171 Page 2 of 6 Exp Fluids 2015 56 171, Fig 2 Sketch illustrating the coordinate system employed in the pre. sent work x and y are the streamwise and cross stream coordinates. respectively while and are coordinates along the direction of the. local tangent and normal to the airfoil surface respectively. e w e e e w 1, Fig 1 Example 1c MTV image pair obtained over a portion of. where a w is the acceleration of the wall pw is the wall pres. the suction surface of an SD 7003 airfoil at angle of attack of. 6 and Reynolds number based on chord of 2 104 flow is from sure is the fluid density w is the wall shear stress vector. left to right in a closed return water tunnel undelayed top and and e is a unit vector in the wall normal direction Not. delayed bottom images are separated by 10 ms Olson et al ing that the last two terms on the right hand side of Eq 1. 2013 Green lines represent phosphorescence produced by mol. point in the direction it can be shown that the z compo. ecules excited by Excimer UV laser at wavelength of 308 nm The. displacement of individual lines during the inter image time delay nent of Eq 1 leads to. t is obtained at every pixel along the undelayed line by correlating. the image of each undelayed line with its delayed counterpart in the. direction normal to the undelayed line pw pw o aw z d. wavelengths allowing measurements extremely close where pw o is a boundary condition specifying the pres. to the wall Furthermore though 1c MTV is known to be sure at an arbitrarily selected point on the wall aw is the. prone to a bias error in the presence of shear due to the surface tangent component of the wall acceleration in the. velocity component parallel to the line of tagged mole plane and z the spanwise component of is com. cules e g see Koochesfahani and Nocera 2007 this error puted from see Lighthill 1963. approaches zero as the wall is approached and if necessary. a recently developed multi time delay 1c MTV technique e. Hammer et al 2013 may be used to correct for this bias. error e e ez 3, where is the vorticity vector with components as indi. 2 Measurement technique and experimental cated by the subscripts and is the kinematic viscosity. details Expressing the z component of vorticity in Eq 3 in terms. of velocity substituting in Eq 2 and assuming the sur. The wall pressure measurement approach discussed here is face motion to be planar i e constrained in the and. based on the relationship between the wall pressure gradi plane yield. ent and the vorticity flux Wu and Wu 1993 provide the. general expression for the wall vorticity flux from a mov 2 u 2 u. pw pw o aw 2 2 d 4, ing boundary in compressible flow In the incompressible o. limit this expression reduces to see Fig 2 for definition of. coordinates where u is the flow velocity component in the direction. Exp Fluids 2015 56 171 Page 3 of 6 171, Equation 4 provides the basis of the MTV based wall seen to assume the shape typical of a boundary layer veloc. pressure measurement approach In particular the high ity profile this is more visible on the upstream half of the. resolution near wall measurement capability of 1c MTV cylinder where the flow accelerates around the cylinder and. enables accurate measurement of the boundary layer the velocities and hence line displacements during the inter. resolved profile u from which the second derivative of image time delay are larger Note that each line image. the surface tangent velocity component can be computed at represents and average of 500 instantaneous images Also. the wall the third term on the right hand side of Eq 4 to facilitate visualization of the velocity profiles shape the. The other two bracketed terms in Eq 4 can be calcu time delay between the image pair shown in Fig 3 7 ms is. lated separately from knowledge of the surface kinematics larger than that used for the measurements 3 ms. On the other hand measurement of the wall shear stress The MTV images are captured using a 1392 1040 pixel. is readily available from knowledge of u via computa pco pixelfly camera The corresponding measurement reso. tion of the first wall normal derivative of the profile at the lution in the wall normal direction is 37 m A total of 500. wall specifically image pairs are acquired at a rate of 4 93 Hz The resulting. velocity time series at each pixel is averaged to obtain the. w 5 mean azimuthal velocity profile in the wall normal direction. The estimated sub pixel accuracy of the measurement of the. where is the dynamic viscosity The z component of the instantaneous and mean velocity is 0 3 and 0 013 pixel RMS. wall shear stress may also be measured with 1c MTV but respectively The corresponding uncertainty is 3 7 and. would require tracking of the tag lines in the z direction 0 16 of the freestream velocity respectively. as well This would require stereoscopic measurements or. other means to also track the displacement of the lines in. the direction normal to the imaging plane 3 Results and discussion. A proof of concept experiment is conducted to demon. strate 1c MTV based measurements of the wall pressure Examples of the measured mean u velocity profile are given. and shear stress For simplicity measurements are con at two azimuthal locations in Fig 3 bottom at 25 and. ducted over a stationary rigid model of a circular cylinder 85 At 25 the profile has negative curvature d2u d 2. in cross flow which simplifies Eq 4 to at the wall implying an accelerating flow favorable pres. sure gradient On the other hand at 85 the curvature. of the profile at the wall is positive indicative of a boundary. pw pw o 2 d 6 layer that is negotiating an adverse pressure gradient It is. o significant to note the high spatial resolution of the 1c MTV. measurements corresponding to 27 velocity measurements. The cylinder model is made from quartz tube with outer per mm or 37 m spacing between the data points ena. diameter of 5 84 cm and an aspect ratio length over diam bling accurate characterization of the slope and curvature of. eter of approximately 10 The cylinder is mounted verti the velocity profile at the wall. cally spanning the full water depth in a 60 cm 60 cm To compute the first and second derivative of each meas. cross sectional test section of a free surface closed return ured velocity profile at the wall a third order polynomial is. water tunnel fit to the profile data A third order is selected because it is. Measurements are conducted at Reynolds number of the minimum required to accommodate profiles possessing. 6000 based on cylinder diameter and freestream velocity an inflection point i e those exhibiting adverse pressure. using a Coherent COMPexPro 205 XeCl 308 nm UV laser gradient as seen at 85 in Fig 3 No particular effort. beam that is steered using mirrors along the center axis of is made in the present proof of concept to consider higher. the quartz tube to emerge perpendicular to the cylinder s polynomial orders or to use other means of computing the. surface in the radial direction at any desired azimuthal derivatives such as explicit or implicit finite difference. location around the cylinder s perimeter The wall normal schemes The estimated uncertainty 95 confidence in. profile of the azimuthal flow velocity is acquired at one azi computing the derivatives is 0 12 and 4 of the largest. muthal location at a time over the range 5 175 magnitude of the first and second derivatives respectively. in steps of 10 A composite of the individual undelayed based on the variance of the polynomial fit coefficients. MTV images is depicted in the top of Fig 3 to demonstrate The measured surface pressure coefficient. the azimuthal locations of the measurements The delayed Cp pw p 0 5 U2 is plotted versus the azimuthal. image is acquired 7 ms after the laser pulse the correspond angle in Fig 4 As seen from Eq 4 to determine the pres. ing composite of the delayed images may be seen at the sure and hence Cp the pressure at some reference point. bottom of Fig 3 where the lines of tagged molecules are on the wall must be known For the present work a Cp of. 171 Page 4 of 6 Exp Fluids 2015 56 171, Fig 3 Top composite undelayed image of the radially tagged regions lution is 37 m 27 points mm The two insets show enlarged views. around a 5 84 cm diameter cylinder at Re 6000 Bottom composite of the measured velocity profiles at the two angular locations marked. delayed image acquired 7 ms after initial tagging Wall normal reso U is the freestream velocity. In Fig 4 the current measurements of Cp are compared. against published experimental and computational data. Over the Reynolds number range of the studies considered. there is hardly any Reynolds number influence on Cp for. 0 60 and the Cp values from all studies agree very. well At higher azimuthal angles a weak Reynolds number. influence is depicted in the Cp based on the literature show. ing a rather small increase in magnitude with increasing. Reynolds number The present data fall in between the low. and high Reynolds number data consistent with the fact that. the current Reynolds number is bounded by the Reynolds. number values of the literature data It is also noteworthy. that the present data agree closely with the experimental. data at Reynolds number of 8000 which is the closest to. the Reynolds number of the current measurements Over. Fig 4 Comparison of the measured circular cylinder mean surface all the results in Fig 4 demonstrate the effectiveness of the. pressure coefficient yellow filled squares against literature data 1c MTV based technique in measuring the wall pressure. Figure 5 shows comparison of the surface friction coeffi. cient Cf w 0 5 U2 distribution measured in the present. unity at the stagnation point 0 is used as the refer work and those extracted from the computations2 reported. ence value Integral 6 is carried out numerically using the. trapezoidal rule 2, Using data sets obtained from private communication with Visbal. Exp Fluids 2015 56 171 Page 5 of 6 171, Fig 6 Comparison of the measured mean surface shear stress distri. Fig 5 Comparison of the measured mean surface shear stress distri bution yellow filled squares against computational results after scal. bution yellow filled squares against computational results at differ ing the computational results to ReD ref 6000. ent Reynolds numbers, measurements in both the wall normal and wall tangent direc. in Sherer and Visbal 2007 and Rizzetta and Visbal 2009 tions is satisfactory Nevertheless it is useful to assess the. Figure 5 shows good qualitative agreement between the pre influence of the measurement resolution on the accuracy of. sent and published data with the current measurements fall measuring Cp and Cf To this end the data post processing pro. ing in between the two CFD data sets consistent with the cedure is repeated when the spacing of the data is coarsened. Reynolds number trend implied by the numerical results by decimation up to a factor of 5 while keeping spacing at. The Reynolds number trend in Fig 5 is examined in light the full measurement resolution For each spacing the devia. of the theoretical scaling of Cf with Reynolds number for tion in the computed Cp and Cf values from those obtained. laminar boundary layers In particular both Blasius zero without decimation is characterized over the full azimuthal. pressure gradient and Falkner Skan nonzero pressure gra range by calculating the rms of the variation of the deviation in. dient boundary, layer similarity solutions lead to Cf scaling Cp and Cf over all azimuthal angles The results are shown in. with 1 Re where Re is the boundary layer Reynolds num Table 1 for reference the plot symbol size of the present data. ber This implies that the Cf values at different Reynolds is 0 09 for Cp Fig 4 and 0 002 for Cf Fig 6 As expected. numbers can be made to collapse on a single common curve worsening the spatial resolution causes increased deviation. by scaling Cf by the ratio of the square root of the Reynolds from the results obtained at full resolution Over the range of. number of the data and a reference Reynolds number This decimation factors considered the deviation remains reason. scaling would be expected to work only when the boundary able except for the measurement of Cp at a decimation factor. layer at different Reynolds numbers is exposed to similar of 5 corresponding to a measurement resolution of 0 185 mm. non dimensional pressure gradient history The Cp results in It is important to note however that these findings are specific. Fig 4 show that the pressure distribution is very weakly if to the present flow configuration and associated parameters. at all dependent on Reynolds number over the range con A systematic parametric study is needed to identify general. sidered here, Accordingly it is expected that the scaling of ized resolution limit requirements in terms of appropriate local. Cf with 1 Re should hold boundary layer length scales. To verify the above hypothesized scaling the two computa A measurement resolution analysis is also conducted for. tional data sets and the present measurements in Fig 5 are re the direction while keeping the resolution unchanged. plotted in Fig 6 after scaling all data sets to a reference Reyn from the original measurement resolution The results are. olds number of the experiments ReD ref 6000 The results summarized in Table 2 for Cp Cf accuracy is independent of. clearly demonstrate the appropriateness of using 1 Re scal resolution The table shows that only by tripling the spac. 1 3 Exp Fluids 2015 56 171 DOI 10 1007 s00348 015 2039 y LETTER Measurement of the wall pressure and shear stress distribution using molecular tagging diagnostics

O dogma central define o paradigma da biologia molecular em que a informa o perpetuada atrav s da replica o do DNA e traduzida atrav s de dois processos A transcri o que converte a informa o do DNA em uma forma mais acess vel uma fita de RNA complementar e atrav s da tradu o que converte a informa o contida no RNA em prote nas Figura 5 Introdu o

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