Flow and heat transfer characterization for …...Institute of Nuclear Technology and Energy Systems Flow and heat transfer characterization for supercritical CO2 during heat rejection

Institute of Nuclear Technology

and Energy Systems

Flow and heat

transfer

characterization for

supercritical CO2

during heat rejection

S. Pandey, E. Laurien, X. Chu

2nd European sCO2 Conference 2018

30-31 August, 2018, Essen Germany.

• Introduction

• Theory & methodology

• Results and discussion

• Application of DNS in modeling

• Summary and future work

University of Stuttgart – Institute of Nuclear Technology and Energy Systems 2

Content

06.09.2018

• Introduction






Content

06.09.2018

06.09.2018University of Stuttgart – Institute of Nuclear Technology and Energy Systems 4

Climate change

• Efficiency increment will bring down the CO2 emission and it will help in

halving the emission by 2050 to limit the average temperature rise

between 2-3 0C

• The lower critical pressure and temperature of carbon dioxide (Pcr=7.38

MPa, Tcr= 304.25 K) as compared to water (Pcr=22.06 MPa, Tcr= 674.09 K)

provide an opportunity to generate power in a reduced operating range.

• 0 ODP and 1 GWP.

• Flexible operation of conventional power plants, assist in integration of

RETs.


Can sCO2 be a HeRo?

University of Stuttgart – Institute of Nuclear Technology and Energy Systems

sCO2 in power cycle

606.09.2018

Recompression- Brayton

cycle

University of Stuttgart – Institute of Nuclear Technology and Energy Systems

sCO2 in power cycle

Recompression- Brayton

cycle

706.09.2018

• Drastic variation in

thermophysical

properties. It can results

in poor heat transfer.


Prediction of heat transfer to sCO2

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Analytical models and correlations

CFD studies based upon turbulence models and LES

CFD studies based upon DNS

• Computationally

inexpensive method

• Simple and easy to

implement

• Accuracy is limited

• Qualitative trend can

be captured

• Moderately

computationally

expensive

• Accuracy is limited

especially in HTD

• Most accurate,

termed as Numerical

experiments

• Highly computer-

intensive, and limited

to simple geometry

Bae et al., 2005

Nemati et al., 2016

Chu et al., 2016

He et al., 2008

Sharabi et al., 2008 Jackson et al., 2012

Pandey et al., 2017 Heating only

• Examine the heat transfer features of sCO2 during the cooling process

• Investigate the effects of turbulence on heat transfer

• Study the potential application of DNS data in modeling


Aims

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• Introduction






Content

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• Low Mach Navier-Stoke equations are used

•𝜕(𝜌)

𝜕𝑡+

𝜕(𝜌𝑈𝑗)

𝜕𝑥𝑗= 0

•𝜕(𝜌𝑈𝑖)

𝜕𝑡+

𝜕(𝜌𝑈𝑖𝑈𝑗)

𝜕𝑥𝑗= −

𝜕𝑃

𝜕𝑥𝑖+

𝜕

𝜕𝑥𝜇

𝜕𝑈𝑖

𝜕𝑥𝑗+

𝜕𝑈𝑗

𝜕𝑥𝑖± 𝜌𝑔𝛿𝑖1

•𝜕(𝜌ℎ)

𝜕𝑡+

𝜕(𝜌𝑈𝑗ℎ)

𝜕𝑥𝑗=

𝜕

𝜕𝑥𝜇

𝜕𝑇

𝜕𝑥𝑗

• Solved in OpenFOAM

• Thermophysical properties taken from NIST REFPROP with a stepwise

spline function

• Overall 2nd order accurate in space and time


Governing equation

• DNS requires a fine mesh resolution

• The resolution should resolve the small turbulence scales for any DNS


Direct numerical simulation

~ 80 Million

cells


Inflow turbulence validation

Introduction Theory & methodology Results & discussion Summary & Future work

• Inflow turbulence is verified with the KTH-FLOW database with velocity

fluctuation and budget of turbulence kinetic energy


Simulation Parameters

Case

acronym

Direction

Of fluid flow

Type of

convection

Heat flux

(kw/m2)

Q+ Gr*×108

FC8q1 - Forced -30.87 -4.32 0

UC8q1 Upward Mixed -30.87 -4.32 1.17

DC8q1 Downward Mixed -30.87 -4.32 -1.17

FC8q2 - Forced -2×30.87 -8.65 0

UC8q2 Upward Mixed -2×30.87 -8.65 2.34

DC8q2 Downward Mixed -2×30.87 -8.65 -2.34

P0 T0 Re0 D Lh

8 MPa 342.05 K 5400 2 mm 30D

𝑄+ =𝑞𝑤𝑅

𝜅0𝑇0 𝑅𝑒0 =

𝑈𝑏,0𝐷

𝜈𝑏,0 𝐺𝑟∗ =

𝑔𝛽𝑞𝑤𝐷4

𝜅0𝜈0


The mesh-resolution requirement

• Resolve the Kolmogorov length scale DNS

• Relates the dissipation to diffusion of turbulent kinetic energy

Big whirls have little whirls,

Which feed on their velocity;

And little whirls have lesser whirls,

And so on to viscosity

in the molecular sense.

- L.F. Richardson

Energy cascade



𝜂 =𝜈3

𝜖/𝜌

0.25

, ΔV =3Δ𝑟Δ𝑟𝜃Δ𝑧, 𝐿 𝜂,𝐿 =

ΔV

𝜂

DC8q2

UC8q2



𝜂𝜃 =𝜂

Pr, 𝐿 𝜂,𝑇 =

ΔV

𝜂𝜃

DC8q2

(dashed lines)

UC8q2

(solid lines)

• Introduction






Content

06.09.2018


Visualization of instantaneous velocity field

z=0D

UC8q2

z=15D z=27.5D

DC8q2


Flow and heat transfer features

Skin friction coefficientNusselt Number

• Heat transfer deterioration : downward flow; contrary to heating

• Derived by Fukagata, Iwamoto and Kasagi (FIK) identity for the first time

for the sole aim to reduce drag force.


Effects of buoyancy on skin friction coefficient


Effects of buoyancy on skin friction coefficient

• Buoyancy (C10) has significant contribution in the skin friction factor.

DC8q2 UC8q2

• From z= 0D to 15D, turbulence decrease in the downward flow, but, then a

recovery can be observed at z=27.5D (in the negative direction)

Why deterioration and why recovery?


Turbulent shear stress

DC8q2UC8q2


Quadrant analyses

• From z=0D to 15D, sweep and ejection events disappears

• At z=27.5D, recovery was observed and surprisingly, inward and outward

interactions, contrary to the conventional belief about turbulence generation.

z=0D z=15D z=27.5D

Case-DC8q2

Ejection

Sweep

Outward

Inward


Visualization of the instantaneous streaks

• From z=0D to 15D, sweep and ejection events disappears because:

• Streaks are stretched in the streamwise direction

Case-DC8q2


Visualization of the coherent structures

Case-DC8q2

• Blue: low-speed streaks

• Green: high-speed streaks

• red: λ2


Anisotropy

Case-DC8q2

• Introduction






Content

06.09.2018


A theory based model: Two-layer model

• Proposed an improve fluid flow and heat transfer (heating and cooling) model

based upon two layer model for sCO2

• Fairly well agreement was observed with experiments, but more refinement is

needed for future applications

Heating of sCO2Cooling of sCO2


A data driven model: Based on deep neural network

• Good agreement! …but

• Machine learning based algorithms are purely data driven (the more the

merrier).

• Generate data with the aid of numerical experiments.

• Introduction






Content

06.09.2018


Summary

• Characterized the heat transfer to sCO2 by means of DNS

• Investigated the reasons for heat transfer deterioration and recovery

• Applied the gained knowledge and DNS data to develop computationally

light model

What’s next?

• Investigate the role of compressibility

• Generalize the computationally light model for different working fluids


Forschungsinstitut für Kerntechnik und Energiewandlung

e.V. (KE e.V.) for doctoral fellowship.

High Performance Computing Centre, Stuttgart for granting

access to Hazel Hen for DNS.

Acknowledgement

Thank you!

e-mail

phone +49 (0) 711 685-

fax +49 (0) 711 685-

University of Stuttgart

Pfaffenwaldring 31 • 70569 Stuttgart • Germany

Sandeep Pandey

62151

62010

Institute of Nuclear Technology and Energy Systems

[email protected]

Institute of Nuclear Technology

and Energy Systems

Documents

Flow and heat transfer characterization for …...Institute of Nuclear Technology and Energy Systems Flow and heat transfer characterization for supercritical CO2 during heat rejection