Space Engineering - Thermal design handbook - Part 13: Fluid Loops

Fluid loops are used to control the temperature of sensitive components in spacecraft systems in order to ensure that they can function correctly.
While there are several methods for thermal control (such as passive thermal insulations, thermoelectric devices, phase change materials, heat pipes and short-term discharge systems), fluid loops have a specific application area.
This Part 13 provides a detailed description of fluid loop systems for use in spacecraft.
The Thermal design handbook is published in 16 Parts:
TR 17603-31-01-31-01 Part 1A    Thermal design handbook – Part 1: View factors
TR 17603-31-01-31-01 Part 2A    Thermal design handbook – Part 2: Holes, Grooves and Cavities
TR 17603-31-01-31-01 Part 3A    Thermal design handbook – Part 3: Spacecraft Surface Temperature
TR 17603-31-01-31-01 Part 4A    Thermal design handbook – Part 4: Conductive Heat Transfer
TR 17603-31-01-31-01 Part 5A    Thermal design handbook – Part 5: Structural Materials: Metallic and Composite
TR 17603-31-01-31-01 Part 6A    Thermal design handbook – Part 6: Thermal Control Surfaces
TR 17603-31-01-31-01 Part 7A    Thermal design handbook – Part 7: Insulations
TR 17603-31-01-31-01 Part 8A    Thermal design handbook – Part 8: Heat Pipes
TR 17603-31-01-31-01 Part 9A    Thermal design handbook – Part 9: Radiators
TR 17603-31-01-31-01 Part 10A    Thermal design handbook – Part 10: Phase – Change Capacitors
TR 17603-31-01-31-01 Part 11A    Thermal design handbook – Part 11: Electrical Heating
TR 17603-31-01-31-01 Part 12A    Thermal design handbook – Part 12: Louvers
TR 17603-31-01-31-01 Part 13A    Thermal design handbook – Part 13: Fluid Loops
TR 17603-31-01-31-01 Part 14A    Thermal design handbook – Part 14: Cryogenic Cooling
TR 17603-31-01-31-01 Part 15A    Thermal design handbook – Part 15: Existing Satellites
TR 17603-31-01-31-01 Part 16A    Thermal design handbook – Part 16: Thermal Protection System

Raumfahrttechnik - Handbuch für thermisches Design - Teil 13: Fluidschleifen

Ingénierie spatiale - Manuel de conception thermique - Partie 13: Boucles fluides

Vesoljska tehnika - Priročnik o toplotni zasnovi - 13. del: Fluidne zanke

General Information

Status
Published
Public Enquiry End Date
26-May-2021
Publication Date
23-Aug-2021
Technical Committee
Current Stage
6060 - National Implementation/Publication (Adopted Project)
Start Date
19-Aug-2021
Due Date
24-Oct-2021
Completion Date
24-Aug-2021

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SLOVENSKI STANDARD
SIST-TP CEN/CLC/TR 17603-31-13:2021
01-oktober-2021
Vesoljska tehnika - Priročnik o toplotni zasnovi - 13. del: Fluidne zanke
Space Engineering - Thermal design handbook - Part 13: Fluid Loops
Raumfahrttechnik - Handbuch für thermisches Design - Teil 13: Fluidschleifen
Ingénierie spatiale - Manuel de conception thermique - Partie 13: Boucles fluides
Ta slovenski standard je istoveten z: CEN/CLC/TR 17603-31-13:2021
ICS:
49.140 Vesoljski sistemi in operacije Space systems and
operations
SIST-TP CEN/CLC/TR 17603-31-13:2021 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------
SIST-TP CEN/CLC/TR 17603-31-13:2021

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SIST-TP CEN/CLC/TR 17603-31-13:2021


TECHNICAL REPORT
CEN/CLC/TR 17603-31-
13
RAPPORT TECHNIQUE

TECHNISCHER BERICHT

August 2021
ICS 49.140

English version

Space Engineering - Thermal design handbook - Part 13:
Fluid Loops
Ingénierie spatiale - Manuel de conception thermique - Raumfahrttechnik - Handbuch für thermisches Design -
Partie 13 : Boucles fluides Teil 13: Flüssigkeitskreisläufe


This Technical Report was approved by CEN on 28 June 2021. It has been drawn up by the Technical Committee CEN/CLC/JTC 5.

CEN and CENELEC members are the national standards bodies and national electrotechnical committees of Austria, Belgium,
Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy,
Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of North Macedonia, Romania, Serbia,
Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom.
























CEN-CENELEC Management Centre:
Rue de la Science 23, B-1040 Brussels
© 2021 CEN/CENELEC All rights of exploitation in any form and by any means Ref. No. CEN/CLC/TR 17603-31-13:2021 E
reserved worldwide for CEN national Members and for
CENELEC Members.

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CEN/CLC/TR 17603-31-13:2021 (E)
Table of contents
European Foreword . 29
1 Scope . 30
2 References . 31
3 Terms, definitions and symbols . 32
3.1 Terms and definitions . 32
3.2 Abbreviated terms. 32
3.3 Symbols . 34
4 General introduction . 46
4.1 Fluid loops . 47
4.2 Comparison between fluid loops and alternative systems . 48
4.2.1 Passive thermal insulations . 48
4.2.2 Thermoelectric devices . 48
4.2.3 Phase change materials (pcm) . 49
4.2.4 Heat pipes . 50
4.2.5 Short-term discharge systems . 50
5 Analysis of a fluid loop . 52
5.1 General . 52
5.2 Thermal performance . 53
5.3 Power requirements . 56
6 Thermal analysis . 58
6.1 General . 58
6.2 Analytical background . 58
6.2.1 Heat transfer coefficient . 58
6.2.2 Dimensionless groups . 60
6.2.3 Simplifying assumptions . 61
6.2.4 Temperature-dependence of fluid properties . 61
6.2.5 Laminar versus turbulent fluid flow . 63
6.2.6 Heat transfer to internal flows . 63
6.2.7 Heat transfer to external flows . 65
2

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6.3 Thermal performance data . 67
6.3.1 Heat transfer to internal flow . 67
6.3.2 Heat transfer to external flows . 83
7 Frictional analysis . 92
7.1 General . 92
7.2 Analytical background . 92
7.2.1 Introduction . 92
7.2.2 Fully developed flow in straight pipes . 93
7.2.3 Temperature-dependence of fluid properties . 97
7.2.4 Several definitions of pressure loss coefficient . 98
7.2.5 Entrance effects . 100
7.2.6 Interferences and networks . 101
7.2.7 Flow chart . 102
7.3 Pressure loss data . 105
7.3.1 Straight pipes . 105
7.3.2 Bends. 106
7.3.3 Sudden changes of area . 113
7.3.4 Orifices and diaphragms . 116
7.3.5 Screens . 119
7.3.6 Valves . 120
7.3.7 Tube banks . 121
7.3.8 Branching of tubes . 124
8 Combined thermal and frictional analysis . 125
8.1 General . 125
8.2 Analogies between momentum and heat transfer . 125
8.2.1 The Reynolds analogy . 125
8.2.2 The Prandtl analogy . 128
8.2.3 The Von Karman analogy. 129
8.2.4 Other analogies . 129
9 Heat transfer enhancement . 130
9.1 General . 130
9.1.1 Basic augmentation mechanisms . 131
9.1.2 Criterion for the evaluation of the several techniques . 132
9.1.3 Index of the compiled data. . 133
9.1.4 Validity of the empirical correlations . 133
9.2 Single-phase forced convection data . 136
3

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10 Working fluids . 170
10.1 General . 170
10.2 Cooling effectiveness of a fluid . 170
10.2.1 Simplified fluid loop configuration . 172
10.2.2 Thermal performance of the simplified loop . 172
10.2.3 Power requirements of the simplified loop . 173
10.2.4 Several examples . 173
10.3 Properties of liquid coolants . 178
10.4 Properties of dry air . 212
11 Heat exchangers . 214
11.1 General . 214
11.2 Basic analysis . 217
11.2.1 Introduction . 217
11.2.2 Analytical background . 218
11.2.3 Exchanger performance . 221
11.3 Exchanging surface geometries . 236
11.3.1 Tubular surfaces . 237
11.3.2 Plate-fin surfaces . 240
11.3.3 Finned tubes . 246
11.3.4 Matrix surfaces . 248
11.4 Deviations from basic analysis . 249
11.4.1 Introduction . 249
11.4.2 Longitudinal heat conduction . 250
11.4.3 Flow maldistribution . 253
11.5 Manufacturing defects . 263
11.5.1 Introduction . 263
11.5.2 Variations of the flow passages . 263
11.5.3 Fin leading edge imperfections. 267
11.5.4 Brazing . 267
11.6 In service degradation . 271
11.6.1 Introduction . 271
11.6.2 Fouling . 271
11.7 Existing systems . 274
12 Pumps . 283
12.1 General . 283
12.2 Specified speed . 287
12.3 Net suction energy . 289
4

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12.4 Requirements for spaceborne pumps . 290
12.5 Commercially available pumps . 291
12.6 European pump manufacturers. 297
13 System optimization . 298
13.1 General . 298
13.2 Basic analysis . 298
13.2.1 Interface heat exchanger. 299
13.2.2 Supply and return plumbing . 300
13.2.3 Radiator . 301
13.3 Special examples. 301
13.3.1 Constraints based on source temperature . 302
13.3.2 Constraints imposed by the integration . 305
14 Two-phase flow . 309
14.1 General . 309
14.2 Pressure loss . 311
14.2.1 Lockhart-martinelli correlation . 311
14.2.2 Improvements upon martinelli correlation . 316
14.3 Annular flow . 317
14.3.1 Ideal annular flow model . 318
14.3.2 Annular flow with entrainment model . 327
14.4 Condensation in ducts . 341
14.4.1 Condensing flow model . 341
14.4.2 Variation of the vapor quality along the duct in the stratified model . 347
14.4.3 Limits of validity of the stratified model . 349
14.4.4 Annular flow model. 350
14.4.5 Variation of the vapor quality along the duct in the annular model . 354
15 Two-phase thermal transport systems . 357
15.1 General . 357
15.1.1 Evolution of thermal transport systems . 357
15.1.2 Two-phase loop general layout . 358
15.1.3 About the nomenclature of this clause. 361
15.2 Tms trade-off study . 361
15.2.1 TMS study baseline . 364
15.2.2 TMS design concepts . 364
15.2.3 Evaluation of tms concepts . 367
15.3 Design for orbital average load . 370
5

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15.3.1 Phase change capacitor performance . 370
15.4 Off-design operation . 376
15.4.1 Temperature control . 378
15.4.2 Instrumentation requirements . 381
15.5 Radiator-loop interaction . 382
15.5.1 Boosting radiator temperature with a heat pump . 383
15.5.2 Thermal-storage assisted radiator . 388
15.5.3 Steerable radiators . 391
15.5.4 Radiators coupling . 402
15.6 Capillary pumped loop (cpl) technology . 404
15.6.1 Advantages of cpl systems . 408
15.6.2 CPL performance constraints . 408
15.6.3 CPL basic system concept . 408
15.7 Components . 411
15.7.1 Pumping systems . 411
15.7.2 Mounting plates . 414
15.7.3 Vapour quality sensors . 416
15.7.4 Fluid disconnects . 420
16 Control technology . 422
16.1 Basic definitions . 422
16.2 General description of control systems . 423
16.2.1 Introduction . 423
16.2.2 Closed-loop control systems . 424
16.2.3 Open-loop control system . 424
16.2.4 Adaptative control systems . 425
16.2.5 Learning control system . 426
16.2.6 Trade-off of open- and closed-loop control systems . 426
16.3 Basic control actions . 431
16.3.1 Introduction . 431
16.3.2 Two-position or on-off control action . 432
16.3.3 Proportional control action (p controller) . 433
16.3.4 Integral control action (i controller). . 434
16.3.5 Proportional-integral control action (pi controller) . 435
16.3.6 Proportional-derivative control action (pd controller) . 436
16.3.7 Proportional-integral-derivative control action (pid controller) . 437
16.3.8 Summary . 438
16.4 Implementation techniques of control laws . 439
6

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16.4.1 Introduction . 439
16.4.2 Devices characterization . 441
16.4.3 Analog-controller implementation techniques . 445
16.4.4 Summary . 456
16.5 Hardware description . 458
16.5.1 Introduction . 458
16.5.2 Controllers . 460
16.5.3 Sensors . 465
16.5.4 Actuators. Control valves . 468
16.6 Control software . 469
16.7 Existing systems . 472
16.7.1 Space radiator system . 472
Bibliography . 476

Figures
Figure 5-1: Schematic representation of the fluid loop. . 52
Figure 6-1: Nusselt numbers, Nu, for fully developed laminar flow through straight pipes
of several cross-sectional shapes. Nu is the Nusselt number for constant
q
heat transfer rate along the duct, and Nu that for constant wall temperature
T
along the duct. From Kays & London (1964) [102]. . 69
Figure 6-2: Nusselt numbers, Nu, vs. ratio, a/b, of short side to long side for fully
developed laminar flow through straight pipes of rectangular cross section.
From Kays & London (1964) [102]. . 70
Figure 6-3: Nusselt numbers, Nu, vs. ratio of inner to outer diameter, r /r , for fully
1 2
developed laminar flow in concentric- circular-tube annuli. Constant heat
transfer rate. From Kays & London (1964) [102]. . 70
Figure 6-4: Influence of coefficients, Z, vs. ratio of inner to outer diameter, r /r , for fully
1 2
developed laminar flow in concentric-circular-tube annuli. Constant heat
transfer rate. From Kays & London (1964) [102]. . 71
Figure 6-5: Nusselt number, Nu, vs. Dean number, K, for fully developed laminar flow
in curved pipe of circular cross section. Constant heat transfer rate. Results
are shown for different Prandtl numbers, Pr. Calculated by the compiler
after Mori & Nakayama (1965) [128]. . 71
Figure 6-6: Thermal entry length Nusselt numbers, Nu, vs. non-dimensional axial
+
distance, x , for laminar flow through straight pipes. Constant wall
temperature. Calculated by the compiler after Kays (1966) [101]. . 72
Figure 6-7: Thermal entry length Nusselt number, Nu , vs. non-dimensional axial
x
+
distance, x , for laminar flow through straight pipes. Constant heat transfer
rate. Also shown the influence coefficient, Z, for laminar flow between
parallel plates with one side insulated. Calculated by the compiler after
Kays (1966) [101]. . 72
Figure 6-8: Thermal entry length Nusselt numbers, Nu , and influence coefficients, Z,
x
+
vs. dimensionless axial distance, x , for laminar flow in concentric-circular-
7

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tube annuli. Constant heat transfer rate. Calculated by the compiler after
Kays (1966) [101]. . 73
Figure 6-9: Thermal entry length Nusselt number, Nu , vs. non dimensional distance
x
+
along the coil centerline, x , for laminar flow through a coil. The results are
given for two values of the ratio, r/R, between the cross-sectional radius
and the coil radius. Constant wall temperature. Calculated by the compiler
after Kubair & Kuloor (1966) [111]. . 73
+
Figure 6-10: Nusselt numbers, Nu, vs. non-dimensional axial distance, x , for the
combined hydrodynamical and thermal entry length. Laminar flow through
straight pipes of circular cross section. Constant wall temperature. Pr = 0.7.
Replotted by the compiler after ESDU 68006 (1968) [48]. . 74
+
Figure 6-11: Local Nusselt number, Nu , vs. non-dimensional axial distance, x , for the
x
combined hydrodynamical and thermal entry length. Laminar flow through
straight pipes of circular cross section. Constant heat transfer rate. Results
are shown for different Prandtl numbers, Pr. Calculated by the compiler
after Heaton et al. (1964) [82]. . 74
Figure 6-12: Local Nusselt number, Nu , and influence coefficient, Z, vs. dimensionless
x
+
axial distance, x , for the combined hydrodynamical and thermal entry
length. Laminar flow between parallel plates, one of them insulated.
Constant heat transfer rate. Results are shown for different Prandtl
numbers, Pr. Calculated by the compiler after Heaton et al. (1964) [82]. . 75
Figure 6-13: Local Nusselt number, Nu , vs. Reynolds number, Re, for fully developed
x
transitional flow through cylindrical ducts of circular cross section. Constant
wall temperature. Gas Flow (Pr ≈ 0.7). From ESDU 68006 (1968) [48]. . 75
Figure 6-14: Nusselt number, Nu, vs. Reynolds number, Re, for fully developed
turbulent flow through cylindrical ducts. Constant heat transfer rate. Results
are shown for different Prandtl numbers, Pr. Calculated by the compiler
after Petukhov & Roizen (1975) [143]. . 76
Figure 6-15: Ratio of Nusselt number at constant heat transfer rate, Nu , to Nusselt
q
number at uniform wall temperature, Nu , vs. Reynolds number, Re, for
T
fully developed turbulent flow through a straight pipe of circular cross
section. Results are shown for different Prandtl numbers, Pr. From Sleicher
& Tribus (1957) [167]. 76
Figure 6-16: Nus
...

SLOVENSKI STANDARD
kSIST-TP FprCEN/CLC/TR 17603-31-13:2021
01-maj-2021
Vesoljska tehnika - Priročnik za toplotno zasnovo - 13. del: Fluidne zanke
Space Engineering - Thermal design handbook - Part 13: Fluid Loops
Raumfahrttechnik - Handbuch für thermisches Design - Teil 13: Fluidschleifen
Ingénierie spatiale - Manuel de conception thermique - Partie 13: Boucles fluides
Ta slovenski standard je istoveten z: FprCEN/CLC/TR 17603-31-13
ICS:
49.140 Vesoljski sistemi in operacije Space systems and
operations
kSIST-TP FprCEN/CLC/TR 17603-31- en,fr,de
13:2021
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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kSIST-TP FprCEN/CLC/TR 17603-31-13:2021

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TECHNICAL REPORT
FINAL DRAFT
FprCEN/CLC/TR 17603-
RAPPORT TECHNIQUE
31-13
TECHNISCHER BERICHT


March 2021
ICS 49.140

English version

Space Engineering - Thermal design handbook - Part 13:
Fluid Loops
Ingénierie spatiale - Manuel de conception thermique - Raumfahrttechnik - Handbuch für thermisches Design -
Partie 13: Boucles fluides Teil 13: Fluidschleifen


This draft Technical Report is submitted to CEN members for Vote. It has been drawn up by the Technical Committee
CEN/CLC/JTC 5.

CEN and CENELEC members are the national standards bodies and national electrotechnical committees of Austria, Belgium,
Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy,
Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of North Macedonia, Romania, Serbia,
Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom.

Recipients of this draft are invited to submit, with their comments, notification of any relevant patent rights of which they are
aware and to provide supporting documentation.

Warning : This document is not a Technical Report. It is distributed for review and comments. It is subject to change without
notice and shall not be referred to as a Technical Report.




















CEN-CENELEC Management Centre:
Rue de la Science 23, B-1040 Brussels
© 2021 CEN/CENELEC All rights of exploitation in any form and by any means Ref. No. FprCEN/CLC/TR 17603-31-13:2021 E
reserved worldwide for CEN national Members and for
CENELEC Members.

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FprCEN/CLC/TR 17603-31-13:2021 (E)
Table of contents
European Foreword . 29
1 Scope . 30
2 References . 31
3 Terms, definitions and symbols . 32
3.1 Terms and definitions . 32
3.2 Abbreviated terms. 32
3.3 Symbols . 34
4 General introduction . 46
4.1 Fluid loops . 47
4.2 Comparison between fluid loops and alternative systems . 48
4.2.1 Passive thermal insulations . 48
4.2.2 Thermoelectric devices . 48
4.2.3 Phase change materials (pcm) . 49
4.2.4 Heat pipes . 50
4.2.5 Short-term discharge systems . 50
5 Analysis of a fluid loop . 52
5.1 General . 52
5.2 Thermal performance . 53
5.3 Power requirements . 56
6 Thermal analysis . 58
6.1 General . 58
6.2 Analytical background . 58
6.2.1 Heat transfer coefficient . 58
6.2.2 Dimensionless groups . 60
6.2.3 Simplifying assumptions . 61
6.2.4 Temperature-dependence of fluid properties . 61
6.2.5 Laminar versus turbulent fluid flow . 63
6.2.6 Heat transfer to internal flows . 63
6.2.7 Heat transfer to external flows . 65
2

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6.3 Thermal performance data . 67
6.3.1 Heat transfer to internal flow . 67
6.3.2 Heat transfer to external flows . 83
7 Frictional analysis . 92
7.1 General . 92
7.2 Analytical background . 92
7.2.1 Introduction . 92
7.2.2 Fully developed flow in straight pipes . 93
7.2.3 Temperature-dependence of fluid properties . 97
7.2.4 Several definitions of pressure loss coefficient . 98
7.2.5 Entrance effects . 100
7.2.6 Interferences and networks . 101
7.2.7 Flow chart . 102
7.3 Pressure loss data . 105
7.3.1 Straight pipes . 105
7.3.2 Bends. 106
7.3.3 Sudden changes of area . 113
7.3.4 Orifices and diaphragms . 116
7.3.5 Screens . 119
7.3.6 Valves . 120
7.3.7 Tube banks . 121
7.3.8 Branching of tubes . 124
8 Combined thermal and frictional analysis . 125
8.1 General . 125
8.2 Analogies between momentum and heat transfer . 125
8.2.1 The Reynolds analogy . 125
8.2.2 The Prandtl analogy . 128
8.2.3 The Von Karman analogy. 129
8.2.4 Other analogies . 129
9 Heat transfer enhancement . 130
9.1 General . 130
9.1.1 Basic augmentation mechanisms . 131
9.1.2 Criterion for the evaluation of the several techniques . 132
9.1.3 Index of the compiled data. . 133
9.1.4 Validity of the empirical correlations . 133
9.2 Single-phase forced convection data . 136
3

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10 Working fluids . 170
10.1 General . 170
10.2 Cooling effectiveness of a fluid . 170
10.2.1 Simplified fluid loop configuration . 172
10.2.2 Thermal performance of the simplified loop . 172
10.2.3 Power requirements of the simplified loop . 173
10.2.4 Several examples . 173
10.3 Properties of liquid coolants . 178
10.4 Properties of dry air . 212
11 Heat exchangers . 214
11.1 General . 214
11.2 Basic analysis . 217
11.2.1 Introduction . 217
11.2.2 Analytical background . 218
11.2.3 Exchanger performance . 221
11.3 Exchanging surface geometries . 236
11.3.1 Tubular surfaces . 237
11.3.2 Plate-fin surfaces . 240
11.3.3 Finned tubes . 246
11.3.4 Matrix surfaces . 248
11.4 Deviations from basic analysis . 249
11.4.1 Introduction . 249
11.4.2 Longitudinal heat conduction . 250
11.4.3 Flow maldistribution . 253
11.5 Manufacturing defects . 263
11.5.1 Introduction . 263
11.5.2 Variations of the flow passages . 263
11.5.3 Fin leading edge imperfections. 267
11.5.4 Brazing . 267
11.6 In service degradation . 271
11.6.1 Introduction . 271
11.6.2 Fouling . 271
11.7 Existing systems . 274
12 Pumps . 283
12.1 General . 283
12.2 Specified speed . 287
12.3 Net suction energy . 289
4

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12.4 Requirements for spaceborne pumps . 290
12.5 Commercially available pumps . 291
12.6 European pump manufacturers. 297
13 System optimization . 298
13.1 General . 298
13.2 Basic analysis . 298
13.2.1 Interface heat exchanger. 299
13.2.2 Supply and return plumbing . 300
13.2.3 Radiator . 301
13.3 Special examples. 301
13.3.1 Constraints based on source temperature . 302
13.3.2 Constraints imposed by the integration . 305
14 Two-phase flow . 309
14.1 General . 309
14.2 Pressure loss . 311
14.2.1 Lockhart-martinelli correlation . 311
14.2.2 Improvements upon martinelli correlation . 316
14.3 Annular flow . 317
14.3.1 Ideal annular flow model . 318
14.3.2 Annular flow with entrainment model . 327
14.4 Condensation in ducts . 341
14.4.1 Condensing flow model . 341
14.4.2 Variation of the vapor quality along the duct in the stratified model . 347
14.4.3 Limits of validity of the stratified model . 349
14.4.4 Annular flow model. 350
14.4.5 Variation of the vapor quality along the duct in the annular model . 354
15 Two-phase thermal transport systems . 357
15.1 General . 357
15.1.1 Evolution of thermal transport systems . 357
15.1.2 Two-phase loop general layout . 358
15.1.3 About the nomenclature of this clause. 361
15.2 Tms trade-off study . 361
15.2.1 TMS study baseline . 364
15.2.2 TMS design concepts . 364
15.2.3 Evaluation of tms concepts . 367
15.3 Design for orbital average load . 370
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15.3.1 Phase change capacitor performance . 370
15.4 Off-design operation . 376
15.4.1 Temperature control . 378
15.4.2 Instrumentation requirements . 381
15.5 Radiator-loop interaction . 382
15.5.1 Boosting radiator temperature with a heat pump . 383
15.5.2 Thermal-storage assisted radiator . 388
15.5.3 Steerable radiators . 391
15.5.4 Radiators coupling . 402
15.6 Capillary pumped loop (cpl) technology . 404
15.6.1 Advantages of cpl systems . 408
15.6.2 CPL performance constraints . 408
15.6.3 CPL basic system concept . 408
15.7 Components . 411
15.7.1 Pumping systems . 411
15.7.2 Mounting plates . 414
15.7.3 Vapour quality sensors . 416
15.7.4 Fluid disconnects . 420
16 Control technology . 422
16.1 Basic definitions . 422
16.2 General description of control systems . 423
16.2.1 Introduction . 423
16.2.2 Closed-loop control systems . 424
16.2.3 Open-loop control system . 424
16.2.4 Adaptative control systems . 425
16.2.5 Learning control system . 426
16.2.6 Trade-off of open- and closed-loop control systems . 426
16.3 Basic control actions . 431
16.3.1 Introduction . 431
16.3.2 Two-position or on-off control action . 432
16.3.3 Proportional control action (p controller) . 433
16.3.4 Integral control action (i controller). . 434
16.3.5 Proportional-integral control action (pi controller) . 435
16.3.6 Proportional-derivative control action (pd controller) . 436
16.3.7 Proportional-integral-derivative control action (pid controller) . 437
16.3.8 Summary . 438
16.4 Implementation techniques of control laws . 439
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16.4.1 Introduction . 439
16.4.2 Devices characterization . 441
16.4.3 Analog-controller implementation techniques . 445
16.4.4 Summary . 456
16.5 Hardware description . 458
16.5.1 Introduction . 458
16.5.2 Controllers . 460
16.5.3 Sensors . 465
16.5.4 Actuators. Control valves . 468
16.6 Control software . 469
16.7 Existing systems . 472
16.7.1 Space radiator system . 472
Bibliography . 476

Figures
Figure 5-1: Schematic representation of the fluid loop. . 52
Figure 6-1: Nusselt numbers, Nu, for fully developed laminar flow through straight pipes
of several cross-sectional shapes. Nu is the Nusselt number for constant
q
heat transfer rate along the duct, and NuT that for constant wall temperature
along the duct. From Kays & London (1964) [102]. . 69
Figure 6-2: Nusselt numbers, Nu, vs. ratio, a/b, of short side to long side for fully
developed laminar flow through straight pipes of rectangular cross section.
From Kays & London (1964) [102]. . 70
Figure 6-3: Nusselt numbers, Nu, vs. ratio of inner to outer diameter, r /r , for fully
1 2
developed laminar flow in concentric- circular-tube annuli. Constant heat
transfer rate. From Kays & London (1964) [102]. . 70
Figure 6-4: Influence of coefficients, Z, vs. ratio of inner to outer diameter, r /r , for fully
1 2
developed laminar flow in concentric-circular-tube annuli. Constant heat
transfer rate. From Kays & London (1964) [102]. . 71
Figure 6-5: Nusselt number, Nu, vs. Dean number, K, for fully developed laminar flow
in curved pipe of circular cross section. Constant heat transfer rate. Results
are shown for different Prandtl numbers, Pr. Calculated by the compiler
after Mori & Nakayama (1965) [128]. . 71
Figure 6-6: Thermal entry length Nusselt numbers, Nu, vs. non-dimensional axial
+
distance, x , for laminar flow through straight pipes. Constant wall
temperature. Calculated by the compiler after Kays (1966) [101]. . 72
Figure 6-7: Thermal entry length Nusselt number, Nu , vs. non-dimensional axial
x
+
distance, x , for laminar flow through straight pipes. Constant heat transfer
rate. Also shown the influence coefficient, Z, for laminar flow between
parallel plates with one side insulated. Calculated by the compiler after
Kays (1966) [101]. . 72
Figure 6-8: Thermal entry length Nusselt numbers, Nu , and influence coefficients, Z,
x
+
vs. dimensionless axial distance, x , for laminar flow in concentric-circular-
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tube annuli. Constant heat transfer rate. Calculated by the compiler after
Kays (1966) [101]. . 73
Figure 6-9: Thermal entry length Nusselt number, Nu , vs. non dimensional distance
x
+
along the coil centerline, x , for laminar flow through a coil. The results are
given for two values of the ratio, r/R, between the cross-sectional radius
and the coil radius. Constant wall temperature. Calculated by the compiler
after Kubair & Kuloor (1966) [111]. . 73
+
Figure 6-10: Nusselt numbers, Nu, vs. non-dimensional axial distance, x , for the
combined hydrodynamical and thermal entry length. Laminar flow through
straight pipes of circular cross section. Constant wall temperature. Pr = 0.7.
Replotted by the compiler after ESDU 68006 (1968) [48]. . 74
+
Figure 6-11: Local Nusselt number, Nu , vs. non-dimensional axial distance, x , for the
x
combined hydrodynamical and thermal entry length. Laminar flow through
straight pipes of circular cross section. Constant heat transfer rate. Results
are shown for different Prandtl numbers, Pr. Calculated by the compiler
after Heaton et al. (1964) [82]. . 74
Figure 6-12: Local Nusselt number, Nu , and influence coefficient, Z, vs. dimensionless
x
+
axial distance, x , for the combined hydrodynamical and thermal entry
length. Laminar flow between parallel plates, one of them insulated.
Constant heat transfer rate. Results are shown for different Prandtl
numbers, Pr. Calculated by the compiler after Heaton et al. (1964) [82]. . 75
Figure 6-13: Local Nusselt number, Nu , vs. Reynolds number, Re, for fully developed
x
transitional flow through cylindrical ducts of circular cross section. Constant
wall temperature. Gas Flow (Pr  0.7). From ESDU 68006 (1968) [48]. . 75
Figure 6-14: Nusselt number, Nu, vs. Reynolds number, Re, for fully developed
turbulent flow through cylindrical ducts. Constant heat transfer rate. Results
are shown for different Prandtl numbers, Pr. Calculated by the compiler
after Petukhov & Roizen (1975) [143]. . 76
Fig
...

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