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Stereoscopic PIV measurements of flow behind an isolated low-speed axial-fan
Experimental Thermal and Fluid Science 28 (2004) 791–802 www.elsevier.com/locate/etfs
Stereoscopic PIV measurements of flow behind an isolated low-speed axial-fan Jong-Hwan Yoon, Sang-Joon Lee
*
Department of Mechanical Engineering, Pohang University of Science and Technology, San 31, Hyo-Ja Dong, Pohang, 790-784, South Korea Received 9 September 2002; received in revised form 28 October 2003; accepted 28 October 2003
Abstract The flow field behind a forward-swept axial-fan with five blades rotating in a water tank has been measured by a stereoscopic particle image velocimetry (SPIV) system based on the translation configuration. In this study, a three-dimensional calibration procedure was employed to compensate the distortion and refraction of particle images. Phase-averaged velocity fields show that the flow behind an axial-fan has a periodic flow structure with respect to the blade phase and the characteristic flow structure is shifted downstream in the succeeding phase. The flow speed of fan wake has a local maximum value in the radial distance of about y=R ¼ 0:75. Strong counter-clockwise tip vortices are shed from the utmost trailing edges of the blade, while relatively weak clockwise trailing vortices exist in the hub region. The phase-averaged velocity and turbulence intensity of the out-of-plane velocity component have large values in the region near the tip vortices and they clearly show the evolution and dissipation of tip vortices and trailing vortices moving toward the tangential direction. 2003 Elsevier Inc. All rights reserved. Keywords: Stereoscopic PIV; Translation configuration; Axial-fan; Phase-averaging
1. Introduction Most fluid flows encountered in our lives are threedimensional (3-D) turbulent flows. Therefore, simultaneous measurement of three orthogonal velocity components is essential for the analysis of 3-D flows such as the flow around a fan or propeller. Conventional 2-D particle image velocimetry (PIV) velocity field measurement techniques using a single camera provide only in-plane velocity components. The information for the out-of-plane flow motion is embedded in the in-plane flow data and the out-of-plane velocity component becomes a source of error in the 2-D PIV measurements. This implies that most previous studies carried out with a 2-D PIV system have more or less perspective errors caused by the out-of-plane velocity component. Fig. 1 illustrates the perspective error ðDXp ¼ Dz M tan hÞ caused by the out-of-plane displacement ðDzÞ. In the case of constant magnification M, the perspective *
Corresponding author. Tel.: +82-54-279-2169; fax: +82-54-2793199. E-mail address: [email protected] (S.-J. Lee). 0894-1777/$ - see front matter 2003 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2003.10.004
error is directly proportional to the viewing angle subtended by the particle position to the optical axis of the recording device. The stereoscopic PIV (SPIV) method can eliminate the perspective error, yielding accurate 3D velocity information. The SPIV techniques usually employ two CCD cameras [1]. Each camera simultaneously captures the same particle displacements at a different angle. The measuring volume is confined by the thickness of the laser light sheet and the imaging area. Two cameras at different angles capture two particle images synchronized with a pulsed laser light sheet. The particle displacements inside the flow images captured by each camera are transposed to 3-D velocity field data by intermediate procedures. Prasad and Adrian [2] measured the flow field under a rotating disk using a SPIV technique with two cameras. They corrected the measurement errors causes by the interface between air, liquid and glass. Soloff et al. [3] acquired the relationship between the 3-D object field and 2-D image field at three different z-locations parallel to the object plane. The mapping function allows the particle displacements to be measured without the system geometry information during image reconstruction.
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Nomenclature R x y z u v w Utip
radius of the axial-fan axial coordinate axis radial coordinate axis tangential coordinate axis axial velocity component radial velocity component tangential velocity component blade tip speed
M Tu Tv Tw xz
Lawson and Wu [4,5] estimated the ratio of out-of-plane to in-plane errors as a function of the off-axis position, camera separation and/or viewing angle. They suggested optimal conditions for the angular displacement SPIV system. The details of SPIV and current state-of-the-art are summarized in the review article of Prasad [1]. One motivation of this study is to develop a precise SPIV system and verify its usefulness by applying it to a complicated 3-D flow behind an axial-fan. Axial-fans have been used in various applications ranged from small home appliances to large fans used in industrial sites. Sometimes they generate acoustic noise in some appliances. Such a problem can be resolved by developing a fan with high efficiency and low noise generation. In order to improve the fan efficiency and reduce the acoustic noise generation of axial-fans, accurate measurements of flow field around the fan is not only essential, but also indispensable for future development of similar turbomachines. Since the fan wake is a complicated 3-D flow, it is not easy to analyze the flow structure with theoretical and numerical means.
xi=(x,y,0) xr=(x+∆x,y+ ∆y,0)
Object plane
x
z
x f =(x+∆x,y+∆y,∆z) θ Lens plane
Xr
Xf X
Xi
Image plane
∆X p
Fig. 1. Perspective error caused by out-of-plane particle motion.
magnification factor fluctuation component of axial velocity pffiffiffiffiffiffi ð u02 =Utip Þ fluctuation component of radial velocity pffiffiffiffiffi ð v02 =Utip Þ fluctuation component of tangential velocity pffiffiffiffiffiffi ð w02 =Utip Þ ov tangential vorticity ox ou oy
Experimental investigations are the logical method to obtain the desired information. Ravindranath and Lakshminarayana [6] measured velocity profiles of flow behind compressor rotor blade using a tri-axial hot-wire probe rotating with the rotor. They found large velocity decay and rapid variation of wake width in the region near the trailing edge of the rotor blade. Inoue and Kuroumaru [7] used a slanted hot-wire anemometry to measure the flow around a compressor rotor. From the phase-averaged flow velocities measured at various points, they analyzed the vortex structures including the trailing vortex and the tip vortex. Morris et al. [8] measured the velocity distribution in the wake of an automotive cooling fan using a hot-wire anemometry. In general, hot-wire anemometry causes significant errors in the reverse flow region. They used a tuft method to determine the flow direction and the velocity signals from the hot-wire probe were phaseaveraged according to the rotation angle of the fan. They confirmed the periodic variation of the fan wake according to the fan blade phase. Accurate flow structure around turbomachinery using conventional pointwise measurement techniques is difficult to obtain due to the strong three-dimensionality and unsteadiness of the flow. Another problem encountered in pointwise measurements stems from the fact that data at different points are measured at different time. Although this problem can be resolved somewhat with adaptation of the conditional phaseaveraging method, however, it does not give the spatial distribution of time resolved data. Recently, PIV techniques have been accepted as a reliable velocity field measurement technique and have been applied to the study on flow around turbomachinery. Shepherd et al. [9] measured the flow around a centrifugal fan and an axial-fan using an optical PIV method. The double-exposed particle images recorded on 35 mm films were processed with the optical method using Fourier transform lens and traverse system. Phaseaveraged vector fields measured at one axial plane were displayed with a vorticity contour. The accuracy and
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spatial resolution of the optical PIV method are not so satisfactory compared with recent digital PIV methods. Sinha and Katz [10] used an auto-correlation PIV technique with a high-resolution CCD camera to measure the velocity fields inside a centrifugal pump according to the rotor phase. Estevadeordal et al. [11] investigated the flow structure in the blade-to-blade region of a low-speed axial-fan using the panel method numerically and PIV velocity field measurements. Wernet [12] applied a digital PIV system to measure flows in the blade passage region of a transonic axial compressor and the diffuser region of a high-speed centrifugal compressor. The time-averaged PIV results show clearly the high-speed fluid packets emerging from the impeller and the flow turning around the diffuser vanes. Three-dimensional flow behind an axial-fan has not been fully understood yet, especially on the phaseaveraged mean velocity field and turbulent structure. The main objective of this study is to investigate the flow structure around a rotating axial-fan model. Two 1 K · 1 K CCD cameras were employed with the SPIV velocity field measurement system. Phase-averaged mean velocity fields, vorticity fields, and turbulence intensity distributions were obtained by phase-averaging 500 velocity fields at several axial planes. These experimental data can be used for validation of numerical predictions and understanding the flow structure in the design process of axial-fans.
2. Stereoscopic PIV Two stereoscopic configurations have been used for SPIV measurements: the translation configuration and the angular displacement configuration. Fig. 2 shows camera arrangement for the translation method for
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SPIV system. In the translation configuration method, the stereoscopic effects are directly related to the distance between the optical axes of the cameras. The optical axis of the first camera is parallel to the optical axis of the second camera. These optical axes are aligned to be perpendicular to the illuminated measurement plane. However, the two optical axes for the angular configuration are neither parallel nor perpendicular to the measurement plane, because the image planes are tilted to focus the whole measuring volume. The tilting of image planes and camera lenses causes image distortion and varying magnification, requiring an elaborate correction process to obtain accurate flow data. We adopted the translation configuration in this study. The translation configuration is simple to apply and causes negligible image distortion compared with the angular configuration. The translation configuration has advantages of convenient mapping and well-focused image over the whole observation area. Since the off-axis aberration restricts the viewing angle, however, the optical lens was carefully chosen for reducing the offaxis aberration. For ray tracing with the translation configuration, it is needed to derive the geometric relationship between the real particle displacements Dx ¼ ðDx; Dy; DzÞ and the projected displacements DX ¼ ðDX1 ; DY1 ; DX2 ; DY2 Þ in the image-recording plane. However, variations of refractive index in the velocity field measurements of a liquid flow (as used in this study) cause optical aberrations and image distortion, giving rise to non-uniformity in the magnification. The image plane over which particle images can be obtained is no longer parallel to the object plane, but tilted slightly at some angle. A small aperture was used to resolve this problem. Image distortion and optical aberration were compensated using the approach developed by Soloff et al. [3]. The relationship between the 3-D object volume and 2-D image plane for each camera can be expressed as X ¼ F ðxÞ
ð1Þ
Here, X ¼ ðX1 ; Y1 ; X2 ; Y2 Þ represents the projected image position and x ¼ ðx; y; zÞ is the real particle position in the object volume. The mapping function F ðxÞ is approximated by a polynomial expression. Soloff et al. [3] used a polynomial that was cubic in the x and y coordinates and quadratic in the z coordinate. In usual translation configurations, however, the image distortion is negligible and the function F ðxÞ can be approximated by a simple polynomial. The simple polynomial function reduces the complexity of the mapping problem and allows easy calculation of the inverse mapping function from the image plane ðX1 ; Y1 ; X2 ; Y2 Þ to the object plane ðx; y; 0Þ. The particle displacement DX can be approximated as Fig. 2. Translation configuration of SPIV measurement.
rF ðxÞDx
ð2Þ
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Here, rF ðxÞ can be calculated from the measured mapping function F ðxÞ and four equations and three unknown particle displacements (Dx, Dy and Dz) can be derived. We arranged two CCD cameras in a symmetric configuration with the angle of h ¼ 8. The equations describing the displacements in the Y direction for the 1st and 2nd image planes were averaged to improve the measurement accuracy of DY1 and DY2 .
3. Experimental apparatus and procedure The SPIV velocity field measurement system consists of two 1 K · 1 K CCD cameras with stereoscopic lens, an Nd:YAG pulse laser, and a four-channel delay generator. The dual-head Nd:YAG laser has a pulse width of 7 ns with a maximum pulse repetition rate of 20 Hz for each head. The stereoscopic lenses employed in this study have special features for tilting and shifting the lenses without any additional adaptors or stages. They were specially designed to minimize optical aberrations and showed high optical performance throughout the experiments. SPIV measurements were carried out in a transparent water tank (340 · 280 · 280 mm) made of acrylic plates. A lid covers the upper free surface to eliminate the free surface effect. As the light ray is passing through the water–air interface, the magnification factor and incident angle are changed by the water–air interface. The ray tracing method [2] has been usually used for the translation configuration SPIV system. However, more general and versatile 3-D calibration method was adopted in this study. The water–air interface between the lens and object plane decreases the incident angle due to larger refractive index of water compared with that of air. Therefore, the perspective error for liquid flow measurements is smaller than that for air flow measurements with the same optical system. The 2-D PIV data for each of the left and right image planes were calculated and interpolated into a rectangular grid of physical object plane. Using the predetermined 3-D calibration results, an augmented system is formed and the 2-D flow displacements are converted into 3-D flow displacement information. Fig. 3 shows schematic diagrams of the axial-fan and the field of view for axial plane measurements. The axial-fan tested in this study has five forward-swept blades. The tip-to-tip diameter and hub diameter of the fan are 50 and 14.3 mm, respectively, leading to a hub-to-tip ratio of 0.286. The isolated axial-fan without casing was installed inside the rectangular water basin. The fan is a 1/10 scale-down model of an outdoor cooling fan used for commercial air-conditioners (LG Electronics Inc.). It is usually operated under a relatively low head. Specifications of the axial-fan tested in this study are listed in Table 1.
(a)
y Flow Direction
Field of view
x
(b) Fig. 3. Schematic diagram of axial-fan and measurement planes: (a) axial fan and four phases, (b) field of view.
Table 1 Specifications of the forward-swept axial-fan tested in this study Tip diameter Hub diameter No. of blades Tip sweep angle Tip rake angle Blade thickness Hub angle Max. camber position Blade space at hub Blade space at mid-span Blade space at nose Blade space at tip
50.0 mm 14.3 mm 5 33 0 2.0 mm 0 0.50 1.67 mm 4.10 mm 3.41 mm 8.88 mm
The SPIV measurements were carried out for four phases shown in Fig. 3(a). A delay generator was used to synchronize the pulse laser and two CCD cameras with phase angle of the axial-fan. The encoder mounted on the servomotor generates trigger signals to synchronize the laser and CCD camera with the resolution of 0.36 for each selected angular position. The signals from the encoder were low-pass filtered to eliminate embedded noise. The time interval between two consecutive parti-
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cle images was set to 1 ms, for which the axial-fan rotates 1.08. Five hundred instantaneous velocity fields were measured for each phase of the fan blade. They were ensemble averaged to obtain the spatial distributions of the phase-averaged mean velocity and turbulence statistics. Tap water was used as the working fluid and silver-coated hollow glass particles of mean diameter of 13 lm were seeded as tracer particles. The rotation speed of the axial-fan was set to 180 rpm throughout the experiments. The SPIV system was calibrated using a rectangular calibration target on which white dots were evenly distributed. The dot diameter was 0.5 mm and the spacing between neighboring dots was 2.5 mm. A translation stage equipped with a micrometer was used to traverse the calibration target aligned with the laser light sheet. The calibration images were captured by two CCD cameras at five different z-planes by translating the calibration target along the z-axis. The mapping function F ðxÞ was calculated using a centroid detection algorithm and least square method. On average, the residual of the approximated mapping function F ðxÞ was smaller than 0.3 pixels for each camera.
4. Results and discussion Table 2 summarizes calibration results of the translation-type SPIV system employed in this study. For rigid body translations, the bias error of in-plane velocity components ðDx; DyÞ is less than about 1.4% and that of the out-of-plane velocity component ðDzÞ is less than about 6.8%. The maximum RMS errors of the in-plane and out-of-plane velocity components are 1.0% and 4.4%, respectively. This indicates that the present camera arrangement causes relatively large error for the out-of-plane velocity component. Lawson and Wu [4] mentioned that the error ratio is dependent on the ratio of camera separation and distance between the object plane and lens in the central region of measuring plane.
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In this study, due to restriction of lateral shifting distance, the measurement errors of the out-of-plane velocity component are about 5 times larger than those of the in-plane velocity components. The spatial distributions of phase-averaged in-plane velocity vectors ðu; vÞ marked as arrows and contour plots of the out-of-plane velocity component ðwÞ at each blade phase are included in Fig. 4. The phase-averaged mean velocity fields clearly show the periodic variation of flow structure behind the axial-fan according to the phase change. At phases 1 and 2, the high-momentum fluid moving toward the center axis of fan wake is clearly observed in the region just behind the fan blade ðx=R 0:4Þ. However, the flow moving outward from the center axis of fan wake is dominant at phase 3. The high-momentum fluid moves slightly toward the hub again at phase 4. The magnitude of in-plane flow speed ðu2 þ v2 Þ1=2 had a maximum value in the mid section of the blade ðy=R 0:75Þ irrespective of phase angle. This result agrees well with the previous study [8]. In the region of x=R > 0:6, the fluid moves outward from the center axis of axial-fan wake regardless of fan phase. The recirculation flow is observed in the hub region ðy=R < 0:3Þ near the axis of rotation and the recirculation region expands with going downstream. The out-of-plane velocity component also shows the periodic variation with respect to the fan phase, especially along the y=R ¼ 0:8 line. The strong out-of-plane velocity ðwÞ exists in the region around the point x=R ¼ 0:2, y=R ¼ 0:8 at phase 1. Then this peak location moves downstream along the horizontal direction through phases 2 and 3. The maximum out-of-plane velocity component occur at the downstream locations of about x=R ¼ 0:35 and 0.5 at phases 2 and 3, respectively. The peak location at phase 4 occurs at x=R ¼ 0:65, but the velocity magnitude is largely decreased and velocity gradient in the near-by region is smoothed, compared with those at previous phases. The region of large out-of-plane velocity component is closely related to the tip vortices shed from the fan blade.
Table 2 Comparison between the preset and measured values for rigid body translations (unit: lm) Real value
Measured In-plane components Dx
Out-of-plane component Dy
Dz
Dy ¼ 500
Mean RMS
)7.0 2.5
501.9 1.6
34.8 10.3
Dz ¼ 2000
Mean RMS
4.5 9.5
1.3 6.2
1958.4 44.7
Dx ¼ 1000, Dy ¼ 1000, Dz ¼ 1000
Mean RMS
1014.4 9.9
1009.5 7.2
1029.3 45.1
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Fig. 4. Spatial distributions of in-plane velocity vectors and out-of-plane velocity contours: (a) phase 1, (b) phase 2, (c) phase 3, (d) phase 4.
From this, we can conjecture that the continuously shed tip vortex is observed at the outermost tip of the fan blade between phases 3 and 4. From the phase-averaged mean velocity field information, the flow structure in the axial plane can be divided into three regions: (1) the immediate wake region where the flow of high-momentum exists and the flow direction changes up and down according to phase angle, (2) the region where the flow is directed away from the axis of rotation, (3) the far wake region where the phase-averaged flow pattern is almost invariant. In far wake region, the velocity magnitude is decreased considerably at further downstream locations, compared with the magnitudes in the near wake field. However, the general flow structure is nearly unchanged regardless of the fan phase. From these results, we can see that the fan blade phase affects dominantly the near wake flow just behind
the axial-fan ðx=R < 0:6Þ. The periodic flow structure according to the phase angle was confirmed through the phase-averaged velocity field data where the flow structure is shifted downstream as the fan rotates from phases 1 to 4. Fig. 5 shows the contours of mean axial velocity component at four different phases. At downstream location of x=R ¼ 0:3, the maximum axial velocity occurs at the mid section of the blade in the range of 0:7 < y=R < 0:8 as shown in Fig. 5(a). Though direct quantitative comparison is difficult due to different fan shape and dissimilar experimental conditions, the general flow structure is in a good agreement with the results of Morris et al. [8] in which the maximum velocity occurs at the mid section ð0:7 < y=R < 0:8Þ at x=R ¼ 0:172. The negative axial-velocity marked as dotted lines exists in the hub region y=R < 0:3. The variation of mean axial velocity with respect to the fan
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Fig. 5. Contour plots of the mean axial velocity component: (a) phase 1, (b) phase 2, (c) phase 3, (d) phase 4.
blade phase is not so large at the downstream region of x=R > 0:6 and in the hub region of y=R < 0:3. The contour plots of the phase-averaged radial velocity component are shown in Fig. 6. The radial velocity distributions show large variation according to the phase angle. In the region of x=R < 0:3, y=R ¼ 0:4–0:7, the radial velocity component has negative values at phases 1 and 2, whereas it turns to positive values at phases 3 and 4. The negative radial velocity may be attributed to the forward-swept geometry of the fan blade that induces trailing vortices at the blade trailing edge between phases 1 and 2. Morris et al. [9] showed that the negative radial velocity component only exists in the region of blade gap around y=R ¼ 0:6. 2-D projection of trajectory of the trailing vortices can be conjectured by tracing the spots having negative radial velocity component. The trailing vortex seems to move toward the hub and shifts downstream direction as the
fan rotates. The trailing vortex is elongated in the radial direction at phases 1 and 2 due to the oncoming flow from the suction side of the fan blade. The positive radial velocity in the region 0:5 < y=R < 0:9 at phases 3 and 4 indicates that the pressure side of the fan blade influences the flow structure and the flow moves outward from the axis of rotation of the fan. The variation of the radial velocity component distribution with respect to the fan phase tends to decrease as the distance from the fan increases. At phases 3 and 4, the radial velocity component has small negative values in the region of y=R > 1:1, over the tip of the fan blade. It may be attributed to the influx of ambient fluid toward the blade tip and generation of the tip vortex between phases 3 and 4. Fig. 7 represents a 3-D display of contours having the same flow speed ðu2 þ v2 þ w2 Þ1=2 . The flow speed is closely related with the pressure distribution and loading of the axial-fan. The flow speed shows small variation in
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Fig. 6. Contour plots of the mean radial velocity component: (a) phase 1, (b) phase 2, (c) phase 3, (d) phase 4.
Fig. 7. 3-D flow structure reconstructed using mean flow speed data.
the azimuthal direction and the maximum loading of the fan occurs at about y=R ¼ 0:75. The flow speed is decreased gradually as the flow goes downstream as discussed in the previous mean velocity field results. Fig. 8 represents the contour plots of tangential vorticity ðxz Þ derived from the phase-averaged velocity field data. This clearly shows the evolution of the tip vortices and trailing vortices according to the fan blade phase. At phase 1, positive tip vortices are located in the region behind the blade tip. The region between the axis of rotation and the mid-section of the fan blade has negative vorticity. At phase 1, a large-scale negative vortex rotating clockwise direction is observed around the location (x=R ¼ 0:25, y=R ¼ 0:4). The tip vortex located at x=R ¼ 0:2 at phase 1 is moved downstream and its center is shifted to x=R ¼ 0:3 at phase 2. The negative vortices at phases 1 and 2 seem to be caused by the trailing vortices located in the blade spacing. At phase 3,
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Fig. 8. Contour plots of mean tangential vorticity xz : (a) phase 1, (b) phase 2, (c) phase 3, (d) phase 4.
another large-scale negative vortex is newly shed from the blade. The negative vortex moves outward from the axis of rotation as the flow goes downstream. This outward motion pushed the positive tip vortices outward with going downstream. The negative vortices located in the lower wake region near the axis of rotation are elongated along the x-axis. The negative vortices at phases 3 and 4 are caused by the swept flow by the pressure side of the fan blade. Two large-scale vortices exist behind the blade tip at phase 1. The center distance between two vortices is about 0.35R. At phase 2, the positive vortices move downward to the axis of rotation and their magnitude is diminished slightly. At phase 4, the tip vortex shed at the previous phase is moved downstream and a new positive tip vortex is shed from the blade tip. These results show the periodic generation and diffusion of the tip and trailing vortices with respect to the phase angle of the fan blade.
The contour plot of equi-tangential vorticity ðxz Þ surface is depicted in Fig. 9. This iso-vorticity surface distribution is difficult to obtain with conventional 2-D PIV measurements and useful to figure out the 3-D vortex structure embedded in the complex axial-fan wake. It shows the quasi-3-D distribution of positive tip vortices shed from the blade tip, trailing vortices and the negative vortices induced by pressure side of fan blade. The positive tip vortices and negative vortices interact strongly in the region 0:6 < y=R < 0:8, as shown in Fig. 9. This seems to be closely related with the maximum loading of the fan at the section of y=R ¼ 0:75. The spatial distributions of the phase-averaged turbulence intensities of three velocity components measured using the SPIV method are shown in Figs. 10–12. Each turbulence intensity distribution was obtained by ensemble phase-averaging of 500 instantaneous velocity fields. The turbulence intensity distributions also show periodic variations according to the fan blade phase.
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Fig. 9. 3-D iso-vorticity structure of tangential vorticity xz .
The axial turbulence intensity has local minimum values in the immediate wake region near y=R ¼ 0:7 behind of the fan blade at phases 1, 3 and 4. However, the radial and tangential turbulence intensities are not so small in this region. Especially, they have large values at phase 2 due to the unblocked space between the fan blades and strong flow interaction with the trailing vortices. In the hub region near the axis of rotation, the three turbulence intensities have small values. It is interesting to compare the three turbulence intensities in the far wake region of x=R > 1. The axial turbulence intensity has large values around the mid height section ðy=R ¼ 0:4–0:6Þ. The location of maximum radial turbulence intensity moves outward in diagonal direction as the fluid goes downstream. However, the tangential turbulence intensity has relatively
Fig. 10. Variations of axial turbulence intensity distribution: (a) phase 1, (b) phase 2, (c) phase 3, (d) phase 4.
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Fig. 11. Variations of radial turbulence intensity distribution: (a) phase 1, (b) phase 2, (c) phase 3, (d) phase 4.
small values in the far wake region. In addition, the local maximum values exist in an alternating manner, resulting from the periodic flow structure and alternating shedding of the tip and trailing vortices. The axial turbulence intensity distributions seem to have close relationships with the tip and trailing vortices shown in Fig. 8. On the other hand, the spatial distributions of the radial and tangential turbulence intensities seem to be influenced dominantly by the tip vortices. The complete experimental data set is available on the website (http:// efcl.postech.ac.kr/data).
5. Conclusion A SPIV technique based on the translation configuration was applied to the flow behind an axial-fan with
five forward-swept blades. The phase-averaged mean velocity fields show a periodic flow structure according to the phase angle of fan blade. The characteristic flow structure at each phase is shifted downstream in the subsequent phase. The counter-clockwise tip vortices are shed from the utmost tip of the blade, while clockwise trailing vortices exist near the hub region. The flow speed of fan wake has a local maximum value in the radial distance of about y=R ¼ 0:75 and has small variation in the azimuthal direction. The region of large outof-plane velocity component is closely related to the tip vortices shed from the blade tip. The spatial distribution of out-of-plane velocity component clearly shows the evolution and dissipation of tip vortices. These experimental data can be used for the validation of numerical predictions and understanding the flow structure in the designing process of axial-fans.
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Fig. 12. Variations of tangential turbulence intensity distribution: (a) phase 1, (b) phase 2, (c) phase 3, (d) phase 4.
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[7] M. Inoue, M. Kuroumaru, Three-dimensional structure and decay of vortices behind an axial flow rotating blade row, J. Eng. Gas Turbines Power 106 (1984) 561–569. [8] S.C. Morris, J.J. Good, J.F. Foss, Velocity measurements in the wake of an automotive cooling fan, Exp. Thermal Fluid Sc. 17 (1998) 100–106. [9] I.C. Shepherd, R.F.L. Fotaine, L.W. Welch, R.J. Downie, Velocity measurement in fan rotors using particle image velocimetry, Laser Anemometry-1994: Advances and Applications ASME FED, vol. 191, 1994, pp. 179–183. [10] M. Sinha, J. Katz, Flow structure and turbulence in a centrifugal pump with a vaned diffuser, in: Proc. 1998 ASME Fluids Engineering Division Summer Meeting, Washington DC, FEDSM98, 21–25 June 1998, p. 5129. [11] J. Estevadeordal, S. Gorgineni, W. Copenhaver, G. Bloch, M. Brendel, Flow field in a low-speed axial fan: a DPIV investigation, Exp. Thermal Fluid Sci. 23 (2000) 11–21. [12] M.P. Wernet, Development of digital particle velocimetry for use in turbomachinery, Exp. Fluids 28 (2000) 97–115.
Stereoscopic PIV measurements of flow behind an isolated low-speed axial-fan Jong-Hwan Yoon, Sang-Joon Lee
*
Department of Mechanical Engineering, Pohang University of Science and Technology, San 31, Hyo-Ja Dong, Pohang, 790-784, South Korea Received 9 September 2002; received in revised form 28 October 2003; accepted 28 October 2003
Abstract The flow field behind a forward-swept axial-fan with five blades rotating in a water tank has been measured by a stereoscopic particle image velocimetry (SPIV) system based on the translation configuration. In this study, a three-dimensional calibration procedure was employed to compensate the distortion and refraction of particle images. Phase-averaged velocity fields show that the flow behind an axial-fan has a periodic flow structure with respect to the blade phase and the characteristic flow structure is shifted downstream in the succeeding phase. The flow speed of fan wake has a local maximum value in the radial distance of about y=R ¼ 0:75. Strong counter-clockwise tip vortices are shed from the utmost trailing edges of the blade, while relatively weak clockwise trailing vortices exist in the hub region. The phase-averaged velocity and turbulence intensity of the out-of-plane velocity component have large values in the region near the tip vortices and they clearly show the evolution and dissipation of tip vortices and trailing vortices moving toward the tangential direction. 2003 Elsevier Inc. All rights reserved. Keywords: Stereoscopic PIV; Translation configuration; Axial-fan; Phase-averaging
1. Introduction Most fluid flows encountered in our lives are threedimensional (3-D) turbulent flows. Therefore, simultaneous measurement of three orthogonal velocity components is essential for the analysis of 3-D flows such as the flow around a fan or propeller. Conventional 2-D particle image velocimetry (PIV) velocity field measurement techniques using a single camera provide only in-plane velocity components. The information for the out-of-plane flow motion is embedded in the in-plane flow data and the out-of-plane velocity component becomes a source of error in the 2-D PIV measurements. This implies that most previous studies carried out with a 2-D PIV system have more or less perspective errors caused by the out-of-plane velocity component. Fig. 1 illustrates the perspective error ðDXp ¼ Dz M tan hÞ caused by the out-of-plane displacement ðDzÞ. In the case of constant magnification M, the perspective *
Corresponding author. Tel.: +82-54-279-2169; fax: +82-54-2793199. E-mail address: [email protected] (S.-J. Lee). 0894-1777/$ - see front matter 2003 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2003.10.004
error is directly proportional to the viewing angle subtended by the particle position to the optical axis of the recording device. The stereoscopic PIV (SPIV) method can eliminate the perspective error, yielding accurate 3D velocity information. The SPIV techniques usually employ two CCD cameras [1]. Each camera simultaneously captures the same particle displacements at a different angle. The measuring volume is confined by the thickness of the laser light sheet and the imaging area. Two cameras at different angles capture two particle images synchronized with a pulsed laser light sheet. The particle displacements inside the flow images captured by each camera are transposed to 3-D velocity field data by intermediate procedures. Prasad and Adrian [2] measured the flow field under a rotating disk using a SPIV technique with two cameras. They corrected the measurement errors causes by the interface between air, liquid and glass. Soloff et al. [3] acquired the relationship between the 3-D object field and 2-D image field at three different z-locations parallel to the object plane. The mapping function allows the particle displacements to be measured without the system geometry information during image reconstruction.
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Nomenclature R x y z u v w Utip
radius of the axial-fan axial coordinate axis radial coordinate axis tangential coordinate axis axial velocity component radial velocity component tangential velocity component blade tip speed
M Tu Tv Tw xz
Lawson and Wu [4,5] estimated the ratio of out-of-plane to in-plane errors as a function of the off-axis position, camera separation and/or viewing angle. They suggested optimal conditions for the angular displacement SPIV system. The details of SPIV and current state-of-the-art are summarized in the review article of Prasad [1]. One motivation of this study is to develop a precise SPIV system and verify its usefulness by applying it to a complicated 3-D flow behind an axial-fan. Axial-fans have been used in various applications ranged from small home appliances to large fans used in industrial sites. Sometimes they generate acoustic noise in some appliances. Such a problem can be resolved by developing a fan with high efficiency and low noise generation. In order to improve the fan efficiency and reduce the acoustic noise generation of axial-fans, accurate measurements of flow field around the fan is not only essential, but also indispensable for future development of similar turbomachines. Since the fan wake is a complicated 3-D flow, it is not easy to analyze the flow structure with theoretical and numerical means.
xi=(x,y,0) xr=(x+∆x,y+ ∆y,0)
Object plane
x
z
x f =(x+∆x,y+∆y,∆z) θ Lens plane
Xr
Xf X
Xi
Image plane
∆X p
Fig. 1. Perspective error caused by out-of-plane particle motion.
magnification factor fluctuation component of axial velocity pffiffiffiffiffiffi ð u02 =Utip Þ fluctuation component of radial velocity pffiffiffiffiffi ð v02 =Utip Þ fluctuation component of tangential velocity pffiffiffiffiffiffi ð w02 =Utip Þ ov tangential vorticity ox ou oy
Experimental investigations are the logical method to obtain the desired information. Ravindranath and Lakshminarayana [6] measured velocity profiles of flow behind compressor rotor blade using a tri-axial hot-wire probe rotating with the rotor. They found large velocity decay and rapid variation of wake width in the region near the trailing edge of the rotor blade. Inoue and Kuroumaru [7] used a slanted hot-wire anemometry to measure the flow around a compressor rotor. From the phase-averaged flow velocities measured at various points, they analyzed the vortex structures including the trailing vortex and the tip vortex. Morris et al. [8] measured the velocity distribution in the wake of an automotive cooling fan using a hot-wire anemometry. In general, hot-wire anemometry causes significant errors in the reverse flow region. They used a tuft method to determine the flow direction and the velocity signals from the hot-wire probe were phaseaveraged according to the rotation angle of the fan. They confirmed the periodic variation of the fan wake according to the fan blade phase. Accurate flow structure around turbomachinery using conventional pointwise measurement techniques is difficult to obtain due to the strong three-dimensionality and unsteadiness of the flow. Another problem encountered in pointwise measurements stems from the fact that data at different points are measured at different time. Although this problem can be resolved somewhat with adaptation of the conditional phaseaveraging method, however, it does not give the spatial distribution of time resolved data. Recently, PIV techniques have been accepted as a reliable velocity field measurement technique and have been applied to the study on flow around turbomachinery. Shepherd et al. [9] measured the flow around a centrifugal fan and an axial-fan using an optical PIV method. The double-exposed particle images recorded on 35 mm films were processed with the optical method using Fourier transform lens and traverse system. Phaseaveraged vector fields measured at one axial plane were displayed with a vorticity contour. The accuracy and
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spatial resolution of the optical PIV method are not so satisfactory compared with recent digital PIV methods. Sinha and Katz [10] used an auto-correlation PIV technique with a high-resolution CCD camera to measure the velocity fields inside a centrifugal pump according to the rotor phase. Estevadeordal et al. [11] investigated the flow structure in the blade-to-blade region of a low-speed axial-fan using the panel method numerically and PIV velocity field measurements. Wernet [12] applied a digital PIV system to measure flows in the blade passage region of a transonic axial compressor and the diffuser region of a high-speed centrifugal compressor. The time-averaged PIV results show clearly the high-speed fluid packets emerging from the impeller and the flow turning around the diffuser vanes. Three-dimensional flow behind an axial-fan has not been fully understood yet, especially on the phaseaveraged mean velocity field and turbulent structure. The main objective of this study is to investigate the flow structure around a rotating axial-fan model. Two 1 K · 1 K CCD cameras were employed with the SPIV velocity field measurement system. Phase-averaged mean velocity fields, vorticity fields, and turbulence intensity distributions were obtained by phase-averaging 500 velocity fields at several axial planes. These experimental data can be used for validation of numerical predictions and understanding the flow structure in the design process of axial-fans.
2. Stereoscopic PIV Two stereoscopic configurations have been used for SPIV measurements: the translation configuration and the angular displacement configuration. Fig. 2 shows camera arrangement for the translation method for
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SPIV system. In the translation configuration method, the stereoscopic effects are directly related to the distance between the optical axes of the cameras. The optical axis of the first camera is parallel to the optical axis of the second camera. These optical axes are aligned to be perpendicular to the illuminated measurement plane. However, the two optical axes for the angular configuration are neither parallel nor perpendicular to the measurement plane, because the image planes are tilted to focus the whole measuring volume. The tilting of image planes and camera lenses causes image distortion and varying magnification, requiring an elaborate correction process to obtain accurate flow data. We adopted the translation configuration in this study. The translation configuration is simple to apply and causes negligible image distortion compared with the angular configuration. The translation configuration has advantages of convenient mapping and well-focused image over the whole observation area. Since the off-axis aberration restricts the viewing angle, however, the optical lens was carefully chosen for reducing the offaxis aberration. For ray tracing with the translation configuration, it is needed to derive the geometric relationship between the real particle displacements Dx ¼ ðDx; Dy; DzÞ and the projected displacements DX ¼ ðDX1 ; DY1 ; DX2 ; DY2 Þ in the image-recording plane. However, variations of refractive index in the velocity field measurements of a liquid flow (as used in this study) cause optical aberrations and image distortion, giving rise to non-uniformity in the magnification. The image plane over which particle images can be obtained is no longer parallel to the object plane, but tilted slightly at some angle. A small aperture was used to resolve this problem. Image distortion and optical aberration were compensated using the approach developed by Soloff et al. [3]. The relationship between the 3-D object volume and 2-D image plane for each camera can be expressed as X ¼ F ðxÞ
ð1Þ
Here, X ¼ ðX1 ; Y1 ; X2 ; Y2 Þ represents the projected image position and x ¼ ðx; y; zÞ is the real particle position in the object volume. The mapping function F ðxÞ is approximated by a polynomial expression. Soloff et al. [3] used a polynomial that was cubic in the x and y coordinates and quadratic in the z coordinate. In usual translation configurations, however, the image distortion is negligible and the function F ðxÞ can be approximated by a simple polynomial. The simple polynomial function reduces the complexity of the mapping problem and allows easy calculation of the inverse mapping function from the image plane ðX1 ; Y1 ; X2 ; Y2 Þ to the object plane ðx; y; 0Þ. The particle displacement DX can be approximated as Fig. 2. Translation configuration of SPIV measurement.
rF ðxÞDx
ð2Þ
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Here, rF ðxÞ can be calculated from the measured mapping function F ðxÞ and four equations and three unknown particle displacements (Dx, Dy and Dz) can be derived. We arranged two CCD cameras in a symmetric configuration with the angle of h ¼ 8. The equations describing the displacements in the Y direction for the 1st and 2nd image planes were averaged to improve the measurement accuracy of DY1 and DY2 .
3. Experimental apparatus and procedure The SPIV velocity field measurement system consists of two 1 K · 1 K CCD cameras with stereoscopic lens, an Nd:YAG pulse laser, and a four-channel delay generator. The dual-head Nd:YAG laser has a pulse width of 7 ns with a maximum pulse repetition rate of 20 Hz for each head. The stereoscopic lenses employed in this study have special features for tilting and shifting the lenses without any additional adaptors or stages. They were specially designed to minimize optical aberrations and showed high optical performance throughout the experiments. SPIV measurements were carried out in a transparent water tank (340 · 280 · 280 mm) made of acrylic plates. A lid covers the upper free surface to eliminate the free surface effect. As the light ray is passing through the water–air interface, the magnification factor and incident angle are changed by the water–air interface. The ray tracing method [2] has been usually used for the translation configuration SPIV system. However, more general and versatile 3-D calibration method was adopted in this study. The water–air interface between the lens and object plane decreases the incident angle due to larger refractive index of water compared with that of air. Therefore, the perspective error for liquid flow measurements is smaller than that for air flow measurements with the same optical system. The 2-D PIV data for each of the left and right image planes were calculated and interpolated into a rectangular grid of physical object plane. Using the predetermined 3-D calibration results, an augmented system is formed and the 2-D flow displacements are converted into 3-D flow displacement information. Fig. 3 shows schematic diagrams of the axial-fan and the field of view for axial plane measurements. The axial-fan tested in this study has five forward-swept blades. The tip-to-tip diameter and hub diameter of the fan are 50 and 14.3 mm, respectively, leading to a hub-to-tip ratio of 0.286. The isolated axial-fan without casing was installed inside the rectangular water basin. The fan is a 1/10 scale-down model of an outdoor cooling fan used for commercial air-conditioners (LG Electronics Inc.). It is usually operated under a relatively low head. Specifications of the axial-fan tested in this study are listed in Table 1.
(a)
y Flow Direction
Field of view
x
(b) Fig. 3. Schematic diagram of axial-fan and measurement planes: (a) axial fan and four phases, (b) field of view.
Table 1 Specifications of the forward-swept axial-fan tested in this study Tip diameter Hub diameter No. of blades Tip sweep angle Tip rake angle Blade thickness Hub angle Max. camber position Blade space at hub Blade space at mid-span Blade space at nose Blade space at tip
50.0 mm 14.3 mm 5 33 0 2.0 mm 0 0.50 1.67 mm 4.10 mm 3.41 mm 8.88 mm
The SPIV measurements were carried out for four phases shown in Fig. 3(a). A delay generator was used to synchronize the pulse laser and two CCD cameras with phase angle of the axial-fan. The encoder mounted on the servomotor generates trigger signals to synchronize the laser and CCD camera with the resolution of 0.36 for each selected angular position. The signals from the encoder were low-pass filtered to eliminate embedded noise. The time interval between two consecutive parti-
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cle images was set to 1 ms, for which the axial-fan rotates 1.08. Five hundred instantaneous velocity fields were measured for each phase of the fan blade. They were ensemble averaged to obtain the spatial distributions of the phase-averaged mean velocity and turbulence statistics. Tap water was used as the working fluid and silver-coated hollow glass particles of mean diameter of 13 lm were seeded as tracer particles. The rotation speed of the axial-fan was set to 180 rpm throughout the experiments. The SPIV system was calibrated using a rectangular calibration target on which white dots were evenly distributed. The dot diameter was 0.5 mm and the spacing between neighboring dots was 2.5 mm. A translation stage equipped with a micrometer was used to traverse the calibration target aligned with the laser light sheet. The calibration images were captured by two CCD cameras at five different z-planes by translating the calibration target along the z-axis. The mapping function F ðxÞ was calculated using a centroid detection algorithm and least square method. On average, the residual of the approximated mapping function F ðxÞ was smaller than 0.3 pixels for each camera.
4. Results and discussion Table 2 summarizes calibration results of the translation-type SPIV system employed in this study. For rigid body translations, the bias error of in-plane velocity components ðDx; DyÞ is less than about 1.4% and that of the out-of-plane velocity component ðDzÞ is less than about 6.8%. The maximum RMS errors of the in-plane and out-of-plane velocity components are 1.0% and 4.4%, respectively. This indicates that the present camera arrangement causes relatively large error for the out-of-plane velocity component. Lawson and Wu [4] mentioned that the error ratio is dependent on the ratio of camera separation and distance between the object plane and lens in the central region of measuring plane.
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In this study, due to restriction of lateral shifting distance, the measurement errors of the out-of-plane velocity component are about 5 times larger than those of the in-plane velocity components. The spatial distributions of phase-averaged in-plane velocity vectors ðu; vÞ marked as arrows and contour plots of the out-of-plane velocity component ðwÞ at each blade phase are included in Fig. 4. The phase-averaged mean velocity fields clearly show the periodic variation of flow structure behind the axial-fan according to the phase change. At phases 1 and 2, the high-momentum fluid moving toward the center axis of fan wake is clearly observed in the region just behind the fan blade ðx=R 0:4Þ. However, the flow moving outward from the center axis of fan wake is dominant at phase 3. The high-momentum fluid moves slightly toward the hub again at phase 4. The magnitude of in-plane flow speed ðu2 þ v2 Þ1=2 had a maximum value in the mid section of the blade ðy=R 0:75Þ irrespective of phase angle. This result agrees well with the previous study [8]. In the region of x=R > 0:6, the fluid moves outward from the center axis of axial-fan wake regardless of fan phase. The recirculation flow is observed in the hub region ðy=R < 0:3Þ near the axis of rotation and the recirculation region expands with going downstream. The out-of-plane velocity component also shows the periodic variation with respect to the fan phase, especially along the y=R ¼ 0:8 line. The strong out-of-plane velocity ðwÞ exists in the region around the point x=R ¼ 0:2, y=R ¼ 0:8 at phase 1. Then this peak location moves downstream along the horizontal direction through phases 2 and 3. The maximum out-of-plane velocity component occur at the downstream locations of about x=R ¼ 0:35 and 0.5 at phases 2 and 3, respectively. The peak location at phase 4 occurs at x=R ¼ 0:65, but the velocity magnitude is largely decreased and velocity gradient in the near-by region is smoothed, compared with those at previous phases. The region of large out-of-plane velocity component is closely related to the tip vortices shed from the fan blade.
Table 2 Comparison between the preset and measured values for rigid body translations (unit: lm) Real value
Measured In-plane components Dx
Out-of-plane component Dy
Dz
Dy ¼ 500
Mean RMS
)7.0 2.5
501.9 1.6
34.8 10.3
Dz ¼ 2000
Mean RMS
4.5 9.5
1.3 6.2
1958.4 44.7
Dx ¼ 1000, Dy ¼ 1000, Dz ¼ 1000
Mean RMS
1014.4 9.9
1009.5 7.2
1029.3 45.1
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Fig. 4. Spatial distributions of in-plane velocity vectors and out-of-plane velocity contours: (a) phase 1, (b) phase 2, (c) phase 3, (d) phase 4.
From this, we can conjecture that the continuously shed tip vortex is observed at the outermost tip of the fan blade between phases 3 and 4. From the phase-averaged mean velocity field information, the flow structure in the axial plane can be divided into three regions: (1) the immediate wake region where the flow of high-momentum exists and the flow direction changes up and down according to phase angle, (2) the region where the flow is directed away from the axis of rotation, (3) the far wake region where the phase-averaged flow pattern is almost invariant. In far wake region, the velocity magnitude is decreased considerably at further downstream locations, compared with the magnitudes in the near wake field. However, the general flow structure is nearly unchanged regardless of the fan phase. From these results, we can see that the fan blade phase affects dominantly the near wake flow just behind
the axial-fan ðx=R < 0:6Þ. The periodic flow structure according to the phase angle was confirmed through the phase-averaged velocity field data where the flow structure is shifted downstream as the fan rotates from phases 1 to 4. Fig. 5 shows the contours of mean axial velocity component at four different phases. At downstream location of x=R ¼ 0:3, the maximum axial velocity occurs at the mid section of the blade in the range of 0:7 < y=R < 0:8 as shown in Fig. 5(a). Though direct quantitative comparison is difficult due to different fan shape and dissimilar experimental conditions, the general flow structure is in a good agreement with the results of Morris et al. [8] in which the maximum velocity occurs at the mid section ð0:7 < y=R < 0:8Þ at x=R ¼ 0:172. The negative axial-velocity marked as dotted lines exists in the hub region y=R < 0:3. The variation of mean axial velocity with respect to the fan
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Fig. 5. Contour plots of the mean axial velocity component: (a) phase 1, (b) phase 2, (c) phase 3, (d) phase 4.
blade phase is not so large at the downstream region of x=R > 0:6 and in the hub region of y=R < 0:3. The contour plots of the phase-averaged radial velocity component are shown in Fig. 6. The radial velocity distributions show large variation according to the phase angle. In the region of x=R < 0:3, y=R ¼ 0:4–0:7, the radial velocity component has negative values at phases 1 and 2, whereas it turns to positive values at phases 3 and 4. The negative radial velocity may be attributed to the forward-swept geometry of the fan blade that induces trailing vortices at the blade trailing edge between phases 1 and 2. Morris et al. [9] showed that the negative radial velocity component only exists in the region of blade gap around y=R ¼ 0:6. 2-D projection of trajectory of the trailing vortices can be conjectured by tracing the spots having negative radial velocity component. The trailing vortex seems to move toward the hub and shifts downstream direction as the
fan rotates. The trailing vortex is elongated in the radial direction at phases 1 and 2 due to the oncoming flow from the suction side of the fan blade. The positive radial velocity in the region 0:5 < y=R < 0:9 at phases 3 and 4 indicates that the pressure side of the fan blade influences the flow structure and the flow moves outward from the axis of rotation of the fan. The variation of the radial velocity component distribution with respect to the fan phase tends to decrease as the distance from the fan increases. At phases 3 and 4, the radial velocity component has small negative values in the region of y=R > 1:1, over the tip of the fan blade. It may be attributed to the influx of ambient fluid toward the blade tip and generation of the tip vortex between phases 3 and 4. Fig. 7 represents a 3-D display of contours having the same flow speed ðu2 þ v2 þ w2 Þ1=2 . The flow speed is closely related with the pressure distribution and loading of the axial-fan. The flow speed shows small variation in
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Fig. 6. Contour plots of the mean radial velocity component: (a) phase 1, (b) phase 2, (c) phase 3, (d) phase 4.
Fig. 7. 3-D flow structure reconstructed using mean flow speed data.
the azimuthal direction and the maximum loading of the fan occurs at about y=R ¼ 0:75. The flow speed is decreased gradually as the flow goes downstream as discussed in the previous mean velocity field results. Fig. 8 represents the contour plots of tangential vorticity ðxz Þ derived from the phase-averaged velocity field data. This clearly shows the evolution of the tip vortices and trailing vortices according to the fan blade phase. At phase 1, positive tip vortices are located in the region behind the blade tip. The region between the axis of rotation and the mid-section of the fan blade has negative vorticity. At phase 1, a large-scale negative vortex rotating clockwise direction is observed around the location (x=R ¼ 0:25, y=R ¼ 0:4). The tip vortex located at x=R ¼ 0:2 at phase 1 is moved downstream and its center is shifted to x=R ¼ 0:3 at phase 2. The negative vortices at phases 1 and 2 seem to be caused by the trailing vortices located in the blade spacing. At phase 3,
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Fig. 8. Contour plots of mean tangential vorticity xz : (a) phase 1, (b) phase 2, (c) phase 3, (d) phase 4.
another large-scale negative vortex is newly shed from the blade. The negative vortex moves outward from the axis of rotation as the flow goes downstream. This outward motion pushed the positive tip vortices outward with going downstream. The negative vortices located in the lower wake region near the axis of rotation are elongated along the x-axis. The negative vortices at phases 3 and 4 are caused by the swept flow by the pressure side of the fan blade. Two large-scale vortices exist behind the blade tip at phase 1. The center distance between two vortices is about 0.35R. At phase 2, the positive vortices move downward to the axis of rotation and their magnitude is diminished slightly. At phase 4, the tip vortex shed at the previous phase is moved downstream and a new positive tip vortex is shed from the blade tip. These results show the periodic generation and diffusion of the tip and trailing vortices with respect to the phase angle of the fan blade.
The contour plot of equi-tangential vorticity ðxz Þ surface is depicted in Fig. 9. This iso-vorticity surface distribution is difficult to obtain with conventional 2-D PIV measurements and useful to figure out the 3-D vortex structure embedded in the complex axial-fan wake. It shows the quasi-3-D distribution of positive tip vortices shed from the blade tip, trailing vortices and the negative vortices induced by pressure side of fan blade. The positive tip vortices and negative vortices interact strongly in the region 0:6 < y=R < 0:8, as shown in Fig. 9. This seems to be closely related with the maximum loading of the fan at the section of y=R ¼ 0:75. The spatial distributions of the phase-averaged turbulence intensities of three velocity components measured using the SPIV method are shown in Figs. 10–12. Each turbulence intensity distribution was obtained by ensemble phase-averaging of 500 instantaneous velocity fields. The turbulence intensity distributions also show periodic variations according to the fan blade phase.
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Fig. 9. 3-D iso-vorticity structure of tangential vorticity xz .
The axial turbulence intensity has local minimum values in the immediate wake region near y=R ¼ 0:7 behind of the fan blade at phases 1, 3 and 4. However, the radial and tangential turbulence intensities are not so small in this region. Especially, they have large values at phase 2 due to the unblocked space between the fan blades and strong flow interaction with the trailing vortices. In the hub region near the axis of rotation, the three turbulence intensities have small values. It is interesting to compare the three turbulence intensities in the far wake region of x=R > 1. The axial turbulence intensity has large values around the mid height section ðy=R ¼ 0:4–0:6Þ. The location of maximum radial turbulence intensity moves outward in diagonal direction as the fluid goes downstream. However, the tangential turbulence intensity has relatively
Fig. 10. Variations of axial turbulence intensity distribution: (a) phase 1, (b) phase 2, (c) phase 3, (d) phase 4.
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Fig. 11. Variations of radial turbulence intensity distribution: (a) phase 1, (b) phase 2, (c) phase 3, (d) phase 4.
small values in the far wake region. In addition, the local maximum values exist in an alternating manner, resulting from the periodic flow structure and alternating shedding of the tip and trailing vortices. The axial turbulence intensity distributions seem to have close relationships with the tip and trailing vortices shown in Fig. 8. On the other hand, the spatial distributions of the radial and tangential turbulence intensities seem to be influenced dominantly by the tip vortices. The complete experimental data set is available on the website (http:// efcl.postech.ac.kr/data).
5. Conclusion A SPIV technique based on the translation configuration was applied to the flow behind an axial-fan with
five forward-swept blades. The phase-averaged mean velocity fields show a periodic flow structure according to the phase angle of fan blade. The characteristic flow structure at each phase is shifted downstream in the subsequent phase. The counter-clockwise tip vortices are shed from the utmost tip of the blade, while clockwise trailing vortices exist near the hub region. The flow speed of fan wake has a local maximum value in the radial distance of about y=R ¼ 0:75 and has small variation in the azimuthal direction. The region of large outof-plane velocity component is closely related to the tip vortices shed from the blade tip. The spatial distribution of out-of-plane velocity component clearly shows the evolution and dissipation of tip vortices. These experimental data can be used for the validation of numerical predictions and understanding the flow structure in the designing process of axial-fans.
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Fig. 12. Variations of tangential turbulence intensity distribution: (a) phase 1, (b) phase 2, (c) phase 3, (d) phase 4.
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