DEVELOPMENT OF NUCLEAR-SPECIFIC CORIOLIS FLOWMETERS BASED ON THE STRAIGHT-TUBE TECHNOLOGY

Transcription

1 Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17-21, 2010, Xi'an, China ICONE DEVELOPMENT OF NUCLEAR-SPECIFIC CORIOLIS FLOWMETERS BASED ON THE STRAIGHT-TUBE TECHNOLOGY Tao Wang * KROHNE Ltd. Wellingborough, U.K. Yousif Hussain KROHNE Ltd. Wellingborough, U.K. ABSTRACT The application of Coriolis flowmeters to various industries has been expanding since they were successfully introduced in the market some 30 years ago. This paper specifically reports the development of Coriolis flowmeters for the nuclear industry based on the latest straight-tube technology. An advanced numerical method combining the strength of commercially available simulation packages and in-house theoretical work was used in the development. This includes the initial prediction of flow sensitivity using the fluidstructure interaction theory for straight flow tubes to ensure sufficient measurement accuracy under various process conditions. It also includes further detailed analysis of the entire flowmeter to make sure its natural frequencies away from the seismic frequency range due to nuclear application safety reasons. Furthermore, a new calibration and testing procedure is reported in this paper, which includes the normal calibration condition and also simulates possible process conditions during the nuclear applications (e.g. varying fluid temperature). Additionally, calculations based on the Design by Formula approach according to the governing codes, particularly ASME Boiler and Pressure Vessel Code, Section III, are also reported. These simplified calculations are of significant importance for Coriolis flowmeters to be applied to nuclear applications. Finally, a case study which involved significant collaboration with a well-known safety-related solution provider in the nuclear industry is described, where Coriolis flowmeters were required to provide accurate measurement for the boric acid make-up subsystem in a pressurised water reactor system. Design checks and special considerations for the fabrication and testing according to the rules of ASME Code Section III together with a quality assurance procedure as described in the case study showed that the developed Coriolis flowmeter can meet the specific requirements of nuclear applications in terms of both measurement performance and safety concerns. 1. INTRODUCTION Coriolis flowmeters are capable of measuring mass flow rate directly by sensing the Coriolis force through one or more fluid-conveying tubes under controlled vibration. They can also provide other process parameters such as density (thus volume flow rate), temperature or concentration. A Coriolis flowmeter is an electromechanical system which essentially consists of two interdependent parts, (mechanical) flow sensor and (electronic) converter. In terms of the measuring tube shape of a Coriolis flow sensor, it can be classified into two major types, straight-tube and bent-tube. Bent-tube Coriolis flow sensors have been practically suitable for greater temperature ranges because stresses created due to temperature gradient in bent tubes are generally less. However, straight-tube sensors have their own advantages such as smaller dimensional envelope, less pressure loss and better drainability etc. For straight-tube sensors, they can be further classified into single or multiple tube configurations. The application of Coriolis flowmeters to various industries has been expanding since they were successfully introduced in the market some 30 years ago. However, there are still some special considerations when applying Coriolis flowmeters to meet the nuclear requirements, for example ASME Boiler and Pressure Vessel Code, Section III [1]. This paper specifically reports the development of Coriolis flowmeters for the nuclear industry based on the latest straight-tube technology. A twin straight-tube configuration is selected for this particular application. *Address all correspondence to this author. 1

2 2. ANALYSIS OF THE STRAIGHT-TUBE CORIOLIS FLOW SENSOR 2.1 Fundamental Theory of the Flow Sensor The measuring section within the flow sensor is basically one or more fluid-conveying tubes, normally driven to vibration at one of their fundamental resonant frequencies. Governing equations of motion for slender fluid-conveying tubes are available in [2]. Since the measuring tubes in practical Coriolis flowmeters are not necessarily long pipes, the equation of motion using the Timoshenko beam theory is more appropriate. Coupled with one dimensional axial flow and considering the pressure and axial stress terms, the governing equation for the transverse deflection u and rotation at a specific point x and time t can be given as follows in (1) for a straight fluid-conveying tube in free vibration, f A f p A p 2 u t 2 2 f A f v 0 2 u x t [ f A f v A p p A f 1 2 ] 2 u x 2 kga p x 2 u x 2 =0 f I f p I p 2 t 2 k G A p u x 2 [E 0 p A f 1 2/ A p ] I p x =0 2 where the fluid is assumed to flow with a uniform and constant velocity v 0, in a tube of internal area A f, to have density f, and to have a rotary inertia I f ; and where the conveying tube has an initial axial stress of 0, mean internal pressure p, density p, cross-sectional area of A p, rotary inertia I p, Young s modulus E, Poisson's ratio, shear modulus G, and shear correction factor k. is a constant: =1 if axial motion is constrained (e.g. a clamped-clamped end condition), or =0 if not constrained. It is worth noting that various terms in (1) have their individual practical importance. For example, the term f A f v 0 indicates the principle of mass flow measurement through the Coriolis force; the terms 0 and p indicate that the flow measurement can be affected by stress and pressure. Equation (1) can be used to predict the signal created by mass flow and the effect of process condition changes. To solve these equations, numeric methods have been particularly popular, which can be implemented by a direct damped method [3] or a linear damping model [4]. The predictions are very useful since they can be used at an early stage of the flow sensor development to make sure the signal is sufficient and less affected by process condition changes. 2.2 Development of the Flow Sensor The development of Coriolis flowmeters follows a stepby-step approach. It started with the application of equation (1) to optimise the measuring tube parameters so that a (1) sufficient mass flow sensitivity can be achieved within a predefined set of constraints (for example flowmeter length). Since the motion of the fluid through the measuring tubes can create Coriolis acceleration, it can be sensed as time delay or phase difference between two sensing positions on the tube. The time delay signal t d is almost linearly proportional to the mass flow rate ṁ by a primary flow calibration factor K R under the reference condition, where ṁ=k R t d (2) It is known that fluid temperature can affect flow measurement for both straight-tube and bent-tube Coriolis flowmeters. One of the temperature effects is due to the fact that material properties can change with temperature. The mostly noticeable material property is the tube elastic modulus E since it is directly related with the stiffness of measuring tubes. In a recent research [5], it was also shown that the thermal expansion of the tube material contributed a certain amount to the overall effect. Apart from the materialrelated temperature effect, the other effect is due to stresses created by temperature gradient. Measuring tubes within a Coriolis flow sensor are generally more or less under a stressed condition. These stresses can be created by thermal loads (e.g. temperature gradient) or mechanical loads (e.g. pressure). Tubes can normally be regarded as a shell structure, which needs predominantly two directions to fully define the stress condition: axial and circumferential. Although the effect of stresses on straight-tube and bent-tube Coriolis flowmeters is different as shown by a recent study [4] using both theoretical and experimental data, it is important to note this effect and make correction or specify allowable errors. Therefore, it is one of the necessary tasks during the development to make sure the Coriolis flowmeter can still provide adequate accuracy under conditions other than the reference calibration condition. Numerical simulations and experimental work at early stages of the development have been proved particularly useful to select the right design parameters and effective correction algorithms. As a result, additional sensors (temperature sensors and strain gauges) are installed on the measuring tube to detect the deviation from the reference condition and provide correction information if needed. Measuring tubes of Coriolis flow sensors are driven at one or more of their resonant frequencies. At the resonant frequency the power consumption is minimum. In order to achieve consistent measurement performance, it is generally required that the modal properties at the driving frequency are not (or least) affected by external conditions. This, thus, requires further detailed analysis beyond the model described in equation (1). Since the structural behaviour of the overall mechanical system is the major concern, fluid-tube interaction is not required where the analysis can be done purely in a structural domain using a general purpose finite element analysis (FEA) package. Another important concern of the structural analysis is to ensure structural integrity under various loads. This has been done according to a Design by Analysis (DBA) approach as described in [6]. 2

3 Apart from the simplified fluid-tube coupling model as described in equation (1) and pure structural analysis, another important consideration is in the fluid domain. In a twin tube configuration, the flow is divided at the inlet while combined at the outlet. A smooth and optimised flow path can minimise the pressure loss (thus reduce the energy cost to pump the flow), reduce cavitation and improve measurement accuracy. Computational fluid dynamics (CFD) plays an important role to achieve an optimal flow path by developing a suitable flow splitter shape. Fig. 1(a) shows a quarter of the flow path when using CFD to optimise the flow splitter (on a DN25 meter). The computational results are analysed and an optimised flow splitter shape is shown in Fig. 1(b). In order to prove the optimality of such a splitter shape, pressure drop through two identical Coriolis flowmeters except for different splitters were measured. The results are shown in Fig. 1(c). With a nominal flow rate at one bar pressure drop for the nonoptimised splitter (a direct transition from a large diameter to two small diameters), the optimised flow splitter can help reduce the pressure drop by more than 20%. (a) A quarter of the flow path to optimise the splitter using CFD (b) Optimised flow splitter shape (c) Pressure drop test (on a different meter size) Fig. 1: Optimisation of the flow splitter 3. CALIBRATION AND TESTING PROCEDURE The calibration of the straight-tube Coriolis flowmeters has been done in a gravimetric water flow rig as schematically shown in Fig. 2 based on a standing start and stop principle. The flow starts from one of the supply tanks and goes through the Coriolis flowmeter. The combination of pump speed and downstream control valve opening is used to obtain a specific flow rate. After the downstream control valve, the flow is then divided into two lines. The batching line goes to the weigh tank, which is the primary reference for calibration. The circulation line goes directly back to the supply tank. Fig. 2: Gravimetric water calibration rig One of the most important concerns for a standing start and stop procedure is to obtain repeatable start and stop conditions for the flow. The calibration rig is fully automated and controlled by a computer to make sure the calibration procedure is repeatable. Once a reference condition under the room temperature is established, the batching line is prepared by delivering a pre-defined small amount of flow to the weigh tank. When the scale reading is stable, both the calibrated Coriolis flowmeter and the scale are tared at the same time. Then a certain amount of flow is delivered to the weigh tank, and the final readings of both the flowmeter and the scale are recorded. This batching procedure is repeated for a few times to reduce the uncertainty. Since the total mass is actually the integration of the mass flow rate over the batching duration, the mass flow rate can be calibrated by comparing the flowmeter reading with the scale reading as a traceable reference. By taking the average of the repeated batches, a primary flow calibration factor K R can be determined. As stated above that fluid temperature and tube stresses can affect the measurement, this calibration rig is particularly designed to be capable of determining additional calibration or correction factors. Apart from the supply tank kept at room temperature, two additional tanks with heating elements at two different temperatures are available. Flows from these additional tanks can provide further comparison data between the calibrated Coriolis flowmeter and the weigh scale using the same batching procedure. The additional calibration factors can be individually determined for each flowmeter, or the statistical average from a number of normal calibrations can be used. Once all calibration factors are determined, the Coriolis flowmeter is verified by a multiple point calibration procedure to confirm its linearity. As a typical example, the result of a five-point calibration is shown in Fig. 3 for a DN25 flowmeter (KROHNE OPTIMASS 1000 S25). At each flow rate, at least three readings were recorded. The data points in Fig. 3 are the average of these repeated readings, and the error bars are the experimental standard deviation. 3

4 still required special expertise thanks to the partnership between NLI (Nuclear Logistics Inc.) and KROHNE [7]. NLI is the largest third party supplier to the global nuclear industry [8]. In order to provide the most comprehensive services and the best equipment to the nuclear industry, NLI has teamed up with KROHNE to offer innovative solutions for nuclear specific flow measurement products. The required Coriolis flowmeters are in-line instruments and should be supplied with ASME Boiler and Pressure Vessel Code, Section III N-Stamp certificates. They are classified as ASME Code Class 3 and Seismic Category I components, where only the pressure boundary is required to be safety related. Apparently, the fundamental technology is still the same for both nuclear applications and other general applications. The difference is mainly the documentation of materials, design, fabrication and testing together with relevant quality assurance procedures according to the specified standards and codes. Fig. 3: A typical five-point calibration result for a straighttube Coriolis flowmeter with a DN25 nominal diameter In-line structure Extended structure A A (a) Spigot made by casting for general applications A - Machining for nuclear applications, or Casting for general applications Fig. 4: Pressure boundary components of the Coriolis flowmeter 4. CASE STUDY FOR NUCLEAR APPLICATIONS In one of the typical cases, several Coriolis flowmeters were required to replace the existing batching flowmeters in the boric acid make-up subsystem to the reactor coolant system of a nuclear generating station in the US. Boric acid is dissolved in the pressurised-water coolant and is used as an important means to control the nuclear reactivity. The straight-tube Coriolis flowmeters were preferred because of the secondary containment as a sufficient pressure boundary together with their higher accuracy in flow measurement, multiple parameter outputs (density, concentration and temperature) and lower maintenance cost. Although Coriolis flowmeters had been widely adopted in other industries, the rigorous quality assurance programme of the nuclear industry (b) Spigot made by machining for nuclear applications Fig. 5: Components specifically made for nuclear applications to meet ASME III requirements In ASME Code Section III, ND-2130 requires that all pressure boundary materials should be provided with a Certified Materials Test Report (CMTR) except those 4

5 exempted by NCA [1]. For the Coriolis flowmeter developed for nuclear applications, the pressure boundary components are shown in Fig. 4 by the hatched areas. The internal measuring tube assembly is not shown because it is not classified as pressure boundary components. Among the pressure boundary components, there are three components highlighted with shaded areas, which requires special considerations. In the design for general applications, these three components are made of stainless steel CF3M which is the casting equivalent to the wrought grade 316L. However, it is rather difficult to upgrade the source material documentation of the castings to meet ASME Code Section III although the casting grade CF3M and the wrought grade 316L are technically equivalent. Therefore, an alternative solution is to use the bar, forging or tube stock and machine it to the required shape. If we use the spigot for example, the comparison between nuclear-specific components and general-purpose components is shown in Fig. 5 with two pictures. To ensure structural integrity for nuclear applications, design reports according to ASME Code Section III have to be provided even though the structural integrity had been checked using different standards for general applications. The Design by Formula (DBF) approach according to the rules of ASME Code Section III, Class 3 is adopted instead of a DBA approach because the DBF approach is specifically described for Classes 2 and 3 [9]. The pressure boundary components are divided to two parts, the in-line structure and extended structure as shown in Fig. 4. For piping loads together with design pressure and temperature, the design check for the in-line structure is done according to ND-3521 by comparing the section modulus at the minimum section with the piping section and according to ND-3643 by comparing the area contributing to reinforcement with the required reinforcement area (e.g. determined in accordance with ND (c)3). The Seismic Category I equipment and systems are designed to remain functional when subjected to a specified seismic event [10]. If the natural frequency of the equipment is 33Hz or higher, it may be analyzed statically. With every structural detail considered in a finite element model (with rigidly fixed flanges), the first natural frequency was estimated to be 128Hz as shown in Fig. 6 with its modal shape. Since this frequency is higher than 33Hz, for seismic loads together with design pressure and temperature, the design check of the extended structure can be conducted statically by modelling the connection between the in-line and extended structures as a piping connection using the equation rules from ND The design specification requires 3g horizontal and 2g vertical accelerations under seismic conditions. In the design check 5g accelerations in three directions is used. As a typical example to provide the design report according to ASME III, the calculations are detailed as follows. From ND-3600 [1], the geometry factors used in the branch load evaluation are: the run pipe outside diameter D o r (or mean radius R mr ) and nominal thickness T r for the cylindrical shell of the in-line structure; the branch pipe outside diameter D ob (or mean radius R mb ), and nominal thickness T b for the cross section A-A (see Fig. 4) of the extended structure. The sustained loads include pressure and the gravity of the overall extended structure, while the occasional loads include the additional seismic condition. The stress under sustained loads is checked by S SL =B 1b PD ob 4T b B 2 b M A Z b 1.5S h (3) and the stress under occasional loads is checked by S OL =B 1 b PD ob 4T b B 2b M A M B Z b 1.8S h (4) where P is the design pressure (200psig or 13.8bar), M A is the maximum moment due to the extended structure weight, M B is the resultant moment created by the seismic accelerations, and Z b is the section modulus of the branch pipe. S h is the allowable stress at the maximum temperature (300 o F or 149 o C), which can be determined by ASME Code Section II as 16.7ksi (or 115MPa). B 1 b and B 2 b are the primary stress indices and the subscripts 1 and 2 identify pressure and bending respectively. According to ND (b)-1, B 1 b =0.5 and B 2b =2.25 R m r T r 2/3 R m b R m r 1/2 T b T r R mb D o b /2 (5) With all parameters determined, the calculation of equations (3) and (4) shows that the stresses under both the sustained and occasional loads are well within the allowable limit. Fig. 6: Finite element analysis to determine the first natural frequency The design reports also include other detailed calculations using the DBF approach according to the rules for ASME III Class 3 components. Apart from the material tests and hydrostatic tests that are required under the ASME codes, additional flow measurement performance tests are also required. These additional performance tests were similar 5

6 to the standard calibration tests as described in Section 3 of this paper, but required more testing points at very low flow rates and required witness by independent inspection personnel according to a quality assurance procedure. A flow rate as low as 0.44% of the maximum nominal flow rate (more than a turn-down of 220:1) was tested and all tested meters were well within the required specification. 5. CONCLUSIONS In order to meet the requirement of providing flow measurement instruments to the nuclear industry with better accuracy, Coriolis flowmeters were developed based on the latest twin straight-tube technology. The development includes advanced numerical analysis of the fluid-tube interaction, detailed structural modelling and computational fluid dynamics. A special calibration and testing procedure is also reported to make sure the Coriolis flowmeter can still provide adequate accuracy under conditions other than the reference calibration condition. In the case study of supplying Coriolis flowmeters to the boric acid make-up subsystem in a pressurised water reactor system, the nuclear-specific Coriolis flowmeters were classified as ASME Code Class 3 and Seismic Category I components. Design checks and special considerations for the fabrication and testing according to the rules of ASME Code Section III together with a quality assurance procedure ensure that the Coriolis flowmeter is safe and accurate to be used for nuclear applications. NOMENCLATURE A f tube internal area A p tube cross-sectional area B 1 b primary stress index due to pressure B 2 b primary stress index due to bending D ob branch pipe outside diameter D o r run pipe outside diameter (for the cylindrical shell of the in-line structure) E tube Young s modulus G tube shear modulus I f fluid rotary inertia I p tube rotary inertia k tube shear correction factor K R flow calibration factor ṁ mass flow rate M A maximum moment due to the extended structure weight M B resultant moment created by the seismic accelerations p mean internal pressure P design pressure R mb branch pipe mean radius R mr run pipe mean radius S h allowable stress at the maximum temperature S O L stress under occasional loads S S L stress under sustained loads t time t d time delay between two motion sensors on the measuring tube T b T r u v 0 x Z b 0 p f branch pipe nominal thickness run pipe nominal thickness transverse deflection flow velocity position at a specific point along the measuring tube section modulus of the branch pipe a constant: =1 if axial motion is constrained (e.g. a clamped-clamped end condition), or =0 if not constrained rotation initial axial stress tube density fluid density tube Poisson's ratio ACKNOWLEDGMENTS We would like to thank Chris Rolph and Billy Aitchison of KROHNE Ltd, UK and Andreas Seidel of KROHNE Messtechnik, Germany for their comments. We would also like to thank other colleagues in NLI for their input. REFERENCES [1] ASME Boiler and Pressure Vessel Committee, Subcommittee on Nuclear Power, 2007, ASME Boiler & Pressure Vessel Code III, Division 1 - Subsection ND, Class 3 Components, Rules for Construction of Nuclear Facility Components. [2] Paidoussis M. P., 1998, Fluid-structure Interactions: Slender Structures and Axial Flow, Academic Press, London. [3] Wang T., Baker R. C., and Hussain Y., 2006, An advanced numerical model for single straight tube Coriolis flowmeters, J. Fluids Eng.-Trans. ASME, 128(6), pp [4] Wang T., and Hussain Y., 2009, Pressure effects on Coriolis mass flowmeters, Flow Measurement and Instrumentation, Submitted. [5] Wang T., and Hussain Y., 2009, Coriolis mass flow measurement at cryogenic temperatures, Flow Measurement and Instrumentation, 20, pp [6] British Standard, 2002, BS EN :2002, Unfired pressure vessels - Part 3: Design. [7] NLI, 2009, Flow and Level Instrumentation for the Nuclear Industry, /products.asp (Accessed on 18 Dec 2009). [8] NLI, 2009, New Nuclear Construction: BRING IT ON!, NLI Newsletter, (Feb 2009). [9] Rao K., 2002, Companion Guide to the ASME Boiler and Pressure Vessel Code. [10] NRC, 2007, Seismic Design Classification, NRC Regulatory Guide