5
METROLOGICAL PROBLEMS IN MEASURING TURBULENCE PARAMETERS D. F. Tartakovskii UDC 389.1.001.12:532.507 The progress of modem science and technology has put before hydrodynamicists many new problems. Of spe- cial interest are problems connected with the design of pneumonic devices, noise generation in turbulent boundary !ayers, heat exchange, mass exchange, and boundary layer control. These problems cannot be solved without using the latest achievements in measuring techniques and mettology. A multitude of turbulent-flow measurements are now being performed throughout the world. The new problems not only made it necessary to improve the accuracy and sensitivity of instruments, but also considerably expanded the number of quantities to be measured. While mea- surements of velocity fluctuations were formerly the main source of information on the turbulence characteristics, liquid flow measurements presently include measurements of the constant components and turbulent fluctuations of pressure, temperature, shearing stresses, thermal flow, the heat exchange coefficient, optical and electric character- istics, and impurity concentrations. Besides mastering an ever-increasing number of the quantities to be measured in turbulent flows, there is continued need for expanding the measurement range, especially toward small values. Hydrodynamic parameters cannot be measured without utilizing the methods and means of the most diverse types of measurement: mechanical, thermal, temperature, electric, optical, etc. Therefore, the present quality of measurement of individual quantities in turbulent flows depends primarily on the sta:e of metrology regarding the individual types of measurement. However, this still does not ensure the unity of hydrodynamic measurements, since no allowances are made for the specific features of the turbulence phenomenon. A pecularity of hydrodynamic measurements is the intimate physical relationship, the intrinsic unity, between the individual quantities measured in turbulent flows, which is due to the turbulent nature of the develop- ment of fluctuations. This relationship manifests itself, for instance, in the equality of the spatial and the time scales of fluctuations of the quantities to be measured, which imposes certain requirements on the dimensions and the dynamic characteristics of measuring transducers if comparable results are to be obtained (expecially in correla- tion measurements). The turbulent origin of fluctuations determines the mutual relationship between the amplitude and the frequen- cy ranges of various quantities. Thus, on the basis of the well-known definition of turbulence as a "superposition of vortices of diminishing dimensions," it can be expected that, due to the effect of viscosity in any turbulent flow, there will be a statistical limit to the dimensions of the smallest vortex, which, in combination with the mean flow velocity, actually determines the maximum frequency of fluctuations sensed by the transducer. It follows from these considerations that, in each individual case, there is a relationship between the statistical lower limits of the peak value of turbulent fluctuations of the parameters to be measured. It is clear that the actual possibility of measuring minimal values of hydrodynamic parameter fluctuations is to a considerable extent determined by the quality of the measuring techniques, the efficiency of the measuring cir- cuits, the noise level in the electronic units of the equipment, and many other factors. Thus, for instance, the noise level in the best laboratory heat-loss anemometers limits measurements of turbulent velocity fluctuations to a value of the order of 0.05-0.1%, which is obviously higher than the lowest possible fluctuation intensity. Nevertheless, the determination of the extremal values of the physical quantities measured in turbulent flows is one of the most pressing problems of the present-day turbulence metrology, since, obviously, only the considera- tion and analysis of all the factors connected with the nature of the process will make it possible to formulate phys- Translated from Izmedtel'naya Tekhnika, No. 6, pp. 28-28, June, 1970. Original article submitted January 12, 1970. @1970 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without permission o[ the publisher. A copy of this article is available from the publisher [or $15.00. 841

Metrological problems in measuring turbulence parameters

Embed Size (px)

Citation preview

M E T R O L O G I C A L PROBLEMS IN MEASURING TURBULENCE PARAMETERS

D. F. T a r t a k o v s k i i UDC 389.1.001.12:532.507

The progress of modem science and technology has put before hydrodynamicists many new problems. Of spe- cial interest are problems connected with the design of pneumonic devices, noise generation in turbulent boundary !ayers, heat exchange, mass exchange, and boundary layer control. These problems cannot be solved without using the latest achievements in measuring techniques and mettology. A multitude of turbulent-flow measurements are now being performed throughout the world. The new problems not only made it necessary to improve the accuracy and sensitivity of instruments, but also considerably expanded the number of quantities to be measured. While mea- surements of velocity fluctuations were formerly the main source of information on the turbulence characteristics, liquid flow measurements presently include measurements of the constant components and turbulent fluctuations of pressure, temperature, shearing stresses, thermal flow, the heat exchange coefficient, optical and electric character- istics, and impurity concentrations. Besides mastering an ever-increasing number of the quantities to be measured in turbulent flows, there is continued need for expanding the measurement range, especially toward small values.

Hydrodynamic parameters cannot be measured without utilizing the methods and means of the most diverse types of measurement: mechanical, thermal, temperature, electric, optical, etc. Therefore, the present quality of measurement of individual quantities in turbulent flows depends primarily on the sta:e of metrology regarding the individual types of measurement. However, this still does not ensure the unity of hydrodynamic measurements, since no allowances are made for the specific features of the turbulence phenomenon.

A pecularity of hydrodynamic measurements is the intimate physical relationship, the intrinsic unity, between the individual quantities measured in turbulent flows, which is due to the turbulent nature of the develop- ment of fluctuations. This relationship manifests itself, for instance, in the equality of the spatial and the time scales of fluctuations of the quantities to be measured, which imposes certain requirements on the dimensions and the dynamic characteristics of measuring transducers if comparable results are to be obtained (expecially in correla- tion measurements).

The turbulent origin of fluctuations determines the mutual relationship between the amplitude and the frequen- cy ranges of various quantities. Thus, on the basis of the well-known definition of turbulence as a "superposition of vortices of diminishing dimensions," it can be expected that, due to the effect of viscosity in any turbulent flow, there will be a statistical limit to the dimensions of the smallest vortex, which, in combination with the mean flow velocity, actually determines the maximum frequency of fluctuations sensed by the transducer.

It follows from these considerations that, in each individual case, there is a relationship between the statistical lower limits of the peak value of turbulent fluctuations of the parameters to be measured.

It is clear that the actual possibility of measuring minimal values of hydrodynamic parameter fluctuations is to a considerable extent determined by the quality of the measuring techniques, the efficiency of the measuring cir- cuits, the noise level in the electronic units of the equipment, and many other factors. Thus, for instance, the noise level in the best laboratory heat-loss anemometers limits measurements of turbulent velocity fluctuations to a value of the order of 0.05-0.1%, which is obviously higher than the lowest possible fluctuation intensity.

Nevertheless, the determination of the extremal values of the physical quantities measured in turbulent flows is one of the most pressing problems of the present-day turbulence metrology, since, obviously, only the considera- tion and analysis of all the factors connected with the nature of the process will make it possible to formulate phys-

Translated from Izmedtel'naya Tekhnika, No. 6, pp. 28-28, June, 1970. Original article submitted January 12, 1970.

@1970 Consul tants Bureau, a div is ion o f Plenum Pub l i sh ing Corporation, 227 West 17th Street, New

York, N. Y. 10011. Al l rights reserved. This art icle cannot be reproduced for any purpose whatsoever

without permiss ion o[ the publisher. A copy o f this article is available from the publ isher [or $15.00.

841

ically substantiated and consistent specifications for measuring instruments, standard measuring devices, and calibra- tion and testing methods. Only a complex approach to the development of measuring instruments and metrology, with an allowance for all the peculiarities of the physical phenomenon and the present level of measurement tech- niques,would secure authentic unity of hydrodynamic measurements and yield results satisfying modem standards.

Work on hydrodynamic metrology is pursued in the following basic directions:

1. Development of theoretical principles of measurement in turbulent flow, investigation of errors, and devel- opment of methods for minimizing them.

2. Development of methods and equipment for the calibration and testing of measuring instruments.

3. Development of methods and equipment for the reproduction of fluctuations of hydrodynamic quantities for the purpose of investigating the operating and standard measuring instruments.

In the field of general theory of measurement in turbulent flows, it is first of all necessary to generalize and systematize the voluminous material on theoretical and experimental investigations of errors in measuring turbulent fluctuations. Of special interest here is the further investigation and improvement of the spatial and the time re- solving power of measuring transducers.

In contrast to measurements in laminar liquid flow, where the dimensions of the transducer's sensing element are of no great importance, the transducer dimensions in turbulence measurements must be matched with the spatial charaeteristics of fluctuations.

The few papers on the effect of the transducer's dimensions on the accuracy in measuring the root-mean-square values, the spectra, and the correlation functions of turbulent fluctuations are mainly theoretical in character and are insufficiently supported by experimental data. The various methods recommended in these papers for correcting the measurement results for the transducer dimensions also need experimental verification.

The above also applies to investigations of the dynamic characteristics of transducers. The complexity of the physical phenomenon and the need for complicated, costly equipment for investigating an apparently simple piece of equipment, such as a transducer for measuring turbulent fluctuations, lead to the fact that most investigators re- strict thernselves to theoretical investigations of the dynamic characteristics (with a minimum number of simple ex- periments, which only qualitatively confirm the theoretical conclusions).

Nevertheless, interesting results were obtained in a number of theoretical papers. Under certain conditions, these results could be used for considerably reducing the measurement errors. For instance, in a paper devoted to an investigation of the dynamic characteristics of thermal receivers [1], it was shown that, in measuring the tem- perature of turbulent flows by means of resistance thermometers in the presence of fluctuations of the convective heat-exchange coefficient that are statistically related to the flow temperature fluctuations, the variance of the thermal receiver readings can be not only lower than the variance of the ambient temperature (as is usually assumed for a constant heat exchange coefficient), but also higher than the variance of the ambient temperature, character- istics of the thermal receiver,and the turbulence intensity. This error can be determined accurately only if the dy- namic characteristics of the thermal receiver are well known. This and many other examples show that further im- provement of the accuracy in measuring turbulent parameter fluctuations depends on the development of experi- mental methods for determining the dynamic characteristics as well as the spatial resolving power of transducers. It is also necessary to carry out further investigations of the accuracy of transducers of different shapes, oriented in different directions in the flow, in measuring turbulent fluctuations.

A large amount of work on the metrology of heat-loss anemometry in water flow is necessary. Due to their good spatial resolving power, broad frequency range, and high sensitivity, heat-loss anemometers occupy a special place among the instruments for turbulence measurements. Heat-loss anemometers are still the only instruments whereby three components of turbulent velocity fluctuations can be measured. Heat-loss anemometers have been used lately for measuring shearing stresses at the surface of circumfluous bodies. Techniques o f heat-loss anemo- merry in liquid flow are being vigorously developed. Essentially, all the basic experimental data concerning the statistical turbulence theory are now obtained by means of heat-loss anemometers. The use of heat-loss anemome- ters for measurements in water has its own specific features.

First of aI1, it is impossible to provide sufficient overheating of the filament because of the possibility of elec- trochemical effects, which would lead to considerable instrumental errors due to changes in the ambient tempera- ture. The presently used methods for the temperature compensation of heat-loss anemometer readings by means of an additional compensating transducer are imperfect, while the applicability and errors of these methods have not been sufficiently investigated.

842

For measurements in water, heat-loss anemometric film transducers with different configurations (wedge, cone, or sphere) have been widely used recently; however, they have not been sufficiently investigated, and they are ap- parently inferior to ordinary filamentary heat-loss anemometric transducers with respect to many parameters.

It is necessary to investigate the errors in heat-loss anemometry caused by the thermal inertia of the film trans- ducer, its shunting by water, the effect of the turbulence intensity and the ambient temperature, the inaccuracy of orientation with respect to the flow, and other factors. A method for estimating the error in measuring the transverse components of velocity fluctuations should be developed.

Special difficulties in turbulent flow measurements are caused by the fact that turbulence constitutes a random fluctuating flow and is three-dimensional in character. As predicted by theory [2], the results obtained in measuring the mean and fluctuation values in such flows can be affected by turbulence. Turbulence apparently has the greatest effect in measuring the mean and fluctuation flow velocities and pressure fluctuations. In this, the measurement re- sults (as well as the calibration) are affected not only by the turbulence intensity, but also by the flow structure (cor- relations of different orders, the relationship between the intensities of different fluctuation velocity components, etc.) as well as the transducer geometry.

The effect of turbulence on the results of mean velocity measurements is illustrated by the experience in mea- suring the velocity profile in the wake behind a cylinder and in the mixing zone in a wind tunnel [3]. The veloci- ties were measured by means of heat-loss anemometric fihn transducers, which were arranged in a row, and a minia- ture Pitot-Prandtl tube. The film heat-loss anemometer was first calibrated by comparing its readings with those of the Htot-Prandtl tube in a flow with low turbulence (of the order of 0.5%). Experiments have shown that, in the high-turbulence zone, where the turbulence amounted to about 10%, the difference between the readings of the Pitot-Prandtl tube and the heat-loss anemometer was about 18%, while the readings of both instruments coincided in the low-turbulence zone.

Systematic investigations of the effect of the structure and characteristics of turbulent flow on the accuracy of individual types of transducers have not been performed until now. This is probably connected with the difficulties in constructing special hydrodynamic equipment whereby controllable variation and accurate measurement of turbu- lence characteristics in a wide range could be secured. However, a higher measurement accuracy in turbulent flow cannot be achieved without carrying out such investigations.

The metrological institutes of our country have important tasks to perform in developing methods and equip- merit for calibrating and testing instruments for measuring turbulent fluctuations. The difficulty of this work con- Sists in the fact that, in spite of the ever-increasing demands of the people's economy, the instrumentation industry does not produce a sufficiently large variety of special instruments for measurements in turbulent liquid flows. The enterprises and organizations engaged in work on hydrodynamics are thus compelled to construct and calibrate the necessary equipment on their own, often at a low technological level, which unavoidably leads to an unjustifiably large variety of instruments used for the same type of measurement. The lack of unique methods for calibrating and testing these instruments produces discrepancies in estimates of the metrological characteristics of the eqniprnent and makes it difficult to generalize and analyze the measurement results. For this reason, the errors of the equip- ment and in the measurement results are oRen not mentioned at all in the domestic and foreign literature devoted to equipment for hydrodynamic measurements. All this considerably complicates the choice of the optimum meth- ods for calibrating and testing the operating instruments, the substantiation of specifications for standard equipment, and its development.

When discussing the calibration of instruments for measuring turbulent fluctuations, it should be borne in mind that we are interested not in the instantaneous values of the quantities measured, but only in the statistically aver- aged values of these fluctuating quantities (the root-mean-square value of pulsations, moments of different orders, spectra, turbulence scales, etc.). One can define two basic approaches to the calibration of such instrmnents.

The first of them is based on statistical calibration methods and is used mainly for calibrating instruments with respect to the mean values of the parameters to be measured (for instance, the mean temperature, mean veloc- ity, etc.). In this case, a high accuracy of calibration with respect to mean values can be achieved by means of comparison with the corresponding standard instruments. The sensitivity of an instrument to fluctuating components is determined by differentiating the static calibration curve, while the frequency range is determined by investigat- ing the dynamic characteristics of the instrmnent. In using this approach, one can hardly expect a high accuracy in measuring the fluctuation components, since the accuracy in determining the dynamic characteristics is usually low, while the corrections are introduced by calculation. A better possibility for improving the accuracy of fluctuation

843

measurements is offered by a different approach to the calibration of instruments for measuring turbulence parame- ters, which is based on producing a standard dynamic signal ("standard turbulence") with known statistical charac- teristics: the variance, the correlation function, the spectrum, etc.

At the VNIIM (All-Union Scientific-Research Institute of Metrology), where a large amount of work is done on producing standard equipraent, the principles of designing standard equipment for the calibration and testing of in- struments for turbulent flow measurements have been developed, and recommendations on testing schemes in this field of measurement have been worked out. On the basis of these recommendations, standard devices were designed, constructed, and investigated, and raethods for calibrating transducers were developed.

We shall mention some work on the standardization of measurements in the field of velocity and temperature fluctuations.

A gravity-type hydrodynamic tunnel for heat-loss anemometer calibration with respect to mean velocity in the range starting at 0.05/see was developed and utilized. The device consists of a pressure-head tank with a useful vol- ume of 16 m s, a vertical channel, a straightening device, a test section, a drain tank, a back-flow channel, a pump, and a measuring tank. The pressure head in the tube is 0.18 M N / m 2, which secures velocities of up to 10 m / s e e in the test section. The velocity can be increased by raising the pressure head. The open-type test section is the basic part of the tunnel. The flow in the test section constitutes a free stream, which flows out of an adapter into a sub- merged volume. Grids and a honeycomb straightener are installed ahead of the test section. The transducer to be calibrated is fastened in a coordinate device. The grids and the interchangeable honeycomb straighteners can be placed at various distances from the convergent channel. They equalize the velocity profile over the cross section of the stream and make it possible to regulate the turbulence intensity at the location of the transducer to be cali- brated. This is absolutely necessary in calibrating instrm-nents for measuring turbulent velocity fluctuations, since it makes it possible to investigate the instrument calibration as a function of the turbulence intensity.

The design of the device provides for interchangeable test sections with convergent channel diameters from 20 to 100 ram, which makes it possible to calibrate not only heat-loss anemometers but also other instruments for flow velocity measurements.

The flow velocity in the device is determined with respect to volumetric discharge by means of the measuring tank. The measuring tank, which has a capacity of 0.13 m s, is provided with a water gauge and a scale, whose divi- sions correspond to volumes of 0.001 in s. The tank filling time is measured by means of an electric timer, which is actuated by signals from two photoelectric cells, covered by a float moving along the water gauge.

The development of computer equipment for automatic velocity readings on a digital panel is about to be completed. The water from the measuring tank flows through a draining valve to the draining tank by means of a pump or is wasted.

The error in calibrating heat-loss anemometr ic transducers by means of the gravity-type device does not ex- ceed 0.8% of the mean flow velocity in the 0 .5 -10-m/see range.

Measurements have shown that, by using interchangeable grids and honeycomb straighteners, the turbulence at the end section of the convergent channel can be regulated within 0.3-10%.

A closed-type hydrodynamic tunnel providing flow velocities of 1-20 m/see has been developed for calibrat- ing crperating instruments by means of comparison with the readings of a standard velocity meter (heat-loss anemo- meter or a head tube). The basic components of this tunnel are similar to the compenents of the gravity-type tun- nel. The head necessary for securing the required flow velocity is created by means of a centrifugal pump. The possibility of increasing the tunnel pressure is provided in order to ensure cavitation-free flow around the transducers to be calibrated. The possibility of heating and cooling the liquid is also provided. Test section variants with con- vergent channel diameters from 20 to 80 mm have been developed. The error in calibrating heat-loss anemometers by means of comparison in a dosed- type hydrodynamic tunnel does not exceed 2-2.5% of the mean flow velocity.

A special hydrodynamic device for investigating instruments for measuring turbulent flow velocity fluctuations in the infralow frequency range has also been constructed. It serves for producing amplitude-regulated harmonic flow velocity fluctuations in the frequency range from 0.1 to 20 cps. A similar device for producing low-frequency temperature fluctuations has been developed.

A method and the equipment for calibrating low-inertia instruments for measuring temperature fluctuations, which uses the solidification point of gallitu-n (29.72 i 0.02~ as the reference point, have been developed.

844

Measurements of turbulent temperature fluctuations in liquid flow are characterized by a small range of the mean temperatures to be measured (of the order of 4-50~ For these measurements, it is inadvisable to calibrate contact transducers by using the boiling point of water as the reference point. For many low-inertia instruments for measuring the turbulence of temperature fluctuations, even short-duration heating to the boiling point of water in- creases the instability of readings. This source of error was eliminated by using the solidification point of gallium.

Metrological work in the field of hydrodynamic measurements also involves many problems connected with the development and investigation of new, contactless measurement methods.

1.

2. 3.

LITERATURE C I T E D

A. M. Azizov, Investigation of the Dynamic Characteristics of Thermal Receivers for Measuring the Tempera- ture of Turbulent Flow, Dissertation [in Russian], VNIIM (1968). L O. Khintse, Mechanism and Theory of Turbulence [in Russian], Fizmatgiz, Moscow (1963). V. A. Kuz'min, A. I. Popov, and D. F. Tartakovskii, in: Automation of Scientific Investigations of Seas and Oceans [in Russian], Izd. MGI AN UkrSSR, Sevastopol' (1968).

848