Relatorio Tecnico de PIV - Analise de Escoamento em Cavidade Cubica

Relatório O relatório deve conter pelo menos os seguintes resultados 1 Descrição do que a referência fez o qual o resultado será validado 2 Descrição da geometria do caso simulado condições iniciais de contorno e condições do escoamento propriedades número de Reynolds e regime de escoamento 3 Parâmetros gerais de configuração dos casos malha esquemas de interpolação passo de tempo métodos e tolerâncias nas soluções dos sistemas algébricos e número de iterações na pressão 4 Resultado da convergência da solução numérica para cada caso 5 Resultados de convergência de malha para a variável de interesse 6 Comparação com os resultados da literatura 7 A discussão dos resultados e clareza na redação técnica do relatório faz parte do critério de avaliação Exp Fluids 2010 48105110 DOI 101007s0034800907155 RESEARCH ARTICLE Realtime image processing for particle tracking velocimetry Mark Kreizer David Ratner Alex Liberzon Received 18 December 2008 Revised 6 July 2009 Accepted 8 July 2009 Published online 23 July 2009 SpringerVerlag 2009 Abstract We present a novel highspeed particle tracking velocimetry PTV experimental system Its novelty is due to the FPGAbased realtime image processing on camera Instead of an image the camera transfers to the computer using a network card only the relevant information of the identified flow tracers Therefore the system is ideal for the remote particle tracking systems in research and industrial applications while the camera can be controlled and data can be transferred over any highbandwidth network We present the hardware and the open source software aspects of the PTV experiments The tracking results of the new experimental system has been compared to the flow visualization and particle image velocimetry measurements The canonical flow in the central cross section of a a cubic cavity 111 aspect ratio in our liddriven cavity apparatus is used for validation purposes The downstream secondary eddy DSE is the sensitive portion of this flow and its size was measured with increasing Reynolds number via increasing belt velocity The size of DSE estimated from the flow visualization PIV and compressed PTV is shown to agree within the experimental uncertainty of the methods applied M Kreizer D Ratner Turbulence Structure Laboratory School of Mechanical Engineering Tel Aviv University Tel Aviv Israel A Liberzon Turbulence Structure Laboratory School of Mechanical Engineering Tel Aviv University 69978 Ramat Aviv Israel email alexlibengtauacil 1 Introduction Threedimensional particle tracking velocimetry is among the stateoftheart experimental methods in fluid mechanics Tropea et al 2007 Dracos 1996 allowing for the fluid velocity and in some cases velocity derivatives fields Lüthi et al 2005 Liberzon et al 2005 to be accurately measured in optically transparent conditions The main requirement of this imaging method in which every particle is tracked in time and space is the appropriate time resolution of the imaging device For very highspeed flows specially designed solutions of siliconstrip detectors Voth et al 1998 2002 or acoustic imaging devices Mordant et al 2004 have been developed Most of the systems however attempt to use optical imaging devices such as CCD or CMOS digital cameras eg Dracos 1996 Raffel et al 1998 Tropea et al 2007 among others The main limitations of the optical applications for the highspeed flows lie in the high data rates that need to be streamed and stored in real time Therefore the main motivation of the presented work is to develop imaging devices that are 1 easy to operate as the digital imaging device and 2 reduce the data rates during particle tracking velocimetry experiments One good solution of this kind was recently proposed by Voth et al see Chan et al 2007 The authors developed a digital circuit which is located between the camera and the framegrabber reducing the data rates by the factor of 100 1000 using thresholdbased binarization algorithm We present a different solution based on the fieldprogrammable gate array FPGA oncameraboard realtime image processing that uses Sobel filter edge detection and fillinhole algorithm The commercially available digital CMOS camera 1280 1024 pixels 8 bit 12 µm per pixel Mikrotron GmbH Germany augmented with the inhouse software for particle tracking httpptvwikinetcipianet 106 Exp Fluids 2010 48105110 was implemented and measured the flow in the liddriven cavity flow To test the developed hardwaresoftware solution it is compared here with the flow visualization and particle image velocimetry PIV results obtained using the same apparatus and the same experimental conditions This is because of a different nature of the particle tracking results sparse scattered gridded data versus the results of the PIV located at fixed locations To quantitatively compare the experimental results we use the size of the downstream secondary eddy DSE the vortical structure in the liddriven cavity flow which is most sensitive to the slight changes in experimental conditions Beyond the comparison of the experimental methods we present an interesting phenomenon related to the size of the DSE in the classic liddriven cavity flow previously unattended A liddriven cavity flow is an ideal model for the flows in industry eg cutouts slots in heat exchanges cavities in chemical mechanical polishing process of silicon wafers and nature eg sediment bed impurities It has also a significant advantage of being numerically resolved hence the experimental results could be compared in many aspects to the fully resolved data sets The most noticeable works are mentioned in the review of Shankar and Deshpande 2000 from which we would like to emphasize the experimental works of Pan and Acrivos 1967 Koseff and Street 1984a Prasad and Koseff 1989 among others Koseff and Street 1984a b c investigated the influences of span aspect ratio SAR on the size of the DSE and partially also its variation with the Reynolds number ReB UbBν B is the streamwise width of the cavity and Ub denotes the belt velocity Their results were based on flow visualization photographs in a cavity of square cross section almost twice larger than our cavity dimensions B D 150 mm We extended the previous studies on the size of the DSE in a square cross section depthwise aspect ratio DAR 11 and SAR 11 liddriven cavity flow using the quantitative experimental methods PIV and PTV in addition to the qualitative flow visualization studies We can check if there are differences between the flow visualization and the velocity field distributions In agreement with the experimental results of Pan and Acrivos 1967 we found that the DSE size diminishes in the range of Reynolds numbers 1000 3500 using PIV and realtime imagecompressed PTV It is a noteworthy result by itself because this particular experimental result contradicts several very accurate twodimensional numerical simulations eg Ghia and Shin 1982 Schreiber and Keller 1983 among others in which the DSE size increases monotonically with the Reynolds number We attributed our findings to the threedimensional nature of the flow in the 111 liddriven cavity domain It is also noteworthy that insight into DSE is important for the instability theories that often rely on the stability analysis of the socalled separating streamline ie the streamline between the primary and secondary eddy see eg Ramanan and Homsy 1994 2 Experimental setup Experimental studies have been performed in the liddriven cavity flow schematically shown in Fig 1 A DC motor drives the plastic belt at a given speed UB controlled by a power supply unit The velocity of the belt is measured directly during the experiment and is accurate to 10 The cubic cavity of 80 mm side length is made of glass and filled with tap water The belt is attached on the mechanical springs and kept under water level to assure proper boundary conditions The hardware used for the particle image velocimetry PIV and flow visualization measurements was CMOS digital camera up to 500 frames per second 1280 1024 pixels pixel size is 12 µm Mikrotron GmbH and NdYLF a b belt laser sheet laser optics CMOS camera glass tank NdYlf double pulsed laser Fig 1 a Schematic view of a liddriven cavity flow facility b Liddriven cavity flow definition sketch and definitions of the flow features according to Koseff and Street 1984 width in the streamwise direction B span spanwise direction L and depth D Note the dimensionless parameters DD and BD of the downstream secondary eddy pulsed laser 80 W providing 20 mJpulse at rates up to 10 kHz The internal trigger of the framegrabber card CLFC from IO Industries was used to set up the time difference between the consequential images The interval varied depending on the belt speed to ensure the average pixel displacement in PIV images of approximately 4 pixels The flow was seeded with hollowglass particles dp 10 μm ρp 102 gcm3 The PIV images were analyzed using the Insight 9 software TSI Inc and interrogation windows of 32 32 pixels 50 overlap FFTbased cross correlation and standard filters were applied At each experimental setting 1000 lower Reynolds range to 2000 higher Reynolds range velocity fields were acquired stored and processed Flow visualization images were processed using Matlab Image Processing Toolbox and the particle tracking was performed using the open source 3DPTV software httpptvwikinetcipianet as described in detail in the following sections 21 Realtime image processing and particle tracking method The presented method is based on the digital CMOS camera which implements the realtime image processing algorithm in the FPGA onboard The algorithm is based on the Sobel edge detection algorithm during which the Sobel discrete operator is applied through the convolution with the following kernels matrix of 3x3 kernels and matrix of 3x3 kernels in order to obtain the horizontal and vertical gradients respectively One can simulate the image processing algorithm in software as shown schematically in Fig 2 Fig 2 Scheme of the realtime image processing algorithm and the respective result Left panel is 280 110 pixels part of the image and the right panel is the zoom on a small window The algorithm presumably includes an image enhancement step through a highpass filter removing background and increasing contrast of the image Sobel edge detection fillin procedure that fills the empty spaces within closed boundaries and finally identification of the objects their area number of pixels to the first order approximation size in horizontalvertical direction and center of mass Center of mass is detected as a ratio of the sum of the values in horizontalvertical direction to the total number of pixels of the object hence we use the intensityweighted average to determine the particle centers In the regular mode our data bandwidth is 625 MBs 1280 1024 pixels 500 frames per second Currently such bandwidth is transmitted by using the socalled Full CameraLink standard The processed data is 20 bytes per object particle The maximum number of objects identified and processed in realtime using the installed FPGA is 1024 objects which at the rate of 500 fps leads to the bandwidth of 98 MBs This amount of data is easily transferrable by using the GigE interface ie typical network standard The data compression rate is 641 It is noteworthy that the presented algorithm is not an image compression algorithm as in the work of Chan et al 2007 but rather an image processing procedure The main difference is in the way the information is processed and stored In the system by Chan et al 2007 relatively simple binarization was applied and the data were stored as binary images Instead in the algorithm implemented in this work the image is processed and only the relevant information stored the particle positions It is therefore limited only to the particle tracking experiments but optimized to achieve best signaltonoise ratio One of the main problems of particle tracking systems is the variation of particles intensity as it moves through a nonuniform eg laser or LED light from one side illumination The particles change their illuminated shape continuously and the system must eventually be able to link the images of such particles in a single trajectory The simple thresholdbased binarization was thoroughly tested in our laboratory and was proven to lack the robustness of the edge detection This is mainly because of the inability to apply few additional steps of lowhighpass filtering in real time to augment thresholdbased binarization and improve its signaltonoise ratio Unfortunately the FPGA of the given digital camera is preinstalled with the Sobel edge detector only and we could not test the performance of other edgedetection schemes We have to stress on a few additional innovative steps with respect to the custom solution of Chan et al 2007 As the FPGA was installed on the camera its size did not changed significantly However a single GigE Internet cable is by far cheaper and safer to use than two thick CameraLink cables that are necessary to stream out of the cameras for up to 650 Mbs The image processing algorithm was applied to the data at the first bottleneck point of the experimental system and all the resulting hardware complexity and price were reduced by a nonnegligible factor The expensive both price and memoryrelated aspects frame grabbers are replaced by offtheshelf network interface card NIC the relevant information particle locations is stored on a standard SATAII hard drive and the whole system can be implemented in principle on a smallsized netbook a mobile computer or even integrated into the highbandwidth intranet system of the laboratory This provides access to remotely controlled particle tracking systems in applications such as large wind tunnels 3 Results and discussion We performed our analysis in the range of Reynolds numbers ReB 9006000 varying the speed of the belt Ub Interesting enough the flow was found to be laminar up to the Reynolds number of 3500 which is in agreement with the results of Koseff and Street 1984b and Prasad and Koseff 1989 who measured Urms at Re 3200 31 Velocity and velocity fluctuation profiles Velocity and velocity fluctuation profiles in the midplanes vertical and horizontal are estimated by using the ensembleaveraged PIV and PTV velocity fields Velocity profiles shown in Fig 3 are found to be in a good agreement with each other and with the classical results in the literature Koseff and Street 1984b Prasad and Koseff 1989 presented as solid line in in Fig 3 The left panel compares the two types of results mean velocity distribution along the vertical central line of the cavity and the rootmean square of the vertical velocity fluctuations along the horizontal midheight line The circles with the error bars are for the compressed PTV results interpolated from the scattered particle locations to the regular grid prior to ensemble averaging and the triangles are from the PIV results The right panel shows the effect of the Reynolds number on the lower half of the mean velocity distribution In agreement with the results of Prasad and Koseff 1989 the boundary layer becomes thinner and the mean velocity gradients consequently increase 32 DSE size analysis Longtime exposure images were obtained using the superposition of single flow visualization captures similar to visualization studies of Koseff and Street 1984c An example of the superposition result and the markers that show the pixel size of the DSE and of the width of the cavity B recalling that the depthwise aspect ratio is 11 is given in Fig 4 These values lead to the results shown here in terms of dimensionless and relative to the given imaging axis DD and BD The ratios of the measurements are shown in Fig 7 for the different Reynolds number experiments The height and the width of the eddy have clearly the same trend decreasing with the increasing Reynolds number 321 Results based on the PIV flow fields PIV images were analyzed by using a commercial software Insight 902 TSI Inc and crossvalidated against the 1989 circles denote the compressed PTV and triangles the PIV results respectively b Effect of increasing Reynolds number of the vertical profile of the horizontal velocity UyUb in the lower half of the cavity Fig 3 a Mean velocity profile at midplane cross section along the vertical central line ie at half width The horizontal axis is for the mean velocity axis of UyUb The vertical axis is for the rms of the vertical velocity fluctuations vrmsxUb multiplied by 10 for the sake of clarity The solid line denotes the results of Prasad and Koseff open source OpenPIV software httpwwwopenpivnet The velocity maps 500 velocity realizations per run were averaged and the following analysis performed using the ensemble average vector maps First the profile of the velocity magnitude V ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u2 þ v2 p is estimated along the diagonal of the cavity connecting the bottom downstream and the top upstream corners shown in Fig 5 The edge of the DSE is defined at the point where the velocity slope changes before it reaches the first maximum starting from the DSE This point is defined as a peak on the derivative of the profile and the zerocrossing point on the plot of the second derivative presented in Fig 5 The analysis is automated and does not require any subjective intervention of the user 322 Results based on the imagecompressed PTV The first output of any particle tracking method is a list of trajectories of particles on very sparse and scattered grid of locations Figure 6 shows one of such flow maps on which all the trajectories from 1000 instantaneous time frames are shown overlaid together and arrows added to show the twocomponent velocity vectors There are two possible routes for the following analysis a a manual method like the one used for the flow visualization images and b an automatic method like the one used for the PIV flow fields that requires a preliminary step of interpolation of the results over a structured grid The result of the two dimensional interpolation and averaging is the vector field of the flow velocity similar to the ensembleaveraged PIV flow map 323 Data reduction The reason to combine the experimental results of the flow visualization PIV and PTV analysis in a single plot in Fig 7 is twofold 1 comparison of various techniques mainly to validate the realtime image processing PTV results obtained here for the first time and 2 an attempt to show the trend of the DSE size with the increasing Reynolds number As pointed out in the introduction the question whether the main eddy size increases and fills the cavity as the Reynolds number increases remained unanswered in literature From the trend shown here it is clear that the size of the main eddy and therefore of the secondary eddies as deduced from the present study of DSE size is finite What is missing in our analysis is the threedimensional structure of the primary and secondary eddies The threedimensional structure of the flow is addressed in another study using the threedimensional particle tracking velocimetry in Lagrangian settings eg Elfassi and Liberzon 2008 4 Summary and conclusions Classical flow configuration in a laminartoturbulent lid driven cavity setup was investigated by utilizing the three quantitative imaging methods flow visualization of long exposure images particle image velocimetry and the novel realtime image processing particle tracking velocimetry PTV This study focused on the two aspects 1 devel opment of the methodology for the tracking using realtime image processing and 2 questioning the finite size of the primary and secondary eddies with the increasing Reynolds numbers The cubic glass cavity SAR 111 of 80 mm side length has been used and the lid velocity was defined Fig 4 Longtime exposure image of the liddriven cavity with markers that show the size of the DSE horizontal and vertical in pixels with respect to the B in pixels 1 0 1 0 02 04 06 08 1 5 0 5 x 10 4 05 0 05 05 0 04 Fig 5 Schematic view of the DSE size estimate using the PIV velocity maps Solid line denotes the velocity profile Ur along the diagonal r and the dashed line is the second derivative q2Urqr2 Exp Fluids 2010 48105110 109 123 through the linear motion of a belt along the top open side of the cavity Our analysis includes image processing FFT based crosscorrelation of PIV images and tracking in a twodimensional slice of the flow tracers We demonstrate the hardware and open source software used to obtain the experimental results The results are in reasonable agree ment with the results in literature and selfmade numerical simulations The developed system is compact as it requires a PC with a standard network card and hard drive Hence it can be installed in the industrial and laboratory experiments using highbandwidth networks and remote control It is however limited to the single type of experiments it was developed for particle tracking velocimetry Acknowledgments The authors are thankful to Reut Elfassi for assistance with the experiments and technical support in the experi mental setup The research has been funded by the Israel Science Foundation and the Wolfson Family Charitable Trust References Chan KY Stich D Voth GA 2007 Realtime image compression for highspeed particle tracking Rev Sci Instrum 782023704 5 pp Dracos T ed 1996 Threedimensional velocity and vorticity measuring and image analysis tecniques vol 4 of ERCOFTAC Kluwer Dordrecht Elfassi R Liberzon A 2008 Experimental study of liddriven cavity flow in the Lagrangian frame of reference In 22 ICTAM conference Adelaide Australia IUTAM Ghia G Shin 1982 High resolutions for incompressible flow using the NavierStokes equations and a multigrid method J Comput Phys 48387411 Koseff J Street R 1984a The liddriven cavity flow a synthesis of qualitative and quantitative observations ASME J Fluids Eng 1064390398 Koseff J Street R 1984b On endwall effects in a liddriven cavity flow J Fluids Eng 106385389 Koseff J Street R 1984c Visualization studies of a shear driven threedimensional recirculating flow J Fluid Eng 1062129 Liberzon A Guala M Luthi B Kinzelbach W Tsinober A 2005 Turbulence in dilute polymer solutions Phys Fluids 173 031707 4 pp Luthi B Tsinober A Kinzelbach W 2005 Lagrangian measurement of vorticity dynamics in turbulent flow J Fluid Mech 52887 118 Mordant N Crawford AM Bodenschatz E 2004 Experimental Lagrangian acceleration probability density function measure ment Phys D193245251 Pan F Acrivos A 1967 Steady flows in rectangular cavities J Fluid Mech 28643655 Prasad A Koseff J 1989 Reynolds number and endwall effects on a liddriven cavity flow Phys Fluids 12208218 Raffel M Willert CE Kompenhans J 1998 Particle image veloc imetry a practical guide Springer Berlin Ramanan N Homsy G 1994 Linear stability of liddriven cavity flow Phys Fluids 6826902701 Schreiber R Keller HB 1983 Driven cavity flows by efficient numerical techniques J Comput Phys 49310333 Shankar PN Deshpande MD 2000 Fluid mechanics in the driven cavity Annu Rev Fluid Mech 32193136 Tropea C Yarin AL Foss JF eds 2007 Springer handbook of experimental fluid mechanics Springer Berlin Voth GA LaPorta A Crawford AM Alexander J Bodenschatz E 2002 Measurement of fluid particle accelerations in fully developed turbulence J Fluid Mech 469121160 Voth GA Satyanarayan K Bodenschatz E 1998 Lagrangian acceleration measurements at large Reynolds numbers Phys Fluids 1022682280 Fig 6 Output of the compressed PTV a Scattered vector field of all the trajectories b interpolated over a structured grid 0 1000 2000 3000 4000 5000 6000 7000 012 017 022 027 032 Fig 7 Main result the size of the DSE measured from the flow visualization 110 Exp Fluids 2010 48105110 123 Escoamento em uma cavidade Este trabalho tem como objetivo reproduzir os resultados de uma referência bibliográfica Será necessária a leitura da referência para entendimento da geometria propriedades do escoamento e condições de contorno Será necessário coletar os dados da referência Note que apesar da literatura demonstrar que o escoamento em uma cavidade tem características de um escoamento 3D considere a aproximação da simulação para um caso 2D Considere o escoamento laminar até Re 5000 e transicional até Re 10000 Faz parte do objetivo do trabalho a escolha do modelo de regime de escoamento a demonstração da convergência numérica de malha comparação com o resultado experimental da referência e discussão dos resultados Table with three columns Caso Matricula Referência 1 Faure 2014 pg 8 Fig 7 e 9 Fig 8 Re 4230 LD 05 2 Faure 2014 pg 8 Fig 7 e 9 Fig 8 Re 4230 LD 1 3 Faure 2014 pg 8 Fig 7 e 9 Fig 8 Re 4230 LD 15 4 Faure 2014 pg 8 Fig 7 e 9 Fig 8 Re 4230 LD 2 5 Douay 2013 pg 8 Re 3750 Fig 6d 2C2D PIV xL 054 6 Douay 2013 pg 8 Re 3750 Fig 6e 2C2D PIV xL 084 7 Kreizer 2010 pg 108 Fig 3a PIV 8 Kreizer 2010 pg 108 Fig 3a compressed PTV 9 10