JPS621221B2 - - Google Patents

Description

[Detailed description of the invention]

Conventionally, in field tests that deal with turbulent flows accompanied by severe vortices, various measurement methods prescribed for steady flows are applied as they are. Since measurement errors caused by these are unknown, highly accurate measurement results cannot be obtained. In order to eliminate this drawback, the present invention deals with the current meter method, which is said to be optimal for direct measurement of large flow rates, and uses a vane wheel type current meter that can be applied to a wide flow velocity range of steady flows of various fluids with different physical properties. We present a calibration formula for a current meter (hereinafter referred to as a current meter), and aim to generalize and improve its accuracy so that it can be used for flows with a large degree of turbulence. The purpose is to establish a flow measurement method. The water calibration formula for conventional current meters assumes that the indicated flow velocity V is a linear function of the impeller rotation speed n in a steady flow, and the values of the constants α and β in the formula are determined by towing water tank tests. . V=an+β (1) The values of a and β in equation (1) are the fluid density ρ, kinematic viscosity ν, and Reynolds number Re (Re=VtR/ν, tR= chord length at the outer diameter point of the blade) When each value of , changes significantly, each must change under these influences. Nevertheless, since the conversion formula for α and β is unknown, this becomes a factor in the occurrence of indication errors. Furthermore, if Equation (1) is applied as is to a turbulent flow with violent vortices, it will be affected not only by changes in the physical property values mentioned above but also by changes in the degree of turbulence of the flow, making it less applicable to field tests. It is unknown. Analysis of the calibration formula for the impeller-type current meter In order to eliminate the above-mentioned drawbacks, we first treat the steady flow of various fluids and define the flow state using the Reynolds number. μo of the current meter impeller (=UR/
V=circumference of the blade tip/flow velocity) is expressed as follows using the function f of the Re number. μo=f(Re) (2) Furthermore, define the dimensionless quantity with. X′=Re−(Re)s, Y′=Re−(Re)s/μo−(μo)s(3) In equation (3), (Re)s is the Re when the impeller rotates steadily for the first time. The number (μo)s is the value of μo at (Re)s. The values of (Re)s and (μo)s can be derived from basic equations representing the torque and thrust of the impeller.
For an ideal current meter, a hyperbolic function relationship can be applied. FIG. 1 is an example of the relationship between the Re~μo curve of a current meter and a hyperbola. In the figure, rectangular coordinates x and y indicate Re and μo, respectively, and the origin o and both asymptotes of the hyperbola are x=a' and y=b'. A in the same figure is the design specification value of the current meter x = (Re) d and y = (μo)
d and B are (Re)s, E is (Re)d, A' is the leg of the perpendicular line drawn from point A to straight line y=b', and the subscript d indicates the design point. Furthermore, let C be the intersection of the extension of line segment BA and y=b', and ∠ABE=∠ACA'=∠β. straight line
Let D be the point where AC=BD on AB, pass through point D and y
Draw a parallel line DN to the axis, and let the intersections with the x-axis and y=b' be B' and N, respectively. Furthermore, it is possible to set the maximum value of μo of the impeller as (μo)max, and to set y=b′≒(μo)max (4), and the value of (μo)max is determined from the design bit. At this time, the slip rate SR of the impeller can be defined as follows. SR=(μo)d/(μo)max (5) In Fig. 1

[Table] Note that the sign of a' in equation (4) is determined from the following conditions.

[Table] Let Q be the intersection of the bisector of ∠A′NB′ and the hyperbola,
When NQ is h, C=h ² /2. The hyperbola shown in Figure 1 is (Re−a′)(μo−b′)=−C (8) Thus, the X′−Y′ response of the current meter is It is shown as follows. X''/Y+X'/Y[(Re)s-a'] +X'[(μo)s-b'] +[(Re)s-a'][(μo)s-b'] =-C ( 9) Once the specifications of the current meter are determined, (μo)s
Since 0 can be assumed, equation (9) shows a linear response. Y' = 1/b' This makes it possible to display.

[Table] Since equation (10) above shows a linear response, equations (8) and (11) are good calibration equations for steady flow. Next, when the current meter is affected by turbulent flow of various fluids, the fluctuation of the fluid velocity field can be specified by the value of the flow turbulence degree TF (a value that includes the strength and size of the turbulence). . At this time, TF
=1 is for steady flow. A good current meter that maintains equation (8) or equation (11) as a calibration formula can be expected to show a linear response even to turbulent flow when the flow turbulence degree TF is a constant value. When the current meter is influenced by various values of the degree of turbulence TF, its μo-Re curve changes in accordance with the degree of influence. Therefore, the response relationship (1-μ _pT /μo) of the current meter to the value of TF of the flow is assumed as follows. 1μ _pT /μo=F ₁ (Re)・F ₂ (TF) (12) μ _pT shown here is μ affected by disturbance.
The values of o, F ₁ and F ₂ are functions of Re and TF, respectively. Furthermore, we define the dimensionless quantity with. X″=1−μ _pT /μo (13) Y″=Re(1−μ _pT /μo) (14) In the case of the steady flow described above, that is, TF=
The μo~Re curve of 1 shows a linear response,
Based on experience, the μ _pT ~Re curve under the influence of turbulence shows an almost linear response, similar to the steady flow case. This straight line can be expressed as follows. Y″=A _T X″+Cr (15) The signs shown in equation (15) are as follows. In the X″ to Y″ coordinates, A _T is the slope of the straight line, and Cr is the intercept of the straight line. Rewriting equation (15), (μo−μ _pT )(Re−A _T )=μoC _T (16) Substituting equation (16) into equation (12), the functional relationship on the right side is expressed as follows. (1-μ _pT / μo) = 1/Re-A _T・C _T (17) Rewriting equation (17), μ _pT = μo (1-C _T /Re-A _T ) (18) (18) This is the calibration formula for current meters that are affected by turbulent flows of various fluids. Each value of A _T and C _T shown in equation (18) is
It can be easily determined by applying actual measurements using a current meter. That is, in the case of turbulent flow,
If the value of (Re) _S is (Re) _sT , then the value of A _T is approximately equal to the value of (Re) _sT . A _T (Re) _sT (19) Furthermore, C _T can be expressed as follows from equations (12) and (17). C _T =F ₃ (TF) (20) F ₃ shown here is a function of TF. Based on actual measurements, this function can be expressed as follows. C _T =ψ(TF-1) (21) The signs shown in equation (21) are defined as follows. φ is the slope of a straight line in log-logarithmic coordinates with (TF-1) on the horizontal axis and C _T on the vertical axis, and ψ is its intercept. Substituting equations (19) and (21) into equation (18), the practical calibration formula for a current meter that is affected by the turbulent flow of various fluids is shown by the following equation. μ _pT = μo [1-ψ(T.F.-1)=/Re-(R
e) _sT ] (22) Equation (22) is for steady flow, that is, TF = 1
Then, μ _pT =μo, and at this time, the response shown by equation (12) is zero. μ _pT = μo (23) The above is the boundary condition considered in this analysis, and it is satisfied. Characteristics of the turbulence measurement method using the impeller-type current meter of the present invention Regarding an embodiment to which the theory of the above-mentioned current meter calibration formula is applied, important characteristics regarding the measurement of flow velocity and flow rate will be briefly described. 1 In the case of steady flow The current meter is a small OTT current meter for water, No. 3, which is said to have good performance on the market. We will discuss the characteristics of current meters in these steady flows. FIG. 2 shows a characteristic curve diagram of a small ott current meter with Reynolds number Re on the horizontal axis and μo on the vertical axis. In the figure, examples of measured values for air, water, and oil are written in the order of symbols x, △, and ○, respectively. Figure 3 is an example of a schematic explanatory diagram of the small ott current meter used, and an example of the main specifications of the impeller is as follows: outer diameter of the impeller = 5
cm, 3 flat blades, pitch = 25cm, blade area = 1914
mm, blade angle 32°10′, area ratio = 0.985, chord ratio =
1.187, material = araldite. Based on the above specification values, the calculation result of the calibration formula (11) according to the present invention is as follows.

[Table] An example of calculation using equation (24) is shown using a solid line in Figure 2 for comparison with actual measured values. Further, in FIG. 2, an example of the calculation result of the water calibration formula based on the water calibration formula (1) which has been commonly used in the past is shown by a dotted line. We will now consider the results of applying both calibration formulas to the above measured values. When the calibration formula according to the present invention is applied to the steady flow of various fluids, as shown in Figure 2, the calculation results using equation (24) are good over a wide flow velocity range, except around the starting flow velocity. Precision is maintained and the indication error is less than ±0.2%. In comparison, the calculation results using OTT's water calibration formula show that when Re < 10 ⁴ , the indication error is between 1% and 30%, and when Re > 10 ⁴ , the error is less than ±0.5%, and the measurement result is The inaccuracy of is becoming clear. Moreover, as mentioned above, the applicability of the conventional calibration formula to various fluids is unclear. Therefore, it is recognized that the calibration formula according to the present invention exhibits good accuracy over a wide range of flow velocities of various fluid flows. 2 Case of Turbulent Flow The calibration formula according to the present invention is applied to water flows in which the values of the degree of turbulence TF of the flows differ greatly, taking into consideration its applicability to turbulent flows accompanied by violent natural vortices. In this case, the value of TF is determined by the sphere measurement method, and a turbulence grid (wire mesh) is used to significantly change the value. The current meter used is the above-mentioned small ott current meter No. 3, and the towing test results in still water are assumed to be a steady flow, which is defined as TF=1. FIG. 4 is an example of a Re~μo curve diagram based on actual measurement values of OTT current meters (four types No. 1, 2, 3, and 4) that are affected by turbulence having various values of TF. Each symbol shown in the figure indicates each flow when the TF value differs greatly, and each value of TF is ◎=
1.0, □=2.3, △=2.8, ×=3.1, and ● and ○ indicate the case of airflow. Using the above-mentioned specification values of ott No. 3, the turbulent flow calibration equation (18) or (22) according to the present invention is expressed as the following equation. μ _pT =μo{1-43.9(T.F.-1) ² . ⁷⁷ /Re-(Re)s [ ^4.96×10-2 (T.F.-1)
³ . ⁷¹ +1]} (25) When TF=1 μo=0.628-290/Re-388, (Re)s=850 An example of the result calculated using equation (25) is shown by the solid line in Figure 4. be. From the same figure, the calibration formula according to the present invention maintains good accuracy, and the value of the indication error is less than ±0.5% near the starting flow velocity of the current meter, and less than ±0.2% when the flow velocity increases, and the value of the indication error is ±0.2% or less when the flow velocity increases. It has become clear that it is adaptable to various areas. The above is true in the case of field tests that deal with turbulent flows accompanied by violent vortices, which have been thought to be unknown in the past.
This shows that the flow rate and flow rate can be measured with good accuracy. 3. Case of Field Test As mentioned above, the turbulent flow calibration formula according to the present invention has been found to maintain good accuracy through laboratory experiments. Therefore, we will examine the formal suitability of our school for field tests that deal with violent turbulence accompanied by natural vortices. In the field test, three types of measuring instruments were installed in the middle of the Chugoku Electric Power Company's Hiroshi Hydroelectric Power Station tailrace channel as shown in Figure 5, and measurements were taken simultaneously. The measuring device is the small ott mentioned above.
These are a No. 3 current meter, a five-hole probe ball that can measure the degree and direction of flow turbulence, and a certified standard Vitot tube. Figure 5 shows the Hiro Power Plant's trough-shaped spillway (top = 2670
mm, bottom = 1942mm, height = 2000mm, length = 40m)
Examples of a plan view, a front view, and a cross-sectional explanatory view of the measuring device are shown, and the explanatory symbols shown in the figures indicate the approximate dimensions of the instruments and water channels used. In addition, in the cross section of the waterway shown in the same figure, the dotted line indicates an average water depth of 1.4 m when the flow rate Q = 6 m ³ /S and 0.8 m when Q = 3.5 m ³ /S. The balls S are fixed to respective support rods OCS, PS, and SS, and these are installed so that they can be freely moved vertically and horizontally by each slider SL. Figure 6 shows an example of the results of measuring the turbulence and flow velocity on the center line of the measurement cross section in the spillway using the above measuring device, and the flow rate in this case is 6 m ³ /S, 45
m ³ /S and 3.5m ³ /S. In this figure, the horizontal axis shows the flow velocity, and the vertical axis shows the water level in the spillway.
It is determined by a current meter and a pitot tube, and based on experience, the flow rate indicated by the pitot tube is treated as the actual flow rate. Furthermore, when the turbulence calibration formula of the present invention is applied to the actual measurement value of the OTT current meter, the value of the degree of turbulence of the flow measured by the current meter becomes almost equal to the actual value measured by the probe ball, and the value of the indicated flow velocity is It is equal to the flow rate indicated by the pitot tube. In Figure 6, examples of each value of flow turbulence are
The distance between the indicated velocity curve of the Pitot tube and the abscissa of the velocity curve indicated by the OTT velocity meter (without the calibration formula applied) is shown to the left of each actual value measured by the OTT velocimeter (no calibration formula applied). This is the reading error of the ott current meter. From the above, when the turbulence calibration formula of the current meter according to the present invention is applied to field tests that handle turbulent flows accompanied by violent natural vortices, it is possible to obtain good accuracy in not only the flow velocity but also the degree of turbulence. This clearly shows that it can be measured with 4 In the case of a prototype small-sized current meter for water Using a commercially available current meter, and based on 1, 2, and 3 above, the calibration equations (11) and (18) of the present invention can be applied to the actual flow test. It maintains good accuracy and exhibits characteristics that improve the deficiencies of conventional current measurement methods. Furthermore, we will design and manufacture a new small water velocity meter, conduct practical tests, and conduct studies to confirm the above-mentioned adaptability. FIG. 7 is an example of a schematic explanatory diagram of a prototype small current meter for water and its flow rate indicating device. In Fig. 7, the rotational speed oscillator installed in the main body of the current meter is a newly devised non-contact type to reduce the resistance torque of the blade axle. That is, the light emitted from the light emitting diode can be sensed by the photodiode through a slit attached to one end of the blade axle in the main body (the other end is the blade wheel). Since the slit is manufactured to rotate with the rotation of the impeller, the structure is such that the number of light projections and breaks caused by the slit can be received by the light receiving section as pulses in the electric circuit. Since this circuit is connected to a digital counter from the lead wire through an amplifier, it is possible to measure the number of revolutions of the impeller relative to the flow velocity. FIG. 8 shows an example of the test results for the above prototype current meter. In Figure 8, the horizontal axis is the Reynolds number Re.
An example of the Re~μo curve of a prototype current meter, where the vertical axis shows the value of μo of the impeller. The specifications of the prototype 4-plate flat blade wheel are: outer diameter = 15 mm, boss diameter = 6 mm, blade angle = 30.
°, chord length = 10.4mm, area ratio = 1.0, pitch =
It is 11.78cm. For comparison, the calibration equation is calculated using the specification values of the prototype current meter and becomes as follows. Furthermore, the solid line shown in Figure 8 is the calculated value using equation (26). water tank and Hiroshima University towing tank) are found to agree with very good accuracy. From the above, it can be confirmed that the calibration formula of the present invention has good adaptability to the prototype current meter. Furthermore, similar results were obtained regarding adaptability to turbulence. As explained above, in order to be able to apply the calibration formula of this invention's impeller-type current meter to steady flow and turbulent flow of various fluids, we defined new dimensionless quantities, performed analysis on the calibration formula, and By eliminating the effects of changes in physical property values and the effects of turbulent flow, it is possible to improve the accuracy of measurements for field tests that deal with naturally violently turbulent vortex flows.
Therefore, as detailed in Turbulence Measurement Method 3, the method of applying the present invention to on-site tests is to easily detect turbulence by using the above-mentioned current meter and pitot tube (or two current meters with different turbulence characteristics) together. It is possible to determine the flow rate as well as the flow rate of the flow.

[Brief explanation of the drawing]

FIG. 1 shows an example of the relationship between the Re~μo curve and the hyperbola of a vane wheel type current meter. Figure 2 shows a small OTT current meter.
Example of Re-μo curve diagram. Figure 3 is a schematic example of a small OTT current meter. The symbols in the figure are: 1...Main body, 2...Support rod, 3...Axle, 4...
... impeller, 5 ... ball bearing, 6 ... bearing holder, 7 ... threaded plug, 8 ... spring, 9 ... pulse generator, 10 ... signal generator. Figure 4 shows a small OTT current meter affected by turbulence.
Example of Re-μo curve diagram. FIG. 5 is an example of a partially cutaway plan view, front view, and cross-sectional explanatory view of the Hiroden Power Plant's rectangular spillway and measuring device. The symbols shown in the figure are SG...Fixed frame, F.
... Rectifier, S. ... Probe, MM ... Multi-tube manometer, VP ... Vacuum pump, B. ... Scaffolding, V.
...Flow rate, OCo...ttmeter, DC...Digital counter, P....Pitot tube, PT...Pressure tank, SL....Slider, SS...Ball support rod, PS...Pitot tube support rod , OCSott support bar. Figure 6 is an example of an actual measurement taken on the center line of the measurement cross section of the Hiroden Power Station spillway. FIG. 7 is an example of a schematic explanatory diagram of a prototype small-sized current meter for water. In addition, the symbol 11 in the figure is an amplifier, and the symbol 12 is a digital counter. Figure 8 is an example of the Re-μo curve diagram of the prototype current meter.

Claims (1)

[Claims] Linear equation u _0T = u ₀ [1-ψ(T.F.-1)=/Re-(Re
) _ST ] [However, u ₀ = circumferential speed of blade tip/flow velocity, u _0T = value of u ₀ affected by turbulence, TF = degree of turbulence of flow, Re = Reynolds number of impeller, (Re) _ST = turbulence The starting Reynolds number of the impeller in a given flow, φ=experimental constant, ψ=experimental constant,] is characterized by eliminating the influence of turbulent flows with different degrees of turbulence on the indicated flow velocity of the impeller-type current meter. Turbulence measurement method using a vane wheel type current meter.