Numerical and experimental study of mechanisms responsible for turbulent secondary flows in boundary layer flows over spanwise heterogeneous roughness

2015 ◽  
Vol 768 ◽  
pp. 316-347 ◽  
Author(s):  
William Anderson ◽  
Julio M. Barros ◽  
Kenneth T. Christensen ◽  
Ankit Awasthi
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Secondary Flow ◽  
Turbulent Kinetic Energy ◽  
Secondary Flows ◽  
Streamwise Vorticity ◽  
Reynolds Stresses ◽  
Spatial Gradients ◽  
Normal Mean ◽  
Layer Flow

We study the dynamics of turbulent boundary layer flow over a heterogeneous topography composed of roughness patches exhibiting relatively high and low correlation in the streamwise and spanwise directions, respectively (i.e. the roughness appears as streamwise-aligned ‘strips’). It has been reported that such roughness induces a spanwise-wall normal mean secondary flow in the form of mean streamwise vorticity associated with counter-rotating boundary-layer-scale circulations. Here, we demonstrate that this mean secondary flow is Prandtl’s secondary flow of the second kind, both driven and sustained by spatial gradients in the Reynolds-stress components, which cause a subsequent imbalance between production and dissipation of turbulent kinetic energy that necessitates secondary advective velocities. In reaching this conclusion, we study (i) secondary circulations due to spatial gradients of turbulent kinetic energy, and (ii) the production budgets of mean streamwise vorticity by gradients of the Reynolds stresses. We attribute the secondary flow phenomena to extreme peaks of surface stress on the relatively high-roughness regions and associated elevated turbulence production in the fluid immediately above. An optimized state is attained by entrainment of fluid exhibiting the lowest turbulent stresses – from above – and subsequent lateral ejection in order to preserve conservation of mass.

LDV Measurements of Periodic Fully Developed Main and Secondary Flows in a Channel With Rib-Disturbed Walls

1993 ◽  
Vol 115 (1) ◽  
pp. 109-114 ◽  
Author(s):  
T.-M. Liou ◽  
Y.-Y. Wu ◽  
Y. Chang
Keyword(s):  
Kinetic Energy ◽  
Secondary Flow ◽  
Turbulent Kinetic Energy ◽  
Secondary Flows ◽  
Laser Doppler Velocimeter ◽  
Parameter Distribution ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Production Term ◽  
Basic Assumptions

Laser-Doppler velocimeter measurements of mean velocities, turbulence intensities, and Reynolds stresses are presented for periodic fully developed flows in a channel with square rib-disturbed walls on two opposite sides. Quantities such as the vorticity thickness and turbulent kinetic energy are used to characterize the flow. The investigated flow was periodic in space. The Reynolds number based on the channel hydraulic diameter was 3.3×104. The ratios of pitch to rib-height and rib-height to chamber-height were 10 and 0.133, respectively. Regions where maximum and minimum Reynolds stress and turbulent kinetic energy occurred were identified from the results. The growth rate of the shear layers of the present study was compared with that of a backward-facing step. The measured turbulence anisotropy and structure parameter distribution were used to examine the basic assumptions embedded in the k–ε and k–ε–A models. For a given axial station, the peak axial mean-velocity was found not to occur at the center point. The secondary flow was determined to be Prandtl’s secondary flow of the second kind according to the measured streamwise mean vorticity and its production term.

On the definition of the secondary flow in three-dimensional cascades

2009 ◽  
Vol 223 (6) ◽  
pp. 667-676 ◽  
Author(s):  
G Persico ◽  
P Gaetani ◽  
V Dossena ◽  
G D'Ippolito ◽  
C Osnaghi
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Secondary Flow ◽  
Boundary Layers ◽  
Complex Geometry ◽  
Flow Direction ◽  
Flow Analysis ◽  
Secondary Flows ◽  
Streamwise Vorticity ◽  
Reference Flow

The present article proposes a novel methodology to evaluate secondary flows generated by the annulus boundary layers in complex cascades. Unlike two-dimensional (2D) linear cascades, where the reference flow is commonly defined as that measured at midspan, the problem of the reference flow definition for annular or complex 3D linear cascades does not have a general solution up to the present time. The proposed approach supports secondary flow analysis whenever exit streamwise vorticity produced by inlet endwall boundary layers is of interest. The idea is to compute the reference flow by applying slip boundary conditions at the endwalls in a viscous 3D numerical simulation, in which uniform total pressure is prescribed at the inlet. Thus the reference flow keeps the 3D nature of the actual flow except for the contribution of the endwall boundary layer vorticity. The resulting secondary field is then derived by projecting the 3D flow field (obtained from both an experiment and a fully viscous simulation) along the local reference flow direction; this approach can be proficiently applied to any complex geometry. This method allows the representation of secondary velocity vectors with a better estimation of the vortex extension, since it offers the opportunity to visualize also the region of the vortices, which can be approximated as a potential type. Furthermore, a proficient evaluation of the secondary vorticity and deviation angle effectively induced by the annulus boundary layer is possible. The approach was preliminarily verified against experimental data in linear cascades characterized by cylindrical blades, not reported for the sake of brevity, showing a very good agreement with the standard methodology based only on the experimental midspan flow field. This article presents secondary flows obtained by the application of the proposed methodology on two annular cascades with cylindrical and 3D-designed blades, stressing the differences with other definitions. Both numerical and experimental results are considered.

Measurements of Losses and Reynolds Stresses in the Secondary Flow Downstream of a Low-Speed Linear Turbine Cascade

2010 ◽  
Author(s):  
G. D. MacIsaac ◽  
S. A. Sjolander ◽  
T. J. Praisner
Keyword(s):  
Kinetic Energy ◽  
Turbulent Flow ◽  
Secondary Flow ◽  
Turbulent Kinetic Energy ◽  
Pressure Probe ◽  
Turbine Cascade ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Hole Pressure ◽  
The Mean

Experimental measurements of the mean and turbulent flow field were preformed downstream of a low-speed linear turbine cascade. The influence of turbulence on the production of secondary losses is examined. Steady pressure measurements were collected using a seven-hole pressure probe and the turbulent flow quantities were measured using a rotatable x-type hotwire probe. Each probe was traversed downstream of the cascade along planes positioned at three axial locations: 100%, 120% and 140% of the axial chord (Cx) downstream of the leading edge. The seven-hole pressure probe was used to determine the local total and static pressure as well as the three mean velocity components. The rotatable x-type hotwire probe, in addition to the mean velocity components, provided the local Reynolds stresses and the turbulent kinetic energy. The axial development of the secondary losses is examined in relation to the rate at which mean kinetic energy is transferred to turbulent kinetic energy. In general, losses are generated as a result of the mean flow dissipating kinetic energy through the action of viscosity. The production of turbulence can be considered a preliminary step in this process. The measured total pressure contours from the three axial locations (1.00, 1.20 and 1.40Cx) demonstrate the development of the secondary losses. The peak loss core in each plane consists mainly of low momentum fluid that originates from the inlet endwall boundary layer. There are, however, additional losses generated as the flow mixes with downstream distance. These losses have been found to relate to the turbulent Reynolds stresses. An examination of the turbulent deformation work term demonstrates a mechanism of loss generation in the secondary flow region. The importance of the Reynolds shear stress to this process is explored in detail.

Vorticity transport in a corner formed by a solid wall and a free surface

2002 ◽  
Vol 465 ◽  
pp. 331-352 ◽  
Author(s):  
L. M. GREGA ◽  
T. Y. HSU ◽  
T. WEI
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Secondary Flow ◽  
Mixed Boundary ◽  
Solid Wall ◽  
Secondary Flows ◽  
Exact Nature ◽  
Streamwise Vorticity ◽  
The Cross ◽  
Vorticity Transport

There is a growing body of literature in which turbulent boundary layer flow along a mixed-boundary corner formed by a vertical solid wall and a horizontal free surface has been examined. While there is consensus regarding the existence of weak secondary flows in the near corner region, there is some disagreement as to the exact nature and origin of these flows. In two earlier works by the authors, evidence was presented supporting the existence of a weak streamwise vortex which rotates in toward the wall at the free surface and down away from the surface along the wall. This ‘inner secondary vortex’ is accompanied by an ‘outer secondary flow’ which transports low-momentum boundary layer fluid up along the wall and outward at the free surface. The magnitudes of the cross-stream velocities associated with these secondary flows were measured to be on the order of 1% of the free-stream speed. In this paper, high-resolution DPIV measurements made in the cross-stream plane are presented. These clearly show the inner and outer secondary flows. The cross-stream vector fields allow computation of terms in the turbulent streamwise vorticity transport equation. These terms indicate mean vorticity transport at the free surface associated with the outer secondary flow. In addition there appears to be a balance between the wall-normal and free-surface-normal fluctuating vorticity reorientation terms.

Interaction Between Inlet Boundary Layer, Tip-Leakage and Secondary Flows in a Low-Speed Turbine Cascade

1994 ◽  
Author(s):  
J. K. K. Chan ◽  
M. I. Yaras ◽  
S. A. Sjolander
Keyword(s):  
Boundary Layer ◽  
Secondary Flow ◽  
Large Scale ◽  
Field Measurements ◽  
Secondary Flows ◽  
Tip Clearance ◽  
Turbine Cascade ◽  
Streamwise Vorticity ◽  
Tip Leakage Flow ◽  
Tip Leakage

An experiment has been conducted in a large-scale linear turbine cascade to examine the interaction between the inlet endwall boundary layer, tip-leakage and secondary flows. Detailed flow field measurements have been made upstream and downstream of the blade row for two values of inlet boundary layer thickness (δ*/c of about 0.015 and 0.04) together with three values of tip clearance (gap heights of 0.0, 1.5 and 5.5 percent of blade chord). In the downstream plane, the total pressure deficits associated with the tip-leakage and secondary flows were discriminated by examining the sign of the streamwise vorticity. For this case, the streamwise vorticity of the two flows have opposite signs and this proved an effective criterion for separating the flows despite their close proximity in space. It was found that with clearance the loss associated with the secondary flow was substantially reduced from the zero clearance value, in contradiction to the assumption made in most loss prediction schemes. Further work is needed, notably to clarify the influence of relative tip-wall motion which in turbines reduces the tip-leakage flow while enhancing the secondary flow.

Measurements of Losses and Reynolds Stresses in the Secondary Flow Downstream of a Low-Speed Linear Turbine Cascade

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
G. D. MacIsaac ◽  
S. A. Sjolander ◽  
T. J. Praisner
Keyword(s):  
Kinetic Energy ◽  
Turbulent Flow ◽  
Secondary Flow ◽  
Turbulent Kinetic Energy ◽  
Pressure Probe ◽  
Turbine Cascade ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Hole Pressure ◽  
The Mean

Experimental measurements of the mean and turbulent flow field were preformed downstream of a low-speed linear turbine cascade. The influence of turbulence on the production of secondary losses is examined. Steady pressure measurements were collected using a seven-hole pressure probe and the turbulent flow quantities were measured using a rotatable x-type hotwire probe. Each probe was traversed downstream of the cascade along planes positioned at three axial locations: 100%, 120%, and 140% of the axial chord (Cx) downstream of the leading edge. The seven-hole pressure probe was used to determine the local total and static pressure as well as the three mean velocity components. The rotatable x-type hotwire probe, in addition to the mean velocity components, provided the local Reynolds stresses and the turbulent kinetic energy. The axial development of the secondary losses is examined in relation to the rate at which mean kinetic energy is transferred to turbulent kinetic energy. In general, losses are generated as a result of the mean flow dissipating kinetic energy through the action of viscosity. The production of turbulence can be considered a preliminary step in this process. The measured total pressure contours from the three axial locations (1.00, 1.20, and 1.40Cx) demonstrate the development of the secondary losses. The peak loss core in each plane consists mainly of low momentum fluid that originates from the inlet endwall boundary layer. There are, however, additional losses generated as the flow mixes with downstream distance. These losses have been found to relate to the turbulent Reynolds stresses. An examination of the turbulent deformation work term demonstrates a mechanism of loss generation in the secondary flow region. The importance of the Reynolds shear stresses to this process is explored in detail.

scholarly journals Endwall Loss in Turbine Cascades

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
John D. Coull
Keyword(s):  
Boundary Layer ◽  
Secondary Flow ◽  
Turbine Blades ◽  
Secondary Flows ◽  
Navier Stokes ◽  
Design Parameters ◽  
Streamwise Vorticity ◽  
Suction Surface ◽  
Blade Thickness ◽  
The Impact

Prior to the detailed design of components, turbomachinery engineers must guide a mean-line or throughflow design toward an optimum configuration. This process requires a combination of informed judgement and low-order correlations for the principle sources of loss. With these requirements in mind, this paper examines the impact of key design parameters on endwall loss in turbines, a problem which remains poorly understood. This paper presents a parametric study of linear cascades, which represent a simplified model of real-engine flow. The designs are nominally representative of the low-pressure turbine blades of an aero-engine, with varying flow angles, blade thickness, and suction surface lift styles. Reynolds-averaged Navier–Stokes (RANS) calculations are performed for a single aspect ratio (AR) and constant inlet boundary layer thickness. To characterize the cascades studied, the two-dimensional design space is examined before studying endwall losses in detail. It is demonstrated that endwall loss can be decomposed into two components: one due to the dissipation associated with the endwall boundary layer and another induced by the secondary flows. This secondary-flow-induced loss is found to scale with a measure of streamwise vorticity predicted by classical secondary flow theory.

Prediction of Solid/Free-Surface Juncture Boundary Layer and Wake of a Surface-Piercing Flat Plate at Low Froude Number

1998 ◽  
Vol 120 (2) ◽  
pp. 354-362 ◽  
Author(s):  
Madhu Sreedhar ◽  
Fred Stern
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Flat Plate ◽  
Froude Number ◽  
Secondary Flows ◽  
Wall Region ◽  
Normal Stresses ◽  
Streamwise Vorticity ◽  
Reynolds Stresses ◽  
Mean Velocity

Results are reported of a RANS simulation investigation on the prediction of turbulence-driven secondary flows at the free-surface juncture of a surface-piercing flat plate at low Froude numbers. The turbulence model combines a nonlinear eddy viscosity model and a modified version of a free-surface correction formula. The different elements of the model are combined and the model constants calibrated based on the premises that the anisotropy of the normal stresses is mainly responsible for the dynamics of the flow in the juncture region, and an accurate modeling of the normal-stress anisotropy as obtained from the data is a primary requirement for the successful prediction of the overall flow field. The predicted mean velocity, streamwise vorticity, turbulent kinetic energy, and other quantities at the juncture are then compared with data and analyzed with regard to findings of related studies. In agreement with the experimental observations, the simulated flow at large depths was essentially two-dimensional and displayed all the major features of zero pressure gradient boundary layer and wake, including the anisotropy of normal stresses in the near-wall region. In the boundary-layer free-surface juncture region, the major features of interest that were predicted include the generation of secondary flows and the thickening of the boundary layer near the free surface. In the wake free-surface juncture region, even though secondary flows and a thickening of the wake width near the free surface were predicted in accordance with the experimental observations, the overall comparison with the experiment was not as satisfactory as the boundary-layer juncture. This is partly due to the lack of a strong coherent flow structure in the wake juncture and the presence of possible wave effects in the wake in the experiments. An examination of the terms in the Reynolds-averaged streamwise vorticity equation reconfirmed the importance of the anisotropy of the normal Reynolds stresses in the production of streamwise vorticity. The free-surface wave elevations were negligible for the present model problem for the nonzero Froude number studied. Finally, concluding remarks are presented with regards to extensions for practical geometries such as surface ship flows.

A Numerical Study on the Generation Mechanism of Turbulence-Driven Secondary Flow in a Square Duct

1993 ◽  
Vol 115 (1) ◽  
pp. 172-175 ◽  
Author(s):  
Hyon Kook Myong
Keyword(s):  
Secondary Flow ◽  
Numerical Study ◽  
Reynolds Shear Stress ◽  
Secondary Flows ◽  
Generation Mechanism ◽  
Streamwise Vorticity ◽  
Reynolds Stresses ◽  
Cross Sectional ◽  
Square Duct ◽  
Vorticity Transport

The generation mechanism of turbulence-driven secondary flows in a square duct is numerically investigated in the present study by using an anisotropic low-Reynolds-number k–ε turbulence model. Special attention is directed to the distributions of turbulence quantities, which are responsible for the secondary flow generation, such as the anisotropy of normal Reynolds stresses and the secondary Reynolds shear stress acting on the cross-sectional plane. The vorticity transport process is also discussed in detail, based on the numerical evaluation of the individual terms which appear in the streamwise vorticity transport equation.

Secondary Flow in Rotating Bends

1978 ◽  
Vol 100 (4) ◽  
pp. 553-560 ◽  
Author(s):  
M. W. Johnson
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Secondary Flow ◽  
Flow Rate ◽  
Rotational Speed ◽  
Total Pressure ◽  
Secondary Flows ◽  
Streamwise Vorticity ◽  
Inlet Distortion ◽  
Finite Difference Techniques

An equation describing the development of streamwise vorticity is derived. The fluid is assumed inviscid and incompressible and to have a gradient of rotating total pressure across the streamtube. The equation is used to calculate, by finite difference techniques, the streamwise vorticity development for bends, rotating straight pipes, rotating axial to radial bends and for a rotating duct representing Eckardt’s impeller passage. The development of secondary flows in centrifugal compressors is discussed. It is concluded that the secondary flows within the boundary layer determine the position of the wake at outlet and probably influence separation. It is also concluded that the wake can be moved by altering mass flow rate, rotational speed or by introducing an inlet distortion to the flow.

Sign in / Sign up

Export Citation Format

Share Document