JPH0530204B2 - - Google Patents
Info
- Publication number
- JPH0530204B2 JPH0530204B2 JP13770284A JP13770284A JPH0530204B2 JP H0530204 B2 JPH0530204 B2 JP H0530204B2 JP 13770284 A JP13770284 A JP 13770284A JP 13770284 A JP13770284 A JP 13770284A JP H0530204 B2 JPH0530204 B2 JP H0530204B2
- Authority
- JP
- Japan
- Prior art keywords
- gas
- ultrasonic
- tube
- determining
- detection means
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Lifetime
Links
- 238000001514 detection method Methods 0.000 claims description 7
- 239000012530 fluid Substances 0.000 claims description 6
- 230000000644 propagated effect Effects 0.000 claims 1
- 238000000034 method Methods 0.000 description 4
- 238000010586 diagram Methods 0.000 description 3
- 238000005259 measurement Methods 0.000 description 2
- 238000011144 upstream manufacturing Methods 0.000 description 2
- 230000000694 effects Effects 0.000 description 1
- 238000009413 insulation Methods 0.000 description 1
- 238000002604 ultrasonography Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01F—MEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
- G01F1/00—Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through a meter in a continuous flow
- G01F1/66—Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through a meter in a continuous flow by measuring frequency, phase shift or propagation time of electromagnetic or other waves, e.g. using ultrasonic flowmeters
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01F—MEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
- G01F1/00—Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through a meter in a continuous flow
- G01F1/76—Devices for measuring mass flow of a fluid or a fluent solid material
- G01F1/86—Indirect mass flowmeters, e.g. measuring volume flow and density, temperature or pressure
Landscapes
- Physics & Mathematics (AREA)
- Fluid Mechanics (AREA)
- General Physics & Mathematics (AREA)
- Electromagnetism (AREA)
- Measuring Volume Flow (AREA)
Description
【発明の詳細な説明】
ａ 産業上の利用分野
本発明は気体の質量流量を超音波を用いて測定
する超音波気体質量流量計に関する。DETAILED DESCRIPTION OF THE INVENTION a. Field of Industrial Application The present invention relates to an ultrasonic gas mass flow meter that measures the mass flow rate of gas using ultrasonic waves.
ｂ 従来技術
質量流量とは、単位時間当りに流路の断面を横
切つて流れる流体の質量を言う。すなわち流路が
管である場合、管の一断面における流速をｖ、密
度をρ、管内部断面積をＡとするとき、質量流量
Ｇは(1)式で与えられる。b. Prior Art Mass flow rate refers to the mass of fluid flowing across the cross section of a flow path per unit time. That is, when the flow path is a pipe, the mass flow rate G is given by equation (1), where v is the flow velocity in one cross section of the pipe, ρ is the density, and A is the internal cross-sectional area of the pipe.
Ｇ＝ρAv ……(1)
測定されるべき流体が理想気体である場合、気
体の圧力をＰ、気体の体積をＶ、気体の平均分子
量をｍ、気体の質量をｗ、一般気体定数をＲ、絶
縁温度をＴとするとき、次の状態方程式が成立す
る。 G=ρAv...(1) When the fluid to be measured is an ideal gas, the pressure of the gas is P, the volume of the gas is V, the average molecular weight of the gas is m, the mass of the gas is w, and the general gas constant is R. , the following equation of state holds true when the insulation temperature is T.
PV＝ｗ／ｍRT ……(2)
気体密度ρは(3)式で与えられるので、(2)式は(4)
式に変形される。 PV=w/mRT...(2) Since the gas density ρ is given by equation (3), equation (2) becomes (4)
It is transformed into Eq.
ρ＝ｗ／ｖ ……(3)
ρ＝Pm／RT ……(4)
(4)式を(1)式に代入することにより次式が得られ
る。 ρ=w/v...(3) ρ=Pm/RT...(4) By substituting equation (4) into equation (1), the following equation is obtained.
Ｇ＝PmAv／RT ……(5)
(5)式は、気体の種類が定つていて平均分子量
ｍ、一般気体定数Ｒおよび管内部断面積が既知で
ある場合、流体の圧力Ｐ、流体の温度Ｔおよび流
速ｖを測定することにより、質量流量Ｇが求めら
れることを意味する。 G=PmAv/RT...(5) Equation (5) shows that when the type of gas is fixed and the average molecular weight m, general gas constant R, and tube internal cross-sectional area are known, the fluid pressure P, the fluid This means that the mass flow rate G is determined by measuring the temperature T and the flow rate v.
従来技術による超音波気体質量流量計において
は、流速ｖは２つの超音波トランスデユーサ間の
距離と、超音波の気体中伝播時間を測定すること
によつて求め、(5)式を用いて質量流量を測定す
る。 In the conventional ultrasonic gas mass flowmeter, the flow velocity v is determined by measuring the distance between two ultrasonic transducers and the propagation time of the ultrasonic wave in the gas, and is calculated using equation (5). Measure mass flow rate.
具体的には、例えば次のようにして測定され
る。 Specifically, for example, it is measured as follows.
管内に距離Ｌだけ隔て管軸方向と角度θをなす
ように２個の超音波トランスデユーサを配設し、
その近傍に圧力センサと温度センサを設ける。 Two ultrasonic transducers are arranged in the pipe so as to be separated by a distance L and form an angle θ with the pipe axis direction,
A pressure sensor and a temperature sensor are provided near it.
管内流速が一様にｖであるとし、気体中の音速
をｃとするとき、気体流の上流側に配設された第
１の超音波トランスデユーサから下流側の第２の
超音波トランスデユーサに到るまでの超音波の伝
播時間t1と、上記第２の超音波トランスデユーサ
から上記第１の超音波トランスデユーサに到るま
での伝播時間t2は、それぞれ次のように与えられ
る。 Assuming that the flow velocity in the pipe is uniformly v and the sound velocity in the gas is c, the flow from the first ultrasonic transducer disposed on the upstream side of the gas flow to the second ultrasonic transducer disposed on the downstream side. The propagation time t1 of the ultrasonic wave until it reaches the user and the propagation time t2 from the second ultrasonic transducer to the first ultrasonic transducer are respectively as follows. Given.
t1＝Ｌ／ｃ＋vcosθ ……(6) t2＝Ｌ／ｃ−vcosθ ……(7) ここでt+とt-を次のように定義する。 t 1 =L/c+vcosθ...(6) t2 =L/c-vcosθ...(7) Here, t + and t- are defined as follows.
t+＝t2＋t1 ……(8)
t-＝t2−t1 ……(9)
(6)，(7)式を代入することにより次のように変形
される。 t + =t 2 +t 1 ...(8) t - =t 2 −t 1 ...(9) By substituting equations (6) and (7), it is transformed as follows.
t-＝2Lvcosθ／c2−v2cos2θ ……(10)
t+＝2Lc／c2−v2cos2θ ……(11)
t-／t+＝vcosθ／ｃ ……(12)
ｃ＝2L／１−（t-／t+）2・１／t+……(13)
ｖ＝2L／１−（t-／t+）2・t-／（t+）2cosθ……(14
)
(13)式、(14)式はt-《t+のとき次のように変形さ
れる。 t - ＝2Lvcosθ／c 2 −v 2 cos 2 θ ……(10) t + ＝2Lc／c 2 −v 2 cos 2 θ ……(11) t − ／t + ＝vcosθ／c ……(12) c=2L/1-( t- /t + ) 2・1/t + ...(13) v=2L/1-(t- / t + ) 2・t - /(t + ) 2 cosθ... (14
) Equations (13) and (14) are transformed as follows when t - <<t + .
ｃ＝2L／t+ ……(15)
ｖ＝2Lt-／（t+）2cosθ ……(16)
(16)式を(5)式に代入することにより、次の質量
流量計算式が得られる。 c=2L/t + ...(15) v=2Lt - /(t + ) 2 cosθ ...(16) By substituting equation (16) into equation (5), the following mass flow rate calculation formula is obtained. It will be done.
Ｇ＝2PmALt-／RT（t+）2cosθ ……(17)
質量流量Ｇは、既知量ｍ，Ｒと、寸法値Ａ，
Ｌ，θと、測定値Ｐ，t-，t+，Ｔから求められ
る。 G=2PmALt - /RT(t + ) 2 cosθ...(17) The mass flow rate G is the known quantities m and R, and the dimension value A,
It is determined from L, θ and the measured values P, t - , t + , T.
ｃ 発明が解決しようとする問題点
(17)式の各因子はそれぞれ誤差の要因となる。気
体の質量流量を精密に測定するためには、上記各
因子の誤差を小さくしなければならない。しかし
（１７）式に基づく限り誤差の逓減に限界がある。c Problems to be solved by the invention Each factor in equation (17) becomes a cause of error. In order to accurately measure the mass flow rate of gas, the errors of each of the above factors must be reduced. However, as long as it is based on equation (17), there is a limit to the gradual reduction of the error.
本発明はマツハ数Ｍを用いて質量流量を測定す
ることにより誤差の小さい質量流量計を提供する
ことを目的とする。 An object of the present invention is to provide a mass flowmeter with small errors by measuring the mass flow rate using the Matsuha number M.
ｄ 問題点を解決するための手段
上記問題点は、寸法数値であるＬを用いる代り
に、特定温度、特定圧力における被測定気体の音
速ｃに対する流速ｖの比率であるマツハ数Ｍ
（ｖ／ｃ）を測定変数とすることにより解決する。d Means to solve the problem The problem mentioned above is that instead of using L, which is a dimensional value, the Matsuhha number M, which is the ratio of the flow velocity v to the sound velocity c of the gas to be measured at a specific temperature and specific pressure, is used.
This is solved by using (v/c) as the measurement variable.
気体中の音速ｃは、気体の圧力Ｐと、定圧比熱
Cpの定積比熱Cvに対する比率γと、密度ρと、
絶対温度Ｔと、一般気体定数Ｒ、および平均分子
量ｍによつて次のように表わされる。 The speed of sound c in a gas is determined by the pressure P of the gas and the specific heat at constant pressure.
The ratio γ of Cp to the constant volume specific heat Cv, the density ρ,
It is expressed as follows using absolute temperature T, general gas constant R, and average molecular weight m.
c2＝γP／ρ（γ＝Cp／Cv） ……(18)
＝γRT／ｍ ……(19)
(18)，(19)式を(1)式に代入することにより、次
式が得られる。 c 2 = γP/ρ (γ = Cp/Cv) ...(18) = γRT/m ...(19) By substituting equations (18) and (19) into equation (1), the following equation is obtained. It will be done.
上記マツハ数Ｍは、超音波トランスデユーサ間
の距離Ｌとは無関係に測定可能な量であり、(20)
式の各因子を測定することにより質量流量Ｇが求
められる。 The above Matsuha number M is a quantity that can be measured regardless of the distance L between the ultrasonic transducers, (20)
The mass flow rate G is determined by measuring each factor in the equation.
マツハ数は、従来技術におけるのと同じ配置の
２つの超音波トランスデユーサを用いて、流れの
上流側と下流側に配設した２つの超音波トランス
デユーサ間の、流れに対して順方向の場合と逆方
向の場合の伝播時間の差と和の比から求めること
ができる。すなわち(12)式から（ｖ／ｃ）を求め
ることができる。(12)式を(20)式に代入すること
によつて次式が得られる。 The Matsuha number is calculated in the forward direction of the flow between two ultrasonic transducers placed upstream and downstream of the flow using two ultrasonic transducers arranged in the same way as in the prior art. It can be determined from the ratio of the difference and sum of propagation times in the case of , and in the case of the opposite direction. That is, (v/c) can be obtained from equation (12). By substituting equation (12) into equation (20), the following equation is obtained.
またシングアラウンド法によつても上記マツハ
数Ｍを求めることができる。シングアラウンド法
の場合、超音波が流速に対して順方向、逆方向に
伝播するときのそれぞれの周波数1，2は次の式
で与えられることが知られている。 The Matsuhha number M can also be determined by the sing-around method. In the sing-around method, it is known that the frequencies 1 and 2 when ultrasound propagates in the forward and reverse directions relative to the flow velocity are given by the following equations.
1＝ｃ＋vcosθ／Ｌ ……(22) 2＝ｃ−vcosθ／Ｌ ……(23) ここで+と-を次のように定義する。 1 =c+vcosθ/L...(22) 2 =c-vcosθ/L...(23) Here, + and - are defined as follows.
+＝1＋2 ……(24)
-＝1−2 ……(25)
(22)，(23)式を(24)，(25)式に代入することによ
り次のように変形される。 + = 1 + 2 ...(24) - = 1 − 2 ...(25) By substituting equations (22) and (23) into equations (24) and (25), it is transformed as follows.
+＝2c／Ｌ ……(26)
-＝2vcosθ／Ｌ ……(27)
したがつてマツハ数Ｍ（ｖ／ｃ）は次の式で与
えられる。 + =2c/L...(26) - =2vcosθ/L...(27) Therefore, the Matsuhha number M(v/c) is given by the following formula.
Ｍ＝-／+cosθ ……(28) このとき質量流量Ｇは(29)式で与えられる。 M= - / + cosθ...(28) At this time, the mass flow rate G is given by equation (29).
ｆ 実施例
第１図は本発明の超音波気体質量流量計の実施
例の概念図である。 f Embodiment FIG. 1 is a conceptual diagram of an embodiment of the ultrasonic gas mass flowmeter of the present invention.
管壁１に２個の超音波トランスデユーサ２，３
が超音波伝播方向が管軸と角度θをなすように配
設され、該超音波トランスデユーサ２，３の近傍
に圧力センサ４と温度センサ５が取付けられてい
る。超音波トランスデユーサ間の超音波伝播時間
から(12)式または(28)式に基づいてマツハ数Ｍをマ
ツハ数計算回路６で求める。該マツハ数計算回路
６の出力と、該圧力センサ４の出力と、該温度セ
ンサ５の出力を入力とする他に、管内気体の平均
分子量ｍ、一般気体定数Ｒ、管断面積Ａなどを入
力回路７から入力された気体質量流量計算回路８
で、(20)式に基づいて気体質量流量が計算され、
表示回路９でそれで表示される。 Two ultrasonic transducers 2 and 3 on the tube wall 1
are arranged so that the ultrasonic propagation direction forms an angle θ with the tube axis, and a pressure sensor 4 and a temperature sensor 5 are installed near the ultrasonic transducers 2 and 3. Based on the ultrasonic propagation time between the ultrasonic transducers, the Matsuh number M is determined by the Matsuh number calculation circuit 6 based on equation (12) or equation (28). In addition to inputting the output of the Matsuha number calculation circuit 6, the output of the pressure sensor 4, and the output of the temperature sensor 5, the average molecular weight m of the gas in the tube, the general gas constant R, the tube cross-sectional area A, etc. are input. Gas mass flow rate calculation circuit 8 input from circuit 7
Then, the gas mass flow rate is calculated based on equation (20),
The display circuit 9 displays it accordingly.
なお超音波の送信・受信は通常の発振器、送信
器、増幅回路を用いて行うことができる。マツハ
数計算回路６の具体的回路は、超音波伝播時間検
出方式として時間差、位相差、シングアラウンド
方式等のどの方法を採用するかに従つて変るが、
マイクロプロセツサー等を用いて当業者であれば
実現できるので具体的回路図は省略する。 Note that ultrasonic waves can be transmitted and received using ordinary oscillators, transmitters, and amplifier circuits. The specific circuit of the Matsuha number calculation circuit 6 varies depending on which method, such as time difference, phase difference, or sing-around method, is adopted as the ultrasonic propagation time detection method.
A person skilled in the art can realize this using a microprocessor or the like, so a specific circuit diagram will be omitted.
ｇ 効果
質量流量測定における誤差が小さくなる。慣例
に従つて任意の変数ｘに対する誤差をδxと表現
するとき、従来技術による場合と、本発明による
場合における質量流量の相対誤差はそれぞれ次の
ように与えられる。g Effect Error in mass flow measurement becomes smaller. When the error for an arbitrary variable x is expressed as δx according to convention, the relative error in mass flow rate in the case of the prior art and in the case of the present invention is given as follows.
従来技術によるとき、質量流量計算式は(17)式
で与えられる。 According to the prior art, the mass flow rate calculation formula is given by equation (17).
Ｇ＝2ALmt-P／RT（t+）2cosθ ……(17) したがつて相対誤差は次式で与えられる。 G=2ALmt - P/RT(t + ) 2 cosθ...(17) Therefore, the relative error is given by the following equation.
｜δG／Ｇ｜＝｜δA／Ａ｜＋｜δL／Ｌ｜＋｜δR／
Ｒ｜＋｜δm／ｍ｜
＋｜δT／Ｔ｜＋｜δP／Ｐ｜＋｜sinθ／cos
θδθ｜＋２｜δt+／t+｜＋｜δt-t-｜……(30)
本発明によつて質量流量を求める計算式は、例
えば(21)式または(29)式である。誤差の計算式は
ほぼ等しいので、例として(21)について誤差の計
算をする。 |δG/G|=|δA/A|+|δL/L|+|δR/
R｜+｜δm/m｜ +｜δT/T｜+｜δP/P｜+｜sinθ/cos
θδθ|+2|δt + /t + |+|δt - t - |...(30) The calculation formula for determining the mass flow rate according to the present invention is, for example, equation (21) or equation (29). Since the error calculation formulas are almost the same, we will calculate the error for (21) as an example.
Ｇ＝mr／RT AP／cosθ -／+ ……(29) したがつて相対誤差は次式で与えられる。 G=mr/RT AP/cosθ - / + (29) Therefore, the relative error is given by the following equation.
｜δG／Ｇ｜＝１／２｜δm／ｍ｜＋１／２｜δγ／
δ｜＋｜δA／Ａ｜＋｜δP／Ｐ｜
＋１／２｜δR／Ｒ｜＋１／２｜δT／Ｔ｜＋｜si
nθ／cosθδθ｜＋｜δt-／t-｜＋｜δt+／t+｜……(3
1)
ここで｜δγ／γ｜≒｜δR／Ｒ｜とみなすと、(31)
式に
よる相対誤差は(30)式による相対誤差に比較し
て、Δだけ少なくなる。 |δG/G|=1/2|δm/m|+1/2|δγ/
δ|+|δA/A|+|δP/P| +1/2|δR/R|+1/2|δT/T|+|si
nθ／cosθδθ｜＋｜δt - /t - ｜＋｜δt + /t + ｜……(3
1) Here, if we consider |δγ/γ|≒|δR/R|, (31)
The relative error based on equation (30) is smaller by Δ compared to the relative error based on equation (30).
Δ＝｜δL／Ｌ｜＋｜δt+／t+｜＋１／２｜δT／Ｔ｜
＋１／２｜δm／ｍ｜ Δ=|δL/L|+|δt + /t + |+1/2|δT/T|
+1/2 | δm/m |
第１図は本発明の超音波質量流量計の実施例の
概念図である。
１……管壁、２，３……超音波トランスデユー
サ、４……圧力センサ、５……温度センサ、６…
…マツハ数計算回路、７……入力回路、８……気
体質量流量計算回路、９……表示回路。
FIG. 1 is a conceptual diagram of an embodiment of the ultrasonic mass flowmeter of the present invention. 1... Pipe wall, 2, 3... Ultrasonic transducer, 4... Pressure sensor, 5... Temperature sensor, 6...
... Matsuha number calculation circuit, 7 ... input circuit, 8 ... gas mass flow rate calculation circuit, 9 ... display circuit.
Claims (1)
あるマツハ数を求めるマツハ数検出手段と、管内
気体の圧力Ｐを求める圧力検出手段と、管内気体
の絶対温度Ｔを求める温度検出手段と、上記マツ
ハ数検出手段によつて得られたマツハ数Ｍ、上記
圧力Ｐ、上記絶対温度Ｔと、管内気体平均分子量
ｍ、管内気体の定圧比熱Cpの定積比熱Cvに対す
る比率γ、管断面積Ａ、一般気体定数Ｒから次式
に従つて気体の質量流量Ｇを計算する質量流量計
算手段とを有することを特徴とする超音波気体質
量流量計。 ２ 上記マツハ数検出手段が、それぞれ流速に対
して順方向、逆方向に流体中を伝播した超音波の
伝播時間t1，t2と、超音波主軸が管軸となす角度
θとから、次式に従つてマツハ数を求める手段で
あることを特徴とする特許請求の範囲第１項記載
の超音波気体質量流量計。 Ｍ＝t2−t1／（t2＋t1）cosθ ３ 上記マツハ数検出手段が、それぞれ流速に対
して順方向、逆方向に流体中に超音波が伝播する
ときのシングアラウンド周波数1，2と超音波主
軸が管軸をなす角度θとから次式に従つてマツハ
数を求める手段であることを特徴とする特許請求
の範囲第１項記載の超音波気体質量流量計。 Ｍ＝（1−2）／（1＋2）cosθ[Scope of Claims] 1. Matsuhha number detection means for determining the Matsuhha number, which is the ratio of the flow velocity of the gas in the tube to the ultrasonic sound velocity, pressure detection means for determining the pressure P of the gas in the tube, and temperature determining means for determining the absolute temperature T of the gas in the tube. a detection means, the Matsuhha number M obtained by the Matsuhha number detection means, the pressure P, the absolute temperature T, the average molecular weight m of the gas in the tube, the ratio γ of the constant pressure specific heat Cp of the tube gas to the constant volume specific heat Cv, 1. An ultrasonic gas mass flowmeter comprising: a mass flow rate calculation means for calculating a gas mass flow rate G from a tube cross-sectional area A and a general gas constant R according to the following equation. 2 The Matsuha number detection means calculates the following from the propagation times t 1 and t 2 of the ultrasonic waves that propagated in the fluid in the forward and reverse directions with respect to the flow velocity, and the angle θ that the ultrasonic principal axis makes with the tube axis. The ultrasonic gas mass flow meter according to claim 1, characterized in that the ultrasonic gas mass flow meter is means for determining the Matsuhha number according to a formula. M=t 2 −t 1 /(t 2 +t 1 )cos θ 3 Sing-around frequencies 1 and 2 when the ultrasonic waves propagate in the fluid in the forward and reverse directions relative to the flow velocity, respectively, are determined by the Matsuha number detection means. 2. The ultrasonic gas mass flowmeter according to claim 1, wherein the ultrasonic gas mass flowmeter is means for determining the Matsuh number from the angle θ between the main axis of the ultrasonic wave and the axis of the tube according to the following equation. M=( 1-2 )/ ( 1 + 2 )cosθ
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP13770284A JPS6117020A (en) | 1984-07-03 | 1984-07-03 | Supersonic wave mass flowmeter for gas |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP13770284A JPS6117020A (en) | 1984-07-03 | 1984-07-03 | Supersonic wave mass flowmeter for gas |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPS6117020A JPS6117020A (en) | 1986-01-25 |
| JPH0530204B2 true JPH0530204B2 (en) | 1993-05-07 |
Family
ID=15204817
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP13770284A Granted JPS6117020A (en) | 1984-07-03 | 1984-07-03 | Supersonic wave mass flowmeter for gas |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JPS6117020A (en) |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR100497228B1 (en) * | 2004-11-30 | 2005-06-23 | (주)오트로닉스 | Automatic measurement system of river discharge using adcp |
-
1984
- 1984-07-03 JP JP13770284A patent/JPS6117020A/en active Granted
Also Published As
| Publication number | Publication date |
|---|---|
| JPS6117020A (en) | 1986-01-25 |
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