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

TRANSFER STANDARD APPLICATIONS

P. Delajoud, M. Girard, M. Bair DH Instruments, Inc.

4765 E. Beautiful Lane Phoenix AZ 85044 USA

Abstract - The use of toroidal throat critical flow Venturi nozzles for the measurement of the mass flow of gasses is well known and described in ISO and ANSI/ASME standards. A new flow module uses nozzles as the basis of a high precision transfer standard system to cover the range of flow from 0.02 to 40 g·s-1 (1 to 2 000 Nl·min-1) and beyond. In the new module, a gas conditioning system defining an isothermal, unidirectional flow stream is combined with a toroidal throat Venturi nozzle. The calculations used to derive flow include secondary corrections not usually considered and are applied at Reynolds numbers well below the limit defined by the ISO standard. The back pressure ratios necessary to assure critical flow in these conditions have been determined experimentally over the full flow range as a function of Reynolds number and at absolute upstream pressures from 20 to 500 kPa for a variety of nozzle sizes. Experiments to evaluate the influence of operating conditions on the measurement precision of the modules have been conducted. The results confirm the suitably of the new design as an intercomparison artifact and as a tool for the dissemination of reference mass flow values.

INTRODUCTION

The measurement of the mass flow of gasses in the range of less than 0.02 to 40 g·s-1 (1 to 2 000 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 dependence on external influences such as ambient pressure, ambient temperature, upstream geometry and upstream pressure. In the bottom 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 increases aggravating temperature influences and eventually the flow regime transitions to turbulent. A well know 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 40 g·s-1 (1 to 2 000 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®.

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 1·105, 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 6·10-3·ºC-1. In the CFN, the influence of temperature on mass flow is inversely proportional to the square root of the temperature which results in an effect four times smaller, or 1.5·10-3·ºC-1. Viscosity affects only the determination of Reynolds number, leading to a negligible secondary effect in the flow calculation. Finally, the CFN has no dependence on differential pressure as 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 this 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 (Cd) 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 1·105. 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 temperature and flow profile just upstream of the nozzle. The nozzle and gas conditioning hardware make up a single integrated flow measurement module. Patents are pending covering various aspects of the new elements design and use.

The CFN based elements are used with an existing mass flow terminal [Figure 1].

Figure 1. molbox1 flow terminal

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.

Figure 2. molbloc-L and molbloc-S flow elements

The CFN based elements (molbloc-S) are similar in appearance to the laminar flow elements (molbloc-L) [Figure 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 [Figure 3]. Twelve sizes with nominal throat diameter from 0.15 mm (0.04 mg·s-1·kPa-1) to 10.7 mm (0.2 g·s-1·kPa-1) are produced to cover a variety of ranges.

Figure 3. Two nozzle designs

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 lower flow rates (up to 1 g·s-1·kPa-1) and one for higher flow rates (2 g·s-1·kPa-1 and above). The main difference between them 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 Figure 4 uses the patented gas temperature conditioning method introduced for the laminar flow elements [6]. 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.

Figure 4. Low flow element with annular gas conditioning

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 is significantly different from the temperature of the body, it cannot be assumed that the gas will be equal to the temperature of the body. It is therefore not possible to know gas temperature accurately 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 [Figure 5]. The thermometer shield is welded to the element body but the thermometer’s reading is not affected by thermal conductivity of the shield since, due to the heat exchanger, the gas temperature is very close to the body temperature. To improve its efficiency, the heat exchanger is made of titanium and the gas passes through narrow, radial slots.

Figure 5. High flow element with radial slot gas conditioning

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 influence is on the order of 3.2·10-5· 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.

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.

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 (KF). Table 1 lists the CFN elements available with their nominal throat diameters, gas conditioning type, and nominal flow when operated in the critical flow regime at upstream pressure of 500 kPa.

Table 1. Standard molbloc-S flow elements

Designator (KF)

Nominal Throat

Diameter [mm]

Gas Conditioning

Type

N2 Flow @ 500 kPa upstream

[g·s-1 (Nl·min-1)] 2E0 0.152 Low 0.02 (1)

5E0 0.241 Low 0.05 (2.5)

1E1 0.340 Low 0.1 (5)

2E1 0.480 Low 0.2 (10)

5E1 0.759 Low 0.5 (25)

1E2 1.07 Low 1 (50)

2E2 1.52 High 2 (100)

5E2 2.40 High 5 (250)

1E3 3.39 High 10 (500)

2E3 4.79 High 20 (1 000)

5E3 7.58 High 50 (2 500)

1E4 10.70 High 100 (5 000)

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 [7]. 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-0.5. Up to 0.2 g·s-1 (10 Nl·min-1), the reference is a gravimetric flow standard in which the amount of gas depleted from a pressurized bottle is measured continuously while flowing [8]. Above 0.2 g·s-1, an additive method is used within a calibration chain to transfer the gravimetric measurements from low flow to higher flow elements. This method, to be described in detail in a future publication, exploits the extensive nature of gas flow and the very high repeatability of individual elements operated under consistent conditions. The validity of the additive method has been verified by comparisons with national measurement institutes at different levels up to the maximum flow of the calibration chain.

The calibration chain currently reaches 40 g·s-1 in N2 and air with an uncertainty of 1.5·10-3 (k=2).

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 volume 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.

Figure 6. Back pressure ratio evaluation setup

For the determination of back pressure ratio, two CFN based flow elements are connected in series with a vacuum pump down stream [Figure 6]. 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 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. Figures 7 and 8 plot the BPR test results for 5E1 (1 mg·s-1·kPa-1), 0.759 mm nominal throat diameter, and 2E3 (40 mg·s-1·kPa-1), 4.79 mm nominal throat diameter, elements.

Figure 7. Critical back pressure ratio evaluation for a 5E1 element

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. Figure 9 shows the maximum critical BPR values found in testing for all the nozzle sizes and plots the average relationship between maximum

Figure 9. Back Pressure Ratio Deviations

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 non-critical 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.

EXPERIMENTAL EVALUATIONS

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.

Repeatability

Figure 10. Repeatability testing setup

To evaluate repeatability, two elements are connected in series as in Figure 10. 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, Figure 11 shows the results of repeating a flow sequence 5 times with a 2E2 (4 mg·s-1·kPa-1), 1.52 mm nominal throat size, element upstream and a 5E2 (10 mg·s-1·kPa-1), 2.40 mm nominal throat size 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 full scale.

Figure 11. Repeatability results

Ambient temperature effect

Figure 12. Ambient temperature dependency testing set up

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 [Figure 12]. 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. Figure 13 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 16·10-6·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.

Figure 13.Ambient temperature testing results

Inlet gas temperature effect

Figure 14. Inlet gas temperature dependency testing set up

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 [Figure 14]. 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. Figure 15 plots the difference between having the gas enter the element at the same temperature as the element and the gas being 10ºC lower and higher than element (element at 10 and 30ºC).

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 ± 0.03 to 0.04 %. To assure that this effect is less than 2·10-4 of the measured value The recommended maximum difference of inlet gas temperature from ambient temperature is 5 ºC.

Figure 15. Effect of changing inlet gas temperature relative to element temperature

Upstream flow path geometry

Figure 16. Upstream geometry effect set up

To evaluate the influence of upstream gas geometry on the flow element measurements, two elements are connected directly in series as in Figure 10 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 [Figure 16]. Figure 17 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.

Figure 17. Effect of upstream geometry

Stability

CFNs are less affected by contamination than laminar flow elements. Over three years experience has been gained with a large group of CFN based flow elements taking conventional gas filtering precautions. This experience demonstrates that the stability over time of the CFN measurements 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.

CONCLUSIONS

The new CFN based elements complement existing LFE based elements and extend the range of the molbloc/molbox® system upward to 40 g·s-1 (2 000 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 ±0.2% 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 depends on the stability of its pressure and temperature measurements. With the system’s redundant pressure and temperature measurements, the user can be alerted of possible drift by disagreement between the two indicating the need for recalibration.

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 gasses other than nitrogen and air, in particular argon, helium, hydrogen and methane.

REFERENCES

[1] DH Instruments, Inc., Product literature, molbloc/molbox Gas Flow Standards, 1999.

[2] Delajoud, P., Girard, M., A High Accuracy, Portable Calibration Standard for Low Mass Flow, Proceedings of XIII IMKEO World Congress of Metrology, 1993.

[3] ISO Standard: 9300, Measurement of Gas Flow by Means of Critical Flow Venturi Nozzles, ISO, 1990.

[4] ASME/ANSI Standard: MFC-7M-1987, Measurement of Gas Flow by Means of Critical Venturi Nozzles, ASME, 1987.

[5] Wright, J., What is the “Best” Transfer Standard for Gas Flow?, Proceedings of Flomeko 11, 2003.

[6] 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, 1995.

[7] 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) 305 – 313, 2000.

[8] Bair, M., The Dissemination of Gravimetric Gas Flow Measurements Through an LFE Calibration Chain, Proceedings of NCSL Conference and Workshop, 1999.