DE102015107584A1 - Method for determining a product of heat capacity and density - Google Patents

Abstract

Method for determining a product of heat capacity and density (Cp · ρ) of a gas or a gas mixture (2) or a value derived therefrom by means of a thermal sensor (1), in particular a thermal flow sensor comprising the following steps: - Determining the thermal thermal conductivity (λ) of the gas or of the gas mixture (2); - Determining a flow rate (Q) of the gas or the gas mixture (2) based on the determined thermal conductivity (λ); - Determining the product of heat capacity and density (Cp · ρ) of the gas or the gas mixture (2) or a value derived therefrom on the basis of the determined thermal conductivity (λ) and the specific flow rate (Q).

Description

The invention relates to a method for determining a product of heat capacity and density of a gas or a gas mixture or a value derived therefrom by means of a thermal sensor, in particular a thermal flow sensor.

For the determination of flow properties, in particular of the flow, of a medium or of a fluid, for example of a gas or gas mixture, thermal flow sensors are known which utilize that a (flowing) medium transports heat. Such flow sensors in this case have the classical structure structure with at least one heating structure and at least one temperature sensor element in order to determine the flow of the medium.

Calorimetric thermal flow sensors determine the flow rate of the fluid in a channel via a temperature difference between two temperature sensor elements located downstream and upstream of the heating structure on a substrate. For this purpose, use is made of the fact that the temperature difference is up to a certain point linear to the flow rate or the flow rate. This method or the method is extensively described in the relevant literature.

A qualitative description of the gas, eg. As the thermal parameters or gas composition is not possible with "classic" designs ("upstream" temperature sensor, heater and "downstream" temperature sensor) and evaluation. Thermal sensors must be calibrated to the medium of the application, changing gas composition and thus the thermal gas parameters, this leads to a measurement error in terms of flow velocity.

Sensors that detect thermal thermal conductivity (in addition to specific heat capacity and density, also a thermal parameter) normally operate in quiescent fluids (no-flow condition).

The object of the invention is to propose a method which makes it possible to determine a thermal parameter of a gas or gas mixture by means of a thermal flow sensor.

• – Bestimmung der Wärmeleitfähigkeit des Gases bzw. des Gasgemisches;
• – Bestimmung einer Flussrate des Gases bzw. des Gasgemisches anhand der bestimmten Wärmeleitfähigkeit;
• – Bestimmung des Produktes aus Wärmekapazität und Dichte des Gases bzw. des Gasgemisches oder eines davon abgeleiteten Wertes anhand der bestimmten Wärmeleitfähigkeit und der bestimmten Flussrate.

The object is achieved by a method for determining a product of heat capacity and density of a gas or a gas mixture or a value derived therefrom by means of a thermal sensor, in particular a thermal flow sensor, wherein the method comprises the following steps:

• - Determination of the thermal conductivity of the gas or the gas mixture;
• - Determining a flow rate of the gas or the gas mixture based on the determined thermal conductivity;
• - Determination of the product of heat capacity and density of the gas or of the gas mixture or of a value derived therefrom on the basis of the determined thermal conductivity and the specific flow rate.

According to the invention, a method for determining the product of density and heat capacity is proposed, in which different parameters, in particular thermal parameters, can be determined by means of different excitation of the heating structure. Thus, the flow rate and then the product of density and heat capacity of the gas or gas mixture can be determined based on the thermal conductivity can be determined via the thermal flow sensor.

Thermal sensors are to be understood as meaning, in particular, thermal flow sensors. These typically have a heating element and two temperature sensing elements spaced from the heating element.

An advantageous embodiment provides that for determining the product of heat capacity and density of the gas or the gas mixture, a heating structure of the thermal flow sensor is excited with a substantially constant power. In particular, it is provided that for determining the product of heat capacity and density of the gas or the gas mixture, a temperature of the heating structure is detected.

An advantageous embodiment provides that, in order to determine the product of heat capacity and density of the gas or of the gas mixture, use is made of a stored first function or values derived therefrom, and wherein the first function has the following relationship: T _heater = f ₁ (λ, ρ · Cp, Q, P), where λ is the thermal conductivity, ρ is the density, Cp is the specific heat capacity Q of the flow rate, P is the power applied to the heater, and T is the _heater temperature of the heating structure. From this first equation, the product of density and heat capacity, the flow rate or the thermal conductivity can be determined. For this purpose it is assumed that the power applied to the heater is essentially constant. The power can be both a DC and AC signal. In In the case where there is no flow velocity or it is substantially zero, the above equation depends only on the thermal conductivity and the applied power. In addition, if the thermal conductivity is known, the temperature of the heater can be determined, in particular calculated.

An advantageous embodiment provides that, to determine the thermal conductivity, a second temperature is detected by means of a second temperature sensor element disposed downstream with respect to a heating structure. In particular, this embodiment provides that, based on the detected second temperature, the thermal conductivity corresponding to the gas or gas mixture is determined and / or that a third function or values derived therefrom is used to determine the corresponding thermal conductivity of the gas or gas mixture or wherein the third function or the values derived therefrom describes the dependence of the second temperature on the flow rate and is substantially independent of the flow rate within a defined range, such that a second temperature for the defined range substantially independent of the flow rate is, determine. Furthermore, the embodiment can provide that, based on the second temperature for the defined area, which is essentially independent of the flow rate, the thermal conductivity is determined.

An advantageous embodiment provides that the flow rate of the gas or of the gas mixture is determined on the basis of the previously determined thermal conductivity and the second temperature of the downstream arranged second temperature sensor element.

The invention will be explained in more detail with reference to the following drawings. It shows:

1 FIG. 2: a cross-section of an embodiment of the flow sensor according to the invention, FIG.

2 : a table in which the three different functional modes of the control and / or evaluation unit are shown one below the other,

3 : an exemplary third function of the second temperature as a function of the flow rate, and

4 : an exemplary first function of the temperature of the heating structure as a function of the flow rate for different values of thermal conductivity and different values of the product of heat capacity and density.

1 shows a cross section of an embodiment of the flow sensor according to the invention 1 , Here, the thermal flow sensor 1 a substrate 3 on top of which a first dielectric layer 6 is applied. Furthermore, the substrate has 3 in a first area 4 a recess 5 on, leaving the first dielectric layer 6 in the first area 4 on the substrate 3 a membrane 7 formed. On this membrane 7 is a heating structure 8th applied such that it is between a first and a second temperature sensor element 9 . 10 along the flow direction of the gas or gas mixture 2 located and serves the gas or gas mixture 2 to heat. The two temperature sensor elements 9 . 10 are also on the first dielectric layer 6 applied and preferably arranged such that they are in the first area 4 lie. The two temperature sensor elements are also referred to as "upstream" and "downstream" temperature sensors or temperature sensor elements, wherein the "upstream" temperature sensor element 9 upstream and the downstream temperature sensor element 10 downstream with respect to the flow direction of the gas or gas mixture and the heating structure is arranged.

By means of these two temperature sensor elements 9 . 10 is the temperature of the heating structure 8th heated gas or gas mixture 2 detected. To protect the heating structure 8th and the two temperature sensor elements 9 . 10 is a second dielectric layer 16 on the first dielectric layer 6 applied. For the determination of a gas or the composition of a gas mixture 2 becomes the substrate 3 opposite side of the second dielectric layer 16 the flowing gas or gas mixture 2 exposed.

The thermal flow sensor 1 further comprises a control and / or evaluation unit 11 which is switchable between three different functional modes and which, the heating structure 8th and controls or controls the two temperature sensor elements according to the function modes. The heating structure is by an excitation signal from the control and / or evaluation 11 driven. The voltage applied to the two temperature sensor elements temperature is controlled by the control and / or evaluation 11 by means of a first response signal 13 and a second response signal 14 detected. The first response signal 13 refers to the first temperature sensor element ("upstream" temperature sensor) and the second response signal 14 to the second temperature sensor element ("downstream" temperature sensor).

Regarding the basic structure of the flow sensor is at this point on the publication "Gas concentration and flow speed measurements using a polymer-based membrane sensor ", in particular the chapter" II. Sensor ", by C. Hepp et al published in the 2013 IEEE Sensors, pages 1-4 The content of this publication is hereby incorporated in this application.

2 shows a table in the three different functional modes of the control and / or evaluation unit 11 are shown with each other, wherein by means of the first functional mode, a flow direction and possibly. a flow rate Q, by means of the second functional mode, a thermal conductivity λ and ggfl. a concentration of the components of the gas mixture and by means of a third functional mode according to the invention, a product of density and specific heat capacity (ρ · Cp) of the gas or of the gas mixture can be determined.

In the first functional mode (first line of in 2 The control and / or evaluation unit controls or regulates the heating structure in such a way that a substantially constant temperature is established at the heating structure T _heater . By means of the response signal 14 is a second temperature T ₂ , the downstream temperature, at the second temperature sensor element 10 , the downstream temperature sensor, by the control and / or evaluation unit 11 determined. The downstream temperature corresponds to the following relationship: T_down = f ₂ (λ, ρ · Cp, Q) (Equation 1)

In a first approximation, this relationship can be regarded as independent of the product of heat capacity Cp and density ρ, so that the following relationship results: T_down ≈ f ₂ (λ, Q) (equation 1.1)

In the event that the thermal conductivity λ of the flowing gas or gas mixture is known, for example because this was determined as described below or the flowing gas or gas mixture is known and thus also the thermal conductivity λ, can be by the control and / or evaluation unit 11 Using equation 1.1 additionally determine a flow rate Q of the flowing gas or gas mixture.

Alternatively, under the condition that the thermal conductivity λ is known, it is possible to iteratively determine the flow rate Q and the product of density times heat capacity ρ · Cp from Equation 1 and Equation 3, since this is a system of equations with two equations (Equation 1) and 3) and two unknowns.

In the second functional mode, the control and / or evaluation unit controls or regulates 11 the heating structure 8th such that these with an excitation signal 12 , which has a substantially constant power, is excited. The excitation signal 12 can also represent an AC signal. Typically, the power is then constant at least on average. An excitation frequency of 1 Hz has proven to be advantageous in the case of an alternating voltage signal.

In the second function mode (first line of in 2 shown table) detects the control and / or evaluation unit 11 by means of the second response signal 14 the second temperature T _{2 applied} to the second temperature sensor element 10 , the "downstream" temperature sensor. This second temperature T ₂ is a third function of the thermal conductivity λ, so that the thermal conductivity λ of the flowing gas or gas mixture can be determined. In particular, the following relationship exists between the second temperature T ₂ and the thermal conductivity λ: T2 = f ₃ (λ) (Equation 2)

As in 3 indicated, an area forms 15 out, in which the second temperature T ₂ at the second temperature sensor element is independent of flow, in particular independent of the flow velocity. In 3 are exemplary of the two gases argon Ar and nitrogen N ₂ , the resulting due to the substantially constant power excitation of the heating structure resulting second temperature or "downstream" temperature as a function of the flow velocity. It can be seen that at a flow rate between 0.2 m / s and 1 m / s forms a substantially constant plateau relative to the second temperature T _2. The height of the plateau is specific to each gas or gas mixture. For argon it is in the illustrated example at 19 K and for nitrogen at 17 K. The height of the plateau or the values, ie the 19 K and 17 K. So, if appropriate data in one of the control and / or evaluation 11 associated memory are stored, the control and / or evaluation a specific gas and its thermal conductivity λ or the concentration of the components of a gas mixture are determined.

For example, can be with the in 3 represented data, which are stored accordingly in the memory, by the control and / or evaluation unit 11 determine whether argon or nitrogen or a gas mixture of argon and nitrogen is present. Argon or nitrogen is in the case that the second temperature T _{2 of} the second temperature sensor element 10 essentially 17 K or 19K is. If a thermal conductivity λ corresponding to the gases is also stored in the storage tank, the control and / or evaluation unit can 11 determine these also for the gas present.

In the case that the second temperature T _{2 of} the second temperature sensor element 10 is between 17 and 19 kelvin, it is possible to determine, for example by assuming a linear relationship, the concentration of the gas mixture of argon and nitrogen. At the in 3 example shown, the second temperature T _{2 of} the second temperature sensor element 18 Kelvin. From this, assuming a linear relationship, the presence of a gas mixture with 50% vol. Argon and 50% vol. Nitrogen (dashed line in 3 shown). For a more precise determination of the concentration of the constituents of the gas mixture, it is advisable to store also for this specific data or a function in the memory, the possibly approximated linear relationship ggfl. even better adapts.

With regard to the two functional modes of the flow sensor, let us now turn to the publication "Gas concentration and flow velocity measurements using a polymer-based membrane sensor", in particular the chapter "IV. Characterization ", by C. Hepp et al published in the 2013 IEEE Sensors, pages 1-4 The content of this publication is hereby incorporated in this application.

In the third functional mode according to the invention, the control and / or evaluation unit controls or regulates 11 the heating structure 8 in turn such that the heating structure 8th is excited with a substantially constant power. With regard to the excitation signal, the second functional mode also applies.

In the third functional mode according to the invention, the control and / or evaluation unit detects the temperature of the heating structure. This temperature can be determined, for example, via a mathematical calculation with the aid of the temperature coefficient (TCR) known for the material of the heating structure, for example platinum. For this purpose, the control and / or evaluation unit detects the resistance of the heating structure and then calculates the temperature. Alternatively, the temperature at the heating structure can also be detected directly by a heating temperature sensor element of the control and / or evaluation unit.

On the basis of this detected temperature of the heating structure, the control and / or evaluation unit determines the product of density and specific heat capacity. For this purpose, the control and / or evaluation unit accesses data stored in the memory, which are present in discrete form, the data representing the following first function: T _heater = f ₁ (λ, ρ · Cp, Q, P) (Equation 3)

In 4 By way of example, such a first function is shown from which the data stored in the memory can be extracted. Of course, it is also conceivable that discrete values are stored instead of the first function.

With the heat conductivity and flow rate as well as the temperature of the heating structure already determined, the product of heat capacity and density can be deduced. In the 4 Curves shown are normalized to air at a temperature of 25 ° C. Furthermore, each curve represents a specific gas or gas mixture, so that the uppermost curve represented, for example, "Gas1" and the curves below corresponding to "Gas2", "Gas3" and "Gas4". As already stated, each curve is specific to a particular gas or gas mixture and must be made available to it before the actual operation of the thermal flow sensor. This can be done, for example, by experimentally recording such curves for the respective gas and depositing the curves in the memory of the thermal flow sensor.

By means of in 4 Thus, the product of heat capacity and density can be determined. This will be briefly illustrated by concrete values in the example below. For this purpose, it is assumed that a value of 2 (λ = 2) was determined for the thermal conductivity by means of the second functional mode and that for the flow rate a value of 0.5 m / s (Q = 0.5 m / s) by means of first function mode was determined. This value is dimensionless and refers to air, ie the thermal conductivity with, for example, the value of 2 twice corresponds to the thermal conductivity of air.

With these values, together with a detected temperature of the heating structure of 357.50 K, the product of heat capacity and density can be determined with the value 2 (c _p ρ = 2). This value is also normalized to air again.

LIST OF REFERENCE NUMBERS

1

Thermal flow sensor

2

Gas or gas mixture

3

substratum

4

First area

5

recess

6

First dielectric layer

7

membrane

8th

heating structure

9

First temperature sensor element

10

Second temperature sensor element

11

Control and / or evaluation unit

12

excitation signal

13

First response signal

14

Second response signal

15

Area where the second temperature is independent of the flow rate

16

Second dielectric layer

Q

Flow rate [m / s]

λ

Thermal thermal conductivity [W / (m · K)]

Cp

Specific heat capacity [J / (kg · K)]

ρ

Density [kg / m3]

ρ · Cp

Product of density times heat capacity [J / K · m3)]

T ₁

First temperature

T ₂

Second temperature

T _heater

Temperature of the heating structure

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited non-patent literature

• "Gas concentration and flow velocity measurements using a polymer-based membrane sensor", in particular the chapter "II. Sensor ", by C. Hepp et al published in 2013 IEEE Sensors, pages 1-4 [0022]
• "Gas concentration and flow velocity measurements using a polymer-based membrane sensor", in particular the chapter "IV. Characterization ", by C. Hepp et al published in 2013 IEEE Sensors, pages 1-4 [0033]

Claims (9)

Method for determining a product of heat capacity and density (C _p · ρ) of a gas or a gas mixture ( 2 ) or a value derived therefrom by means of a thermal sensor ( 1 ), in particular a thermal flow sensor, comprising the following steps: - Determining the thermal thermal conductivity (λ) of the gas or of the gas mixture ( 2 ); Determination of a flow rate (Q) of the gas or of the gas mixture ( 2 ) based on the determined thermal conductivity (λ); - Determination of the product of heat capacity and density (Cp · ρ) of the gas or of the gas mixture ( 2 ) or a value derived therefrom on the basis of the determined thermal conductivity (λ) and the determined flow rate (Q). A method according to claim 1, wherein for determining the product of heat capacity and density (Cp · ρ) of the gas or of the gas mixture ( 2 ) a heating structure ( 8th ) of the thermal flow sensor ( 1 ) is excited with a substantially constant power. A method according to claim 2, wherein for determining the product of heat capacity and density (Cp · ρ) of the gas or of the gas mixture ( 2 ) a temperature of the heating structure (T _heater ) is detected. Method according to one or more of the preceding claims, wherein for the determination of the product of heat capacity and density (Cp · ρ) of the gas or of the gas mixture ( 2 ) is based on a stored first function or values derived therefrom and wherein the first function has the following relationship: T _heater = f ₁ (λ, ρ · Cp, Q, P), where λ is the thermal conductivity, ρ is the density, Cp is the specific heat capacity Q of the flow rate, P is the power applied to the heater, and T is the _heater temperature of the heating structure. Method according to one or more of the preceding claims, wherein, for determining the thermal conductivity, a second temperature (T ₂ ) is determined by means of a reference to a heating structure ( 8th ) arranged downstream of the second temperature sensor element ( 10 ) is detected. A method according to claim 5, wherein based on the detected second temperature (T ₂ ) for the gas or gas mixture ( 2 ) corresponding thermal conductivity (λ) is determined. A method according to claim 5 or 6, wherein for determining the corresponding thermal conductivity (λ) of the gas or the gas mixture ( 2 a third function or values derived therefrom are used, the third function or the values derived therefrom describing the dependence of the second temperature (T ₂ ) on the flow rate (Q) and in a defined range substantially independent of the flow rate (Q), so that a second temperature (T ₂ ) can be determined for the defined area, which is essentially independent of the flow rate (Q). The method of claim 7, wherein based on the second temperature (T ₂ ) for the defined area, which is substantially independent of the flow rate (Q), the thermal conductivity (λ) is determined. Method according to one or more of the preceding claims, wherein the flow rate (Q) of the gas or of the gas mixture ( 2 ) based on the previously determined thermal conductivity (λ) and the second temperature (T ₂ ) of the downstream arranged second temperature sensor element ( 10 ) is determined.

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