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Register a new userExtensive characterization of a high Reynolds number decelerating boundary layer using advanced optical metrology
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Added by
Jean-Philippe Laval
Publication date
2017
fields
Physics
and research's language is
English
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An experiment conducted in the framework of the EUHIT project and designed to characterize large scale structures in an adverse pressure gradient boundary layer flow is presented. Up to 16 sCMOS cameras were used in order to perform large scale turbulent boundary layer PIV measurements with a large field of view and appropriate spatial resolution. To access the span-wise / wall-normal signature of the structures as well, stereoscopic PIV measurements in span-wise/wall-normal planes were performed at specific stream-wise locations. To complement these large field of view measurements, long-range micro-PIV, time resolved near wall velocity profiles and film-based measurements were performed in order to determine the wall-shear stress and its fluctuations at some specific locations along the model.
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An experiment was performed using SPIV in the LMFL boundary layer facility to determine all the derivative moments needed to estimate the average dissipation rate of the turbulence kinetic energy, $varepsilon = 2 u langle s_{ij}s_{ij} rangle$ where $s_{ij}$ is the fluctuating strain-rate and $langle~rangle$ denotes ensemble averages. Also measured were all the moments of the full average deformation rate tensor, as well as all of the first, second and third fluctuating velocity moments except those involving pressure. The Reynolds number was $Re_theta = 7500$ or $Re_tau = 2300$. The results are presented in three separate papers. This first paper (Part I) presents the measured average dissipation, $varepsilon$ and the derivative moments comprising it. It compares the results to the earlier measurements of cite{balint91,honkan97} at lower Reynolds numbers and a new results from a plane channel flow DNS at comparable Reynolds number. It then uses the results to extend and evaluate the theoretical predictions of cite{george97b,wosnik00} for all quantities in the overlap region. Of special interest is the prediction that $varepsilon^+ propto {y^+}^{-1}$ for streamwise homogeneous flows and a nearly indistinguishable power law, $varepsilon propto {y^+}^{gamma-1}$, for boundary layers. In spite of the modest Reynolds number, the predictions seem to be correct. It also predicts and confirms that the transport moment contribution to the energy balance in the overlap region, $partial langle - pv /rho - q^2 v/2 rangle/ partial y$ behaves similarly. An immediate consequence is that the usual eddy viscosity model for these terms cannot be correct. The second paper, Part II, examines in detail the statistical character of the velocity derivatives. The details of the SPIV methodology is in Part III, since it will primarily be of interest to experimentalists.
An SPIV experiment using two orthogonal planes simultaneously was performed in the LML boundary layer facility to specifically measure all of the derivative moments needed to estimate the dissipation rate of the Turbulence Kinetic Energy. The Reynolds number was $Re_theta = 7500$ or $Re_tau = 2300$. A detailed analysis of the errors in derivative measurements was carried out, as well as applying and using consistency checks derived from the continuity equation. The random noise error was quantified, and used to ``de-noise the derivative moments. A comparison with a DNS channel flow at comparable Reynolds number demonstrated the capability of the technique. The results were further validated using the recent theory developed by George and Stanislas 2020. The resulting data have been extensively used in parts I and II of the present contribution to study near wall dissipation. An important result of the present work is the provision of reliable rules for an accurate assessment of the dissipation in future PIV experiments.
The modified Townsend-Perry attached eddy model of Vassilicos et al (2015) combines the outer peak/plateau behaviour of rms streamwise turbulence velocity profiles and the Townsend-Perry log-decay of these profiles at higher distances from the wall. This model was validated by these authors for high Reynolds number tur- bulent pipe flow data and is shown here to describe equally well and with about the same parameter values turbulent boundary layer flow data from four different facilities and a wide range of Reynolds numbers. The model has predictive value as, when extrapolated to the extremely high Reynolds numbers of the SLTEST data obtained at the Great Salt Lake Desert atmospheric test facility, it matches these data quite well.
Four well-resolved LESs of the turbulent boundary layers around a NACA4412 wing section, with Rec ranging from 100,000 to 1,000,000, were performed at 5 degree angle of attack. By comparing the turbulence statistics with those in ZPG TBLs at approximately matching Re_tau, we find that the effect of the adverse pressure gradient (APG) is more intense at lower Reynolds numbers. This indicates that at low Re the outer region of the TBL becomes more energized through the wall-normal convection associated to the APG. This is also reflected in the fact that the inner-scaled wall-normal velocity is larger on the suction side at lower Reynolds numbers. In particular, the wing cases at Rec = 200,000 and 400,000 exhibit wall-normal velocities 40% and 20% larger, respectively, than the case with Rec = 1,000,000. Consequently, the outer-region energizing mechanism associated to the APG is complementary to that present in high-Re TBLs.
Intense fluctuations of energy dissipation rate in turbulent flows result from the self-amplification of strain rate via a quadratic nonlinearity, with contributions from vorticity (via the vortex stretching mechanism) and the pressure Hessian tensor, which we analyze here using direct numerical simulations of isotropic turbulence in periodic domains of up to $12288^3$ grid points, and Taylor-scale Reynolds numbers in the range $140-1300$. We extract the statistics of various terms involved in amplification of strain and additionally condition them on the magnitude of strain. We find that strain is overall self-amplified by the quadratic nonlinearity, and depleted via vortex stretching; whereas pressure Hessian acts to redistribute strain fluctuations towards the mean-field and thus depleting intense strain. Analyzing the intense fluctuations of strain in terms of its eigenvalues reveals that the net amplification is solely produced by the third eigenvalue, resulting in strong compressive action. In contrast, the self-amplification terms acts to deplete the other two eigenvalues, whereas vortex stretching acts to amplify them, both effects canceling each other almost perfectly. The effect of the pressure Hessian for each eigenvalue is qualitatively similar to that of vortex stretching, but significantly weaker in magnitude. Our results conform with the familiar notion that intense strain is organized in sheet-like structures, which are in the vicinity of, but never overlap with regions of intense vorticity due to fundamental differences in their amplifying mechanisms.
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