Experimental Thermal and Fluid Science

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1 Experimental Thermal and Fluid Science 32 (2008) Contents lists available at ScienceDirect Experimental Thermal and Fluid Science journal homepage: Study of an integrated thermal sensor in different operational modes, under laminar, transitional and turbulent flow regimes Ch. Stamatopoulos a, A. Petropoulos b, D.S. Mathioulakis a, *, G. Kaltsas b,c a Fluids Section, National Technical University of Athens (NTUA), 9 Heroon Polytechniou Avenue, Zografou, Greece b IMEL/NCSR Demokritos, P.O. Box 60228, Aghia Paraskevi, Athens, Greece c Department of Electronics, Technological Educational Institution (TEI) of Athens, Egaleo, Athens, Greece article info abstract Article history: Received 28 November 2007 Received in revised form 11 June 2008 Accepted 12 June 2008 The behaviour of a thermal flow sensor attached to the wall of a square tube is examined, exposed to gas flow for Reynolds numbers in the range Consisting of a polysilicon heater and a pair of thermopiles, the sensor s three output signals (heater power, its electric resistance and the thermopile signal) are analyzed as a function of Re. Employing three different modes of operation (constant power (CP), constant voltage (CV) and constant temperature (CT)), it was found that the sensor sensitivity maximizes in CT mode. Heater power and its resistance vary with Re a where a changes significantly for Re > The thermopile signal, which corresponds to the streamwise temperature gradient across the heater, in contrast to the other two signals, is more sensitive in detecting flow disturbances. Its fluctuations increase with a high rate close to Re = 1800, a value which is smaller than the corresponding increase of the other two signals. The probability density function (pdf) of its fluctuations is negatively skewed consistently for the range 1500 < Re < 11,000 while for Re > 11,000 it turns to a symmetric one. The pdf of the other two signals do not show any systematic trends with Re. The most striking difference of the thermopile signal behaviour compared to the other two is its multivalued relationship with Re in the range 2000 < Re < 11,000. Ó 2008 Elsevier Inc. All rights reserved. 1. Introduction * Corresponding author. addresses: mathew@fluid.mech.ntua.gr (D.S. Mathioulakis), G.Kaltsas@ ee.teiath.gr (G. Kaltsas). The miniaturization of sensors has been made possible by advances in the technologies originating in the semiconductor industry, and as a result the emergent field of microsensors has grown rapidly during the last 10 years. The term microsensor is now commonly used to describe a miniature device that converts a non electrical quantity, such as wall shear stress, pressure, temperature, etc., into an electrical signal. Integrated silicon sensors have the advantage that they can be mass fabricated and combined with an integrated circuit on the same chip. Most of the integrated flow sensors presented in the literature are based on the monitoring of the heat transferred to a moving fluid from a heated part of a sensor. In fluid mechanics, microsensors, compared with conventional ones, can be used more effectively in detecting flow structures. Additionally, using their output signal, the significant issue of flow control can be faced in greater success due to the more accurate flow monitoring [1,2]. The necessity of employing microsensors stems from the fact that the higher the Reynolds number, the smaller the length and time scales of the flow structures are. Based on appropriate techniques, sensors with a size of a few viscous wall units are fabricated nowadays, so that their presence does not disturb the fluid motion. Moreover, due to their small size, thermal inertia is negligible for the case of thermal sensors, allowing the measurement of fast fluctuating flow quantities [3 5]. As they can be closely spaced, they are also able to provide a picture of the flow field with a good spatial and temporal resolution. Therefore, complex flow phenomena like turbulence and in general time dependent flows can be better studied via these sensors, revealing information which is not possible to be traced by the conventional measurement techniques. In the context of the present work, a silicon thermal flow sensor is examined, for various flow conditions and operational modes, being fabricated using porous silicon technology [6]. 2. Experimental A Si integrated thermal flow sensor was used in the present work. The main parts of the sensor and its dimensions are illustrated in Fig. 1. It consists of a polysilicon heater and two Al-polysilicon thermopiles located symmetrically on both sides of the heater. Porous silicon was used as thermal isolation layer from the silicon substrate. The cold thermopile contacts are used as reference for /$ - see front matter Ó 2008 Elsevier Inc. All rights reserved. doi: /j.expthermflusci

2 1688 Ch. Stamatopoulos et al. / Experimental Thermal and Fluid Science 32 (2008) Fig. 1. Thermal sensor basic dimensions. ambient temperature since they are situated on top of the silicon substrate, being an efficient thermal conductor. The effect of the thermopile hot contact temperature drift can be compensated by placing the cold thermopile junction outside to flow as reported previously [7]. Measuring the thermopile output voltage, the corresponding hot contact temperature value can be extracted due to Seebeck effect [8]. Detailed description of this device is presented elsewhere [9,10]. A square smooth tube 1.5 m long with a cross-section of 5 5 mm was used for the present study, with pure nitrogen as the flowing medium at a temperature of 20 C. The sensor was mounted 1.1 m far from the tube inlet so as the flow is fully developed at this location. The critical inlet length L, in order for laminar flow to be fully developed is given by the following formula [11]: h i 1=1:6 L=D ¼ 0:619 1:6 þð0:0567reþ 1:6 ð1þ where Re is the Reynolds number being expressed as Re = UD/m, Uis the bulk fluid velocity, D is the hydraulic diameter equal to 5 mm and m the fluid kinematic viscosity, which has the value of m 2 /s for nitrogen at 20 C. According to the analysis that is presented in the following paragraph, the critical Re at which transition to turbulence initiates is close to This specific value corresponds to an inlet length of 114D = 0.57 m, according to (1). When the flow becomes turbulent an inlet length of 100D, which in the present case stands for 0.5 m, is sufficient to obtain a fully developed turbulent flow [12]. Two Brooks 5850 flow meters in the range of 0 10 SLPM (Standard lt/min) and SLPM were used in order to define the reference flow rate. When power is applied to the heater of the sensor with the fluid being stagnant, a homogenous temperature distribution is formed and the two hot thermopile contacts are exposed to the same temperature. However, when flow is applied perpendicular to the longitudinal heater axis, the upstream thermopile is cooled while the downstream one is heated due to the released heat conveyed in the main flow direction. Therefore, a temperature difference is established, which is directly related to the fluid flow rate [13]. The heater resistance is an increasing function of temperature [10], thus the evaluation of the proposed sensor was performed in three different modes of operation: constant voltage (CV), constant power (CP) and constant temperature (CT). A specially designed circuit was fabricated to this respect, which could supply controllable power to the sensor and simultaneously monitor the signals from the heater and the thermopiles with a sampling frequency of 2.5 KHz [14]. Therefore, all the time mean values of the measured quantities were calculated based on the above mentioned sampling rate and for an integration time of approximately 15 s. The CV mode is the simplest configuration since constant voltage is applied to the heater without any other stabilization scheme. In CP (or CT) operation mode, the microcontroller program that the electronic circuit implements, calculates the input voltage which is necessary for power (or resistance) stabilization, through the power (or temperature) stabilization algorithm, and this specific voltage is applied to the heater. Therefore, constant voltage mode (CV), or constant power (CP) or constant temperature (CT) is applied to the heater and the corresponding flow rate is extracted from the thermopile voltage difference. For each mode (CV, CP, CT) the calorimetric principle of operation was used, thus the thermopile voltage difference was continuously monitored. The specially designed interface electronics provide the ability of monitoring the heater temperature as well and therefore this parameter was also included in the sensor evaluation. All the modes of operation were implemented for each reference flow rate, so as to maintain the optimum comparability of the corresponding results. 3. Analysis of sensor operation The heat-rate generated by the heater due to electric current passing through it, is balanced by four different heat losses, namely the one which is transferred to the fluid by convection, Q 1,by radiation Q 2, the conductive heat-rate Q 3, taking place along the longitudinal axis of the heater and the silicon substrate, and the heat-rate stored in the heater mass Q 4. Due to the relative small temperature difference between the heater wall and the ambient fluid temperature (of the order of 150 C), the heat-rate Q 2 due to radiation is not significant as well as Q 4 due to the small heater mass. Based on hot wire anemometry experience, Q 3 is normally of the order of 15% of the total power, being minimized the longer the heater main axis with respect to its diameter is, and the lower the thermal conductivity of the heater material is [15]. Based on the previous analysis, the major part of the electric power of the heater is transferred to the fluid due to forced convection, given by the following equation RI 2 ¼ haðt w T a Þ ð2þ where R is the electric resistance of the heater, I the heater electric current, h the heat-transfer coefficient, A the area of the heater exposed to the fluid, T w the mean heater temperature, and T a the fluid ambient temperature. This specific effect was also experimentally verified by Wang and Vafai [16] in a channel with a number of flush mounted and protruding heat sources. The heat-transfer coefficient is an increasing function of the fluid velocity, related to this through the Nusselt number Nu. The latter is a function of the Reynolds number Re and the fluid Prandtl number Pr, namely Nu / Re a Pr b The exact expression of Nu depends on the type of flow (laminar-turbulent, internal external flow), the surface geometry and whether heating or cooling takes place. For the case of a heated cylinder in cross flow, the exponent a of the above expression (3) increases from 0.33 to for a Re range and the exponent b is equal to 0.33, for fluids with Pr > 0.6 [17]. Nitrogen which is used as the flowing medium in the present work has a Prandtl number equal to 0.7. For laminar flow over a flat plate the exponent a is equal to 0.5, whereas for turbulent flow this is equal to 0.8, for both uniform wall temperature and uniform wall heat flux [17]. When the flow is turbulent inside a duct, Nu for the entire length of the duct depends on Re 0.8 [17]. Consequently, the heater power and its electric resistance as well as the streamwise temperature difference across the heater, measured by the thermopiles, are related to the fluid velocity in a non linear manner. Details of the sensor behaviour are presented in the following paragraph for various flow states and three operational modes. ð3þ

3 Ch. Stamatopoulos et al. / Experimental Thermal and Fluid Science 32 (2008) Results and discussion In the context of the present work the sensor output signals were recorded for a Re range , covering the three basic flow regimes: laminar, transitional and turbulent. The thermopile signal which corresponds to the temperature difference across the heater in the streamwise direction was analyzed as well as the heater power and its electric resistance for the three modes of operation, CT, CP and CV. Fig. 2 shows the time mean heater power variation versus Re for CT and CV modes of operation. It is characteristic that for both modes the supplied electric power to the heater increases with increasing fluid velocity, apparently due to the increased heat-rate transferred to the fluid by convection. This is in accordance with the formulas presented in the previous paragraph, where Nu increases with Re. Moreover, in these formulas there is an increase of the exponent of Re when the flow from laminar turns to turbulent. The latter is reflected to a change of the curve slopes in Fig. 2 beyond Re = 2200, being more evident for the CT mode. Based on the CT curve, it is verified that the heater power for Re < 2200 is proportional to Re and for Re > 2200 this is proportional to Re The much smaller increase of the heater power when it operates in CV mode (see Fig. 2) is due to the cooling of the heater when the fluid velocity increases. This results in a reduction of the temperature difference (T w T a ), while in CT mode the latter remains constant. Since the heat-transfer is dependent on both the fluid velocity and the temperature difference (T w T a ), it is obvious from eq. (2) that in CT mode (T w T a = CT) the heater power will be higher compared with that of the CV mode. Fig. 3 illustrates the time mean heater electric resistance as a function of Re in two modes of operation (CV, CP). A drop of heater resistance is observed with increasing fluid velocity due to its cooling and its rate of decrease is enhanced for Re > As it was previously mentioned the heater resistance is a monotonically increasing function of temperature. An indication that the flow regime changes from laminar to turbulent is also given by an increase of the fluctuations of the heater power and its resistance beyond a certain Re associated with an increased level of flow disturbances. This behaviour is shown in Fig. 4 which presents the standard deviation of the power fluctuations as a function of Re for both CV and CT mode. For Re > 2000 higher Fig. 3. Time mean heater electric resistance versus Re. Fig. 4. Heater power fluctuations versus Re. Fig. 2. Time mean heater power versus Re. power fluctuation values appear. A similar behaviour is also observed in the fluctuations of the heater resistance for Re > 2200 for both modes of operation as Fig. 5 illustrates. It is noticeable that the increase of the fluctuations level of both the heater and its resistance occurs prior to the increase of the Reynolds exponent related to their time mean values. Very interesting information about the flow regime is also provided by the thermopiles signal. Fig. 6 shows the time mean thermopiles signal which reflects the streamwise temperature difference DN across the heater as a function of Re. Due to forced heat convection the upstream thermopile is cooled down whereas the downstream one is heated, being inside the heater thermal boundary layer. Therefore, DN is expected to be an increasing function of Re. This behavior is clearly illustrated in Fig. 6, excluding the range 6500 < Re < 11,000, where the signal drops. The drop of DN,

4 1690 Ch. Stamatopoulos et al. / Experimental Thermal and Fluid Science 32 (2008) Fig. 5. Heater electric resistance fluctuations versus Re. Fig. 7. Thermopile signal fluctuations versus Re. Fig. 6. Time mean thermopiles signal versus Re. although the released thermal power increases in this Re interval, can be attributed to the fact that the upstream temperature is significantly affected by the heater under the certain flow conditions. It is also worthy to notice that similar tendencies appear in all operation modes. Namely, the thermopile voltage increases monotonically up to Re = 6500 (local maximum), then it drops up to Re = 11,000 (local minimum) and for higher Re it increases again. Apparently, the thermopile output signal cannot be used as a tool for bulk fluid velocity measurements in the range 2000 < Re < 11,000 (see Fig. 6), since there is no monotonic relationship between input and output signals. However, outside this Re region, the thermopile signal can be used for flow sensing, exhibiting different sensitivities according to the mode of operation. Namely, CT mode presents high sensitivity, CP lower and CV the smallest one (see Fig. 6). A careful analysis of this signal provides interesting information about the flow behavior. Its standard deviation versus Re is presented in Fig. 7 for all modes of operation. A sharp increase of the DN fluctuations appears at a Re of This value is smaller than the corresponding one of the heater power and its resistance fluctuations (see Figs. 4 and 5). Also, from Fig. 7 it is clear that two local maxima at Re = 4380 and Re = 8760, respectively and a local minimum at Re = 6570 appear. It seems that the temperature gradient across the heater is more sensitive than the heater power or its resistance in detecting turbulent or non turbulent structures. As it is mentioned by Bruun [18] temperature seems to be a better means of detecting turbulent or not turbulent zones than fluid velocity or vorticity. Also, for Re > 11,000, the rms of DN drops progressively reaching a plateau at the highest examined Re According to Gavarini et al. [19] the critical Reynolds number for pipe flow, below which any flow disturbances decay, is between 1760 and 2300, based on experimental evidence. Also, according to Fischer [20] transition to turbulence due to natural disturbances in a two dimensional channel initiates at about Re = 2000 and the flow becomes fully turbulent at Re = According to Hagen [17] flow transition in a pipe takes place in the interval 2300 < Re < 10,000. Therefore, the non monotonous variation of the thermopiles signal output in the interval 2000 < Re < 11,000 (see Fig. 6) is associated with the transitional status of the flow. A basic feature of the transient flow is the existence of turbulent spots, regions of high level of velocity fluctuations, which moving downstream grow both streamwise and spanwise [21,22]. For a stationary sensor, like the one in the present work, the flow changes to turbulent when a turbulent coherent structure passes over it and then it returns to laminar again. Examining the probability density function (PDF) of the velocity fluctuations, it appears to have a Gaussian (symmetric) shape when the flow is fully turbulent due to the randomness of the flow, whereas if the flow is transitional, the PDF is not symmetric [22]. Examining the PDFs of the three output signals of the sensor, it was found that only the thermopile signal showed a consistent variation as a function of Re. Fig. 8 includes the PDFs for several Re in the region 1700 to 28,000. It is observed that for 1700 < Re < 11,000 the PDF show systematically a negative skewness (Fig. 8a f), whereas for Re > 11,000 this is minimized and it becomes eventually a symmetric one at high Reynolds numbers (Fig. 8g and h). According to an experimental study and a direct numerical simulation of pipe flow [23] at Re = 5300 it was found that the skewness factor of the streamwise velocity component fluctuations is positive next to

5 Ch. Stamatopoulos et al. / Experimental Thermal and Fluid Science 32 (2008) Fig. 8. PDF of thermopile signal versus Re. the wall and negative for a distance from p the wall greater than 30 wall units, namely 30m/u *, where u ¼ ffiffiffiffiffiffiffiffiffiffiffi s w =q and s w is the wall shear stress. An estimate of s w can be obtained using the known Blasius formula for turbulent pipe flows [12] s w qu ¼ 2 0:079Re 0:25 ð4þ In the present study the thermopiles are 380 lm far from the wall (equal to the silicon layer thickness), a distance which becomes greater than 30 wall units when Re exceeds Assuming that the thermopiles output is related to the fluctuations of the streamwise velocity component, the PDF negative skewness agrees with the findings of the above mentioned work. The skewness factor S of the temperature fluctuations dt 0 defined as S ¼ hdt 03 i=r 3 where the symbol hi means time average value and r the standard deviation as well as the flatness factor F, defined as [24] F ¼ hdt 04 i=r 4 were calculated versus Re for the three modes of operation (Fig. 9 and Fig. 10, respectively). It is interesting to note that both S and F of the thermopile signal become maximum in the range 1500 < Re < 2000, where transition initiates, and at high Re numbers ð5þ ð6þ Fig. 9. Skewness of thermopile PDF versus Re. Fig. 10. Flatness of thermopile PDF versus Re.

6 1692 Ch. Stamatopoulos et al. / Experimental Thermal and Fluid Science 32 (2008) Fig. 11. FFTs of thermopile signal versus Re. S tends to zero and F to 3, the latter value characterizing the Gaussian distribution. The frequency content of the thermopiles signal, below 1.25 khz (one half of the sampling frequency), was obtained applying a Fourier analysis. Fig. 11 presents the amplitude of the Fourier analysis versus frequency for various Re numbers. This amplitude increases with Re, demonstrating a maximum at Re 11,000 and it decreases for higher Re. This behavior is in agreement with similar observations reported for a flow over a flat plate [18], according to which the amplitude of the FFTs maximizes in the transitional stage of the flow, and it drops in the turbulent one. 5. Conclusions The behavior of a thermal flow sensor attached to the wall of a square cross-section straight tube is examined as a function of Reynolds number, in the range , covering three flow regimes: laminar, transitional and turbulent. The sensor consisting of a polysilicon heater and a pair of thermopiles which record the wall temperature difference across the heater in the streamwise direction operates under three different modes: constant temperature (CT), constant power (CP) and constant voltage (CV). The three output signals of the sensor that is, the heater power, its electric resistance and the temperature difference, provide information about the flow behaviour under various flow regimes. In CT mode, the heater power increases with increasing bulk fluid velocity, being proportional to Re for Re < 2200 (laminar region) and proportional to Re for higher Re. There is a similar behaviour when the sensor operates in CV mode, the sensitivity of which is much smaller compared with CT mode, due to the resistance cooling. The heater electric resistance drops with increasing fluid velocity in both CP and CV modes, with almost the same sensitivity, being a function of Re n, the exponent n changing at Re = The thermopile output signal increases monotonically with increasing Re, excluding the interval 6500 < Re < 11,000, where this drops. Due to the multi valued relationship between the thermopile signal and Re, this cannot be used for bulk flow measurement in the region 2000 < Re < 11,000. However, in contrast to the heater power and its resistance, thermopile signal seems to be more sensitive in detecting flow disturbances. Analyzing the thermopile signal fluctuations, their rms increases sharply at a lower Re than the other two signals and it takes high values in the range 1800 < Re < 11,000 where the flow is transitional, being reduced in the fully turbulent regime. Their PDFs show a negative skewness in the transitional flow regime tending to a normal distribution for Re > 11,000 for which the flow is fully turbulent. References [1] Gad-el-Hak, The MEMS Handbook, CRC Press, New York, [2] N.T. Nguyen, Dötzel, Asymmetrical locations of heaters and sensors relative to each other using heater arrays: a novel method for designing multi-range electrocaloric mass-flow sensors, Sensors and Actuators A: Physical 62 (1 3) (1997) [3] M. Dijkstra, M.J. de Boer, J.W. Berenschot, T.S.J. Lammerink, R.J. Wiegerink, M. Elwenspoek, Miniaturized thermal flow sensor with planar-integrated sensor structures on semicircular surface channels, Sensors and Actuators A 143 (2008) 1 6. [4] Tae Hoon Kim, Sung Jin Kim, Development of a micro-thermal flow sensor with thin-film thermocouples, Micromechanics Microengineering 16 (2006) [5] Zhiyong. Tan, Mitsuhiro. Shikida, Masafumi Hirota, Yan Xing, Kazuo Sato, Takuya Iwasaki, Yasuroh Iriye, Characteristics of on-wall in-tube flexible thermal flow sensor under radially asymmetric flow condition, Sensors and Actuators A 138 (2007) [6] G. Kaltsas, A.A. Nassiopoulos, Frontside bulk silicon micromachining using porous-silicon technology, Sensors and Actuators A 65 (1998) [7] N.T. Nguyen, A.H. Meng, J. Black, R.M. White, Integrated flow sensor for in situ measurement and control of acoustic streaming in flexural plate wave micropumps, Sensors and Actuators A: Physical 79 (2) (2000) [8] A.W. Van HerwaardenP.M. Sarro, Thermal sensors based on the seebeck effect, Sensors and Actuators 10 (1986) [9] G. Kaltsas, A.A. Nassiopoulos, A.G. Nassiopoulou, Characterization of a silicon thermal gas-flow sensor with porous silicon thermal isolation, IEEE Sensors Journal 2 (5) (2002) [10] G. Kaltsas, A.G. Nassiopoulou, Novel C-MOS compatible monolithic silicon gas flow sensor with porous silicon thermal isolation, Sensors and Actuators A 76 (1999) [11] F. Durst, S. Ray, B. Unsal, O.A. Bayoumi, The development lengths of laminar pipe and channel flows, Journal of Fluids Engineering, ASME 127 (2005) [12] H. Schlichting, Boundary-Layer Theory, seventh ed., McGraw-Hill Book Company, New York, 1979.

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