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