THE IMPLEMENTATION OF TOROIDAL THROAT VENTURI NOZZLES TO MAXIMIZE PRECISION IN GAS FLOW TRANSFER STANDARD APPLICATIONS

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1 Presented 2005 JUNE FLOMEKO Peebles, SCOTLAND THE IMPLEMENTATION OF TOROIDAL THROAT VENTURI NOZZLES TO MAXIMIZE PRECISION IN GAS FLOW TRANSFER STANDARD APPLICATIONS Pierre Delajoud, Martin Girard, Michael Bair DH Instruments, Inc. 1 INTRODUCTION The measurement of the mass flow of gases in the range up to 50 g s -1 (2500 Nl min -1 ) is important in a variety of industrial processes and research fields. Precise and stable transfer standards are an indispensable part of the system to support these measurements. Filling the transfer standard role effectively requires instruments that are transportable and easy to use with minimal sensitivity to external influences such as ambient pressure, ambient temperature, upstream geometry and upstream or downstream pressure. In the lower part of this flow range, the transfer standard role has been filled effectively by instruments based on laminar flow elements [1, 2]. However, as flow increases, the differential pressure differential pressure across the laminar element increases aggravating temperature influences and eventually the flow regime transitions to turbulent. A well known alternative, particularly for higher flows, is the toroidal throat, critical flow Venturi nozzle. A new flow element based on critical flow nozzles (CFN) has been developed to complement existing laminar flow modules using a common mass flow terminal. The new elements cover the range of flow from 0.02 to 50 g s -1 (1 to 2500 Nl min -1 ) and beyond. The laminar flow elements are known under the trade name molbloc-l and the CFN based elements are designated molbloc-s. 2 DESCRIPTION OF THE CRITICAL FLOW NOZZLE BASED TRANSFER STANDARD Use of Venturi nozzles in the critical flow regime to measure gas mass flow is well known and described in ISO and ANSI/ASME standards [3, 4]. These prescribe the shape of the Venturi nozzle and their application as primary standards in which flow is calculated based on measured throat diameter and very specific conditions of use. The conditions include Reynolds number of the flow greater than , and specific upstream flow path geometry and pressure and temperature measurement locations. The dominant influences on measurements made with critical flow nozzles (CFN) and laminar flow elements (LFE) are quite different. In the LFE, the dominant uncertainties are in knowledge of gas temperature and of the differential pressure across the laminar flow path. The influence of temperature on gas density and viscosity results in a combined effect of ºC -1. In the CFN, the influence of temperature on mass flow is inversely proportional to the square root of the temperature so it is four times smaller than in the LFE, or ºC -1. Viscosity affects only the determination of Reynolds number, leading to a negligible secondary influence in the flow calculation. Finally, the CFN has no dependence on differential pressure since when the regime is critical, flow is insensitive to downstream pressure. The pressure dependence is on the absolute pressure upstream of the nozzle, which is relatively easy to measure compared to the wide range of differential pressure across an LFE if it is to be used over a reasonably wide range [5]. In the new mass flow elements, the emphasis is on optimizing use of CFNs as transfer standards, not strict adherence to the recommendations contained in the ISO and ANSI/ASME standards. In the transfer standard application, the objective is to obtain maximum precision and stability over time. The conventional equation for the calculation of flow is used but the discharge coefficient (C d ) is determined by comparison with a flow reference, not by calculation from throat dimensions. The calculations are applied at Reynolds numbers well below the prescribed Secondary corrections not normally considered, such as change in throat area with pressure and temperature are applied. The nozzle is installed in a block which includes dedicated hardware to condition the gas 2005 DH Instruments, Inc. Page 1

2 temperature and flow profile just upstream of the nozzle. The nozzle and gas conditioning hardware make up a single integrated flow measurement module. A United States patent covers various aspects of the new elements design and use [6]. The CFN based elements are used with an existing mass flow terminal [Fig. 1]. The mass flow terminal includes two identical absolute pressure transducers, two ohmic measurement circuits to read the element s platinum resistance thermometers, a microprocessor, memory, a keypad, a display and standard computer interfaces. The terminal was introduced commercially in the early 1990s to support LFEs (molbloc-l). New software can be loaded into the terminal flash memory to support the new CFN based elements (molbloc-s). The CFN based elements are characterized for use in one of two pressure ranges. The standard range is from 50 to 500 kpa absolute upstream pressure giving rangeability of 10:1 with vacuum downstream and about 3.5:1 with atmosphere downstream. The low range is from 20 to 200 kpa absolute upstream pressure giving rangeability of 10:1 with vacuum downstream. These pressure ranges correspond to the ranges of the transducers available in the standard and low pressure versions of the mass flow terminal. A 2 MPa version of the terminal is planned. The nozzle geometry is designed with the objective of obtaining critical back pressure ratios that are a function of Reynolds number across nozzle sizes. To this end, the different nozzle sizes are geometrically homothetic, remaining proportionally identical in conical divergent angle and ratio of divergent section length to throat diameter as throat diameter changes. Critical back pressure ratio limits have been determined experimentally as a function of Reynolds number for each of the nozzle sizes. The CFN based elements (molbloc-s) are similar in appearance to the laminar flow elements (molbloc-l) [Fig. 2]. The nozzle is a Venturi with the ISO 9300 shape. Two different nozzle designs are used to maintain the proportional consistency of the divergent section described above [Fig. 3]. Twelve sizes with nominal throat diameter from 0.15 mm to 10.7 mm are produced to cover a variety of ranges. These provide nominal flow to pressure ratios of 0.04 mg s -1 kpa -1 (2 Ncc min -1 kpa -1 ) to 0.2 g s -1 kpa -1 (10 Nl min -1 kpa -1 ) DH Instruments, Inc. Page 2

3 2.1 Temperature Considerations A gas conditioning system is integrated into the element. Its function is to define an isothermal, unidirectional flow stream as the gas enters the nozzle throat. There are two designs, one for flow rates up to 1 g s -1 kpa -1 (50 Nl min -1 ) and another for higher flow rates. The main difference between the two is in the gas conditioning system and gas temperature measurement method. In the opinion of the authors, the main limitation in the reproduceability of conventional CFN flow measurements at low flow comes from differences in the temperature of the gas at the point at which its temperature is measured (two piping diameters upstream of the nozzle per ISO9300) and the nozzle throat. The difference is due to thermal exchange between the gas and the piping as the gas travels through it. This can cause the gas to enter the nozzle at a temperature significantly different from the measured temperature. Two designs of the sonic nozzle based element, depending on flow rate, have been developed to overcome this problem. The design for flow up to 1 g s -1 (50 Nl min -1 ), illustrated in Fig. 4 uses the patented gas temperature conditioning method introduced for the laminar flow elements [7]. The gas flows through a narrow, annular gap between relatively massive stainless steel bodies upstream of the nozzle. The large surface of thermal exchange between the steel parts and the flowing gas, the small mass of gas and its relatively low velocity, cause the gas to assume the temperature of the body before it enters the nozzle. The temperature of the gas upstream of the nozzle is assumed to be equal to the temperature of the body. The temperature of the body is measured by two platinum resistance thermometers embedded symmetrically in the body. At flows greater than 1 g s -1 (50 Nl min -1 ), the velocity of the gas through the element body is such that, if the temperature of the gas entering the body is significantly different from the temperature of the body, it cannot be assumed that the gas and body temperatures become equal. It is therefore not possible to know gas temperature well by measuring body temperature. In this case, the gas temperature is measured by two thinly shielded platinum resistance thermometers mounted in the gas flow path just upstream of the nozzle. A different gas heat exchanger design is used whose objective is to bring the gas temperature close to the body temperature, and therefore ambient temperature, before its temperature is measured and it enters the nozzle [Fig. 5]. Since the gas temperature is very close to the body temperature, the thermal conductivity between the body and the thermometer shield, does not significantly influence the thermometer reading of the gas temperature. To improve its efficiency, the heat exchanger is made of titanium and the gas passes through narrow, radial slots. Both designs also consider the need to know the temperature of the nozzle itself to correct for change in throat diameter with change in temperature of the nozzle material. This 2005 DH Instruments, Inc. Page 3

4 influence is on the order of ºC -1 which can easily be significant relative to the system s repeatability. It is also a Type B uncertainty. The nozzle is closely captured within the element body and its temperature follows the evolution of the body temperature. In the low flow design, the measurement of the body temperature gives the temperature of the nozzle directly. In the high flow design, as the heat exchanger causes the gas to take on a temperature near the temperature of the body, the measurement of the gas temperature adequately approximates the temperature of the nozzle. The change in the throat diameter is calculated using the difference between the measured temperature and 20 ºC, the conventional dimensional reference temperature. 2.2 Flow Straightening In the practical use of the CFN based elements as transportable transfer standards, it is imperative that they be free of installation influences. For example, it is often necessary to put a tee fitting upstream when two elements are used in parallel. In both flow element designs, the heat exchanger also acts as a flow straightener, whose objective is to assure a consistent flow profile in the element bore upstream of the nozzle regardless of gas delivery geometry upstream of the element. In the high flow element, the two shielded platinum resistance thermometers are placed side by side away from the nozzle throat axis to minimize perturbations in the gas stream entering the throat. Experimental measurements have been made to evaluate the influence of upstream flow path geometry. 2.3 Standard Element Configurations The CFN based elements (molbloc-s) are produced with standard nozzle sizes, designated by their nominal N2 gas flow per kpa of upstream absolute pressure (K F ). Table 1 lists the CFN elements available with each one s nominal throat diameter, gas conditioning type and nominal flow when operated in the critical flow regime at upstream pressure of 500 kpa. Designator (K F ) [Ncc min -1 kpa -1 ] Table 1 - Standard molbloc-s flow elements Nominal Throat Diameter [mm] Gas Conditioning Type N kpa upstream [g s -1 (Nl min -1 )] 2E Low 0.02 (1) 5E Low 0.05 (2.5) 1E Low 0.1 (5) 2E Low 0.2 (10) 5E Low 0.5 (25) 1E Low 1 (50) 2E High 2 (100) 5E High 5 (250) 1E High 10 (500) 2E High 20 (1 000) 5E High 50 (2 500) 1E High 100 (5 000) 2005 DH Instruments, Inc. Page 4

5 3 CALIBRATION OF THE CRITICAL FLOW NOZZLE BASED FLOW ELEMENTS Calibration of a CFN based flow element has two steps. In the first step, the throat diameter is determined by comparison with a reference flow standard in nitrogen at the nozzle s maximum flow rate, using the theoretical value of the discharge coefficient assuming ideal geometry as proposed by Ishibashi [8]. The diameter thus determined is compared to the diameter obtained by dimensional measurement. A difference in the two values greater than the tolerance of the dimensional measurement indicates manufacturing defects in geometry and the nozzle is not used. In the second step, coefficients a and b of the discharge coefficient equation are determined by comparison with a reference flow standard over the nozzle s full range of operation. The values of a and b are found by a linear regression of the comparison results as a function of Re The flow standards used are from a primary flow calibration chain using a gravimetric technique up to 0.2 g s -1 (10 Nl min -1 ) and a successive addition technique to build up the gravimetric values up to 50 g s -1 (2500 Nl min -1 ). The calibration chain and its two methods are summarized below and will be described in detail in a future publication. 3.1 Gravimetric flow standard In the gravimetric flow standard [Fig. 6], the mass of gas depleted from a pressurized cylinder (1) sitting on a precision mass balance (2) is measured continuously while flowing through a flexible catenary tube (3). The flow is controlled at a fixed point by a thermal mass flow controller (4). The flow measured by the CFN flow element being calibrated (5) is calculated by its flow terminal (6), using nominal nozzle size discharge coefficients, and integrated over time. The difference between the total mass integrated by the flow element and the mass depleted from the cylinder over the same period of time gives an error which is used to adjust the nozzle discharge coefficients. Of course, the results depend on the stability of the balance used to measure the mass of gas depleted from the pressurized cylinder. To eliminate the drift of the balance over time, a taring platform (7) is used. The taring platform periodically lifts the cylinder off the balance and replaces it with a known reference mass (8) whose mass is equivalent to the empty cylinder. The balance readings are corrected by the indicated variation of the reference mass over time. This method greatly reduces the uncertainty in the force measurement made by the balance and assures that tests can be run over periods of time long enough for a significant amount of mass to be depleted from the cylinder relative to the balance s range. The gravimetric flow standard uses a force balanced mass comparator with resolution of 0.1 mg. Typically, 10 g total mass of gas is depleted to complete a flow point. Time is measured by a high precision, interfaceable clock. Ambient conditions around the gas cylinder are measured real time (9) to make a continuous air buoyancy correction. Reproduceability of measurements is on the order of ± and measurement uncertainty is less than ± (k=2) for flow rates from 2 mg s -1 (100 Ncc min -1 ) to 0.2 g s -1 (10 Nl min -1 ). The gravimetric flow standard is used to calibrate the CFN flow elements with K F of 2E0 to 1E2 [Table 1] directly up to 0.2 g s -1 (10 Nl min -1 ) and to establish the 0.2 g s -1 starting point of the successive addition flow standard DH Instruments, Inc. Page 5

6 Fig. 6 - Gravimetric calibration system 3.2 Successive addition flow standard The gravimetric standard gives very acceptable results up to 0.2 g s -1 (10 Nl min -1 ). Above this flow rate, effects from the influences of temperature caused by gas expansion become excessive. A method to build up the lower flow reference values defined by the gravimetric standard to higher flows through a calibration chain made up of CFN based flow elements has been developed [Fig. 7]. This additive method exploits the extensive nature of flow and the very high repeatability of the CFN based flow elements when used to measure a specific point under consistent conditions. A link in the calibration chain consists of two upstream flow elements in parallel and a third downstream element [Fig. 8]. Flow is built up in the link by successive addition of the flow through the two upstream flow elements and transfer from the downstream element to the upstream elements. For example, two 50 Nl min -1 (1E2) flow elements are upstream and a 250 Nl min -1 (5E2) element is downstream. The two 50 Nl min -1 elements have been calibrated at 10 Nl min -1 by the gravimetric flow standard. First, both upstream elements (A, B) are opened simultaneously to flow 10 Nl min -1 each onto the downstream element. This transfers a well defined 20 Nl min -1 point to the downstream element (C). Then, only one upstream element (A) is connected and the 20 Nl min -1 point is reproduced on the downstream element (C) and transferred to the upstream element (A). This is repeated 2005 DH Instruments, Inc. Page 6

7 with the second upstream element (B). Now, both upstream elements can be flowed in parallel to define a point of 40 Nl min -1 on the downstream element. The 40 Nl min -1 point is transferred back up to each of the two upstream elements, after which the two are used in parallel to transfer 80 Nl min -1 back down to the downstream element. The complete procedure is performed on two 250 Nl min -1 downstream elements. In the next link of the chain, the two 250 Nl min -1 elements are then used in parallel upstream of a 1000 Nl min -1 element starting at 40 Nl min -1 and obtaining 80, 160 and 320 Nl min -1 by successive addition, and so on through high flow element ranges up to 2500 Nl min -1. In each link of the chain, the upstream and downstream element nozzles are always of a size ratio (4:1 or 5:1) such that when the two upstream flows are added, the downstream pressure stays low enough so that the upstream nozzles stay choked and the downstream pressure has no effect on the upstream nozzles. To maintain the ratio, the chain has two sides. One side consists 5E1, 2E2, 1E3, 5E3 flow elements. The other side consists of 1E2, 5E2, 2E3, 1E4 elements. For the sake of clarity only one side is show in Fig. 7. The successive addition method builds up a starting primary reference flow value to much higher flow adding only the uncertainty due to the short term reproduceability of the flow elements used. The linearity of the flow elements or of the associated pressure measurements does not contribute to the uncertainty in the flow points, but the results quantify the linearity of the flow elements. Repeating the process allows its reproducebability to be very well estimated. The calibration chain of CFN based flow elements using successive additions starts at 0.2 g s -1 (10 Nl min -1 ) and currently reaches 50 g s -1 (2500 Nl min -1 ) in N 2 with measurement uncertainty of less than ± (k=2). The uncertainty estimate has been verified by comparisons with national measurement institutes at different levels up to the maximum flow rate. 4 CRITICAL FLOW BACK PRESSURE RATIO The ratio of pressure downstream and upstream of the nozzle is referred to as back pressure ratio (BPR). The BPR is considered critical when flow through the nozzle is insensitive to downstream pressure variation. In most practical applications, the maximum critical BPR is important as it defines the rangeability of the element. The BPR at which flow transitions from the critical to non-critical regime has been evaluated experimentally with nitrogen and air for the different nozzle throat sizes used. For the determination of back pressure ratio, two CFN flow elements are connected in series with a vacuum pump down stream [Fig. 9]. The two nozzle sizes are selected so that the upstream nozzle BPR is well within the critical range throughout the test. A control valve is inserted between the downstream 2005 DH Instruments, Inc. Page 7

8 element and the vacuum pump. The vacuum pump, when unrestricted by a control valve, is able to maintain a BPR of less than 0.1. A regulator upstream of both elements is used to set flow. Using the regulator, the flow is adjusted so that absolute pressure upstream of the downstream element is 10, 20, 50 and 100 kpa. At each flow rate, the upstream and downstream nozzle readings are compared. At each upstream pressure, the downstream valve is closed, in increments, causing the pressure immediately downstream of the downstream element to increase. At each downstream pressure increment, the readings of the two elements are recorded and their difference is compared to the original reading differences. When the ratio of the upstream and downstream element readings changes significantly from the original difference, the critical BPR has been exceeded and the test proceeds to the next pressure increment. Figure 10 plots the BPR test results for mm, 1 mg s -1 kpa -1 (50 Ncc min -1 kpa -1 ) and 4.79 mm, 40 mg s -1 kpa -1 (2 Nl min -1 kpa -1 ) nominal throat diameter nozzles. Fig Critical back pressure ratio evaluation for 5E1 and 2E3 CFN flow elements 2005 DH Instruments, Inc. Page 8

9 The maximum BPR at which flow is critical is a function of the Reynolds number. The value is independent of nozzle size and sufficiently consistent to make it practical for a standard Reynolds number dependent value of maximum BPR to be used for day to day operational limits. Fig. 11 shows the maximum critical BPR values found in testing for all the nozzle sizes and plots the average relationship between maximum critical flow BPR and Reynolds number. The limit of -3 sigma from the average is used in the mass flow terminal as a go/no go alert for the operator. When BPR is greater than this limit, a warning of noncritical flow is given. The evaluation process of new nozzles includes verifying that their critical BPR falls within the standard limits. Examination of nozzles whose critical BPR is out of the limits usually reveals defects in geometry relative to the desired throat profile. 5 EXPERIMENTAL EVALUATIONS Fig Back pressure ratio deviations As the CFN based elements are used as calibrated transfer standards, their evaluation has mainly focused on measurements of repeatability, the magnitude of environmental influences and stability over time. 5.1 Repeatability To evaluate repeatability, two elements are connected in series as in Fig. 12. A sequence of flow rates is set and the disagreement between the two at each flow rate is recorded. The sequence is repeated. For example, Fig. 13 shows the results of repeating a flow sequence 5 times with a 1.52 mm, 4-1 mg s -1 kpa (200 Ncc min -1 kpa -1 ) nominal throat diameter element upstream and a 2.40 mm, 10 mg s -1 kpa -1 (500 Ncc min -1 kpa -1 ) nominal throat diameter element downstream. The disagreement of individual readings from the two nozzles is compared to the average disagreement. The repeatability relative to the measured value decreases as the flow decreases. This is attributed to the upstream pressure transducers for which repeatability is a function of their full scale DH Instruments, Inc. Page 9

10 5.2 Ambient Temperature Effect Fig Repeatability results To evaluate the influence of ambient temperature on the flow element, the downstream element of two connected in series is placed in an environmental chamber and the upstream element is left at ambient laboratory temperature (23ºC, ± 1). A heat exchanger is placed in the chamber to assure that the gas entering the downstream element is at the same temperature as the element [Fig. 14]. A series of flow values is set using flow control hardware upstream of the two elements and the disagreement between the two elements is recorded at each point. First, the two elements are compared with both at ambient temperature. Then, the chamber temperature is changed. After temperature stabilization, the same nominal flow points are run. Comparing the disagreement in the flow indicated by the two elements at ambient temperature with the disagreement observed when the downstream element and gas entering it are at a different temperature isolates the influence of changing the temperature of the element, within the limits of the repeatability of the two elements. Fig. 15 plots the influence of changing the downstream element temperature from ambient to 10 and 35 ºC using the same size flow elements as in the repeatability test. The results show that the temperature measurement and compensation for both the expansion of the nozzle throat and the characteristics of the flowing gas work well. The linear thermal expansivity of the stainless steel nozzle material is ºC -1. Over the 25 ºC temperature range studied, the effect on flow is about four times greater than the difference observed after compensation. This shows not only that the design to determine nozzle temperature is effective but also, that the mathematical modelization of gas compressibility, viscosity, isentropic coefficient and nozzle critical flow function with pressure and temperature is correct DH Instruments, Inc. Page 10

11 5.3 Inlet Gas Temperature Effect Fig Ambient temperature testing results To evaluate the influence of inlet gas temperature on the flow element measurements, the setup and procedure are the same as for the ambient temperature effect evaluation but the gas heat exchanger is kept outside of the chamber [Fig. 16]. This causes the gas delivered to the downstream element to remain at ambient temperature. As the temperature of the downstream element is changed, the influence of changing the difference between the element and the gas inlet temperature can be observed. Fig. 17 plots the difference between having the gas enter the element at the same temperature as the element and the gas being 10 ºC lower and higher than element (element at 10 and 30 ºC). This test evaluates the efficiency of the high flow heat exchanger. The deviation increases as flow increases and the sign of the deviation depends on the sign of the difference between the inlet gas and element temperatures. In the test, a difference of +10 and 10 ºC leads to a relative deviation of ± 3 to To assure that this effect is less than ± of the measured value The recommended maximum difference of inlet gas temperature from ambient temperature is 5 ºC DH Instruments, Inc. Page 11

12 Fig Effect of changing inlet gas temperature relative to element temperature 5.4 Upstream Flow Path Geometry To evaluate the influence of upstream gas geometry on the flow element measurements, two elements are connected directly in series as in Fig. 18 and compared. Then an elbow is introduced between the two and the measurements are repeated. Finally, a double elbow (equivalent to one leg of a tee fitting) is placed between the two and the measurements are repeated [Fig. 18]. Fig. 19 plots the influence of a single and double elbow upstream of the element relative to a straight pipe. It is well known that CFNs used in compliance with the ISO standard have little sensitivity to upstream geometry. The design of these CFN based elements keeps the influence within their observed repeatability DH Instruments, Inc. Page 12

13 Fig Effect of upstream geometry 5.5 Stability CFNs are less affected by contamination than laminar flow elements. Over five years experience has been gained with a large group of CFN based flow elements taking conventional gas filtering precautions. This experience demonstrates that the observed stability over time of flow measurements made with CFN elements is overwhelmingly linked to the stability of the upstream pressure measurement devices. With regular recalibration of the pressure transducers used, no systematic evolution in the nozzle throat diameters has been able to be detected. 6 CONCLUSIONS The new CFN based elements complement existing LFE based elements and extend the range of the molbloc/molbox system upward to 50 g s -1 (2500 Nl min -1 ) and beyond. The block design, which combines the Venturi nozzle and gas conditioning hardware into an integrated assembly supported by a standard flow terminal, simplifies operation and maximizes repeatability. The design features intended to minimize sensitivity to ambient conditions appear to do so, in the same magnitude as the flow measurement system s repeatability. The calibrated CFN based elements are easy to use and reliable standards for laboratory and other applications. They currently provide one year measurement uncertainty of ± of reading (k=2) with repeatability an order of magnitude better. When used as transfer standards, the uncertainty in flow they are able to provide is limited by the uncertainty in the references available to calibrate them, not by the molbloc/molbox system itself. They are also ideal check standards and intercomparison artifacts. The compact and rugged presentation of the elements and flow terminal make them easily transportable. The integration of the nozzles, gas conditioning and pressure and temperature measurement assures consistent auxiliary measurements and operating conditions which maximizes repeatability. Ultimately, the stability over time of the CFN based flow measurement system 2005 DH Instruments, Inc. Page 13

14 depends on the stability of its pressure and temperature measurements. With the system s redundant measurement of these parameters, the user can be alerted to possible drift without referring to an external standard. On-going development is extending the range of the CFN based elements higher by increasing the upstream pressure range. Work is also under way to characterize them with gases other than nitrogen and air, in particular argon, helium, hydrogen and methane. 7 REFERENCES [1] DH Instruments, Inc., Product literature, molbloc/molbox Gas Flow Standards, [2] Delajoud, P., Girard, M., A High Accuracy, Portable Calibration Standard for Low Mass Flow, Proceedings of XIII IMKEO World Congress of Metrology, [3] ISO Standard: 9300, Measurement of Gas Flow by Means of Critical Flow Venturi Nozzles, ISO, [4] ASME/ANSI Standard: MFC-7M-1987, Measurement of Gas Flow by Means of Critical Venturi Nozzles, ASME, [5] Wright, J., What is the Best Transfer Standard for Gas Flow?, Proceedings of Flomeko 11, [6] Delajoud, P.R., Critical Gas Flow Measurement Apparatus and Method, US Patent No. 6,732,596, [7] Delajoud, P.R., Precision Gas Mass Flow Measurement Apparatus and Method for Maintaining Constant Fluid Temperature in a Thin, Elongated Flow Path, US Patent No. 5,445,035, [8] Ishibashi, M., Takamoto, M., Theoretical Discharge Coefficient of a Critical Circular-arc Nozzle with Laminar Boundary Layer and its Verification by Measurements Using Super-accurate Nozzles, Flow Measurement Instrumentation, 11 (4) , DH Instruments, Inc. Page 14