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

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
• ICS: 49.140 - Space systems and operations
• Technical Committee: I13 - Imaginarni 13
• Current Stage: 6060 - National Implementation/Publication (Adopted Project)
• Start Date: 19-Aug-2021
• Due Date: 24-Oct-2021
• Completion Date: 24-Aug-2021
• Mandate: M/496 - Mandate addressed to CEN, CENELEC and ETSI to develop standardisation regarding space industry (Phase 3 of the process)
• Ref Project: CEN/CLC/TR 17603-31-13:2021 - Space Engineering - Thermal design handbook - Part 13: Fluid Loops

Overview

SIST-TP CEN/CLC/TR 17603-31-13:2021 - Space Engineering: Thermal design handbook - Part 13: Fluid Loops is a technical report that provides a comprehensive description of fluid loop systems used for spacecraft thermal control. Published by SIST as the European Technical Report (CEN/CLC/TR) in August 2021, this Part 13 explains when and how fluid loops are used to maintain component temperatures, and compares fluid loops with alternative thermal-control approaches (insulation, heat pipes, phase‑change materials, thermoelectrics, etc.).

Key topics and technical content

This handbook section covers practical and analytical material essential to design and analysis of spacecraft fluid loops, including:

• General principles of fluid loop architecture and trade-offs versus passive and active alternatives
• Thermal analysis
  • Heat transfer coefficients, dimensionless groups (Reynolds, Prandtl), laminar vs turbulent regimes
  • Heat transfer to internal and external flows; temperature-dependent fluid properties
• Frictional analysis
  • Pressure loss methods for straight pipes, bends, sudden area changes, orifices, valves and branching networks
  • Entrance effects and flow-chart approaches for network evaluation
• Combined thermal and frictional analysis and analogies between momentum and heat transfer
• Heat transfer enhancement techniques and empirical performance data for single-phase forced convection
• Working fluids: coolant effectiveness, liquid coolant properties and dry air data
• Heat exchangers: basic performance, geometries (tubular, plate-fin, finned tubes, matrix surfaces), manufacturing defects and in-service degradation (fouling)
• Pumps: spaceborne pump requirements, specified speed, net suction energy, and commercial options
• System optimization: interface exchangers, plumbing, radiator integration, and design constraints
• Two‑phase flow and systems: pressure loss correlations, annular/condensing flows, two‑phase loop layouts, capillary‑pumped loops and thermal management system (TMS) trade-offs

Practical applications and users

This Part 13 is essential for:

• Spacecraft thermal engineers designing liquid cooling loops or two‑phase thermal transport systems
• Systems and avionics engineers integrating thermal control with power and mechanical subsystems
• Component manufacturers (pumps, heat exchangers, tubing, valves) validating space requirements
• Test engineers and analysts performing thermal/fuidic simulations, sizing radiators and pumps, estimating pressure loss and heat transfer performance
• Project managers and procurement teams specifying technical requirements for space-qualified thermal hardware

Keywords: Space Engineering, Thermal design handbook, Fluid Loops, spacecraft thermal control, heat exchangers, pumps, two‑phase flow, thermal analysis.

Related standards

Part 13 is one of 16 Parts in the Thermal design handbook series (Parts 1–16), including topics such as View factors, Heat Pipes (Part 8), Radiators (Part 9), Phase‑Change Capacitors (Part 10), Cryogenic Cooling (Part 14) and Thermal Protection System (Part 16) - useful cross-references for integrated spacecraft thermal design.

Standards Content (Sample)

SLOVENSKI STANDARD
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
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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.
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
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
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
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
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
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-
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: Nusselt number, Nu, vs. Reynolds number, Re, for fully developed
turbulent 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 Kays (1966) [101]. . 77
Figure 6-17: Influence coefficient, Z, vs. Reynolds number, Re, for fully developed
turbulent flow between parallel plates. Constant heat transfer rate. Results
are shown for different Prandtl numbers, Pr. Calculated by the compiler
after Kays (1966) [101]. . 77
Figure 6-18: Nusselt number, Nu , and influence coefficient, Z , vs. Reynolds number,
11 1
Re, for fully developed turbulent flow in concentric-circular-tube annuli. r /r
1 2
= 0,2. Constant heat transfer rate. Results are shown for different Prandtl
numbers, Pr. Calculated by the compiler after Kays (1966) [101]. . 78
Figure 6-19: Nusselt number, Nu , and influence coefficient, Z , vs. Reynolds number,
22 2
Re, for fully developed turbulent flow in concentric-circular-tube annuli. r /r
1 2
= 0,2. Constant heat transfer rate. Results are shown for different Prandtl
numbers, Pr. Calculated by the compiler after Kays (1966) [101]. . 78
Figure 6-20: Nusselt number, Nu , and influence coefficient, Z , vs. Reynolds number,
11 1
Re, for fully developed turbulent flow in concentric-circular-tube annuli. r /r
1 2
= 0,5. Constant heat transfer rate. Results are shown for different Prandtl
numbers, Pr. Calculated by the compiler after Kays (1966) [101]. . 79
Figure 6-21: Nusselt number, Nu , and influence coefficient, Z , vs. Reynolds number,
22 2
Re, for fully developed turbulent flow in concentric-circular-tube annuli. r /r
1 2
= 0,5. Constant heat transfer rate. Results are shown for different Prandtl
numbers, Pr. Calculated by the compiler after Kays (1966) [101]. . 79
-0.4
Figure 6-22: Nusselt number times Prandtl number to the minus 0.4 power, NuPr , vs.
Reynolds number, Re, for fully developed turbulent flow in helically coiled
tubes. The results are given for two values of the ratio, r/R, between the
cross-sectional radius and the coil radius. Constant heat transfer rate.
Calculated by the compiler after an experimental correlation obtained by
Seban & McLaughlin (1963) [162] from data for water. . 80
Figure 6-23: Thermal entry length Nusselt numbers, Nu, vs. non-dimensional axial
distance, x/D, for fully developed turbulent flow through a straight pipe of
circular cross section. Constant wall temperature. Pr = 0.01. Results are
shown for different Reynolds numbers, Re. Calculated by the compiler after
Kays (1966) [101]. . 80
Figure 6-24: Thermal entry length Nusselt numbers, Nu, vs. non-dimensional axial
distance, x/D, for fully developed turbulent flow through a straight pipe of
circular cross section. Constant wall temperature. Pr = 0.7. Results are
shown for different Reynolds numbers, Re. Calculated by the compiler after
Kays (1966) [101]. . 81
Figure 6-25: Ratio of thermal entry length Nusselt number, Nu , to Nusselt number for
x
fully developed turbulent flow, Nu, vs. non-dimensional axial distance, x/D.
Straight pipe of circular cross section. Constant heat transfer rate. Pr =
0.01. Results are shown for different Reynolds numbers, Re. Calculated by
the compiler after Kays (1966) [101]. . 81
Figure 6-26: Ratio of thermal entry length Nusselt number, Nux, to Nusselt number for
fully developed turbulent flow, Nu, vs. non-dimensional axial distance, x/D.
Straight pipe of circular cross section. Constant heat transfer rate. Re =
10 . Results are shown for different Prandtl numbers, Pr. Calculated by the
compiler after Kays (1966) [101]. . 82
Figure 6-27: Ratio of thermal entry length Nusselt number, Nu , to Nusselt number for
x
fully developed turbulent flow, Nu, vs. non-dimensional axial distance, x/D .
E
Parallel plates at distance 2D , one of them insulated. Constant heat
E
transfer rate. Also shown the influence coefficient, Z. Results are shown for
three different Prandtl numbers, Pr, and two Reynolds numbers, Re.
Calculated by the compiler after Kays (1966) [101]. . 82
Figure 6-28: Nusselt number, Nu, vs. Reynolds number, Re. Flow of a fluid having
constant physical properties over a constant temperature circular cylinder
whose axis is normal to the incoming flow. From ESDU 69004 (1969) [50]. . 84
Figure 6-29: Effect of variable fluid properties, (a) and (b), and of inclination angle, (c),
on the Nusselt number corresponding to the flow of a fluid over a constant
temperature cylinder. Nu (Nu ) can be deduced from Figure 6-28. From
b 90°
ESDU 69004 (1969) [50]. . 85
Figure 6-30: Guide for the selection of the curves given in Figure 6-31 and Figure 6-32
concerning in-line tube banks of different relative pitches. From ESDU
73031 (1973) [57]. . 86
Figure 6-31: Reference Nusselt number, Nu , for Pr = 1, as a function of Reynolds
r b
number, Re. In-line tube banks. See Figure 6-30 for the meaning of the
numbers which appear on the curves. From ESDU 73031 (1973) [57]. . 87
Figure 6-32: Reference Nusselt number, Nu , for Pr = 1, as a function of Reynolds
r b
number. Re. In-line tube banks. See Figure 6-30 for the meaning of the
numbers which appear on the curves. From ESDU 73031 (1973) [57]. . 88
Figure 6-33: Reference Nusselt number, Nur, for Prb = 1, as a function of Reynolds
number. Re. In-line tube banks. Staggered tube banks. From ESDU 73031
(1973) [57]. . 89
Figure 6-34: Effect of the Prandtl number, Pr , on the reference Nusselt number, Nu ,
b r
for both in-line and staggered tube banks. From ESDU 73031 (1973) [57]. . 89
Figure 6-35: The factor F to account for variable fluid properties. From ESDU 73031
(1973) [57]. . 90
Figure 6-36: The factor F accounting for abnormal number of rows vs. that number, N.
From ESDU 73031 (1973) [57]. . 90
Figure 6-37: The factor F accounting for the effect of yaw vs. the inclination angle, θ.
From ESDU 73031 (1973) [57]. . 90
Figure 6-38: The factor F for estimating the Nusselt number of the n-th row. From
ESDU 73031 (1973) [57]. . 91
Figure 7-1: Friction characteristics associated with four types of roughness geometry.
Notice that the equivalent roughness is different in every case. From
Reynolds (1974). . 96
Figure 7-2: Friction factor, λ , as a function of Reynolds number, Re, for different
c
values of the relative roughness, e/D: Cylindrical tubes of circular cross
section. From Idel'cik (1969) [97]. . 105
Figure 7-3: Correction factor, K, to be used when the cross section of the duct is not
circular. Laminar flow. K = 1 for turbulent flow through hydraulically smooth
ducts. From ESDU 66027 (1966) [46]. . 105
Figure 7-4: Boundary between short and long circular arc bends. From ESDU 67040
(1967) [47]. . 106
Figure 7-5: Boundaries between laminar, transitional and turbulent flows in long circular
arc bends. From ESDU 67040 (1967) [47]. . 106
Figure 7-6: Pressure loss coefficient per unit bend angle, c /θ, as a function of the
K
dimensionless radius of curvature of bend centerline, R/D, for different
values of Reynolds number, Re. Either circular or square cross section.
From ESDU 67040 (1967) [47]. . 107
Figure 7-7: Pressure loss coefficient, c , as a function of the dimensionless radius of
K
bend centerline, R/D, for different values of Reynolds number, Re. Laminar
flow through short circular arc bends. From ESDU 67040 (1967) [47]. . 108
Figure 7-8: Pressure loss coefficient, c , as a function of the dimensionless radius of
K
bend centerline, R/D, for different values of bend angle, θ. Turbulent flow
through short circular arc bends. Either circular or square cross section.
From ESDU 67040 (1967) [47]. . 109
Figure 7-9: Pressure loss coefficient, c , for short circular arc bends, having a short
K
downstream tangent of length, L , as a function of L /D, for different values
d d
of the dimensionless radius of bend centerline, R/D. Turbulent flow. Either
circular or square cross section. From ESDU 67040 (1967) [47]. . 110
Figure 7-10: The factor α1 to account for the aspect-ratio of the bend cross section.
From ESDU 67040 (1967) [47]. . 110
Figure 7-11: The factor α to account for the bend angle. From ESDU 67040 (1967)
[47]. . 111
Figure 7-12: Pressure loss coefficient, c , for single mitre bends, as a function of bend
K
angle, θ, for different values of the dimensionless length, L /D, of the
d
downstream tube. Turbulent flow. Either circular or square cross section.
From ESDU 67040 (1967) [47]. . 111
Figure 7-13: Factor β, which account for the interaction between two 90° -circular arc
bends-, as a function of the dimensionless distance between both bends,
L /D. From ESDU 68035 (1968) [49]. . 112
a
Figure 7-14: Factor β, which account for the interaction between two mitre bends, as a
function of the dimensionless distance between both bends, L /D. From
a
ESDU 68035 (1968) [49]. . 113
Figure 7-15: Total-pressure loss coefficient, c , as a function of Reynolds number,
Kt
Re 1, for different values of the area ratio, ψ. Enlargement with a duct
D
downstream 4D long. Uniform incoming flow at low Reynolds number.
From ESDU 72011 (1972) [54]. . 113
Figure 7-16: Different velocity profiles upstream of a sudden enlargement. From ESDU
72011 (1972) [54]. . 114
Figure 7-17: Total-pressure loss coefficient, c , as a function of area ratio, ψ.
Kt
Enlargement with a duct downstream 4D long. Numbers on curves indicate
the velocity profile in Figure 7-22 for which the curve applies. From ESDU
72011 (1972) [54]. . 114
Figure 7-18: Static-pressure loss coefficient, -c , as a function of area ratio, ψ.
Ks
Enlargement with a duct downstream 4D long. Numbers on curves indicate
the velocity profile in Figure 7-22 for which the curve applies. From ESDU
(1972) [54]. . 115
Figure 7-19: Total-pressure loss coefficient, c , as a function of Reynolds number,
Kt
Re , for different values of the area ratio, ψ. The pressure loss coefficient
D2
is expressed in terms of the dynamic pressure at clause 6. From Idel'cik
(1969) [97]. . 115
Figure 7-20: Reference values of the pressure loss coefficient, c , as a function of the
K
ratio, φ, of the area available for fluid flow to the total area of the duct cross
section. Perforated plates and orifices. From ESDU 72010 (1972) [53]. . 116
Figure 7-21: The factor α to account for the effect of plate thickness when t/d < 0,8. c
3 Ko
is given in Figure 7-19. From ESDU 72010 (1972) [53]. . 117
Figure 7-22: The factor α to account for the effect of plate thickness when t/d ≥ 0,8.
c is given in Figure 7-19. From ESDU 72010 (1972) [53]. . 118
K0,8
Figure 7-23: Comparison between the pressure loss coefficients, c , in the intermediate
K
region calculated by assuming either of the two extreme cases, fully-
separated or reattached orifice flow. From ESDU 72010 (1972) [53]. . 119
Figure 7-24: Reference pressure loss coefficient, c , as a function of porosity, φ.
Kr
Round-wire gauzes. From ESDU 72009 (1972) [52]. 119
Figure 7-25: Factor α to account for low Reynolds number effects in round-wire
gauzes. Reynolds number based on the wire diameter. From ESDU 72009
(1972) [52]. . 120
Figure 7-26: Reference pressure loss coefficient, c , as a function of Reynolds
Kr
number, Re, for diaphragm and butterfly valves fully open. Prepared by the
compiler after ESDU 69022 (1969) [51]. . 120
Figure 7-27: Factor α , which accounts for the partial opening of the valve, as a
fun
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