/ Engineering Note
Title: LCLS-II Cryoplant Flowmeter Sizing
Note Number: LCLSII-4.8-EN-0803
Author(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.

1Scope

2Venturi Flowmeter Fundamentals

3Summary of Flow-Meter Sizing Calculations:

4.References

5.APPENDIX

1Scope

This 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:-
  2. Gas Management Pannel [1]
  3. Inlet to 4.5 K Cold Box (HP, MP & LP Flow) [1]
  4. Ambient Vaporizer [2]
  5. Recovery Compressor [3]
  6. 4K Cold Box System (4K MCB) 30 K cold compressor return flow [4]
  7. 2K Cold Box System (SCB) [5]
  8. Liquid Helium Storage Dewar System (LHD) [6]
  9. Interface Box and Transfer Line System (ITL) [7]

2Venturi FlowmeterFundamentals

Figure 1: Geometric Profile of the Classical Venturi Tube [8]

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 theISO 5167-1 standard. Equation 1 can be rearranged for calculating differential pressure for a given mass flow rate

/ (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 =
K / Isentropic exponent
/ Pressure ratio = P2/P1

3Summary 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 / Description / Design Basis / Ref.
4K Cold Box- Bayonnet / FI22190 / 4K Cold Box System-30 K Flow from 2K Cold Box / Max Flow: Mode1: Sub-Atm Flow
Min Flow: Mode7: Sub-Atm Flow / [9]
2 K Cold Box / FI41200 / 2K Cold Box-30 K Flow Discharge / Max Flow: Mode1: Sub-Atm Flow
Min Flow: Mode7: Sub-Atm Flow / [9]
FI41500 / 2K Cold Box-4.5 K Supply from Dewar / Max Flow: Mode1: Sub-Atm Flow
Min Flow: Mode7: Sub-Atm Flow / [9]
Interface Box / FI51011 / 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 Box / Max Flow: Mode1, Max Capacity
Min Flow: Mode 8, 50% of Standby / [9]
FI21025 / MP Return from 4.5 K Cold Box / Max Flow: Mode5, Max Fill
Min Flow: Mode 8, 50% of Standby / [9]
FI21015 / LP Return from 4.5 K Cold Box / Max Flow: Mode5, Max Fill
Min Flow: Mode 8, 50% of Standby / [9]
FI21000 / Ambient Vaporizer Return / Max Flow: Mode3, Max Liq Flow
Min Flow: Mode1, Max Liq. Flow / [9]
FI71020 / Recovery Bypass / Max Capacity of Recovery Comp.
FI71030 / Recovery Discharge / Max Capacity of Recovery Comp.
/ Engineering Note
Title: LCLS-II Cryoplant Flowmeter Sizing
Note Number: LCLSII-4.8-EN-0803
Author(s): Viswanath Ravindranath / Page 1 of 10

Table 2: Summary of Cryoplant Flowmeters

Location / Valve / Description / Pipe 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 / 47.96
FI41500 / 2K Cold Box-4.5 K Supply from Dewar / 2 / 0.86 / 1.25 / 5 / 215 / 106.2
Interface Box / FI51011 / Mix Valve for 4K Supply / 1 / 0.7 / 5 / 300 / 60 / 129.54
FI51013 / Mix Valve for LTTI Supply / 1 / 0.7 / 5 / 300 / 30 / 30.63
FI51015 / 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 / 20.56
FI21025 / MP Return from 4.5 K Cold Box / 8 / 3.8 / 2.37 / 306 / 573 / 32.58
FI21015 / LP Return from 4.5 K Cold Box / 12 / 5.7 / 1.1 / 306 / 720 / 22.30
FI21000 / Ambient Vaporizer Return / 6 / 2.6 / 1.1 / 306 / 150 / 22.78
FI71020 / Recovery Bypass / 1 / 0.5 / 12 / 300 / 36 / 75.68
FI71030 / Recovery Discharge / 1.25 / 0.58 / 13 / 300 / 36 / 43.13

4.References

1. 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

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 Note
Title: LCLS-II Cryoplant Flowmeter Sizing
Note Number: LCLSII-4.8-EN-0803
Author(s): Viswanath Ravindranath / Page 1 of 10

APPENDIX

Table A1 : 4K Cold Box 30 K Return Flow Venturi Flowmeter Calculations
Table A2 : 2K Cold BoxVenturi Flowmeter Calculations
Table A3 : Interface Box Venturi Flowmeter Calculations
Table A4 : Warm Helium Gas Flowmeter Calculations