Thermal Bi-Morph Valve Operated MicrothrusterBy: Sai Siva Kare UIN 661961324,

The University of Illinois at Chicago, Department of Mechanical Engineering

Abstract

Space exploration is one of the most interesting and challenging subject in science. Challenging because the equipment used in exploration is highly complex. Like conventional satellite they need propulsion system for obtaining desired attitude. This has paved way for designing micro propulsion systems called microthrusters. The device discussed here work on the principle of thermal bimorph actuation. The top beam element selected is silicon whereas the bottom beam is of aluminum. Applying voltage potential in aluminum beam results into heating of the beam, which results into expansion of aluminum. Due to difference between coefficient of expansion of aluminum and silicon, aluminum expands more compared to silicon thus resulting into bending. This bending opens inlet port of a converging-diverging nozzle, simultaneously heating the liquid propellant. For temperature of Aluminum reaching to 227°C (dT=200°C) maximum tip deflection of cantilever was observed to be 2.5µm. The inlet of nozzle has cross sectional area of 2500µm2 whereas throat area is 738.74 µm2 , the exit section area is designed to be 2216.22 µm2. Analytical calculation shows a thrust of 0.31µN is possible with this device and a power consumption of 6.32 mW is observed. The temperature obtained in the aluminum beam is approximately 300°C when a dc voltage of 0.35V is applied. Various references are taken in order to minimize assumptions and take the project closer to reality. Also some optimization and compensation has been done using MATLAB to further reduce assumed parameters. To my best knowledge this device is first of its kind which can be used to handle liquid material safely, avoiding any spillage and exposure to radiation in zero gravity environment. This specific design is chosen to demonstrate that its possible to fabricate nozzles normal to the substrate and control its characteristic. An array of such devices can be used to maneuver the satellite anyway required.

1. Introduction:

The era and amazing interest of miniaturized satellite started in 1990s mostly because of the low cost and the low weight of the system, which can be easily transported as secondary payloads [1]. These kind of satellites are classified as small, micro, nano, pico and femto satellites [2] [3]. The beginning missions of these satellites included functions that doesn’t required any attitude adjustment or propulsion. They had a working life of few months and at most a year [4]. After their mission is complete these satellites were destined to form space junk, which is a potential danger in itself. Adding a propulsion system to these satellites not only make them more capable systems but also reduces the risk of space junk by enabling the system to self-destruct via atmosphere re-entry on completion of mission. The propulsion of such satellites is a new challenge for engineers as it requires small thrusters (microthrusters) with a very small profile and wet weight.

MEMS community has addressed this design problem very well by fabricating miniaturized propulsion systems called microthrusters. These systems use various methods to produce thrust, some of the popular methods for example are vapourizing liquid microthruster (VLM) that uses liquid propellant [5] [6], solid propellants [7] [8] and electrospray technology [9] and very famous, electrospray propulsion [10].

The system we are going to discuss here is a VLM based system. Which uses microheater embedded in the bimorph beam, which also opens and closes the nozzle inlet. The device consists of an enclosed chamber to hold water (test liquid), a converging diverging nozzle and thermal bimorph valve actuator. Prime focus of this paper will be on the design of the actuator and the nozzle. A brief

description for design of microfluidic channels for propellant transport is also discussed. To my knowledge this device is first of its kind which operates valve while vaporizing the propellant or producing thrust. This device is not only limited to space application but also applicable to microfluidic transport.

The actuator that controls the valve consists of three layers consisting of heating element, a high coefficient of expansion element and a low coefficient of expansion element, which form a differential heating composite beam. The nozzle with converging section is anisotropically etched in silicon while the diverging section is realized by ion etching to control the half angle of diverging section. Possibility of using other suitable alloys and materials have also been discussed giving the readers a good scope of possibilities.

MEMS actuators can be broadly classified by magnetic, electrostatic and thermal actuators. Magnetic actuation is very reliable and efficient for macro scale but requires high input voltage and generally does not scales well with miniaturization at MEMS scale. Whereas electrostatic actuation is quite popular because of its ease of fabrication and low inputs (such as piezoelectric actuation in MEMS resonators) [11]. Thermal actuator are another attractive option because of their low power consumption and high displacement (even bi-directional [12]) and small response time in order of milliseconds [13]. Also there is no possibility of pull-in and parasitic capacitance when compared to electrostatic actuation. Which further strengthens the use of this principle in my design. The nozzle design is unique and to my best knowledge never utilized before. The design require use of both anisotropic etching and ion beam etching for making the converging and diverging section of the nozzle. To validate this both analytical and Fluent (ANSYS) simulations have been produced, with excerpts from text as well. Detailed fabrication steps have been illustrated in order to demonstrate the intricate steps that are necessary to realize the complete working principle of the device. Some of the parameters are assumed for the sake of simplicity and inaccessibility to tests. But various optimizing algorithms have been used balance

various parameters using MATLAB. Detailed results have been provided to the reader at the end. Finally an interesting test setup is also provided which can be used for observing the nozzle exhaust by using just some household items.

2. Design of the valve

The thermal bimorph must be able to bear high temperature loads and high stress along with fast response time for high frequency application or instant thrust (in this paper). The first new design of thermally driven microvalve for fluid control (pneumatic control) was developed in 1994 by Lisec et al., which used cross members that buckle under thermal loading to open a port which was anisotropically etched on the substrate [14]. After which a lot of research have been carried out. Which led to development of various types of materials for constructing the beam and fabrication steps to increase the life of thermal actuator which is subjected to high thermal loading. These materials include ceramics (zirconia) [15] and alloys [16]. TiAl alloys have also shown potential as bimorph actuators which show negligible deflection of 5µm for a beam length of 500µm. It has been found out that TiAl can reach up to 500° C without forming hillocks and stress gradients when compared to Aluminum, which is unstable at high temperatures [16]. I am using Polysilicon as the top layer and Aluminum for the bottom layer, the properties are obtained from a Technical Report on material properties of MEMS, and ANSYS Engineering Materials for simulation. Since both bonded beam have different thermal coefficient of expansion they expand with different strain. This differential strain results in a certain curvature in the composite beam. This curvature is very important for our device because it will define the distance of the heat source from the nozzle inlet. Detailed calculations and procedure are provided in the following steps.

Cross section of the device.

2.1 Design of Cantilever Bimorph

In 1992 Doring et al. reported a high frequency (1ms) thermal bimorph cantilever actuator which was capable of directing fluid duct at high switch rates [17]. Some of the devices that have similar principles of the one discussed here have also been designed such as high output valve to amplify the actuation, thus the output[18]. The material property set and the dimension considerations are given in the table 1. A schematic diagram from Solidworks® shows the realization of the cantilever beam in figure 1, with complete dimensions of the cantilever (mm).

Fig 1: Schematic of composite beam.

Table 1: Material Properties.

Consider the following line diagram in figure 2. Since the thermal coefficient of expansion of silicon is smaller than Aluminum, aluminum expands more compared to silicon which results in bending of the

composite beam. This bending may be assumed as a segment of circle with radius r. s represents the arc of composite beam. d is the total deflection of the beam. This can be found out by following equations given in the steps.

Fig 2: Line diagram showing the geometry of beam bending.

Assumptions:

1. Thickness of Silicon is double of Aluminum2. Pressure inside the chamber pc= 3 Bar3. Pressure at exit pe= 25 mBar4. Temperature of aluminum = 227°C

Optimizing and finding beam dimensions:

Optimization is required to find a valid deflection such that it’s neither small nor large, it should be within practical limits.

Material 2 is the Silicon and Material 1 is Aluminum.

The design is initiated by assuming that thickness of aluminum beam is half of

silicon beam, i.e.t 1=12

t2 , this is important

to form a relation between the thickness of material (beam) and the maximum tip deflection, t2 vs tip deflection.

This is done using MATLAB and plotting the relation between silicon beam thickness and tip deflection, as shown in the figure 3.

Analytical equation for beam bending is used [19] and MATLAB code is provided in the appendix.

1r=

6×w1 w2 E1 E2 t1 t2(t 1+t 2)(α 1−α 2)× ∆ T(w1 E1 t1

2)2+(w 2 E2 t 22)2+2× w1 w2 E1 E2t 1 t2 ×(2t 1

2+2t 22+3 t1 t2)

d=r−rcosθ

Silicon

Aluminum

Material property Silicon Aluminum (Al alloy in FEA)

Length (l) 100µm 100µmWidth (w) 50µm 50µmThickness (t) 30µm 15µmYoung’s Mod (E) 158Gpa 69GpaThermal expansion Coefficient (α)

2.9*10-6

ppm/°C25*10-6 ppm/°C

Temperature(°C)dT 200°C -

The graph below shows design point which is used to simulate the concept.

Fig 3: Plot between Silicon beam thickness and tip deflection.

2.2 Design of Nozzle

Few parameters of nozzle is referred from a research paper. Consider the following cross sectional line diagram of the nozzle in figure 4.

Fig 4: Line diagram showing the geometry of nozzle.

Optimizing and finding beam dimensions:

The nozzle that we are using is a converging-diverging nozzle (cd-nozzle). The converging nozzle has a fixed dimension in the sense that the half angles are fixed by anisotropic etching of the silicon, i.e. 54.7°.

The divergent section’s profile is fixed, which is conical. If we make it by anisotropic etching, flow separation will occur near the walls. For optimum performance of conical diffuser the half angle at exit should be designed between

12° and 18° [20]. We can save weight by increasing the half angle which decreases the nozzle length but at the cost of performance.

Now if the steam escaping the nozzle is saturated, it will not expand faster and also freezes at exit creating icing problems. To avoid this the steam must be superheated or expansion ratio (area at exit/ area at throat) should be decreased. Since the temperature is fixed for the aluminum=227°C (dT=200°C) we will design the expansion ratio accordingly.

Formulas to consider:Thrust, F=m ve+( pe− pa) Ae=CF pc A t

Mass Flow rate , m= FI sp

=pc At

c=

ve

g

Characteristic velocity , c=√RTψ

CF=ψ √ 2 γγ−1

¿¿

ψ=√γ ( 2γ +1 )

γ+1γ−1

Where ve is the nozzle exit velocity (m s−1), P total pressure (Pa), pe nozzle exit pressure (Pa), pa ambient pressure (Pa), pc chamber pressure (pa), Atnozzle throat area, I sp specific impulse (s), T temperature (K), Ae nozzle exit area, Ar

area ratio= A e

A t, V volume of the chamber, R gas

constant (J Kg−1 K) and γ specific heat ratio. Calculations

γ= 1.32ψ=0.671c=715.9

Optimizing Cf and Ar we ge t following graph:

Our Design Point

Fig 5: Plot between Area Ratio and Coefficient of Thrust.

We can observe that Cf increases with area ratio. But in our design we have to optimize out throat area considering:

1. Thickness of wafer. 2. Area of cantilever covering the nozzle inlet3. Anisotropic etching pattern of converging

section.4. Length of Converging nozzle = 40µm.5. Area ratio = 3 , which give Cf = 1.622

The thinnest wafer present is of 275 µm [21]. If we consider etching the chamber uses 185µm (may be not possible in practical) this leaves total nozzle length = 90µm. Figure 6 shows the complete diagram of the nozzle with dimensional consideration.

Fig 6: Line diagram showing the geometry of nozzle.

Now consider figure 7. In this we can find the dimension of throat. For this we need the distance

between the inlet and the throat section which is by design equal to = 40µm.

Fig 7: Line diagram showing the converging section and diverging section.

For converging section length = 40µm

Inlet area = 2500 µm2 (dictated by width of beam)

The throat area At = (27.18)2 µm2=738.74 µm2

Therefore Ae= 2216.22 µm2 = 47 µm

Which gives diverging half angle of 12° (approx., 11.25° actual) for a diverging section length of 50µm, which is exactly we need. Now consider figure 8. The divergent section has a length of 50µm. And we know the area ratio. This gives us complete dimensions of the divergent section. All these dimensions will be used in the simulation in ANSYS.

3. Results and Calculation

Firstly we will calculate the power required for the microheater to convert water at 27°C into steam at 227°C.

Assumptions:

1. Pressure inside the chamber=3bar2. Volume of chamber=5 time volume of

composite beam.

Volume of the entire beam is given by:

L ×w × ( t 1+t 2 )=200× 50× (30+15 ) µm3=4.5 ×105 µm3=.45 ×10−12m3

Taking density of water to be 1000kg/m3 and volume of chamber=volume of water, we get mass of water m inside the chamber:

m=5 × .45 × 10−12×1000=2.25 nkg

Enthalpy of water at 27°C, 1Bar=113.19 kJ/kg [22] [23]

Enthalpy of water at 27°C, 3Bar=113.47 kJ/kg

Our Design Point

Enthalpy of steam at 227°C, 3Bar=2921.15kJ/kg

So, the heat required = 2921.15-113.19=2807.96kJ/kg

For 2.25 nkg, heat required=6.32 mW (per second flow)

Now we have

At = (27.18)2 µm2=738.74 µm2

pc= 3 Bar

Cf = 1.622, Therefore

F=CF pc A t=1.622×3 × 105×738.74 × 1 0−12=0.36 mN , Also

m=pc A t

c=3× 105× 738.74 ×1 0−12

715.9=0.31µ kg

s

* Which is comparable to other lab tested devices [5].

4. Fabrication steps

Fabrication steps are obtained by studying previous works in the field of microthruster and other MEMS devices as well, which may not be the exact methods that can be applied. [5] [6] [24] [25]. Table 2 shows major fabrication steps of the bottom half which will house the nozzle and the bimorph. We will be considering the fabrication of cantilever bimorph operated valve only, as the C-C valve will have similar fabrication steps with one extra fixed support.

Wafer cleaning by Piranha cleaning process followed by thermal oxide growth at 1100°C. Oxide thickness of 1.0µm to protect the mask#1 during anisotropic etching of silicon.

Photolithography and anisotropic etching of silicon to open cavity for fabricating cantilever and nozzle.

Photoresist coating. Mask#2 positive photolithography, for

opening anchor point for the cantilever. Isotropic etching of silicon.

Mask#3 positive photolithography, for anisotropic etching of the silicon, for making the converging part of the nozzle.

TMAH at temperature around 70°C (etch rate @ 1.2min/µm).

Removal of oxide layer by immersing the wafer into Buffer HF, to selectively remove SiO2.

Photoresist deposit to cover the converging nozzle for subsequent Aluminum deposit.

Mask#4 positive photolithography, for opening the anchor.

Deposition of Aluminum electrode (or the lower member of the cantilever beam). Vacuum evaporation of Aluminum at substrate temperature of 140°C, followed by sintering at 450°C (high vacuum, high temperature PVD process).

Electrical insulation required (SiO2, CVD) to avoid conduction by silicon layer (negligible).

High rate deposition of microcrystalline silicon using conventional plasma-enhanced chemical vapor deposition. [24] Since we need thicker material at

the top. Photoresist deposit. Mask#5 Negative photolithography for

forming the entire cantilever structure.

Backside etching of diverging section of the nozzle using RIE.

12° to 18° half angle taper [24]. This is very crucial for avoiding flow

separation in divergent section due to larger angle (54.7°). [25]

Photoresist removal.

Packaging of the device. Anodic bonding.

Microfluidic channeling for liquid propellant supply.

*Image not to scale.

Table 2: Fabrication steps.

5. ANSYS Simulation (Static Structural and Thermal Electric)

Figure 8 shows total deformation on application of thermal load of 227°C in Aluminum metal. Beam bending is a complex phenomenon, and hogging or sagging can’t be determined by just looking at it. Chenpeng Hsu and Wensyang Hsu state in their FEM research that initial deflection may change the behavior of the beam [26]. So care should be taken to deposit beam in such a way that it doesn’t sag from the beginning, to prevent it from bending downward and eventually rubbing in the substrate without opening the valve.

We can see that analytical deflection of the tip (here red in color) was 2.2µm, and FEM simulation gives us value 2.5µm which holds good considering the static structural model doesn’t allow flow of heat from Al to Si.

Fig 8: Total deformation in static structural simulation.

This figure 9 shows Thermal-Electrical stimulation. When 0.35V potential is applied across Aluminum a temperature rise of 300°C approximately is observed. The purpose of this simulation is to show the spread of thermal gradient across the entire composite beam. Mesh control was left to auto in this case.

Fig 9: Temperature distribution in the composite beam at 0.35V.

Close to Analytical value

In figure 10 the Fluent (ANSYS) results were found as expected. The first contour shows pressure distribution in the nozzle. The inlet (leftmost) has pressure input of 3Bar which is the high pressure side showed in red. As we move rightwards the pressure reduces as velocity keeps on increasing in the converging section, further extending till final pressure at exit is reached which has a numerical value of 25 mBar (lowest, blue region).

Fig 10: Static pressure (pa) contours, left to right- inlet, throat and exit.

This figure 11 shows velocity contour. The velocity is maximum at the exit which it should be. The exit velocity here is 544m/s. Since this conical nozzle is designed with nozzle exit half angle of 11.25° we can observe the flow is separating near the exit walls. To avoid this we have to keep the nozzle exit half angle of diverging section in-between 12° to 18°, stated previously in calculations.

Fig 11: Velocity contours.

This figure 12 shows contour for Mach number. The green region in the throat shown that the Mach number is nearly ‘1’ here. Which is very important in cd-nozzle design. If Mach number doesn’t reach ‘1’ at the throat, the gases will not reach supersonic velocity at exit as the supersonic diffuser will fail to perform its function.

Fig 12: Mach number. Mach#=1 at throat.

6. Discussion

The results obtained and calculation done considering theoretical models are well within limits. This shows that design is quite possible to make. Some of the important parameters to consider here are temperature of operation, thrust produced, mass flow rate of the gases, life of the device and form factor. If made, this will be the smallest microthruster that doesn’t uses solid propellant.

One important factor to consider here is the temperature variation in the space. It’s reported that temperature changes are quite harsh in space ranging from -170°C to 123°C by Miracle Israel, Intern at Astrome Technologies. Which should be considered to avoid freezing and expansion of the propellant. Also radiations at those levels are consideration to prevent premature combustion.

Finally microfluidic channels that can be etched to feed the microthruster should be able to keep the device primed. When the bimorph heats up the propellant near the nozzle the gases escaping it will

develop suction near the nozzle inlet, failing to supply fuel at a constant rate may result into failure of the bimorph due to overheating, as the fuel cools the bimorph, also it will result in failure of thrust.

Here we didn’t discuss about the electrical contacts. Proper doping of the substrate and choosing the material will improve the performance of the system. I recommend an insulation layer between the aluminum electrode and the silicon electrode to avoid conduction of silicon. If allowed, then controlling the dimension is required.

7. Testing Of Nozzle Exhaust Characteristics.

7.1 Schlieren imaging [27] [28]

Schlieren imaging can be used for observing the exhaust. In this method simple equipment are needed such as tripod, a concave mirror, a point light source (LED) and a camera. The setup is shown in the figure 13.

Fig 13: Schlieren imaging setup.

When the exhaust from the microthruster enters the light field it changes the refractive index of the medium which filled the view previously. This results in the refraction of incoming light rays. Which can be easily seen in the figure 14.

Fig 14: exhaust from microthruster [].

7.2 Sensitive cantilever setup [28] [6]

In this testing method a small cantilever made of foil is place few millimeter below the microthruster nozzle exit. A small silicon chip is placed on the beam and laser is shown on the chip which acts as a mirror. A small deflection in the cantilever displaces the mirror thus deviating the incident laser light which is calibrated according to the thrust. A schematic from a research paper shows the complete setup. The cantilever has to be heated up to a certain temperature in order to evaporate

the condensate, if not done, the cantilever will bend due to condensate mass.

Fig 15: Cantilever test setup.

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Appendix1. Matlab code and plot 1

2. Matlab code and plot2