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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
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• 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 3
Content
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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.
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Can sCO2 be a HeRo?
University of Stuttgart – Institute of Nuclear Technology and Energy Systems
sCO2 in power cycle
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Recompression- Brayton
cycle
University of Stuttgart – Institute of Nuclear Technology and Energy Systems
sCO2 in power cycle
Recompression- Brayton
cycle
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• Drastic variation in
thermophysical
properties. It can results
in poor heat transfer.
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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
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Aims
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• Introduction
• Theory & methodology
• Results and discussion
• Application of DNS in modeling
• Summary and future work
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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
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Governing equation
• DNS requires a fine mesh resolution
• The resolution should resolve the small turbulence scales for any DNS
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Direct numerical simulation
~ 80 Million
cells
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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
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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
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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
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The mesh-resolution requirement
𝜂 =𝜈3
𝜖/𝜌
0.25
, ΔV =3Δ𝑟Δ𝑟𝜃Δ𝑧, 𝐿 𝜂,𝐿 =
ΔV
𝜂
DC8q2
UC8q2
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The mesh-resolution requirement
𝜂𝜃 =𝜂
Pr, 𝐿 𝜂,𝑇 =
ΔV
𝜂𝜃
DC8q2
(dashed lines)
UC8q2
(solid lines)
• Introduction
• Theory & methodology
• Results and discussion
• Application of DNS in modeling
• Summary and future work
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Content
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Visualization of instantaneous velocity field
z=0D
UC8q2
z=15D z=27.5D
DC8q2
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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.
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Effects of buoyancy on skin friction coefficient
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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?
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Turbulent shear stress
DC8q2UC8q2
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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
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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
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Visualization of the coherent structures
Case-DC8q2
• Blue: low-speed streaks
• Green: high-speed streaks
• red: λ2
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Anisotropy
Case-DC8q2
• Introduction
• Theory & methodology
• Results and discussion
• Application of DNS in modeling
• Summary and future work
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Content
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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
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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
• Theory & methodology
• Results and discussion
• Application of DNS in modeling
• Summary and future work
University of Stuttgart – Institute of Nuclear Technology and Energy Systems 31
Content
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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
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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!
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
Institute of Nuclear Technology
and Energy Systems