# Impact of cavity shape on thermal accelerometer parameters

TOULME Valentin¹, Ben-Salk Soukaina², Faucher Marc², Combette Philippe¹, Giani Alain¹

1 IES 34000 Montpellier, France

2 IEMN 59 652 Villeneuve d'Ascq

## Introduction

For many years, many kinds of accelerometers have been developed for measuring vibration, shock, inertial motion. The most widely used principles of operation are based on piezoelectric or piezoresistive effects or capacitive changes.

Nevertheless, the existence of the solid proof mass in the accelerometers brings some disadvantages, such as low shock survival rating and a complex fabrication process. Convective Thermal Accelerometer (ATC), developed for the last fifteen years, is a good alternative to solve the previous problems since it works on thermal convection with no moving parts and could survive and measure very high levels of shock up to tens to thousands of g.

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INSTITUT
D'ÉLECTRONIQUE
ET DES SYSTÈMES

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La perception numérique
RESISTE

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## Thermal accelerometer principle

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$\Delta T \text{ prop. } \Gamma$

$$ \text{Sensibility } [^{\circ}\text{C/g}] = \frac{\Delta T [^{\circ}\text{c}]}{\Gamma [\text{g}]} $$

$$ \Delta T = 2.Ra.T*(r, r_0, r_i) $$

Ra : Rayleigh number

The heating wire generates a thermal gradient in the cavity gas, which will be deformed under the effect of the acceleration. The difference of temperature between two detectors, divided by acceleration intensity corresponds to the sensor's response. The analysis of the sensitivity's evolution gives us the ATC measure range. [1]

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## Results of simulations

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We consider the linearity domain, and therefore the measurement range, corresponds to the range where the sensitivity is constant.

As we can see :

* With a cavity size less than 100 µm, we can measure a range of acceleration up to 100 000g.

* There is a slight difference between three models, but no very significant.

* The presence of detectors has almost no influence on the response (for steady-state simulations).

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For the curve of sensitivity as function of cavity diameter, the slope of the curve equal to 3, which correspond to the cubic terme in analytical sensitivity's equation [1] [3].

$$ S = \frac{\Delta T}{\Gamma} = 2 \frac{\rho^2 \cdot \beta \cdot C_p}{\mu \cdot \lambda} (T_i - T_0)^2 \cdot r_i^3 \cdot T * (r, r_0, r_i) $$

## CFD ATC modeling

CFD simulations are performed with Ansys Fluent. Results are calculated in steady-state mode with Coupled method.

Three models has been performed :

- Cylinder model (most simplified model)

- Hexagonal model without detectors (semi real model)

- Hexagonal model with detectors (real model)

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Hexagonal model
- without acceleration -

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Hexagonal model
- with acceleration -

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Cylinder model
- with acceleration -

### Previous Simulations [2]

* → Four sizes of cavity has been simulated, from 1500µm to 150µm

* → Range of acceleration between 1g to 100 000g

### New Simulations

* → Size of cavity has been lowered to 75µm

* → Range of acceleration up to 1 000 000g

## Conclusion / Futur Work

As showed in results section, we consider the measurement range where the sensitivity is constant in the log-log diagram. The measure range increase as the cavity size decreases. As we can see on the sensitivity / acceleration diagram, to obtain a measure range up to 100 000g, the cavity size must be less than 100 µm.

Furthermore, in steady-state operation, the shape or presence of detectors has little or no influence on the sensor response.

### Futur work

* → 3D Simulation of sensitivity (real model)

* → 2D and 3D transient simulations to determined sensor's bandwith

## References

[1] A. Garraud, « Amélioration des performances et nouveau concept de détecteurs de capteurs inertiels à détection thermique », Thesis Université Montpellier II 2011.

[2] A. Garraud, P. Combette, J. M. Gosalbes, B. Charlot, et A. Giani, « First high-g measurement by thermal accelerometers », in 2011 16th International Solid-State Sensors, Actuators and Microsystems Conference

[3] A. Garraud, P. Combette, F. Pichot, J. Courteaud, B. Charlot, et A. Giani, « Frequency response analysis of an accelerometer based on thermal convection », J. Micromechanics Microengineering, vol. 21, n°3, 2021

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Contact :
valentin.toulme@umontpellier.fr

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