EMRP 2009 Metrology for Liquefied Natural Gas (LNG) ENG03 LNG. (WP1-Tasks and Final report)

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1 CESAME EXADEBIT SA CESAME-EXADEBIT EXADEBIT S.A. 43 route de l Aérodrome F Poitiers Cedex Tél. : 33(0) Fax : 33(0) cesame@cesame-exadebit.fr EMRP 2009 Metrology for Liquefied Natural Gas (LNG) ENG03 LNG Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements (WP1-Tasks and Final report) A.STRZELECKI A.OUERDANI Y.LEHOT C.WINDENBERGER J.P. VALLET March 2013 The research leading to the results discussed in this report has received funding from the European Metrology Research Program (EMRP). The EMRP is jointly funded by the EMRP participating countries within Euramet and the European Union EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 1/72

2 Summary 1. INTRODUCTION 3 2. AIR BASED EXPERIMENTS [D1.4.4] Introduction Means of measurements Description of the reference facility for flowrate measurements at CESAME EXADEBIT Description of the simplified DN80 Cryogenic LDV Measurement Package and testing conditions Description of the seeding system Velocity measurements by means of the Laser Doppler Velocimeter Measurement and acquisition of test parameters (Pressure, Temperature, Flow velocity, reference flow rate) Measurement conditions and conduction testing procedure Pressure loss of the LDV cryogenic measurement system Mean velocity and turbulence profiles Analysis of the LDV measurements Method 1: Determination of the optimum limits of integration Method 2: Determination of the correlation function FLOWRATE MEASUREMENT BY MEANS OF THE LDV CRYOGENIC SYSTEM Determination of the volume flowrate by means of the integration method Determination of the volume flowrate by means of a local velocity measurement Conclusion DESIGN OF A CALIBRATION UNIT [D.1.4.5] Introduction Interfringe Calibration Doppler frequency Calibration Assessment of the uncertainty Assessment of the uncertainties for all measurands [D.1.4.4] Assessment of the uncertainty on the discharge coefficient Assessment of the uncertainty on the reference mass flowrate Assessment of the uncertainty on the reference volume flowrate Assessment of the uncertainty on the reference velocity (v ref ) Assessment of the uncertainty on the velocity measured by the LDV Uncertainty on the flowrate measurement by integration of the velocity profile (Method 1) Uncertainty on the flowrate measured by means of a localized velocity measurement (Method 2) LNG FLOWRATE MEASUREMENTS BY MEANS OF A LDV [D.1.4.5] Introduction Industrial modus for LNG flowrate measurements with a LDV Proposed design of a cryogenic LDV measurement package for different volume flowrates and pipe size ranks Nominal diameter D of the Cryogenic LDV measurement system Pressure loss Size of the Cryogenic LDV Measurement System Choice of method Assessment of the uncertainty Risk assessment of the LNG flowrate measurement with a LDV CONCLUSION BIBLIOGRAPHY 44 EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 2/72

3 1. INTRODUCTION The overall objective of this Joint Project Research METROLOGY for LNG is to contribute to a significant reduction of uncertainty in the determination of transferred energy in LNG custody transfer processes. The more specific objectives of this JRP can be summarized as follows: WP1 Developing traceability for LNG flow meters WP2 Testing and evaluating LNG quantity metering systems WP3 Improving LNG composition measurement systems WP4 Reducing uncertainties in LNG density and calorific value calculations WP5 Contributing to measurement guidelines, written standards and legal metrology. The project consists of five technical work packages, one creating impact and one management work package. The first four work packages will improve and develop new metrological infrastructure for LNG measurements. The proposed work can be summarized by the development of new measurement standards, methods and procedures and by the assessment of state-of-theart measurement systems through reviewing of design principles, analyzing feedback and real data from industrial users and by performing laboratory and in-field testing. The results of work packages 1-4 will be used in work package 5 to provide input to the development of international standards, guidelines and regulations. Custody transfer operations consist of measuring the energy of transferred LNG by measuring volume, density and gross calorific value. For completeness it must be added that the measurement of the energy of the gas displaced during the transfer is also an integral part of the custody transfer process. Better understood and improved volume measurements are addressed in WP1 and WP2. The density measurement problem is addressed in WP4, and WP3 deals with improving techniques to determine the LNG composition and thereby the gross calorific value. A very promising alternative to the state-of-the-art static volume measurements is the dynamic principle of flow metering. WP1 addresses the great technological challenge of creating traceability for LNG flow meters that currently does not exist anywhere in the world. Providing a direct link to SI with a very small uncertainty and disseminating that link to a range of flows has never been done before and will be a unique achievement. The project will develop the know-how to ultimately provide traceability to the full range of LNG flows. The goal of this work package is the development of metrologically-sound traceability schemes for LNG flow metering. A novel cryogenic flow metering technology, Laser Doppler Velocimetry (LDV), will be explored as promising an alternative to ultrasonic and coriolis flow metering. LADG will perform a feasibility study of LDV technology applied to LNG flow metering. The study will focus on the technological challenges and solutions for extending the LDV method to cryogenic temperatures, and on the estimation of the uncertainty that can be realistically achieved with such a system. EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 3/72

4 A first report (May 2011) [1] presented a synthesis of the definition of the needs for LNG flowrate measurements and a literature survey concerning the technical feasibility of a cryogenic LDV measurement package. Flowrate measurement based on LDV is a mature technology for gaseous natural gas. The German National Laboratory pigsar achieved with a LDV technology the primary flowrate standard for natural gas under high pressure up to 50 bar and flowrates up to 6500 m3/h, with a relative flowrate uncertainty of 0.1 % [6]. Through a literature survey, this report evaluated the conditions for using this LDV technology to measure LNG flowrates: seeding system, optical access, interfringe calibration and flow measurement uncertainty. A second report (July 2012) [2] presented the technical feasibility study for a cryogenic LDV metering system: numerical flow simulations have been performed to optimise the internal shape (convergent, throat, divergent) of the measurement package design of the optical windows design of two systems of seeding design of an interfringe calibration unit. The cryogenic LDV measurement system was manufactured and allows the performance of measurements in the LNG unloading conditions on a test bench in the laboratory CESAME EXADEBIT with a substitution fluid (dry air). Similarity of the Reynolds number was used to simulate the LNG flow conditions with pressurized air at CESAME. This report presents: the simplified LDV Cryogenic Package Measurement, the seeding system and the reference loop for flowrate measurements at CESAME EXADEBIT [D1.4.4] air-based experiments with Reynolds number simulating LNG conditions [D1.4.4] the assessment of the flowrate accuracy [D1.4.4] the conclusion concerning the feasibility to perform flowrate measurements on cryogenic fluids by means of LDV [D1.4.5]. EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 4/72

5 2. AIR BASED EXPERIMENTS [D1.4.4] 2.1. Introduction CESAME EXADEBIT studied the possibility of measuring the flowrate of LNG with the cryogenic LDV measuring system by means of a velocity measurement based on the laser Doppler velocimetry in cryogenic conditions. To achieve this goal, two possibilities are considered: integration of the velocity profile in a section known establish a relation between a measured local velocity and the volume flowrate. In the first case, it is necessary to define the measuring section adapted to measure the velocity profile and to find a robust criteria for defining the limits of integration as a function of the pipe Reynolds number. In the second case, the dependence of the relationship between the local velocity and the flowrate must be considered as a function of the Reynolds number. To achieve these objectives, the flow in the measurement system has been characterized on the calibration loop M1 of the CESAME EXADEBIT laboratory by means of velocity measurements using a LDV. For these experiments, the absolute pressure was in the range 1.5 to 10 bar and the pipe velocity in the range 1-57 m.s -1. These test conditions allowed the achievement of pipe Reynolds numbers between 10 4 and The experimental methods used and the results of velocity measurements are presented in this section. EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 5/72

6 2.2. Means of measurements Description of the reference facility for flowrate measurements at CESAME EXADEBIT The pressurized calibration facility for medium and high flowrates at CESAME EXADEBIT can generate flowrates from 8 m 3 /h to m 3 /h (normal conditions). A set of twelve Venturi nozzles (nominal flowrate: 1.5 to 1000 m 3.h -1.bar -1 ) operating in sonic conditions is used for the determination of the standard mass flowrate. The test pressure range is from 1 bar up to 45 bar (absolute). Compressed dry air stored in a 110 m 3 vessel under 200 bar (absolute) is used as the test fluid. The air coming from the storage vessel goes through the valves and the heating control system. This one adjusts the suitable temperature and pressure upstream the nozzles automatically. The pipe lines bear the reference nozzles chosen according to the flow patterns to be generated for the tests. The longest testing pipeline is 50 m long with nominal diameters from DN25 up to DN300. The meter under test is placed on a pipeline downstream the set of nozzles. This configuration allows a comparison between the reference and tested device mass flows. The pressure and the temperature can be measured at the level of the meter in test in order to determine the volume flowrate going through. The real gas effects are taken into account by applying compressibility factor corrections to the thermodynamic conditions where the measurement is taken. A set of control valves placed downstream the tested instrument allows adjustment of the suitable back pressure for calibration [between 1.5 to 10 bar (absolute pressure) for these tests]. This operation is automated and controlled from a board located in a room near the test rig. Data acquisition and calculations are performed by an automatic computing system located in the same control room. These nozzles are traceable to National Standards by mean of a (P, V, T, time) method. EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 6/72

7 Fig. 1 Diagram of the calibration facility for medium and high flowrates at CESAME EXADEBIT EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 7/72

8 Description of the simplified DN80 Cryogenic LDV Measurement Package and testing conditions The model is composed of three parts: - The cryogenic seeding part - The conditioning part (containing the convergent) with the measuring cross-section - The divergent part. The seeding part is equipped with an access for the seeding probes in cryogenic conditions, and with two windows for particles visualization. The conditioning part is provided with windows which allow passage of laser beams for measuring the velocity profile at the exit of the convergent. The downstream part of the Cryogenic LDV Measurement Package contains the divergent. These three parts are located inside a vacuum chamber to ensure thermal insulation. The entire model is equipped with pressure and temperature taps: - Upstream the convergent (P, T) - Throat of the convergent (P) - Downstream the divergent (P, T). Fig. 2 Description of the simplified Cryogenic LDV Measurement Package EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 8/72

9 Fig. 3 Cryogenic LDV Measurement Package (3D model horizontal cut) EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 9/72

10 Description of the seeding system For these tests with air under pressure up to 10 bar seeding is done by generating micronic particles of DHES Di (2-ethylhexyl) sebacate, sebacic acid (photo below) 8D upstream the Cryogenic LDV Measurement Package. Fig. 4 Seeding System operating up to 10 bar maximum working backpressure EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 10/72

11 Velocity measurements by means of the Laser Doppler Velocimeter The velocity profiles are measured by means of a Laser Doppler Velocimeter DANTEC (Figure 6) in the backscattering mode (Figure 5) with the following specifications: - Wavelength of the laser line = 532 nm green line of a frequency doubled Nd:YAG laser - Focal length = 160 mm - System configuration = backscattering mode - Data acquisition and signal processing = DANTEC BSA Flow Software (Figure 7) - Traverse system controlled from the PC running BSA Flow Software for laser displacements - Size of the measurement volume: l = mm and L = mm - Interfringe spacing = µm. Fig. 5 Backscatter configuration Fig. 6 LDV System in operation EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 11/72

12 Fig. 7 Data acquisition and signal processing EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 12/72

13 Measurement and acquisition of test parameters (Pressure, Temperature, Flow velocity, reference flow rate) The mean and the RMS velocity profiles are measured in a specific cross-section downstream the throat of the convergent of the Cryogenic LDV Measurement Package for each condition below: Upstream convergent Pressure P bar(a) 1.5 Nominal Velocity at the throat of the convergent without seeding v m.s -1 Reynolds number in the pipe (D = 80 mm) Re D Mass flowrate through the sonic nozzles Q m kg.s E E E E E E E E E Table 1: Measurement conditions In addition to the measurement of the mean and the RMS velocity profiles, the following physical quantities are measured: - Mass Flowrate generated by the reference nozzles chosen according to the flow patterns to be generated for the tests - Upstream nozzles Pressure (bar absolute) and Temperature ( C) - Upstream convergent Pressure (bar absolute) and Temperature ( C) - Differential Pressure (bar) between upstream and the throat of the convergent - Downstream divergent Pressure (bar absolute) and Temperature ( C). EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 13/72

14 Measurement conditions and conduction testing procedure Measurements conditions The testing pipeline (diameter D = 80 mm) is 34D long upstream and 18D long downstream the Cryogenic LDV Measurement Package. Due to the spacing between the two laser beams and the focal length, it is not possible to measure complete velocity profiles within 16 mm from the exit of the throat of the convergent. Furthermore, to allow the passage of the laser beams, the measurement section is larger (80 mm) that the section of the throat (d = 40 mm). Therefore, velocity profiles have been measured between 16 mm and 24 mm from the outlet of the throat with a step of 2 mm, from -40 mm to 40 mm (Y-axis) relative to the axis of the convergent (X-axis). In order to extrapolate the velocity profiles at the exit of the throat, for each test the velocity on the axis (X-axis) was measured between 12mm and 28 mm from the exit of the throat Testing procedure a) Convergent calibration without seeding C D = f(re d ) curve: For each of the test conditions, the mass flowrate is imposed through sonic nozzles and the upstream pressure is kept constant. The suitable back pressure for each test is adjusted by mean of a set of control valves placed downstream the Cryogenic LDV Measurement Package. When the flowrate is established, the differential pressure between the inlet and the outlet of the convergent of the Cryogenic LDV Measurement Package is measured without seeding for different Reynolds numbers. In this case, the flowrate measured by means of the sonic nozzle is the reference flowrate, and is used to calibrate the flowrate measured with the differential pressure device of the convergent. If we assume that this flowrate measurement is similar to a venturi tube method, from the standard ISO (venturi tubes), the mass flowrate is expressed: Q m = C D ε 1 1 β 4 πd 4 2 2ρ P The calibration curve C D = f(re d ) of the differential device is plotted on Figure 8. This calibration curve of the discharge coefficient C D versus the throat Reynolds number is used with a process of iterative calculation to determine the total mass flowrate (air + seeding) flowing through the Cryogenic LDV Measurement Package. The measurement uncertainty of the total reference flowrate is evaluated in the paragraph 5.2. EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 14/72

15 C D Convergent calibration curve C D =f(re d ) E E E E E E E E E+06 Re d Fig. 8 Discharge coefficient of the convergent C D versus the throat Reynolds number - Calibration curve b) Differential Pressure and velocity profile measurements at the throat of the convergent with seeding: For each of the test condition, when the flowrate is established with seeding, the velocity profile is measured a few millimetres downstream the throat of the convergent by mean of the LDV system (see 2.3 and 2.4). Simultaneously, the differential pressure is measured between the inlet and outlet of the convergent of the Cryogenic LDV Measurement Package. From the calibration curve previously determined, for each of the test conditions, the measurement of the differential pressure is used to calculate the Reference Mass Flowrate at the throat of the convergent. The integration of the velocity profile is used to calculate the flowrate measured by the Cryogenic LDV Measurement Package (see 2.5). EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 15/72

16 2.3. Pressure loss of the LDV cryogenic measurement system The average total pressure loss P for the Cryogenic LDV Measurement system is expressed as a fraction K of the dynamic throat velocity: P K = 1 2 ρ v d 2 The total pressure loss coefficient of the LDV measurement system is measured during the tests for a throat Reynolds number value between 5x10 4 and 1.5x10 6. The mean value of the pressure loss coefficient is K = This value is of the same order of magnitude as that of a venturi with a cone angle of 7 and a beta ratio β = 0.5. As a reminder, the non-recoverable pressure loss (without the Moody loss) for this type of venturi is K =0.2 and 10 times less than that of a thin plate orifice Mean velocity and turbulence profiles The velocity profiles (Mean and RMS value) for all the tested flow conditions (Pressure = 1.5; 5; 10 bar and throat mean reference velocity = 5; 20; 57 m.s -1 ) are presented in Annex 1. Only typical results are presented in this section. Figure 9 presents the influence of the throat velocity (V d = 5; 20; 57 m.s -1 ) on the mean velocity profiles V/V axis = f(r/r) downstream the throat (X = 16 mm) and for an absolute pressure P = 5 bar. All the mean velocity profiles are superimposed except on the outside of the left shear zone. This defect may be due to a leakage problem in the body of the model. The central portions of the velocity profiles are flat and show the action of the convergent. The same characteristics are found for other pressures tested (Figure 11). For higher pressures and Reynolds numbers, the flat region increases and the shear zone decreases. This result demonstrates that the influence of the Reynolds number on the velocity profile decreases with this increase. Figure 10 presents the influence of the throat velocity (V d = 5; 20; 57 m.s -1 ) on the RMS velocity profiles V rms /V axis = f(r/r) downstream the throat (X = 16 mm) and for an absolute pressure P = 5 bar. All the RMS velocity profiles are very well superimposed. The maximum of the velocity fluctuation corresponds to the zone of maximum shear of the mean velocity profile and is located on a cylinder of the same diameter as the throat, d = 40 mm. The same characteristics are found for other pressures tested (Figure 12). EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 16/72

17 Mean Velocity Profiles (Pressure = 5 bar) 5 ms-1 20 ms-1 57 ms v (16mm) /v axis (16mm) r/r Fig. 9 Influence of the throat velocity on the mean velocity profiles downstream the throat (X = 16 mm); absolute pressure = 5 bar; V d = 5; 20; 57 m.s -1 (--- throat diameter) Turbulence Profiles (Pressure = 5 bar) ms-1 20 ms-1 57 ms-1 Série4 Série5 v RMS (16mm) /v axis (16mm) (%) r/r Fig. 10 Influence of the throat velocity on the RMS velocity profiles downstream the throat (X = 16 mm); absolute pressure = 5 bar; V d = 5; 20; 57 m.s -1 (--- throat diameter) EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 17/72

18 Mean Velocity Profiles (20 m.s -1 ) 1.2 Pressure 1.5 bar Pressure 5 bar Pressure 10 bar v (16 & 24 mm) /v axis (16 & 24 mm) r/r Fig. 11 Influence of the absolute pressure on the mean velocity profiles downstream the throat; absolute pressure = 1.5; 5; 10 bar; V d = 20 m.s -1 (--- throat diameter) Turbulence Profiles (20 m.s -1 ) 120 Pressure 1.5 bar Pressure 5 bar Pressure 10 bar v RMS (16 & 24 mm) /v axis (16 & 24 mm) (%) r/r Fig. 12 Influence of the absolute pressure on the RMS velocity profiles downstream the throat; absolute pressure = 1.5; 5; 10 bar; V d = 20 m.s -1 (--- throat diameter) EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 18/72

19 2.5. Analysis of the LDV measurements Two methods are examined to determine the volume flowrate from velocity measurements performed by the LDV: Integration of the velocity profile measured downstream of the throat Calculation of the volume flowrate from a local velocity measured downstream of the throat. For the first method, the volume flowrate is obtained by integrating the flow velocity across section S where R is the radius: Q V R = 2π v(r)rdr For this method, it is necessary to find a criterion for determining the limits R of integration. The method of defining this criterion will be presented. For the second method, the basic idea of the previous designed convergent is to get very symmetrical velocity profiles to allow a very repeatable and fast profile measurement. Once the boundary layer has been measured, the volume flowrate measurement can be reduced to a single point measurement (center line velocity measurement): 0 Q V = π R 2 v For a given Reynolds number, the output velocity is given by the relation 4Q v = π d and the ratio between the velocity on the axis v axis (measured by the LDV system) and the output velocity v is a constant function of the Reynolds number Re d with v v axis = V 2 A(Re d ) Re v dρ µ = = d 4 Q m πµ d These relations allow the calculation of the volume flowrate from the velocity measured at one point downstream the throat on the axis of the pipe. 2 Q = π R v = V π R 2 v axis A(Re d ) To implement this second method, it is necessary to establish the correlation function between the volume flowrate and the local velocity measured and the influence of the Reynolds number. EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 19/72

20 Method 1: Determination of the optimum limits of integration In all cases tested (throat Reynolds number between 5x10 4 and 1.5x10 6 ), the reference flowrate and the velocity profile measured by the LDV are determined. The integration limit R 0 is obtained by an iterative calculation on the value of R that allows the finding of the reference flowrate with a residue less than From the results obtained, the influence of the throat Reynolds numbers on the optimal value R o is studied and presented in Annex 2 and 3 of the report. Only typical results are presented in this section. Figures 13 and 14 show that the maximum of the velocity fluctuation coincides with the optimal limit R o of integration and is located close on a cylinder of the same diameter as the throat, d = 40 mm. The same characteristics are found for other pressures tested. Figures 15 and 16 present the optimal integration limits versus the throat Reynolds number respectively for a pressure P = 5 bar and all the pressures tested in the experiments (P = 1.5; 5; 10 bar). In the latter case, the range of Reynolds numbers tested extends from 5x10 4 to 1.5x10 6. For each pressure, tables A2, A4, A6 (Annex 2) present the mean value of the optimal integration limit and the dispersion. For all pressures, the mean value of the optimal integration limit R 0 /R ranges between and and the dispersion between 1 to 2%. If the lowest Reynolds numbers of the order of 10 4 are not taken into account, the optimal integration limit is 1.03 and the dispersion 1%. If we consider that these results are obtained for Reynolds numbers between 10 4 and 10 6 and from an industrial point of view the Reynolds numbers are rather in the range of 10 7 [2], we can predict the dispersion in these conditions will be greatly reduced. Indeed, for large Reynolds numbers, the velocity profiles are self-similar, and the dispersion of the optimal integration limits will be reduced. EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 20/72

21 Mean Velocity Profile (Pressure = 5 bar) ms-1 Integration Limits Série2 1.0 v (16mm) /v axis (16mm) Fig Velocity profiles 16 mm downstream the throat and position of the optimal integration limits (green lines) to calculate the volume flowrate using the velocity profile s integration method; absolute pressure = 5 bar; V d = 20 m.s -1 (--- throat diameter) r/r Turbulence Profile (Pressure = 5 bar) ms-1 Integration Limits Série2 v RMS (16mm) /v a xis (1 6mm) (%) Fig. 14 RMS velocity profiles 16 mm downstream the throat and position of the optimal integration limits (green lines) to calculate the volume flowrate using the velocity profile s integration method; absolute pressure = 5 bar; V d = 20 m.s -1 (--- throat diameter) r/r EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 21/72

22 (Optimal Integration Limits)/R = f(re d ) Pressure = 5 bar 1.2 (Optimal Integration Limits)/R Re d 0.0E E E E E E E E E+05 Fig. 15 Position of the optimal integration limit (Optimum limit/ Throat diameter) versus the throat Reynolds number; absolute pressure = 5 bar (Optimal Integration Limits)/R = f(re d ) (Optimal Integration Limits)/R E E E E E E E E E+06 Fig. 16 Position of the optimal integration limit (Optimum limit/ Throat diameter) versus the throat Reynolds number; absolute pressure = 5; 10 bar Re d EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 22/72

23 Method 2: Determination of the correlation function In all cases tested (throat Reynolds number Re d between 5x10 4 and 1.5x10 6 ), the reference flowrate Q vref, the mean velocity at the throat section V ref mean and the mean axial velocity V axis measured 16 mm downstream the throat by the LDV are determined. The influence of the throat Reynolds numbers on the ratio V axis /V ref mean = A(Re d ) is presented in Annex 2 and 3 of the report. Only typical results are presented in this section. Figures 17 and 18 present the ratio V axis /V ref mean versus the throat Reynolds number Re d respectively for a pressure P = 5 bar and all the pressure tested in the experiments (P = 1.5; 5; 10 bar). In the latter case, the range of Reynolds numbers tested extends from 5x10 4 to 1.5x10 6. For each pressure, tables A2-A4-A6 (Annex 2) present the mean value of the ratio V axis /V ref mean and the dispersion. For all pressures, the ratio V axis /V ref mean ranges between and and the dispersion between 0.5 to 2%. If the lowest Reynolds numbers of the order of 10 4 are not taken into account, the mean ratio is of the order of 1.01 and the dispersion 0.5 or 1%. The measurement point at Re d =5x10 5 seems to be erroneous and must be checked with further experiments. This point is removed from the analysis. If we take into account that these results are obtained for Reynolds numbers between 10 4 and 10 6 and from an industrial point of view the Reynolds numbers are rather in the range of 10 7 [2], we can predict the dispersion in these conditions will be also as in Method 1 greatly reduced. Indeed, for large Reynolds numbers, the velocity profiles are self-similar, and the dispersion of the correlation function V axis /V ref mean = A(Re d ) will be reduced. EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 23/72

24 v axis (16mm) /v mean ref = f(re d ) Pressure = 5 bar v axis (16mm) /v mean ref E E E E E E E E E+05 Fig. 17 Axial Mean Velocity (V axis / V mean ref ) 16mm downstream the throat versus the throat Reynolds number; absolute pressure = 5 bar Re d v axis (16 mm) /v ref throat = f(re d ) 1.2 v axis (16 mm) /v ref throa t E E E E E E E E E+06 Fig. 18 Axial Mean Velocity (V axis / V mean ref ) 16mm (5 and 10 bar tests) downstream the throat versus the throat Reynolds number; absolute pressure = 5; 10 bar Re d EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 24/72

25 3. FLOWRATE MEASUREMENT BY MEANS OF THE LDV CRYOGENIC SYSTEM From the measurement of the mean velocity by means of the LDV, two methods are available to measure the flowrate with the cryogenic LDV measurement system: Method 1 by integrating the velocity profile Method 2 by correlating the flowrate with a localized velocity measurement Determination of the volume flowrate by means of the integration method For the integration method, the volume flowrate is obtained by integrating the flow velocity across a section S where R is the radius of the section Q V = R 2π v(r)rdr 0 The LDV measurement system measures the velocity profile downstream the throat and it is necessary to have a criterion for determining the limits R o of integration. For each pressure, tables A2, A4, A6 (Annex 2) presents the error on the flowrate when a mean optimal limit is used. For all Reynolds numbers tested, if the two measurement points with a Reynolds number of the order of 10 4 to be checked are not taken into account, the error on the flowrate extends between -0.6% and +0.6%. These initial results are promising insofar as LDV measurement conditions have not been optimised at this stage of the feasibility study. In particular, the step for the determination of velocity profiles is 2 mm, which is insufficient to obtain accurate integrations. On the other hand, this resolution does not permit to use of the maximum of the RMS velocity profiles to improve the criterion for determining the optimal integration limits. A spatial resolution of mm will be more suitable. This choice of 2 mm was made to reduce the measurement time to focus on the range of pressures tested. If we take into account that these results are obtained for Reynolds numbers between 10 4 and 10 6 and from an industrial point of view the Reynolds numbers are rather in the range of 10 7 [2], we can predict the accuracy in these conditions will be greatly improved. Indeed, for large Reynolds numbers, the velocity profiles are self-similar, and the dispersion of the optimal integration limits will be reduced. The assessment of the uncertainty ( 5.6) on the volume flowrate leads to a value of 0.4%. The most important contribution to the overall uncertainty of this calculation comes from the limits of integration. The accuracy of the reference flowrate measurement directly affects the calculation of the optimal integration limits. The evaluation of uncertainties in the paragraph 5 shows that the method leads to uncertainty over 3%, when the throat flow velocity is less than or equal to 35 m.s -1. The low differential pressure measured at the convergent causes this degraded uncertainty. For the highest velocities (V ref = 57 m.s -1 ), the uncertainty on the reference flowrate is 0.4%. EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 25/72

26 Proposals to improve the accuracies of flowrate measurement by this method are as follows: Improve the criteria to determine the optimal integration limits Decrease the measurement step of the LDV to 0.1/0.2 mm and increase the spatial resolution Study the possibility of using use the maxima of the RMS velocity profiles to improve the determination of the optimal integration limits Improve accuracy on the measurement of the reference flowrate to reduce the uncertainty on the criteria to determine the optimal integration limits Validate by numerical simulation and experiments the beneficial role of Reynolds numbers of the order of Realize validation experiments in cryogenic conditions on a calibration facility. The work carried out within the framework of this feasibility study shows that an uncertainty of the order of 0.4% on the measurement of volume flowrate can be achieved by means of the integration method. Reynolds numbers of about 10 7 in industrial conditions allow improved accuracy and target accuracy of 0.2% seems realistic Determination of the volume flowrate by means of a local velocity measurement The volume flowrate is calculated by means of the following expressions: 2 Q = π R v = V π R 2 v axis A(Re d ) Re v dρ µ = = d 4 Q m πµ d To implement this second method, it is necessary to know the correlation function A(Re d ). The assessment of the uncertainty ( 5.7) on the volume flowrate leads to a value of 0.6%. The most important contribution to the overall uncertainty of this calculation comes from the correlation function A(Re d ). It is possible to reduce the uncertainty on the correlation function A(Re d ) by improving the accuracy of the measurement for the reference flowrate in the experiment. Indeed, the accuracy of the latter directly affects the accuracy of the correlation function. On the other hand, the application of this method to industrial conditions leads to Reynolds numbers greater than In the case of this feasibility study, the maximum Reynolds number was 1.5x10 6. The results show that for higher Reynolds numbers, the uncertainty on the correlation function may be significantly reduced. The fundamental interest of this method is that it allows an instantaneous measurement of the volume flowrate and a temporal integration determines the volume of fluid flowing in the pipe during a given time. EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 26/72

27 Proposals to improve the accuracies of flowrate measurement by this method are as follows: Improve the accuracy of determining the correlation function by improving the accuracy on the reference flowrate during the experiments Validate by numerical simulation and experiments the beneficial role of Reynolds numbers higher than corresponding to actual industrial Reynolds numbers Achieve validation experiments in cryogenic conditions on a calibration facility. The work carried out shows that an uncertainty of the order of 0.6% on the measurement of volume flowrate can be achieved. Reynolds numbers of about 10 7 in industrial conditions allow improved accuracy and target uncertainty of 0.2% seems realistic Conclusion The feasibility study has shown by preliminary tests realized with pressurized air (1-10 bar) on a simplified prototype of cryogenic LDV measurement system it was possible to measure flowrate with an accuracy of 0.4% (Method 1 by integrating the velocity profile) and 0.6% (Method 2 by a local measure of the instantaneous velocity after conditioning the flow by a convergent (beta ratio β=d/d=0.5). The air-based experiments achieved at the CESAME EXADEBIT laboratory with a throat Reynolds number ranges from 5x10 4 to 1.5x10 6 with a simplified Cryogenic LDV measurement system show that the accuracy in real industrial conditions with Reynolds numbers of , can achieve relative accuracies of 0.2% under cryogenic conditions with the improvements proposed above. Both methods improved can lead to accuracy of 0.2%. However, the former requires a measurement time higher than the second, which is in the ratio of time proportional to the number of measurement points of the velocity profile for Method 1. The fundamental interest of the Method 2 is that it allows an instantaneous measurement of the volume flowrate and a temporal integration permits the determination of the volume of fluid flowing in the pipe during a given time. The first method, if it is possible to reduce the measurement time, may be used for constant flowrates. EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 27/72

28 4. DESIGN OF A CALIBRATION UNIT [D.1.4.5] 4.1. Introduction The fundamental equation of an LDV is given by: v = i * f D (1) Where i is the fringe spacing and f D is the Doppler frequency. The Doppler frequency is measured by the signal processor while the fringe spacing is determined by the optics λ 0 i = (2) θ 2nsin 2 Where λ0 the wavelength of the laser and θ is the angle of the beam intersection angle. The angle is then related to f, the focal length of the lens, and L, the spacing between the exit beams by θ = 2 tan 1 L 2f (3) L Fig. 19 Schematic view of the laser beams from the LDV EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 28/72

29 4.2. Interfringe Calibration The calibration can be done in a laboratory accredited by COFRAC in the field of anemometry such as CETIAT, whose best uncertainty is x i (1µm < i < 15 µm). The calibration is carried out without and with the windows used on the LDV Measurement Package by means of an assembly on which the laser source and the windows are fixed. The position of each element is identical to that of the LDV Measurement Package. Thus, it is possible to estimate the influence of the positioning of the windows on the uniformity of the interfringe in the measurement volume. Laser probe without (or with) windows fixed on the displacement system Rotating disk Focal length Fig. 20 Interfringe Calibration Unit EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 29/72

30 Fig. 21 Laser probe and windows assembly 4.3. Doppler frequency Calibration The uncertainty of the Doppler frequency is dependent on the LDV system used. The order of magnitude is: U k (f D ) = 10-3 x f D (k=2) for a Doppler frequency between 10 khz and 10 MHz. Several laboratories are accredited in the domain time/frequency to ensure traceability to the Doppler frequency Assessment of the uncertainty An example of assessing the uncertainty on the velocity measurement with the LDV is developed in 5.5. The relative expanded uncertainty is U k (V LDV ) = 0.14 % (k=2). EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 30/72

31 5. ASSESSMENT OF THE UNCERTAINTIES FOR ALL MEASURANDS [D.1.4.4] 5.1. Assessment of the uncertainty on the discharge coefficient The reference flowrate is measured by means of the differential pressure between the inlet and the outlet of the convergent of the Cryogenic LDV Measurement Package. The discharge coefficient C D of the convergent is determined by calibration using the following formula (ISO ): C D = ε Q π d 4 m 2 1 -β 4 2 P ρ with Q m the reference flowrate measured by sonic nozzles located upstream of the LDV measurement package. Uncertainty budget on the discharge coefficient is detailed in the following table: Ref. Source of Uncertainty Nominal Value Uncertainty Probability distribution Standard uncertainty Sensitivity Coefficient Contribution to overall uncertainty Value x i Unity Value U(x i) Type Value u(x i) Unity c i Unity [c i * u(x i)]² A.1 Repeatability 1.00E E-08 B.1 Sonic nozzles ref. flowrate (Q m) kg/s Normal kg/s s/kg 1.23E-06 B.2 Expansion coeff. (ε ) Normal E-07 B.3 Differential Pressure ( P) 1.74E+04 pa 5.00E+01 Normal 2.50E+01 pa -2.90E-05 pa E-07 B.4 Upstream Pressure (P) 9.98E+05 pa 1.86E+02 Normal 9.29E+01 pa -5.05E-07 pa E-09 B.5 Upstream Temperature (T) k 0.07 Normal 0.04 k 1.70E-03 k E-09 B.6 Compressibility coeff. (Z) Normal E-09 B.7 Gas constant (R) J/mol.k 1.41E-05 Normal 8.16E-06 J/mol.k 6.06E-02 (J/mol.k) E-13 B.8 Gas molar mass (M) kg/mol 2.51E-06 Normal 1.45E-06 kg/mol -1.74E+01 (kg/mol) E-10 Convergent Discharge coeff. (C D) Combined uncertainty Expanded uncertainty (k = 2) E E-03 Relative expanded uncertainty 0.28 % The relative expanded uncertainty on the discharge coefficient C D is: U k (C D )= 0.28 % (k=2) EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 31/72

32 Recapitulation of results: Reynolds number Discharge coefficient Expanded Uncertainty Re d C D U k (C D ) (k=2) [%] 2.06E E E E E E C D Uncertainty on the discharge coefficient Calibration curve C D =f(re d ) Re d 0.0E E E E E E E E E+06 Fig. 22 Uncertainty on the Discharge coefficient of the convergent C D - Calibration curve EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 32/72

33 5.2. Assessment of the uncertainty on the reference mass flowrate The reference mass flowrate is determined according to the formula (ISO ): Q m = CD 1-β 4 π ε d Pρ With d the throat diameter and ρ the fluid density upstream of the convergent of the LDV measurement package. Uncertainty budget on the mass reference flowrate is detailed in the following table for Q m = kg/s and P = 5 bar: Ref. Source of Uncertainty Nominal Value Uncertainty Probability distribution Standard uncertainty Sensitivity Coefficient Contribution to overall uncertainty Value x i Unity Value U(x i) Type Value u(x i) Unity c i Unity [c i * u(x i)]² A.1 Repeatability 1.00E-04 1 kg/s 1.00E-10 B.1 Convergent Discharge coeff. (C D) Normal E-06 B.2 Expansion coeff. (ε) Normal E-08 B.3 Differential Pressure ( P) 9.38E+03 pa 1.80E+01 Normal 9.00E+00 pa 2.28E-05 kg/s.pa 4.21E-08 B.4 Upstream Pressure (P) 4.98E+05 pa 1.63E+02 Normal 8.15E+01 pa 4.29E-07 kg/s.pa 1.22E-09 B.5 Upstream Temperature (T) k 0.07 Normal 0.04 k -7.33E-04 kg/s.k 6.58E-10 B.6 Compressibility coeff. (Z) Normal E-10 B.7 Gas constant (R) J/mol.k 1.41E-05 Normal 8.16E-06 J/mol.k 2.57E-02 kg/s.(j/mol.k) 4.41E-14 B.8 Gas molar mass (M) kg/mol 2.51E-06 Normal 1.45E-06 kg/mol -7.38E+00 kg/s.(kg/mol) 1.14E-10 Qm ref throat kg/s Combined uncertainty 1.25E-03 kg/s Expanded uncertainty 2.50E-03 kg/s (k = 2) 0.6 % The relative expanded uncertainty on the mass reference flowrate is: U k (Q mref ) = 0.6 % (k=2) EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 33/72

34 Recapitulation of results: Pressure P Flowrate Q m Expanded Uncertainty U k (Q m ) (k=2) [bar] [kg.s -1 ] [%] Assessment of the uncertainty on the reference volume flowrate The reference volume flowrate is obtained by: The combined uncertainty on the reference volume flowrate is calculated by the equation: U Q Q 2 Q ρ Q 2 v = Q ρ v 2 v 2 v v ( Q ) = u ( Q ) + u ( ρ) + 2 r u( Q ) u( ρ) v m With r the correlation coefficient between Q m and ρ. m Uncertainty budget on the volume reference flowrate is detailed in the following table for Q v = 258 m 3 /h and P = 5 bar: Source of Uncertainty nominal value uncertainty Probability Contribution to standard uncertainty sensitivity coefficient distribution overall uncertainty Value xi Unity Value U(xi) Type Value u(xi) Unity ci Unity [ci * u(xi)]^2 Repeatability 1 - reference flowrate (Qm) 4.277E-01 kg/s 2.57E-03 Normal 1.28E-03 kg/s 6.04E+02 m3/kg 6.00E-01 density fluid ρ 5.96 kg/m3 1.79E-03 Normal 8.94E-04 kg/m3-4.33e+01 (m3/s)/(kg/m3) 1.50E-03 correlation coefficient - - Normal 1.12E-06 (kg/m3)² -5.23E+04 ((m3/kg)*(m3/s))/( kg/m3) -5.88E-02 Qv m3/h Combined uncertainty 7.37E-01 m3/h m Q Q m Q ρ m Expanded uncertainty (K=2) Relative expanded uncertainty 1.47E+00 m3/h 0.6 % The relative expanded uncertainty on the volume reference flowrate is: U k (Q vref ) = 0.6 % (k=2) EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 34/72

35 From this uncertainty assessment, as the uncertainty on the density is negligible compared to the mass flowrate, the uncertainties on the volume and the mass flowrates are equivalent: U k (Q mref ) U k (Q vref ) Assessment of the uncertainty on the reference velocity (v ref ) The relation between the volume flowrate and the velocity is given by: Q v = v S The combined uncertainty on the reference velocity is calculated by the equation: U v Q 2 v S 2 2 ( v) = u ( Q ) + u ( S) v As the uncertainty on the section S can be neglected compared to the uncertainty on the volume flowrate, the uncertainties on the reference volume flowrate and the reference velocity are equivalent: U k (v ref ) U k (Q vref ) en % v 2 Recapitulation of results: Mean reference velocity v ref Expanded Uncertainty U k (v ref ) (k=2) [m.s -1 ] [%] These important uncertainties values can be explained by the absolute uncertainty on the lowest differential pressures measured for the calibration of the convergent. EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 35/72

36 5.5. Assessment of the uncertainty on the velocity measured by the LDV The fundamental equation of an LDV system is given by: v = i * f D The combined uncertainty on the velocity is then given by the equation: with u(v) = v u i 2 2 ( i) u( f ) ( kσ) + f D D + n 2 u(i) the uncertainty on the fringe spacing calibration u(f D ) the uncertainty on the Doppler frequency calibration σ the experimental standard deviation n the number of repetitions for estimating the mean velocity k the student coefficient. To ensure the traceability of the LDV system, CESAME EXADEBIT chose to calibrate the fringe spacing by the "CETIAT" Cofrac accredited laboratory, and the frequency calibration via the Cofrac accredited "Laboratory Time - Frequency of Besançon". The best uncertainty given by the CETIAT laboratory on the calibration of the fringe i is *i. The best uncertainty given by "Laboratory Time - Frequency of Besançon" on the calibration of the frequency f D is *f D. Uncertainty budget on the velocity measured by the LDV system is detailed in the following table: Ref. Source of Uncertainty Probability Uncertainty Standard uncertainty Sensitivity Coefficient distribution Contribution to overall uncertainty Value U(xi) Unity Type Value u(xi) Unity ci Unity [ci * u(xi)]^2 A.1 Repetability % E+00 B.1 Fringe spacing calibration (i) 8.00E-02 % Normal 4.00E-02 % E-03 B.2 doppler frequency calibration (fd) 1.00E-01 % Normal 5.00E-02 % E-03 B.3 variation of fringe sapcing 1.30E-02 % rectangular 7.51E-03 % E-05 B.4 misalignment for LDA-DISK 1.50E-02 % rectangular 8.66E-03 % E-05 B.5 Traversing system 3.00E-02 % rectangular 1.73E-02 % E-04 B.5 Thermal expansion effects (± 5 C) 9.00E-03 % rectangular 5.20E-03 % E-05 relative Combined uncertainty 0.07 % Relative expanded uncertainty (k=2) 0.14 % The relative expanded uncertainty on the velocity measured by means of the LDV is: U k (V LDV ) = 0.14 % (k=2) EMRP LNG D1-4-4&5 Pre-studying of Laser Doppler Velocimetry (LDV) for LNG Flow Measurements 36/72