Modeling and optimization of a multi-tubular solar receiver for … · solar receiver for solar-driven high temperature electrolysis Meng Lin 1, Sophia Haussener 1 1Laboratory of

Lin, TFESC2015, August 2015 1 /18

Modeling and optimization of a multi-tubular solar receiver for solar-driven high

temperature electrolysis

Meng Lin1, Sophia Haussener1

1Laboratory of Renewable Energy Sciences and Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL),

Lausanne, Switzerland


• Solar driven high-temperature co-/electrolysis

Motivation and Introduction

Receiver

PV

Electricity

Steam/CO2700-1000oC

Electrolyzer

H2/CO

H2O/CO2

Siemens

Eloenerji

~20%

~20%DLR Prototype

Radiative heat transfer

Flow boiling in tubes

Natural convection

Conduction

Solar energy

Concentration


Motivation and IntroductionFlow boiling with complex physics:• Nucleating of bubbles• Bubbles growth and coalescence• Segregation of vapor and liquid phase• Evaporation of liquid in mist flow and

partial films

Heat transfer in receiver cavity:• Non-uniform distribution of

heat flux• Non-uniform temperature

distribution

1D separated model for two

phase flow

3D numerical model for

heat transfer inside the receiver cavity

Convergence(Temperature)

ResultsYes

No

1D

Hea

t flu

x p

rofil

e al

on

g th

e tu

be

Ray tracing

Solar flux at aperture

3D simulation difficult

3D simulation necessary

Thome, J. R. (2004). Engineering data book III. Wolverine Tube Inc.

1D model (single tube): Boiling flow inside tubes

3D model (multi-tube): Heat transfer inside the receiver

Conduction (insulation)

Conduction (tube wall)

Radiation Natural convection


Model development (1D model for single tube)

1D model for two-phase flow in horizontal tube:

Escanes, F., Perez-Segarra, C. D., & Oliva, A. (1995). Numerical simulation of capillary-tube expansion devices. International Journal of Refrigeration, 18(2), 113-122.

Assumptions (in control volume):1. The velocity of liquid and gas are constant but not necessarily equal.2. Thermodynamic equilibrium between phases (temperature and pressure are equal).3. Empirical correlations are used to relate the frictional pressure drop and the void

fraction to the independent variables of the flow. 4. CO2 and H2O are considered well mixed.

Collier, J. G., & Thome, J. R. (1994). Convective boiling and condensation. Oxford university press.


Model development (1D model for single tube)

i om m=ɺ ɺ

i o g,o g,o g,i g,i l,o l,o l,i l,i W( )

sin( )

p p A m v m v m v m v P z

mg

τθ

− = − + − + ∆

+

ɺ ɺ ɺ ɺ ɶ

W l,o l,i g,o g,o l,o ,i g,i l,i( ) ( ) ( )gq P z m e e m e e m e e∆ = − + − + −ɺ ɺ ɺ ɺ

Mass conservation:

Momentum equation :

Energy equation :

Conservation equations

2

W 28

fm

Aτ

ρ=ɺ

W W( )q T Tα= −ɺ

Empirical correlations

Escanes, F., Perez-Segarra, C. D., & Oliva, A. (1995). Numerical simulation of capillary-tube expansion devices. International Journal of Refrigeration, 18(2), 113-122.

l

l g g l(1 ) ( / )

x

x x v v

ρερ ρ

=+ −

10.25l g

0.5g g l l

1.18(1 x)( ( ))1(1 0.2(1 x))( )

gx x x

m

σ ρ ρε

ρ ρ ρ ρ

− − −−= + − + + ɺ

Rouhani et al. (1969)

2l frf f φ=

l 0.25

0.079

Ref =

2fr 0.045 0.0035

h l

3.42FHE

Fr Weφ = +

(Blasius equation )


Flow pattern maps

Stratified

Stratified wavy

Intermittent Annular

Mist

Kattan-Thome-Favrat (KTF) flow pattern Map: Dry angles:

highdry strat

high low

m m

m mθ θ

−=

−ɺ ɺ

ɺ ɺ

AnnularIntermittent

Stratified wavy Stratified

xmax

high

low

Stratified flow

dry stratθ θ=

(x<xmax)

maxdry max max

max

(2 )1

x x

xθ π θ θ−= − +

−(x>xmax)

maxθ


Heat transfer coefficient

0.8 0.4g 0.023Re Pr gk

dα =

dry g dry l(2 )

2

θ α π θ αα

π+ −

=

Dittus-Boelter (1930)

3 3 1/3l nb cb( )α α α= +

Thome, J. R. (2004). Engineering data book III. Wolverine Tube Inc.

Heat transfer coefficient based on flow pattern:

Gas phase:

Liquid phase:

0.12 0.55 0.5 0.67nb r r w55 ( log )p p M qα − −= −

0.69 0.4 lcb l l0.0133Re Pr

kαδ

=

For each element：：：：

gα

lα

A heat transfer coefficient profile in radial direction

3D heat transfer coefficient profile

All elements

Cooper (1984)

Kattan (1998)


Example: Absorber tubeBoundary conditions:

1D model(Matlab code)

3D model(Fluent)

Outside wall: Concentrated solar power (typical distribution)

Inner wall: heat transfer coefficient and fluid temperature

Wall ends: Non-slip and adiabatic

Inlet condition: Temperature, flow rate, pressure

Tube wall: heat flux

Heat losses

Pressure outlet

4heat losses W nc W o0.8 (T T )q T hσ= + −ɺ

solarq C DNI= ×ɺ

21/6

128/279/16

0.3870.60 , 10

1 (0.559 / Pr)

RaNu Ra

= + ≤

+ Churchill and Chu (1975)Tube

0360

90

180

270

Lobon et al. (2014)


Model validation Parameters ValueTube length 510 mInner radius 0.05 mOuter radius 0.07 m

Inlet temperature 478.15 KMass flow rate 0.47 kg/s

Direct normal isolation 822 W/m2

Optical efficiency 0.632Inlet pressure 3.43 MPa

Heat loss (liquid) 1278 W/m2

Heat loss (two phase) 1828 W/m2

Heat loss (vapor) 2323 W/m2

Lobón, D. H., Baglietto, E., Valenzuela, L., & Zarza, E. (2014). Modeling direct steam generation in solar collectors with multiphase CFD. Applied Energy, 113, 1338-1348.

0 100 200 300 400 500

460

470

480

490

500

510

520

530

540

550

560

570 Predicted data Experimental data

Tem

per

atu

re (

K)

Lenght (m)Length (m)

0 100 200 300 400 500

3.05x106

3.10x106

3.15x106

3.20x106

3.25x106

3.30x106

3.35x106

3.40x106

3.45x106

Pre

ssu

re (

Pa)

Lenght (m)

Predicted data Experimental data

Length (m)

Lin, TFESC2015, August 201510 /18

Performance evaluation

• Solar thermal efficiency: heat losst

solar,receiver

1Q

Qη = −

ɺ

ɺ

• Maximum wall-fluid temperature difference :

• Mean heat transfer coefficient in two-phase flow region:

maxT∆

tph


Baseline and reference case parameters

Simulation parameter Ref. Unit

Direct normal irradiance, DNI 1 kWm-2

Concentration 1000

Inlet pressure 15 bar

Mass flux 200 kgm-2s-1

Inner tube diameter 10 mm

Wall thickness 1 mm

Ambient temperature, T0 298.15 K

Target temperature 1000 K

PV efficiency, ηpv 15%

Solar field optical efficiency, ηop 50%


4 6 8 10 12 14 16 18 200

1

2

3

4

5

6

7

8

Tube inner diameter (mm)

6 8 10 12 14 16 18 20

3.30

3.35

3.40

Inlet pressure (bar)

4 6 8 10 12 14 16 18 200.2

0.3

0.4

0.5

0.6

Tube inner diameter (mm)

20000

25000

30000

35000

40000

500

550

600

650

700

KW/m2K

6 8 10 12 14 16 18 200.2

0.3

0.4

0.5

0.6K

Inlet pressure (bar)

W/m2K

20000

25000

30000

35000

40000

550

600

650

700

Design guidelinesInlet pressure Tube inner diameter

15bar 12mmtη maxT∆tphtη maxT∆tph

t,η, tph

max, T∆

Tube lengthm

Tube lengthm


300 600 900 1200 1500 1800

2

4

6

8

10

12

Concentration ratio100 200 300 400 500 6000

1

2

3

4

5

6

7

Mass flux (kg/m2s)

100 200 300 400 500 6000.2

0.3

0.4

0.5

0.6

Mass flux (kg/m2s)

25000

30000

35000

40000

45000

0

200

400

600

800

1000

1200

1400

W/m2K K

300 600 900 1200 1500 18000.2

0.3

0.4

0.5

0.6

Concnetration ratio

25000

30000

35000

40000

45000

0

200

400

600

800

1000

1200

KW/m2K

Design guidelinesMass fluxConcentration ratio

750 350tη maxT∆tph tη maxT∆tph

t,η, tph

max, T∆

Tube lengthm

Tube lengthm

Concentration

Concentration


0.0 0.2 0.4 0.6 0.8 1.00.2

0.3

0.4

0.5

0.6

Mass fraction of CO2

0

10000

20000

30000

40000

600

800

1000

1200

1400

1600K

W/m2K

tη maxT∆tph

Design guidelinesMass fraction of CO2

t,η, tph

max, T∆

0.0 0.2 0.4 0.6 0.8 1.00.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Mass fraction of CO2

0.1

Tube lengthm


Optimized design

Optimized Parameters Values

Inlet pressure 15bar

Tube inner diameter 12mm

Tube thickness 1mm

Concentration ration 750

Mass flux 350 kgm-2s-1

Target outlet temperature 1000K

Tube length 6.0225m

CO2 mass fraction 0

0 1 2 3 4 5 60

10000

20000

30000

40000

50000

60000 Heat transfer coefficient Pressure

Tube length (m)

He

at tr

ansf

er c

oeffi

cie

nt (

W/m2 K

)

1400000

1435000

1470000

1505000

Pre

ssur

e (P

a)

0 1 2 3 4 5 6

200

400

600

800

1000

1200

1400p=15bar,d=12mm,m=350kg/m2s,CR=750

Flu

id te

mpe

ratu

re (

K)

Tube length (m)

Fluid temperature Wall temperature

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00

200

400

600

800

1000

1200

Vapor quality

Mas

s flu

x (k

g/m2 s)

Stratified Wavy

Mist

Intermittent andAnnular

Stratified

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00

200

400

600

800

1000

1200

Vapor quality

Ma

ss fl

ux (

kg/m

2 s)


Mist

Stratified Wavy

Stratified

t 38.8%η =

max 410.7KT∆ =234102.8W/m Ktph =

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00

200

400

600

800

1000

1200

Mas

s flu

x (k

g/m2 s)

Vapor quality


Mist

Stratified Wavy

Stratified


Optimized design?

0 200 400 600 800 1000

0.39

0.40

0.41

0.42

DNI

Sol

ar th

erm

al e

ffic

ienc

y

400

600

800

1000

Out

let f

luid

tem

pera

ture

(K

)

• Efficiency variation with irradiance changes

heat losst

solar,receiver

1Q

Qη = −

ɺ

ɺ


• Development of a novel general receiver model to predict performance of multi-tube receiver for concurrent steam and CO2 heating

• Model integrates:– 1D multi-phase single-tube model – detailed 3D multi-tube cavity model

• Various geometrical as well as operational conditions were investigated and optimized.

- Inlet pressure has minor effect on the efficiency.- Larger tube diameter leads to higher thermal efficiency but longer tube length and higher .

- Low concentration is preferred.- High mass flux leads to better efficiency.- Mix CO2 and H2O could enhance the thermal efficiency.

• Experiment will be conducted to modified the flow pattern under high flux with non-uniformity.

Summary and conclusion

maxT∆


Acknowledgements

[email protected]@epfl.chhttp://lrese.epfl.ch

Thank you for your attention!

Questions?

The SOPHIA research project is funded by the Fuel Cell and Hydrogen Joint Under-taking (FCH JU) under the Grant Agreement Number 621173. The information contained in this work reflects the views of the authors only.

Chinese Scholarship Council

Moises Romero, DLRHans-Peter Streber, DLR

Documents

Modeling and optimization of a multi-tubular solar receiver for … · solar receiver for solar-driven high temperature electrolysis Meng Lin 1, Sophia Haussener 1 1Laboratory of