scholarly journals Effect of Incidence Angle on Entropy Generation in the Boundary Layers on the Blade Suction Surface in a Compressor Cascade

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1049 ◽  
Author(s):  
Shi ◽  
Ma

The entropy generation that occurs within boundary layers over a C4 blade at a Reynolds number of 24,000 and incidence angles (i) of 0°,2.5°,5°,7.5°, and 10° are investigated experimentally using a particle image velocimetry (PIV) technique. To clarify the entropy generation process, the distribution of the entropy generation rates (EGR) and the unsteady flow structures within the PIV snapshots are analyzed. The results identify that for a higher incidence angle, the separation and transition occur further upstream, and the entropy generation in the boundary layer increases. When the separation takes place at the aft portion of the blade, the integral EGR decrease near the leading edge, remain minimal values in the middle portion of the blade, and increase sharply in the vicinity of the mean transition. More than 35% of the entropy generation is generated at the region downstream of the mean transition. When the separation occurs at the fore portion of the blade, the contributions of mean-flow viscous dissipation decrease to less than 20%. The entropy generation with elevated value can be detected over the entire blade. The entire integral entropy generation in the boundary layer increases sharply when the laminar separation bubble moves upstream to the leading edge.


1994 ◽  
Vol 116 (4) ◽  
pp. 586-596 ◽  
Author(s):  
P. L. Andrew ◽  
Wing-fai Ng

The turbulent character of the supersonic wake of a linear cascade of fan airfoils has been studied using a two-component laser-doppler anemometer. The cascade was tested in the Virginia Polytechnic Institute and State University intermittent wind tunnel facility, where the Mach and Reynolds numbers were 2.36 and 4.8 × 106, respectively. In addition to mean flow measurements, Reynolds normal and shear stresses were measured as functions of cascade incidence angle and streamwise locations spanning the near-wake and the far-wake. The extremities of profiles of both the mean and turbulent wake properties´ were found to be strongly influenced by upstream shock-boundary -layer interactions, the strength of which varied with cascade incidence. In contrast, the peak levels of turbulence properties within the shear layer were found to be largely independent of incidence, and could be characterized in terms of the streamwise position only. The velocity defect turbulence level was found to be 23 percent, and the generally accepted value of the turbulence structural coefficient of 0.30 was found to be valid for this flow. The degree of similarity of the mean flow wake profiles was established, and those profiles demonstrating the most similarity were found to approach a state of equilibrium between the mean and turbulent properties. In general, this wake flow may be described as a classical free shear flow, upon which the influence of upstream shock-boundary-layer interactions has been superimposed.



2019 ◽  
Vol 865 ◽  
pp. 1085-1109 ◽  
Author(s):  
Yutaro Motoori ◽  
Susumu Goto

To understand the generation mechanism of a hierarchy of multiscale vortices in a high-Reynolds-number turbulent boundary layer, we conduct direct numerical simulations and educe the hierarchy of vortices by applying a coarse-graining method to the simulated turbulent velocity field. When the Reynolds number is high enough for the premultiplied energy spectrum of the streamwise velocity component to show the second peak and for the energy spectrum to obey the$-5/3$power law, small-scale vortices, that is, vortices sufficiently smaller than the height from the wall, in the log layer are generated predominantly by the stretching in strain-rate fields at larger scales rather than by the mean-flow stretching. In such a case, the twice-larger scale contributes most to the stretching of smaller-scale vortices. This generation mechanism of small-scale vortices is similar to the one observed in fully developed turbulence in a periodic cube and consistent with the picture of the energy cascade. On the other hand, large-scale vortices, that is, vortices as large as the height, are stretched and amplified directly by the mean flow. We show quantitative evidence of these scale-dependent generation mechanisms of vortices on the basis of numerical analyses of the scale-dependent enstrophy production rate. We also demonstrate concrete examples of the generation process of the hierarchy of multiscale vortices.



2015 ◽  
Vol 783 ◽  
pp. 379-411 ◽  
Author(s):  
I. Marusic ◽  
K. A. Chauhan ◽  
V. Kulandaivelu ◽  
N. Hutchins

In this paper we study the spatial evolution of zero-pressure-gradient (ZPG) turbulent boundary layers from their origin to a canonical high-Reynolds-number state. A prime motivation is to better understand under what conditions reliable scaling behaviour comparisons can be made between different experimental studies at matched local Reynolds numbers. This is achieved here through detailed streamwise velocity measurements using hot wires in the large University of Melbourne wind tunnel. By keeping the unit Reynolds number constant, the flow conditioning, contraction and trip can be considered unaltered for a given boundary layer’s development and hence its evolution can be studied in isolation from the influence of inflow conditions by moving to different streamwise locations. Careful attention was given to the experimental design in order to make comparisons between flows with three different trips while keeping all other parameters nominally constant, including keeping the measurement sensor size nominally fixed in viscous wall units. The three trips consist of a standard trip and two deliberately ‘over-tripped’ cases, where the initial boundary layers are over-stimulated with additional large-scale energy. Comparisons of the mean flow, normal Reynolds stress, spectra and higher-order turbulence statistics reveal that the effects of the trip are seen to be significant, with the remnants of the ‘over-tripped’ conditions persisting at least until streamwise stations corresponding to $Re_{x}=1.7\times 10^{7}$ and $x=O(2000)$ trip heights are reached (which is specific to the trips used here), at which position the non-canonical boundary layers exhibit a weak memory of their initial conditions at the largest scales $O(10{\it\delta})$, where ${\it\delta}$ is the boundary layer thickness. At closer streamwise stations, no one-to-one correspondence is observed between the local Reynolds numbers ($Re_{{\it\tau}}$, $Re_{{\it\theta}}$ or $Re_{x}$ etc.), and these differences are likely to be the cause of disparities between previous studies where a given Reynolds number is matched but without account of the trip conditions and the actual evolution of the boundary layer. In previous literature such variations have commonly been referred to as low-Reynolds-number effects, while here we show that it is more likely that these differences are due to an evolution effect resulting from the initial conditions set up by the trip and/or the initial inflow conditions. Generally, the mean velocity profiles were found to approach a constant wake parameter ${\it\Pi}$ as the three boundary layers developed along the test section, and agreement of the mean flow parameters was found to coincide with the location where other statistics also converged, including higher-order moments up to tenth order. This result therefore implies that it may be sufficient to document the mean flow parameters alone in order to ascertain whether the ZPG flow, as described by the streamwise velocity statistics, has reached a canonical state, and a computational approach is outlined to do this. The computational scheme is shown to agree well with available experimental data.



Author(s):  
Byung-Young Min ◽  
Jongwook Joo ◽  
Jomar Mendoza ◽  
Jin Lee ◽  
Guoping Xia ◽  
...  

In this paper, wall-resolved LES computations for a compressor cascade from Ecole Centrale de Lyon [1] are presented. A computational grid containing about 600 million computational cells was used in these simulations. This grid resolves the details of tripping strips used in the experiments, located near the leading edge of the blade on both suction and pressure sides. Endwall turbulent boundary layer at cascade inlet was measured to be at a momentum thickness based Reynolds number of about 7000 to 8000, with quite a bit of variation in the pitchwise direction. In order to avoid the cost of simulating the entire duct upstream of the cascade, and any auxiliary flat plate boundary layer simulations, the inlet fluctuations for LES computations were generated using digital filtering method for synthetic turbulence generation [27]. Turbulence statistics from a database of high fidelity eddy simulations of flat plate boundary layers (at similar Reynolds numbers) from KTH Royal Institute of Technology in Stockholm [28] were used to fully define the properties of the cascade inlet boundary layer. In this paper, time-averaged results from three LES computations for this configuration are presented — one with no inlet fluctuations at the cascade endwall at the domain inlet, and then two computations with inlet fluctuations and boundary layers at Reθ of 7000 and 8183. These provide a sensitivity of LES predictions of corner separation in the cascade to the boundary layer thickness at cascade inlet. A comparison of these simulations with prior DDES (and RANS) simulations from UTRC [26], as well as existing LES results from Ecole Centrale de Lyon [12], allows to further the understanding of critical elements of the endwall flow physics. More specifically, it provides more insight into which phenomena need to be sufficiently resolved (e.g. horseshoe vortex) in order to capture both the average behavior of the corner separation, as well as its unsteady dynamics. In addition, it provides new information which will help define best practice guidelines for the use of eddy simulations to resolve endwall features in compressors at off-design conditions.



An experimental investigation has been made of turbulent boundary layer response to harmonic oscillations associated with a travelling wave imposed on an otherwise constant freestream velocity and convected in the freestream direction. The tests covered oscillation frequencies of 4-12 Hz for freestream amplitudes of up to 11% of the mean velocity. Additional steady flow measurements were used to infer the quasi-steady response to freestream oscillations. The results show a welcome insensitivity of the mean flow and turbulent intensity distributions to the freestream oscillations tested. An approximate analysis based on these results has been developed. It is probably of limited validity but it does provide a useful guide to the physical processes involved. The effects on boundary layer response of varying the travelling wave convection velocity and frequency of oscillation are illustrated by the analysis and show a behaviour broadly similar to that of laminar boundary layers. The travelling wave convection velocity exhibits a dominant influence on the turbulent boundary layer response to freestream oscillations.



Author(s):  
Dimitri P. Tselepidakis ◽  
Sung-Eun Kim

This paper presents the computation of the flow around a controlled diffusion compressor cascade. Features associated with by-pass transition close to the leading edge — including laminar leading-edge separation — contribute significantly to the evolution of the boundary layer on the blade surface. Previous studies have demonstrated that conventional k-ε models, based on linear or non-linear Boussinesq stress-strain relations, are able to capture by-pass transition in simple shear, but are unable to resolve transitional features in complex strain, like the leading-edge separation bubble, which is of considerable influence to the suction-side flow at high inlet angle. Here, the k-ω turbulence model has been implemented in a nonstaggered, finite-volume based segregated Reynolds-Averaged Navier-Stokes solver. We demonstrate that this model, if properly sensitized to the generation of turbulence by irrotational strains, is capable of capturing the laminar leading-edge separation bubble. The real flow around the leading edge is laminar and the transition is only provoked on the reattachment region. Additional investigation of transition in a flat-plate boundary layer development has also produced reasonably promising results.



1997 ◽  
Vol 353 ◽  
pp. 205-220 ◽  
Author(s):  
P. W. HAMMERTON ◽  
E. J. KERSCHEN

In Hammerton & Kerschen (1996), the effect of the nose radius of a body on boundary-layer receptivity was analysed for the case of a symmetric mean flow past a two-dimensional body with a parabolic leading edge. A low-Mach-number two-dimensional flow was considered. The radius of curvature of the leading edge, rn, enters the theory through a Strouhal number, S=ωrn/U, where ω is the frequency of the unsteady free-stream disturbance and U is the mean flow speed. Numerical results revealed that the variation of receptivity for small S was very different for free-stream acoustic waves propagating parallel to the mean flow and those free-stream waves propagating at an angle to the mean flow. In this paper the small-S asymptotic theory is presented. For free-stream acoustic waves propagating parallel to the symmetric mean flow, the receptivity is found to vary linearly with S, giving a small increase in the amplitude of the receptivity coefficient for small S compared to the flat-plate value. In contrast, for oblique free-stream acoustic waves, the receptivity varies with S1/2, leading to a sharp decrease in the amplitude of the receptivity coefficient relative to the flat-plate value. Comparison of the asymptotic theory with numerical results obtained in the earlier paper confirms the asymptotic results but reveals that the numerical results diverge from the asymptotic result for unexpectedly small values of S.



Author(s):  
B. K. Hazarika ◽  
C. Hirsch

The flow around a circular leading edge airfoil is investigated in an incompressible, low turbulence freestream. Hot-wire measurements are performed through the separation bubble, the reattachment and the recovery region till development of the fully turbulent boundary layer. The results of the experiments in the range of Reynolds numbers 1.7×103 to 11.8×103 are analysed and presented in this paper. A separation bubble is present near the leading edge at all Reynolds numbers. At the lowest Reynolds number investigated, the transition is preceded by strong low frequency oscillations. The correlation given by Mayle for prediction of transition of short separation bubbles is successful at the lower Reynolds number cases. The length of the separation bubble reduces considerably with increasing Reynolds number in the range investigated. The turbulence in the reattached flow persists even when the Reynolds number based on momentum thickness of the reattached boundary layer is small. The recovery length of the reattached layer is relatively short and the mean velocity profile follows logarithmic law within a short distance downstream of the reattachment point and the friction coefficient conforms to Prandtl-Schlichting skin-friction formula for a smooth flat plate at zero incidence.



Author(s):  
Yunfei Wang ◽  
Xiuming Sui ◽  
Kai Zhang ◽  
Xiaorong Xiang ◽  
Qingjun Zhao

The evolution mechanism of the boundary layer and coherent structures in a low-pressure turbine blade is discussed. Five different incidence angles over the T106A blade for a Mach number Ma = 0.404 and Reynolds number Re = 0.6 × 105 (based on the axial chord and outlet velocity) are performed using large eddy simulation method. The calculation results at +7.8 incidence angle are agreed well with the experimental and direct numerical simulation data. The influence of the incidence angle on the flow field is mainly shown at the front of the suction side and pressure side. As the incidence angle changes from positive to negative, the separation bubble near the leading edge disappears and the blade loading decreases gradually. When the incidence angle reduces to −5°, separation bubble appears near the leading edge of the pressure side. At the case of incidence angle equaling −10°, the length of time-averaged separation bubble on the pressure side grows to 39% axial chord and the evolution process of the coherent structures is extremely complex. The spanwise vortexes roll up near the leading edge and gradually evolve into streamwise vortexes. High-energy fluid in the main flow was driven to near-wall zone by the rotating effect of streamwise vortexes, which increases the fluid momentum inside the boundary layer. The streamwise vortexes are stretched by the strong acceleration of the flow until they transport to the trailing edge.



1993 ◽  
Author(s):  
Philip L. Andrew ◽  
Wing-fai Ng

The turbulent character of the supersonic wake of a linear cascade of fan airfoils has been studied using a two–component Laser Doppler Anemometer. The cascade was tested in the Virginia Polytechnic Institute and State University intermittent wind tunnel facility, where the Mach and Reynolds numbers were 2.36 and 4.8 × 106, respectively. In addition to mean flow measurements, Reynolds normal and shear stresses were measured as functions of cascade incidence angle and streamwise locations spanning the near–wake and the far–wake. The extremities of profiles of both the mean and turbulent wake properties were found to be strongly influenced by upstream shock–boundary–layer–interactions, the strength of which varied with cascade incidence. In contrast, the peak levels of turbulence properties within the shear layer were found to be largely independent of incidence, and could be characterized in terms of the streamwise position only. The velocity defect turbulence level was found to be 23%, and the generally–accepted value of the turbulence structural coefficient of 0.30 was found to be valid for this flow. The degree of similarity of the mean flow wake profiles was established, and those profiles demonstrating the most similarity were found to approach a state of equilibrium between the mean and turbulent properties. In general, this wake flow may be described as a classical free shear flow, upon which the influence of upstream shock–boundary–layer–interactions has been superimposed.



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