pneumatic control, flow coefficient, solenoid valve. NOMENCLATURE m. [kg] mass of gas in the chamber p. [Pa] absolute pressure. A. [m2] orifice cross-section.
Conference on Modelling Fluid Flow (CMFF’03) The 12 International Conference on Fluid Flow Technologies Budapest, Hungary, September 3 - 6, 2003 th
EXPERIMENTAL INVESTIGATION ON PNEUMATIC COMPONENTS Zoltán MÓZER, student
Ákos TAJTI, student
Viktor SZENTE, assistant lecturer Department of Fluid Mechanics Budapest University of Technology and Economics Bertalan Lajos u. 4 – 6., H-1111 Budapest, Hungary Tel.: (+36 1) 463 4072, Fax: (+36 1) 463 3464 ABSTRACT Pneumatic Electric Braking Systems (EBS) are frequently used in commercial vehicles. These systems are controlled at about 100 Hz, thus the dynamic behaviour of them is essential to know. Since solenoid valves are playing important role in control, the knowledge on the dynamic behaviour of these valves is essential. This paper presents the development of a computer-controlled experimental facility, for investigation of the Cq flow coefficient. This documentation presents the comparison of the experimental methods to international literature and numerical flow simulations. Key Words: pneumatic control, flow coefficient, solenoid valve NOMENCLATURE m [kg] mass of gas in the chamber p [Pa] absolute pressure orifice cross-section A [m2] [-] orifice mass flow parameter Cm [ ° K / (m / s ) ] orifice flow coefficient Cq [kg/s] mass flow rate Qm R [J/kg/ºK] perfect gas constant T [ºK] temperature chamber volume V [m3] κ [-] specific heat ratio Subscripts and Superscripts cr values at critical pressure ratio d downstream values u upstream values
1. INTRODUCTION From the beginnings of the 90’s, companies started to develop and manufacture intelligent electro-pneumatic braking systems [1]. In these devices the procedure of sensing and execution is done by electro-pneumatic elements, like sensors and Electric Braking System (EBS) modulators. The electric control makes the braking process much faster, and provides safety-enhancing methods, like the ABS (Antilock Braking System) function [2, 3]. The EBS modulator is an essential part of a modern electro-pneumatic braking system, which ensures the controlled pressure in the brake chamber, in all conditions. This way it can provide continuous connection between the wheels and the road surface, increasing safety [4]. Electro-pneumatic magnetic valves execute the control itself, inside the modulator. The valves are controlled by electric signals from the control equipment. These valves create fast, impulse-like flow between the volumes at different pressure with less than 0.01s periodic times. Thus, the electrodynamic features of the magnetic valves (openclose time), geometrical and hydrodynamic (flow rate) properties, influence the operation of the whole pneumatic system. There are two main ways of investigation of dynamic behaviour of the magnetic valves: • •
Experimental investigations Numerical simulations
By experimental investigations the validity of the numerical model could be verified. The comparison between the measured and the simulated solution can be made easily, and if the difference between the results is small enough, the numerical model can be used for further research and development, reducing the cost of the expensive and time-consuming measurements. In case of experimental investigations, a lot of characteristic values have to be considered at the same time, e.g. the pressure ratio, the temperature before the valves and the flow rate through the valves, which makes the measurement more complicated. In order to make the research and development projects simpler with more accurate results, a computer controlled measuring device has been built recently in the laboratory of the Department of Fluid Mechanics. The bench is fully automated, which uses a computer-controlled data acquisition device. The advantages of this sophisticated bench are that the recording of the measured data is quick and accurate, and the PC support provides easy reload and analysis of the collected data. This paper introduces the bench with a nonstandard “from-chamber-to-chamber” measurement setup, and the principles of the pneumatic features of the magnetic valves. The suitability of the device for dynamic measurements will be interpreted through case studies. With the experimental measurements, the flow coefficient Cq – which characterizes the valve pneumatically – will be determined. As an earlier work a 3D model of the valve has been created using FLUENT CFD (Computational Fluid Dynamics) software. Another value of flow coefficient can be calculated with the help of CFD simulation, and the results of this method can be easily compared to the measurement data. An important goal of the project was to demonstrate that the results coming from different ways are quite similar, and this fact allows using the CFD model in further research and development projects. The big advantage of this is that the expensive and time– consuming measurements can be avoided.
(sonic velocity) as the upstream pressure (pu) is much bigger compared to the downstream pressure (pd). In that case the mass flow rate of the gas is proportional to the upstream pressure and independent from the downstream pressure.
2. THE THEORY OF THE ORIFICE FLOW In pneumatic energy transferring systems, the control and the energy transfer is carried out by pressurized gas. A number of elements are working in choked flow circumstances. The main feature of choked flows is that there are places where the velocity of the flow reaches the velocity of sound
the mass flow parameter Cm is a function of the pressure ratio pd/pu:
2.1. Ideal case During the measurement the flow is stationary. As ideal case, it is assumed that in the throttling port the flow is inviscid and heat isolated. In this case, according to the standard, the mass flow rate Qm of the gas flowing through the throttling port can be calculated with the following expression [5]:
Qm = A ⋅ Cm ⋅
pu
(1)
Tu
where A is the orifice cross-section, pu and Tu are the upstream pressure and temperature, respectively, and Cm is the mass flow parameter. Sonic velocity appears under the critical pressure ratio. This ratio can be calculated using Eq. (2) in the case of air (κ=1.4): κ
pd 2 κ −1 = = 0.528 + p κ 1 u cr
(2)
where pd is the downstream pressure and κ is the specific heat ratio of the gas.
pd pu
If the flow is sonic, i.e.
pd ≤ then pu cr
the mass flow parameter Cm is constant: 1
Cm =
2 ⋅κ 2 κ −1 ⋅ R ⋅ (κ + 1) κ + 1
(3)
where R is the perfect gas constant.
pd pd > then pu pu cr
If the flow is subsonic, i.e.
2
Cm =
p κ p 2 ⋅κ ⋅ d − d R ⋅ (κ + 1) pu pu
γ +1 κ
(4)
2.2. Considering the viscosity with the flow rate In the ideal case the Eqs. (1), (3), (4) can be used to calculate the mass flow rate, but the real value of the mass flow is different. The reason of this is the contraction of the gas jet, which occurs in the orifice due to viscosity. By the multiplication of the calculated ideal mass flow and the Cq
