1、4674 An Algorithm of Stereoscopic Particle Image Velocimetry for Full-Scale Room Airflow Studies Yigang Sun, Ph.D. Lingying Zhao, Ph.D. Associate Member ASHRAE Yuanhui Zhang, Ph.D., P.E. Member ASHRAE Xinlei Wang, Ph.D. Member ASHRAE ABSTRACT One challenge in indoor air qualitystudies is the measure
2、- ment of three-dimensional air velocity profiles in an airspace so that the nature of airflow can be better understood and appropriate ventilation systems can be designed. There is much dispute over a variety of computationalfluid dynamics (CFD) models, primarily due to a lack of credible data to v
3、ali- date those models. This study aimed to develop a stereoscopic particle imaging velocimetry (SPIV) system suitable for measurement of full-scale room three-dimensional airflow. The SPIV method is based on the principle of parallax to extract a third (z-direction) velocity component using two cam
4、eras. We have developed a new three-dimensional algo- rithm in the particle streak mode (PSM) that only requires two cameras to acquire three velocity components (x, y, z) andflow directions in a three-dimensional volume, rather than in a thin layer of a plane. The two-camera approach is expected to
5、 greatly simplifi the image acquisition and data processing and improve the accuracy by eliminating the error caused by the third camera image or some special techniques employed to resolve directional ambiguity. The three-dimensional image volume can contain a full range of three-dimensional veloci
6、- ties. In this new three-dimensional SPIVsetup, two cameras are placed at diferent angles to view the illuminated$eld and to capture particle displacement images that contain the influ- ence of the third velocity component. Theparallax efect allows us to obtain different two-velocity component vect
7、or maps from each camera. The diferences between the two images arise from the third velocity component and the geometrical config- uration of the two cameras. Afer image calibration, this third velocity component can be calculated. The two cameras will be set at diferent exposure times, thus acquir
8、ing diflerent lengths of streaks for the same particle path. The differences of the exposure then can be used to distinguish theflow direc- tions. INTRODUCTION Stereoscopic particle image velocimetry (SPIV), which can provide instantaneous velocity distributions over an area or space in a flow field
9、, has been studied by a number of researchers (Arroyo and Greated 199 1 ; Coupland and Halli- well 1992; Sinha and Kuhlman 1992; Malik et al. 1993; Robinson and Rockwell 1993; Prasad and Adrian 1993; Grant et al. 1995; Hinsch 1995; Scholzen and Moser 1996; Willert 1997; Grant et al. 1998; Lawson and
10、 Wu 1999; Bearman et al. 1999; Palero et al. 2000). Existing stereoscopic configuration may be classified as translational method or angular displace- ment method. These currently available stereoscopic systems, however, are very difficult to precisely position. The transla- tional systems (Arroyo a
11、nd Greated 199 1 ; Prasad and Adrian 1993) require that the object plane, lens plane, and image plane all be parallel to each other, and the lens of all the cameras must be in the same plane. The errors in the system setups can be significant when the concerned area or space is large, e.g., in full-
12、scale rooms. The common area viewed by all cameras is usually small unless some special techniques are adopted, which increases the difficulties in the system setups and produces additional image recording errors. Angular displacement methods (Prasad and Jensen 1995; Scholzen and Moser 1996; Lawson
13、and Wu 1997; Willert 1997; Lawson and Wu 1999) have fewer requirements for the alignment of the system setups than translational systems. But these methods still require that the optical axes of all cameras remain in the same plane and intersect the object plane at the system axis. Yigang Sun is a v
14、isiting scholar, Yuanhui Zhang is a professor, and Xinlei Wang is an assistant professor in the Department of Agricultural Engineering, University of Illinois at Urbana-Champaign. Lingying Zhao is an assistant professor in the Department of Food, Agricultural and Biological Engineering, Ohio State U
15、niversity, Columbus. 02004 ASHRAE. 75 The errors in the system arrangement could again be signifi- cant when the concerned area or space is large. The measure- ment volume of both configurations is a mere sheet of very limited depth. To resolve directional ambiguity, often more than two cameras are
16、installed or special techniques, such as image shifting, are employed, which multiplies the work for system setup and/or image processing and adds an error source. An algorithm for stereoscopic PIV in the particle streak mode is presented in this paper. The SPIV technique based on the algorithm requ
17、ires no special conditions except for the two cameras having a common viewing area of the object as large as possible without blocking each other. Through calibration, the orientations, locations, and imaging parameters of two cameras can be determined with satisfactory precision. Direc- tional ambi
18、guity is eliminated by making use of the difference between the exposure times of the two cameras. The setup of the system is substantially simplified compared with the exist- ing technology, and the measurement volume is much larger than other systems available now. HARDWARE OF A THREE-DIMENSIONAL
19、PIV SYSTEM IN PSM The hardware of a three-dimensional PIV system in the particle streak mode consists of a particle seeding system, an illumination system, an image recording system, and an image and data processing system. Particle Seeding System To visualize a flow for PIV, the flow has to be seed
20、ed with small, neutrally buoyant tracer particles. The seeding particles should have the physical density of the host flow and be as small as possible to guarantee good follower behavior but large enough to reflect sufficient light in suitable illumination and to be captured by the image recording s
21、ystem. In the parti- cle streak mode, the concentration of seeding particles should be low enough that individual particle streak images can be identified. illuminating System Illumination is a key component in a traditional PIV measurement system. Unlike an illumination system for a traditional PIV
22、, the light for this algorithm is not required to be transferred into a thin sheet because it is used for volume measurement. The light source should also not be pulsed for this operating mode. The light intensity, however, should be high enough and its distribution be uniform enough in the whole ob
23、servation volume to ensure clear images of streaks in the area of concern. Image Recording System Two high resolution cameras are required for the system. The shutters of the two cameras can be synchronously opened with a controller, and their exposure times can be set at high accuracy. If the airfl
24、ow in a room of 18 feet (5.5 m) width is (x, y, z) QiParticlc Figure 1 Schematic of stereoscopic PIK measured using the system, and the diameters of the seeding particles are about 2 mm, a resolution of about 3000 pixels horizontally is needed for the cameras. Intensified cameras or some digital cam
25、eras with high IS0 speed can operate at low light levels and decrease the requirement for the illumination system. Image and Data Processing System Digital cameras have their own computer interface and the captured images can be easily transferred to computers. However, framegrabbing by computers in
26、 real time is gener- ally impossible at present because of the high resolution of the photos. The purpose of image processing is to obtain informa- tion about positions, orientations, and sizes of every streak on the photos. Some commercial software for this kind of image processing is available. Ho
27、wever, image processing is usually very time consuming if the illumination is not very good and the concentration of seeding particles is high. Therefore, a high-speed personal computer with a large memory capacity is needed for data processing based on the algorithm presented below, especially when
28、 the number of streaks on a pair of photos is large. STEREOSCOPIC CONFIGURATION AND CALIBRATION One critical step in a stereoscopic PIV study is to establish the relationship between a photo coordinate and the room coordinate that contains the particle of concern. Consider a generic case in which ca
29、mera i (i = 1,2, *-, a), views a particle with coordinate (x, y, z) in a three-dimensional room airspace as shown in Figure 1. Assume the local coordinate for camera i is (ni, y;, z; ). The axis coincides with the optical axis of the camera lens and the lens center is located at oi (xoi,yoi, zoi). 7
30、6 ASHRAE Transactions: Research In Figure 1, the distance between the camera lens center and the film is di. The particle image on the film is the negative image of the actual particle location. Therefore, the directions of the Xi and ri are opposite to xi and y;, respectively. In the photo image, t
31、he particle is the negative image of that on the film. Thus, the particle in the two-dimensional photo image (Xi, K), which is a two-dimensional image, represents the actual relative location of the particle (x, y, z) in the three- dimensional fluid field. The magnification from the film to photo im
32、age (including the transformation from ordinary length unit to pixel in which the photo image is measured) is Mi. The relationship between the room coordinate system, o- xyz, and camera i coordinate system, oi - xiyizi , can be writ- ten as: where A; denotes the 3 x 3 matrix of the factors al,; (1,
33、m =1,2, 3), the direction cosines of the xi, yi, zi axes in the o-xyz coordinate system, and it is an orthogonal matrix, for (4 -1 T A; =Ai . From Figure 1, the relationship between the particle posi- tion (xi, yif, z; ) in the camera i coordinates and its image posi- tion (Xi, YJ on the photo can b
34、e written as: Mjdi x. = -Xfi +xo; ZIi (3) Equation 3 can also be rewritten in the following form: 1 o -xoi o Zli ZIi Zli i 22i 23i 24i 3li 32; 33i 34; (;I O001 where Zli ZIi ZIi M,d,x M,di - Midi 1 =c 34; = zoi Z i b. = - Midi Thus from Equation 5, we have After eliminating bi,Xj and I: can derived
35、from Equation 6. (7) Because the photo image is two-dimensional, the zi can not be determined based on the photo image taken by camera i only. In order to determine the third dimension, another photo image taken from an alternative location is required. Now we consider two photos for the same partic
36、le at the point (x, y, z) taken by two different cameras, i.e., i = 1, 2. According to 77 I I Photo 2 Figure 2 The match of streaks on two synchronous photos taken by two diferent cameras, respectively. We define Sll, S2i, S31, S12, S22, and S32 as follows: 11 = clllXl +1211 “131 21 = c2iix1+c221y1+
37、c231 31 = 311Xi + 3211 331 12 = c112x2 “1222 + 132 22 = c212x2 + 222 2 + 232 32 = 31ZX2 3222 + 332 (9) Solving Equation 8 yields the solutions for x, y, and z: Equation 7 and 1 O are the relationships between the coor- dinates x, y, andz of the particle in the room coordinate system and its correspo
38、nding imaging coordinates Xi and on the photos taken by camera 1 and camera 2. There is no special condition for the setup of the cameras such as distance between all cameras and the viewing plane. Theoretically, the two cameras with the same optical axis will result in failing calculation of the ve
39、locity component of the particles that are locating on the optical axis line when the cameras shutters are triggered. In reality, it is impossible to position the two cameras with the same optical axis, but rather the two cameras will be positioned at different positions and orientations for obtaini
40、ng all velocity components. It is possible to obtain the cameras parameters in Equa- tions 7 or 8 by direct measurements. However, it will be diffi- cult to do so with satisfactory accuracy. Calibration is an alternative method to obtain these parameters. In Equation 7, we can assign d34i to be 1. I
41、n that case, the values of ck,;(k = 1,2, 3 ; j = 1,2) and bi in Equations 7 and 8 are differ- ent from those in Equations 5 and 6, but the relationships represented by Equations 5 and 6 with new ck .; and bi are still valid. There are eleven unknown coefficients in Equation 7 for each camera, and th
42、ey are indirectly restrained by Equation 2. Because of the nonlinearity of Equation 2, it is more conve- nient to calibrate the imaging system only using Equation 7 without considering Equation 2. So, we need to calibrate the J imaging system with six different spatial points at least. After acquiri
43、ng the data of all the calibrating points, the spatial point (xj, yj, z,) and its image on the corresponding photo taken by camera i (q? y,) (j=l, 2, ., n, n 2 6), we can get the values of the parameters by solving Equation 7 using the least- squares approach of linear regression problems. DETERMINA
44、TION OF MAGNITUDE AND DIRECTION OF VELOCITY To determine the three-dimensional location of every streak on photos and the velocity they represent, two cameras must be synchronized and the streaks in two images must be matched. First, we assume that the two camera shutters open at the same time, and
45、that the exposure time of camera 1 is Il, and that of camera 2 is t2. The difference between tl and t2 must be large enough to be detected in image processing. From Equation 8, we have: E (21 32 - 31 s22)(c142 - 141) + (3112 - I 132)(242 - 241 ) + s22212c342c34 = o (1 1) Equation 11 is the relations
46、hip between the two images (Xj, q) (i = 1,2) of the same point (x, y, z) in the room airspace. As shown in Figure 2, we select streak j on photo 1 taken by camera 1, and substitute each of its endpoint coordinates XIAi and YlA, (orXIBjand YlB,) into Equation 11. Then, by substi- tuting the x& and of
47、 the endpoints of every streak on photo 2 taken by camera 2, we can calculate 6,k or 6Bk (k= 1,2, . . . , 2 multiplies the total number of streaks on photo 2), which is the calculated value of the part between the two equal marks in Equation 1 1. If 16, I is less than a threshold, it implies that th
48、e velocity components can be calculated using the two images. The threshold limit is a preset value determined via iteration. We should substitute the coordinates of point C of streak j on photo 1 and the coordinates of the other endpoint of the streaks on photo 2 into Equation 1 1. We select the st
49、reak whose second endpoint has minimum 16,l as the matching pair of streak j on photo 1. The direction of the streak on photo 2 is pointing from the first endpoint to the second endpoint, and the direction of the streak on photo 1 is in the direction from the endpoint that matches the first endpoint of the streak on photo 2 to its other endpoint. For example, if endpoint A of streak j and endpoint D of streak k have a 16, I that is less than the threshold, then we substitute the coordinates of point C, and the coordinate
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