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.

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.

Three-Dimensional Turbulent Flow of the Tip Leakage Vortex in an Axial Compressor Rotor Passage

2000 ◽  
Author(s):  
Hongwei Ma ◽  
Haokang Jiang
Keyword(s):  
Turbulent Flow ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Radial Component ◽  
Reynolds Stresses ◽  
Compressor Cascade ◽  
Suction Surface ◽  
Tip Leakage Vortex ◽  
Tip Leakage ◽  
Compressor Rotor

Three-dimensional turbulent flow of the tip leakage vortex in a single-stage axial compressor rotor passage is studied using a 3-Component Laser Doppler Velocimetry. The measurement results indicate that the tip leakage vortex originates at about 10% axial chord, 8% pitch away from the suction surface, and becomes strongest at about 30% chord. With the flow downstream, the vortex core moves toward the pressure surface and to a lower radial location, leading to substantial flow mixing, blockage and turbulence in the tip region. The radial component of turbulence intensities is found to be the highest while the axial-radial component of Reynolds stresses is the largest. Breakdown of the leakage vortex occurs inside the rear rotor passage, which makes the flow more turbulent in a wider region downstream. This viewpoint is confirmed by the measurements of unsteady static pressure on the casing wall. Breakdown of a leakage vortex is observed clearly in a compressor cascade with a small clearance. Unsteady interactions of the broken vorticities and the suction surface’s boundary layer are shown obviously inside the downstream passage.

Flow Field Unsteadiness in the Tip Region of a Transonic Compressor Rotor

1997 ◽  
Vol 119 (1) ◽  
pp. 122-128 ◽  
Author(s):  
S. L. Puterbaugh ◽  
W. W. Copenhaver
Keyword(s):  
Flow Field ◽  
High Performance ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Vortex Interaction ◽  
Tip Leakage Vortex ◽  
Tip Leakage ◽  
Transonic Compressor ◽  
Compressor Rotor ◽  
Operating Points

An experimental investigation concerning tip flow field unsteadiness was performed for a high-performance, state-of-the-art transonic compressor rotor. Casing-mounted high frequency response pressure transducers were used to indicate both the ensemble averaged and time varying flow structure present in the tip region of the rotor at four different operating points at design speed. The ensemble averaged information revealed the shock structure as it evolved from a dual shock system at open throttle to an attached shock at peak efficiency to a detached orientation at near stall. Steady three-dimensional Navier Stokes analysis reveals the dominant flow structures in the tip region in support of the ensemble averaged measurements. A tip leakage vortex is evident at all operating points as regions of low static pressure and appears in the same location as the vortex found in the numerical solution. An unsteadiness parameter was calculated to quantify the unsteadiness in the tip cascade plane. In general, regions of peak unsteadiness appear near shocks and in the area interpreted as the shock-tip leakage vortex interaction. Local peaks of unsteadiness appear in mid-passage downstream of the shock-vortex interaction. Flow field features not evident in the ensemble averaged data are examined via a Navier-Stokes solution obtained at the near stall operating point.

The Behavior of the Casing Boundary Layer With the Presence of Tip Leakage Vortex

2018 ◽  
Author(s):  
Xi Nan ◽  
Feng Lin ◽  
Takehiro Himeno ◽  
Toshinori Watanabe
Keyword(s):  
Boundary Layer ◽  
Skin Friction ◽  
Three Dimensional ◽  
Pressure Rise ◽  
Rotating Stall ◽  
Tip Leakage Vortex ◽  
Tip Leakage ◽  
Transonic Compressor ◽  
Flow Loss ◽  
Produce Flow

Casing boundary layer effectively places a limit on the pressure rise capability achievable by the compressor. The separation of the casing boundary layer not only produce flow loss but also closely related to the compressor rotating stall. The motivation of this paper is to present a viewpoint that the casing boundary layer should be paid attention to in parallel with other flow factors on rotating stall trigger. This paper illustrates the casing boundary layer behavior by displaying its separation phenomena with the presence of tip leakage vortex at different flow conditions. Skin friction lines and the corresponding absolute streamlines are used to demonstrate the three-dimensional flow patterns on and near the casing. The results depict a Saddle, a Node and several tufts of skin friction lines dividing the passage into four zones. The tip leakage vortex is enfolded within one of the zones by the separated flows. All the flows in each blade passage are confined within the passage as long as the compressor is stable. The casing boundary layer of a transonic compressor is also examined in the same way, which results in qualitatively similar zonal flows that enfolds the tip leakage vortex. This research develops a new way to study the casing boundary layer in rotating compressors. The results may provide a first-principle based explanation to stalling mechanisms for compressors that are casing sensitive.

scholarly journals Rotational Effects on Reynolds Stresses in the Solar Convection Zone

1991 ◽  
Vol 130 ◽  
pp. 98-100
Author(s):  
P. Pulkkinen ◽  
I. Tuominen ◽  
A. Brandenburg ◽  
Å. Nordlund ◽  
R.F. Stein
Keyword(s):  
Reynolds Stress ◽  
Convection Zone ◽  
Rotation Axis ◽  
Three Dimensional ◽  
External Parameter ◽  
Reynolds Stresses ◽  
Solar Convection Zone ◽  
Hydrodynamic Simulations ◽  
Solar Convection ◽  
Good Agreement

AbstractThree-dimensional hydrodynamic simulations are carried out in a rectangular box. The angle between gravity and rotation axis is kept as an external parameter in order to study the latitude-dependence of convection. Special attention is given to the horizontal Reynolds stress and the ∧-effect (Rüdiger, 1989). The results of the simulations are compared with observations and theory and a good agreement is found.

On the Constitutive Relation for the Reynolds Stresses and the Prandtl-Kolmogorov Hypothesis of Effective Viscosity in Axisymmetric Strained Turbulence

1999 ◽  
Vol 122 (1) ◽  
pp. 48-50 ◽  
Author(s):  
J. Jovanovic´ ◽  
I. Otic´
Keyword(s):  
Strain Rate ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Constitutive Relation ◽  
Effective Viscosity ◽  
Constitutive Relations ◽  
Reynolds Stresses ◽  
Reynolds Stress Tensor ◽  
The Mean ◽  
Mean Strain

The constitutive relation for the Reynolds stress tensor is considered for turbulence developing in axisymmetric strain fields. It is confirmed that the Reynolds stress tensor is aligned linearly with the mean strain rate. In contrast to the Prandtl-Kolmogorov, hypothesis, the effective viscosity is found to grow in proportion to the anisotropy of turbulence and the length scale based on the magnitude of the mean strain rate. Using invariant theory the effective viscosity is determined for the limiting states of turbulence. Additional analysis of the constitutive relations is supplemented for the dissipation and pressure-strain correlations. It is shown that analytical derivations are in excellent agreement with the data obtained from direct numerical simulations. [S0098-2202(00)02801-7]

Unsteady Flow Behavior due to Breakdown of Tip Leakage Vortex in an Axial Compressor Rotor at Near-Stall Condition

2000 ◽  
Author(s):  
Masato Furukawa ◽  
Kazuhisa Saiki ◽  
Kazutoyo Yamada ◽  
Masahiro Inoue
Keyword(s):  
Unsteady Flow ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Surface Boundary ◽  
Pressure Side ◽  
Suction Surface ◽  
Tip Leakage Vortex ◽  
Tip Leakage ◽  
Pressure Surface ◽  
Compressor Rotor

The unsteady flow nature caused by the breakdown of the tip leakage vortex in an axial compressor rotor at near-stall conditions has been investigated by unsteady three-dimensional Navier-Stokes flow simulations. The simulations show that the spiral-type breakdown of the tip leakage vortex occurs inside the rotor passage at the near-stall conditions. Downstream of the breakdown onset, the tip leakage vortex twists and turns violently with time, thus interacting with the pressure surface of the adjacent blade. The motion of the vortex and its interaction with the pressure surface are cyclic. The vortex breakdown causes significant changes in the nature of the tip leakage vortex, which result in the anomalous phenomena in the time-averaged flow fields near the tip at the near-stall conditions: no rolling-up of the leakage vortex downstream of the rotor, disappearance of the casing wall pressure trough corresponding to the leakage vortex, large spread of the low-energy fluid accumulating on the pressure side, and large pressure fluctuation on the pressure side. As the flow rate is decreased, the movement of the tip leakage vortex due to its breakdown becomes so large that the leakage vortex interacts with the suction surface as well as the pressure one. The interaction with the suction surface gives rise to the three-dimensional separation of the suction surface boundary layer.

Experimental Study on the Three-Dimensional Flow Within a Compressor Cascade With Tip Clearance: Part I—Velocity and Pressure Fields

1993 ◽  
Vol 115 (3) ◽  
pp. 435-443 ◽  
Author(s):  
S. Kang ◽  
C. Hirsch
Keyword(s):  
Three Dimensional ◽  
Leading Edge ◽  
Surface Flow ◽  
Tip Clearance ◽  
Tip Vortex ◽  
Compressor Cascade ◽  
Three Dimensional Flow ◽  
Tip Leakage Vortex ◽  
Tip Leakage ◽  
Dimensional Flow

Experimental results from a study of the three-dimensional flow in a linear compressor cascade with stationary endwall at design conditions are presented for tip clearance levels of 1.0, 2.0, and 3.3 percent of chord, compared with the no-clearance case. In addition to five-hole probe measurements, extensive surface flow visualizations are conducted. It is observed that for the smaller clearance cases a weak horseshoe vortex forms in the front of the blade leading edge. At all the tip gap cases, a multiple tip vortex structure with three discrete vortices around the midchord is found. The tip leakage vortex core is well defined after the midchord but does not cover a significant area in traverse planes. The presence of the tip leakage vortex results in the passage vortex moving close to the endwall and the suction side.

Three-Dimensional Turbulent Flow in the Tip Region of an Axial Compressor Rotor Passage at a Near Stall Condition

2001 ◽  
Author(s):  
Hongwei Ma ◽  
Haokang Jiang
Keyword(s):  
Turbulent Flow ◽  
Large Scale ◽  
Three Dimensional ◽  
Axial Flow ◽  
Leading Edge ◽  
Rotating Stall ◽  
Suction Surface ◽  
Tip Leakage Vortex ◽  
Tip Leakage ◽  
Compressor Rotor

This paper presents an experimental study of the three-dimensional turbulent flow field in the tip region of an axial flow compressor rotor passage at a near stall condition. The investigation was conducted in a low-speed large-scale compressor using a 3-component Laser Doppler Velocimetry and a high frequency pressure transducer. The measurement results indicate that a tip leakage vortex is produced very close to the leading edge, and becomes the strongest at about 10% axial chord from the leading edge. Breakdown of the vortex periodically occurs at about 1/3 chord, causing very strong turbulence in the radial direction. Flow separation happens on the tip suction surface at about half chord, prompting the corner vortex migrating toward the pressure side. Tangential migration of the low-energy fluids results in substantial flow blockage and turbulence in the rear of a rotor passage. Unsteady interactions among the tip leakage vortex, the separated vortex and the corner flow should contribute to the inception of the rotating stall in a compressor.

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