边界层中流场,速度矢量场检测方案(CCD相机)

智能文字提取功能测试中

18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics ·LISBON|PORTUGAL· JULY 4-7，2016 Submicron Resolution Long-Distance Micro-PlV Measurements in a Rough-WallBoundary Layer Bercelay Niebles Atencio1*， Mikhael Tokarev2， Valery Chernoray1 1： Dept. of Applied Mechanics， Chalmers University of Technology， Gothenburg， Sweden 2： Kutateladze Institute of Thermophysics， Siberian Branch of Russian Academy of Sciences， Novosibirsk， Russia * Correspondent author： bercelay.niebles@chalmers.se Keywords： PIV processing， Micro PIV， Boundary Layer， Roughness Function ABSTRACT The prediction of the mean flow and turbulence structure of a boundary layer on surfaces with different type andshape of roughness is still one of the major questions in fluid mechanics. The specific character of wall roughness interms of shape， size and distribution strongly varies from case to case and an equivalent roughness concept wasintroduced in order to enable engineers to design systems with rough walls. The current paper shows a method toobtain the roughness function of different surface roughness by using a small-scale rig with rotating disks and along-distance microscopic PIV in order to obtain submicron resolution inside the boundary layer developed on thedisks when they rotate. This rig was designed and constructed for the optical measurements and consists of anelectric motor which drives the disks that are rotating in the middle of a 20-liter water tank. The measurements wereperformed on surfaces with different degree of roughness. These are a smooth reference， three antifouling coatingsused in marine applications， two different sand roughness and one case of periodic roughness. All measurementswere performed at two different Reynolds numbers (5.7×10 and 1.15×10)， corresponding to disk rotational speedsof 300 and 600 rpm. Field mean velocity profiles were calculated by averaging vertical bins with 1-pixel (px) width.Every point of a mean velocity profile was based on near 200 instant velocity values obtained from 2000 PIV imagepairs by using particle tracking approach. The results of a wall shear stress study of the smooth disk case were usedtogether with torque measurements and the micro-PIV measurements for the different rough surfaces to come upwith their dimensionless velocity profiles. The results show that as expected，the velocity profiles are shifteddownwards due to the roughness presence. Finally， the skin friction coefficients of the different cases are comparedwith previous studies and the roughness function is determined for the different surfaces. The roughness function isvery useful in some industries such as in the naval architecture field， where the drag can be better estimated and theadverse effect can be better counteracted. 1. Introduction One of the major and still actual questions in fluid mechanics is the prediction of the mean flowand turbulence structure of the turbulent boundary layer on a surface with different type andshape of wall roughness. The specific character of wall roughness in terms of shape， size and distribution strongly variesfrom case to case and an equivalent roughness was introduced in order to enable engineers to design systems with rough walls. The equivalent sand roughness concept was introduced byMoody (1944) and is widely accepted as a standard approach to account for the roughnessinfluence on skin friction factors. This concept assumes that a given arbitrary-shape roughness isrepresented by an equivalent homogeneous sand roughness， which is composed of denselypacked spheres. The height of the equivalent sand roughness has to be chosen such that thefriction factor for the roughness under consideration is equal to that for the equivalent sandroughness at high Reynolds numbers (i.e. in the fully rough regime). In engineering practice， it iscommonly assumed that the corresponding equivalent roughness is the same for all Reynoldsnumbers. The corresponding values of the equivalent sand grain roughness have beendetermined experimentally for many materials and surface finish in the past and thus can betaken from general tables of correspondence. However， values in these tables in most cases aregiven as ranges， and thus provide only a low degree of accuracy. Furthermore， for any new typeof surface roughness the correlation has to be derived again from numerous expensiveexperiments. The aim of an ongoing research project at Chalmers is to develop a more optimal and accuratemethod for obtaining the roughness function for an arbitrary surface roughness. The main ideaof the method is to replace expensive high-Reynolds number experiments by tests in a small-scale rig and subsequently by calculations with a resolved CFD. A small-scale test method utilizing rotating disks (Granville， 1972) is used. The advantage of thismethod is that the disks with different surface roughness can easily be manufactured and theentire disk surface can be scanned by a high-precision laser scanner. According to Granville， thefluid dynamic drag is accurately determined from disk torque measurements and the roughnessfunction (Hama， 1954) is evaluated from a theoretical analysis. In order to validate this method，boundary layer measurements are necessary. Since the boundary layer on a rotating disk is verythin， we use a long-distance microscopic PIV in order to obtain a submicron resolution. Inaddition， CFD calculations and results from other researchers are presented for comparison. 2. Experimental Setup 2.1. General description of the rig and the setup A rotating disk rig based on Granville's experiments was designed and constructed for themeasurements. The disk rotates by an electric motor in the middle of a 20-liter water tank. Figure1 shows a schematic of the measurement setup. Disks with radius R，= 150 mm were used. The PIV measurements were performed at a radiusR =135 mm. The test disks had different surface roughness as listed in Table 1. The study includes a smooth reference， three different marine paint coatings， two different sandpaperroughness and one case of periodic roughness. For each case， the measurements wereperformed aat two different rotational Reynolds numbers equal to 5.7×10 and 1.15×10corresponding to disk rotational speeds of 300 and 600 rpm. The rotational Reynolds number Re is defined in terms of the rotational speed ω and theviscosity v as (Granville， 1972)： Fig 1. Schematic of the measurement set up. To the upper right， a frontal view of the water tank is shown with thedisk and the point where measurements were taken (red dot in the tank). Roughness cases A， B and C correspond to realistic surfaces of antifouling paints used in marineapplications. The way to obtain the coatings with different roughness is explained in detail inSavio et al. (2015). The coating applications were made by spraying the surfaces to give the threelevels of roughness A， B and C. Level A of roughness simulates an optimal new build ship or fullblast dry docking paint application. The second level (B) of roughness represents a poorlyapplied coating and roughness C represents a severe case of underlying roughness accumulatedfrom many dry dockings and a very poor application. The test disks were scanned by MartinAxelsson， R&D Chemist from Jotun A/S (Norway) using a 3D laser profilometer from whichroughness parameters， such as the average roughness height k， were determined. The values ofthe average roughness for the sandpaper cases (80-grit and 400-grit) were obtained from theFederation of European Producers of Abrasives (FEPA) website and the roughness for the periodic case was measured with a micrometer. Figures 2 shows typical roughness geometryscans (for surfaces B and C). Figure3 shows the disk with the 80-grit sandpaper case. Table 1. Experimental cases of surface roughness with their average heights in micrometers. Smooth A B C 80-G 400-G Periodic 0.55 13 33 55 201 35 500 30(a) 10 25 (b) Fig 2. Surface scans showing roughness type B (a) and type C (b). Dimensions in mm. Fig 3. Rough disk with the 80-grit sandpaper and a PMMA insert installed. 2.2. PIV Measurement Setup Measurement of boundary layer profiles on disks is a challenging task due to very smallthickness of the boundary layer (3 - 5 mm). In order to measure the azimuthal velocitycomponent near the disk wall with the high spatial resolution and to capture the inner layer ofthe turbulent boundary layer， a microscopic optics was used. The optical magnification Mduring the experiments was M = 4 - 12 times， so that the 1.5 - 4 mm area of interest wasprojected on a 16-mm camera image sensor. A long distance microscope (Questar QM1) waslocated at a distance 560 mm from the measurement point， as shown in figure 1， to provide themaximal possible magnification and the minimal depth-of-field of 155 um， which defined thespatial resolution of the method. The microscope is the Maksutov Cassegrain Catadioptric typewith two mirrors and had the f-number #f=8.7 for the used configuration of optics. For flow seeding， spherical PMMA particles (Microparticles GmbH) with the minimum diameter1 um were used. The particle density 1.19 g/cm is close to the water density and the particlesare small enough to follow the flow faithfully. The illumination is performed by a pulseddouble-cavity Nd：YAG 532-nm laser with the pulse energy of 200 mJ (Quantel EverGreen EVG00200)， and pulse duration less than 10 ns. Time separation between pulses of laser were 6 -20 us to keep relatively the same particle displacement in the images between different cases. Abeam was aligned into a thin 0.5 mm laser sheet with a cylindrical LaVision sheet optics that waslocated on a laser-guiding arm. The averaging depth of the measurement was defined by thedepth-of-field of the optics rather than the illumination domain. Transferred and magnified the scattering field of the flow with tracers was registered by amonochrome double-frame CCD camera ImagerProX 4M (LaVision GmbH) with 2048 pixel by2048 pixel resolution， 14-bit pixel depth， and 7.4- u m pixel size. The camera recording time wassynchronized with the specific angle of rotation of the test disk through a signal from a Hallsensor. For the rotation speed 600 rpm， the camera registered image pairs every secondrevolution as its maximum frame rate at full resolution in double frame mode was 8.2 fps.Registered images had particle images in the form of a diffraction pattern with a central circularpart and several rings around it as shown in figures 4 and 5 (b). The particle image size was near8 pixels in diameter. We used DaVis 8.2.2 software (LaVision GmbH) for data acquisition duringthe experiment. This software also controlled a timing device (LaVision GmbH) to trigger laserpulses and image recording. Geometrical calibration of the measurement field was done by ametal wire with a known diameter 0.85 mm which was imaged in the measurement area beforethe actual experiment. 2.3. Procedure for Localization of the Wall One of important issues was localization of the wall position in the images. For this purpose， a10-mm radial transparent insert made of PMMA plastic was embedded in the disk as shown infigure 3 to provide a reflective surface. Another purpose of this insert was to reduce excessivelight scattering from the rough surface that decreases the signal to noise ratio of particle imagesnear the surface. Additionally， the light-sheet was stopped down using an orifice located afterthe LaVision sheet optics to avoid the reflections from the surfaces outside the transparent insert.The wall location was determined by reflections of the tracers near the wall as shown in figure 4.It was located by a peak velocity at the wall position since the reflected particles had decreasingvelocity in the direction away from the wall resembling a mirrored velocity profile in horizontaldirection. The wall location was carefully adjusted parallel to the vertical image coordinatebefore the experiments to simplify the image processing. The camera recording synchronizationwith the specific angle of the test disk rotation was performed to carry out the measurements atfixed angular disk position and to freeze the disk at one position in a recording image. 2.4. PIV Data Processing For data processing we used a tracking based approach with the identification of individualparticle images in both recorded PIV image pairs and finding the correspondence between them.The particle image tracking was complicated by the large diffraction pattern size with the brightmultiple rings， parts of which were identified as separate standalone particles with the standardavailable algorithms for the PTV method. In order to decrease this multiple identification， theraw images were pre-processed by correlating them with the Airy diffraction disk templateintensity distribution， which was extracted from one of the recorded images. Examples of theused templates are shown in figure 5. The analytical template was obtained following theequation 2 (Raffel et. al， 2007)： Where is the Bessel function of the first kind of order one and I， is a constant multiplier. Thisis the theoretical solution for a diffraction image of a light point source through a circularaperture. However， according to our tests the real particle image templates as one shown infigure 5 (b) gave better results for the particle identification efficiency. An example of thenormalized correlation of the experimental image with the template from figure 5 (b) andobtained vector field of the particles is presented in figure 6. As can be seen the applied imagepreprocessing equalizes the intensity of the particle images regardless their original brightnessand size， which helps to identify more objects and decrease the number of erroneousidentifications linked with multiple rings in the Airy diffraction pattern. Having low particle concentration on the images of the order of 5×10 particles per squaredpixels (px’)， the mean distance between neighboring tracers was approximately 150 px. Arelatively simple nearest neighbor algorithm for a corresponding particle search in both frameswas used， because the maximum possible displacement did not exceed 50 px orone third of themean distance between particles for the mentioned particle concentration. Particles without apair in one of the frames were rejected. Final mean velocity profiles were calculated by averaging vertical bins with 1 px width. Everypoint of a velocity profile was based upon near 200 instant velocity values obtained from 2000PIV image pairs by using particle tracking approach described above. Fig 4. Example of particle images and their reflections by the wall. Fig 5. Used correlation templates for identification of a particle diffraction pattern： (a) an analytical Jinc template， (b) a real diffraction template from a PIV image. Fig 6. A pre-processed particle image by the normalized correlation with the real diffraction pattern. The velocityvectors obtained from the particle tracking algorithm are shown over the image. Accuracy of the particle identification algorithm can be assessed as 0.5 px due to the relativelylarge particle diameter 8 px. Hence， for two identifications of start and end positions we get theaccuracy of an obtained particle displacement as 1 px. This equals 4.3% at the region with thehalf disk velocity or absolute errors 0.18 m/s and 0.36 m/s for the disk rotational speeds of 300and 600 rpm. The assessment of the accuracy of the obtained mean velocity profile gives 0.5% forthe same region. Generally speaking， the velocity profiles shown in the literature are based on the fact that theflow is moving over a fixed wall. However， given the characteristic of the flow (which moveswith its highest velocity at the wall， dragged by the disk)， the velocity profile obtained would bedifferent (reversed). For that reason， a transformation of the reference system was done， so thefinal velocity profile can be easily compared to the ones seen in the literature. 2.5. Torque Measurements Resisting moment (or torque) measurements were performed for all disk cases in order todetermine the wall shear stresses. For doing that， a Kistler type 4503A torque meter was installedon the rig connecting the electric motor and the rotating disk shaft (as seen in figure 1). Thetorque sensor operates based on the strain gauge principle. The torque meter output wasmonitored by an analogue to digital converter (ADC) controlled by a PC. The torque wasmeasured for rotational velocities from 0 to 600 rpm. The measurement procedure has includeda warm up of the running rig and the measurement equipment for at least one hour beforeexperiments. First the torque of the shaft and bearings with seals was measured without a diskand these readings were subtracted from the measured total torque in order to obtain the torqueof the disks. 3. CFD Setup The different cases were also simulated by a CFD software which is StarCCM+ version 9.06.009.The domain for the simulations was chosen to be an area of 5 mm x20 mm of the total scannedsurface described in section 2.1. The mesh was generated in ICEM CFD version 17.0 and adependency test was carried out to check how the wall shear stress changes while varying themesh density. Table 2 shows details of the final mesh sizes for the cases A， B and C. Thetolerance is describing the difference in wall shear stress between two refinements (the optimalmesh that was used for simulations versus the most refined mesh) and is a measure of theaccuracy of the mesh used for simulations. Table 2. Number of mesh cells in millions (M) for the simulations of the painted surfaces. A B C SIZE 3.8 M 6.3M 7.5 M TOLERANCE 0.2% 0.4% 0.6% Once the mesh was obtained， then the physical model used for the computations was asfollows： Steady flow Segregated flow Reynolds-Average Navier Stokes (RANS) ° K-omega Shear Stress Transport (SST) turbulence model ·All y+ wall treatment. The simulations were carried out using mass flow as input，so that the bulk velocity through thedomains were 4.24 m/s and 8.48 m/s (which were the tangential velocities at 300 and 600 rpm).A converged result was considered when the values of the wall shear stress showed asymptoticbehavior and the difference in the last 20 iterations was 0.1% For post-processing of the results， first the zero-plane wall was determined. The zero-plane waschosen to be the value of the average roughness k subtracted from the y location of the roughwall for cases A， B and C. For sandpaper cases， since they were simulated from a smooth walldomain (adding the roughness as an input data in the physics model)， the zero-plane wall waslocated at the y location of the bottom wall. The same applied for the periodic case simulation.From the zero-plane wall， planes at different distances were created. The average values of thebulk velocity on those planes were obtained and the wall shear stress is also obtained from theresults. We are then able to plot the velocity profiles. 4. Results 4.1. Velocity profiles In order to obtain the dimensionless velocity profiles for the different rough cases， adetermination of the wall shear stress on the smooth disk at different Re was carried out inprevious tests. The results are shown in figure 7. As we already know the torques for all the cases， by calculating the torque ratio rough/smoothfor all cases， one is able to estimate the local skin friction coefficient and therefore， the wall shearstress for the rough cases， because the local skin friction coefficient was already determined forthe smooth case. We can do that because the skin friction coefficient increases in the sameproportion as the resisting moment or torque if we keep disk radius constant (Granville 1972).Table 3 summarizes the torque measurement results. Table 3. Torque measurements for different roughness in N-m (Overall error 3.5%) RPM A B C 80-Grit 400-Grit Periodic Smooth 300 0.20 0.23 0.24 0.32 0.20 0.36 0.16 600 0.65 0.82 0.87 1.39 0.90 0.93 0.58 Once the wall shear stresses were determined， the dimensionless velocity profiles can beobtained because the spatial distributions of mean velocities were determined during the PIVpost-processing. The law of the wall (von Karmán， 1930) is applied to obtain the different plots，according to Fig 7. Local skin friction coefficient versus Reynolds number for the smooth disk case. Where the von Kármán constant is k=0.41 and B=5.1. The velocity U and the wall coordinate yare made dimensionless with friction velocity U， and viscosity v. Figures from 8 to 14 show thevelocity profiles for the different cases obtained from PIV. Cases smooth and roughness A， B andC are also compared with CFD simulations. (b) Fig 8. Dimensional (a) and dimensionless (b) velocity profiles for the smooth case compared with CFD. (a) (b) Fig 9. Dimensional (a) and dimensionless (b) velocity profiles for the rough case A compared with CFD. (a) (b) Fig 10. Dimensional (a) and dimensionless (b) velocity profiles for the rough case B compared with CFD. (a) Fig 11. Dimensional (a) and dimensionless (b) velocity profiles for the rough case C compared with CFD. (a) (b) Fig 12. Dimensional (a) and dimensionless (b) velocity profiles for the rough case 80-grit sandpaper. (a) (b) Fig 13. Dimensional (a) and dimensionless (b) velocity profiles for the rough case 400-grit sandpaper. (a) (b) Fig 14. Dimensional(a) and dimensionless (b) velocity profiles for the periodic rough case. As can be seen from the figures， the velocity profiles between experiments and CFD agree (or atleast are close) for the smooth and rough case A. That is， for the smallest roughness cases. As theroughness increases， the difference between the CFD and the experiments is more noticeable.The experiments show that the dimensionless velocity profiles move more downwards as theroughness increase which is the expected behavior. This downwards displacement of thevelocity profile in the rough cases with respect the smooth case is known as the roughnessfunction， Au (more details will be given in section 4.3). It is also noticeable that the profiles ingeneral exhibit a similar slope as in the theoretical law of the wall lines， but maybe in some casesthe slope looks different， which might suggest a different value of the von Kármán constant.However， the determination of the value of this constant is beyond the scope of the presentpaper. The CFD predictions do not behave as the experiments for cases B and C. The velocity profilesdo move downwards， but not as much as we can see from the PIV results. From the dimensional velocity profiles， we can also see disagreement between the experimentsand the CFD computations. One could think that the velocities in the simulations are not wellpredicted and that could explain the disagreement compared with the velocity profiles from thePIV measurements.The simulation of surfaces with extremely complicated and randomroughness is quite challenging as can be shown from these results. It might be worth trying with another turbulence model to see if the velocities are better predicted and depending on this，decide whether the mesh needsto be changed. Even with such disagreement in thedimensionless velocity profiles from the CFD simulations， one is able to get the intercept of theprofiles with the y- axis (extending the lines) and from this intercept， we can get the CFDroughness function， which will be shown later. 14.2.Skin Friction Coefficients Skin friction coefficients Cr were determined as explained at the beginning of this chapter. Figure15 shows the resulting plot with results from other researchers working with similar roughness.Figure 15 shows that in general， the skin friction coefficients for the rough cases lie above thesmooth line (as they should) derived by Schultz-Grunow and described in Schlichting (1979). The plot also shows that the sandpaper cases for Re=5.7×10 lie above the smooth line more orless at the same distance as shown by the skin friction coefficients in Shapiro (2004) and Schultz(2002)， taking into account that those results were obtained at higher Reynolds numbers. Theskin friction coefficient at Re=1.15×10for the sandpaper cases is overestimated， especially forthe 80-grit sandpaper case. 一 Re Fig 15. C，vs Reynolds numbers for different cases， including results from Shapiro (2004) and Schultz (2002). 4.3. Roughness Function The effect of roughness in the log-law profile is represented by the roughness function， AUwhich is the downward shift in the log-law profile (Flack and Schultz， 2010) resulting in： The roughness function shows the velocity deficit due to roughness and there are many ways toexpress it. One of those ways was proposed by Hama (1954) using the skin friction coefficientsfor the rough and smooth cases at the same Reynolds number： By using equation 5， one can plot the roughness function to see its dependence onadimensionless parameter called roughness Reynolds number， k defined as： Here k is a roughness length scale (in this case the roughness average value)， U. is the frictionvelocity √(t/p) with t as wall shear stress， p as the density of the fluid and v the viscosity.Figure 16 shows the roughness function plot of the paints (cases A， B and C) obtained whenequation 5 is applied， compared with roughness function from CFD simulations and from thePIV profiles. For comparison， the uniform sand line of Nikuradse (1933) is shown. As can beseen， the CFD and PIV roughness functions are not exactly the same， but are close. The case Bshows the largest difference between both methods at the low roughness Reynolds number. Theroughness function obtained from Hama's equation is underestimated in all the cases. In general，we can see similarities between CFD and results from PIV， which is desirable， but the best wouldbe to get agreement between these results and other methods (like Hama’s). This has to befurther investigated. It is also possible for the different rough surfaces to behave like the uniform sand curve ofNikuradse if the roughness length is scaled. For example， if the roughness length (in this case theaverage) is around 4 times larger for the cases A， B and C， we can almost collapse the roughnessfunction obtained from PIV results into the uniform sand curve as shown in figure 17. Theimportance of expressing the roughness in terms of Nikuradse sand-grain lies in the fact that wecan use Moody's chart (1944) and get the corresponding friction factor. This is widely used inengineering applications. It is always desirable to compare experimental data with computations and get agreement. Thisis sometimes difficult when the physics of the problem is not trivial. As might be inferred fromthe results， in order to get reliable skin frictions and roughness functions from CFD， we need tobe carefully set up the case. Otherwise， it might be enough performing CFD once for the smoothsurface and different Re， then validate it with PIV measurements and use torque test data for thedifferent rough surfaces. A Hama A CFD米 A PIVB HamaB CFD米 B PIV C Hama C CFD 米 C PIVSand Curve Fig 16. Roughness function plot for the paints and sandpaper cases Fig 17. Roughness function after scaling the roughness height 4. Conclusions Long-Distance Micro-PIV measurements in the boundary layer of rotating flow over disks withdifferent surface roughness were performed in order to validate disk resisting moment (ortorque) measurements. These torque measurements can be used to determine the fluid dynamicdrag and the roughness function of different rough surfaces. The skin friction coefficients and wall shear stresses were determined using values from thesmooth case disk and from torque measurements. Using the velocities obtained from the micro-PIV measurements， the dimensionless velocity profiles were plotted. These profiles show adeficit in velocity as expected and this deficit is represented by a downshift in the profile withrespect to the smooth theoretical velocity profile. The skin friction coefficients and the roughness functions were obtained for the different casesand compared with results given by the velocity profiles and other researchers. The roughnessfunction calculated using a former expression seems underestimated when compared with PIVresults. The CFD computations might not be needed for all roughness cases but just for the smooth caseto be validated with experiments， but if they are required， another turbulence model or bettermesh have to be used. That is some work to be done in the future. The results suggested that this is a promising technique that might help increase the knowledgeand the understanding of the boundary layer in flows over rough surfaces. 5. Acknowledgements This research is supported by the EU FP7 Project“Low-toxic cost-efficient environment-friendlyantifouling materials" (BYEFOULING) under Grant Agreement no. 612717. We also thank JotunA/S and their staff for all the support and help during the development of this project. 6. References ( Federation of European Producers of Abrasives， FEPA (http：//www.fepa-abrasives.org/). ) Flack K， Schultz M (2010).Review of Hydraulic Roughness Scales in the Fully Rough Regime.Journal of Fluids Engineering 132：0412031-04120310. Granville P (1972). The Torque and turbulent boundary layer of rotating disks with smooth andrough surfaces， and in drag-reducing polymer solutions. Dept. of the Navy Naval Ship Researchand Development Center， Report 3711. Hama F (1954). Boundary-Layer Characteristics for Rough and Smooth Surfaces. TransactionsSNAME 62：333-351. Moody L (1944). Friction Factors for Pipe Flow. Trans. ASME 66：671-688. Nikuradse J (1933). Laws of Flow in Rough Pipes. NACA Thecnical Memorandum 1292. Raffel M， Willert C， Wereley S， Kompenhans J (2007). Particle image Velocimetry. A PracticalGuide. Springer， New York. Savio L， Ola Berge B， Koushan K， Axelsson M (2015). Measurements of added resistance due toincreased roughness on flat plates. In proc. of 4th Int. Conf. on Advanced Model MeasurementTechnology for the Maritime Industry (AMT'15). ( Schlichting H(1979). Boundary-Layer Theory.McGraw-Hill，New York. ) ( Schultz M ( 2 002). T he Relationship B e tween Fr i ctional Resistance and Roughness for SurfacesSmoothed by Sanding. Journal of Fluids Engineering 124：492-499. ) Shapiro Th (2004)， The Effect of Surface Roughness on Hydrodynamic Drag and Turbulence，USNA- Trident Scholar project report 327. ( von Kármán Th (1931) Mechanical Similitude and Turbulence. NACA Technical Memorandum611. ) The prediction of the mean flow and turbulence structure of a boundary layer on surfaces with different type andshape of roughness is still one of the major questions in fluid mechanics. The specific character of wall roughness interms of shape, size and distribution strongly varies from case to case and an equivalent roughness concept wasintroduced in order to enable engineers to design systems with rough walls. The current paper shows a method toobtain the roughness function of different surface roughness by using a small-scale rig with rotating disks and along-distance microscopic PIV in order to obtain submicron resolution inside the boundary layer developed on thedisks when they rotate. This rig was designed and constructed for the optical measurements and consists of anelectric motor which drives the disks that are rotating in the middle of a 20-liter water tank. The measurements wereperformed on surfaces with different degree of roughness. These are a smooth reference, three antifouling coatingsused in marine applications, two different sand roughness and one case of periodic roughness. All measurementswere performed at two different Reynolds numbers (5.7×105 and 1.15×106), corresponding to disk rotational speedsof 300 and 600 rpm. Field mean velocity profiles were calculated by averaging vertical bins with 1-pixel (px) width.Every point of a mean velocity profile was based on near 200 instant velocity values obtained from 2000 PIV imagepairs by using particle tracking approach. The results of a wall shear stress study of the smooth disk case were usedtogether with torque measurements and the micro-PIV measurements for the different rough surfaces to come upwith their dimensionless velocity profiles. The results show that as expected, the velocity profiles are shifteddownwards due to the roughness presence. Finally, the skin friction coefficients of the different cases are comparedwith previous studies and the roughness function is determined for the different surfaces. The roughness function isvery useful in some industries such as in the naval architecture field, where the drag can be better estimated and theadverse effect can be better counteracted.