📝 Abstract

This paper presents a numerical simulation and experimental results of a one-dimensional thermal inclinometer with the cavity filled of gas and liquid. The sensor principle consists of one heating resistor placed between two detectors. When the resistor is electrically powered, it creates a symmetrical temperature profile inside a micromachined silicon cavity. By applying a tilt to the sensor, the profile shifts in the same direction of the sensible axis corresponding to the horizontal one to one. The temperature profile and the sensitivity according to the CO2 gas and mineral oil SAE50 have been studied using numerical resolution of fluid dynamics equations with the computational fluid dynamics (CFD) software package Fluent V6.2. We have shown that the sensitivity of liquid sensors is higher than the gas sensors one. By using micromachined silicon technique, a thermal inclinometer with one pair of detectors placed at 300 um from the heater has been made. Experimental measurements corroborate with the numerical simulation.

💡 Analysis

This paper presents a numerical simulation and experimental results of a one-dimensional thermal inclinometer with the cavity filled of gas and liquid. The sensor principle consists of one heating resistor placed between two detectors. When the resistor is electrically powered, it creates a symmetrical temperature profile inside a micromachined silicon cavity. By applying a tilt to the sensor, the profile shifts in the same direction of the sensible axis corresponding to the horizontal one to one. The temperature profile and the sensitivity according to the CO2 gas and mineral oil SAE50 have been studied using numerical resolution of fluid dynamics equations with the computational fluid dynamics (CFD) software package Fluent V6.2. We have shown that the sensitivity of liquid sensors is higher than the gas sensors one. By using micromachined silicon technique, a thermal inclinometer with one pair of detectors placed at 300 um from the heater has been made. Experimental measurements corroborate with the numerical simulation.

📄 Content

9-11 April 2008 ©EDA Publishing/DTIP 2008

ISBN: 978-2-35500-006-5 Micromachined Inclinometer Based on Fluid Convection N. Crespy1, J. Courteaud1, P. Combette1, P. Temple Boyer2, A. Giani1, A. Foucaran1 1IES: Institut Electronique du Sud 5 place Eugène Bataillon 34095 Montpellier, France 2LAAS: Laboratoire d’Analyse et d’Architecture des Systèmes 7 avenue du colonel Roche 31077 Toulouse, France

Abstract-This paper presents the experimental and theoretical study of an inclinometer based on heat exchange. The principle of the sensor is composed of a resistance heater placed between two detectors and suspended in a cavity filled with fluid. In this study, several fluids such as liquid or gaseous, were used. The temperature gradient and sensitivity as a function of fluid were studied by using the numerical resolution of equations of fluid dynamics with the Computational Fluid Dynamics (CFD) software Fluent V6.2. We showed that the sensitivity of the “liquid sensors” is greater than “gas sensors” one. The experimental measurements corroborate with numerical simulation. In addition, we have demonstrated that the sensitivity of the sensor is proportional to the Rayleigh number which is characteristic of the natural convection flow.

I.
INTRODUCTION The inclinometer is a special type of the accelerometer. It is gravity which acts on the sensor, as shown in Fig. 1. It is widely used in the field of military industries, robotics systems, seismic monitoring and particularly in automotive applications, such as chassis regulation and over-roll detection. The inclinometer presented in this paper resists to high accelerations (about 50000 g) because it have no proof mass and a small size because of its micromachined elaboration.

This study presents the experimental results and numerical simulations of a one-dimensional thermal inclinometer. The principle of the sensor is based on the heat exchange of a suspended resistance heater placed between two detectors. When the resistance is electrically powered, it creates a symmetrical temperature gradient within a micromachined silicon cavity filled with gas or liquid. The angle of inclination is deducted from the measure of the acceleration due to the gravity projected on the sensitive axis (Fig. 1).

Fig. 1. The sensor principle. II.
THEORY In the present study, we consider that the heat exchange in the fluid occurred principally by natural convection and weakly by radiation. The natural convection is governed by the buoyancy forces and this phenomenon between a surface and a fluid may be considered as a conduction problem in an moving environment. The equations to be implemented are those of fluid mechanics and those of conduction. However, in a flow in contact with a wall temperature Tp, there is a thin layer of viscous fluid which is considered as laminar [1]. This area is called the thermal boundary layer. Within this zone, the maximum temperature variation is defined by:
) ( 99 .0 0 T Tp −

(1) With Tp temperature of the wall and T0 reference temperature.
We admit that there is no mixing of material in the direction perpendicular to the wall and the heat is preferably transmitted by conduction in the boundary layer.

Outside of this zone, the heat is transmitted by mixing of the fluid particles, causing rapid equalization of temperature. The heat flux φ across the boundary layer obeys the Fourier’s law: ) .( . 0 T T S p th − = δ λ φ

(2) With λ thermal conductivity, δth thickness of the thermal boundary layer, S surface.

However, the problems related to thermal convection are complex, it is often impossible to know the thickness of the boundary layer. In natural convection, we use a modified form and empirical understanding of the law Fourier: ) .( . 0 T T S h p −

φ

(3) With h convection coefficient

The determination of the coefficient of convection is not easy because it is not constant and it depends on many parameters. Generally, it is expressed globally for the whole surface, and so it is an average value for the system. As 9-11 April 2008 ©EDA Publishing/DTIP 2008

ISBN: 978-2-35500-006-5 précised previously, it varies locally and depends on the nature of the fluid and the surrounding temperature (it increases with temperature), the fluid’s velocity of circulation in the vicinity of the plate (it increases with speed), the orientation (vertical or horizontal) and dimensions of the surface. The experimental study of all of these properties is not achievable and therefore dimensional analysis is used to group the parameters that influence a convection phenomenon.

For the dimensional analysis, five dimensionless numbers are deduced which are the Reynolds number Re, the Nusselt number Nu, the Prandt number Pr, the Grashof number Gr and the Rayleigh number Ra.

The Reynolds number is defined by the ratio of inertial forces

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