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.

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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-
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.
---------------------- Page: 3 ----------------------
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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

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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

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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

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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
heat transfer rate along the duct, and Nu 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
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,

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

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

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

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

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

number at uniform wall temperature, Nu , vs. Reynolds number, Re, for
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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kSIST-TP FprCEN/CLC/TR 17603-31-13:2021
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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kSIST-TP FprCEN/CLC/TR 17603-31-13:2021
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

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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

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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

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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
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
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,

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

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

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

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

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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