emrp 2009 metrology for liquefied natural gas (lng) eng03 lng · the german national laboratory...

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EMRP LNG D1-4-2&3 Technical feasibility study completed and a technical implementation plan ready 1/38

CESAME-EXADEBIT S.A. 43 route de l’Aérodrome F. 86036 Poitiers Cedex Tél. : 33(0)5 49 37 91 26 Fax : 33(0)5 49 52 85 76 E-mail : [email protected]

EMRP 2009

Metrology for Liquefied Natural Gas (LNG) ENG03 LNG

Technical feasibility study completed

and a technical implementation plan ready (Task 1.4.2 & 1.4.3 WP1)

A.STRZELECKI A.OUERDANI Y.LEHOT C.WINDENBERGER July 2012

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

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Summary

1. INTRODUCTION 3 2. CRYOGENIC LDV MEASUREMENT PACKAGE [D.4.2] 4

2.1. Introduction 4 2.1.1. Reminder of the constraints listed 5 2.1.2. Characteristics used 6

2.2. Design of the convergent and the divergent 7 2.2.1. Design of the convergent 7 2.2.2. Design of the divergent 10

2.3. Optical access for the laser beams 10 2.3.1. Ambient atmospheric conditions / Glass / Vacuum interfaces 10 2.3.2. Vacuum / Glass / Cryogenic Fluid interfaces 10 2.3.3. Calculation of translation values Δy1, δy2 et Δy2 12

2.4. Flow simulation 13 2.4.1. Introduction 13 2.4.2. Limiting Conditions of the calculation 14 2.4.3. Validation of the calculations on a standardised venturi 17 2.4.4. Simulation of the flow in the Cryogenic LDV Measurement Package 19

2.5. Design of a seeding system 22 2.6. Design of the LDV Measurement Package 24 2.7. Risk assessment on the measurements with the proposed measurement package 27

3. CALIBRATION UNIT [D.4.3] 28 3.1. Introduction 28 3.2. Design of the calibration unit 29

4. ASSESSMENT OF THE FLOW RATE UNCERTAINTY [D.4.3] 31 4.1. Formulation of the velocity measurement by LDV 31 4.2. Uncertainty of the measurement of a moving particle’s velocity 32

4.2.1. Uncertainty of the value of the interfringe i calibrated bythe turning disk method 32 4.2.2. Uncertainty of the Doppler frequency 33 4.2.3. Uncertainty of the measurement of the flow velocity at one point 33

4.3. Uncertainty on flow rate measurement 35 5. CONCLUSION 37 6. BIBLIOGRAPHY 38

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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 summarised by the development of new measurement standards, methods and procedures and by the assessment of state-of-the-art measurement systems through reviewing of design principles, analysing 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. A previous report (May 2011) [1] presented a synthesis of the definition of the needs for LNG flow rate measurements and a literature survey concerning the technical feasibility of a cryogenic LDV measurement package. Flow rate measurement based on LDV is a mature technology for gaseous natural gas. The German National Laboratory “pigsar™” achieved with a LDV technology the primary flow rate standard for natural gas under high pressure up to 50 bar and flow rates up to 6500 m3/h, with a relative flow rate uncertainty of 0.1 %.

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Through a literature survey, this report evaluated the conditions for using this LDV technology to measure LNG flow rates: seeding system, optical access, interfringe calibration and flow measurement uncertainty. This report presents: 1. The technical feasibility study of a cryogenic LDV measurement package completed and a

technical implementation plan ready [D.4.2], 2. The design of an interfringe calibration unit [D.4.3], 3. The assessment of the flow rate uncertainty [D.4.3].

2. CRYOGENIC LDV MEASUREMENT PACKAGE [D.4.2]

2.1. Introduction The study of the technical feasibility of a cryogenic LDV measurement package is presented. For this purpose, propositions to design the different parts of the measurement package are given: optimisation of the conditioning of the flow by means of a convergent, design of the seeding unit, design of the optical accesses for the laser beams. A risk assessment of the measurement with the LDV proposed package will be done.

The cryogenic LDV measurement package (Figure 1) consists of a LDV Measurement Unit and a Seeding Unit.

Fig. 1 – Schematic Cryogenic LDV Measurement Package The measurement LDV Unit consists of a convergent optimized for conditioning the cryogenic flow before measuring the local velocity at the throat section by means of the LDV. This velocity measurement allows the deduction of the volume flow rate of LNG. To process the LDV measurement, it is necessary to introduce into the model two laser beams that intersect at a measurement volume that must be moved across the throat section of the convergent. These laser beams are introduced through two specific optical windows. The first one is an interface between the cryogenic liquid (LNG at T = -166 °C and pressure <10 bar) and the isolation vacuum chamber (-166 °C in Air <Temperature <20 °C and pressure 10-5 to 10-6 Torr).

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The second window is an interface between the isolation vacuum chamber and the ambient atmospheric conditions. The isolation chamber must also be equipped with a heating system to prevent pollution of the windows when the temperature of the model increases or decreases. To characterize the flow in the prototype by means of flow visualizations and LDV measurements, three optical accesses are provided. These windows need a very precise spatial positioning to conserve the optical characteristics of the laser beams in the measurement volume. In addition, these windows have to withstand great variation of temperature (Temperature from -190 °C to 30°C) and pressure (Pressure = 1 to 10 bar). The seeding unit (Figure 1) permits the injection of micronic particles necessary for the LDV measurement. To control the seeding, two optical accesses are provided on the seeding unit. Vacuum insulation is also provided for this seeding unit. We present in this section preliminary studies implemented to design the technical implementation plan of the LDV measurement cryogenic package and plans for a prototype that can be manufactured and tested in cryogenic conditions including: 1. The design of the convergent 2. The optical accesses for the laser beams 3. The flow simulation inside the LDV measurement unit 4. The design of the seeding unit 5. The technical implementation plan of the cryogenic LDV measurement package Finally, a risk assessment on the measurements with the proposed cryogenic LDV measurement package is presented in this paragraph.

2.1.1. Reminder of the constraints listed As stated in our report "EMRP LNG D1-4-1 Report with Preliminary conclusion" of May 2011 [1], the object of the task D1.4.2 is to study the technical feasibility of a cryogenic LDV Measurement Package that allows us to perform measurements in the LNG unloading conditions on a test bench in the laboratory with a substitution fluid (like dry air, for example). As the NIST laboratory (USA) [2] is equipped with test loop in liquid nitrogen (-196 °C), we decided to study a cryogenic LDV measurement package that also allows us to perform measurements with this fluid. Constraints provided by unloading of LNG are:

- Maximum pipe diameter = 900 mm - Maximum flow rate = 10000 m3/h - Maximum absolute pressure = 10 bar - Maximum velocity of the fluid = 10 m/s

Constraints on the NIST test loop in Liquid Nitrogen:

- Pipe diameter D = 80 mm - Throat diameter d to be determined - Maximum flow rate = 42 m3/h - Maximum absolute pressure = 10 bar

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The relationship ⎟⎟⎠

⎞⎜⎜⎝

⎛∗=

4dvq

2

V π makes it possible to determine the diameter of the measuring

section "d" that achieves the volume flow "qv" up to the test loop in liquid nitrogen (42 m3/h) to the maximum velocity "v" of the LNG in discharging phase (10 m/s). The diameter of the measuring section will be d = 40 mm to achieve the above conditions.

2.1.2. Characteristics used The specifications used for the study of cryogenic LDV measurement package are as follows: - Measurement package composed of two coaxial pipes isolated by a vacuum

=> Materials and inner connection flanges in stainless steel for use in liquid nitrogen or in liquid natural gas, and materials and connection flanges in stainless steel for a vacuum insulation

=> Inner piping with a soldered optical glass access for use in liquid nitrogen => Outer piping with an optical glass access sized for use under vacuum => Pressure measurement upstream and downstream of the measuring cross-section to evaluate the flow rate

=> Temperature measurement downstream of the divergent - Size of the piping to a connection to the test loop in liquid nitrogen and line test in dry air => Diameter D = 80 mm - Maximum operating pressure => 10 bar - Maximum velocity of the fluid => 10 m/s - Maximum flow rate => 42 m3/h - Cross-section diameter of the throat "d" => d = 40 mm - Upstream Convergent => Venturi-type profile to study - Downstream Divergent => Divergent profile to study (length, angle)

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2.2. Design of the convergent and the divergent

2.2.1. Design of the convergent

In order to make the velocity profile as independent as possible of :

- The flow conditions upstream of the measurement system

- The Reynolds number in the LDV measurement zone

- The flow is conditioned by means of a convergent.

This element allows the acceleration of the flow to create a pressure drop and to make the velocity profile at the throat as uniform as possible. This can allow us to obtain from one single LDV velocity measurement on the axis, the mass flow of the LNG and to ensure eventually an instantaneous measurement of the flow with reference to time.

These elements will be defined during the scheduled preliminary air tests at CESAME EXADEBIT within the framework of this research programme.

Otherwise, in addition to the LDV measurement, it is possible to control the LNG flow rate with a precision in the order of 1.5%, by measuring the pressure drop upstream and downstream of the convergent by means of a differential pressure sensor.

The sizing of the convergent of this first prototype of Cryogenic LDV Measurement Package requires us to define:

• The pipe diameter D

• The rate of contraction (d2/D2) and the throat section of the convergent

• The shape and the length L of the convergent

Preliminary testing of the first prototype will be carried out in air pressure in the CESAME EXADEBIT laboratory. Trials in cryogenic conditions can be achieved at NIST (USA) or in the European loop calibration currently under study (VSL Netherlands). To perform these tests, a nominal diameter D = 80 mm was chosen.

The NIST cryogenic calibration loop allows a maximum flow of liquid nitrogen of 42 m3/h. The velocity limit at the throat section of the convergent to 10 m/s led to a diameter d = 40 mm, with a rate of contraction (d2/D2) = 0.25.

For air testing, to maintain the assumption of incompressibility of the gas and ensure optimal conditions for the LDV measurements, Mach number M at the throat section of the convergent is limited to M < 0.15. This leads to a flow velocity less than 15 m/s upstream and 51 m/s at the throat section. To characterize the influence on the velocity profile for a wide range of Reynolds numbers, the prototype will be designed to allow testing under a pressure of 10 bar with a cryogenic fluid (liquid nitrogen or LNG) or air at room temperature (15 °C < T < 30 °C).

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The shape of the convergent has been established based on the indications of Lalo (2006) [3]:

• To optimize the velocity of the flow profile and to minimize the boundary layer at the entrance of the throat section as much as possible

• To make the velocity profile below the throat section more uniform.

The convergent length L must be greater than 2.5d, the value of 2.7d is used, that is to say, L = 108 mm. The defining shape of the convergent is made up of two third-degree polynomials related in an inflection point at two-fifths of the total length of the convergent from the entry (Figure 2). The largest radius of curvature is therefore out of the convergent (Figure 2).

By applying the following conditions we use a matrix system which after resolution gives the expressions of the two polynomials:

• Total length of the convergent L = 0.108 m and 2/5*L = 0.0648 m

• A (-0.108) = 0.04 ; B(0) = 0.02 ; A (-0.0648) = B (-0.0648)

•

• =

• = = 0

From which

and

a0 = 49.61 b0 =22.05

a1 = 9.65 b1 = 4.29

a2 = 0.35 b2 = 0.00

a3 = 0.03 b3 = 0.02

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Fig. 2 – Theorical shape of the convergent

Fig. 3 – 2D drawing of the convergent

Flow

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2.2.2. Design of the divergent To reduce the pressure drop of the LDV Measurement Package and limiting flow separation in the divergent, a total angle of 7.7° was chosen.

Fig. 4 – Design of the divergent

2.3. Optical access for the laser beams The specifications led us to select:

- A soldered or glued optical glass access for the inner pipe in contact with the cryogenic fluid (cryogenic or pressurised air / vacuum interface or ambiant air),

- A vacuum insulation, - A soldered optical glass access for the outer pipe (ambient air / vacuum interface).

The sizing of the optical accesses must take into account the thickness and the refractive index of the different interfaces as a function of the focal length of the laser used.

2.3.1. Ambient atmospheric conditions / Glass / Vacuum interfaces The refractive index of air (n1 = 1.00027) and vacuum (n3 = 1) are very close. We can then consider that the incident angle of laser beams (α1) is equivalent in the air and in vacuum, before and after passing through the glass window with parallel faces. On the other hand, the focal length of the lens of the laser will be extended to a size Δy1 (Figure 5).

2.3.2. Vacuum / Glass / Cryogenic Fluid interfaces

The focal length is increased by (Δy2 + δy2) due to the path of the laser beams through: - vacuum, - the second glass window, - and the cryogenic fluid

which all have different refractive indices (Figure 5).

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Fig. 5 – Optical access from ambient atmospheric conditions to LNG

n2 (glass)

y1 Δy1

Δy1

d1

y'1

b

a

α1

α2

P

P

n1 (air)

n3 (vacuum)

α1

α3

α4

d2

c

A O

P'

P''

P

n5 (LNG)

n4 (glass)

B

C

Δy2

y'2

δy2

y2

d3

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2.3.3. Calculation of translation values Δy1, δy2 et Δy2 Geometrical laws: a = . = b .

b = . =

=

c = Refraction law:

sin = sin sin = sin

Applying the law of refraction, in conjunction with geometrical relationships, yields an analytical expression for the displacement y1, as

= = (1)

= (2) For the 3 layers of different refractive indices (n3, n4 and n5), e.g. vacuum, glass and cryogenic fluid, the additional displacement in the fifth layer is:

= or

This equation, combined with relationships (1) et (2), yields

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These equations are used to validate the choice of the technical characteristics of the laser used and the design of optical access for acquisitions over the entire measuring section. Angle of incidence of the beams in the air: α1 = 7.13° Focal length: f = 160 mm

Refractive Index Dimension

Ambient Air 1.00027 /

Kodial 1.487 d1 = 6 mm

Vacuum 1 d3 = 50 mm

Quartz 1.46 d2 = 6.3 mm LNG (cross-section) 1.29 D = 40 mm Displacement Δy1 1.98 mm

Displacement δy2 28.43 mm

Displacement Δy2 2.00 mm

Total Displacement 134.71 mm Thus, the converging lens of focal length f = 160 mm can be positioned up to 25.29 mm from the outer window and allow to carry out measurements across the entire diameter of the measuring section.

2.4. Flow simulation

2.4.1. Introduction The purpose of numerical simulations presented here is to calculate the theoretical flow of LNG in the Cryogenic LDV Measurement Package. For this, it is necessary to make a mesh of the internal part of the model. The design of the venturi used being close to the definition of a standard venturi, the calculation will be validated by comparing the discharge coefficient CD of the standard venturi, obtained from numerical simulations, to those obtained by application of the standard NF EN ISO 5167-4. Then, the meshes and the boundary conditions defined in this first simulation will be reused to define the geometry of the Cryogenic LDV Measurement Package. Later, these calculations can be achieved in cryogenic conditions for different Reynolds numbers to obtain an assessment of the relationship between the velocity on the axis below the throat section of the venturi and the flow velocity. These results will be validated by the future tests with air under pressure at CESAME EXADEBIT.

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2.4.2. Limiting Conditions of the calculation Figure 6 shows the mesh of a cylindrical half-pipe of 12 m length and diameter D = 80 mm. The convergence of grid computing is studied using three different models. These meshes have 300 stitches in the axial direction and 30, 60 and 90 stitches in the radial direction (on a half-diameter). The study led us to choose a mesh size of 300 x 60 to carry out simulations.

Fig. 6 – The mesh size of a cylindrical semi-conductor To obtain a fully developed profile in the pipe that is necessary for the limiting conditions as input data for the numerical simulation of the standard venturi, a calculation was made on a pipe of 12 m length with a uniform velocity input profile. The input data are: Mass Flow rate qm = 0.88 kg/s Absolute pressure P = 106 Pa Temperature T = 293 K Density ρ = 12.13 kg/m3 Mean velocity m/s15v = Pipe diameter D = 80 mm

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Figure 7 shows the evolution of the axial velocity as a function of position in the pipe: vaxis velocity is constant from a distance equal to 10*D corresponding to the length to establish the profile. Figure 8 shows the fully developed velocity profile used as input boundary condition for numerical simulation of the venturi. The result (black curve) is in accordance with the profile of Nikuradse (red curve).

The calculation of ratios v

v axis gives the following results for a Reynolds number of 7.3*105:

- 16.1v

v=axis for Nikuradse

- 16.1v

v=axis for the numerical simulation

Fig. 7 – Axial velocity in the straight pipe

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Fig. 8 – Fully developed velocity profile in the pipe Figure 9 shows the turbulence profile (fluctuations / local mean velocity) in the pipe. This turbulence ranges from 3.5% on the axis to 7.25% near the wall.

Fig. 9 – Turbulence intensity profile for the fully developed profile

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2.4.3. Validation of the calculations on a standardised venturi The results of numerical simulation for a standard venturi are presented in this paragraph. The fully developed profile is injected at 6*D upstream of the convergent. Figure 10 shows the contours of velocity magnitude in the venturi. The venturi leads to an acceleration of the velocity from 15 m/s at the entrance to 60 m/s in the throat section.

Fig. 10 – Contours of velocity magnitude in the venturi

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Figure 11 shows Velocity profiles in the venturi for the positions X = 0 mm, 20 mm and 60 mm from the entrance of the throat section. Profile becomes uniform for X = 20 mm, i.e. in the middle of the neck. Profile at X = 60 mm is at the beginning of the divergent and presents a lower velocity on the axis.

Fig. 11 – Velocity profiles at different positions in the venturi Figure 12 shows absolute pressure magnitude in the venturi and highlights the pressure drop in the neck. The calculated differential pressure between the upstream of the convergent (located at –D) and downstream of the convergent (located at +d/2) leads to a value ΔP = 1.9501*104 Pa. This result allows us to calculate the discharge coefficient of the venturi: CD = 0.9978 For this venturi, the NF EN ISO 5167-4 standard gives a discharge coefficient CD = 0.995. The close agreement between these two results validates the choices made for these simulations (entry, exit, mesh ...). These conditions will be reused for the numerical simulation of the Cryogenic LDV Measurement Package.

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Fig. 12 – Absolute pressure magnitude in the venturi

2.4.4. Simulation of the flow in the Cryogenic LDV Measurement Package The results of numerical simulation for the Cryogenic LDV Measurement Package are presented in this paragraph. Compared to the standard venturi, the shape of the convergent has been modified (§ 2.2.1) and the length of the throat section doubled (Lcol = 80 mm). Figure 13 shows the contours of velocity magnitude in the Cryogenic LDV Measurement Package.

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Fig. 13 – Contours of velocity magnitude in the Cryogenic LDV Measurement Package Figure 14 shows velocity profiles for the positions X = 0 mm, 40 mm and 90 mm from the entrance of the throat section. Profile becomes uniform for X = 0 mm, i.e. just out of the throat section. Then the boundary layers develop in the throat section and lead to a slight increase of the velocity on the axis. The velocity profile stays uniform. For the position X = 90 mm (i.e. 10 mm downstream of the throat in the divergent), the profile stays uniform with a decrease of the velocity on the axis. Therefore, LDV measurements will be conducted in this area.

Velocity magnitude (m/s)

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Fig. 14 – Velocity profiles at different positions in the Cryogenic LDV Measurement Package

Fig. 15 – Absolute pressure magnitude in the Cryogenic LDV Measurement Package

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2.5. Design of a seeding system The seeding unit (Figure 6) is being designed for industrial LNG applications. The choice of the seeding system determines the measurement accuracy. Two alternative systems are proposed: a) injection of micronic bubbles upstream of the LDV measurement volume by local boiling of LNG using a small electrical current or b) injection of a small flow rate of gas or liquid to generate micronic particles. Figure 7 presents the seeding probe.

Fig.16 – Seeding Unit

Fig.17 – Seeding probes

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For the tests with air under pressure provided at CESAME EXADEBIT, seeding will be done by generating micronic particles of DHES Di (2-ethylhexyl) sebacate, sebacic acid (photo below).

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2.6. Design of the LDV Measurement Package The LDV Measurement Package consists of four main elements:

- Upstream element allowing the seeding of particles, - Intermediate element containing the convergent, upstream of the measurement cross-

section and of the optical axis, - Element containing the diffuser downstream of the LDV Measurement Package, - Outer pipe for the vacuum insulation, with optical access.

Fig.18 – Cryogenic LDV Measurement Package (3D view)

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Fig.19 – Cryogenic LDV Measurement Package (3D view – horizontal cut)

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Fig.20 – Cryogenic LDV Measurement Package (2D view – horizontal cut)

193 120 207 135

945

290

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2.7. Risk assessment on the measurements with the proposed measurement package Performing measurements in metrological cryogenic conditions with the proposed LDV Measurement Package can lead to the following difficulties: • Mechanical maintenance of portholes in cryogenic and pressurized conditions, • Maintenance of the window transparency (condensation is possible due to the temperature

gradient), • Problems of optical birefringence associated with mechanical stresses on the glass during

pressurized or cryogenic temperature setting of the model. Theoretically, the mechanical stresses must be absorbed by the glass fixing systems (soft bonding or titanium brazing),

• Regularity of interfringe values in the measurement volume, • Maintenance of perfect parallelism of the two windows in a measurement situation, • The Signal/Noise value of the LDV system depends on the stability and quality of the optical

mounts, • Quality of flow downstream of the convergent in the measuring section, • Control of seeding upstream of the measuring volume (density, size and lifetime of the

injected particles).

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3. CALIBRATION UNIT [D.4.3]

3.1. Introduction The quality of the interfringe calibration unit determines the uncertainty of the cryogenic LDV measurement. The design and realistic implementation of the calibration process are proposed in this section. In principle, the velocity obtained from V = i*fD can be used as primary standard for airspeed measurement if both the fringe spacing i (length scale) and the Doppler frequency fD (timer) are calibrated at specified uncertainty levels. In this work, we calibrate the entire LDV system directly by a calibration of the interfringe i with a LDV system coupled with a measurement of the velocity V determined by the known tangential velocity of micronic particles on the surface of a thick rotating glass wheel. A rotating disk is a primary standard for velocity. The velocity from a rotating disk is:

rFr rπω 2v == where r is the disk radius, ω is the rotational speed in radians/s, and Fr is the rotational frequency in Hz (revolutions/s). For the calibration of the LDV Cryogenic Measurement System, we need to take into account the two optical windows during the calibration. The laboratory CETIAT (France) is an accredited laboratory for calibration of the interfringe of Laser Doppler Anemometer compared to a rotating disk in the range from 1 micron to 15 microns with an expanded uncertainty better than 0.05%. We will use this competence to calibrate the cryogenic LDV measurement package by setting a special assembly that integrates two optical windows in the path of the two convergent laser beams. The specific calibration mounting of the LDV interfringe by a rotating disk in the presence of optical windows is presented in the following paragraph.

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3.2. Design of the calibration unit The LDV Calibration Unit consists of:

- A mounting bracket for the laser source of the LDV system, - A glass window strictly identical to the outer optical window of the LDV Measurement

Package (Ambient air/Vacuum interface), - A glass window strictly identical to the inner optical window of the LDV Measurement

Package (Vacuum/LNG interface), - Two mounting brackets for positioning (in a perfect parallel) the two windows at a

distance from one another identical to that defined on the LDV Measurement Package, - A rotating glass disk coupled to a motor with an optical encoder and controlled by a

computer, the assembly being fixed on a table with micrometric displacement. This table is used to adjust the positioning of the rotating disk from the measuring volume of the LDV system.

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Fig. 21 – Schematic View of the LDV Calibration Unit

LDV System Outer glass window Inner glass window

Table with micrometric displacement

Motor with optical encoder controlled by a computer

Rotating glass disk

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4. ASSESSMENT OF THE FLOW RATE UNCERTAINTY [D.4.3]

4.1. Formulation of the velocity measurement by LDV The fundamental equation of an LDV is given by:

Dfi *v = (3) Where i is the fringe spacing and fD is the Doppler frequency. The Doppler frequency is measured by the signal processor while the fringe spacing is determined by the optics

2sin2

0

θλ

ni = (4)

Where 0λ 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 D, the spacing between the exit beams by

⎟⎠⎞

⎜⎝⎛= −

f2tan2 1 Dθ (5)

Fig. 22 – Schematic view of the laser beams from the LDV

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4.2. Uncertainty of the measurement of a moving particle’s velocity

The velocity is determined from equation (3). The uncertainty of the measurement of the velocity by the LDV system is therefore directly related to the uncertainty of the Doppler frequency and to to the uncertainty on the interfringe i. The combined uncertainty in velocity is then given by the equation (while disregarding the correlation term):

(6)

with: u(i) the standard deviation on the mean interfringe in the measuring volume u(fD) the standard deviation on the LDV Doppler frequency σ the experimental standard deviation n the number of repetitions to estimate the velocity V k the Student coefficient function of n

4.2.1. Uncertainty of the value of the interfringe i calibrated bythe turning disk method For this project, the turning disk method was chosen for the calibration of the interfringe i . This method consists of placing the particles on the edge of a disk of known diameter by positioning the measurement volume on the edge of the disk. The interfringe i can be determined by comparing the linear velocity of the particles to the velocity measured by the Laser Doppler Velocimeter.

Fig. 23 – Schematic view of the laser beams on the spinning disk surface

i

i

( )n

kuViuiVVu D

D

22

22

2

)f(f

)()( σ+⎟⎟

⎠

⎞⎜⎜⎝

⎛∂∂

+⎟⎠⎞

⎜⎝⎛

∂∂

=

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The components of uncertainty for the determination of the interfringe i with this method are:

- the alignment of the laser with the disk axis - the value of the disk diameter - the measurement of the rotational speed of the disk - the value of the Doppler frequency - the non-uniformity of the interfringes in the measurement volume - the alignment of the laser with the axis of the portholes of the LDV Measurement Package

The calibration can be done in a laboratory accredited by COFRAC in the field of anemometry such as CETIAT, whose best uncertainty is 5.10-4 * i (1µm < i < 15 µm). There is another method based on the direct measurement of the angle of incidence θ between the laser beams, with the help of a calibrated turntable at the centre of which a mirror is placed. By knowing exactly the wavelength 0λ we can determine i from the equation (4). The two methods are equivalent in terms of accuracy [3].

4.2.2. Uncertainty of the Doppler frequency The uncertainty of the Doppler frequency is dependent on the LDV system used. The order of magnitude is: Uk (fD) = 7.10-4*fD (k=2) for a Doppler frequency between 3 KHz and 15 MHz inclusive. Several laboratories are accredited in the domain time/frequency to ensure traceability to the Doppler frequency.

4.2.3. Uncertainty of the measurement of the flow velocity at one point The motion of a single spherical particle in a flow can be written in the following equation [5].

(7) where the subscript p and f represent particle and fluid respectively. The second term in the equation represents the viscous drag force. The third term gives the force from the pressure gradient in the vicinity of the particle due to the fluid acceleration. The fourth term is the resistance force of an inviscid fluid to the acceleration of the particle. The fifth term is the buoyancy force due to the density difference between the particle and the fluid. The final term is the “Basset history integral”, which defines the resistance b caused by the unsteadiness of the flow field.

CESAME EXADEBIT SA


This equation is valid only in the Stokes flow region, in which the relative Reynolds number of the particle is much less than 1.0. For a large Reynolds number, the viscous drag term needs to be corrected by adding a more general form for the drag coefficient CD,

where

For the horizontal forced flow case, the gravity force is perpendicular to the mean velocity of the flow. By assuming that the sixth term in equation (7) can be neglected and the turbulence fluctuation of the velocity can be averaged over time t for the steady state turbulent flow, the particle velocity in the vertical direction can be expressed as:

where vp is the vertical velocity component of the particle. This is the slip velocity caused by gravity. We can also simplify and integrate equation (7) in the flow direction for the same condition,

where u is the horizontal velocity component of the particle and ( ) ffppd ηρρτ 18/2/2 += . Here the characteristic time τ gives a good estimation of how fast the particles respond to the change of the flow motion.

CESAME EXADEBIT SA


The above simplified formulation applied to a gas particle of diameter dp = 1 μm injected into the LNG leads to a response time of τ = 0.5 μs. In this case, the difference between the fluid velocity and that of the injected particle velocity is considered as negligible. The uncertainty of the measurement of the flow velocity can be considered equal to the uncertainty of the measurement of the particle speed (6).

4.3. Uncertainty on flow rate measurement The volume flow rate is obtained by integrating the flow velocity across section S

∫=R

V rdrrvq0

)(2π

where R is the radius of section S. 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 flow rate measurement can be reduced to a single point measurement (center line velocity measurement).

v2RqV π= For a given Reynolds number, the output velocity is given by the relation

2

4v

dqV

π=

and the ratio between the velocity on the axis vaxis (measured by the LDV system) and the output velocity v

is a constant function of the Reynolds number Re

)Re(v

vAaxis =

with

dqd m

μπμρ 4vRe ==

These relations allow us to calculate the volumetric flow from the measurement at one point on the axis of the pipe.

)Re(v

v 22

ARRq axis

V ππ ==

CESAME EXADEBIT SA


With this method, the principal components of uncertainty are: - Uncertainty of the value of the radius value of the measured section - Uncertainty of the integration of the velocity profile v - Uncertainty of the measurement of the velocity of the velocity on the axis axisv

- Uncertainty of the modelling of the relationship )Re(v

vAaxis = .

That is to say:

)()v(v

)v(v

)()( 222

22

22

2 Auq

uq

RuRq

qu axisaxis

VVVV σ+⎟⎟

⎠

⎞⎜⎜⎝

⎛∂∂

+⎟⎠⎞

⎜⎝⎛

∂∂

+⎟⎠⎞

⎜⎝⎛

∂∂

=

The computer evaluation of these components will be carried out during the tests at CESAME EXADEBIT scheduled for the fourth quarter of 2012.

CESAME EXADEBIT SA


5. CONCLUSION This report has presented the concept of a cryogenic LDV Measurement Package. The optical access points for the LDV measurements have been studied and sized to allow velocity measurements with high accuracy. The design of the internal geometry (convergent, throat, divergent) has been validated by computer simulations. The two systems of seeding have been studied, designed and integrated into the model (gas injection or formation of micro-bubbles). The calibration system has been studied and defined. The causes of uncertainty of the flow measurement have been identified. The risks have been evaluated. After this important phase of design, manufacture of Cryogenic LDV Measurement Package is underway. The next step in this research programme will be to validate the entire system of measurement by LDV tests with pressurized air at CESAME EXADEBIT by similarity of Reynolds number.

CESAME EXADEBIT SA


6. BIBLIOGRAPHY [1] STRZELECKI A., OUERDANI A., LEHOT Y.,WINDENBERGER Y. [2011] "Pre-studying of Laser Doppler Velocimetry for LNG flow measurement” , Metrology for LNG, Technical report N°1, May 2011. [2] FRIEND D., LEWIS M., [2010] “Early LNG Program and LN2 Cryogenic Flow Measurement Facility at NIST”, 1rst LNG Metrology Workshop, November 2010, Stockholm (Sweden),. [3] LALO M. [2006] "Atomisation d'un film liquide mince par action combinée des instabilités de Kelvin-Helmholtz et de Faraday – Application aux injecteurs aérodynamiques des turbomachines aéronautiques", PhD Thesis, december 2006, Ecole Nationale de l'Aéronautique et de l'Espace, Toulouse (France). [4] CARE I. [2010] "Faibles vitesses d’air : une nouvelle référence entre 0,05 m/s et 2m/s pour l’étalonnage des anémomètres", Revue française de métrologie Vol. 2010.1, N°21. [5] YEH T.T., Hall J.M.[2007] “Air Speed Calibration Service”, NIST Special Publication 250-79, National Institute of Standards and Technology, Gaithersburg, Maryland (USA). [6] MELLING A., [1997] "Tracer particles and seeding for particle image velocimetry". Measurement Science & Technology, 1997. 8(12): p. 1406-1416.

emrp 2009 metrology for liquefied natural gas (lng) eng03 lng · the german national laboratory...

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