MEASUREMENT OF TURBULENCE STATISTICS USING HOT WIRE ANEMOMETRY

Transcription

1 MEASUREMENT OF TURBULENCE STATISTICS USING HOT WIRE ANEMOMETRY Mrgan Thangadrai +, Atl Kmar Son *, Mritynjay Singh +, Sbhendra *, Vinoth Kmar ++, Ram Pyare Singh +, Pradip K Chatterjee + + Thermal Engineering, CSIR-CMERI, Drgapr, India * Stdent, Asansol Engineering College, Asansol, West Bengal, India ++ Gradate stdent, Department of Aerospace Engineering, DSCET, Chennai, India mrgan.thangadrai@gmail.com Abstract: The higher order statistical moments of the trblence signal are essential for finding the qality of the flow at any given location. In the present stdy, these moments are sed for characterizing the flow field at the test section of low speed wind tnnel in CSIR-CMERI. The flctating velocity inside the wind tnnel is measred sing a mlti channel hot wire anemometry system. The calibration of probes and the effect of overheat ratios of constant temperatre anemometry system on the sensitivity of velocity, trblence measrements are discssed in detail. The higher order moments, e.g., mean, variance, skewness and flatness factor, of flctating velocity and the trblence intensity are calclated at varios location along the lateral direction of the test section. It has been fond that the higher order moments are highly essential in characterizing the flow qality at the test section besides trblence intensity. Keywords: Hot wire Anemometry, Wind Tnnel Testing, Trblence, Data Acqisition, statistical moments Nomenclatre Re - Reynolds nmber A - Cross section area v - Velocity R - Resistance a - Overheat ratio T - Temperatre E - Voltage otpt U - niform velocity in the test section S - Skewness factor F - Flatness factor A, B, n - Calibration coefficients Sbscripts 1 - Condition at contraction inlet 2 - Condition at test section inlet w - wire 1

2 1. Introdction Hot wire anemometry (HWA) has been sed for many decades to measre the nsteady velocity flctations and trblence in both internal and external flows. It has two modes of operation (constant crrent (CCA) and constant temperatre (CTA)) depending on the way in which the sensor heating crrent is controlled. In CCA, the crrent to the sensor is kept constant and variations in sensor resistance cased by the flow are measred by monitoring the voltage drop variations across the sensor. In CTA, the wire is placed in a feedback circit which maintains the wire at a constant resistance and hence constant temperatre. Flctations in the cooling of the wire are seen as variations in wire crrent. CTA is sed for velocity measrements exclsively, becase it exhibits considerably higher freqency response than the CCA. It has very high spatial resoltion and captres eddies of size smaller than millimeter as the sensing element is in micron size (5 µm) with small length (1 mm). It offers an efficient and affordable soltion for mapping of velocity and trblence distribtion with high freqency p to 100 khz. Comprehensive information abot HWA system's principle, operation and applications are given in Brn (1995). Althogh laser Doppler anemometry (LDA) has gained increasing se in recent years, there are many reasons, inclding costs and technical merits, HWA is preferred in wind tnnel experiments for measring the trblence. HWA is sed for flow-rate measrements in a wide range of applications in sbsonic flows (Bradshaw, 1971; Hinze, 1975; Emrich, 1981). It is also sed in shock tbe flows for measring the compressible trblence (Briasslis, 1995). Trblence measrements sing HWA had started several decades ago (Cooper and Tlin, 1955) as the flid motions characterized by large Reynolds nmbers (Re) invariably involve trblent phenomena. The free stream trblence (FST) which affects the bondary layer behavior plays a vital role in determining the force and heating characteristics of aerodynamic objects. In the proposed stdy, flow qality (FST) inside the low speed wind tnnel is characterized sing the HWA system. At first, the hotwire probes sed for measring the flctating velocity is calibrated inside the wind tnnel against the velocity measred sing micro manometer and Pitot static tbe. Next, the trblence intensity is measred sing the calibrated probes with different overheat ratios. Finally the significance of higher order moments on the flow qality inside the test section is stdied in detail. 2. Experimental Apparats and procedre The open circit sbsonic wind tnnel with the test section area of m 2 existing in CSIR-CMERI is sed for the proposed stdy (Fig.1). It has a overall length of 8.2 m. The settling chamber entrance area is m 2. A sqare honeycomb (cell area of m 2 ) and three screens of wire mesh size m 2, m 2, and m 2 are placed inside the settling 2

3 chamber for breaking down the large scale trblent strctres. The wind tnnel has ' ' v = v A A ) a contraction ratio of 11 which frther decreases the size of eddies ( convected into the test section. It has a test section of length 1.3 m. Two sction fans are placed inside the diffser for generating the pressre difference to initiate the flow inside the tnnel. The velocity in the test section is varied sing two variable freqency drive (VFD) attached with AC motors. The maximm velocity in the test section is 35 m/s. The laboratory conditions are maintained with the help of air conditioners and dehmidifier. The local temperatre and pressre are measred sing analog barometer and a digital thermometer from SATO. The test section steady velocity is measred sing a DP Measrements micro manometer (DPM TT 550S Dry Cell) and a Pitot static tbe (4 in 1). Fig. 1 Wind tnnel with DAQ system and hotwire anemometry system 2.1 Hot Wire Anemometry Velocity flctations inside the test section are measred sing a 4 channel HWA system. HWA works based on the principle of heat convection to the flid from electrically heated wire exposed in the flow. It is a transdcer that senses the changes in heat transfer from a small, electrically heated sensor. Its operation relies on the variation of the electrical resistance of the sensor material with temperatre. The relation between resistance and temperatre for a metallic condctor can be expressed by means of the temperatre coefficient of resistance (TCR): R = R 1 + a T - T T

4 Higher order terms are negligible for the normally sed sensor materials. TCR vale a 0 refers to 20 C. The electrical heat inpt to the wire is lost by convection, condction and radiation. Q = Q 2 ERw (R +R ) E h 2 w B = Condction+ Convection+Radiation The radiation losses are mch less than 0.1% of the electrical inpt nder normal operating conditions and can be neglected. As the length of the wire (l=2 mm) is mch larger than the diameter (d=5 µm), the cross section area responsible for condction is negligible compared to the convection area. Hence, only heat loss is de to convection, the HWA otpt voltage can be related to the velocity (Lekakis, 1996). A variety of heat-transfer correlations for heated sensors of infinite length have been developed and are often modified to predict the behavior of hot wires and expressed in non-dimensional form (N). N = f Re,Pr,M,Gr,Kn, 2l,a,γ,β d where Re,Pr,M,Gr,Kn are the Reynolds, Prandtl, Mach, Grashof and Kndsen nmbers respectively; γ specific heat ratio; β flow angle Fortnately, most applications permit a significant redction on the nmber of dependent parameters and the details are given in Lekakis (1996). If we assme a, gamma and beta constant, the above eqation is redced to n 2 N = f Re N = a+b Re or E = A +BU This expression was derived by King (1914) based on the potential flow assmption. n 2.2 Calibration procedre Fig. 2 King's law fit with voltage data The hotwire probes are first calibrated inside the test section for the entire measring range (0 to 35 m/s). The voltage signal from HWA for different velocities are acqired sing a NI PXI 4462, 24 bit, 200 ks/s, 4 analog inpt channel simltaneos card installed in the NI PXIe-1062Q chassis. The voltage data are sampled with the freqency of 25 ks/s sing a program written in LABVIEW 2011 software. The test 4

5 section niform velocity is measred sing a micro manometer. Figre 2 shows the voltage data plotted against velocity measred sing micro manometer. The crve fitting tool available in MATLAB is sed for finding the calibration coefficients A, B and n. These coefficients are incorporated in voltage signal for calclating the velocity. 2.3 Statistical analysis of Trblence Description of trblences was given in Hinze as; "Trblent flid motion is an irreglar condition of the flow in which the varios qantities show a random variation with time and space coordinates, so that statistically distinct average vales can be discerned." The following qantities are sed for characterizing the trblence signals in the present paper Trblence Intensity Trblence Intensity (TI) is a percentage scale for characterizing trblence level. ' It is defined as TI = U where is the Root-Mean-Sqare (RMS) of the velocity flctations and U is the mean velocity. An idealized flow of air with absoltely no flctations wold have a TI vale of 0% Probability Density Fnction (PDF) The probability density fnction (PDF) also called as probability distribtion fnction. The PDF of a fnction defined as P(). P() is the probability that a specified vale will be fond between and + d and the sm of all P() is taken to be nity. Experiments show that p() can be represented by the Gassian (normal) distribtion 2 1 P() = exp(- ). where σ 2π 2σ velocity. The significance of 2 σ is the standard deviation of the σ is that the probability of occrrence of otside the range, for example, 2 < < -2 is only 4.6%. Any skewness in the observed PDF of the flctating signal particlarly near the wall may be linked to the brsting process (Eckelmann, 1974) in trblence. One of the important ses of the PDF is in constrction of varios moments of trblence qantities. These statistical moments (or central moments) give information on the properties of the velocities Statistical moments of Trblence The first statistical moment is the mean and it is defined as, = - p() d It is a weighted average of with P() being the weighting fnction. It gives the average velocity over a given period of time which is necessary to calclate static loads on objects (McDonogh, 2007). However the flctations are also important 5

6 component which is responsible for any nsteady loads. The second central moment gives the variance and it is defined as, 2 '2 ' ' p( ) d - σ = Here is sed as it is sally associated with deviation from the mean. Variance is a measre of how far a set of nmbers are spread ot. It is important since it allows to compte the dispersion of a set of variables arond their mean. It describes the pattern in which vales flctate arond the mean. It is often important to limit the vale p to which nsteadiness is taken into consideration. The third central moment gives the skewness factor and defined as, '3 '3 = '3 p( ' ) d ' S = (σ ) Skewness factor is a measre of degree of asymmetry of a distribtion. It can be observed directly from the shape of the PDF. If the PDF of a fnction is symmetric (Gassian), the skewness is zero. If a time series exhibits more negative vales than positive ones, skewness will be negative, and conversely. Skewness observed in trblence experiments is sally (bt not always) negative. As mentioned earlier, any skewness in the PDF represent a strong sorce of trblence generation. The forth central moment gives the flatness factor which is defined as, '4 '4 '4 ' ' = p( ) d or F = (σ) Flatness factor ((also called krtosis)) represents the deviation from the Gassian profile. Any fnction having large flatness vales is more sharply peaked in Gassian distribtions, and conversely. The flatness factor of a Gassian distribtion is three. It is noted by Tennekes and Lmley (1972) that the vales of flatness are large if the PDF has relatively large vales in its tails, i.e., it does not go to zero as fast as Gassian as the argment approaches. This occrs when time series of the fnction contain significant nmbers of sharp peaks, and is related to intermittency as discssed by Frisch [80]. Here, all these qantities are examined in detail for characterizing flow qality of the low speed wind tnnel. 3. Reslts and discssion First, the variation of trblence intensity (TI) inside the test section at middle is measred for velocity p to 32 m/s and plotted in Fig. 3. TI withot honeycomb and screens showed the vale as high as 15% at the test section. It is redced to less than 1% after installing the honeycomb and the screens in the settling chamber. It is also observed that the increase in over heat ratio (a) of the HWA has enhanced the sensitivity of the trblence measrement and resolved the finer vortical strctres. The variation of velocity measred from hotwire probes are significant at low velocity (Fig.4). This is de to the lack of energy cascading and dissipation of small scale vortices at the test section as the flow acceleration in the contraction section is directly proportional to velocity. 6

7 Fig. 3 Variation of trblence intensity with velocity Fig. 4 Percentage variation velocity from hotwire anemometry Fig. 5 shows the PDF obtained for two velocities at three different locations inside the wind tnnel test section. The middle section data represent the location of probe at 140 mm from bottom and 150 mm from the left side. The exact position of left and right probes are 50 mm and 250 mm from the test section left wall. It has been observed that the PDF obtained at the middle (a, b) of the test section and at 250 mm from left (e, f) follows near Gassian distribtion for both velocities. However the PDF obtained at 50 mm has deviated from Gassian distribtion and skewed towards right side. This shows that the flow qality at right side of the test section is mch better compared to the left side. This can be frther verified with the higher order moments of the velocity signal shown in Table 1. Table 1 shows the TI, mean, variance, skewness and flatness factor obtained from the flctating velocity at above mentioned three locations and two velocities. These experiments are performed for 5 times for repeatability check. TI at 50 mm is high compared to the TI vale at 250 mm. The first moment (mean) at 50 mm showed a 7.6% variation of mean velocity at 10.5 m/s and it is redced to 6.2% at 22.5 m/s. However, the mean variation at 250 mm is less than 2%. The skewness factor at 250 mm is almost zero or less than zero. This shows the good qality of flow in the right side. The flatness factor is 3 for Gassian and it will be arond three for any good wind tnnel. Here, the left side flatness factor is very high (4.9) and it shows that the flctations is spread over long distance (can also be seen in variance). 7

8 Fig.5 Probability distribtion fnction at varios locations inside the wind tnnel Location Pitot tbe TI in velocity % Mean Variance Skewness Flatness Middle Middle At 50 mm from left At 50 mm from left At 250 mm from left At 250 mm from left Table 1 shows the Trblence statistics of the acqired velocity signal 8

9 4. Conclsions A mlti channel hot wire anemometry system has been sed for characterizing the flow inside the wind tnnel. The overheat ratio (OHR) of the hot wire anemometry system plays a major role on the sensitivity of the flow measrement. Maintaining the OHR as high as possible is highly recommended for trblence measrements. The importance of statistical moments of flctating signal and their effects on flow qality is stdied. It has been fond that the velocity flctations are highly skewed at left side of the test section compared to the right side thogh the TI is almost same throghot the test section. Higher vale of flatness factor is also evident for strong flctations in the left side. This skewness in velocity distribtion was cased by leakage of flow in the left side opening. The higher order moments showed almost niform throghot the test section after the leakage was repaired. It showed that thogh the TI is widely sed for characterizing the flow in the test section, It does not garantee good flow qality if the higher order moments are not taken into consideration. Acknowledgements The athors acknowledge the Department of Science and Technology (DST), India for providing partial financial spport throgh FAST Track Yong Scientist Scheme for establishing the wind tnnel facility and the Director, CSIR-CMERI for his constant spport in carrying ot this research work. References Brn HH (1995) Hot wire anemometry Principles and Signal Analysis. Oxford University Press, New York, USA. Bradshaw P (1971). An Introdction to Trblence and its Measrement. Oxford, Pergamon Press. Briasslis G, Honkan A, Andreopolos J, Watkins CB (1995) Application of hot-wire anemometry in shock-tbe flows. Experiments in Flids 19, Cooper RD, Tlin MP (1955) Trblence measrements with the hot-wire anemometer, Wind Tnnel AGARDograph 12. Eckelman H (1974) The strctre of the viscos sblayer and the adjacent wall region in a trblent channel flow. J. Flid Mech.,65, 439. Emrich RJ (1981) Methods of Experimental Physics. Academic Press. New York Frisch U (1995) Trblence, the Legacy of A. N. Kolmogorov, Cambridge University Press, Cambridge. Hinze JO (1975). Trblence. New York, McGraw-Hill. Lekakis L (1996) Calibration and signal interpretation for single and mltiple hot-wire/hot-film probes. Meas. Sci. Technol. 7, McDonogh (2004) Introdctory Lectres On Trblence-- Physics, Mathematics and Modeling. Departments of Mechanical Engineering and Mathematics University of Kentcky. Tennekes H, Lmley JL (1972). A First Corse in Trblence. MIT Press,