Modeling and control of Rankine based waste heat recovery systems - - PowerPoint PPT Presentation

Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion

Modeling and control of Rankine based waste heat recovery systems for heavy duty trucks

Vincent GRELET1,2,3, Thomas REICHE1, Madiha NADRI2, Pascal DUFOUR2 and Vincent LEMORT 3

1Volvo Group Trucks Technology Advanced Technology and Research, 1 avenue Henri Germain, 69800 Saint

Priest, France

2Universit´

e de Lyon, Lyon F-69003, Universit´ e Lyon 1, CNRS UMR 5007, Laboratory of Process Control and Chemical Engineering (LAGEP), Villeurbanne 69100, France

3LABOTHAP, University of Liege, Campus du Sart Tilman Bat. B49 B4000 Liege, Belgium

International Symposium on Advanced Control of Chemical Processes 7-10 June, Whistler, British Columbia, Canada

1/21 Grelet et al., ADCHEM 2015 paper 098

Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion

Table of contents

1

Context and motivations

2

Waste heat recovery Rankine cycle based

3

Studied system

4

Control oriented modeling Model assumptions and governing equations Heat transfer Working fluid properties Discretization

5

Controller development Implementation constraint Model identification State of the art PID controller Nonlinear model inversion Controllers structure

6

Simulation results

7

Conclusion and next steps

8

Contacts and discussion

2/21 Grelet et al., ADCHEM 2015 paper 098

Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion

Context and motivations

In nowadays heavy duty engines, a major part of the chemical energy contained in the fuel is released to the ambient through heat.

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Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion

Context and motivations

In nowadays heavy duty engines, a major part of the chemical energy contained in the fuel is released to the ambient through heat. Waste heat recovery based on the Rankine cycle is a promising technique to increase fuel efficiency.

3/21 Grelet et al., ADCHEM 2015 paper 098

Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion

Context and motivations

In nowadays heavy duty engines, a major part of the chemical energy contained in the fuel is released to the ambient through heat. Waste heat recovery based on the Rankine cycle is a promising technique to increase fuel efficiency. Long and frequent transient behavior

• f the heat sources makes good

control strategies mandatory.

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Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion

Waste heat recovery Rankine cycle based

Rankine cycle is widely known and used for power generation. It is based on four basic transformations:

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Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion

Waste heat recovery Rankine cycle based

Rankine cycle is widely known and used for power generation. It is based on four basic transformations:

The liquid is compressed from condensing to evaporating pressure (1 → 2).

4/21 Grelet et al., ADCHEM 2015 paper 098

Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion

Waste heat recovery Rankine cycle based

Rankine cycle is widely known and used for power generation. It is based on four basic transformations:

The liquid is compressed from condensing to evaporating pressure (1 → 2). It is then pre-heat, vaporize and superheat (2 → 3).

4/21 Grelet et al., ADCHEM 2015 paper 098

Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion

Waste heat recovery Rankine cycle based

Rankine cycle is widely known and used for power generation. It is based on four basic transformations:

The liquid is compressed from condensing to evaporating pressure (1 → 2). It is then pre-heat, vaporize and superheat (2 → 3). It expands from evaporating to condensing pressure (3 → 4).

4/21 Grelet et al., ADCHEM 2015 paper 098

Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion

Waste heat recovery Rankine cycle based

Rankine cycle is widely known and used for power generation. It is based on four basic transformations:

The liquid is compressed from condensing to evaporating pressure (1 → 2). It is then pre-heat, vaporize and superheat (2 → 3). It expands from evaporating to condensing pressure (3 → 4). It condenses and goes back to liquid state (4 → 1).

4/21 Grelet et al., ADCHEM 2015 paper 098

Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion

Studied system

5/21 Grelet et al., ADCHEM 2015 paper 098

Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion Model assumptions and governing equations Heat transfer Working fluid properties Discretization

Model assumptions and governing equations

Model assumptions Geometry is reduced to a single pipe in pipe HEX. Secondary (or transfer) fluid always in single phase. Conduction is neglected. Pressure drops are neglected. Pressure dynamic is neglected. Fluid properties are evaluated at the

• utlet of each node.

Mass flow rates are supposed constant along the HEX. Governing equation

Internal fluid Across,f ∂ρf hf ∂t + ∂ ˙ mf hf ∂z + ˙ qf ,int = 0. (1) Internal pipe wall ˙ qf ,int + ˙ qg,int = ∂mw,intcpw,int Tw,int ∂t . (2) External fluid ∂ ˙ mgcpg Tg ∂z + ∂ ˙ mgcpg Tg ∂t + ˙ qg,int + ˙ qg,ext = 0. (3) External pipe wall ˙ qg,ext + ˙ qamb,ext = ∂mw,extcpw,ext Tw,ext ∂t . (4)

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Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion Model assumptions and governing equations Heat transfer Working fluid properties Discretization

Heat transfer

Heat transfer coefficients αg = αref ,g ˙ m

ng g

(5) αf ,liq = αref ,f ,liq ˙ m

nf ,liq f

(6) αf ,2ϕ = αf ,liq . . . . . .

• (1 − q)0.01
• (1 − q) + 1.2q0.4 ρf ,sat,liq

ρf ,sat,vap

0.37−2.2

+ . . . . . . q0.01 αf ,vap αf ,liq

• 1 + 8 (1 − q)0.7 ρf ,sat,liq

ρf ,sat,vap

0.67−2−0.5

(7) αf ,vap = αref ,f ,vap ˙ m

nf ,vap f

(8)

7/21 Grelet et al., ADCHEM 2015 paper 098

Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion Model assumptions and governing equations Heat transfer Working fluid properties Discretization

Heat transfer

Heat transfer EGR boiler Heat transfer exhaust boiler

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Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion Model assumptions and governing equations Heat transfer Working fluid properties Discretization

Working fluid properties

Working fluid properties models Temperature: Tf =    aT,liqh2

f + bT,liqhf + cT,liq

if hf ≤ hsat,liq Tsat,liq + q (Tsat,vap − Tsat,liq) if hsat,liq ≥ hf ≤ hsat,vap aT,vaph2

f + bT,vaphf + cT,vap

if hf ≥ hsat,vap (9) Density ρf =    aρ,liqh2

f + bρ,liqhf + cρ,liq

if hf ≤ hsat,liq

1 aρ,2ϕhf +bρ,2ϕ

if hsat,liq ≥ hf ≤ hsat,vap aρ,vaph2

f + bρ,vaphf + cρ,vap

if hf ≥ hsat,vap (10)

9/21 Grelet et al., ADCHEM 2015 paper 098

Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion Model assumptions and governing equations Heat transfer Working fluid properties Discretization

Working fluid properties

Temperature model validation Density model validation

10/21 Grelet et al., ADCHEM 2015 paper 098

Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion Model assumptions and governing equations Heat transfer Working fluid properties Discretization

Discretization

The continuous set of equation (1,2,3,4) is discretized with respect to space based finite differences. A finite volume approach is chosen where the HEX is split into n longitudinal cell. The vector u contains the manipulated variable ˙ mf ,0 and the input disturbances: ˙ mg,L, Tg,L, hf ,0, Pf ,0.

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Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion Model assumptions and governing equations Heat transfer Working fluid properties Discretization

Discretization

The system of equations defining the response of the ith cell of the discretized model is:

˙ xi = fi (xi , u), (11) where: u = ˙ mf ,0 Pf ,0 hf ,0 ˙ mg,L Tg,L

• ,

(12) xi = hf ,i Tw,int,i Tg,i Tw,ext,i

• ,

(13) fi (xi , u) =             

˙ mf

• hf ,i−1−hf ,i
• −αf ,i Aexch,f ,int
• Tf ,i −Tw,int,i
• ρf ,i Vf

αf ,i Aexch,f ,int

• Tf ,i −Tw,int,i
• +αg Aexch,g,int
• Tg,i −Tw,int,i
• ρw,int Vw,int

˙ mg cpg

• Tg,i−1−Tg,i
• −αg
• Aexch,g,int
• Tg,i −Tw,int,i
• −Aexch,g,ext
• Tg,i −Tw,ext,i
• ρg,i Vg cpg

αambAexch,amb,ext

• Tamb−Tw,ext,i
• +αg Aexch,g,ext
• Tg,i −Tw,ext,i
• ρw,ext Vw,ext

             . (14)

12/21 Grelet et al., ADCHEM 2015 paper 098

Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion Implementation constraint Model identification State of the art PID controller Nonlinear model inversion Controllers structure

Implementation constraint

Classical automotive electronic control unit (ECU) constrains the implementation of controllers: Simulink based environment. Controller must be discretized in time. Backward Euler integration scheme has to be used with a sample time of 20ms. Calculation must stay as simple as possible (problems have to be rescaled to avoid the use of high computational capacity demand functions).

13/21 Grelet et al., ADCHEM 2015 paper 098

Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion Implementation constraint Model identification State of the art PID controller Nonlinear model inversion Controllers structure

Model identification

First order plus time delay models are identified in open loop around several

• perating points with output error

minimization algorithm. The dynamic relation between the working fluid temperature and mass flow variations is: ∆Tf ,L ∆ ˙ mf = G 1 + τs e−Ds. (15) According to the non linearity of model 11 FOPTD parameters vary a lot.

14/21 Grelet et al., ADCHEM 2015 paper 098

Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion Implementation constraint Model identification State of the art PID controller Nonlinear model inversion Controllers structure

State of the art PID controller

State of the art controller in the automotive industry is the PID controller. A well known improvement is the gain scheduling approach.

Gains are calculated offline and linearly interpolated according to the mass flow sensor signal.

Several PID tuning methods have been compared on a load step change.

15/21 Grelet et al., ADCHEM 2015 paper 098

Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion Implementation constraint Model identification State of the art PID controller Nonlinear model inversion Controllers structure

Nonlinear model inversion

Fastest dynamics (i.e. fluid and gas) are canceled. Single phases working fluid heat transfer coefficients are assumed constant. The system of equations defining the response of the ith cell can be written:            = ˙ mf

• hfi−1 − hfi
• + ˙

Qfinti

∂Twinti ∂t

= ˙ Qfinti + ˙ Qginti = ˙ mgcpg

• Tgi−1 − Tgi
• + ˙

Qginti + ˙ Qgexti

∂Twexti ∂t

= ˙ Qgexti + ˙ Qambexti . (16) The expression of the feedforward term Ufeedforward is then straightforward: Ufeedforward =

N

• i=1

˙ Qfinti hf0 − hfL . (17)

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Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion Implementation constraint Model identification State of the art PID controller Nonlinear model inversion Controllers structure

Controllers structure

Feedback controller

17/21 Grelet et al., ADCHEM 2015 paper 098

Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion Implementation constraint Model identification State of the art PID controller Nonlinear model inversion Controllers structure

Controllers structure

Nonlinear controller

17/21 Grelet et al., ADCHEM 2015 paper 098

Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion

Simulation environment

Pump and expansion machine models are added to represent the high pressure part

• f the Rankine system.

Pump model: ˙ mf = ρf ,in Npump 60 Ccpumpηvol,pump. (18) Expansion machine: ˙ mf = keq

• ρf ,inPf ,in
• 1 − Pf ,in

Pf ,out

−2

. (19)

18/21 Grelet et al., ADCHEM 2015 paper 098

Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion

Controller comparison

Initial set point and disturbances change are not handle by PID controller. The non linear controller reduce the deviation from +/-10℃with the PID to +/-3℃.

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Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion

Conclusion and next steps

Conclusion A control strategy for temperature management of WHRS Rankine cycle based is presented. Main objective to stabilize the temperature around a given set point is better achieved by using a non linear controller. Non linear controller is compliant with implementation constraint relative to automotive industry. Next steps Controller sensitivity to parameters mismatch. Controller robustness. Optimal high level control strategy (set points generation).

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Context and motivations Waste heat recovery Rankine cycle based Studied system Control oriented modeling Controller development Simulation results Conclusion and next steps Contacts and discussion

Contacts and discussion

Authors

Vincent GRELET: vincent.grelet@volvo.com Thomas REICHE: thomas.reiche@volvo.com Madiha NADRI: nadri@lagep.univ-lyon1.fr Pascal DUFOUR: dufour@lagep.univ-lyon1.fr Vincent LEMORT: vincent.lemort@ulg.ac.be

Acknowledgement

This PhD thesis is collaboration between UCBL1, ULg and Volvo Trucks which is gratefully acknowledged for the funding. The French ministry of higher education and research for the financial support of the CIFRE PhD thesis 2012/549 is also acknowledged.

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