Normal Reynolds Stress Components Research Articles

Effect of Tip Gap Size on the Tip Flow Structure and Turbulence Generation in a Low Reynolds Number Compressor Cascade

Abstract Efficient and compact axial compressors are currently undergoing rapid development for use in microcooling systems and small-scale vehicles. Limited experimental work concentrates on the inner flow field of the compressors working at such low Reynolds numbers (Re∼104). This study examines the vortical structures and the resulting turbulence production in the transitional flow over a C4 compressor blade at a Reynolds number Re of 24,000, with a specific focus on the impact of tip clearance. The particle image velocimetry measurements reveal the tip flow structures in detail, including the tip leakage vortex (TLV) and its induced complex vortical structures. The tip secondary flow at the low Reynolds number can be divided as the tip leakage flow (TLF)/vortex and transitional boundary layer both at the end walls and the blade surfaces. The TLV propagates at the highest spanwise positions and farthest pitchwise positions at the middle tip gap size (τ/C = 3%) for the three tip gap sizes investigated. The tip flow fluctuations decrease from τ/C = 5% to τ/C = 3% and then increase from τ/C = 3% to τ/C = 1%. The spatial distribution, streamwise evolution, and individual Reynolds normal stress components contributing to the turbulent kinetic energy (TKE) are discussed. The primary contributors to the turbulence generation are examined to elucidate the flow mechanism leading to the distinct anisotropic turbulence structure in the tip region with various tip gap sizes.

Effects of Axial Casing Grooves on the Structure of Turbulence in the Tip Region of an Axial Turbomachine Rotor

Abstract Challenges in turbulence modeling in the tip region of turbomachines include anisotropy, inhomogeneity, and non-equilibrium conditions, resulting in poor correlations between Reynolds stresses and the corresponding mean strain-rate components. The geometric complexity introduced by casing grooves exacerbates this problem. Taking advantage of a large database collected in the refractive index-matched liquid facility at Johns Hopkins University (JHU), this paper examines the effect of axial casing grooves on the distributions of turbulent kinetic energy (TKE), Reynolds stresses, anisotropy tensor, and TKE production rate in the tip region of an axial turbomachine. The comparisons are performed at flowrates corresponding to prestall and best efficiency points of the untreated machine. Common features include high TKE near the tip leakage vortex center and in the shear layer connecting it to the blade suction side tip corner. The turbulence is highly anisotropic and inhomogeneous, with the anisotropy tensor shifting from one-dimensional (1D) to 2D and 3D structures over small distances. With the grooves, the flow structure, hence the distribution of Reynolds stresses, becomes more complex. Additional sites with elevated turbulence include the corner vortex that develops at the entrance to the grooves, and in the flow jetting out of the grooves into the passage. Consistent with trends of the production rates of normal Reynolds stress components, the grooves increase the axial but reduce the radial velocity fluctuations as the inflow and outflow from the groove interact with the passage flow. These findings might assist the development of Reynolds stress models suitable for tip flows.

Investigation on noise from shock/isotropic turbulence interaction using direct numerical simulation

Direct numerical simulation of shock/isotropic turbulence interaction combining Lighthill’s acoustic analogy is conducted to study the influence of shock/turbulence interaction (STI) on the turbulence noise in the farfield. The acoustic statistics are adopted to quantify the influence of STI on the turbulence noise. The results show that STI increases the power spectral density in almost the whole frequency band and obviously amplifies the acoustic intensity. Based on the numerical results and the theoretical analysis, the primary noise sources are identified. The normal Reynolds stress components in the transverse direction contribute greatly to the noise at the observers. By applying the Rankine-Hugoniot relation and the spatial and temporal Fourier analysis on the simplified noise source, the mechanisms of turbulence noise variation under STI are also investigated, which can be divided into three parts. First, the compression effect of the shock wave increases the downstream density. Second, STI increases the value of turbulent kinetic energy spectrum over the entire wavenumber range. Third, the noise sources in the high frequency band are amplified under STI. Additionally, the transverse velocities are filtered in wavenumber space and the influence of STI on turbulence noise is studied from the perspective of the turbulence scales. The contribution of acoustic intensity radiated from “smaller” or “larger” turbulence scales is decreased, and the contribution of acoustic intensity radiated from the interaction of “smaller” and “larger” turbulence scales is increased under STI.

Aerofoil trailing‐edge noise prediction models for wind turbine applications

AbstractThis paper proposes a modified TNO model for the prediction of aerofoil trailing‐edge noise for wind turbine applications. The capabilities of the current modified model and four variants of the TNO model are analysed through a comprehensive study which includes 10 aerofoils and involves two different wind tunnels. The Reynolds numbers considered are between 1.13 and 3.41 million, and the effective angles of attack are between −2.20° and 13.58°. The merit of a model is assessed by comparing two aspects of the numerically predicted and the experimentally measured sound pressure level spectra: the sound pressure level difference between two different aerofoils at similar lift coefficients within a certain frequency range (referred to as the delta noise); and the closeness in terms of spectral magnitude and shape of the predicted and measured sound pressure level spectra. The current modified model is developed by deriving new formulations for the computation of the wall pressure fluctuation spectrum. This is achieved by using the approximate ratio of the normal Reynolds stress components for an anisotropic flow over a flat plate to estimate the vertical Reynolds stress component, and by introducing new stretching factors to take the effects of turbulent flow anisotropy into account. Compared with the four TNO model variants tested, the current modified model has strong delta noise prediction ability, and is able to predict sound pressure level spectra that are more consistent and closer to measurements for the vast majority of aerofoils and flow conditions tested in the two wind tunnels. Copyright © 2017 John Wiley & Sons, Ltd.

Study of the Turbulent Velocity Field in the Near Wake of a Bluff Body

An experimental characterization of the turbulent flow structure formed downstream of a vertically mounted circular bluff body is performed. Three components of an instantaneous velocity field are measured using the stereo particle image velocimetry technique at the symmetry plane. The average velocity and the turbulent properties are analyzed. The results indicate a recirculation zone consisting of a toroidal vortex with similar dimensions for all Reynolds numbers. The largest turbulent fluctuations are found at the stagnation point region. The observed anisotropy of the normal Reynolds stress components is associated with the stagnation point flow, whereas the cross-correlation component extreme occurs in high strain rate regions. An analysis of the Reynolds tensor anisotropy using the Lumley triangle is performed, revealing that the largest departures from isotropy occur at high shear regions and also within the vortex.

Numerical simulation of grid-generated turbulent particulate flow by three-dimensional Reynolds stress

A three-dimensional (3D) Reynolds stress turbulence model based on 3D Reynolds-averaged Navier-Stokes equations has been elaborated for grid-generated turbulence in particulate downward flow arranged in the channel domain of the square cross section. The model presented considers both the enhancement and attenuation of turbulence by means of the additional terms of the transport equations of the normal Reynolds stress components. It allows us to carry out calculations covering the long distance of the channel length without using algebraic assumptions for various components of the Reynolds stress. The results obtained show the effects of particles and mesh size of the turbulence generating grids on turbulence modification. In particular, the presence of solid particles at the initial period of turbulence decay results in the pronounced enhancement of turbulence that diminishes appreciably downwards in the area of typical channel turbulent flow. As the results show, the character of modification of all three normal components of the Reynolds stress taking place at the initial period of turbulence decay are uniform almost all over the channel cross sections. The increase in the grid mesh size slows down the rate of the turbulence enhancement which is caused by particles.

Flow field characterization of a rotating cylinder

Direct numerical simulation is used to study the flow field around an infinitely long circular cylinder rotating in fluid with no outer boundary. Wall shear stresses and normal pressure fluctuations are considered with reference to flat, non-rotating geometries to help identify any flow field differences introduced by Coriolis forces. In the present case, Coriolis forces are experienced only by the turbulence field. The dominant effect is to decrease the streamwise turbulent velocity level relative to the other two components. A consequential effect is that the two components of wall shear stress fluctuations become almost equal and spectra for streamwise and spanwise wall shear stress fluctuations become almost identical. This is a distinctly different behaviour from that of non-rotating flat plate and straight pipe flows. Instantaneous wall shear stress fluctuations indicate a near wall flow structure similar to that of other boundary layers with sweeps and ejections. No flow reversals of wall shear stress are indicated. A good correlation of the wall shear stresses and the turbulent kinetic energy exists for y + < 10. Budgets of Reynolds normal stress components illustrate the role played by Coriolis forces in the production and redistribution of turbulence energies. Wall pressure fluctuations are found to be of much larger spatial extent than velocity fluctuation scales while the probability density distribution of pressure fluctuations is almost Gaussian but does display a Reynolds number effect for skewness and Kurtosis. The ratio of rms pressure fluctuations to mean streamwise wall shear stress follows closely that for flat plate boundary layer and channel flows.

Turbulence Measurements of Separate-Flow Nozzles with Pylon Interaction Using Particle Image Velocimetry

Particle image velocimetry measurements for separate-flow nozzles with bypass ratio five have recently been obtained in the NASA Langley Jet Noise Laboratory. The six configurations tested include a baseline configuration with round core and fan nozzles, an eight-chevron core nozzle at two different clocking positions, and repeats of these configurations with a pylon included. One run condition representative of takeoff was investigated for all cases. The unsteady flowfield measurements complement recent computational, acoustic, and mean flowfield studies performed at NASA Langley for the same nozzle configurations and run condition. The baseline configuration measurements show good agreement with existing mean and turbulent flowfield data. Nonetheless, the baseline configuration turbulence profile indicates an asymmetric flowfield, despite careful attention to concentricity. The presence of the pylon increases the upper shear layer turbulence levels while simultaneously decreasing the turbulence levels in the lower shear layer. In addition, a slightly shorter potential core length is observed with the addition of the pylon. Finally, comparisons of computational results with current measurements are favorable for mean flow, slightly overpredicted for Reynolds shear stress, and underpredicted for Reynolds normal stress components.

Nonlinear two-equation model taking into account the wall-limiting behavior and redistribution of stress components

Nonlinear k–e models have been extensively used in technological applications. It is clear from the assessment of the existing nonlinear k–e models using DNS databases that the nonlinear models can not satisfy and reproduce exactly the wall-limiting behavior and the anisotropy of Reynolds normal stress components. Especially, the Reynolds normal stress component, \(\overline{u_2^2}\) , in the wall-normal direction, which is proportional to x24 near the wall, is not satisfied. Since the wall-limiting behavior of Reynolds normal stress components in the nonlinear model is determined by the turbulence energy k, which is proportional to x22 in the model, the Reynolds stress components, \(\overline{u_1^2}\) , \(\overline{u_2^2}\) and \(\overline{u_3^2}\) , are proportional to x22. In this study, we have proposed a new nonlinear k–e model which satisfies exactly the wall-limiting behavior of Reynolds normal stress components in the inertial and the noninertial frames. The proposed model can also predict well the anisotropy of the Reynolds normal stress components near the wall.

Determination of the magnitudes and signs of flow parameters by hot-wire anemometry. Part I. Measurements using hot-wire X probes

Using two commercially available hot-wire X probes, a conventional measurement technique, and the evaluation method described here, the magnitude of the time-averaged velocity vector and the magnitudes of the Reynolds normal stress components as well as the magnitudes and signs of the Reynolds shear stress components can be determined. The evaluation method employs as a basis the spatial directional sensitivity of hot-wire probes and involves the squaring of the anemometer’s output signal. Furthermore, the region of applicability of this method is discussed.

3-D turbulence structure and phase distribution measurements in bubbly two-phase flows

Turbulent bubbly air/water two-phase up and down flows in a circular test section were investigated. Important flow quantities such as local void fraction, liquid velocity and the Reynolds stresses were measured using both single-sensor and three-sensor hot-film anemometer probes. For up flows, it was found that the bubbles tended to migrate toward the wall and thus the void fraction profile showed a distinct peak near the wall. In contrast, for down flows, it was found that the bubbles tended to migrate toward the center of the pipe causing void “coring”. It was also found that the observed wall peaking and coring phenomena, and thus the radial void distribution in up and down flows, could be predicted by considering the turbulence structure of the continuous phase and lateral lift force acting on the dispersed phase (i.e. the bubbles). All Reynolds stress components were measured using a special 3-D conical probe. In two-phase flows, the normal Reynolds stress components ( i.e. u 2, v 2 and w 2 ) showed nearly flat profiles in the core region ( r/R < 0.8) and, except near the wall, the turbulence structure was more anisotropic compared to single-phase flows. Normally, the presence of the bubbles increased the level of turbulence in the flow. However, because the bubbles in turbulent two-phase flow enhance dissipation as well as promoting the production of turbulence kinetic energy, it was found that for higher flow rates the presence of bubbles suppressed the level of turbulence.

Free and mixed convective flow of air in a heated cavity of variable rectangular cross section and orientation

Free and mixed convection in a strongly heated cavity of rectangular cross section have been investigated experimentally, to observe the effects of cavity shape and inclination and of ambient wind on the velocity and temperature distributions. The long edges ( c = 0.533 m) of the cavity were horizontal and parallel to an axis around which the cavity could be rotated. The aperture plane was either vertical (a = 0°), or inclined facing downward at a = 20° or a = 45°. The height of the aperture, b , was always 0.0947 m, while the depth of the cavity, a , was set so that = 0.5, 1.0, or 1.46. The bottom and back walls were electrically heated but the top wall was indirectly heated by conduction and radiation. The absolute average temperature of the wall, T c , was 2.21 times the absolute temperature at infinity, T^, and the Grashof number based on the difference of these two temperatures, with physical properties evaluated at T"^, was 4.2 x 10 7 . The Prandtl number was that of air, Pr « 0.7. In the studies of mixed convection, the axis of rotation was horizontal and normal to the ambient wind, U ^. When the aperture faced directly upstream the inclination angle was a = 0°. The Reynolds number, Re = was bU / v , varied from Re = 120-1100, where free convection was dominant, to Re = 2000-8740, where forced convection was dominant. For both free and mixed convection, wall and gas temperatures were measured with thermocouples and shadowgraph pictures were taken. For pure free convection, three time-averaged velocity components, the corresponding normal Reynolds stress components and one off-diagonal Reynolds stress component were measured by using a two-colour laser-Doppler velocimeter with the assistance of a minicomputer for automated data collection and reduction. The experiments were largely exploratory and revealed a wealth of interesting phenomena. These include instabilities that have previously been seen in more simply bounded flows and periodic oscillations that seem unique to the open cavity. This application of laser-Doppler velocimetry is interesting in its own right, confronting large variations in index of refraction, extraordinarily high percentage fluctuations in velocity and density and great difficulty in assuring the uniform distribution of light-scattering particles.