Engineering NoteTitle: LCLS-II Cryoplant Flowmeter SizingNote Number: LCLSII-4.8-EN-0803Author(s): Viswanath Ravindranath Page 1 of 10
Originator: Viswanath Ravindranath, SLAC Cryogenics Integration Group
Approver: Hongyu Bai, SLAC Cryogenics Integration Group Leader
Approver: Dana Arenius, JLAB Cryogenics Plant CAM
Approver: Marc Ross, Cryogenic System Manager
Revision History:Revision Date Released Description of Change
R0 Month Day, Year Original release.
1 Scope.....................................................................................................................................22 Venturi Flowmeter Fundamentals.......................................................................................23 Summary of Flow-Meter Sizing Calculations:....................................................................44. References............................................................................................................................65. APPENDIX.............................................................................................................................7
Engineering NoteTitle: LCLS-II Cryoplant Flowmeter SizingNote Number: LCLSII-4.8-EN-0803Author(s): Viswanath Ravindranath Page 2 of 10
1 ScopeThis engineering note establishes the minimum requirements for the helium gas venturi flow meters to be used for measuring flows in the following location
1. Warm gas helium flow meters:-
a. Gas Management Pannel [1]
b. Inlet to 4.5 K Cold Box (HP, MP & LP Flow) [1]
c. Ambient Vaporizer [2]
d. Recovery Compressor [3]
2. 4K Cold Box System (4K MCB) 30 K cold compressor return flow [4]
3. 2K Cold Box System (SCB) [5]
4. Liquid Helium Storage Dewar System (LHD) [6]
5. Interface Box and Transfer Line System (ITL) [7]
2 Venturi Flowmeter Fundamentals
Figure 1: Geometric Profile of the Classical Venturi Tube [8]
Engineering NoteTitle: LCLS-II Cryoplant Flowmeter SizingNote Number: LCLSII-4.8-EN-0803Author(s): Viswanath Ravindranath Page 3 of 10
The classical venturi tube is made of three sections namely, Section A is the entrance cylinder, Section B is conical convergent section, Section C is the cylindrical throat and Section E is the conical divergent section. The minimum recommended dimension and requirements for these four sections is specified in Sec.10.1.2 through 10.1.4 of the -ISO 5167-1 standard.
The following equation for calculating the flow through a venturi-meter for a measured differential pressure is provided in Sec.5 of the ISO 5167-1 standard. Equation 1 can be rearranged for calculating differential pressure for a given mass flow rate
mv=C
√1−β4ϵ π
4d2 √2∆ P ρ1
(1)
where,
C Discharge Coefficient, C = 0.995 for machined convergent section
β Diameter ratio, d/D
d Venturi throat diameter
D Upstream internal pipe diameter
ΔP Differential Pressure
ρ1 Fluid density at the venturi inlet conditions (P1, T1)
ε Expansion factor = ϵ=√( K τ2K
K−1 )( 1−β4
1−β4 τ2K )(1−τ
K−1K
1−τ )K Isentropic exponent
τ Pressure ratio = P2/P1
Engineering NoteTitle: LCLS-II Cryoplant Flowmeter SizingNote Number: LCLSII-4.8-EN-0803Author(s): Viswanath Ravindranath Page 4 of 10
3 Summary of Flow-Meter Sizing Calculations:Table1 summarizes the design basis used for the sizing of the flow meters. Table 2 provides a summary of the flow-meter calculations. The calculation details are provided in the Appendix section.
Table 1: Design Basis for Flow-Meters Sizing
Location Valve DescriptionDesign Basis Ref.
4K Cold Box- Bayonnet FI22190 4K Cold Box System-30 K Flow
from 2K Cold BoxMax Flow: Mode1: Sub-Atm FlowMin Flow: Mode7: Sub-Atm Flow
[9]
2 K Cold BoxFI41200 2K Cold Box-30 K Flow
DischargeMax Flow: Mode1: Sub-Atm FlowMin Flow: Mode7: Sub-Atm Flow
[9]
FI41500 2K Cold Box-4.5 K Supply from Dewar
Max Flow: Mode1: Sub-Atm FlowMin Flow: Mode7: Sub-Atm Flow
[9]
Interface BoxFI51011 Mix Valve for 4K Supply Cool Down Flow [11]FI51013 Mix Valve for LTTI Supply Cool Down Flow [11]FI51015 Mix Valve for HTTS Supply Cool Down Flow [11]
Warm Piping
FI21045 HP Supply to 4.5 K Cold BoxMax Flow: Mode1, Max CapacityMin Flow: Mode 8, 50% of Standby
[9]
FI21025 MP Return from 4.5 K Cold BoxMax Flow: Mode5, Max FillMin Flow: Mode 8, 50% of Standby
[9]
FI21015 LP Return from 4.5 K Cold BoxMax Flow: Mode5, Max FillMin Flow: Mode 8, 50% of Standby
[9]
FI21000 Ambient Vaporizer Return Max Flow: Mode3, Max Liq FlowMin Flow: Mode1, Max Liq. Flow
[9]
FI71020 Recovery Bypass Max Capacity of Recovery Comp.FI71030 Recovery Discharge Max Capacity of Recovery Comp.
Engineering NoteTitle: LCLS-II Cryoplant Flowmeter SizingNote Number: LCLSII-4.8-EN-0803Author(s): Viswanath Ravindranath Page 5 of 10
Table 2: Summary of Cryoplant Flowmeters
Location Valve DescriptionPipe Size
[NPS]
Venturi Throat Size [in]
Pin [atm]
Tin [K]
Max Flow [g/s]
ΔP [in. H2O]
4K Cold Box- Bayonnet FI22190 4K Cold Box System-30 K Flow from 2K
Cold Box 4 1.77 1.2 30 215 47.96
2 K Cold Box FI41200 2K Cold Box-30 K Flow Discharge 4 1.77 1.2 30 215 47.96FI41500 2K Cold Box-4.5 K Supply from Dewar 2 0.86 1.25 5 215 106.2
Interface BoxFI51011 Mix Valve for 4K Supply 1 0.7 5 300 60 129.54FI51013 Mix Valve for LTTI Supply 1 0.7 5 300 30 30.63FI51015 Mix Valve for HTTS Supply 1 0.7 5 300 60 129.54
Warm Piping FI21045 HP Supply to 4.5 K Cold Box 8 3.8 19.45 310 1310 20.56FI21025 MP Return from 4.5 K Cold Box 8 3.8 2.37 306 573 32.58FI21015 LP Return from 4.5 K Cold Box 12 5.7 1.1 306 720 22.30FI21000 Ambient Vaporizer Return 6 2.6 1.1 306 150 22.78FI71020 Recovery Bypass 1 0.5 12 300 36 75.68FI71030 Recovery Discharge 1.25 0.58 13 300 36 43.13
4. References1. LCLS-II Main Compressor System (MCS) P&ID-79120-0002
2. LCLS-II Cooldown/Clean-up Distribution System (CDUS) P&ID-79120-0002
3. LCLS-II He Recovery System (HRS) P&ID-79520-0000
4. LCLS-II Main 4.5K Cold Box Test P&ID-79221-0001
5. LCLS-II 2K Cold Box with Cold Compressors (SCB) P&ID-79222-0000
6. LCLS-II LHe Storage Dewar System (LHD) P&ID-79720-0001
7. LCLS-II 4K/2K Plants Interfaces Boxes P&ID-79420-0000
8. Measurement of Fluid flow by means of pressure differential devices-Part 1: ISO 5167-1 (1991)
9. Technical Specification for the Procurement of CHL 4.5K Cold Box System – LCLS-II-4.8-CT-0284
Engineering NoteTitle: LCLS-II Cryoplant Flowmeter SizingNote Number: LCLSII-4.8-EN-0803Author(s): Viswanath Ravindranath Page 6 of 10
10. Technical Specification for 2K Cold Compressors – 79222-S001
11. LCLS-II CDS DB Mixing Chamber Cooldown Rate Control-LCLS-II-4.9-EN-0291
Engineering NoteTitle: LCLS-II Cryoplant Flowmeter SizingNote Number: LCLSII-4.8-EN-0803Author(s): Viswanath Ravindranath Page 7 of 10
APPENDIX
Table A1 : 4K Cold Box 30 K Return Flow Venturi Flowmeter Calculations
Engineering NoteTitle: LCLS-II Cryoplant Flowmeter SizingNote Number: LCLSII-4.8-EN-0803Author(s): Viswanath Ravindranath Page 8 of 10
Table A2 : 2K Cold Box Venturi Flowmeter Calculations
Engineering NoteTitle: LCLS-II Cryoplant Flowmeter SizingNote Number: LCLSII-4.8-EN-0803Author(s): Viswanath Ravindranath Page 9 of 10
Table A3 : Interface Box Venturi Flowmeter Calculations
Engineering NoteTitle: LCLS-II Cryoplant Flowmeter SizingNote Number: LCLSII-4.8-EN-0803Author(s): Viswanath Ravindranath Page 10 of 10
Table A4 : Warm Helium Gas Flowmeter Calculations