }_\text {C,adi}\) :

Adiabatic compressor enthalpy rise

\(\varDelta h_\text {C,is}\) :

Isentropic compressor enthalpy rise

\(\varDelta h_\text {C,dia}\) :

Diabatic compressor enthalpy rise

\(\varDelta \dot{H}_\text {Oil}\) :

Oil enthalpy change over the turbocharger

\(\varepsilon\) :

Emissivity of surface

\(\eta _\text {C,is}\) :

Isentropic compressor efficiency

\(\eta _\text {C,is,adi}\) :

Isentropic adiabatic compressor efficiency

\(\eta _\text {TC}\) :

Overall turbocharger efficiency

\(\eta _\text {TC,mech}\) :

Mechanical turbocharger efficiency

\(\eta _\text {T,comb}\) :

Combined turbine efficiency

\(\eta _\text {T,comb,adi}\) :

Combined adiabatic turbine efficiency

\(\eta _\text {T,is,adi}\) :

Isentropic adiabatic turbine efficiency

\(\theta\) :

Specific heat transfer coefficient of the turbocharger

\(\lambda\) :

Thermal conductivity

\(\lambda _\text {adi}\) :

Adiabatic work coefficient

\(\lambda _\text {dia}\) :

Apparent work coefficient

\(\lambda _\text {Euler,m}\) :

Theoretical Euler work coefficient determined out of hot gas stand measurement

\(\lambda _\text {Euler,th}\) :

Theoretical ideal Euler work coefficient

\(\lambda _\text {q}\) :

Heat transfer coefficient

\(\mu\) :

Slip factor

\(\varPi _{\text {C}}\) :

Compressor pressure ratio

\(\varPi _{\text {T}}\) :

Turbine pressure ratio

\(\rho _\text {t1}\) :

Density at the compressor inlet

\(\sigma\) :

Stefan–Boltzmann constant

\(\varphi _2\) :

Flow coefficient at impeller outlet

\(\phi _\text {t1}\) :

Global flow number at the compressor inlet

\(\dot{m}_\text {C}\) :

Compressor mass flow rate

\(\dot{m}_\text {C,cor}\) :

Corrected compressor mass flow rate

\(\dot{m}_\text {T}\) :

Turbine mass flow rate

\(\dot{m}_\text {T,red}\) :

Reduced turbine mass flow rate

\(\dot{Q}\) :

Heat flow

\(\dot{Q}_\text {BH,C}\) :

Heat flow from bearing housing to compressor via conduction

\(\dot{Q}_\text {BH,Dif}\) :

Heat flow from bearing housing into the working fluid via forced convection

\(\dot{Q}_\text {BH,ext}\) :

External bearing housing heat flow

\(\dot{Q}_\text {BH,Oil}\) :

Heat flow from bearing housing into turbocharger oil circuit via forced convection

\(\dot{Q}_\text {C,total}\) :

Total heat flow into the compressor

\(\dot{Q}_\text {CH,Vol}\) :

Heat flow from compressor housing into working fluid via forced convection

\(\dot{Q}_\text {CH,ext}\) :

External compressor housing heat flow

\(\dot{Q}_\text {enb}\) :

Measured energy balance

\(\dot{Q}_\text {TC,ext,meas}\) :

Determined external turbocharger heat transfer

\(\dot{Q}_\text {TC,ext,model}\) :

Modeled external turbocharger heat transfer

\(\dot{Q}_\text {T,BH}\) :

Heat flow from turbine to bearing housing via conduction

\(\dot{Q}_\text {TH,ext}\) :

External turbine housing heat flow

\(\dot{Q}_\text {Vol,TH}\) :

Heat flow from turbine volute to turbine housing via forced convection

\(a_x\) :

Correlation coefficient

A :

Contact area

\(A_\text {in}\) :

Internal surface area

\(A_\text {out}\) :

Outer surface area

\(c_e\) :

Local speed of sound at the compressor inlet

\(c_\text {p,C}\) :

Specific heat capacity at constant pressure of compressed air

\(c_\text {p,T}\) :

Specific heat capacity at constant pressure of exhaust gas

\(D_2\) :

Impeller tip diameter

Gr:

Grashof number

k :

Thermal conductivity

\(k_{\text {c}}\) :

Heat transfer parameter

\(k_\text {df}\) :

Disc friction parameter

\(L_\text {Char}\) :

Characteristic length

\(M_{\text {u}}\) :

Tip speed Mach number

\(n_\text {Eng}\) :

Engine speed

\(n_\text {TC}\) :

Turbocharger speed

\(n_\text {T,red}\) :

Reduced turbine speed

Nu:

Nusselt number

\(P_{\text {C}}\) :

Compressor power

\(P_\text {C,is,adi}\) :

Isentropic adiabatic compressor power

\(P_{\text {F}}\) :

Friction power of the turbocharger

Pr:

Prandtl number

\(P_{\text {T}}\) :

Turbine power

\(P_\text {T,is}\) :

Isentropic turbine power

\(q_\text {C,a}\) :

Specific heat flow into the compressor after compression

\(q_\text {C,b}\) :

Specific heat flow into the compressor before compression

\(q_\text {C,total}\) :

Total specific heat flow into the compressor

Re:

Reynolds number

\(T_\text {1,b.C}\) :

Charge air temperature before compressor

\(T_\text {2,a.C}\) :

Charge air temperature after compressor

\(T_\text {3,b.T}\) :

Exhaust temperature before turbine

\(T_\text {4,a.T}\) :

Turbine outlet temperature

\(T_\text {Amb}\) :

Ambient temperature

\(T_\text {BH,CS}\) :

Bearing housing surface temperature on the compressor side

\(T_\text {BH,TS}\) :

Bearing housing surface temperature on the turbine side

\(T_\text {BP}\) :

Surface thermocouple temperature on the compressor back plate

\(T_\text {CH}\) :

Surface thermocouple temperature on the compressor housing

\(T_\text {CH,mean}\) :

Mean surface thermocouple temperature on the compressor housing

\(T_{\text {F}}\) :

Fluid temperature

\(T_\text {Oil,in}\) :

Turbocharger oil circuit inlet temperature

\(T_\text {Oil,out}\) :

Turbocharger oil circuit outlet temperature

\(T_\text {t1}\) :

Total temperature at compressor inlet

\(T_\text {t2}\) :

Total temperature at compressor outlet

\(T_\text {t2,is}\) :

Total temperature at compressor outlet in isentropic state of change

\(T_\text {t3}\) :

Total temperature at turbine inlet

\(T_\text {TH}\) :

Surface thermocouple temperature on the turbine housing

\(T_\text {TH,mean}\) :

Mean surface thermocouple temperature on the turbine housing

\(T_W\) :

Wall temperature

\(T_1\)/\(T_2\) :

Wall-face temperature

\(u_\text {2}\) :

Impeller blade tip speed

\(u_\text {C,cor}\) :

Corrected compressor impeller blade tip speed

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Acknowledgements

The author would like to thank John P. Watson from BorgWarner Turbo Systems for his great support by providing the hot gas test bench measurements, the empirical turbocharger friction power correlation and the CAD model of the turbocharger hardware.

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Authors and Affiliations

  1. Robert Bosch GmbH, Powertrain Solutions, Wernerstraße 51, 70469, Stuttgart-Feuerbach, Germany

    Marcel Lang, Torsten Eggert & Robin Schifferdecker

  2. Institut für Kolbenmaschinen (IFKM), Karlsruher Institut für Technologie, Karlsruhe, Germany

    Thomas Koch

  3. BorgWarner Turbo Systems, Asheville, USA

    John P. Watson

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Lang, M., Koch, T., Eggert, T. et al. A holistic consideration of turbocharger heat transfer analysis and advanced turbocharging modeling methodology in a 1D engine process simulation context. Automot. Engine Technol. 5, 113–136 (2020). https://doi.org/10.1007/s41104-020-00062-1

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