JP7633518B2 - Microwave frequency determination method, level measurement device, and level measurement method - Google Patents

Description

The present invention relates to a method for determining an appropriate microwave frequency in a level measurement device that uses microwaves to measure the level of the bath surface inside a furnace, such as the slag surface of a converter, and to a level measurement device and level measurement method that use this method.

In the steelmaking process using a converter, molten pig iron is charged into the converter and blown into the molten iron through a lance to adjust the composition of the molten iron and produce molten steel. As the blowing process progresses, slag is produced on the surface of the molten material (molten pig iron or molten steel) in the converter.

In order to improve productivity in the above steelmaking process, it is important to increase the flow rate of the gas (oxygen flow rate) blown from the lance and shorten the time required for blowing. However, if the gas flow rate is increased too much, slopping (the phenomenon in which foamed slag overflows from the furnace throat) and spitting (the phenomenon in which slag is scattered by the jet) will occur, resulting not only in a decrease in yield, but also in the possibility of problems such as the adhesion of ingots and slag to the furnace throat, exhaust hood, etc., hindering operation.

Therefore, in order to improve productivity, it is important to accurately measure the bath surface (slag surface) level in the converter in real time and to accurately grasp behavior such as slag foaming, which is a precursor to slopping, in real time.

For this reason, for example, as shown in Patent Documents 1 and 2, radar-type level measurement devices have been proposed that use microwaves to measure the level of the slag surface of the molten material charged into a converter.

During blowing (especially decarburization blowing), a lot of dust is generated from the bath surface inside the furnace, making it difficult to measure the bath surface level using a camera or laser. Even if microwaves with a longer wavelength than visible light are used, some attenuation of the microwaves due to dust is unavoidable, so it is desirable to use microwaves with as low a frequency as possible. From this perspective, the level measurement devices described in Patent Documents 1 and 2 use microwaves with frequencies below the X-band (approximately 10 GHz or less).

However, because there are restrictions on the size of the opening that can be installed in the exhaust hood of a converter, there is also an upper limit to the size of the antenna of the level measuring device that can be installed in this opening (for example, the total of the transmitting antenna and receiving antenna must be 600 mm or less). When the antenna size is constant, the higher the microwave frequency, the greater the antenna gain and the stronger the received microwave signal. Conversely, when the antenna size is constant and the microwave frequency is lowered, the antenna gain becomes smaller and the strength of the received microwave signal becomes weaker.

In other words, there is a trade-off between the dust permeability of microwaves and the antenna gain of the antenna, and simply lowering the frequency to improve dust permeability will not allow for accurate measurement of the bath surface level. Therefore, it is necessary to select an appropriate microwave frequency that achieves both dust permeability and antenna gain.

Non-Patent Document 1 describes the basic theory of radar-based remote sensing.

JP 2016-180126 A JP 2018-53347 A

Shoichiro Fukao and Kyosuke Hamazu, "Radar Remote Sensing of Weather and Atmosphere", Kyoto University Press, 2005

The objective of the present invention is to provide a method for determining an appropriate microwave frequency for a level measurement device that uses microwaves to measure the level of the bath surface inside a furnace, such as the slag surface of a converter, and a level measurement device and level measurement method that use this method.

In order to solve the above problems, the present invention provides a microwave frequency determination method for determining a microwave frequency for use in a level measurement device that measures a bath surface level in a furnace, the method comprising the steps of:
The level measuring device has an antenna that transmits microwaves toward the bath surface and receives the microwaves reflected from the bath surface, and a signal processing unit that calculates the level of the bath surface based on the microwaves received by the antenna, and the level measuring method includes a received signal strength calculation step of calculating the received signal strength of the microwaves, which is represented by the amount of microwave attenuation due to dust in the furnace and the antenna gain of the antenna, as a function of the microwave frequency, a noise level calculation step of calculating the noise level, which is represented by the thermal noise of the signal processing unit and the radiation noise from the bath surface, as a function of the microwave frequency, and a frequency determination step of determining the frequency of the microwaves so that the S/N ratio determined by the received signal strength of the microwaves calculated in the received signal strength calculation step and the noise level calculated in the noise level calculation step is equal to or greater than a predetermined threshold value.

According to the frequency determination method of the present invention, in the received signal strength calculation step, the microwave received signal strength, which is represented by the amount of microwave attenuation due to dust in the furnace and the antenna gain of the antenna, is calculated as a function of the microwave frequency. In other words, the microwave received signal strength is calculated taking into account the frequency dependence of both dust permeability and antenna gain. In addition, in the noise level calculation step, the noise level, which is represented by the thermal noise of the signal processing unit of the level measurement device and the radiation noise from the bath surface, is calculated as a function of the microwave frequency. That is, both the microwave received signal strength and noise level are calculated as functions of the microwave frequency by the received signal strength calculation step and the noise level calculation step.
According to the frequency determination method of the present invention, since both the microwave reception signal strength and the noise level are expressed as functions of the microwave frequency, it is possible to determine the microwave frequency in the frequency determination step so that the S/N ratio determined by the microwave reception signal strength and the noise level is equal to or greater than a predetermined threshold value. In other words, it is possible to determine an appropriate microwave frequency that provides an S/N ratio equal to or greater than a predetermined threshold value.

上記の式（１）において、Ａ［ｄＢ／ｍ］は前記アンテナから送信されたマイクロ波の単位長さ当たりの減衰量、ｆ［Ｈｚ］は前記マイクロ波の周波数を示す。上記の式（２）及び式（３）において、πは円周率、ｃ［ｍ／ｓ］は光速、ｄ［ｋｇ／ｍ^３］は粉塵濃度、ρ［ｋｇ／ｍ^３］は粉塵粒子の真比重、Ｄ［ｍ］は粉塵粒子の粒径（直径）、Ｖ_Ｄ［ｍ^３］は粒径Ｄの単一の粉塵粒子の体積、ｑ_Ｄは粉塵粒子の粒子数基準の粒径分布を示す。上記の式（４）及び式（５）において、ε_ｒは粉塵粒子の複素比誘電率、μ_ｒは粉塵粒子の複素比透磁率を示す。 Specifically, for example, in the received signal strength calculation step, the amount of attenuation of the microwaves due to dust in the furnace can be calculated based on the following formulas (1) to (5).

In the above formula (1), A [dB/m] is the attenuation per unit length of the microwave transmitted from the antenna, and f [Hz] is the frequency of the microwave. In the above formulas (2) and (3), π is the circular constant, c [m/s] is the speed of light, d [kg/ ^m3 ] is the dust concentration, ρ [kg/ ^m3 ] is the true specific gravity of the dust particle, D [m] is the particle size (diameter) of the dust particle, _VD [ ^m3 ] is the volume of a single dust particle with particle size D, and _qD is the particle number-based particle size distribution of the dust particles. In the above formulas (4) and (5), _εr is the complex relative dielectric constant of the dust particle, and _μr is the complex relative magnetic permeability of the dust particle.

In order to solve the above-mentioned problems, the present invention provides a level measurement device for measuring the level of a bath surface in a furnace, comprising an antenna for transmitting microwaves toward the bath surface and receiving the microwaves reflected by the bath surface, and a signal processing unit for calculating the level of the bath surface based on the microwaves received by the antenna, the level measurement device performing a received signal strength calculation step of calculating the received signal strength of the microwaves, represented by the amount of microwave attenuation due to dust in the furnace and the antenna gain of the antenna, as a function of the frequency of the microwaves, a noise level calculation step of calculating the noise level, represented by the thermal noise of the signal processing unit and the radiation noise from the bath surface, as a function of the frequency of the microwaves, and a frequency determination step of determining the frequency of the microwaves so that the S/N ratio determined by the received signal strength of the microwaves calculated in the received signal strength calculation step and the noise level calculated in the noise level calculation step is equal to or greater than a predetermined threshold value , and the level measurement device measures the level of the bath surface using microwaves of the frequency determined in the frequency determination step.
The present invention is also provided as a level measurement method for measuring the level of a bath surface in a furnace, comprising the steps of: determining a microwave frequency to be used in the level measurement device by the above-mentioned microwave frequency determination method; and measuring the level of the bath surface using the level measurement device that uses microwaves of the determined frequency.
According to the level measurement device and level measurement method of the present invention, it is possible to accurately measure the bath surface level using microwaves of an appropriate frequency determined by the frequency determination method of the present invention.

In the level measurement device and method of the present invention, it is conceivable that the bath surface level may be measured using microwaves with a frequency of, for example, 15 to 19 GHz.

The level measurement device and the level measurement method according to the present invention are preferably used when the furnace is a converter and the bath surface is a slag surface.

According to the present invention, it is possible to determine an appropriate microwave frequency in a level measurement device that uses microwaves to measure the bath surface level in a furnace.

FIG. 1 is an explanatory diagram for explaining a schematic configuration of a converter and a level measurement device according to an embodiment of the present invention. 2 is an explanatory diagram for explaining a schematic relationship between a transmission wave transmitted from the antenna shown in FIG. 1 and a reception wave received by the antenna. FIG. 2 is a flow diagram showing steps of a microwave frequency determination method according to one embodiment of the present invention. FIG. 2 is a diagram showing particle number-based particle size distribution of dust particles used in the examples. In the examples, the received signal strength, noise level and signal-to-noise ratio are calculated as a function of frequency.

Hereinafter, with reference to the attached drawings as appropriate, one embodiment of the present invention will be described, taking as an example a case in which the furnace whose level is to be measured is a converter and the bath surface in the furnace whose level is to be measured is the slag surface.
1A and 1B are explanatory diagrams for explaining the schematic configuration of a converter and a level measurement device according to this embodiment, in which Fig. 1A is a diagram showing the overall configuration of the converter and the level measurement device, and Fig. 1B is a diagram showing the circuit configuration of the level measurement device.

As shown in FIG. 1(a), in the steelmaking process in a converter, molten pig iron 2 is charged into the converter 1, and gas such as oxygen is blown into the molten pig iron 2 from a lance 4 to adjust the composition of the molten pig iron 2 and produce molten steel. As the blowing process progresses, slag is produced on the surface of the molten material (molten pig iron 2 or molten steel) in the converter 1. The level measurement device 100 according to this embodiment measures in real time the level of the surface (slag surface) 3 of the slag produced in the converter 1. The level of the slag surface 3 refers to the height of the slag surface 3 as viewed from the bottom of the converter 1 or a specified reference position.

The blowing process in the converter 1 generates steam, dust, and other particles inside the converter 1, so an exhaust hood 5 is provided near the throat of the converter 1 to prevent the generated dust from being released into the external environment. This exhaust hood 5 has an opening 51 for inserting the lance 4 into the converter 1 and an opening 52 in which the antenna 10 provided in the level measurement device 100 is located.

1, the level measurement device 100 includes an antenna 10 that transmits microwaves toward a slag surface 3, which is the bath surface in a furnace, and receives the microwaves reflected by the slag surface 3, and a signal processor 20 that is connected to the antenna 10 and calculates the level of the slag surface 3 based on the microwaves received by the antenna 10. The signal processor 20 of this embodiment also has a function of controlling the transmission of microwaves from the antenna 10.
In this embodiment, the antenna 10 includes a microwave transmitting antenna 10a and a microwave receiving antenna 10b. The antennas 10a and 10b are conical horn antennas. As shown by the dashed arrow in Fig. 1(a), microwaves are transmitted from the transmitting antenna 10a toward the slag surface 3 in the converter 1, and the microwaves reflected by the slag surface 3 are received by the receiving antenna 10b. The level of the slag surface 3 is measured by calculation in the signal processing unit 20. However, the present invention is not limited to this, and it is also possible to use a single antenna 10 that serves both transmission and reception.

The signal processing unit 20 of this embodiment is configured to measure the level of the slag surface 3 by a so-called FM-CW method, which uses a beat wave generated by mixing a microwave (hereinafter, appropriately referred to as a "transmitted wave") transmitted from the transmitting antenna 10a toward the slag surface 3 with a microwave (hereinafter, appropriately referred to as a "received wave") reflected by the slag surface 3 and received by the receiving antenna 10b. However, the present invention is not limited to this, and it is also possible to adopt a configuration for measuring the level of the slag surface 3 by other methods, such as using a phase difference of a microwave of a single frequency.
As shown in FIG. 1B, the signal processing unit 20 of this embodiment includes an oscillator 21, a power amplifier 22, a mixer 23, a low-noise amplifier 24, an IF amplifier 25, a low-pass filter 26, an AD converter 27, and a computer 28.

FIG. 2 is an explanatory diagram for explaining a schematic relationship between a transmission wave transmitted from the antenna 10 and a reception wave received by the antenna 10. As shown in FIG.
The oscillator 21 of the signal processing unit 20 generates a frequency modulated waveform, i.e., a waveform whose frequency changes over time, and transmits this waveform to the power amplifier 22 and mixer 23. The power amplifier 22 amplifies this waveform and then transmits it to the transmitting antenna 10a. As a result, a transmission wave whose frequency f changes linearly for each sweep period is transmitted from the transmitting antenna 10a as shown in Fig. 2. In the example shown in Fig. 2, the frequency modulation width of the transmission wave is F [Hz], and the transmission wave has a sweep period ST [s].

As shown in FIG. 2, the received wave received by the receiving antenna 10b has a frequency modulation width of F [Hz] and a sweep period of ST [s], just like the transmitted wave. However, the received wave has a time delay Δt [s] relative to the transmitted wave that is proportional to the distance R to the slag surface 3 being measured. This time delay Δt [s] is proportional to the frequency difference Δf [Hz] between the transmitted wave and the received wave at the same time. This received wave is amplified by the low-noise amplifier 24 and then transmitted to the mixer 23. In the mixer 23, the transmitted wave and the received wave are mixed (more precisely, the output waveform of the oscillator 21 and the output waveform of the low-noise amplifier 24 are mixed) to generate a beat wave having a frequency Δf.

The beat wave generated by the mixer 23 is amplified by an IF amplifier 25, and after unnecessary high frequency components are removed by a low pass filter 26, it is AD converted by an AD converter 27 and input to a computer 28. A program for performing FFT (Fast Fourier Transform) processing and the like is installed in the computer 28, and the computer 28 performs FFT processing on the AD converted beat wave to generate a power spectrum with frequency as the horizontal axis. The frequency Δf is identified by detecting the peak position of this power spectrum, and it is possible to calculate the time delay Δt and, ultimately, the distance R to the slag surface 3 from the identified frequency Δf.
In addition, instead of the power spectrum with the frequency on the horizontal axis, it is also possible to generate a power spectrum with the distance corresponding to each frequency on the horizontal axis and directly calculate the distance R to the slag surface 3 by detecting the peak position of this power spectrum.

The level measurement device 100 according to this embodiment is capable of measuring the distance R to the slag surface 3 and thus the level of the slag surface 3 as described above, but is characterized by the method of determining the frequency f of the microwaves used (corresponding to the frequency f of the waveform generated by the oscillator 21). This point will be explained below.

Figure 3 is a flow diagram showing the steps of the microwave frequency determination method according to this embodiment. As shown in Figure 3, the frequency determination method according to this embodiment has a received signal strength calculation step ST1, a noise level calculation step ST2, and a frequency determination step ST3. Each step ST1 to ST3 will be described below.

<Received signal strength calculation step ST1>
In the received signal strength calculation step ST1, the received signal strength of the microwave (specifically, the strength of the received wave received by the receiving antenna 10b), which is represented by the amount of microwave attenuation due to dust in the converter 1 and the antenna gain of the antenna 10, is calculated as a function of the microwave frequency f.

上記の式（１）において、α、βは、それぞれ以下の式（２）及び式（３）で表される。なお、式（１）において、αに比例する項（４．３４×αｆ^４）はレイリー散乱を表し、βに比例する項（４．３４×βｆ）は吸収減衰を表す。

上記の式（２）及び式（３）において、πは円周率、ｃ［ｍ／ｓ］は光速、ｄ［ｋｇ／ｍ^３］は粉塵濃度（ダスト濃度）、ρ［ｋｇ／ｍ^３］は粉塵粒子の真比重、Ｄ［ｍ］は粉塵粒子の粒径（直径）、Ｖ_Ｄ［ｍ^３］は粒径Ｄの単一の粉塵粒子の体積、ｑ_Ｄは粉塵粒子の粒子数基準の粒径分布を示す。
式（２）におけるＫ_αの右側に位置する項（以下の（２ａ）に示す項）は、飛散している全ての粉塵粒子の影響を考慮するために、粉塵粒子の粒径Ｄに依存する影響因子Ｄ^６を粒子数基準の粒径分布ｑ_Ｄで重み付け平均することを意味する。同様に、式（３）におけるＫ_βの右側に位置する項（以下の（３ａ）に示す項）は、飛散している全ての粉塵粒子の影響を考慮するために、粉塵粒子の粒径Ｄに依存する影響因子Ｄ^３を粒子数基準の粒径分布ｑ_Ｄで重み付け平均することを意味する。

[Microwave attenuation due to dust]
The amount of microwave attenuation by dust can be quantified by a model of microwave scattering by dust particles flying above the molten material in the converter 1. The amount of attenuation A per unit length of the microwave (electromagnetic wave) transmitted from the antenna 10 is expressed by the following formula (1) where the unit is [dB/m] and the attenuating side is a positive value, and the microwave frequency is f [Hz].

In the above formula (1), α and β are expressed by the following formulas (2) and (3), respectively. Note that in formula (1), the term proportional to α (4.34×αf ⁴ ) represents Rayleigh scattering, and the term proportional to β (4.34×βf) represents absorption attenuation.

In the above equations (2) and (3), π is the circular constant, c [m/s] is the speed of light, d [kg/m ³ ] is the dust concentration, ρ [kg/m ³ ] is the true specific gravity of a dust particle, D [m] is the particle size (diameter) of a dust particle, V _D [m ³ ] is the volume of a single dust particle of particle size D, and q _D is the particle number-based particle size distribution of dust particles.
The term on the right side of _Kα in equation (2) (term shown in (2a) below) means that, in order to take into account the influence of all flying dust particles, the influence factor ^D6 that depends on the particle size D of the dust particles is weighted and averaged with the particle size distribution _qD based on the particle number. Similarly, the term on the right side of _Kβ in equation (3) (term shown in (3a) below) means that, in order to take into account the influence of all flying dust particles, the influence factor ^D3 that depends on the particle size D of the dust particles is weighted and averaged with the particle size distribution _qD based on the particle number.

上記の式（４）及び式（５）において、ε_ｒは粉塵粒子の複素比誘電率、μ_ｒは粉塵粒子の複素比透磁率を示す。
なお、式（４）で表されるＫ_α及び式（５）で表されるＫ_βについては、それぞれ複素比誘電率のみを考慮した以下の式（４ａ）及び式（５ａ）が公知である。具体的には、例えば、非特許文献１の第４２頁に記載の式（３．１７）を第５１頁に記載の式（３．６６）に当てはめて、散乱と吸収とに分けて記述すれば、式（４ａ）及び式（５ａ）が得られる。

しかしながら、転炉１内で飛散している粉塵粒子には、酸化鉄や金属鉄等の磁性体も含まれていることから、本実施形態では、磁気双極子の影響を考慮して、式（４）及び式（５）に示すように、複素比透磁率μ_ｒを含む形に修正している。 Moreover, K _α in the above formula (2) is expressed by the following formula (4), and K _β in the above formula (3) is expressed by the following formula (5).

In the above formulas (4) and (5), _εr represents the complex relative dielectric constant of the dust particle, and _μr represents the complex relative permeability of the dust particle.
For _Kα expressed by formula (4) and _Kβ expressed by formula (5), the following formulas (4a) and (5a) are known, which consider only the complex relative dielectric constant. Specifically, for example, formula (3.17) described on page 42 of Non-Patent Document 1 is substituted into formula (3.66) described on page 51, and the formulas are written separately for scattering and absorption, to obtain formulas (4a) and (5a).

However, since the dust particles scattered within the converter 1 also contain magnetic materials such as iron oxide and metallic iron, in this embodiment, the formulas are modified to include the complex relative permeability _μr as shown in Equation (4) and Equation (5) in consideration of the influence of the magnetic dipole.

Equation (1) explained above indicates that the higher the microwave frequency f, the greater the attenuation of the microwave due to dust particles (attenuation A per unit length of the microwave).

上記の式（６）において、ηはアンテナ１０の開口効率、ｒ［ｍ］はアンテナ１０の半径、λ［ｍ］はマイクロ波の波長を示す。
なお、上記の式（６）は、非特許文献１の第２３頁に記載の式（２．８３）に有効開口面積Ａｅ＝η×πｒ^２を代入することにより得られる。 [Antenna Gain of Antenna 10]
The antenna gain G of the antenna 10, which determines the performance of the level measurement device 100, is expressed by the following equation (6).

In the above formula (6), η is the aperture efficiency of the antenna 10, r [m] is the radius of the antenna 10, and λ [m] is the wavelength of the microwave.
The above formula (6) can be obtained by substituting the effective opening area Ae=η× ^πr2 into formula (2.83) described on page 23 of Non-Patent Document 1.

上記の式（７）を単位ｄＢｉで書き換えると、以下の式（８）となる。

上記の式（７）及び式（８）は、マイクロ波の周波数ｆが高いほど、アンテナ１０のアンテナ利得Ｇが大きくなることを示している。 Since c=fλ holds between the speed of light c, frequency f, and wavelength λ, the above equation (6) can be rewritten as the following equation (7).

When the above formula (7) is rewritten in units of dBi, the following formula (8) is obtained.

The above equations (7) and (8) show that the higher the frequency f of the microwave, the greater the antenna gain G of the antenna 10.

上記の式（９）において、Ｐｔ［ｄＢ］はマイクロ波の送信信号強度（具体的には、送信用アンテナ１０ａから送信される送信波の強度）、σ［ｄＢｓｍ］は測定対象であるスラグ面３のレーダ反射断面積を示す。
なお、非特許文献１の第３８頁に記載の式（３．８）をｄＢ単位に変換すると、粉塵粒子によるマイクロ波の減衰量を考慮していない、一般的なレーダ方程式である、以下の式（９ａ）が得られる。

上記の式（９）は、この式（９ａ）に、スラグ面３までの往復距離２Ｒでのマイクロ波の減衰量の項である－２ＡＲを加えると共に、ｃ＝ｆλに基づき、波長λを周波数ｆ及び光速ｃで書き換えたものである。 [Calculation of received signal strength]
In the received signal strength calculation step ST1, the received signal strength P r of the microwave is calculated based on the following equation (9) using the attenuation _A per unit length of the microwave and the antenna gain G of the antenna 10 described above.

In the above equation (9), Pt [dB] represents the microwave transmission signal strength (specifically, the strength of the transmission wave transmitted from the transmitting antenna 10a), and σ [dBsm] represents the radar cross section of the slag surface 3 to be measured.
Incidentally, when equation (3.8) described on page 38 of Non-Patent Document 1 is converted to dB units, the following equation (9a) is obtained, which is a general radar equation that does not take into account the attenuation of microwaves due to dust particles.

The above equation (9) is obtained by adding a term −2AR, which is the microwave attenuation term over a round trip distance of 2R to the slag surface 3, to equation (9a), and rewriting the wavelength λ in terms of frequency f and speed of light c based on c=fλ.

The radar cross section σ of the slug surface 3 to be measured, the complex relative dielectric constant _εr of the dust particles, the complex relative magnetic permeability _μr of the dust particles, the particle number-based particle size distribution _qD of the dust particles, the true specific gravity ρ of the dust particles, and the dust concentration d are previously obtained, the maximum distance to the slug surface 3 is determined as the distance R used in equation (9), and equations (1) and (8) are substituted for A and G in equation (9), respectively, so that equation (9) can be expressed as a function of the microwave frequency f. Therefore, the microwave received signal strength P _r can be calculated with respect to the frequency f.
The radar cross section σ of the slag surface 3 can be calculated, for example, by using electromagnetic field analysis using the finite element method or by measuring the received signal strength of microwaves from the slag surface 3 in advance. The measured particle size distribution _qD can be measured, for example, by collecting dust particles passing through the exhaust hood 5 and using an optical particle size distribution meter for the collected dust particles. The dust concentration d can be measured, for example, by attaching an optical dust concentration meter to the exhaust hood 5.

<Noise level calculation step ST2>
In the noise level calculation step ST2, the noise level represented by the thermal noise of the signal processing unit 20 (specifically, the AD converter 27) and the radiation noise from the slag surface 3 is calculated as a function of the microwave frequency f.

上記の式（１０）において、ｋＢ［ｍ^２ｋｇ／ｓ^２Ｋ］はボルツマン定数、ｆ_ｓ［Ｈｚ］はＡＤ変換器２７のサンプリング周波数（ＡＤ変換器２７で取得できる周波数の帯域幅の２倍に相当）、Ｔ［Ｋ］はＡＤ変換器２７の温度を示す。 [Thermal noise of AD converter 27]
The main noise occurring in the level measurement device 100 is the thermal noise of the signal processing unit 20, and in particular, the thermal noise of the AD converter 27. The thermal noise _Nt of the AD converter 27 is expressed by the following equation (10).

In the above equation (10), kB [ ^m2 kg/ ^s2 K] is the Boltzmann constant, _fs [Hz] is the sampling frequency of the AD converter 27 (corresponding to twice the bandwidth of the frequency that can be acquired by the AD converter 27), and T [K] is the temperature of the AD converter 27.

そして、ローパスフィルタ２６のカットオフ周波数で決められる帯域幅によって算出される波長幅Δλ、発熱源であるスラグ面３のうち受信用アンテナ１０ｂの視野に入る面積Ｓ、アンテナ１０に入り込む立体角Ωを分光放射輝度Ｌ（λ，Ｔ_ｔ）に乗算して、ｄＢ単位に変換すると、輻射ノイズＮ_ｒは、以下の式（１２）で表される。

上記の式（１１）及び式（１２）において、Ｃ_１は放射の第１定数、Ｃ_２は放射の第２定数、Ｔ_ｔ［Ｋ］は測定対象であるスラグ面３の温度である。 [Radiation noise from slag surface 3]
In this embodiment, since the molten material in the converter 1 is at a high temperature of 1000° C. or more, the influence of electromagnetic waves in the microwave band emitted from the slag surface 3 cannot be ignored. Since the electromagnetic waves emitted from the slag surface 3 are incoherent, they are detected as white noise by the receiving antenna 10b. A signal corresponding to this white noise is mixed with the transmission wave (output waveform of the oscillator 21) in the mixer 23, amplified by the IF amplifier 25, passed through the low-pass filter 26, AD converted by the AD converter 27, and input to the computer 28. Therefore, the radiation energy in the bandwidth determined by the cutoff frequency of the low-pass filter 26 is considered as the magnitude of the radiation noise. Therefore, when calculating the radiation noise _Nr , the spectral radiance L(λ, _Tt ) per unit bandwidth and per unit solid angle is calculated according to Planck's law, which is expressed by the following formula (11).

Then, by multiplying the spectral radiance L(λ, Tt) by the wavelength width Δλ calculated by the bandwidth determined by the cutoff frequency of the low-pass filter 26, the area S of the slag surface 3, which is the heat source, that is within the field of view of the receiving antenna 10b, and the solid angle Ω into the antenna ₁₀ , and converting the result into dB units, the radiation noise _Nr is expressed by the following equation (12).

In the above formulas (11) and (12), C ₁ is the first constant of radiation, C ₂ is the second constant of radiation, and T _t [K] is the temperature of the slag surface 3 to be measured.

[Noise level calculation]
The sum of the thermal noise _Nt and radiation noise _Nr of the AD converter 27 described above plus the noise figure NF [dB] of the circuit constituting the signal processing unit 20 becomes the noise input to the AD converter 27. This noise can be reduced by performing signal processing in the computer 28. As the signal processing for reducing the noise, for example, three processes, FFT processing, oversampling, and coherent integration, are considered. The noise reduction amount _Ns obtained by combining these three processes is expressed by the following formula (13), where the number of FFT points is N _FFT , the sampling frequency of the AD converter 27 is f _s as described above, the number of coherent integrations is n, and the bandwidth of the intermediate frequency signal after passing through the low-pass filter 26 (the bandwidth of the frequency that the beat wave can take) is BW.

ＡＤ変換器２７の温度Ｔ、スラグ面３の温度Ｔ_ｔを予め求めておけば、ｃ＝ｆλが成り立つため、式（１０）～式（１４）によって算出されるノイズレベルＮも、マイクロ波の周波数ｆの関数で表される。このため、周波数ｆに対してノイズレベルＮを計算することができる。 Finally, in the noise level calculation process ST2, the noise level N is calculated based on the following equation (14) using the thermal noise _Nt of the AD converter 27 expressed by equation (10), the radiation noise _Nr expressed by equation (12), the noise figure NF of the circuit constituting the signal processing unit 20, and the noise reduction amount _Ns expressed by equation (13), all of which are described above.

If the temperature T of the AD converter 27 and the temperature _Tt of the slag surface 3 are obtained in advance, c=fλ is established, and therefore the noise level N calculated by the formulas (10) to (14) can be expressed as a function of the microwave frequency f. Therefore, the noise level N can be calculated with respect to the frequency f.

<Frequency determination step ST3>
In the frequency determination step ST3, an S/N ratio is calculated based on the microwave reception signal strength P _r calculated in the reception signal strength calculation step ST1 and the noise level N calculated in the noise level calculation step ST2. Specifically, the ratio (difference when expressed in dB) between the microwave reception signal strength P _r and the noise level N is calculated as the S/N ratio. As described above, since both the microwave reception signal strength P _r and the noise level N are expressed as functions of the microwave frequency f, the S/N ratio is also expressed as a function of the microwave frequency f.
Therefore, in the frequency determining step ST3, the frequency f of the microwaves (range of frequency f) can be determined so that the calculated S/N ratio is equal to or greater than a predetermined threshold value Th (for example, 10 dB).

In the level measurement device 100 according to this embodiment, the oscillator 21 of the signal processing unit 20 is set to generate a waveform of the frequency f determined by executing the received signal strength calculation process ST1, the noise level calculation process ST2, and the frequency determination process ST3 described above. Specifically, in this embodiment, in order to measure the level of the slag surface 3 using the FM-CW method, the frequency range determined by the frequency modulation width F (see FIG. 2) of the waveform generated by the oscillator 21 is set to be included in the range of the determined frequency f. When the oscillator 21 generates a waveform of a single frequency (when the level of the slag surface 3 is measured using microwaves of a single frequency), it is sufficient to set this single frequency to be included in the range of the determined frequency f.

In this embodiment, the noise reduction amount _Ns is taken into consideration when calculating the noise level N in the noise level calculation process ST2. However, if signal processing for reducing noise is not performed, the noise level N may be calculated without taking into consideration the noise reduction amount _Ns .

In addition, in this embodiment, the furnace to be measured for level is a converter 1, and the bath surface in the furnace for level measurement is the slag surface 3. However, the present invention is not limited to this, and can also be applied to, for example, measuring the level of the charge in a blast furnace, the bath surface level in the lower part of a blast furnace, or the bath surface level of a copper refining furnace.
In addition, in this embodiment, an example has been described in which the antenna 10 has a configuration separated into a transmitting antenna 10a and a receiving antenna 10b, but the present invention is not limited to this, and it is also possible to use a single integrated transmitting and receiving antenna that serves both transmitting and receiving purposes.

Hereinafter, an example in which an appropriate microwave frequency f is determined for the level measurement device 100 according to this embodiment will be described.
In this embodiment, when calculating the received signal strength P _r , the following conditions were used: the distance R to the slug surface 3 was 25 [m], the true specific gravity ρ of the dust particle was 4490.5 [kg/m ³ ], the complex relative dielectric constant ε _r of the dust particle was 62.4+14.1j, the complex relative magnetic permeability μ _r of the dust particle was 1.24+0.59j, the dust concentration d was 50 [g/m ³ ], 100 [g/m ³ ], and 200 [g/m ³ ], the radar cross section σ of the slug surface 3 was -43 [dBsm], and the microwave transmission signal strength Pt was 10 [dBm]. In addition, the particle size distribution shown in FIG. 4 was used as the particle number-based particle size distribution q _D of the dust particles. The vertical axis of FIG. 4 indicates the particle number of dust particles having each particle size shown on the horizontal axis as a ratio to the total particle number.
In addition, when calculating the noise level N, the following conditions were used: the temperature _Tt of the slag surface 3 to be measured was 1700 [°C], the temperature T of the AD converter 27 was 40 [°C], the noise figure NF was 21.5 [dB], the number of FFT points N _FFT was 2048 points, the sampling frequency B of the AD converter 27 was 1.2 [MHz], and the number of coherent integrations n was 1.
Under the conditions described above, the received signal strength calculation step ST1, the noise level calculation step ST2, and the frequency determination step ST3 are performed to calculate the received signal strength P _r , the noise level N, and the S/N ratio as functions of the frequency f.

Fig. 5 shows the results of calculations of the received signal strength P _r , the noise level N, and the S/N ratio as functions of frequency f in this embodiment. Fig. 5(a) shows the results when the dust concentration d is 50 [g/m ³ ], Fig. 5(b) shows the results when the dust concentration d is 100 [g/m ³ ], and Fig. 5(c) shows the results when the dust concentration d is 200 [g/m ³ ].
5, as the frequency f increases, the noise level N increases monotonically, but the received signal strength P _r fluctuates to have a maximum value due to the balance between the attenuation of microwaves due to dust and the antenna gain of the antenna 10, since the attenuation of _microwaves due to dust increases, as well as the antenna gain of the antenna 10. As a result, it is found that there is an optimal frequency f at which the S/N ratio has a maximum value.

For example, if it is considered that the distance R to the slag surface 3 can be measured if the S/N ratio is 10 dB or more, and the threshold value Th is set to 10 dB, when the dust concentration d is 50 g/m ³ , the S/N ratio is equal to or greater than the threshold value Th when the frequency f indicated by the arrow in the figure is in the range of 8 to 72 GHz (the S/N ratio has a maximum value near 25 GHz), and this range can be determined as an appropriate frequency f range, for example. Also, when the dust concentration d is 100 g/m ³ , the S/N ratio is equal to or greater than the threshold value Th when the frequency f indicated by the arrow in the figure is in the range of 8 to 32 GHz (the S/N ratio has a maximum value near 18 GHz), and this range can be determined as an appropriate frequency f range, for example. However, as shown in Fig. 5(c), when the dust concentration d is 200 [g/ ^m3 ], there is no frequency f at which the S/N ratio is equal to or greater than the threshold value Th of 10 dB. In this case, it is necessary to review the threshold value Th, increase the microwave transmission signal strength, reduce the noise level N, or perform other measures.
Although not shown in the figure, the upper limit of the dust concentration d at which there exists a frequency f at which the S/N ratio is 10 dB or more is 130 [g/m ³ ], and the frequency f at which the S/N ratio reaches its maximum value is 16.5 [GHz]. When the dust concentration d is 130 [g/m ³ ], if the frequency modulation width F required for distance measurement based on the FM-CW method is 3 [GHz], then the appropriate frequency f range can be determined to be, for example, 15 to 19 [GHz].

1... Converter (furnace)
3... Slag surface (bath surface)
4: Lance 5: Exhaust hood 10, 10a, 10b: Antenna 20: Signal processing unit 23: Mixer 26: Low-pass filter 100: Level measuring device ST1: Received signal strength calculation process ST2: Noise level calculation process ST3: Frequency determination process

Claims (4)

A method for determining a microwave frequency for use in a level measurement device for measuring a bath surface level in a furnace, comprising:
The level measuring device includes an antenna that transmits microwaves toward the bath surface and receives the microwaves reflected from the bath surface, and a signal processing unit that calculates the level of the bath surface based on the microwaves received by the antenna,
a receiving signal strength calculation step of calculating a receiving signal strength of the microwave, which is represented by an attenuation amount of the microwave due to the dust in the furnace and an antenna gain of the antenna, as a function of a frequency of the microwave;
a noise level calculation step of calculating a noise level represented by thermal noise of the signal processing unit and radiation noise from the bath surface as a function of the frequency of the microwave;
a frequency determination step of determining a frequency of the microwave such that an S/N ratio determined by the received signal strength of the microwave calculated in the received signal strength calculation step and the noise level calculated in the noise level calculation step is equal to or greater than a predetermined threshold value;
A method for determining a microwave frequency comprising: 2. The microwave frequency determination method according to claim 1, wherein in the received signal strength calculation step, an amount of attenuation of the microwave due to dust in the furnace is calculated based on the following formulas (1) to (5).

In the above formula (1), A [dB/m] is the attenuation per unit length of the microwave transmitted from the antenna, and f [Hz] is the frequency of the microwave. In the above formulas (2) and (3), π is the circular constant, c [m/s] is the speed of light, d [kg/ ^m3 ] is the dust concentration, ρ [kg/ ^m3 ] is the true specific gravity of the dust particle, D [m] is the particle size (diameter) of the dust particle, _VD [ ^m3 ] is the volume of a single dust particle with particle size D, and _qD is the particle number-based particle size distribution of the dust particles. In the above formulas (4) and (5), _εr is the complex relative dielectric constant of the dust particle, and _μr is the complex relative magnetic permeability of the dust particle. A level measuring device for measuring the level of a bath surface in a furnace,
An antenna that transmits microwaves toward the bath surface and receives the microwaves reflected from the bath surface, and a signal processing unit that calculates the level of the bath surface based on the microwaves received by the antenna,
The level measuring device includes:
a receiving signal strength calculation step of calculating a receiving signal strength of the microwave, which is represented by an attenuation amount of the microwave due to the dust in the furnace and an antenna gain of the antenna, as a function of a frequency of the microwave;
a noise level calculation step of calculating a noise level represented by thermal noise of the signal processing unit and radiation noise from the bath surface as a function of the frequency of the microwave;
a frequency determination step of determining a frequency of the microwave such that an S/N ratio determined by the received signal strength of the microwave calculated in the received signal strength calculation step and the noise level calculated in the noise level calculation step is equal to or greater than a predetermined threshold value;
A level measuring device that measures the level of the bath surface using microwaves having the frequency determined in the frequency determination process . A level measurement method for measuring a bath surface level in a furnace, comprising the steps of:
A step of determining a frequency of a microwave used in the level measurement device by the microwave frequency determination method according to claim 1 or 2;
measuring the level of the bath surface using the level measuring device using microwaves of the determined frequency ;
A level measurement method comprising the steps of :

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