Performance Test of MEMS-Fabricated Critical Flow Venturi Nozzles

Performance Test of MEMS-Fabricated Critical Flow Venturi Nozzles Chih-Chung Hu 1, Win-Ti Lin 2, Cheng-Tsair Yang 2, Wen-Jay Liu 1 1 Department of Electronic Engineering, Kao Yuan University of Technology, Kaohsiung, Taiwan 70101 2 Center for Measurement Standards, Industrial Technology search Institute, Hsinchu, Taiwan 30042 Abstract Four types of silicon sonic nozzles for the throat dimension around 90 m are investigated at ynolds number ranging from 6 10 2 to 8 10 3. With a specially designed clamping holder, the silicon nozzle is able to operate at an upstream pressure of 13.8 10 5 Pa and the above. The critical pressure ratio for choking is insensitive to, for which the averaged value is about 0.36. The time length required for the silicon nozzle to reach thermal equilibrium with sonic flow is about 10 minutes. The maximum deviation of discharge coefficients obtained at five different individual days in two months is less than 0.02%, signifying a good long-term stability. Keywords: critical flow Venturi nozzle; silicon sonic nozzle; small sonic nozzle 1. Introduction Sonic nozzles are well known as standard flow systems due to the simplicity, high accuracy and stability. The measurements by sonic nozzles can follow the international standard ISO 9300 [1] for ynolds number > 2.1 10 4. For small sonic nozzles of throat diameters < 200µm or ynolds numbers << 2.1 10 4, the nozzle performances may deviate from the data provided in ISO 9300. Though small sonic nozzles have been widely used in the measurement and control systems for industrial or laboratorial applications, [2-5] these nozzles are not easily achievable due to the difficulty of machining, and the geometries of the flow passage are hardly consistent with the toroidal or cylindrical Venturi nozzle specified in ISO 9300. [1,3] Several non-iso-typed sonic nozzles with the throat diameter ranging from 100 to 200 m were examined by Bignell [3], including a shrinking glass tube, a water-cutting head, and a nozzle with rectangular throat. Additionally, Nakao and Takamoto [6] investigated a quadrant type of sonic nozzle, i.e., a ISO-typed nozzle but without its divergent part. The results indicate that with careful calibrations the non-iso-typed nozzles are able to serve as standard meters. [3,6] In contrast to the conventional machining of small metal nozzles, MEMS technique provides an alternative to carry out efficient fabrications, though it is still difficult for ISO-typed nozzles. Mammana et al. [7], for example, used an electrochemical etching process on a tungsten wire to form a convergentdivergent profile. Diamond was deposited on the shaped tungsten wire and the wire was then removed by etching process eventually to leave the diamond nozzle with a throat diameter of 217 m. Preliminary results of the nozzle implied the possibility of practical application. On the other hand, MEMS technique has also been applied to create micro thrusters for micro satellites. [8-10] Though the thrust efficiency was mainly concerned in these cases, [8-10] the concept of batch processing on a silicon wafer can be applied to fabricate micro-scaled Venturi sonic nozzles economically. 1

In this study, four types of silicon nozzles were fabricated, for the throat area around the order of 90 m 90 m. The nozzles were examined of their characteristics at the ynolds number ranging from 6 10 2 to 8 10 3. In the following, ynolds number effect on discharge coefficient, back-pressure conditions for choking, [5,6] transient behavior due to thermal effect, [3,11] maximum sustainable pressure, and long-term stability are presented. (a) flow Fig. 1 Type A Type B Type C Type D Four types of nozzle configurations employed. (b) Fig. 2 SEM pictures of silicon nozzles (a) type A, 90µm in throat, and (b) a cutting of type B, 95µm in throat. 2. Fabrication of silicon sonic nozzles The technique of KOH anisotropic etching was applied to fabricate silicon sonic nozzles. Through the square openings precisely aligned on Si 3 N 4 etch mask deposited on a <100> silicon wafer, the KOH etchant would recess along the <111> crystalline planes of the wafer. [12] Instead of having a circular cross-section normal to the flow direction, the achieved silicon nozzle bears a square cross-section, similar to a pyramidal orifice. The slopes of the side walls with respect to the wafer surface are 54.7, which results in a 35.3 half angle for the nozzle. The thickness of the wafer is 505µm. For installation concern, the nozzle chip cut from the silicon wafer has a dimension of 7mm 7mm, and thus more than one hundred chips could be obtained from a 4 wafer. fer to Fig. 1 for the schematic drawings of the four types of silicon nozzles investigated, i.e. type A to type D. As seen, the divergent part of the sonic nozzle is gradually enlarged from type A to type D. From the experimental results shown later, one can realize the effect of the divergent part on the performance of silicon sonic nozzle. During the experiments, type A and type D nozzles are actually the same nozzle chip. That is to say, type D nozzle is an inverse installation of type A nozzle with respect to the flow direction. See Fig. 2a for the picture of type A, taken by a scanning electron microscope (SEM). On the other hand, the nozzle bodies for types B and C comprise convergent and divergent parts. For example, the length of the convergent section is 2 times of the divergent section for type B. The half angles for the convergent and divergent parts are all 35.3. See also in Fig. 2b for a cutting of type B nozzle. As a similar situation to types A and D, type C nozzle is an inverse installation of type B nozzle. Hence, the ratio of convergent to divergent sections is 1/2 for type C. In this study, the nominal dimension for the throat of types A and D is 90µm and 95µm for types B and C. It is noted that the uncertainty of this dimension is about ±2µm, leading to an uncertainty of about ±4% of the throat area. 3. Experimental facilities Since silicon is a brittle material and the present 2

test rig is used for traditional stainless sonic nozzles, a special design of clamping holder was developed. Hence, the nozzle chips can be prevented from any stress concentrations and also compatible with the test rig. Experiments were carried out in the flow measurement laboratory of the Center for Measurement Standards, Industrial Technology search Institute (CMS/ITRI), Taiwan. Two kinds of standard meters were employed for this study. For < 4 10 3, a laminar flow element was installed in the upstream circuit of the test rig to measurement the mass flow rate through the silicon nozzle, see Fig. 3a. For > 4 10 3, a calibrated stainless sonic nozzle whose diameter is 0.296mm was connected in the downstream of the silicon nozzle to form a nozzle-to-nozzle system, [5,6] see Fig. 3b. In this study, represents the real ynolds number, which is based on the true mass flow rate and the nominal dimension of the nozzle throat. [1] The expanded uncertainties for the flow rate measurement in both cases are all 0.2%. the maximum pressure that would cause a fracture of the silicon nozzle was wondered at the beginning of experiments. The flow upstream the silicon nozzle was pressurized up to 200psi, about 13.8 10 5 Pa, which is the maximum ability of the present system, and kept stationary for 30 minutes. Then, the pressure was decreased and increased repeatedly for several times. After the test, no damages were found on the silicon nozzle chip, revealing the chip with the present clamping holder is able to sustain a pressure of 13.8 10 5 Pa at least. Cd 0.86 0.84 0.82 0.80 0.78 0.76 0.74 Type A Type D 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Fig. 4 Cd versus for types A and D. (a) (b) Fig. 3 Test facilities for silicon micron nozzles; (a) using a laminar flow element as standard, (b) using a standard nozzle downstream. 4. Experimental sults Before examining the discharging characteristics, ynolds number effects on the discharging characteristics of the four types of silicon nozzles are shown in Figs. 4 and 5 for = 6 10 2 to 8 10 3. In Fig. 4, the triangular and rhombic symbols denote the discharge coefficients, Cd, [1] for types A and D, respectively. As seen, the Cd values for type A are relatively insensitive to. For example, the Cd value at the highest is 0.838, while the Cd value at the lowest is only 0.18% below. In fact, this distribution curve has a similar appearance to the data of cylindrical type in ISO 9300. [1] According to ISO 9300, the relation between discharge coefficient and ynolds number is described as n Cd = a b, where a, b, n are coefficients for the fitting. From the experimental data of type A, the coefficients are a 3

= 0.8388, b = 0.0684, and n = 0.2. The maximum deviation from the fitting curve is less than 0.01%, signifying a good linearity. A different appearance is observed on the data of type D. Namely, the Cd value decreases with and reaches a value of 0.758 asymptotically. Since the nozzles of types A and D are actually the same nozzle chip, direct comparison of the results suggests that the effective throat area of type A is about 10% larger than type D. In Fig. 5, the circular and square symbols denote the results for types B and C, respectively. For these two nozzles, the Cd distributions do not conform well with either toroidal ISO type for n = 0.5 or cylindrical ISO type for n = 0.2. Whereas, the Cd values of type B can be fitted well by n = 0.7 for < 4 10 3 and approaches a constant of 0.8408 for > 4 10 3. As for the case of type C, the fitting curve with n = 0.7 can predict the experimental data for the full range of with an acceptable error of about ±0.1%. It is also observed that the Cd values for type C are slightly larger than those of type B in the higher range of. Since types B and C are the identical nozzle chip, the differences of the Cd values are directly due to the flow situations in the nozzles. Comparisons between Figs. 4 and 5 should be taken with care because of the large uncertainty for the measurement of throat dimension. The smaller Cd values of types A and D relative to types B and C for > 3 10 3 seem to imply thicker boundary layers; however, it requires more accurate measurements of the dimension to support this observation. A critical flow Venturi nozzle can provide a stable flow without being influenced by the downstream conditions only when the nozzle is choked in the throat region. In general, the ratio of downstream to upstream pressure of the nozzle serves as a choking parameter. In this study, the critical pressure ratio, denoted as CPR, is defined as the discharge coefficient becomes 0.1% below the initial value at choking condition, which signifies a breakdown of choking. [6] Fig. 6 gives the deviations of the discharge coefficient for the aforementioned four types of nozzles obtained at around 3.3 10 3. Herein, P b denotes the downstream pressure of the nozzle, and P u is the upstream pressure. By the marked deviation line of -0.1%, the CPRs for the four types at this ynolds number are easily identified. As an example, the CPR value for type B is about 0.37. Cd deviation (%) 0.86 0.84 0.82 0.80 0.78 1.0 0.0-1.0-2.0-3.0 Type B Type C 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Fig. 5 Cd versus for types B and C. Type A, =3300 Type B, =3440 Type C, =3460 Type D, =3050-0.1% 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Pb/Pu Fig. 6 Deviations of Cd versus pressure ratio at =3300 for types A to D. The CPRs obtained at three different ynolds numbers for each of the nozzle type are given in Fig. 7. Apparently, the CPRs for types B and C, marked as circular and square symbols, respectively, prevail 4

over types A and D. The averaged CPR for type B is about 0.36 over the ynolds numbers examined, and 0.32 for type C. Meanwhile, types A and D show a relative poor choking ability, for which most of the CPR values are less than 0.2. The results shown in Fig. 8 evidence a common situation that a convergent-divergent nozzle could choke at a greater back pressure than a convergent or a divergent nozzle. [13] It is also noted that the CPRs for the cases examined do not vary drastically with. As a reference, in this same ynolds number range, the CPRs for the quadrant nozzles by Nakao and Takamato [6] varied from 0.24 to 0.4. CPR 0.6 0.5 0.4 0.3 0.2 Type A Type B Type C Type D In order to evaluate the reproducibility of the silicon nozzle in a long term, the discharge coefficients of type C were taken at five different individual days in two months. As seen in Fig. 9, the data of Cd coincide well to each other. The maximum deviation at each ynolds number examined is less than 0.02%, showing a great stability. deviation (%) 0.08 0.04 0.00-0.04 Type C, =3500 0 4 8 12 16 20 t (min.) Fig. 8 Variation of Cd after started for type C. 0.1 0.86 0.0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Fig. 7 CPR versus for types A to D. It is known that a time period is usually required for a nozzle to reach its thermal equilibrium with sonic flow. [3,12] For example, the glass nozzle of Bignell [3] required about 1 hour. To clarify the transient behavior of silicon nozzles, type C nozzle was further examined to measure the time length for the equilibrium state. Before the test, the standard meter was warmed up through a bypass circuit to prevent any unpredicted drift. Fig. 8 shows the deviation of the Cd value with time at = 3.5 10 3. The deviations in reference to the equilibrium state are less than 0.05%. Though negligible, the deviation decreases asymptotically to zero in a time length of about 10 minutes. Cd 0.84 0.82 0.80 0.78 Type C 2007/3/23 2007/5/8 2007/5/9 2007/5/16 2007/5/17 0 1000 2000 3000 4000 Fig. 9 producibility of Cd for type C. 5. Concluding marks In this study, four types of silicon sonic nozzles, fabricated by KOH-etched batch processing to achieve substantial cost saving, are investigated. With the specially designed clamping holder, the nozzle chips are sustainable up to a pressure of 13.8 10 5 Pa and the above. Among the four types examined, 5

types B and C have their averaged critical pressure ratio of 0.36 and 0.32, respectively, while types A and B are below 0.2. The result signifies that silicon nozzles with a convergent-divergent geometry would behave better performances. The silicon nozzle requires a time length of about 10 minutes to reach thermal equilibrium with sonic flow. Actually, the deviation in the transient process is below 0.05%, which can be eliminated in most cases. On the other hand, the silicon nozzle also shows a very good long-term stability. Since the limitation of paper length, detailed of the experimental data aren t presented here. However, from the results shown above, the silicon nozzles are readily applicable to the small flow regime. In the near future, the silicon nozzles of throat dimension < 90 m will be investigated experimentally and numerically. Acknowledgement The authors would like to acknowledge the funding support of National Science Council, Taiwan, ROC, on this work, under the contract numbers of NSC95-2221-E-244-026-. ferences [1] ISO 9300: Measurement of gas flow by means of critical flow Venturi nozzles, 2003. [2] Hayakawa M., Ina Y., Yokoi Y., Takamoto M., Nakao S., Development of a transfer standard with sonic Venturi nozzles for small mass flow rates of gases. Flow Measurement and Instrumentation 11, 279-283, 2000. [3] Bignell N., Using small nozzles as secondary flow standards. Flow Measurement and Instrumentation 11, 329-337, 2000. [4] Miralles B. T., Preliminary considerations in the use of industrial sonic nozzles, Flow Measurement and Instrumentation 11, 345-350, 2000. [5] Park K.A, Choi Y.M, Choi H.M, Cha T.S, Yoon B.H, The evaluation of critical pressure ratio of sonic nozzles at low ynolds numbers. Flow Measurement and Instrumentation 12, 37-41, 2001. [6] Nakao S., Takamoto M., Choking phenomena of sonic nozzles at low ynolds numbers. Flow Measurement and Instrumentation 11, 285-291, 2000. [7] Mammana S. S., Salvadon M. C., Characterization of diamond sonic micronozzles and microtube. J. Vac. Sci. Technol. B 21(5), 2034-2037, 2003. [8] Bayt R. L., Ayon A. A., Breuer K. S., Performance evaluation of MEMS-based micronozzles. 33 rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, AIAA paper 97-3169, July 7-9, 1997. [9] Bayt R. L., Breuer K. S., Systems design and performance of hot and cold supersonic microjets. 39 th AIAA Aerospace Science Meeting and Exhibit, AIAA paper 2001-0721, January 8-11, 2001. [10] Hao P.F., Ding Y. T., Yao Z. H., He F., Zhu K. Q., Size effect on gas flow in micro nozzles. J. Micromech. Microeng. 15, 2069-2073, 2005. [11] Bignell N., Choi Y. M., Thermal effects in small sonic nozzles. Flow Measurement and Instrumentation 13, 17-22, 2002. [12] Madou M. J., Fundamentals of microfabrication, CRC Press, Boca Raton, New York, 1997. [13] James E. A., Gas dynamics, second edition, Ally and Bacon, 1984. 6