WO1988009484A1

WO1988009484A1 - Method and apparatus for measuring the volume of a gas in a container

Info

Publication number: WO1988009484A1
Application number: PCT/SE1988/000266
Authority: WO
Inventors: Tore Hesthamar; Patrick SÖDERLUND
Original assignee: Metator Kb
Priority date: 1987-05-21
Filing date: 1988-05-20
Publication date: 1988-12-01
Also published as: SE8702101D0; SE8702101L

Abstract

A method for measuring the volume (V) of a gas in a container (1) comprises obturation of the vent(s) (3) of the container and then introduction or withdrawal of a known gaseous mass flow (dm/dt) into and out of the container (1), respectively. The pressure change (dp/dt) caused by the mass flow and the sound velocity (u) in the container are determined, and the volume of the gas in the container is calculated by the formula: V = u2 dm/dt 1/dp/dt, wherein V is the volume to be determined, u is the sound velocity, dm/dt is the mass flow, and dp/dt is the pressure change. An apparatus for carrying out the method has means (4) for obturation of the vents (3), means (5) for introducing or withdrawing a known gaseous mass flow (dm/dt), transducers (6, 7) for measuring the pressure and the sound velocity as well as calculating means (8). The means for introducing or withdrawing a known gaseous mass flow can include a mass flow can include a mass flow regulator.

Description

METHOD AND APPARATUS FOR MEASURING THE VOLUME OF A GAS IN A CONTAINER

The present invention relates to a method for measuring the volume (V) of a gas in a container, said method comprising obturation of the vent(s) of the container, introduction or withdrawal of a known gaseous mass flow into and out of the container, res¬ pectively, and determination of the pressure change caused by the mass flow. The invention also relates to an apparatus for carrying the method into effect, comprising means for obturating the vent(s) of the container, means for introducing or withdrawing a known gaseous mass flow into and out of the container, respectively, and means disposed in the container for determining the pressure change caused by the mass flow. Volume measuring is an old and well-known problem.

To measure the volume of liquids in tanks and containers, use is often made of floats and other level indicators, a technique for which the volume of the container as a function of the liquid level within the container must be known to make a determination of the volume possible. However, these apparatuses for volume measur¬ ing suffer from the disadvantage of not giving an accurate result if the container in which the measure¬ ment is carried out, is in motion so that splashing might occur or the surface of the liquid might tilt relative to the container.

In order to solve this problem, methods have been developed which are based on the principle that the volume of the liquid can be determined by measuring the gas volume above the liquid in the container, provided the volume of the container is known. To determine the gas volume, use is made of well-known gas laws, such as the general equation of state, pV = — R T wherein p = absolute pressure, V = volume, = mass, M = molar weight, R = the gas constant, and T = absolute temperature; Boyle's law, p_Q V_Q = = p v, ; and the equation of state for adiabatic changes of state, p„ = p, V, ^κ wherein κ is the ratio between the specific heat capacity at constant pressure and constant volume for the gas present in the con¬ tainer. When the last-mentioned formula is used, κ con¬ stitutes a problem. Firstly, the value of κ is not known for all gases. One example of this is petrol vapour which is a not well defined hydrocarbon com¬ position for which κ is not known. Secondly, κ varies with the temperature. When the temperature changes in a gas are slow, κ can be calculated, provided the temperature and the pressure of the gas are known. However, when the temperature changes are rapid, this is impossible because there is no time for evaporation and condensation so that no state of equilibrium can form.

The method based on the two first-mentioned gas laws, i.e. the general equation of state and Boyle's law, most often comprises volume changes implemented by means of pistons or other moving parts. In certain applications, e.g. volume measurements in fuel tanks on aircraft, aspects of reliability and maintenance imply that the number of moving parts should be as low as possible. A method of measuring gas volumes, based on Boyle's law, but not comprising a change of volume, is described in GB 2,082,778A according to which the gas volume in a container is determined by introduction of a gas flow into the container through a very narrow restriction and under conditions such that the tempe¬ rature change is negligible and the pressure change in the container is small during the measuring operation. The gas flow introduced into the container can either be held constant or measured. In the first case, the volume is determined as

V = N-C zzzR dt

wherein N is the mass flow, C is a constant and dp/dt is the pressure change in the container. In the second case, the volume is determined as

K-A(P,-P) V = d£ dt

wherein K is a constant, A is the atmospheric pressure, P,-P is the pressure drop across the restriction, and dp/dt is the pressure change in the container. Both of these expressions include constants which must be determined, and this is done by calibration. The calibration constants depend, however, on the temperature, which means that, in case this measuring method is to be used in environments with varying temperature, e.g. in aircraft tanks, the calibration constants must be determined for each temperature and, furthermore, the temperature must be determined on each measuring occasion, and this is unpractical and difficult.

Furthermore, since the method is based on Boyle's law, the temperature has to be constant during the measur- ing procedure, which can be difficult to achieve because energy has then to be abducted from the measuring con¬ tainer under controlled conditions. Therefore, methods based on adiabatic changes of state are preferred, but then one is again faced with the problem of κ. Finally, the pressure change must be small, which sets a limit to the accuracy of this measuring method.

The above-mentioned drawbacks of the method according to GB 2,082,778A make this method unsuitable, if not impossible to use in environments where the temperature varies.

Therefore, the object of the present invention 5 is to propose a new method for measuring the volume of a gas in a container and a new apparatus for carrying the method into effect, thereby eliminating the above- mentioned drawbacks.

This object is achieved by means of a method for 10 measuring the volume of a gas in a container, which is characterised in that the sound velocity in the gas is determined and the gas volume calculated by the formula

wherein V is the volume to be determined, u is the sound velocity, dm/dt is the mass flow, and dp/dt

20 is the pressure change.

The apparatus for carrying the method into effect is characterised by means for determining the sound velocity in the gas and by calculating means connected to the means for introducing or withdrawing the gaseous

25 mass flow and to the means for determining the pressure change and the sound velocity, for calculation of the volume.

This method and this apparatus are particularly, but not exclusively suitable and intended for volume

30 measurements in aircraft fuel tanks because there are virtually no moving parts and also because standard components can be used and because the fuel tanks in certain types of aircraft are vented, today already, by the injection of gas into the tank. The method

35 according to the present invention is based on the general equation of state for adiabatice changes of state, but the problem of κ has been eliminated, and the method can be used at varying temperatures without knowledge of the value of κ and without necessitating temperature measurement.

An embodiment of the invention will be described below, reference being had to the accompanying drawing which illustrates schematically an apparatus according to the invention.

The apparatus for measuring the volume of a gas in a container 1 having an inlet 2 and an outlet or vent 3, comprises, as is seen from the drawing, a valve mechanism 4 for obturation of the vent 3. The apparatus also has means 5 for injection of a gaseous mass flow into the tank 1. The gaseous mass flow may consist of air or some other gas. The means 5 may comprise either a commercially available mass flow regulator adjusting the mass flow dm/dt at a constant predetermined value, or, if the mass flow is allowed to vary, a mass flow measuring device which also is commercially available and by which the mass flow can be measured. The apparatus also comprises a trans¬ ducer 6 disposed in the tank 1 and permitting measure¬ ment of the pressure change in the tank, caused by the mass flow. The pressure transducer 6 may be a linear transducer of absolute values, by means of which the pressure p in the tank is measured con¬ tinuously and the output signal of which is sampled at short intervals for calculation of the pressure change dp/dt. The tank also contains a transducer 7 for measuring the sound velocity u. Said transducer 7 can be a common ultrasonic transducer of the type which is used in distance-determining, and permits determination of the sound velocity by measuring the time needed for a sound signal to cover a known dis¬ tance. The transducers 6 and 7 as well as the mass flow regulator or the mass flow measuring device are connected to a calculating means 8 which may be, for example, a microcomputer. In order to derive the formula on which the measuring method is based, use is made of the general gas law

PV = R T ... (2)

wherein p = absolute pressure, V = volume, m = mass, M = molar weight, R = the gas constant and T = the absolute temperature, and of the general equation of state for adiabatic changes of state

κ (3)

^P0 ^V0 ⁼ ?! ^Vl

wherein κ is the ratio between the specific heat capacity at constant pressure and at constant volume. The formula 3 can be reformulated as

Because the volume is constant,

V m ^c - κp (- -) dm ..(5) m is obtained, i.e.

dp = κp —m dm ... (6 )

If p is eliminated by means of the general equation of state,

dp = κ§R T ^ i dm ... (7)

is obtained. If the sound velocity u = /κRT/M is inserted in this expression

dp = u — dm ... (8 ) is obtained. Therefore the volume V can be measured as

For practical reasons, dm and dp are measured separately and with regard to time, whereby

is obtained.

Upon measurement, a gaseous mass flow is introduced through the inlet 2. The magnitude of the mass flow is known, either in that the mass flow regulator, where appropriate, adjusts the mass flow to a known value, or in that the mass flow measuring device measures the magnitude of the mass flow. During measurement, the vent 3 is obturated by means of the valve 4. Then the pressure change dp/dt is measured by means of the transducer 6 and the sound velocity u by means of the transducer 7. The microcomputer 8 receives these signals and calculates the volume by means of the formula above.

The mass flow should be so small that the pressure change will have time to spread to the whole tank, but yet so large as to prevent any exchange of heat with the surroundings so that the change of state is decidedly adiabatic.

The embodiment described above is, of course, only an example, and can be modified in many ways within the scope of the appended claims. Instead of injecting a gas into the tank, it would be possible, for example, to suck a known gaseous mass flow out of the tank and to measure the resulting pressure change and the sound velocity. It should also be pointed out that the measuring method is not limited to measurements in aircraft tanks, but can be used in all types of applications where measurement of a gas volume is included,

Claims

1. Method for measuring the volume (V) of a gas in a container (1), said method comprising obturation of the vent(s) (3) of the container, introduction or withdrawal of a known gaseous mass flow (dm/dt) into and out of the container (1), respectively, and determination of the pressure change (dp/dt) caused by the mass flow, c h a r a c t e r i s e d in that the sound velocity (u) in the gas is determined and the gas volume calculated by the formula

V = u² ^dt dp ^λ dt

wherein V is the volume to be determined, u is the sound velocity, dm/dt is the mass flow, and dp/dt is the pressure change.

2. Method according to claim 1, c h a r a c ¬ t e r i s e d in that the sound velocity (u) is determined by measuring the time it takes for a sound signal to cover a known distance.

3. Apparatus for measuring the volume (V) of a gas in a container (1), comprising means (4) for obturating the vent(s) (3) of the container, means (5) for introducing or withdrawing a known gaseous mass flow (dm/dt) into and out of the container (1), respectively, and means (6) disposed in the container for determining the pressure change caused by the mass flow, c h a r a c t e r i s e d by means for determining the sound velocity (u) in the gas and by calculating means (8) connected to the means (5) for introducing or withdrawing the gaseous mass flow and to the means (6, 7) for determining the pressure change (dp/dt) and the sound velocity (u) , for cal¬ culation of the volume (V) .