JP4577193B2 - Flow field measurement method using particle tracking method - Google Patents

Flow field measurement method using particle tracking method Download PDF

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JP4577193B2
JP4577193B2 JP2005337651A JP2005337651A JP4577193B2 JP 4577193 B2 JP4577193 B2 JP 4577193B2 JP 2005337651 A JP2005337651 A JP 2005337651A JP 2005337651 A JP2005337651 A JP 2005337651A JP 4577193 B2 JP4577193 B2 JP 4577193B2
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明彦 忠政
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Panasonic Corp
Panasonic Electric Works Co Ltd
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Matsushita Electric Works Ltd
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Description

本発明は、流体中にトレーサ粒子を混入させ、トレーサ粒子の位置を非接触で計測することにより流場を計測する粒子追跡法を用いた流場計測方法に関するものである。   The present invention relates to a flow field measurement method using a particle tracking method in which a flow field is measured by mixing tracer particles in a fluid and measuring the position of the tracer particles in a non-contact manner.

従来から、流体中に微小粒子であるトレーサ粒子を混入させ、位置計測装置によって非接触でトレーサ粒子の位置を追跡し、流体の速度分布を求める技術が知られている。この種の技術において、個々のトレーサ粒子を追跡し、各トレーサ粒子の速度ベクトルを求める技術はＰＴＶ（Particle Tracking Velocimetry）と呼ばれている。ＰＴＶによって得られるトレーサ粒子の速度ベクトルからは速度分布が求められ、さらに速度分布からは、渦度、せん断ひずみ速度、流線などを求めることができる。このように、速度分布を求めたり、速度分布から流体の振る舞いに関する情報を抽出したりすることで流場に関する定量的な計測がなされる。つまり、流場が計測される。   2. Description of the Related Art Conventionally, a technique is known in which tracer particles, which are fine particles, are mixed in a fluid, the position of the tracer particles is tracked in a non-contact manner by a position measurement device, and the velocity distribution of the fluid is obtained. In this type of technique, a technique for tracking individual tracer particles and obtaining a velocity vector of each tracer particle is called PTV (Particle Tracking Velocimetry). From the velocity vector of the tracer particles obtained by PTV, a velocity distribution can be obtained. Further, from the velocity distribution, vorticity, shear strain velocity, streamline, and the like can be obtained. As described above, the flow field is quantitatively measured by obtaining the velocity distribution or extracting the information on the behavior of the fluid from the velocity distribution. That is, the flow field is measured.

ところで、位置計測装置としては主としてＴＶカメラが用いられており、トレーサ粒子の速度ベクトルを求める方法には、単独のＴＶカメラで撮像した時間差を持つ複数枚の２次元画像において対応するトレーサ粒子の位置関係を求める２次元ＰＴＶと、複数台のＴＶカメラで撮像した画像内で同じトレーサ粒子同士を対応付け、ＴＶカメラの視差を考慮してトレーサ粒子の３次元位置を求める３次元ＰＴＶとが知られている。   By the way, a TV camera is mainly used as the position measuring device, and the method for obtaining the velocity vector of the tracer particles is the position of the corresponding tracer particles in a plurality of two-dimensional images having time differences imaged by a single TV camera. Two-dimensional PTV for obtaining a relationship and three-dimensional PTV for associating the same tracer particles in an image captured by a plurality of TV cameras and obtaining a three-dimensional position of the tracer particles in consideration of the parallax of the TV camera are known. ing.

ただし、２次元ＰＴＶでは、トレーサ粒子の移動方向がＴＶカメラによる撮像平面に交差しているとトレーサ粒子の速度ベクトルを正確に抽出することができない。そこで、トレーサ粒子の速度ベクトルを求める必要があるときには３次元ＰＴＶが採用される（たとえば、特許文献１参照）。
特許第３５９９９３８号公報 However, in the two-dimensional PTV, the velocity vector of the tracer particle cannot be accurately extracted if the moving direction of the tracer particle intersects the imaging plane by the TV camera. Therefore, when it is necessary to obtain the velocity vector of the tracer particles, a three-dimensional PTV is employed (for example, see Patent Document 1).
Japanese Patent No. 3599938

ところで、３次元ＰＴＶではトレーサ粒子の３次元位置を追跡することができるから、速度ベクトルを正確に抽出することができるが、流場の特定箇所における速度分布を検出しようとすれば、多数個のトレーサ粒子について３次元位置を検出しなければならず、個々のトレーサ粒子の追跡が困難になる。一方、追跡が容易になるようにトレーサ粒子の個数を少なくすれば、位置計測装置の空間分解能に対して相対的にトレーサ粒子の個数が少なくなるから、位置計測装置の空間分解能に対して相対的に流場の特定箇所における速度分布の抽出精度が低下することになる。   By the way, since the three-dimensional PTV can track the three-dimensional position of the tracer particles, the velocity vector can be accurately extracted. However, if a velocity distribution at a specific location in the flow field is to be detected, a large number of The three-dimensional position must be detected for the tracer particles, making it difficult to track individual tracer particles. On the other hand, if the number of tracer particles is reduced so as to facilitate tracking, the number of tracer particles is reduced relative to the spatial resolution of the position measurement device. In addition, the extraction accuracy of the velocity distribution at a specific location in the flow field is lowered.

本発明は上記事由に鑑みて為されたものであり、その目的は、位置計測装置で計測されるトレーサ粒子の追跡が容易であり、しかも速度分布を抽出する際には位置計測装置の空間分解能に見合う程度に多数個のトレーサ粒子の位置を用いて速度分布を精度よく抽出することができるようにした粒子追跡法を用いた流場計測方法を提供することにある。   The present invention has been made in view of the above reasons, and its purpose is to easily trace the tracer particles measured by the position measuring device, and to extract the velocity distribution, the spatial resolution of the position measuring device. It is an object of the present invention to provide a flow field measurement method using a particle tracking method in which the velocity distribution can be accurately extracted by using the positions of a large number of tracer particles as much as possible.

請求項１の発明は、撹拌翼の回転に伴って撹拌翼の回転軸を中心とする流動を生じる撹拌槽内の流体にトレーサ粒子を混入させ、非接触かつ所定の時間間隔で位置計測を行う位置計測装置によりトレーサ粒子の３次元位置を追跡し、トレーサ粒子の位置の時間変化により撹拌槽内の流場を計測する方法であって、撹拌翼の回転軸の延長方向を一つの座標軸に持つ２次元平面を設定し、トレーサ粒子の３次元位置の追跡で得た原データを回転軸の回りに回転させることにより原データを前記２次元平面の位置に配置した後、２次元平面の位置に配置した原データを用いて流場を計測することを特徴とする。   According to the first aspect of the present invention, tracer particles are mixed in the fluid in the agitation tank that generates a flow around the rotation axis of the agitation blade as the agitation blade rotates, and position measurement is performed at a predetermined time interval without contact. This is a method of tracking the three-dimensional position of tracer particles with a position measuring device and measuring the flow field in the agitation tank according to the time change of the position of the tracer particles, with the extension direction of the rotation axis of the agitation blade as one coordinate axis After setting the two-dimensional plane and rotating the original data obtained by tracking the three-dimensional position of the tracer particles around the rotation axis, the original data is arranged at the position of the two-dimensional plane, and then placed at the position of the two-dimensional plane. The flow field is measured using the arranged original data.

この方法では、流体に撹拌翼の回転軸を中心とする流動が生じていることを利用し、トレーサ粒子と回転軸の延長方向とを含む平面に対するトレーサ粒子の速度ベクトルの向きが、撹拌翼の回転方向における位置には依存しないとみなしている。言い換えると、トレーサ粒子の３次元位置の追跡で得られる速度ベクトルのような原データは、回転軸の回りに回転させても情報が失われることなく保存されることに着目している。したがって、回転軸を一つの座標軸に持つ２次元平面を設定し、原データを回転軸の軸回りに回転させることにより設定した２次元平面に原データを配置することにより、原データが持つ情報を保存しながらも、２次元平面に多数の原データを集約して配置することができる。つまり、位置計測装置の空間分解能に対して流体に混入させるトレーサ粒子の個数を比較的少なくすることができるから、位置計測装置において計測したトレーサ粒子の位置の追跡が容易になる。しかも、１枚の２次元平面に原データを集めて配置するから、流場を計測する際には２次元平面に集められた多数個の原データを用いることができ、位置計測装置の空間分解能に見合う程度に多数個のトレーサ粒子を用いて速度分布を精度よく抽出することができる。また、速度ベクトルのようなベクトル量だけではなく、原データから求められるスカラー量についても精度よく抽出することができる。   In this method, the fluid flows around the rotation axis of the stirring blade, and the direction of the velocity vector of the tracer particle with respect to the plane including the tracer particle and the extension direction of the rotation shaft is It is assumed that it does not depend on the position in the rotational direction. In other words, attention is paid to the fact that the original data such as the velocity vector obtained by tracking the three-dimensional position of the tracer particle is preserved without being lost even if it is rotated around the rotation axis. Therefore, by setting a two-dimensional plane having a rotation axis as one coordinate axis and arranging the original data on the two-dimensional plane set by rotating the original data around the axis of the rotation axis, the information possessed by the original data can be obtained. While saving, a large number of original data can be aggregated and arranged on a two-dimensional plane. That is, since the number of tracer particles mixed into the fluid can be relatively reduced with respect to the spatial resolution of the position measurement device, the position of the tracer particles measured by the position measurement device can be easily tracked. Moreover, since the original data is collected and arranged on a single two-dimensional plane, when measuring the flow field, a large number of original data collected on the two-dimensional plane can be used, and the spatial resolution of the position measurement device Therefore, the velocity distribution can be extracted with high accuracy by using a large number of tracer particles as much as possible. Further, not only the vector quantity such as the velocity vector but also the scalar quantity obtained from the original data can be accurately extracted.

請求項２の発明では、請求項１の発明において、前記撹拌槽の内側面は前記撹拌翼の回転軸を中心とする回転体形状に形成されていることを特徴とする。   According to a second aspect of the invention, in the first aspect of the invention, the inner surface of the agitation tank is formed in a rotating body shape centered on the rotation axis of the agitation blade.

この方法は、速度ベクトルの向きが撹拌翼の回転方向における位置には依存しない流場を撹拌槽の内側面の形状により実現するものであり、撹拌槽の内側面の形状は回転軸に直交する断面が円形であることが多いから、本発明の技術を多くの撹拌槽に適用することができる。   This method realizes a flow field whose direction of the velocity vector does not depend on the position of the stirring blade in the rotation direction by the shape of the inner surface of the stirring tank, and the shape of the inner surface of the stirring tank is orthogonal to the rotation axis. Since the cross section is often circular, the technique of the present invention can be applied to many stirring tanks.

請求項３の発明は、請求項１または請求項２の発明において、前記トレーサ粒子に関する原データを前記２次元平面の位置に配置するにあたり、１個のトレーサ粒子に関する隣接した２位置の差である速度ベクトルの始点と終点とのいずれか一方を２次元平面に位置させることを特徴とする。   According to a third aspect of the present invention, in the first or second aspect of the invention, when the original data relating to the tracer particle is arranged at a position on the two-dimensional plane, the difference between two adjacent positions relating to one tracer particle is obtained. One of the start point and the end point of the velocity vector is positioned on a two-dimensional plane.

この方法によれば、速度ベクトルの始点と終点とのいずれか一方を２次元平面に位置させているから、すべての速度ベクトルが２次元平面を起点として並び、速度分布を２次元平面上で一目瞭然で検出することができる。   According to this method, since either the start point or the end point of the velocity vector is located on the two-dimensional plane, all the velocity vectors are arranged starting from the two-dimensional plane, and the velocity distribution can be clearly seen on the two-dimensional plane. Can be detected.

本発明の構成によれば、位置計測装置の空間分解能に対して流体に混入させるトレーサ粒子の個数を比較的少なくすることができるから、位置計測装置において計測したトレーサ粒子の位置の追跡が容易になるという利点があり、しかも、１枚の２次元平面に原データを集めて配置するから、流場を計測する際には２次元平面に集められた多数個の原データを用いることができ、位置計測装置の空間分解能に見合う程度に多数個のトレーサ粒子を用いて速度分布を精度よく抽出することができるという利点を有する。   According to the configuration of the present invention, since the number of tracer particles mixed into the fluid can be relatively reduced with respect to the spatial resolution of the position measurement device, the position of the tracer particles measured by the position measurement device can be easily tracked. Moreover, since the original data is collected and arranged on a single two-dimensional plane, a large number of original data collected on the two-dimensional plane can be used when measuring a flow field. This has the advantage that the velocity distribution can be extracted with high accuracy using a large number of tracer particles to the extent that matches the spatial resolution of the position measuring device.

以下に説明する実施形態では、図１に示すように、有底円筒状であって軸方向を上下方向に一致させて設置される撹拌槽１の中に、複数枚（図示例では６枚）の羽根２ａを有した撹拌翼２が配置される。撹拌翼２には撹拌槽１の軸方向に沿った中心線上に回転軸３が設けられる。回転軸３は上端部に結合されたモータ４により回転駆動力が与えられる。   In the embodiment described below, as shown in FIG. 1, a plurality of pieces (six pieces in the illustrated example) are provided in the stirring tank 1 which has a bottomed cylindrical shape and whose axial direction is aligned with the vertical direction. A stirring blade 2 having a plurality of blades 2a is disposed. The stirring blade 2 is provided with a rotating shaft 3 on a center line along the axial direction of the stirring tank 1. The rotary shaft 3 is given a rotational driving force by a motor 4 coupled to the upper end portion.

撹拌槽１の内側面は軸方向に直交する断面が円形であるから、撹拌槽１の内側面は撹拌翼２の回転軸３を中心とする回転体形状に形成されていることになる。回転体形状としては、軸方向における直径が変化しない円筒状のほか、軸方向の位置に応じて直径が変化する形状を採用することも可能である。また、撹拌翼２は回転軸３を対称軸として対称性を有するように形成されている。具体的には、回転軸３の下端部から回転軸３の回転方向における等角度間隔で羽根２ａが放射状に突設される。したがって、撹拌槽１に流体７を注入し、モータ４により回転軸３を回転させると、撹拌槽１の中の流体７に撹拌翼２の回転軸３を中心とする流動が生じる。   Since the inner surface of the stirring vessel 1 has a circular cross section perpendicular to the axial direction, the inner surface of the stirring vessel 1 is formed in a rotating body shape centering on the rotating shaft 3 of the stirring blade 2. As the shape of the rotating body, it is possible to adopt a cylindrical shape whose diameter in the axial direction does not change, and a shape whose diameter changes according to the position in the axial direction. The stirring blade 2 is formed so as to have symmetry with the rotation axis 3 as the axis of symmetry. Specifically, the blades 2 a are projected radially from the lower end portion of the rotating shaft 3 at equal angular intervals in the rotating direction of the rotating shaft 3. Therefore, when the fluid 7 is injected into the stirring tank 1 and the rotating shaft 3 is rotated by the motor 4, the fluid 7 in the stirring tank 1 flows around the rotating shaft 3 of the stirring blade 2.

本実施形態では３次元ＰＴＶの技術を用いて撹拌槽１の中の流体７に生じるの流場を計測するるために、撹拌槽１の中の流体７には微粒子（粒子径が０．５〜１５０μｍ）であるトレーサ粒子が混入される。また、トレーサ粒子の３次元位置を計測するために位置計測装置５が設けられる。位置計測装置５は、２台のＴＶカメラ５ａ，５ｂを用いてトレーサ粒子を所定の時間間隔で撮像し、両ＴＶカメラ５ａ，５ｂの視差を利用して多数のトレーサ粒子の３次元位置を被接触で計測する。すなわち、位置計測装置５ではトレーサ粒子について撹拌槽１の中での３次元位置の情報を持つ３次元画像を生成する。   In the present embodiment, in order to measure the flow field generated in the fluid 7 in the stirring tank 1 using the three-dimensional PTV technique, the fluid 7 in the stirring tank 1 has fine particles (particle diameter of 0.5). Tracer particles (˜150 μm) are mixed. A position measuring device 5 is provided for measuring the three-dimensional position of the tracer particles. The position measuring device 5 uses two TV cameras 5a and 5b to image the tracer particles at a predetermined time interval, and uses the parallax of both TV cameras 5a and 5b to detect the three-dimensional positions of many tracer particles. Measure by contact. That is, the position measuring device 5 generates a three-dimensional image having information on the three-dimensional position in the stirring tank 1 for the tracer particles.

ここにおいて、ＴＶカメラ５ａ，５ｂを用いて撹拌槽１の外部からトレーサ粒子を撮像するから、撹拌槽１は透明材料により形成される。また、３次元位置は回転軸３に並行な方向をｚ軸とする直交座標系において求める。この場合、各ＴＶカメラ５ａ，５ｂを、光軸がｚ軸に直交し、かつ両ＴＶカメラ５ａ，５ｂの光軸が互いに直交するように配置すれば、各ＴＶカメラ５ａ，５ｂで撮像された画像の水平方向がそれぞれｘ方向，ｙ方向に対応することになる。   Here, since the tracer particles are imaged from the outside of the stirring tank 1 using the TV cameras 5a and 5b, the stirring tank 1 is formed of a transparent material. Further, the three-dimensional position is obtained in an orthogonal coordinate system with the direction parallel to the rotation axis 3 as the z axis. In this case, if each TV camera 5a, 5b is arranged so that the optical axis is orthogonal to the z-axis and the optical axes of both TV cameras 5a, 5b are orthogonal to each other, the image is captured by each TV camera 5a, 5b. The horizontal direction of the image corresponds to the x direction and the y direction, respectively.

位置計測装置５には流場解析装置６が接続されており、流場解析装置６は、コンピュータを用いた一種の画像処理装置であって、位置計測装置５で生成された３次元画像を対象として以下の画像処理を行う。３次元画像は所定時間ごとに得られているから、各３次元画像の中でトレーサ粒子の対応付けを行い、各トレーサ粒子を追跡する必要がある。トレーサ粒子の追跡には、時間軸方向において隣接する２枚ずつの３次元画像の間でトレーサ粒子を対応付ける。トレーサ粒子を追跡する技術については種々提案されているので、適宜の技術を採用すればよい。   A flow field analysis device 6 is connected to the position measurement device 5, and the flow field analysis device 6 is a kind of image processing device using a computer, and targets a three-dimensional image generated by the position measurement device 5. The following image processing is performed. Since the three-dimensional image is obtained every predetermined time, it is necessary to associate the tracer particles in each three-dimensional image and track each tracer particle. For tracking tracer particles, tracer particles are associated between two adjacent three-dimensional images in the time axis direction. Various techniques for tracking tracer particles have been proposed, and appropriate techniques may be employed.

流場解析装置６では、トレーサ粒子の追跡後に各トレーサ粒子ごとに速度ベクトルを原データとして求める。いま、時刻ｔ１と時刻ｔ２（＞ｔ１）とにおける３次元画像において、１個のトレーサ粒子について３次元位置がそれぞれ［Ａ］（ｔ１）＝（ｘ１，ｙ１，ｚ１）、［Ａ］（ｔ２）＝（ｘ２，ｙ２，ｚ２）であったとし、速度ベクトル［Ｕ］（ｔ）の時刻として始点位置の時刻ｔ１を採用し、Δｔ＝ｔ２−ｔ１とおけば、速度ベクトル［Ｕ］（ｔ１）は、次式で表される。なお、以下では、ベクトルを［Ａ］という形式で表す。
［Ｕ］（ｔ１）＝｛［Ａ］（ｔ２）−［Ａ］（ｔ１）｝／Δｔ
＝（（ｘ２−ｘ１）／Δｔ，（ｙ２−ｙ１）／Δｔ，（ｚ２−ｚ１）／Δｔ）
ところで、本実施形態における流場は撹拌翼２の回転軸３を中心とする流動を生じるから、回転軸３を中心とする撹拌翼２の回転方向におけるどの位置であっても、回転軸３を含む２次元平面に対する速度ベクトルは等価に扱うことができる。つまり、回転軸３を中心として回転方向のどの位置においても幾何学的には同一であると言える。そこで、回転方向の位置成分を除去しやすいように、トレーサ粒子の３次元位置を直交座標系から円筒座標系に変換する。この変換を容易にするために、直交座標系における原点の位置は回転軸３の上に設定しているものとする。 The flow field analyzer 6 obtains a velocity vector as original data for each tracer particle after tracing the tracer particle. Now, in the three-dimensional image at time t 1 and time t 2 (> t 1 ), the three-dimensional position of each tracer particle is [A] (t 1 ) = (x 1 , y 1 , z 1 ). , [A] (t 2 ) = (x 2 , y 2 , z 2 ), the time t 1 of the start point position is adopted as the time of the velocity vector [U] (t), and Δt = t 2 − If t 1 is set, the velocity vector [U] (t 1 ) is expressed by the following equation. In the following, the vector is expressed in the format [A].
[U] (t 1 ) = {[A] (t 2 ) − [A] (t 1 )} / Δt
= ((X 2 −x 1 ) / Δt, (y 2 −y 1 ) / Δt, (z 2 −z 1 ) / Δt)
By the way, since the flow field in the present embodiment generates a flow around the rotating shaft 3 of the stirring blade 2, the rotating shaft 3 can be moved at any position in the rotation direction of the stirring blade 2 around the rotating shaft 3. The velocity vector for the two-dimensional plane that is included can be treated equivalently. That is, it can be said that it is geometrically the same at any position in the rotation direction around the rotation axis 3. Therefore, the three-dimensional position of the tracer particle is converted from the orthogonal coordinate system to the cylindrical coordinate system so that the position component in the rotation direction can be easily removed. In order to facilitate this conversion, it is assumed that the position of the origin in the orthogonal coordinate system is set on the rotation axis 3.

なお、とくに限定する趣旨ではないが、撹拌槽１と撹拌翼２との寸法関係は、以下のように設定した。すなわち、撹拌槽１の内径は２００ｍｍ、撹拌槽１内の流体７の高さは２００ｍｍ、撹拌翼２の外径は５０ｍｍ、撹拌翼２の回転軸３に沿う方向の幅は１０ｍｍ、撹拌槽１の内底面から撹拌翼２の下面までの高さは１００ｍｍとした。この条件では、回転軸３の回転方向のすべての位置において幾何学的に同一であるという条件を満たすことができた。   Although not specifically limited, the dimensional relationship between the stirring tank 1 and the stirring blade 2 was set as follows. That is, the inner diameter of the stirring tank 1 is 200 mm, the height of the fluid 7 in the stirring tank 1 is 200 mm, the outer diameter of the stirring blade 2 is 50 mm, the width of the stirring blade 2 in the direction along the rotating shaft 3 is 10 mm, and the stirring tank 1 The height from the inner bottom surface to the lower surface of the stirring blade 2 was 100 mm. Under this condition, it was possible to satisfy the condition that all the positions in the rotation direction of the rotating shaft 3 were geometrically the same.

時刻ｔにおけるトレーサ粒子の３次元位置を直交座標系で表したときに、［Ａ］（ｔ）＝（ｘ（ｔ），ｙ（ｔ），ｚ（ｔ））であり、円筒座標系で表したときに［Ａ］（ｔ）＝（ｒ（ｔ），θ（ｔ），ｚ（ｔ））であるとすれば、数１の関係が成立する。   [A] (t) = (x (t), y (t), z (t)) when the three-dimensional position of the tracer particle at time t is expressed in the orthogonal coordinate system, and expressed in the cylindrical coordinate system. If [A] (t) = (r (t), θ (t), z (t)) at this time, the relationship of Equation 1 is established.

Figure 0004577193
Figure 0004577193

上述したように、撹拌槽１の中の流場が回転方向のすべての位置において幾何学的に同一であって、速度ベクトルが回転軸３の回転方向の位置の影響を受けないとみなせる場合には、円筒座標系における角度成分θを無視することができる。つまり、回転軸３の回転方向の各位置の速度ベクトルについて、回転方向の各位置においてｚ軸を含むように設定した２次元平面に対する情報にのみ着目すればよいと言える。   As described above, when the flow field in the stirring tank 1 is geometrically the same at all positions in the rotation direction, and the velocity vector can be regarded as not affected by the position of the rotation shaft 3 in the rotation direction. Can ignore the angle component θ in the cylindrical coordinate system. That is, it can be said that the speed vector at each position in the rotation direction of the rotation shaft 3 need only focus on information on a two-dimensional plane set to include the z axis at each position in the rotation direction.

そこで、図２、図３に示すように、ｚ軸を一つの座標軸に持つ基準となる２次元平面ＰＬを設定し、回転軸３の回転方向の各位置においてｚ軸を一つの座標軸に持つように設定した２次元平面に対する各位置の速度ベクトルの関係を、２次元平面ＰＬとの関係に置き換える。つまり、基準となる２次元平面ＰＬの位置に、原データである速度ベクトルを配置するように速度ベクトル［Ｕ］（ｔ）の座標を変換する。座標変換にあたっては、速度ベクトルの始点を２次元平面ＰＬの上に位置させる。時刻ｔ１の速度ベクトル［Ｕ］（ｔ１）であれば、始点である３次元位置［Ａ］（ｔ１）を２次元平面ＰＬの上に位置するように、着目するトレーサ粒子について座標変換を行う。 Therefore, as shown in FIGS. 2 and 3, a reference two-dimensional plane PL having the z-axis as one coordinate axis is set, and the z-axis is set as one coordinate axis at each position in the rotation direction of the rotation axis 3. The relationship of the velocity vector at each position with respect to the two-dimensional plane set to is replaced with the relationship with the two-dimensional plane PL. That is, the coordinates of the velocity vector [U] (t) are converted so that the velocity vector that is the original data is arranged at the position of the reference two-dimensional plane PL. In coordinate conversion, the start point of the velocity vector is positioned on the two-dimensional plane PL. If the velocity vector [U] (t 1 ) at time t 1 , coordinate conversion is performed on the tracer particle of interest so that the three-dimensional position [A] (t 1 ) that is the starting point is positioned on the two-dimensional plane PL. I do.

ここでは、基準とする２次元平面ＰＬをｘｚ平面とし、回転軸３の回転方向の角度θをｘ軸の正の向きからｙ軸の正の向きに向かう回転方向で求めるものとする。この場合、時刻ｔ１において、着目するトレーサ粒子の円筒座標系での位置が（ｒ（ｔ１），θ（ｔ１），ｚ（ｔ１））であるとすれば、速度ベクトル［Ｕ］（ｔ１）を角度θ（ｔ１）だけ回転させることにより、２次元平面ＰＬに位置させることができる。数１によれば、θ（ｔ１）＝ｔａｎ−１（ｙ（ｔ１）／ｘ（ｔ１））であるから、時刻ｔについて一般化し、角度がθ（ｔ）である位置の速度ベクトル［Ｕ］（ｔ）＝（ｕｘ，ｕｙ，ｕｚ）について、２次元平面ＰＬ上の速度ベクトル［Ｕ］ｂへの座標変換を行うとすれば、数２のようになる。なお、速度ベクトル［Ｕ］（ｔ）のうちｚ成分ｕｚについては座標変換の影響を受けない。 Here, the reference two-dimensional plane PL is the xz plane, and the angle θ in the rotation direction of the rotation shaft 3 is obtained from the rotation direction from the positive direction of the x axis toward the positive direction of the y axis. In this case, if the position of the tracer particle of interest in the cylindrical coordinate system at time t 1 is (r (t 1 ), θ (t 1 ), z (t 1 )), the velocity vector [U] By rotating (t 1 ) by an angle θ (t 1 ), it can be positioned on the two-dimensional plane PL. According to Equation 1 , since θ (t 1 ) = tan −1 (y (t 1 ) / x (t 1 )), the velocity vector is generalized for time t and the angle is θ (t). If coordinate transformation is performed on [U] (t) = (u x , u y , u z ) to a velocity vector [U] b on the two-dimensional plane PL, Equation 2 is obtained. Note that the z component u z in the velocity vector [U] (t) is not affected by the coordinate transformation.

Figure 0004577193
Figure 0004577193

数２に示す座標変換を、すべてのトレーサ粒子について行えば、回転軸３の回転方向におけるトレーサ粒子の位置にかかわらず、着目するトレーサ粒子の速度ベクトル［Ｕ］（ｔ）を２次元平面ＰＬに対する速度ベクトル［Ｕ］ｂとして扱うことが可能になる。その結果、たとえば、１個のトレーサ粒子に着目するだけでも２次元平面ＰＬの上では多数個の速度ベクトル［Ｕ］ｂとして扱うことが可能になる。また、原データである速度ベクトルを２次元平面ＰＬに集約することにより多数個のデータとして扱うことが可能になるから、ＴＶカメラ５ａ，５ｂの分解能に対するトレーサ粒子の個数を減らしてトレーサ粒子の追跡を容易にしながらも、流場の計測に用いるデータの密度を高めることによって、流場を精度よく計測することができるようになる。速度ベクトルからは、回転軸３を含む断面内での流体７の速度分布を求めることができ、また、速度分布の微分演算や積分演算によって、せん断ひずみ速度、流線などを求めることができる。 If the coordinate transformation shown in Equation 2 is performed for all the tracer particles, the velocity vector [U] (t) of the tracer particle of interest with respect to the two-dimensional plane PL is obtained regardless of the position of the tracer particle in the rotation direction of the rotation axis 3. It can be handled as the velocity vector [U] b . As a result, for example, even if attention is paid to one tracer particle, it can be handled as a large number of velocity vectors [U] b on the two-dimensional plane PL. Also, since the velocity vector as the original data can be handled as a large number of data by consolidating it on the two-dimensional plane PL, the number of tracer particles with respect to the resolution of the TV cameras 5a and 5b can be reduced to trace the tracer particles. However, it is possible to measure the flow field with high accuracy by increasing the density of data used for the measurement of the flow field. From the velocity vector, the velocity distribution of the fluid 7 in the cross section including the rotating shaft 3 can be obtained, and the shear strain velocity, streamline, and the like can be obtained by differential calculation and integral calculation of the velocity distribution.

なお、上述した方法では、速度ベクトルを２次元平面ＰＬに配置するから、回転軸３の回転方向における速度ベクトルの情報は失われるが、回転軸３に直交する断面内あるいは回転軸３に沿った断面内での速度分布の情報は保たれている。速度分布、せん断ひずみ速度、流線などを撹拌槽１の内部空間の各位置に対応付けるには、２次元平面ＰＬの上での演算の後に、撹拌槽１の各空間へのデータの再配置を行う。   In the above-described method, since the velocity vector is arranged on the two-dimensional plane PL, information on the velocity vector in the rotation direction of the rotation shaft 3 is lost, but the cross section orthogonal to the rotation shaft 3 or along the rotation shaft 3 is lost. Information on the velocity distribution in the cross section is maintained. In order to associate the velocity distribution, shear strain rate, streamline, etc. with each position in the internal space of the stirring tank 1, the data is rearranged in each space of the stirring tank 1 after the calculation on the two-dimensional plane PL. Do.

また、上述の例では速度ベクトル［Ｕ］（ｔ）の始点位置を２次元平面ＰＬに一致させる例を示したが、基準となる２次元平面ＰＬに速度ベクトル［Ｕ］（ｔ）の終点を一致させてもよい。この場合、数２の角度θ（ｔ１）として、ｔａｎ−１（ｙ（ｔ２）／ｘ（ｔ２））を用いる。 In the above example, the start point position of the velocity vector [U] (t) is matched with the two-dimensional plane PL. However, the end point of the velocity vector [U] (t) is set on the reference two-dimensional plane PL. You may match. In this case, tan −1 (y (t 2 ) / x (t 2 )) is used as the angle θ (t 1 ) of Equation 2 .

上述した動作を図４に簡単にまとめる。まず、撹拌槽１内のトレーサ粒子について位置計測装置５を用いて３次元位置を計測する（Ｓ１）。得られた３次元画像において着目するトレーサ粒子を追跡し（Ｓ２）、さらに、回転軸３の回転方向におけるトレーサ粒子の位置と基準となる２次元平面ＰＬとの間の角度差θ（ｔ）を求める（Ｓ３）。また、着目するトレーサ粒子について速度ベクトル［Ｕ］（ｔ）を求める（Ｓ４）。速度ベクトル［Ｕ］（ｔ）を２次元平面ＰＬの上に配置するように座標変換を施す（Ｓ５）。２次元平面ＰＬに配置された速度ベクトル［Ｕ］ｂにより流場を計測し（Ｓ６）、速度分布やせん断ひずみ速度などを求める。２次元平面ＰＬ上での流場計測の結果を撹拌槽１内の空間に展開することにより、撹拌槽１の中の流場を出力する（Ｓ７）。この結果は、コンピュータのモニタ装置のような出力装置に出力される。 The operations described above are summarized in FIG. First, the three-dimensional position of the tracer particles in the stirring tank 1 is measured using the position measuring device 5 (S1). The tracer particle of interest is tracked in the obtained three-dimensional image (S2), and the angle difference θ (t) between the position of the tracer particle in the rotation direction of the rotation shaft 3 and the reference two-dimensional plane PL is calculated. Obtain (S3). Further, the velocity vector [U] (t) is obtained for the tracer particle of interest (S4). Coordinate transformation is performed so that the velocity vector [U] (t) is arranged on the two-dimensional plane PL (S5). The flow field is measured by the velocity vector [U] b arranged on the two-dimensional plane PL (S6), and the velocity distribution, shear strain velocity, and the like are obtained. The flow field in the stirring tank 1 is output by developing the result of the flow field measurement on the two-dimensional plane PL in the space in the stirring tank 1 (S7). This result is output to an output device such as a computer monitor.

本発明に用いる装置の概略構成図である。It is a schematic block diagram of the apparatus used for this invention. 同上における直交座標系と円柱座標系との関係を示す斜視図である。It is a perspective view which shows the relationship between the orthogonal coordinate system and cylindrical coordinate system in the same as the above. 同上における直交座標系と円柱座標系との関係を示す平面図である。It is a top view which shows the relationship between the orthogonal coordinate system and cylindrical coordinate system in the same as the above. 同上の動作説明図である。It is operation | movement explanatory drawing same as the above.

符号の説明Explanation of symbols

１ 撹拌槽
２ 撹拌翼
３ 回転軸
４ モータ
５ 位置計測装置
６ 流場解析装置
ＰＬ ２次元平面 DESCRIPTION OF SYMBOLS 1 Stirring tank 2 Stirring blade 3 Rotating shaft 4 Motor 5 Position measuring device 6 Flow field analyzer PL Two-dimensional plane

Claims (3)

撹拌翼の回転に伴って撹拌翼の回転軸を中心とする流動を生じる撹拌槽内の流体にトレーサ粒子を混入させ、非接触かつ所定の時間間隔で位置計測を行う位置計測装置によりトレーサ粒子の３次元位置を追跡し、トレーサ粒子の位置の時間変化により撹拌槽内の流場を計測する方法であって、撹拌翼の回転軸の延長方向を一つの座標軸に持つ２次元平面を設定し、トレーサ粒子の３次元位置の追跡で得た原データを回転軸の回りに回転させることにより原データを前記２次元平面の位置に配置した後、２次元平面の位置に配置した原データを用いて流場を計測することを特徴とする粒子追跡法を用いた流場計測方法。   The tracer particles are mixed with the fluid in the agitation tank that generates a flow around the rotation axis of the agitator blades as the agitator blades rotate, and the tracer particles are non-contacted and measured at predetermined time intervals. It is a method of tracking the three-dimensional position and measuring the flow field in the stirring vessel by the time change of the position of the tracer particle, and setting a two-dimensional plane having the extension direction of the rotating shaft of the stirring blade as one coordinate axis, By rotating the original data obtained by tracking the three-dimensional position of the tracer particles around the rotation axis, the original data is arranged at the position of the two-dimensional plane, and then the original data arranged at the position of the two-dimensional plane is used. A flow field measurement method using a particle tracking method characterized by measuring a flow field. 前記撹拌槽の内側面は前記撹拌翼の回転軸を中心とする回転体形状に形成されていることを特徴とする請求項１記載の粒子追跡法を用いた流場計測方法。   The flow field measurement method using the particle tracking method according to claim 1, wherein an inner surface of the stirring tank is formed in a rotating body shape centering on a rotation axis of the stirring blade. 前記トレーサ粒子に関する原データを前記２次元平面の位置に配置するにあたり、１個のトレーサ粒子に関する隣接した２位置の差である速度ベクトルの始点と終点とのいずれか一方を２次元平面に位置させることを特徴とする請求項１または請求項２記載の粒子追跡法を用いた流場計測方法。   In arranging the original data regarding the tracer particle at the position of the two-dimensional plane, one of the start point and the end point of the velocity vector, which is the difference between two adjacent positions regarding one tracer particle, is positioned on the two-dimensional plane. A flow field measurement method using the particle tracking method according to claim 1 or 2.
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