Strojniški vestnik - Journal of Mechanical Engineering 61(2015)7-8, 477-485 © 2015 Journal of Mechanical Engineering. All rights reserved. D0l:10.5545/sv-jme.2015.2471 Original Scientific Paper Received for review: 2015-01-27 Received revised form: 2015-05-02 Accepted for publication: 2015-06-23 Determination of Undissolved Air Content in Oil by Means of a Compression Method Adam Burecek* - Lumir Hruzik - Martin Vasina VSB - Technical University of Ostrava, Department of Hydromechanics and Hydraulic Equipment, Czech Republic This article describes a combination of experimental and mathematical methods for the determination of undissolved air content in hydraulic oil. The experimental part consists of the determination of the oil bulk modulus, considering the influence of undissolved air by means of a volume compression method in a steel pipe. A multiphase model of an oil/undissolved air mixture is subsequently defined using Matlab SimHydraulics software. The multiphase model permits the volume compression of oil and air bubbles independently of each other. Furthermore, time dependencies of pressures are mathematically simulated during the compression of the multiphase mixture of oil and undissolved air for different concentrations of the latter. The undissolved air content is determined by comparing the mathematically simulated and experimentally measured time dependencies of pressure increases. Keywords: oil/air mixture, bulk modulus, undissolved air content, hydraulic system Highlights • Experimental determination of secant bulk modulus and tangent bulk modulus of oil by means of a compression method. • Multiphase mathematical model of compressibility of oil/undissolved air mixture. • Mathematical simulation and measurement of time dependence of pressure during compression of oil/undissolved air mixture in steel pipe. • Determination of undissolved air content in oil by comparing the mathematical model with the measurement. • The undissolved air concentrations in the measured hydraulic system were determined in the range of 0.22 % to 0.49 %. 0 INTRODUCTION Basic properties of liquids are described by their density, viscosity and compressibility, which can be expressed by bulk modulus [1] and [2], resistance to deformation, or capacity. Liquid with a content of undissolved air is considered to be a mixture. The bulk modulus of the liquid/undissolved air mixture is significantly influenced by the concentration of undissolved air in the mixture. The mixture bulk modulus generally increases with increasing liquid pressure and decreasing temperature [3]. It is possible to determine the mixture's bulk modulus by different experimental methods, e.g. by acoustic [4] and [5], capacity [6], piezoelectric impedance [7] or volume [8] methods. Hydraulic oil, which is the most frequently used energy carrier in hydraulic systems, is the investigated liquid in this paper. The air content in hydraulic oil is typically in two states, i.e. in dissolved and undissolved states. In the dissolved (i.e. diffused) state, air in hydraulic oil is in the form of oxygen and nitrogen molecules that are mixed with oil molecules. The contents of other gases in air are negligible in comparison to the oxygen and nitrogen volumes. In the case of the undissolved state, the oxygen and nitrogen molecules are clumped together. For this reason, air bubbles are created. A volume of released and dissolved air in oil is given by Henry's law [9]. Oil with air bubbles creates an oil/undissolved air mixture. The mixture is characterized mainly by a higher compressibility, which corresponds to the relevant bulk modulus (sometimes referred to as effective bulk modulus). Therefore, the effective bulk modulus of an oil/air mixture includes the influence of undissolved air [4], [10] and [11]. The compressibility of the oil/ undissolved air mixture has a negative influence on the static and dynamic properties of hydraulic systems [12]. For this reason, it is necessary to eliminate the air content in this mixture. For a more accurate definition of a mathematical multiphase model of the mixture, it is necessary to define not only the oil bulk modulus, but also the undissolved air content, which is very difficult to measure. There are different methods for the experimental determination of the undissolved air content. It is possible to measure the bubble size distribution in liquid, e.g. by image analysis [13], drift flux analysis [14], as well as by acoustical [15], optical [16] and electro-resistivity [17] methods. However, a given method of the bubble size measurement is generally applicable for a certain bubble size range [18]. The aim of the paper is to describe a specially developed method for the determination of the undissolved air content in hydraulic oil on the basis *Corr. Author's Address: VSB - Technical University of Ostrava, Department of Hydromechanics and Hydraulic Equipment, 17. listopadu 15/2172, Ostrava - Poruba 708 33, Czech Republic, adam.burecek@vsb.cz 477 Strojniški vestnik - Journal of Mechanical Engineering 61(2015)7-8, 477-485 of a comparison of experimental measurements and mathematical modelling. 1 THEORETICAL BACKGROUNDS 1.1 Dissolved Air in Oil Air in the dissolved state presents a chemical bond of oxygen and nitrogen molecules to oil molecules. Petroleum oils will generally dissolve 8.5 % ± 0.5 % by volume of air at atmospheric pressure and room temperature [19]. For pressures higher than atmospheric levels, absorption follows Henry's law, which is defined as [20]: H = Cm. C (1) where H is the dimensionless Henry's constant, Cair is the solute concentration in air, and CoU is the solute concentration in oil. The amount of dissolved air increases with increasing liquid pressure [21]. In the case of a disturbance from the equilibrium state as a consequence of pressure or temperature changes, air molecules are released and air bubbles are generated. For this reason, an oil/air mixture is created, or the air can be further dissolved in oil. This process is time-dependent. The time of the air release in oil is much shorter in comparison to the time of its dissolution. 1.2 Undissolved Air in Oil and Its Influence on Bulk Modulus of Oil/Air Mixture Dissolved air in oil is most frequently released to the undissolved state (i.e. to air bubbles) at pressure and temperature changes. Air bubbles can also enter the oil through different leaks. The oil/undissolved air mixture thus obtained has different properties in comparison to oil without air bubbles. It is possible to partly reduce the formation of bubbles at high operating pressures or by means of de-aeration devices, i.e. so-called gas separators. The bulk modulus, which is important in a mathematical model, is a significant property of the oil/undissolved air mixture. It is desirable to achieve high values of the bulk modulus in practice. The bulk modulus of the oil/undissolved air mixture is affected by many factors, e.g. by the pressure, temperature and volume of undissolved air. The amount of undissolved air has the greatest influence on the bulk modulus of the oil/ undissolved air mixture, mainly at low pressures. In this case, the air is much more compressible. The oil/undissolved air mixture can be defined as a multiphase mixture in mathematical models. The bulk modulus of the multiphase mixture is changed according to pressure and the amount of undissolved air. Then, the bulk modulus KPM of the multiphase oil/ air mixture is given by the equation [2], [22] and [23]: 1 + a kpm = ko ■ ( Y/n Pa Pa + P 1 + a- KO 1/n Pa (2) '(Pa + P ) (n+1)/n where KO is the bulk modulus of oil without air content, a = Vc/VO is the relative air content in oil at atmospheric pressure, Va is the air volume at atmospheric pressure, VO is the oil volume at atmospheric pressure, n is the isentropic coefficient (n = 1.4), p is the working pressure, and pa is the atmospheric pressure. The above-mentioned equation allows the inclusion of the compression of the oil volume and undissolved air independently of each other. The oil bulk modulus KO is defined by the following equation [1] and [2]: K = Vo ¿P AVn ' (3) where Ap is the pressure difference, and AVO is the difference of oil volume before and after compression. The bulk modulus of the oil/undissolved air mixture can also be taken into account in a mathematical model in a simplified manner. It is possible to assume a single-phase mixture, in which the compressibility of air bubbles is included in the bulk modulus KM of the oil/undissolved air mixture. In this case, the bulk modulus is defined by a constant for the given working pressure p. There is a certain inaccuracy in the mathematical model, especially at lower pressures. The thermodynamic effect, which is affected by the compression speed, occurs during the compression of the oil/undissolved air mixture. The isothermal effect proceeds at slow compression. In contrast, the isentropic effect is typical for rapid progressive compression. There are four different bulk modulus types of the oil/undissolved air mixture. From one standpoint, there are the secant bulk modulus and the tangent bulk modulus of the mixture [24] and [25] (see Fig. 1). Furthermore, each of these can be further divided into isothermal and isentropic moduli [26]. 478 Bureček, A. - Hružik, L. - Vašina, M. Strojniski vestnik - Journal of Mechanical Engineering 61(2015)7-8, 477-485 Fig. 1. Determination of secant (S) bulk modulus and tangent (T) bulk modulus of oil/undissolved air mixture The secant bulk modulus KM,S of the mixture is defined by the formula [10] and [25]: K = V m ,s r m Ap ÂVI (4) where VM is the volume of oil/undissolved air mixture, and AVM is the volume difference of an oil/undissolved air mixture before and after compression. The tangent bulk modulus KM ,T of the mixture is expressed by the equation [10] and [25]: K = V ■ m ,t m d p dV7 Fig. 2. Schematic diagram of experimental hydraulic circuit for determination of bulk modulus of oil/undissolved air mixture (5) Fig. 3. View of experimental hydraulic circuit for determination of bulk modulus of oil/undissolved air mixture 2 EXPERIMENTAL MEASUREMENT OF INVESTIGATED MIXTURE 2.1 Description of the Experimental Equipment The schematic diagram of the experimental equipment is shown in Fig. 2. The equipment consists of the hydraulic pump HP, the check valve CV, the relief valve RV, the steel pipe P, the seat valve SV, the reservoir R, the measuring equipment M 5050, the measuring point MP, and the pressure sensor PS. The M 5050 measuring equipment allows scanning, display and recording of measuring data from sensors that are used in hydraulics (e.g. from pressure, temperature and flow sensors). The hydraulic pump HP represents a flow source of the hydraulic system. If the seat valve SV at the pipe end (see Fig. 3) is open, hydraulic oil flows through the pipe P and the valve into the reservoir R. The seat valve is subsequently closed and, therefore, the flow through the valve is interrupted. Nevertheless, the pump HP supplies further liquid to the pipe P. Therefore, oil pressure is increased and a mixture of oil and air bubbles is compressed inside the steel pipe P. If the pressure of the mixture is increased to the value (i.e. p = 200 bar), which is adjusted by the relief valve, the relief valve RV is opened and subsequently the mixture of oil and air bubbles flows from the pump HP through the relief valve RV into the reservoir R. At the same time, the oil/undissolved air mixture in the pipe is compressed under the pressure that is adjusted by the relief valve RV. The pressure increase in the pipe was measured depending on the time. The pressure of the oil/undissolved air mixture inside the pipe P was recorded by the pressure sensor PS and the M 5050 measuring equipment. An example of the time dependence of the pressure p is shown in Fig. 4. The time interval At of the pressure scanning was set to 1 ms in this case. Measuring data were 479 Determination of Undissolved Air Content in Oil by Means of a Compression Method Strojniški vestnik - Journal of Mechanical Engineering 61(2015)7-8, 477-485 processed using Hydrowin software. The parameters of the steel pipe P are as follows: outside diameter DP = 0.03 m, inside diameter dP = 0.022 m, wall thickness sP = 0.004 m, length lP = 1.88 m, Young's modulus of elasticity EP = 2.1*10n Pa and Poisson ratio vP = 0.3. 250 200 150 100 50 0 S 03 £ O s3 /