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

2021 ◽  
pp. 1-46
Author(s):  
Huang Chen ◽  
Yuanchao Li ◽  
Subhra Shankha Koley ◽  
Joseph Katz
Keyword(s):  
Reynolds Stress ◽  
Turbulence Modeling ◽  
Suction Side ◽  
Vortex Center ◽  
Reynolds Stresses ◽  
Tip Leakage ◽  
Stress Components ◽  
Anisotropy Tensor ◽  
Stress Models ◽  
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 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. Comparisons are performed at flow rates corresponding to prestall and best efficiency points of the untreated machine. Common features include high TKE near the tip leakage vortex center, and in 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 to 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 interacts with the passage flow. These findings might assist the development of Reynolds stress models suitable for tip flows.

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

2020 ◽  
Author(s):  
Huang Chen ◽  
Yuanchao Li ◽  
Subhra Shankha Koley ◽  
Joseph Katz
Keyword(s):  
Strain Rate ◽  
Reynolds Stress ◽  
Suction Side ◽  
Reynolds Stresses ◽  
Flow Rates ◽  
Tip Leakage ◽  
Anisotropy Tensor ◽  
Stress Models ◽  
Turbomachine Rotor ◽  
Mean Strain

Abstract Challenges in predicting the turbulence in the tip region of turbomachines include anisotropy, inhomogeneity, and non-equilibrium conditions, resulting in poor correlations between the Reynold 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 JHU, this paper examines the evolution of turbulence in the tip region of an axial turbomachine with and without axial casing grooves, and for two flow rates. The semi-circular axial grooves are skewed by 45° in the positive circumferential direction, similar to that described in Müller et al. [1]. Comparison to results obtained for an untreated endwall includes differences in the distributions of turbulent kinetic energy (TKE), Reynolds stresses, anisotropy tensor, and dominant terms in the TKE production rate. The evolution of TKE at high flow rates for blade sections located downstream of the grooves is also investigated. Common features include: with or without casing grooves, the TKE is high near the tip leakage vortex (TLV) 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 demonstrating shifts from one dimensional (1D) to 2D and to 3D structures over small distances. Furthermore, the correlation between the mean strain rate and Reynolds stress tensor components is poor. With the grooves, the flow structure, hence the distribution of Reynolds stresses, becomes much more complex. Turbulence is also high in 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 production rates of normal Reynolds stress components, the grooves increase the axial and reduce the radial velocity fluctuations compared to the untreated endwall. These findings introduce new insight that might assist the future development of Reynolds stress models suitable for tip flows.

Education Committee Best Paper of 1995 Award: Methods of Classical Mechanics Applied to Turbulence Stresses in a Tip Leakage Vortex

1996 ◽  
Vol 118 (4) ◽  
pp. 622-629 ◽  
Author(s):  
J. G. Moore ◽  
S. A. Schorn ◽  
J. Moore
Keyword(s):  
Stress Tensor ◽  
Reynolds Stress ◽  
Classical Mechanics ◽  
Three Dimensional ◽  
Surface Model ◽  
Reynolds Stresses ◽  
Tip Leakage Vortex ◽  
Tip Leakage ◽  
Stress Tensors ◽  
Principal Directions

Moore et al. measured the six Reynolds stresses in a tip leakage vortex in a linear turbine cascade. Stress tensor analysis, as used in classical mechanics, has been applied to the measured turbulence stress tensors. Principal directions and principal normal stresses are found. A solid surface model, or three-dimensional glyph, for the Reynolds stress tensor is proposed and used to view the stresses throughout the tip leakage vortex. Modeled Reynolds stresses using the Boussinesq approximation are obtained from the measured mean velocity strain rate tensor. The comparison of the principal directions and the three-dimensional graphic representations of the strain and Reynolds stress tensors aids in the understanding of the turbulence and what is required to model it.

scholarly journals Study on bubble-induced turbulence in pipes and containers with Reynolds-stress models

2022 ◽  
Author(s):  
Yixiang Liao ◽  
Tian Ma
Keyword(s):  
Numerical Simulation ◽  
Reynolds Stress ◽  
Large Scale ◽  
Bubbly Flow ◽  
Reynolds Stress Model ◽  
Viscosity Models ◽  
Stress Components ◽  
Specific Source ◽  
Stress Models ◽  
Made In

AbstractBubbly flow still represents a challenge for large-scale numerical simulation. Among many others, the understanding and modelling of bubble-induced turbulence (BIT) are far from being satisfactory even though continuous efforts have been made. In particular, the buoyancy of the bubbles generally introduces turbulence anisotropy in the flow, which cannot be captured by the standard eddy viscosity models with specific source terms representing BIT. Recently, on the basis of bubble-resolving direct numerical simulation data, a new Reynolds-stress model considering BIT was developed by Ma et al. (J Fluid Mech, 883: A9 (2020)) within the Euler—Euler framework. The objective of the present work is to assess this model and compare its performance with other standard Reynolds-stress models using a systematic test strategy. We select the experimental data in the BIT-dominated range and find that the new model leads to major improvements in the prediction of full Reynolds-stress components.

Comparison of DDES and URANS for Unsteady Tip Leakage Flow in an Axial Compressor Rotor

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Yangwei Liu ◽  
Luyang Zhong ◽  
Lipeng Lu
Keyword(s):  
Reynolds Stress ◽  
Large Scale ◽  
Turbulence Modeling ◽  
Axial Compressor ◽  
Small Time ◽  
Detached Eddy Simulation ◽  
Tip Leakage Flow ◽  
Time Step ◽  
Tip Leakage ◽  
Eddy Simulation

Tip leakage vortex (TLV) has a large impact on compressor performance and should be accurately predicted by computational fluid dynamics (CFD) methods. New approaches of turbulence modeling, such as delayed detached eddy simulation (DDES), have been proposed, the computational resources of which can be reduced much more than for large eddy simulation (LES). In this paper, the numerical simulations of the rotor in a low-speed large-scale axial compressor based on DDES and unsteady Reynolds-averaged Navier–Stokes (URANS) are performed, thus improving our understanding of the TLV dynamic mechanisms and discrepancy of these two methods. We compared the influence of different time steps in the URANS simulation. The widely used large time-step makes the unsteadiness extremely weak. The small time-step shows a better result close to DDES. The time-step scale is related to the URANS unsteadiness and should be carefully selected. In the time-averaged flow, the TLV in DDES dissipates faster, which has a more similar structure to the experiment. Then, the time-averaged and instantaneous results are compared to divide the TLV into three parts. URANS cannot give the loss of stability and evolution details of TLV. The fluctuation velocity spectra show that the amplitude of high frequencies becomes obvious downstream from the TLV, where it becomes unstable. Last, the anisotropy of the Reynolds stress of these two methods is analyzed through the Lumley triangle to see the distinction between the methods and obtain the Reynolds stress. The results indicate that the TLV latter part in DDES is anisotropic, while in URANS it is isotropic.

Methods of Classical Mechanics Applied to Turbulence Stresses in a Tip Leakage Vortex

1995 ◽  
Author(s):  
Joan G. Moore ◽  
Scott A. Schorn ◽  
John Moore
Keyword(s):  
Stress Tensor ◽  
Reynolds Stress ◽  
Classical Mechanics ◽  
Surface Model ◽  
Strain Rate Tensor ◽  
Reynolds Stresses ◽  
Tip Leakage Vortex ◽  
Tip Leakage ◽  
Stress Tensors ◽  
Principal Directions

Moore et al. measured the six Reynolds stresses in a tip leakage vortex in a linear turbine cascade. Stress tensor analysis, as used in classical mechanics, has been applied to the measured turbulence stress tensors. Principal directions and principal normal stresses are found. A solid surface model, or 3-d glyph, for the Reynolds stress tensor is proposed and used to view the stresses throughout the tip leakage vortex. Modelled Reynolds stresses using the Boussinesq approximation are obtained from the measured mean velocity strain rate tensor. The comparison of the principal directions and the 3-d graphical representations of the strain and Reynolds stress tensors aids in the understanding of the turbulence and what is required to model it.

On Euclidean invariance of algebraic Reynolds stress models in turbulence

2003 ◽  
Vol 476 ◽  
pp. 63-68 ◽  
Author(s):  
J. WEIS ◽  
K. HUTTER
Keyword(s):  
Reynolds Stress ◽  
Reynolds Stress Model ◽  
Simple Extension ◽  
Stress Model ◽  
Algebraic Relation ◽  
Reynolds Stresses ◽  
Coordinate Systems ◽  
Stress Models ◽  
Algebraic Reynolds Stress Model ◽  
Euclidean Invariance

This article shows how Euclidean invariance can be preserved in the so-called algebraic Reynolds stress model (ARSM) approximation. This approximation is used to reduce the transport equation for the Reynolds stresses to an explicit algebraic relation. A number of known models, which make use of this approximation, are not form-invariant under transformations to rotating coordinate systems. A simple extension is presented to show how this artifact can be removed.

A Priori Analysis of Explicit Algebraic Stress Models for a Turbulent Flow Through a Straight Square Duct

2004 ◽  
Author(s):  
H. Naji ◽  
O. El Yahyaoui ◽  
G. Mompean
Keyword(s):  
Turbulent Flow ◽  
Reynolds Stress ◽  
Stokes Equations ◽  
A Priori ◽  
Proximity Effects ◽  
Navier Stokes ◽  
Wall Region ◽  
Square Duct ◽  
Anisotropy Tensor ◽  
Stress Models

The ability of two explicit algebraic Reynolds stress models (EARSMs) to accurately predict the problem of fully turbulent flow in a straight square duct is studied. The first model is devised by Gatski and Rumsey (2001) and the second is the one derived by Wallin and Johansson (2000). These models are studied using a priori procedure based on data resulting from direct numerical simulation (DNS) of the Navier-Stokes equations, which is available for this problem. For this case, we show that the equilibrium assumption for the anisotropy tensor is found to be correct. The analysis leans on the maps of the second and third invariants of the Reynolds stress tensor. In order to handle wall-proximity effects in the near-wall region, damping functions are implemented in the two models. The predictions and DNS obtained for a Reynolds number of 4800 both agree well and show that these models are able to predict such flows.

scholarly journals On the Effects of Tip Clearance and Operating Condition on the Flow Structures Within an Axial Turbomachine Rotor Passage

2019 ◽  
Vol 141 (11) ◽  
Author(s):  
Yuanchao Li ◽  
Huang Chen ◽  
David Tan ◽  
Joseph Katz
Keyword(s):  
Particle Image ◽  
Suction Side ◽  
Tip Clearance ◽  
Flow Structures ◽  
Narrow Gap ◽  
Piv Measurements ◽  
Tip Leakage ◽  
Image Velocimetry ◽  
Stereo Particle Image Velocimetry ◽  
Turbomachine Rotor

Abstract Effects of tip clearance size and flowrate on the flow around the tip of an axial turbomachine rotor are studied experimentally. Visualizations and stereo-particle image velocimetry (PIV) measurements in a refractive index-matched facility compare the performance, leakage velocity, and the trajectory, growth rate, and strength of the tip leakage vortex (TLV) for gaps of 0.49% and 2.3% of the blade chord, and two flowrates. Enlarging the tip clearance delays the TLV breakup in the aft part of the rotor passage at high flowrates but causes earlier breakup under pre-stall conditions. It also reduces the entrainment of endwall boundary layer vorticity from the separation point where the leakage and passage flows meet. Reducing the flowrate or tip gap shifts the location of the TLV detachment from the blade suction side (SS) upstream to points where the leakage velocity is 70–80% of the tip speed. Once detached, the growth rates of the total shed circulation are similar for all cases, i.e., varying the gap or flowrate mostly shifts the detachment point. The TLV migration away from the SS decreases with an increasing gap but not with the flowrate. Two mechanisms dominate this migration: initially, the leakage jet pushes the TLV away from the blade at 50% of the leakage velocity. Further downstream, the TLV is driven by its image on the other side of the endwall. Differences in migration rate are caused by the smaller distance between the TLV and its image for the narrow gap, and the increase in initial TLV strength with decreasing flowrate and gap.

scholarly journals Non-Equilibrium Scaling Applied to the Wake Evolution of a Model Scale Wind Turbine

Energies ◽  
2019 ◽  
Vol 12 (14) ◽  
pp. 2763 ◽  
Author(s):  
Victor P. Stein ◽  
Hans-Jakob Kaltenbach
Keyword(s):  
Wind Turbine ◽  
Reynolds Stress ◽  
Wake Region ◽  
Reynolds Stresses ◽  
Self Similarity ◽  
Horizontal Axis Wind Turbine ◽  
Velocity Deficit ◽  
Stress Components ◽  
Far Wake ◽  
Non Equilibrium

The present paper addresses the evolution of turbulence characteristics in wind turbine wakes immersed in a turbulent boundary layer. The study thereby focuses on finding physically consistent scaling laws for the wake width, the velocity deficit, and the Reynolds stresses in the far wake region. For this purpose, the concept of an added wake is derived which allows to analyse the self-similarity of the added flow quantities and the applicability of the non-equilibrium dissipation theory. The investigation is based on wind tunnel measurements in the wake of a three-bladed horizontal axis wind turbine model (HAWT) immersed in two neutrally-stratified turbulent boundary layers of different aerodynamic roughness length. The dataset also includes wake measurements for various yaw angles. A high degree of self-similarity is found in the lateral profiles of the velocity deficit and of the added Reynolds stress components. It is shown that these can be described by combined Gaussian shape functions. In the vertical, self-similarity can just be shown in the upper part of the wake. Moreover, it is observed that the degree of self-similarity is affected by the ground roughness. Results suggest an approximately constant anisotropy of the added turbulent stresses in the far wake, and the axial scaling of the added Reynolds stress components is found to be in accordance with non-equilibrium dissipation theory. It predicts a x − 1 decay of the added turbulent intensity I + , and a x − 2 evolution of the added Reynolds shear stresses Δ u i ′ u j ′ ¯ and the velocity deficit Δ u . Based on these findingsa semi-empirical model is proposed for predicting the Reynolds stresses in the far wake region which can easily be coupled with existing analytical wake models. The proposed model is found to be in good agreement with the measurement results.

Turbulence in Compressible Mixing Layers

1998 ◽  
Vol 120 (1) ◽  
pp. 48-53 ◽  
Author(s):  
Foluso Ladeinde ◽  
Wei Liu ◽  
Edward E. O’Brien
Keyword(s):  
Reynolds Stress ◽  
Turbulent Mixing ◽  
Turbulence Modeling ◽  
Mixing Layers ◽  
Correlation Tensor ◽  
Triple Correlation ◽  
Anisotropy Tensor ◽  
Homogeneous Shear Flow ◽  
Short Time ◽  
Grid Independence

The direct numerical simulation (DNS) of two-dimensional compressible turbulent mixing layers is reported in this paper for convective Mach numbers Mc = 0.5, 0.8 and 1.0. All scales of flow are resolved with a 2562 grid, although results are also obtained for 642, 962 and 1282 grids for the purpose of determining the effective accuracy and grid-independence of our calculations. The effect of Mach number is also reported for all the Reynolds stress tensor components and for the “shear” components of the anisotropy tensor, the dissipation tensor, pressure-strain, and the triple correlation tensor. The short-time behaviors of some of these quantities are similar to those reported by Sarkar (1995) for homogeneous shear flow, in spite of the differences in the problem type and initial and boundary conditions. The relative magnitudes and signs of the unclosed terms in the Reynolds stress equations provide information on those that have to be retained for turbulence modeling as well as the sense of their contribution.

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