Contents: 2024 | 2023 | 2022 | 2021 | 2020 | 2019 | 2018 | 2017 | 2016 | 2015 | 2014 | 2013 | 2012 | 2011 | 2010 | 2009 | 2008 | 2007 | 2006 | 2005 | 2004 | 2003 | 2002 | 2001

2007, 10

A. N. Gromov

Fluid level measurements using acoustical technique, which takes inhomogeneity of fluid into account

language: Russian

received 21.01.2007, published 04.05.2007

Download article (PDF, 400 kb, ZIP), use browser command "Save Target As..."
To read this document you need Adobe Acrobat © Reader software, which is simple to use and available at no cost. Use version 4.0 or higher. You can download software from Adobe site (


The ultrasonic level gages which use acoustic technique are widely used for measuring of fluid level in vessels. If the medium is inhomogeneous the measurement has a bias error. Moreover, it is impossible to evaluate the measurement error as the properties of the medium along the axis of the vessel are unknown.
The proposed method is based on the theory of solving the Sturm-Liouville inverse problem for two spectra and is free from this error. The main point of the method is as follows. The motion of acoustic disturbance is described by the equation of acoustics for flat-layered medium which contains unknown vertical coordinate dependences of sound velocity and fluid density. As a result of measurement some properties of solution are obtained. Next unknown coefficients of this equation and finally required level can be found. The advantage of the approach proposed is that a variety of factors related to the characteristics of the medium in which the wave is propagated are taken into account automatically. By complicating the description of wave propagation, introducing additional characteristics of the medium into the equation of motion, and describing the process in more and more adequate form, accuracy of measurements can be increased.
Numerical simulation of the level measurement process for the method based on the theory of solving the Sturm-Liouville inverse problem for two spectra is presented. The exponential profile of sound velocity is used for numerical simulation. The availability of analytical dependences makes it possible to calculate quite simply the initial data which are obtained in physical simulation as a measurement result.
The efficiency of the proposed method, the algorithms of its realization and the possibility to use it in intelligent microprocessor instruments are shown.

Keywords: ultrasonic measurements, acoustic measurements, fluid level measurement, inhomogeneous medium, Sturm-Liouville inverse problem, numerical simulation

16 pages, 2 figures

Сitation: A. N. Gromov. Fluid level measurements using acoustical technique, which takes inhomogeneity of fluid into account. Electronic Journal “Technical Acoustics”,, 2007, 10.


1. Громов А. Н. Метод измерения уровня, учитывающий физические свойства среды на пути распространения акустического сигнала. Cборник трудов XI сессии Российского Акустического Общества, 2001, т. 2, с. 262–265.
2. Бардышев В. И., Громов Ю. И., Громов А. Н., Овчаренко А.Т., Римский-Корсаков А. В. Резонансный акустический уровнемер. Акуст. журн., 2000, т. 46, №3, с. 320–324.
3. Римлянд В. И., Кондратьев А. И., Калинов Г. А. О точности измерения уровня жидкости в резервуарах акустическим эхо-методом. Акуст. журн., 2001, т. 47, №4, с. 564–566.
4. Клюев М. С., Клюев С. П., Краснобородько В. В. О погрешностях акустического измерения уровня жидкости и методах их снижения. Акуст. журн., 1999, т. 45, №6, с. 825–831.
5. Кабатчиков В. А. Ультразвуковой уровнемер. Патент РФ на изобретение №2064666, 1996.
6. Nyce D. S., Togneri M. G., Bulkowski R. S. Magnetostrictive position sensing probe with waveguide referenced to tip for determining fluid level in a container. US Patent №5848549, 1998.
7. Римлянд В. И., Калинов Г. А. Акустический тракт автоматизированной системы измерения уровня жидкости в резервуарах. Сборник трудов XI сессии российского акустического общества, 2001, т. 2, с. 265–274.
8. Викторов В. А. Резонансный метод измерения уровня, М.: Энергия, 1969.
9. Бобровников Г. Н., Катков А. Г. Методы измерения уровня, М.: Машиностроение, 1977.
10. Хамидуллин В. К. Ультразвуковые контрольно-измерительные устройства и системы. Л.: Изд-во Ленинградского ун-та, 1989, 249 с.
11. Stapleton et al. Ultrasonic liquid measuring device for use in storage tanks containing liquids having a non-uniform vapor density. US Patent №5085077, 1992.
12. Либерман В. В., Личков Г. Г. Радарные уровнемеры. Прошлое, настоящее, будущее. Промышленные АСУ и контроллеры, 2006, №8.
13. Левитан Б. М. Обратные задачи Штурма-Лиувилля. М.: Наука, 1984.
14. Романов В. Г. Обратные задачи математической физики. М.: Наука, 1984.
15. Бреховских Л. М., Годин О. А. Акустика слоистых сред. М.: Наука, 1989.
16. Прудников А. П., Брычков Ю. А., Маричев О. И. Интегралы и ряды. М.: Наука, 1981.
17. Аристов П. А., Громов А. Н., Курносов Н. М., Скрыпников С. Н., Хасиков В. В. Аппаратно-программное обеспечение нового поколения интеллектуальных полевых приборов технологии Fieldbus Foundation. Датчики и системы, 2001, №11, с. 10–14.


Anatoly Gromov graduated from the Faculty of Mechanics and Mathematics at the Moscow State University in 1971. At present he is an instructor of the Applied Mathematics Department at the Odintsovo Humanitarian University. Scientifics interests: theoretical acoustics, numerical methods.

e-mail: an_gromov(at)