边界层流动中边界层显微速度矢量场检测方案(CCD相机)

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iopscience.iop.org IOP Publishingdoi：10.1088/1742-6596/760/1/012008XXII Fluid Mechanics Conference (KKMP2016)Journal of Physics： Conference Series 760 (2016) 012008 Home Search Collections Journals AbouttContact usMy lOPscience Combined Differential Interferometry and Long-range pPlV measurements of a temperaturedriven boundary layer flow This content has been downloaded from IOPscience. Please scroll down to see the full text.2016 J. Phys.： Conf. Ser.760 012008 (http：//iopscience.iop.org/1742-6596/760/1/012008) View the table of contents for this issue， or go to the journal homepage for more Download details： IP Address： 219.143.130.209 This content was downloaded on 09/02/2017 at 02：19 Please note that terms and conditions apply. You may also be interested in： Use of the PIV technique for an indirect determination of the microchannel cross-section passagegeometry G Puccetti， B Pulvirenti and G L Morini On the effect of velocity gradients on the depth of correlation in PIV B Mustin and B Stoeber Microfluidic mixing and separation Klas Hjort and Zhigang Wu Slip length measurement of gas flow Abdelhamid Maali， Stephane Colin and Bharat Bhushan F2DPR： a fast and robust cross-correlation technique for volumetric PlV Thomas Earl， Young Jin Jeon， Bertrand Lecordier et al. Combined Differential Interferometry andLong-range uPIV measurements of a temperaturedriven boundary layer flow S Kordell， T Nowakl， R Skodal and J Hussongl Ruhr-Universitat Bochum， Chair of Fluid Machinery， UniversitatsstraBe 150，44801 Bochum，Germany E-mail： stephan.kordel@ruhr-uni-bochum.de Abstract. In the present study Differential Interferometry and Long-range uPIV aresuccessfully combined for a benchmark experiment of an accelerating temperature drivenboundary layer flow. Spatial resolutions of 405 m for the interference and 101 pm for the uPIVmeasurements could be achieved. The results of the combined measurements are comparedwith results of numerical simulations. Temperature and velocity profiles are compared withtheoretical values and a relation between Nusselt number and Grashof number could be workedout. 1. Introduction Several optical measurement techniques are available nowadays that have been used forsimultaneous measurements of velocity and temperature or concentration distributions. Praisneret al. [1] for example combined a liquid crystal sensing system and PIV to determinethe convective heat transfer and the flow field of a turbulent water channel flow..In flowsituations where transient scalar fields such as density or pressure distributions have to bedetermined， interference methods have been the first choice for many decades. The most commoninterference techniques for flow studies are Mach-Zehnder Interferometry (MZI) and DifferentialInterferometry (DI) [2]..Goldstein and Eckert 3] used a Mach-Zehnder Interferometer tothe study the steady state and transient development of a free convection thermal boundarylayer about a uniformly heated vertical plate.Early studies on simultaneous density andvelocity field measurements were utilized by Skarman et al. [4. They combined holographicinterferometry with 3D-PTV measurements to capture temperature and flow fields.Whileinterference techniques are often used to measure density fields in gas flows， applicationsto weakly compressible liquid flows are scarce [5]. Iben et al.. [6] performed pressure fieldmeasurements in cavitating liquid flows by means of Mach-Zehnder Interferometry.In the present work simultaneous velocity and temperature field measurements were successfullyperformed， combining for the first time Long-range PIV and Differential Interferometry with a standard double-pulsed Nd：YAG laser. In the present study we present results on the timedependent temperature and velocity fields in a temperature driven circulation flow in a cuvettethat was created by aheated side wall. Figure 1：(a) Side view of cuvette； thermocouples are indicated with Ti to T3； (b) Optical set-upof the combined measurement technique 2. Set-up 2.1. Optical System The experimental set-up of the combined measurement technique of Long-range uPIV andDifferential Interferometry (DI) as shown in Fig.1b was established and tested. Details can befound in Kordel et al [7]. A double pulsed dual cavity Nd：YAG laser (Nano S 65-15 PIV， NitronLasers， 入= 532 nm) is used at a frequency of 5 Hz. Using a combination of a half wave plate anda polarizing beam splitter cube the pulsed beam is split into two separate parts of approximately5 % (beam 1) and 95% (beam 2) laser intensity. After passing a spatial filter system beam 1 iswidened to a bundle of parallel light which passes the test section in positive z-direction. Thesecond beam (beam 2) is deflected unchanged in such a way that it enters the test section innegative x-direction. Suspended Rhodamine B coated fluid tracers (Microparticles GmbH) of25.07 ±0.2 _m nominal diameter in the middle plain of the test section (z=0) are excited inmeans of a volume illumination by the laser beam. Both， the laser light and the fluorescencesignal are passing along z-axis， are then focused by a lens before separated again by a dichroicmirror. While the particle light transmits the dichroic mirror and is then recorded directly bya 12 bit dual frame CCD camera (Imager Pro SX， LaVision) the laser light is reflected. Thereflected laser light passes a Wollaston prism and a polarizer which creates interference fringesin the image plane. Two far-field microscopes (Infinity K2， DistaMax) with 2.18 x magnificationyield a field of view (FOV) of 3.246 mm x 3.874 mm for the full camera sensor of 2456 x 2058pixel. 2.2. Measurement Section An optically accessible cuvette (Hellma GmbH Co. KG) is used for all measurements (see Fig.1a). The cuvette has a thickness of b=10 mm and one side wall was replaced by a brass plate.It is closed with a plastic plug to avoid a free surface. Heat is supplied to the plate by a 10Qresistor and a 4 W power supply. Along the y-axis the near wall water temperature is measuredby three thermocouples (T1 -T3) which reach approximately 400 pim into the fluid and have aspacing of 2 mm， 8mm and 14 mm to the bottom wall of the cuvette. 3. Measurement procedure For all measurements a total time series of 60s at a frequency of 5 Hz was recorded. Theheating process was started with 2s delay to measure the initial fluid temperature (ambient temperature) and eventual background flows in the cuvette. At each time step both， DI anduPIV camera， record a double image pair. This leads to a total amount of 600 double imagesfor one measurement sequence. The interframing time was set to dt = 5 ms..EHence， theparticle image displacement is ~ 10 pixel in the final stage of the measurement sequence. Due torefraction effects in the DI image the particle image density for the used 25.07 pim Rhodamine Bparticles was limited to 3.9 ×10-4 particle pixel-1 within the FOV. The orientation of the fringepattern can be adopted by the rotation Wollaston prism. In this evaluation all measurementsare done with an fringe orientation angle of a=±45°. 4. Evaluation 4.1. Differential Interferometry An in-house matlab code is used for the evaluation of the recorded interferograms. It evaluatesthe density gradient based on the relative fringe displacement AS/S as follows [8]： Here， S denotes the direction normal to the fringe orientation. K is the Gladstone-Daleconstant which was evaluated for a temperature range of 20℃≤T≤40°C.. Wavelength入， measurement volume thickness d and the distance between neighboring light rays b [9] arecharacteristic quantities of the set-up and constant throughout all measurements. To determine AS/S a fourth order polynomial was fitted to each fringe of the pattern and wasthen compared to a linear equation extracted from a initial not displaced reference fringe. Thelocal gradient evaluation by the fringe pattern limits the spatial resolution to the fringe spacingS. In order to receive a continuous fringe displacement field a 2D surface polynomial was fittedto the displacement values.From this the density gradient field in G-direction was derived.Hence， this is not necessary the gradients main direction， measurements are repeated with 90°rotated Wollaston prism. Again the density gradient field， now in n d叭+iwirection is determined. Afinal coordinate transformation gives the gradient in x-and y-direction. With a reference temperature from the thermocouples the temperature field can be derived byintegration [10]. To compensate for refraction effects， which may lead to an overestimation of the density gradient，an a priory calibration procedure was implemented in the set-up. With the help of a calibrationplate and a blue LED the refraction induced image distortion is measured by means of anBackground Oriented Schlieren (BOS) evaluation. A mapping function for each time step isapplied for fringe image. 4.2. Long-range uPIV The evaluation of the recorded particle images is done with commercial software DaVis 8.2.2(LaVision GmbH). Before the evaluation of the particle image shift several preprocessing stepsare performed to improve the signal-to-noise ratio reaching a mean background signal of about0.16 counts. The PIV evaluation uses a 2D multi-pass cross-correlation algorithm. To achievereliable cross-correlation results of more than 95% probability the particle density has to be> 5 per interrogation window [11]. Therefore， a final window size of 128 x 128 pixel with 5%overlapping was chosen， leading to a vector spacing of 101 pim. 5. Results 5.1. Temperature and Velocity fields Figs. 2a and 2b show the temperature and a velocity field within a Region of Interest (ROI) of0.82 mm≤Ax≤3mm spacing to the heated side wall and 12.8 mm ≤Ay ≤ 15.5 mm spacingto the bottom wall of the combined measurement technique at t= 30s. Since a fully transient doi：10.1088/1742-6596/760/1/012008 ttt Figure 2： (a) Measured temperature field； (b) Measured velocity field； (c) Temperature field(contour plot) and velocity field (vectors) derived from simulations； Experimental and numericalresults at t=30s flow is investigated， the velocity field (see Fig.2b) is computed by cross-correlation of onedouble image pair. As mentioned in section 4.1 the temperature field (Fig. 2a) is a result of twoseparate measurements. Out of three independent repetitive measurements the local maximumstandard deviation of measured density gradient fields in C direction was determined to be lessthan omax =4%. Hence， the computation of the main density gradient out of two measurementsis a fair procedure. Nevertheless， our aim in future studies is to record the density gradientsin (and n direction simultaneously. Therefore a second Wollaston prism is needed， which willbe placed in a separated beam path before recombined again. The result is a grid pattern asdiscussed in section 6. Fig. 2c shows results of numerical simulations at the same time step. The three dimensionalflow problem has been simulated using ANSYS CFX. For simulations both， the brass plate andthe fluid have been modeled with cuboid elements on a Cartesian grid. The first 3 mm spacingto the heated side wall were resolved with 300 elements in x-direction with 4.6 million cells inthe domain. The heat source is represented by a point source supplying 4 W. For the brass platea specific heat capacity of 376 Jkg-lK-1 and a heat transfer coefficient of 454 Wm-2K-1 forthe heat transfer between brass and fluid have been estimated. Glass walls are modeled with noslip wall boundary conditions and a heat transfer coefficient of 5.1 Wm-2K-1. Both， experimental and numerical results are in good agreement. Local temperature deviationsof up to 1.2C in the near wall region can be detected. Our assumption is that these differencesoriginate from deviations in the actual and numerically assumed heat transfer coefficient andpower input， which lead to different wall temperatures in the simulation and the experiment.As the actual alloy composition for the used brass wall is unknown the heat transfer coefficientwas assumed from standard material tables [12]. (a) ()Az Figure 3： ((a) Dimensionless temperature profiles and (b) Dimensionless velocity magnitudeprofiles in the dimensionless normal wall direction Ax for height of Ay = 14mm from thebottom wall at different time steps； yellow indicated theoretical computations of Ostrach [13] 5.2. Temperature and Velocity profiles of the accelerating flow Fig. 3 shows the temperature and velocity profiles of the wall normal direction Ac averagedover 12.8 mm ≤^y ≤ 15.5 mm and the corresponding standard deviation as a function of timeand therefore of the Prandtl number. The profiles are shown for 0.82mm≤Ax ≤ 3 whichcorresponds to the depicted ROI. Because of the steady growth of the temperature profile atime independent and dimensionless scale was chosen. For comparison theoretical profiles for alaminar convection flow of a vertical plate with homogeneous temperature distribution accordingto Ostrach [13] are plotted in yellow for a Prandtl number of 10. The Prandtl number decreaseswith higher temperature and in this case with higher velocities. The profiles are in good qualita-tive agreement with theoretical predictions. Differences emanate from different inflow conditionsof the present experimental compared to those depicted by Ostrach. time s] Figure 4： (a) Nusselt numbers averaged over for 12.8 mm≤Ay ≤15.5 mm according to (2) atdifferent time steps； (b) averaged scaled Grashof number AyGr-1/4 for 12.5 mm ≤Ay ≤ 15.5 mm Additionally Nusselt and Grashof numbers were determined according to： Here， Ay = 14 mm denotes the distance from the bottom wall. oT/ox is the temperaturegradient in normal wall direction and Tw the wall temperature. Both values were extractedfrom a first order polynomial fit to the temperature profiles.To =21.2°C denotes thestarting temperature of the fluid measured by the thermocouples， g denotes the accelerationof gravity， B is the isobaric cubic expansion coefficient and v is the kinematic viscosity for waterat T=21.2C. o denotes the hydrodynamic boundary layer thickness. Since there is a proportionality between Grashof number and hydrodynamic boundary layerthickness according to (4)， Nu and AyGr-1/4 are shown in Fig.4a and 4b. Fig. 4 shows the Nusselt numbers and the hydraulic boundary layer thickness as a functionof time for both， numerical and experimental results. While in both cases the slopes are similar，there is an offset between the absolute values. It may be noted that both， Nusselt number andGrashof number are mainly a function of wall temperature and as mentioned in section 5.1， thenear wall temperature in the simulation differs from that in the actual experiment. Early studies of Goldstein and Eckert 3] showed that the unsteady free convection boundary layer grows with time before shrinking again to approach a steady state value. Obviously thetime series shown here， covers the phase of hydrodynamical boundary layer shrinking. Accordingto a relation obtained by Sparrow and Gregg [14] for this phase of flow problem following relationcan be expressed： It could be found that the factor k ≈ 0.5 here for Pr=5.7. 6. Conclusion and Outlook Combined Differential Interferometry and Long-range uPIV measurements could be successfullyapplied to a temperature driven boundary layer flow.Spatial resolutions of 405um forDifferential Interferometry and 101 _im for Long-range uPIV could be achieved. The comparisonbetween measurement and simulations results showed local temperature deviations of less than1.2℃， which lead to deviations in the temporal evolution of the Nusselt number and thethickness of the hydrodynamic boundary layer at the same time. While the Nusselt numbersincreased for all observed time steps， the hydrodynamics boundary layer reduces simultaneouslyTheoretical results of a steady laminar convective flow with a vertical heated plate are in goodqualitative agreement to the observed flow problem. In future studies the measurement technique will be improved by implementing a secondWollaston Prism into the set-up. For this the separated laser light after the dichroic mirror(see Fig 1b) has to be split into two parallel beams each passing one Wollaston prism. Beforeentering the camera the signals have to be recombined again. The result on the camera chip is agrid pattern. Furthermore， to investigate all characteristics of the boundary layer development，long time scale measurement are planned. References ( [1] Praisner T J， Sabatino D R and S mith C R 2001 Experiments in Fluids 30 1- 1 0 ) 2]1Egbers C， Brasch W， Sitte B， Immohr J and Schmidt J R 1999 Measurement Science andTechnology 10 866-877 ③Goldstein R and Eckert E 1960 International Journal of Heat and Mass Transfer 1日 Skarman B. Becker Jand Wozniak K 1996 Flow Measurement and Instrumentation 7 1-6 Woisetschlager J， Pretzler G， Jericha H， Mayrhofer N and Pirker H P 1998 Ecperiments inFluids 24 102-109 Iben U，Morozov A， Winklhofer E and Wolf F 2011 Experiments in Fluids 50 597-611 Kordel S， Nowak T， Skoda R and Hussong J (accepted) 2016 Esperiments in Fluids [8] Merzkirch W 1987 Flow visualization 2nd ed (Orlando： Acad. Press) 9] SmallR D， Sernas V A and Page R H 1972 Applied Optics 11 858 [10] Agrawal A， Raskar R and Chellappa R 2006 Computer Vision ECCV 2006 vol 3951 (Berlin，Heidelberg： Springer Berlin Heidelberg) pp 578-591 ( [11] . ] Raffel M(ed) 2007 Particle image velocimetry： a p ractical guide 2nd ed ( Heidelberg； NewYork： Springer) ) ( [12] Verein Deutscher Ingenieure and Gesellschaft Verfahrenstechnik und Chemieingenieurwesen(eds) 2013 VDI-Warmeatlas 1 1 th ed (Berlin： Springer Vieweg) ) ( [13] Ostrach S 1953 Trans. Am. Soc. M ec. Engrs 7 5 1287-12 9 0 ) ( [14] Sparrow E and Gregg J 1956 Trans. ASME 78 435-440 ) Published under licence by IOP Publishing Ltd In the present study Dierential Interferometry and Long-range PIV aresuccessfully combined for a benchmark experiment of an accelerating temperature drivenboundary layer flow. Spatial resolutions of 405 μm for the interference and 101 μm for the PIVmeasurements could be achieved. The results of the combined measurements are comparedwith results of numerical simulations. Temperature and velocity proles are compared withtheoretical values and a relation between Nusselt number and Grashof number could be worked out.