WO2015088452A1

WO2015088452A1 - Thermal mass flow meter and the gas-identification method

Info

Publication number: WO2015088452A1
Application number: PCT/SI2014/000070
Authority: WO
Inventors: Klemen RUPNIK; Jože KUTIN; Ivan BAJSIČ
Original assignee: Univerza V Ljubljani, Fakulteta Za Strojništvo- Lmps
Priority date: 2013-12-13
Filing date: 2014-12-02
Publication date: 2015-06-18
Also published as: SI24577A

Abstract

The subject of the invention is a thermal mass flow meter and a gas-identification method. The thermal mass flow meter according to the invention is characterized by comprising at least two thermal flow sensors with different constructional parameters and/or different operational parameters, and by the capability to identify the type of gas flowing through the thermal mass flow meter employing the gas-identification method according to the invention. The gas- identification method is characterized in that the mass flow readings for different types of gases are determined on the basis of the output signals and the measurement characteristics of at least two thermal flow sensors, these mass flow readings are used as the inputs for the gas- identification algorithm, and the identified gas is the gas that represents the optimal solution of the defined objective function.

Description

THERMAL MASS FLOW METER AND THE GAS-IDENTIFICATION METHOD

SUMMARY OF THE INVENTION

The subject of the invention is a thermal mass flow meter comprising at least two thermal flow sensors with different constructional and/or operational parameters, and a gas-identification method. The field of the presented invention is the measurement of mass flow rate by thermal mass flow meters. The thermal mass flow meter according to the invention is used to measure the mass flow rate of different types of gases and to perform the gas-identification method. The gas-identification method according to the invention is used for the identification of the type of gas flowing through the thermal mass flow meter. The thermal mass flow meter according to the invention can be used together with a control valve and control electronics to form a thermal mass flow controller.

The technical problem that is not yet satisfactorily solved is the measurement of mass flow rate by a thermal mass flow meter if the type of gas actually flowing through the thermal mass flow meter is unknown. The measurement characteristic of the thermal mass flow meter, which relates the output signal and the measured mass flow rate, depends on the composition and the type of gas. In conventional thermal mass flow meters, an appropriate correction factor has to be applied in order to properly measure the mass flow rate of a gas that is different to the gas used for the calibration. Another option is to perform the calibration for various gases and then the proper measurement characteristic has to be selected when a conventional thermal mass flow meter is being used. In both cases, the gas that is actually flowing through the conventional thermal mass flow meter has to be known.

The task and objective of the invention is the development of the thermal mass flow meter with capabilities to measure the mass flow rate of different types of gases and to identify the type of gas flowing through the thermal mass flow meter.

The objective is realized with the thermal mass flow meter according to the invention, comprising at least two thermal flow sensors with different constructional parameters and/or different operational parameters and employing the gas-identification method according to the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be presented with examples of the implementation and figures showing the following:

Figure 1 : Scheme of the thermal mass flow meter according to the invention.

Figure 2: Scheme of the cross-sectional view of the thermal flow sensor.

Figure 3: Schemes of the cross-sectional views of some possible designs of the thermal flow sensor.

Figure 4: Measurement characteristics of two different thermal flow sensors for two different types of gases. The principle of the gas-identification method is presented.

Figure 5: Block diagram of the gas-identification method.

Figure 6: Relative differences in the mass flow readings for different types of gases as a function of the parameter n₂, for n_\ - 0.5. The actual gas is air.

Figure 7: Measurement characteristics of the thermal flow sensor with the circular cross- section.

Figure 8: Measurement characteristics of the thermal flow sensor with the square cross-section.

Figure 9: Relative differences in the mass flow readings for different types of gases. The actual gas is air. The results of the validation experiment are presented with symbols.

Figure 10: Results of the validation experiment for the gas-identification method. The actual gas is air. CONSTRUCTION AND OPERATION OF THE THERMAL MASS FLOW METER

The thermal mass flow meter according to the invention is presented in Fig. 1. It comprises at least two thermal flow sensors, for example, the thermal flow sensors 1 and 2, and the gas- temperature sensor 3 that measures the temperature of the gas T_g. The sensors 1-3 are exposed to the mass flow of a gas with the mass flow rate q,_n. The sensors 1-3 are installed in the same cross-sectional plane of the pipe 4 or in different cross-sectional planes of the pipe 4. The sensors 1-3 are connected to the electronics 5 within the enclosure 6. The pipe 4 is part of the thermal mass flow meter, or it is a part of the pipeline into which the thermal mass flow meter is inserted. The gas-temperature sensor 3 is optional, because one or more of the thermal flow sensors may operate alternately in the function of a thermal flow sensor and in the function of a gas-temperature sensor.

A scheme of the cross-sectional view of a typical embodiment of the thermal flow sensor is shown in Fig. 2. The thermal flow sensor typically comprises a sensing element 7 on a support structure 8, filling material 9 and a sheath 10. The sensing element 7 is connected to the electronics 5 with the connecting leads. Different types of the sensing element 7 can be used, for example, a wire-wound resistance temperature detector or a thin-film resistance temperature detector. The sensing element 7 has typically two functions; it is simultaneously heated with the electrical power and used to measure the temperature. The thermal flow sensor may optionally comprise an extra heater, for example, a resistor element that is heated with the electrical power, and so the sensing element 7 is only used to measure the temperature.

The electronics 5 typically comprises:

- power-supply electronics that supply the electrical powers i and Ρ₂ to the thermal flow sensors 1 and 2, respectively,

- measurement electronics that determine the temperature of the gas T_g measured by the gas- temperature sensor 3,

- measurement electronics that determine the temperatures T_\ and Γ₂, measured by the thermal flow sensors 1 and 2, respectively,

a controller that maintains the constant temperature differences, ATj = T - T and AT₂ = T₂ - T ' or the constant electrical supplies, a processor that calculates the mass flow readings and implements the algorithm of the gas- identification method according to the invention.

Each of the thermal flow sensors is typically operated in one of two modes:

Constant temperature-difference mode: a constant temperature difference between the temperature of the sensing element within the thermal flow sensor and the temperature of the gas AT is maintained. The electrical power P changes with the mass flow rate of the gas

Constant power mode: a constant electrical supply (the electrical power P, the electrical current 1 or the electrical voltage V) is maintained. The temperature difference between the temperature of the sensing element within the thermal flow sensor and the temperature of the gas AT changes with the mass flow rate of the gas q_m.

The output signals of the thermal flow sensors 1 and 2 can be, for example, written as (PIAT)_\ and (PIAT)2, respectively. On the basis of the output signals {PIAT)_\ and ( /ΔΙ)₂ and the measurement characteristics of the thermal flow sensors 1 and 2, respectively, the mass flow readings q_m>\ and q_m^, respectively, are obtained.

For the realization of the gas-identification method according to the invention, the thermal flow sensors, for example, the thermal flow sensors 1 and 2 in the embodiment presented in Fig. 1, have to be different in terms of constructional parameters and/or operational parameters:

(i) Fig. 3 shows schemes of the cross-sectional views of some possible designs of the thermal flow sensor. Different constructional parameters of the thermal flow sensors may be achieved in terms of:

- the shapes of the cross-sections; for example, one thermal flow sensor has circular cross-section 10 and the other thermal flow sensor has pentagonal cross-section 1 1, hexagonal cross-section 12, triangular cross-section 13 or square cross-section 14- 17, etc.,

the orientations of the cross-sections with respect to the flow direction; for example, the square sheaths 14 and 15 of the thermal flow sensors have the same shapes and equal dimensions of the cross-sections, but different orientations with respect to the flow direction, the dimensions of the cross-sections; for example, the sheaths 15 and 16 of the thermal flow sensors have the same shapes but different side lengths,

the variations of the constructional parameters in the axial direction of the thermal flow sensors in terms of shapes, orientations and/or dimensions of the cross- sections; for example, the diameters of the thermal flow sensors vary differently along the thermal flow sensors, or the thermal flow sensors have different lengths,

- the internal structures in terms of geometries, dimensions and/or materials; for example, the wire-wound resistance temperature detector is used as the sensing element in one thermal flow sensor and the thin-film resistance temperature detector is used as the sensing element in the other thermal flow sensor, or the filling materials in the thermal flow sensors have different thermo-physical properties such as the thermal conductivities.

The particular external design of a thermal flow sensor may be obtained with:

a sheath that is manufactured with the particular shape of the cross-section; for example, sheaths 10-16,

an additional sheath with a particular shape that may be placed on the existing sheath; for example, the sheath 17 is placed on the sheath 18.

(ii) Different operational parameters of the thermal flow sensors may be achieved in terms of:

- the maintained constant temperature differences are not the same, ΔΤ_\≠ Δ ₂, for the constant temperature-difference mode,

- the maintained constant electrical powers are not the same, P_\≠ P₂, for the constant power mode.

It should be clearly understood that the thermal mass flow meter according to the invention is not limited to the presented embodiment comprising two thermal flow sensors. In general, the thermal mass flow meter according to the invention may comprise more than two thermal flow sensors, whereby each of the thermal flow sensors has different constructional and/or operational parameters according to the description above, without departing from the scope of the invention. REALIZATION OF THE GAS-IDENTIFICATION METHOD

Fig. 4 shows the principle of the gas-identification method. The curves in Fig. 4 represent the measurement characteristics of two different thermal flow sensors 1 and 2 within the thermal mass flow meter according to the invention for two different types of gases, for example, gas A and gas B. Gas A is considered to be the actual gas flowing through the thermal mass flow meter. If the proper measurement characteristics (in this case for gas A) are employed, the mass flow readings of the thermal flow sensors 1 and 2 are equal: q_m^ = q ^- In contrast, if improper measurement characteristics (in this case for gas B) are employed, the mass flow readings are not equal: q_m^≠ q_m, ^-

For a practical realization of the gas-identification method, the relative difference between the mass flow readings should be as great as possible if improper measurement characteristics are employed. In the case of selection of improper measurement characteristics, the difference between the mass flow readings of the thermal flow sensors 1 and 2, q_m>\ and q_m^, respectively, depends on the difference between the constructional parameters and/or the difference between the operational parameters of the thermal flow sensors 1 and 2, respectively. Therefore, at least two thermal flow sensors with different constructional and/or operational parameters are required for the realization of the gas-identification method.

The block diagram of the gas-identification method is presented in Fig. 5. The gas is flowing through the thermal mass flow meter with the mass flow rate q_m. The output signals of the thermal flow sensors 1 and 2 are (Ρ/ΔΤ)_\ and (Ρ/ΔΙ)₂, respectively. Database 19 contains the information regarding the measurement characteristics for the defined set of gases, for example, calibration constants, look-up tables, conversion factors, measurement models, mathematical models, etc., and other information regarding the thermal mass flow meter. The output signals of the thermal flow sensors and the information from database 19, for example, data Bi, data B₂ ... data B , are used to perform the mass flow reading calculation 20 in order to obtain the mass flow readings: q_m}^Bi), q_m ^Bl) ... q_m ^B>,);

<7_m,2 ^(¾) · · · 4_m,2 ^{(¾) for the} §^ases B_j, j = \ ... N from the defined set of gases. The mass flow readings are inputs for the gas- identification algorithm 21 with the objective function that originates from the difference between the mass flow readings of the thermal flow sensors, for example, the mass flow readings of the thermal flow sensors 1 and 2. The identified gas is the gas that represents the optimal solution of the defined objective function,

The gas-identification algorithm 21 , is realized, for example, as:

The relative difference between the mass flow readings of the thermal flow sensors 1 and 2 is calculated for each gas B_j,j = 1 . . . N: ε(¾) (¾)/ (¾)_!

(1)

The identified gas is the gas that minimizes the objective function, which is defined as the absolute value of the relative difference in the mass flow readings

The statistical significance of the difference in the mass flow readings for each gas B_j = 1 ... N is evaluated with the normalized error:

where U \ q_{m l} ^{y ,!} j and U q_{m 2} ^J' j consider the dispersion that could be reasonably

(B ) (B )

attributed to the mass flow readings q_{m l} ^y and q_{m 2} , respectively; for example, u q_m ^B'^ and u[_i q_{m 2} ^B'^ are the expanded measurement uncertainties of the mass flow readings. The values of the measurement uncertainties are stored in the database 19. If

E M > 1 , the difference in the mass flow readings for gas B_j is statistically significant, and if ) < 1 , the difference in the mass flow readings for gas B_j is statistically insignificant. If the difference in the mass flow readings is statistically significant for a particular gas, this gas can be identified as an improper gas. The difference between the mass flow readings of the thermal flow sensors 1 and 2 must be statistically significant for all but one gas from the defined set of gases in order to identify the proper gas with a sufficient degree of confidence. THEORETICAL BACKGROUND OF THE GAS-IDENTIFICATION METHOD

A simple mathematical model will be employed to study the difference between the mass flow readings of two different thermal flow sensors (i = 1, 2) for different types of gases if improper measurement characteristics are employed. The thermal flow sensors are assumed to be inserted into a pipe with a uniform gas flow with the temperature T_g and the mass flow rate q_m - pVA , where p is the density of the gas, V is the average velocity and A is the pipe cross- sectional area. The intensity of the convective heat transfer from the surface of the i-th thermal flow sensor to the gas flow is determined by the convective heat transfer coefficient /*,. The temperature of the sensing element within the z^'-th thermal flow sensor is Γ, = T_g + ΔΓ,·. The constant temperature difference Δ 7_/ is maintained by supplying the electrical power P_t = 7½² to the sensing element, where R, is the electrical resistance of the sensing element and 7, is the electrical current passing through the sensing element within the z^'-th thermal flow sensor. If only one-dimensional heat transfer in the radial direction is assumed, the output signal of the z^'-th thermal flow sensor is:

where the constants c_1;, and ¾ depend on the dimensional and material properties of the z^'-th thermal flow sensor. The convective heat transfer coefficient for a cylinder in a cross-flow is often defined by the power model:

Nu = a Pr^m Re_D" , (4) which relates the Nusselt number Nu = hD I λ , the Prandtl number Pr = c_pr\ I λ and the

Reynolds number Re_D = pVD/ r\ , where D is the external characteristic length of the thermal flow sensor, and a, m and n are parameters of the power model. The thermodynamic and transport properties of the gas, i.e., the thermal conductivity λ, the specific heat at constant pressure c_p and the dynamic viscosity η, are evaluated at the film temperature:

T + T

(5) where T_s is the temperature of the surface of the i-th thermal flow sensor and T_g is the temperature of the gas.

Considering V = q_m I pA , the convective heat transfer coefficient for the z^'-th thermal flow sensor can be written as:

(6)

For a given mass flow rate q_m, the output signal of the i-th. thermal flow sensor is ( /Δ7),. If the measurement characteristics for gas A and gas B are employed, the mass flow readings are q_{m t} ^{A) and q_m , respectively (see Fig. 4). The difference between the mass flow readings

Qn,,i^(A) q_m ^B) is evaluated on the basis of the same output signal, i.e., ( /

that results in equal heat transfer coefficients (according to Eq.

(3)):

(7)

Considering Eqs. (6) and (7), the ratio between the mass flow readings of the i-th thermal flow sensor is:

9r, \ cp>' ^B J

If the actual gas is gas A and the measurement characteristics for gas A are employed, the mass flow readings of the thermal flow sensors 1 and 2 are equal:

M _

l m ,l (9)

In contrast, if the actual gas is gas A and the measurement characteristics for gas B are employed, the mass flow readings of the thermal flow sensors 1 and 2 are not equal and the relative difference in the mass flow readings is:

If equal surface temperatures for both thermal flow sensors 1 and 2 are assumed, i.e., T_{s l} = T_{s 2} , then the following gas properties are equal: c_{p l} = c_{p 2} , r\_{ = η₂ and λ, = λ₂ . Because m is typically a constant value of about 1/3, w, = m₂ is also taken into account and Eq. (10) simplifies to:

Relative differences in the mass flow readings for different types of gases as a function of the parameter n₂ are presented in Fig. 6. Air is considered as the actual gas (gas A) and the parameter n\ is set to a constant value of 0.5. The thermodynamic and transport properties of the gases were determined using the NlST REFPROP database for a film temperature of 25 °C and a pressure of 100 kPa. If the proper measurement characteristics are employed (in this case for air), then ε = 0 . In contrast, if the measurement characteristics for oxygen, nitrous oxide, carbon dioxide or argon are employed, then |ε| > 0 and |ε| is also increasing with the difference between n% and ri\.

EXAMPLE OF THE IMPLEMENTATION OF THE GAS-IDENTIFICATION METHOD

The thermal mass flow meter comprising two thermal flow sensors 1 and 2 with circular and square cross-sections, respectively, was assembled and calibrated for the following types of gases: air, oxygen, nitrous oxide, carbon dioxide and argon. The reference mass flow rates were set and measured with the reference measurement system. For the thermal flow sensors 1 and 2, the same temperature differences AT = ΔΓ₂ were maintained. The output signals ( /Δ7)ι and ( /Δ7)₂ were measured. The obtained measurement characteristics of the thermal flow sensors 1 and 2 are presented in Figs. 7 and 8, respectively. The information regarding these measurement characteristics was stored in the database 19.

Fig. 9 shows the relative differences between the mass flow readings of the thermal flow sensors 1 and 2 with circular and square cross-sections, respectively, for different types of gases that were calculated from the measurement characteristics. If the measurement characteristics are selected properly (in this case for air), then ε = 0, but otherwise |ε| > 0 .

The experimental validation of the gas-identification method was performed at a mass flow rate of about 225 g/min of air. The results of the validation experiment are presented graphically in Fig. 9 (with symbols) and numerically in Fig. 10. Due to achieving the minimum absolute value of the relative difference in the mass flow readings |ε|, air would be properly identified as the actual gas. However, the difference in the mass flow readings is statistically insignificant for air and oxygen, and thus neither of these two gases can be identified as improper gas with a sufficient degree of confidence for this particular case. The calculation of the normalized error considered the dispersion that could be reasonably attributed to the mass flow readings of

= u[q_m}^B<] l q_m}^B<] = 1.1 % .

Claims

1. The thermal mass flow meter for the measurement of mass flow rate of gases, characterized by comprising at least two thermal flow sensors with different constructional parameters in terms of:

- the shapes of the cross sections and/or

- the dimensions of the cross-sections and/or

- the orientations of the cross-sections with respect to the flow direction and/or

- the variations of constructional parameters in the axial direction of the thermal flow sensors in terms of shapes, orientations and/of dimensions of the cross-sections and/or

- the internal structures in terms of geometries, dimensions and/or materials,

and/or different operational parameters in terms of:

- the maintained temperature differences or

- the maintained electrical supplies,

whereby the said thermal mass flow meter has the capability to identify the type of gas flowing through the thermal mass flow meter employing the gas-identification method.

2. A flow meter according to claim 1, characterized in that one or more of the said thermal flow sensors operate alternately in the function of a thermal flow sensor and in the function of a gas-temperature sensor.

3. A flow meter according to claim 1 or 2, characterized in that the said thermal mass flow meter is used together with a control valve and control electronics to fom a thermal mass flow controller.

4. Use of the flow meter according to claim 1, 2 or 3 for the identification of the type of gas flowing through the flow meter employing the gas-identification method.

5. The gas- identification method for the identification of the type of gas flowing through a thermal mass flow meter, characterized in that:

- the mass flow readings for different types of gases are determined on the basis of the output signals and the measurement characteristics of at least two thermal flow sensors,

- the mass flow readings of at least two thermal flow sensors are used as the inputs for the gas-identification algorithm, - the objective function in the gas-identification algorithm originates from the difference between the mass flow readings of at least two thermal flow sensors,

- the identified gas is the gas that represents the optimal solution of the defined objective function.

A gas-identification method according to claim 5, characterized in that the said objective function is defined as the relative difference between the mass flow readings of the thermal flow sensors.

A gas-identification method according to claim 5, characterized in that the said objective function is defined as the normalized error considering the dispersion that could be reasonably attributed to the difference between the mass flow readings of the thermal flow sensors.