Method for Measuring Internal Liquid Level of Sealed Metal Container by Ultrasonic

Abstract: The liquid level measurement method considers only the echoes energy inside the metal wall detected directly. By analyzing the sound field distribution and the characteristics of the round piston transducer in the metal wall, we proposed the concept of “energy circle” and calculated the two critical positions automatically. Finally, we achieved the accurate calibration of the inner liquid level from the outside of the sealed metal container.


Introduction
The accurate measurement of liquid level in the sealed metal container is an important guarantee for the realization of the production process detection and realtime control [1].Especially in aviation, petroleum and chemical industry and other special areas of production, the liquid in metal sealed container mostly are volatile, flammable, explosive, corrosive mixtures.At present, there are several kinds of ultrasonic measurement methods have been widely used, but all of them have some deficiency more or less which affect the precision of liquid level measurement.
First, in the ultrasonic penetrative method [2,3], sound waves must penetrate the liquid medium and is easily affected by internal impurities and bubbles in liquid which will lead to more errors.In addition, if the measured liquid medium is poor transmittance or the diameter of container is larger, then the echoes signal may be very weak or undetectable.It will lead to a very small difference in strength of the echoes signal in different cases which is not easy to distinguish, and ultimately will make the determination of the liquid level become difficult.
Second, the ultrasonic measurement methods which have been proposed in recent years are more advanced and accurate, but the equipment for determining the liquid level are increasingly complex and expensive [4][5][6].
Therefore, in this paper, we will avoid the deficiencies and research how to easily resolve and simply improve the measuring method of the liquid level in sealed metal container.

Theory
According to the knowledge of ultrasound [7][8][9], the length of the near field N and the diffusion angle θ are given by Eq. ( 1) and Eq. ( 2) respectively [10].
Normally, the geometry size is much larger than the wave length for the plane round piston transducer.Its beam shape comprises two different regions in the medium [11], which are near-field and far-field region or called cylindrical and diverging region shown as Figure 1.Furthermore, since the sound intensity is proportional to the square of amplitude, the sound intensity along the central axis has the same distribution characteristics.
The wall of metal container is regarded approximately as semi-infinite isotropic solid medium, and the ultrasonic propagation complies with the laws of reflection and refraction of sound waves [8].The reflection coefficient R is given by the Eq. ( 3).
Where: ρ is the medium density, c is the speed of sound in the medium, θ i is the incidence angle, θ t is the transmission angle.
Assuming the thickness of the wall is L, the detector is a round piston transducer which has the function of receiving and transmitting, its center frequency is f and the radius is a, perpendicular to the outer surface of the wall of the metal container, the transducer is excited to transmit a ultrasonic beam into the wall which will be projected onto the inner surface of the wall and will form a circular area in which the energy is concentrated relatively.
In this paper, we called the projected circular area as "energy circle".Assuming the "energy circle" diameter is h and according to Eq. ( 2), the value of h is given by Eq. ( 4).
In the actual detecting process, when the detection transducer moved from bottom to top along the outer surface of the metal container wall, the "energy circle" will locate in three different states.
Assuming that the attenuation coefficient of ultrasonic wave in the metal container wall is P 0 , the incident sound pressure in an excitation period is, the acoustic impedance of the metal container wall is Z m = ρ m c m , the acoustic impedance of gaseous medium is Z g = ρ g c g , the acoustic impedance of liquid medium is Z 1 = ρ 1 c 1 .
It is assumed that the energy of the reflection has been decayed to a very small amount after n times in the metal wall.
When the "energy circle" below the interface of the liquid level, the total energy P tl received by the receiving transducer is given by Eq. ( 5): In the same way, when the "energy circle" above the interface of the liquid level, the total energy P tg received by the receiving transducer is given by Eq. ( 6): When the "energy circle" is divided into two parts by the liquid level shown as Figure 2, In this state, the calculation of the "energy circle" will be the superposition of two states: In the Eq. ( 7), if the Δh are critical value 0 or 1, the Eq. ( 7) will become to the Eq. ( 5) and Eq. ( 6) respectively.
Therefore, with the increasing of the Δh from 0 to h, the "energy circle" is moved from the state below the liquid level to the state above the liquid level.In this process, and the total energy P t received by the receiving transducer is linear with the ratio Δh.
For a given testing environment and the transducer locates a fixed position, the values of the P t are constant.Therefore, we can find the two critical height of h d and h u corresponding to the two critical states, the actual liquid level h 1 will be given by the Eq. ( 8).

Experimental
In the experiments, we use a sealed metal container for homogeneous aluminum alloy, the length, the width and the height of which are designed respectively for 500mm, 300mm, 400mm, the wall thickness of the four side plates of which are respectively 50mm, 40mm, 25mm, 8mm, the bottom and the cover thickness of which are 150mm, the liquid medium and the gaseous medium in which are water and air.
Considering the propagation characteristics of the ultrasonic in the metal container wall, we selected two kinds of round piston transducers whose center frequency f are 1MHz and whose diameters are 10mm and 20mm respectively.Excitation voltage used in the experiment u is 225V, the repetition frequency of excitation pulse is, the repetition period is.
According to the analysis in the second section, we measured the position of the liquid level under the conditions of different thickness of the metal wall, and take L=50mm as an example.
The echoes signals shown in Figure 3 are the two states that the "energy circle" are above and below the liquid level respectively within a transmission period 0.01s.In addition, in Figure 3b, the signals in the dashed blue box are the echoes signals that the transmitting ultrasonic beam passing through a gas or a liquid medium was reflected by the opposite inner surface of the metal container wall, which is not adapted in this contribution.
From Figure 3a and 3b, we can see that the echoes signals in the metal wall measured disappeared about after the time of s when the "energy circle" is below the liquid level; and after the time about s, the echoes signals in the metal wall measured also disappeared when the "energy circle" is above the liquid level.About s later, the signals penetrating the gaseous or liquid medium were reflected back from the opposite wall of the metal container.
In Figure 3, the time section from 0.000008s to 0.0003s could be used as effective regional to calculate echoes energy.Based on the detection environment and conditions, there are,,,,.
In Figure 4, the vertical axis represents the energy received by the receiving transducer, the horizontal axis shows the radius of "energy circle", and it can be seen that the change of the energy is consistent with the change law of the theoretical analysis in section 2.2.Table 1 shows the actual measurement results under different wall thickness.From the experimental data in Table 1 it can be seen that the bigger the diameter of the transducer, the more concentrated the ultrasonic beam, the smaller the divergence angle, the longer the near-field length, the smaller the interval between two critical positions, high sensitivity and lower resolution; the smaller the diameter of the transducer, the more scattered the ultrasonic beam, the greater the divergence angle, the smaller the length of the near-field, the larger the interval between two critical positions, low sensitivity and high resolution.

Discussion and conclusion
The selection of initial conditions in the experiment of the third section, such as the center frequency and the radius of the detection transducer and the voltage of the excitation pulse, needs according to the actual testing environment, the material of metal container and the physical characteristics of the medium measured in the container, considering the discussion of ultrasonic sound field in the first section, and programming to achieve the automatic optimization of parameters selected to avoid using the experimental value directly.It will be more conducive to simplify the detection process and improve the measuring accuracy.

Figure 1 .
Figure 1.Beam shape and the acoustic characteristics of the plane round piston transducer

Figure 2 .
Figure 2. The "energy circle" is divided into two parts by the liquid level

Figure 3 .
Figure 3.The echoes signals in the metal wall as the thickness L=50mm, (a) the energy circle is above the liquid level, (b) the energy circle is below the liquid level

Figure 4 .
Figure 4.The change law of the actual total energy received by the receiving transducer under the 50mm thickness of the metal container wall.

Table 1 .
The results of measurements (mm)