Abstract

Interest in aircraft electrification and hydrogen fuel cells is driving demand for efficient waste heat management systems. Ultimately, most of the heat must be rejected to the freestream air. Ducted heat exchangers, also called ducted radiators, are the most common and effective way to do this. Engineers manually design ducted heat exchangers by adjusting the duct's shape and heat exchanger's configuration to reduce drag and transfer sufficient heat. This manual approach misses potential performance improvements because engineers cannot simultaneously consider all of the complex interactions between the detailed duct shape, heat exchanger design, and operating conditions. To find these potential gains, we apply gradient-based optimization to a three-dimensional ducted heat exchanger computational fluid dynamics (CFD) model. The optimizer determines the duct shape, heat exchanger size, heater exchanger channel geometry, and coolant flowrate that minimize the ducted heat exchanger's power requirements while rejecting enough heat. Gradient-based optimization enables the use of nearly 100 shape design variables, creating a large design space and allowing fine-tuning of the optimal design. When applied to an arbitrary, poorly performing baseline, our method produces a nuanced and sophisticated ducted heat exchanger design with five times less cruise drag. Employing this method in the design of electric and fuel cell aircraft thermal management could uncover performance not achievable with manual design practices.

References

1.
Adler
,
E. J.
, and
Martins
,
J. R. R. A.
,
2023
, “
Hydrogen-Powered Aircraft: Fundamental Concepts, Key Technologies, and Environmental Impacts
,”
Prog. Aerosp. Sci.
,
141
, p.
100922
.10.1016/j.paerosci.2023.100922
2.
Brelje
,
B.
, and
Martins
,
J. R. R. A.
,
2019
, “
Electric, Hybrid, and Turboelectric Fixed-Wing Aircraft: A Review of Concepts, Models, and Design Approaches
,”
Prog. Aerosp. Sci.
,
104
, pp.
1
19
.10.1016/j.paerosci.2018.06.004
3.
Meredith
,
F. W.
,
1935
,
Cooling of Aircraft Engines With Special Reference to Ethylene Glycol Radiators Enclosed in Ducts
(Aeronautical Research Committee Reports and Memoranda No. 1683),
Air Ministry
, London, UK.
4.
Hoerner
,
S. F.
,
1965
,
Fluid-Dynamic Drag
,
Hoerner Fluid Dynamics
,
Bakersfield, CA
.
5.
Silverstein
,
A.
,
1939
, “
Experiments on the Recovery of Waste Heat in Cooling Ducts
,” NACA, Hampton, VA, Report No. NACA-SR-111.
6.
Rauscher
,
M.
, and
Phillips
,
W. H.
,
1941
, “
Propulsive Effects of Radiator and Exhaust Ducting
,”
J. Aeronaut. Sci.
,
8
(
4
), pp.
167
174
.10.2514/8.10671
7.
Çengel
,
Y. A.
, and
Ghajar
,
A. J.
,
2015
,
Heat and Mass Transfer
, 5th ed.,
McGraw-Hill
, New York.
8.
Incropera
,
F. P.
,
DeWitt
,
D. P.
,
Bergman
,
T. L.
, and
Lavine
,
A. S.
,
2007
,
Fundamentals of Heat and Mass Transfer
, 6th ed.,
Wiley
, Hoboken, NJ.
9.
Kays
,
W. M.
, and
London
,
A. L.
,
1984
,
Compact Heat Exchangers
, 3rd ed.,
McGraw-Hill
,
New York
.
10.
Hendricks
,
T. J.
,
Mcenerney
,
B.
,
Drymiotis
,
F.
,
Furst
,
B.
, and
Shevade
,
A.
,
2017
, “
Design and Testing of High-Performance Mini-Channel Graphite Heat Exchangers in Thermoelectric Energy Recovery Systems
,”
ASME
Paper No. IMECE2017-72411.10.1115/IMECE2017-72411
11.
Anibal
,
J. L.
, and
Martins
,
J. R. R. A.
,
2024
, “
Adjoint-Based Shape Optimization of a Plate-Fin Heat Exchanger Using CFD
,”
Appl. Therm. Eng.
,
252
, p.
123570
.10.1016/j.applthermaleng.2024.123570
12.
Anibal
,
J.
,
2023
, “
Aerodynamic Shape Optimization of Heat Exchangers
,” Ph.D. thesis,
University of Michigan
,
Ann Arbor, MI
.
13.
Sundén
,
B.
,
2007
, “
Computational Fluid Dynamics in Research and Design of Heat Exchangers
,”
Heat Transfer Eng.
,
28
(
11
), pp.
898
910
.10.1080/01457630701421679
14.
Claus
,
R. W.
,
Evans
,
A. L.
,
Lylte
,
J. K.
, and
Nichols
,
L. D.
,
1991
, “
Numerical Propulsion System Simulation
,”
Comput. Syst. Eng.
,
2
(
4
), pp.
357
364
.10.1016/0956-0521(91)90003-N
15.
Hendricks
,
E. S.
, and
Gray
,
J. S.
,
2019
, “
pyCycle: A Tool for Efficient Optimization of Gas Turbine Engine Cycles
,”
Aerospace
,
6
(
8
), p.
87
.10.3390/aerospace6080087
16.
Jasa
,
J. P.
,
Brelje
,
B. J.
,
Mader
,
C. A.
, and
Martins
,
J. R. R. A.
,
2019
, “
Coupled Design of a Supersonic Engine and Thermal System
,”
World Congress of Structural and Multidisciplinary Optimization
, Beijing, China, May 20–24, pp.
1
7
.https://websites.umich.edu/~mdolaboratory/pdf/Jasa2019b.pdf
17.
Brelje
,
B. J.
,
Jasa
,
J. P.
,
Martins
,
J. R. R. A.
, and
Gray
,
J. S.
,
2019
, “
Development of a Conceptual-Level Thermal Management System Design Capability in OpenConcept
,” NATO Research Symposium on Hybrid/Electric Aero-Propulsion Systems for Military Applications (
AVT-RSY-323
), Trondheim, Norway, May 8–10, pp.
1
17
.https://www.researchgate.net/publication/372761014_Development_of_a_conceptuallevel_thermal_management_system_design_capability_in_OpenConcept
18.
Kellermann
,
H.
,
Lüdemann
,
M.
,
Pohl
,
M.
, and
Hornung
,
M.
,
2020
, “
Design and Optimization of Ram Air–Based Thermal Management Systems for Hybrid-Electric Aircraft
,”
Aerospace
,
8
(
1
), p.
3
.10.3390/aerospace8010003
19.
Sóbester
,
A.
,
2007
, “
Tradeoffs in Jet Inlet Design: A Historical Perspective
,”
J. Aircr.
,
44
(
3
), pp.
705
717
.10.2514/1.26830
20.
Madabhushi
,
R. K.
,
Levy
,
R.
, and
Pincus
,
S. M.
,
1987
, “
Design of Optimum Ducts Using an Efficient 3-D Viscous Computational Flow Analysis
,”
Conference Paper GRC-E-DAA-TN55806
,
NASA
, University Park, PA, pp.
147
166
.https://ntrs.nasa.gov/api/citations/19930074227/downloads/19930074227.pdf
21.
Chiang
,
C.
,
Koo
,
D.
, and
Zingg
,
D. W.
,
2022
, “
Aerodynamic Shape Optimization of an S-Duct Intake for a Boundary-Layer Ingesting Engine
,”
J. Aircr.
,
59
(
3
), pp.
725
741
.10.2514/1.C036632
22.
He
,
P.
,
Martins
,
J. R. R. A.
,
Mader
,
C. A.
, and
Maki
,
K.
,
2019
, “
Aerothermal Optimization of a Ribbed U-Bend Cooling Channel Using the Adjoint Method
,”
Int. J. Heat Mass Transfer
,
140
, pp.
152
172
.10.1016/j.ijheatmasstransfer.2019.05.075
23.
Gray
,
J. S.
,
Mader
,
C. A.
,
Kenway
,
G. K. W.
, and
Martins
,
J. R. R. A.
,
2018
, “
Modeling Boundary Layer Ingestion Using a Coupled Aeropropulsive Analysis
,”
J. Aircr.
,
55
(
3
), pp.
1191
1199
.10.2514/1.C034601
24.
Yildirim
,
A.
,
Gray
,
J. S.
,
Mader
,
C. A.
, and
Martins
,
J. R. R. A.
,
2022
, “
Boundary Layer Ingestion Benefit for the STARC-ABL Concept
,”
J. Aircr.
,
59
(
4
), pp.
896
911
.10.2514/1.C036103
25.
Lamkin
,
A. H. R.
,
Yildirim
,
A.
,
Martins
,
J. R. R. A.
, and
Wukie
,
N. A.
,
2023
, “
Advancements in Coupled Aeropropulsive Design Optimization for High-Bypass Turbofan Engines
,”
AIAA
Paper No. 2023-3591.10.2514/6.2023-3591
26.
Abdul-Kaiyoom
,
M. A. S.
,
Yildirim
,
A.
, and
Martins
,
J. R. R. A.
,
2023
, “
RANS-Based Multipoint Aeropropulsive Design Optimization of an Over-Wing Nacelle Configuration
,”
AIAA
Paper No. 2023-3588.10.2514/6.2023-3588
27.
Chapman
,
J. W.
,
Schnulo
,
S. L.
, and
Nitzsche
,
M. P.
,
2020
, “
Development of a Thermal Management System for Electrified Aircraft
,”
AIAA
Paper No. 2020-0545.10.2514/6.2020-0545
28.
Adler
,
E. J.
,
Brelje
,
B. J.
, and
Martins
,
J. R. R. A.
,
2022
, “
Thermal Management System Optimization for a Parallel Hybrid Aircraft Considering Mission Fuel Burn
,”
Aerospace
,
9
(
5
), p.
243
.10.3390/aerospace9050243
29.
White
,
A. S.
,
Waddington
,
E.
,
Merret
,
J. M.
,
Greitzer
,
E. M.
,
Ansell
,
P. J.
, and
Hall
,
D. K.
,
2022
, “
System-Level Utilization of Low-Grade, MW-Scale Thermal Loads for Electric Aircraft
,”
AIAA
Paper No. 2022-3291.10.2514/6.2022-3291
30.
Waddington
,
E. G.
,
Merret
,
J. M.
, and
Ansell
,
P. J.
,
2023
, “
Impact of Liquid-Hydrogen Fuel-Cell Electric Propulsion on Aircraft Configuration and Integration
,”
J. Aircr.
,
60
(
5
), pp.
1588
1600
.10.2514/1.C037237
31.
Drela
,
M.
,
1996
, “
Aerodynamics of Heat Exchangers for High-Altitude Aircraft
,”
J. Aircr.
,
33
(
1
), pp.
176
184
.10.2514/3.46919
32.
Drela
,
M.
,
1990
, “
Newton Solution of Coupled Viscous/Inviscid Multielement Airfoil Flows
,”
AIAA
Paper No. 1990-1470.10.2514/6.1990-1470
33.
Musto
,
M.
,
Bianco
,
N.
,
Rotondo
,
G.
,
Toscano
,
F.
, and
Pezzella
,
G.
,
2016
, “
A Simplified Methodology to Simulate a heat exchanger in an Aircraft's Oil Cooler by Means of a Porous Media Model
,”
Appl. Therm. Eng.
,
94
, pp.
836
845
.10.1016/j.applthermaleng.2015.10.147
34.
Patrao
,
A. C.
,
Jonsson
,
I.
,
Xisto
,
C.
,
Lundbladh
,
A.
, and
Grönstedt
,
T.
,
2024
, “
Compact Heat Exchangers for Hydrogen-Fueled Aero Engine Intercooling and Recuperation
,”
Appl. Therm. Eng.
,
243
, p.
122538
.10.1016/j.applthermaleng.2024.122538
35.
Hendricks
,
T. J.
,
Tarau
,
C.
, and
Dyson
,
R. W.
,
2021
, “
Hybrid Electric Aircraft Thermal Management: Now, New Visions and Future Concepts and Formulation
,” 2021 20th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (
iTherm
), San Diego, CA, June 1–4, pp.
467
476
.10.1109/ITherm51669.2021.9503205
36.
Martins
,
J. R. R. A.
,
2022
, “
Aerodynamic Design Optimization: Challenges and Perspectives
,”
Comput. Fluids
,
239
, p.
105391
.10.1016/j.compfluid.2022.105391
37.
Martins
,
J. R. R. A.
, and
Ning
,
A.
,
2022
,
Engineering Design Optimization
,
Cambridge University Press
,
Cambridge, UK
.
38.
Gray
,
J. S.
,
Hwang
,
J. T.
,
Martins
,
J. R. R. A.
,
Moore
,
K. T.
, and
Naylor
,
B. A.
,
2019
, “
OpenMDAO: An Open-Source Framework for Multidisciplinary Design, Analysis, and Optimization
,”
Struct. Multidiscip. Optim.
,
59
(
4
), pp.
1075
1104
.10.1007/s00158-019-02211-z
39.
Anibal
,
J.
,
Mader
,
C. A.
, and
Martins
,
J. R. R. A.
,
2022
, “
Aerodynamic Shape Optimization of an Electric Aircraft Motor Surface Heat Exchanger With Conjugate Heat Transfer Constraint
,”
Int. J. Heat Mass Transfer
,
189
, p.
122689
.10.1016/j.ijheatmasstransfer.2022.122689
40.
Yildirim
,
A.
,
Gray
,
J. S.
,
Mader
,
C. A.
, and
Martins
,
J. R. R. A.
,
2021
, “
Coupled Aeropropulsive Design Optimization of a Podded Electric Propulsor
,”
AIAA
Paper No. 2021-3032.10.2514/6.2021-3032
41.
Mader
,
C. A.
,
Kenway
,
G. K. W.
,
Yildirim
,
A.
, and
Martins
,
J. R. R. A.
,
2020
, “
ADflow: An Open-Source Computational Fluid Dynamics Solver for Aerodynamic and Multidisciplinary Optimization
,”
J. Aerosp. Inf. Syst.
,
17
(
9
), pp.
508
527
.10.2514/1.I010796
42.
Yildirim
,
A.
,
Kenway
,
G. K. W.
,
Mader
,
C. A.
, and
Martins
,
J. R. R. A.
,
2019
, “
A Jacobian-Free Approximate Newton–Krylov Startup Strategy for RANS Simulations
,”
J. Comput. Phys.
,
397
, p.
108741
.10.1016/j.jcp.2019.06.018
43.
Spalart
,
P.
, and
Allmaras
,
S.
,
1994
, “
A One-Equation Turbulence Model for Aerodynamic Flows
,”
La Rech. Aerosp.
,
1
, pp.
5
21
.https://turbmodels.larc.nasa.gov/Papers/RechAerosp_1994_SpalartAllmaras.pdf
44.
Coletti
,
F.
,
Verstraete
,
T.
,
Bulle
,
J.
,
Van der Wielen
,
T.
,
Van den Berge
,
N.
, and
Arts
,
T.
,
2013
, “
Optimization of a U-Bend for Minimal Pressure Loss in Internal Cooling Channels–Part ii: Experimental Validation
,”
ASME J. Turbomach.
,
135
(
5
), p.
051016
.10.1115/1.4023031
45.
Kenway
,
G. K. W.
,
Mader
,
C. A.
,
He
,
P.
, and
Martins
,
J. R. R. A.
,
2019
, “
Effective Adjoint Approaches for Computational Fluid Dynamics
,”
Prog. Aerosp. Sci.
,
110
, p.
100542
.10.1016/j.paerosci.2019.05.002
46.
Secco
,
N.
,
Kenway
,
G. K. W.
,
He
,
P.
,
Mader
,
C. A.
, and
Martins
,
J. R. R. A.
,
2021
, “
Efficient Mesh Generation and Deformation for Aerodynamic Shape Optimization
,”
AIAA J.
,
59
(
4
), pp.
1151
1168
.10.2514/1.J059491
47.
Chan
,
W. M.
, and
Steger
,
J. L.
,
1992
, “
Enhancements of a Three-Dimensional Hyperbolic Grid Generation Scheme
,”
Appl. Math. Comput.
,
51
(
2–3
), pp.
181
205
.10.1016/0096-3003(92)90073-A
48.
Roache
,
P. J.
,
1998
, “
Verification of Codes and Calculations
,”
AIAA J.
,
36
(
5
), pp.
696
702
.10.2514/2.457
49.
Coppeans
,
A. W. C.
,
Fidkowski
,
K. J.
, and
Martins
,
J. R. R. A.
,
2023
, “
Comparison of Finite Volume and High-Order Discontinuous Galerkin Based Aerodynamic Shape Optimization
,”
AIAA
Paper No. 2023-1845.10.2514/6.2023-1845
50.
Lyu
,
Z.
,
Kenway
,
G. K. W.
, and
Martins
,
J. R. R. A.
,
2015
, “
Aerodynamic Shape Optimization Investigations of the Common Research Model Wing Benchmark
,”
AIAA J.
,
53
(
4
), pp.
968
985
.10.2514/1.J053318
51.
Brelje
,
B. J.
, and
Martins
,
J. R. R. A.
,
2018
, “
Development of a Conceptual Design Model for Aircraft Electric Propulsion With Efficient Gradients
,”
AIAA
Paper No. 2018-4979.10.2514/6.2018-4979
52.
Manglik
,
R. M.
, and
Bergles
,
A. E.
,
1995
, “
Heat Transfer and Pressure Drop Correlations for the Rectangular Offset Strip Fin Compact Heat Exchanger
,”
Exp. Therm. Fluid Sci.
,
10
(
2
), pp.
171
180
.10.1016/0894-1777(94)00096-Q
53.
Hajdik
,
H. M.
,
Yildirim
,
A.
,
Wu
,
N.
,
Brelje
,
B. J.
,
Seraj
,
S.
,
Mangano
,
M.
,
Anibal
,
J. L.
, et al.,
2023
, “
pyGeo: A Geometry Package for Multidisciplinary Design Optimization
,”
J. Open Source Software
,
8
(
87
), p.
5319
.10.21105/joss.05319
54.
Lambe
,
A. B.
, and
Martins
,
J. R. R. A.
,
2012
, “
Extensions to the Design Structure Matrix for the Description of Multidisciplinary Design, Analysis, and Optimization Processes
,”
Struct. Multidiscip. Optim.
,
46
(
2
), pp.
273
284
.10.1007/s00158-012-0763-y
55.
Kreisselmeier
,
G.
, and
Steinhauser
,
R.
,
1979
, “
Systematic Control Design by Optimizing a Vector Performance Index
,”
International Federation of Active Controls Symposium on Computer-Aided Design of Control Systems
, Zurich, Switzerland, Aug. 29–31, pp.
113
117
.10.1016/S1474-6670(17)65584-8
56.
Sederberg
,
T. W.
, and
Parry
,
S. R.
,
1986
, “
Free-Form Deformation of Solid Geometric Models
,”
SIGGRAPH Comput. Graph.
,
20
(
4
), pp.
151
160
.10.1145/15886.15903
57.
Gill
,
P. E.
,
Murray
,
W.
, and
Saunders
,
M. A.
,
2005
, “
SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization
,”
SIAM Rev.
,
47
(
1
), pp.
99
131
.10.1137/S0036144504446096
58.
Wu
,
N.
,
Kenway
,
G.
,
Mader
,
C. A.
,
Jasa
,
J.
, and
Martins
,
J. R. R. A.
,
2020
, “
pyOptSparse: A Python Framework for Large-Scale Constrained Nonlinear Optimization of Sparse Systems
,”
J. Open Source Software
,
5
(
54
), p.
2564
.10.21105/joss.02564
You do not currently have access to this content.