Study Of Turbulent Wake Of An Airfoil Physical Education Essay

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In the present study, constant temperature hot-wire anemometry was used to investigate the turbulent near-wake of an airfoil subjected to the effects of curvature and pressure gradient.

The wake is generated by placing a NACA 0012 airfoil of 0.150 m chord length at one chord length upstream of a 90° bend. The measurements were carried out at a single mainstream air velocity of 14.09 m/s and an angle of attack of α=-3°. A single cross-wire probe was used and consisted of dual sensors, which were used to measure the mean velocity and turbulence quantities in two dimensions. These include the streamwise and normal components of velocity (U and V), the corresponding turbulence intensities (Urms and Vrms), and the turbulence shear stress (-u'v'). In addition airfoil static pressures on the upper and under sides of the airfoil are studied. The results show symmetrical profiles of pressure distribution at the angle of attack stated, which leads to the conclusion the approaching flow was not parallel to the airfoil but at an angle, which suggests that the flow angle imposed by the duct increased (negatively) with streamwise distance. The results also showed the turbulence stresses are enhanced on the inner side but suppressed on the outer side of the wake.

1. Introduction

Hot wire anemometry is used to measure the mean and fluctuating instantaneous fluid velocity of turbulent flows, and provides measurements of turbulent intensities and shear stresses. The technique has been developed since other devices are limited with respect to measuring turbulent flow parameters. For example Pitot-static tubes lack the sensitivity to measure the large changes in velocity in the small time scale. They are only able to measure the local velocity and not the average velocity. They are also limited in that it cannot resolve the small scale near wall boundary layer, where the geometrical size of tube is greater than the layer. However hot wire probe diameters are only one micron in size, and therefore are small enough to resolve boundary layers and can sense rapid changes in velocity.

The present study was conducted using Constant Temperature Anemometry (CTA). In constant temperature anemometry the controlling circuitry tries to maintain a constant resistance and temperature in the wire, whilst the variation of current is measured. Typically the probes wires can be heated to temperatures of 300°C, by passing current through the wire its resistance causes electrical energy to be converted to thermal energy (eq. 1.1). When the probe is placed in fluid flow, where its temperature is elevated above that of the fluid, heat transfer from the wire to the fluid occurs by forced convection. The fluid effectively has a cooling effect on the probe, and the rate of convective heat transfer is therefore a function of the velocity of the fluid and the proportional difference between fluid and probe temperatures. In equilibrium conditions (voltage difference across the wire is zero), there is a balance between the electrical circuit keeping the resistance constant (and so its temperature) and the heat loss to the fluid. As the flow velocity increases, the wire cools down; its resistance decreases, and thus results in a bridge imbalance. This imbalance is represented by the voltage signal across the Wheatstone bridge. To balance the bridge, the current in the circuit is increased, the sensor wire heats up and the resistance is increased until the circuit is balanced. The system allows for rapid response to the changes in the flow, and so the sensor temperature and resistance can be maintained constant with changes in the flow velocity. The voltage drop across the bridge can be used to represent the probe current. This relationship is expressed in eq. 1.2 and is known as the "King's law". It is not a universal expression and it is necessary to calibrate the probe to determine unknown constants A and B.



2. Objectives

The main objective of the present experimental investigation was to gain understanding of the techniques involved in CTA by obtaining experimental data in the near wake of an airfoil subjected to an angle of attack and curvature. These include the streamwise and normal components of velocity (U and V), the corresponding turbulence intensities (Urms and Vrms), and the turbulence shear stress (-u'v'). ). In addition airfoil static pressures on the upper and under sides of the airfoil are studied.

3. Description of Equipment

The experimental investigation was carried out using the wind tunnel facility at Brunel University; Figure A1.1 presents the dimensioned layout of the wind tunnel used. The tunnel is open return type, meaning the air is recycled locally to surrounding environment. Laboratory air is drawn into the tunnel, by a centrifugal fan via a bank of filters. The fan delivers the air to a short straight section, which contains honeycomb, and then to a diffuser fitted with three wire-meshes before entering a contraction section; leading to the main horizontal straight square test section, followed shortly by a 90° curvature. The combination of honeycomb, diffuser, wire-meshes (break up larger eddies) and contraction section creates uniform low turbulent flow of less than 0.5% of the free stream velocity.

The test section accommodates the wake generating body in which a symmetrical untripped NACA 0012 airfoil of 0.150 m chord length was used. The streamwise mean velocity component, normal and shear turbulence stresses where measured close to the trailing edge. The measurements were taken in the normal (radial) direction using DANTEC 90N10 constant temperature hot-wire anemometer system and a single cross-wire probe, namely DANTEC 55P63. The probe was aligned 0° at point of measurement, relative to horizontal plane of the laboratory coordinate system. The probe calibration was performed using a DANTEC calibrator system.

The static pressure distributions on the airfoil upper and lower surfaces were measured using 20 pressure tapping (Figure A1.3) connected to an electronic precision micro-manometer, in conjunction with a 20-channel pressure scanner box. The tubing from the airfoil was collectively arranged within the support of the airfoil, so not to disrupt flow.

Previous studies conducted using the same facilities, showed that the presence of the 90° bend creates curved wakes. The bend causes the free stream flow to approach the airfoil with an angle of 4°. In the present study the airfoil was positioned with a negative angle of attack of α=-3° by rotating the airfoil anticlockwise toward oncoming flow.

A Pitot-static tube was used to measure the static and stagnation pressures during the tunnel calibration. The end of the Pitot-static tube is turned through a 90° angle, so that it could face the air stream and be aligned parallel with the flow.

The static pressure drop across the contraction section was also measured in the tunnel calibration process. The static pressure drop was determined from pressure tappings located at the entrance and exit of the contraction assembly.

4. Calibration

The present investigation involved two types of calibration, namely, the wind tunnel calibration and the probe velocity calibration. For the stand alone cross wire probe an automated calibration procedure was followed with the StreamLine® calibrator.

4.1. Tunnel calibration

The aim of the tunnel calibration was to obtain a relationship between the static pressure drop along the contraction section of the tunnel, and the Pitot-static pressure reading at station 1. The procedure of tunnel calibration is as follows. The Pitot-static tube was set up at the mid-height of the test section. The difference between the stagnation pressure and the static pressure, which yields the dynamic pressure, was measured by connecting the static and stagnation pressure tapping to the digital micromanometer. The pressure tappings at the entrance and exit of contraction section are connected to another micro-manometer, to obtain the pressure difference across the contraction. The tunnel air velocity was progressively increased by increasing the speed of the centrifugal fan. At each incremental step the chamber pressure difference and the dynamic pressure from the Pitot-static tube were read. The atmospheric pressure and temperature were measured at the start and end of the tunnel calibration to monitor the changes in the ambient conditions.

The density of air ρa was calculated from,

(eq. 4.1)

Where, R is the gas constant for air and Pa is the static atmospheric pressure. The results from the tunnel calibration are plotted in Figure A2.1, showing a linear relationship between the contraction section pressure and the dynamic pressure.

During the experiments when the Pitot-static tube was removed, the velocity of air is calculated using the recorded dynamic pressure in conjunction with the atmospheric pressure and temperature which were measured using a barometer. The mainstream velocity Uo at station 1 was obtained using,

(eq. 4.2)

this can be rearranged, yielding,

(eq. 4.3)

In eq. 4.3 ρw is the density of water and g = 9.81 m/s2. The pressure difference across the Pitot-static tube hw (in mm of water) represents the dynamic pressure, which can be obtained using the linear relationship from tunnel calibration and the known chamber static pressure difference.

4.2. Hot wire calibration

The automatic calibration of the crosswire probe used in the wake measurements was conducted using the DANTEC StreamLine® calibrator with the StreamWare® application software. This is because it is time consuming to remove the wake generating body in order to calibrate the free stream velocity within the tunnel. Furthermore if the measurement device is not replaced in the same position inconsistencies between measurements would occur.

The process of probe velocity calibration aims to establish a relationship between the CTA bridge output voltage and the flow velocity. In an automatic calibration the probe sensors are exposed to a set of known or predetermined flow velocities.

The flow unit operates from a pressurized air supply from an external compressor and creates a free jet through an outlet nozzle. To achieve the desired air velocity range of 0 to 20 m/s, the correct diameter nozzle is used at the outlet of the flow unit. These nozzles designed to minimise the boundary layer development at the tip, and thus ensure a flat jet profile. A probe holder, mounted on top of the flow unit, was used to fix the probe into position to ensure that the prongs were parallel to the oncoming jet and located them in the centre of the free jet; ensuring the sensor is in line with the exit plane of the nozzle.

The StreamLine® system temperature probe was used to measure the ambient temperature changes during the calibration. As stated earlier, in a CTA, the current is adjusted to maintain a constant Rw and Tw. Provided that the surrounding air temperature Ta can be measured. The ambient temperature during the experiments can vary from the calibration temperature. Therefore StreamLine® system accommodates input from the temperature probe and uses temperature information to correct anemometer data (correct output voltage) when changes in the flow temperature occur, before velocity decomposition.

Upon initialization, StreamWare® automatically generated a set of equally spaced incremental velocity points that were based on the predefined velocity limits of the calibration and the number of specified calibration points in this case there are 10 points. At each calibration point, the flow unit automatically adjusted the velocity of the jet to achieve the closest value of the corresponding point generated by the StreamWare® software. This was done by way of several iterations, until the difference between the calculated air velocity and the measured air velocity was small enough that it satisfied the set maximum allowable error of the calibration. In the present investigation, a calibration error of ±0.5% was defined. Once the flow unit had achieved the desired air jet velocity, the StreamLine® frame automatically measured the corresponding output bridge voltage from the probe sensor. The process was repeated for all the generated calibration points. A fourth-order polynomial was then used to fit the calibration data for velocity U against output bridge voltage E, which was used by StreamWare® as a transfer function when converting the data from voltages into velocities.

5. Data acquisition

For time-averaged analysis such as mean velocity and RMS quantities it is required that the time between samples is at least two times larger than the time scale of the velocity fluctuations. In the present investigation the choice for the sampling frequency is based on the highest value used from previous work conducted. Such previous work also indicated that beyond the optimum sampling frequency there is no significant changes in the parameters of interest namely, mean velocity and RMS quantities. The experiment in the present study was conducted at a sampling frequency of 10 kHz for the mainstream velocity of 14.09m/s. A sampling time of 15 seconds was employed; this corresponds to a sample size of 150,000 samples per CTA channel for the mainstream velocity.

6. Discussion of Experimental Results

The results of measurements of static pressure on the airfoil mean velocity and turbulence quantities from the experimental investigations are discussed herein. The main results are divided into static pressure distribution, and the turbulent properties in the near wake region. Hot-wire measurements were conducted using a single stand alone cross-wire probe.

6.1. Normalized form of the experimental results

The mean velocity and turbulence quantities were normalized with respect to the free stream velocity at station 1. The pressure coefficient was calculated using the static pressure Po and freestream velocity Uo at station 1, from the relationship,

(eq. 6.1)

6.2. Tunnel calibration

The tunnel calibration is presented in Figure A2.1. There is a linear relationship between the dynamic pressure measured using a Pitot-static tube and the static pressure measured using pressure tappings on the contraction section.

6.3. Pressure distributions on the airfoil

The wake characteristics depend strongly on the boundary layer development on the airfoil, which in turn is influenced by the orientation of the airfoil with respect to the oncoming flow. Note that the angle of attack referred to here, represents the angle between the chord of the airfoil and the horizontal axis. The static pressure distributions over the upper and lower surfaces of the airfoil are presented in Figure A2.2. In this study the airfoil was rotated anti-clockwise (leading edge down) corresponding to a negative angle of attack of α=-3°.

The results show both upper and lower side pressure profiles approach the same distribution, where they begin to collapse and attain profiles which would be expected for an airfoil almost parallel to the oncoming flow. This agrees with previous work where the flow approaching the airfoil was found not to be parallel to the airfoil, but instead approaches with an angle of 4°. The results do show a slight difference in pressure distribution between the top and bottom sides, with a greater pressure on the underside, indicating generation of lift. This does suggest the airfoil was not completely aligned with the oncoming flow.

The pressure distribution for both top and bottom increase after tapping 10, which coincides with the maximum thickness of airfoil. The abrupt increase from tapping 10 to 12 on the upperside indicates the presence of a separation bubble, there is no evidence of flow separation on the lower side.

6.4. Consistency with previous work

The profiles of mean velocity and turbulence quantities measured at the mid-span, near the trailing edge of the airfoil presented in Figures A2.3 to A2.7, show the distributions are in good agreement with the previous measurements, in the wake with respect to the alignment of the flow at negative angle of attack. There are, however, small quantitative differences in the profiles of streamwise turbulence intensity and turbulence shear stress (Figures A2.6 and A2.7 respectively). There is an absence of the characteristic double peak in the streamwise turbulent intensity and the magnitude of the negative peak shear stress is greater than the positive peak stress. These differences may be attributed to differences in the experimental conditions.

6.5. Profiles of mean and turbulence quantities in the near-wake

The measurements were obtained using a rake accommodating the cross-wire sensor, which was located in the near wake x/c=1.05 from the trailing edge of the airfoil. Measurements were conducted at the midspan of the tunnel, z/H=0.5) location. The rake was traversed in the normal (y) direction so that the probe recorded a complete profile of the wake at this streamwise location. The mean velocity and turbulence intensity profiles are presented in Figures A2.3 to A2.7.

Streamwise mean velocity profile

The variation of mean velocity in the streamwise direction is presented in Figure A2.3. When an angle of attack is created the velocity and pressure distributions about the airfoil are modified causing changes in the main characteristics of the wake. The wake centerline is above the center line of the duct. The profile is almost symmetrical about the wake centre line, due to the alignment of the flow with the airfoil. The difference between free stream velocity and the wake velocity is greater on the inner side than the outer. This is because the presence of the bend causes the inner side velocity of the free stream to be greater than the free stream velocity of the outer side. The fluctuation of the profile on the inner side immediately after the wake is unexpected and is absent in previous work, this could suggest errors in the probe measurements. Contaminants are a possibility for the source of this error.

Normal mean velocity profile

Similar observations can be made of the normal mean velocity, which can be seen in Figure A2.4. However the results show a greater order of magnitude compared with the streamwise profile.

Streamwise turbulence intensity

The streamwise turbulent intensity measured is presented in Figure A2.5. The variation of turbulence intensity is almost symmetrical about the wake center line. This is in line with the results for the mean velocity profile stated earlier. The wake center line is positioned above the duct centerline much like the mean velocity profiles.

Normal turbulence intensity

The distribution of normal turbulence intensity near the trailing edge is presented in Figure A2.6. In contrast to the streamwise turbulence intensity, the profile of normal turbulence intensity displays an asymmetric distribution. Again similarly to the streamwise turbulence intensity the profile shows the wake centerline above the duct centerline.

Turbulence Shear stress

Figure A2.7 presents the profile of turbulence shear stress in the normal direction. The turbulence shear stress becomes zero and changes sign at the wake center, which coincides with the location of minimum velocity. The profile shows a positive peak on the inner side and a negative peak on the outer side, which correspond to points of maximum mean shear either side of the wake center line. The peaks are consistent with the alignment of the airfoil with the oncoming flow direction. The profile is asymmetric, with the magnitude of the negative peak lower than the positive peak, this does not show agreement with previous work where the opposite is true.

U and V Turb

The turbulence profiles for the streamwise and normal components U and V are presented in Figures A2.8 and A2.9, respectively. The turbulence measurements outside the wake are 0.7% and 0.5% respectively. This verifies that the flow exiting the contraction is uniform as was stated previously with a low percentage turbulence of typically 0.5%.

6.6. Instantaneous velocity components for point in free stream and point within wake

The instantaneous velocity components U and V are presented in Figures A2.10 to A2.13, for a single point within the wake region and for a single point in the free stream region. They show the magnitude of fluctuation within the wake region is greater than the fluctuation in the free stream, due to turbulent nature of the wake.

7. Conclusion

The experimental static pressure on the upper and lower surfaces of the airfoil, at the condition of α=-3° with respect to the horizontal, showed the results indicated favourable conditions for separation to occur on the upper surface near the trailing edge. Results indicated the presence of a separation bubble near the maximum thickness of the airfoil on the topside. The angle resulted in symmetrical distributions of pressure gradient profiles that would be expected for an airfoil parallel to the oncoming flow. From these results it was deduced that the approaching flow was not parallel to the airfoil but at an angle, which suggests that the flow angle imposed by the duct increased (negatively) with streamwise distance.

The mean velocity and turbulence intensity profiles in the wake were characterised by single peaks. The normal and streamwise profiles for mean velocity and the streamwise turbulent intensities all show symmetrical distribution about the wake centreline, with the exception of normal turbulence intensity. The effect of the curvature makes all the profiles offset above the duct centreline. The symmetrical profiles are in agreement with what is expected with the near alignment of the airfoil with oncoming flow.

Stresses displayed a single peak, and the profiles of turbulence shear stress in the wake were more strongly influenced by the curvature and pressure gradient than the normal stresses. The enhancement of turbulence on the inner side of the wake, and its suppression on the outer side, were as expected, based on previous work.

Appendix I: Wind tunnel and airfoil schematics

Figure A1.1: A schematic of the wind tunnel457



Station 2

Station 1

All dimensions in mm




Figure A1.2: A schematic of the airfoil depicting sign convention used for angle of attack (not drawn to scale).

Figure A1.3: Schematic of airfoil cross-section with locations of the pressure tappings.

Appendix II - Experimental Results

Figure A2.1: Tunnel Calibration.

Figure A2.2: Pressure coefficient on the airfoil.

Figure A2.3: Mean streamwise velocity in the wake region.

Figure A2.4: Mean normal velocity in the wake region.

Figure A2.5: Streamwise turbulence intensity in the wake region.

Figure A2.6: Normal turbulence intensity in the wake region.

Figure A2.7: Turbulence shear stress in the wake region.

Figure A2.8: U Turb in streamwise direction.

Figure A2.9: V Turb in normal direction.

Figure A2.10: Plot of instantaneous streamwise velocity U versus time for measurement point in free stream region

Figure A2.11: Plot of instantaneous normal velocity V versus time for measurement point in free stream region

Figure A2.12: Plot of instantaneous streamwise velocity U versus time for measurement point within wake.

Figure A2.13: Plot of instantaneous normal velocity V versus time for measurement point within wake.