Yvan Maciel

Self-Similarity in the Outer Region of Adverse-Pressure-Gradient Turbulent Boundary Layers

This paper presents a consistent theory of self-similarity and of equilibrium in the outer region of turbulent boundary layers that explains recent experimental findings on the subject, including new ones presented here. The theory is first presented in a general form where the outer scales are left unspecified and it is not assumed that the mean velocity defect and the Reynolds stresses share a common velocity scale. It is shown that the main results of the traditional similarity theory remain valid even in this case. Common outer scaling with the Zagarola-Smits length and velocity scales is then chosen. A new pressure gradient parameter is introduced to characterize the local effect of the pressure gradient in all flow conditions including strong adverse-pressure-gradient conditions. By analyzing several adverse-pressure-gradient flow cases, it is shown that self-similarity of the mean velocity defect profile is reached in all cases in localized but significant flow regions. The same is, however, not true of the Reynolds stress profiles. In agreement with the similarity analysis, the self-similar velocity defect profile is found to be a function of the pressure gradient and most flows studied here are only in an approximate state of equilibrium in the region of self-similar defect profiles despite the excellent collapse of the profiles.

Analysis of a Turbulent Boundary Layer Subjected to a Strong Adverse Pressure Gradient

A strongly decelerated turbulent boundary layer is investigated by direct numerical simulation. Transition to turbulence is triggered by a trip wire which is modelled using the immersed boundary method. The Reynolds number close to the exit of the numerical domain is Reθ = 2175 and the shape-factor is H = 2.5. The analysis focuses on the latter portion of the flow with large velocity defect, at higher Reynolds numbers and further from the transition region. Mean velocity profiles do not reveal a logarithmic law. Departure from the law of the wall occurs throughout the inner region. The production and Reynolds stress peaks move to roughly the middle of the boundary layer. The profiles of the uv correlation factor reveal that u and v become less correlated throughout the boundary layer as the mean velocity defect increases, especially near the wall. The structure parameter is low in the present flow, similar to equilibrium APG flows and mixing layers, and decreases as the mean velocity defect increases. The statistics of the upper half of the boundary layer resemble those of a mixing layer. Furthermore, various two-dimensional two-point correlation maps are obtained. The Cvv and Cww correlations obtained far from the transition region at Reθ = 2175 and at y/δ = 0.4 coincide with results obtained for a ZPG boundary layer, implying that the structure of the v,w fluctuations is the same as in ZPG. However, Cuu indicates that the structure of the u fluctuation in this APG boundary layer is almost twice as short as the ZPG one. The APG structures are also less correlated with the flow at the wall. The near-wall structures are different from ZPG flow ones in that streaks are much shorter or absent.

Draft tube flow phenomena across the bulb turbine hill chart

In the framework of the BulbT project launched by the Consortium on Hydraulic Machines and the LAMH (Hydraulic Machine Laboratory of Laval University) in 2011, an intensive campaign to identify flow phenomena in the draft tube of a model bulb turbine has been done. A special focus was put on the draft tube component since it has a particular importance for recuperation in low head turbines. Particular operating points were chosen to analyse flow phenomena in this component. For each of these operating points, power, efficiency and pressure were measured following the IEC 60193 standard. Visualizations, unsteady wall pressure and efficiency measurements were performed in this component. The unsteady wall pressure was monitored at seven locations in the draft tube. The frequency content of each pressure signal was analyzed in order to characterize the flow phenomena across the efficiency hill chart. Visualizations were recorded with a high speed camera using tufts and cavitation bubbles as markers. The predominant detected phenomena were mapped and categorized in relation to the efficiency hill charts obtained for three runner blade openings. At partial load, the vortex rope was detected and characterized. An inflection in the partial load efficiency curves was found to be related to complex vortex rope instabilities. For overload conditions, the efficiency curves present a sharp drop after the best efficiency point, corresponding to an inflection on the power curves. This break off is more severe towards the highest blade openings. It is correlated to a flow separation at the wall of the draft tube. Also, due to the separation occurring in these conditions, a hysteresis effect was observed on the efficiency curves.

Power break off in a bulb turbine: wall pressure sensor investigation

A measurement campaign using unsteady wall pressure sensors on a bulb turbine draft tube was performed over the power and efficiency break off range of a N11 curve. This study is part of the BulbT project, undertaken by the Consortium on hydraulic machines and the LAMH (Hydraulic Machine Laboratory of Laval University). The chosen operating points include the best efficiency point for a high runner blade angle and a high N11. Three other points, with the same N11, have been selected in the break off zone of the efficiency curve. Flow conditions have been set using the guide vanes while the runner blade angle remained constant. The pressure sensors were developed from small piezoresistive chips with high frequency response. The calibration gave an instrumental error lower than 0.3% of the measurement range. The unsteady wall pressure was measured simultaneously at 13 locations inside the first part of the draft tube, which is conical, and at 16 locations in the circular to rectangular transition part just downstream. It was also measured at 11 locations along a streamwise line path at the bottom left part of the draft tube, where flow separation occurs, covering the whole streamwise extent of the draft tube. For seven radial-azimuthal planes, four sensors were distributed azimuthally. As confirmed by tuft visualizations, the break off phenomenon is correlated to the presence of flow separation inside the diffuser at the wall. The break off is linked to the appearance of a large recirculation in the draft tube. The efficiency drop increases with the size of the separated region. Analysis of the draft tube pressure coefficients confirms that the break off is related to diffuser losses. The streamwise evolution of the mean pressure coefficient is analyzed for the different operating conditions. An azimuthal dissymmetry of the mean pressure produced by the separation is detected. The pressure signals have been analyzed and used to track the separation zone depending on the operating conditions. Spectral analysis of these signals reveals a low frequency unsteadiness generated by the flow separation.

Flow separation in a straight draft tube, particle image velocimetry

As part of the BulbT project, led by the Consortium on Hydraulic Machines and the LAMH (Hydraulic Machine Laboratory of Laval University), the efficiency and power break off in a bulb turbine has been investigated. Previous investigations correlated the break off to draft tube losses. Tuft visualizations confirmed the emergence of a flow separation zone at the wall of the diffuser. Opening the guide vanes tends to extend the recirculation zone. The flow separations were investigated with two-dimensional and two-component particle image velocimetry (PIV) measurements designed based on the information collected from tuft visualizations. Investigations were done for a high opening blade angle with a N11 of 170 rpm, at best efficiency point and at two points with a higher Q11. The second operating point is inside the efficiency curve break off and the last operating point corresponds to a lower efficiency and a larger recirculation region in the draft tube. The PIV measurements were made near the wall with two cameras in order to capture two measurement planes simultaneously. The instantaneous velocity fields were acquired at eight different planes. Two planes located near the bottom wall were parallel to the generatrix of the conical part of the diffuser, while two other bottom planes diverged more from the draft tube axis than the cone generatrix. The last four planes were located on the draft tube side and diverged more from the draft tube axis than the cone generatrix. By combining the results from the various planes, the separation zone is characterized using pseudo-streamlines of the mean velocity fields, maps of the Reynolds stresses and maps of the reverse-flow parameter. The analysis provides an estimation of the separation zone size, shape and unsteady character, and their evolution with the guide vanes opening.

Hairpin Structures in a Turbulent Boundary Layer under Stalled-Airfoil-Type Flow Conditions

Hairpin structures in the outer region of a turbulent boundary layer subjected to a strong adverse pressure gradient have been studied using PIV. The external flow conditions are similar to those found on the suction side of airfoils in trailing-edge post-stall conditions. Even if the flow is very different from zeropressure- gradient turbulent boundary layers, the gross features of the hairpin vortices and hairpin packets remain similar, even as separation is approached. The hairpin vortices are however slightly more inclined with respect to the wall, and their streamwise separation is smaller when scaled with the boundary layer thickness. The upward growth of the hairpin packets in the streamwise direction is also more important. The variations of these properties are consistent with the variations of the mean strain rates, in particular rates of streamwise contraction and wall-normal extension.

Investigation of Flow Separation in a Diffuser of a Bulb Turbine

A three-dimensional unsteady flow separation in the straight diffuser of a model bulb turbine is investigated using tuft visualizations, unsteady wall pressure sensors, and particle image velocimetry (PIV). Experimental results reveal a link between the flow separation zone extension and the sudden drop in turbine performances. The flow separation zone grows as the flow rate increases past the best efficiency operating point (OP). It starts on the bottom wall and expands azimuthally and upstream. It deviates and perturbs the flow far upstream. Despite high unsteadiness, a global separation streamline pattern composed of a saddle point and a convergence line emerges.

Coherent structures in a zero-pressure-gradient and a strongly decelerated boundary layer

Coherent structures in a strongly decelerated large-velocity-defect turbulent boundary layer (TBL) and a zero pressure gradient (ZPG) boundary layer are analysed by direct numerical simulation (DNS). The characteristics of the one-point velocity stastistics are also considered. The adverse pressure gradient (APG) TBL simulation is a new one carried out by the present authors. The APG TBL begins as a zero pressure gradient boundary layer, decelerates under a strong adverse pressure gradient, and separates near the end of the domain in the form of a very thin separation bubble. The one-point velocity statistics in the outer region of this large-defect boundary layer are compared to those of two other large-velocity-defect APG TBLs (one in dynamic equilibrium, the other in disequilibrium) and a mixing layer. In the upper half of the large-defect boundary layers, the velocity statistics are similar to those of the mixing layer. The dominant peaks of turbulence production and Reynolds stresses are located in the middle of the boundary layers. Three-dimensional spatial correlations of (u, u) and (u, v) show that coherence is lost in the streamwise and spanwise directions as the velocity defect increases. Near-wall streaks tend to disappear in the large-defect zone of the flow to be replaced by more disorganized u motions. Near-wall sweeps and ejections are also less numerous. In the outer region, the u structures tend to be shorter, less streaky, and more inclined with respect to the wall than in the ZPG TBL. The sweeps and ejections are generally bigger with respect to the boundary layer thickness in the large-defect boundary layer, even if the biggest structures are found in the ZPG TBL. Large sweeps and ejections that reach the wall region (wall-attached) are less streamwise elongated and they occupy less space than in the ZPG boundary layer. The distinction between wall-attached and wall-detached structures is not as pronounced in the large-defect TBL.

A Study of a Separated Turbulent Boundary Layer in Stalled-Airfoil-Type Flow Conditions

The experimental study of the turbulent boundary layer and its separation under external flow conditions similar to those found on the suction side of airfoils in trailing-edge post-stall conditions has been performed. The flow is characterized by a very narrow suction peak with a minimum pressure coefficient of -16 at a Reynolds numbers of 1.5×10 6 , based on an effective chord length of 2.5 m. Special care was taken to achieve a nearly twodimensional mean flow. Detailed boundary layer measurements were carried out with a PIV system and a two-sensor wall probe. They cover the region downstream of the suction peak where the boundary layer is subjected to a very strong adverse pressure gradient and has suffered from an abrupt transition from strong favorable to strong adverse pressure gradients. The experiments show that in spite of these severe conditions, the boundary layer is able to recover a state of equilibrium and maintain it up to the separation point. In the equilibrium zone, the mean velocity and all the measured Reynolds stress components share common self-similarity scales, namely δ and Ueδ*/δ. These similarity scales are not valid for the separated zone. These findings support the conclusion of Castillo and Wang (J. Fluids Eng., Vol. 126, 2004) that most nonequilibrium flows are actually able to reach a local equilibrium state.

The Structure of APG Turbulent Boundary Layers

The characteristics of three-dimensional intense uv-structures (Qs) in a strongly decelerated large-velocity-defect boundary layer are analyzed. The Q2 and Q4 structures are found to be different from those of turbulent channel flows studied by Lozano-Duran et al. (J Fluid Mech 694:100–130, 2012). They are less streamwise elongated, less present near the wall and wall-detached structures are more numerous. Moreover, contrary to channel flows, wall-detached Q2, and Q4 structures contribute significantly to the Reynolds shear stress.