Evaluation of Higher-Order Terms in the Throughflow Approximation Using 3D Navier-Stokes Computations of a Transonic Compressor Rotor

1999 ◽  
Author(s):  
Stephane Baralon ◽  
Lars-Erik Eriksson ◽  
Ulf Håll
Keyword(s):  
Three Dimensional ◽  
Meridional Flow ◽  
Tip Clearance ◽  
Navier Stokes ◽  
Flow Conditions ◽  
Peak Efficiency ◽  
Transonic Compressor ◽  
Compressor Rotor ◽  
Dimensional Distribution ◽  
Viscous Stresses

Two three-dimensional Reynolds-averaged Navier-Stokes solutions of the Nasa 67 transonic compressor rotor with tip clearance, computed at near-peak efficiency and near-stall flow conditions, have been circumferentially averaged in order to evaluate the circumferential spatial fluctuation terms such as u′u′, u′v′, u′w′, etc. The three-dimensional distribution of these fluctuations is presented and physically interpreted for the two flow conditions. Then, the meridional distributions of the tangential average of each of these fluctuation terms, the so-called perturbation stresses, are described and interpreted for the two flow conditions. A meridional throughflow computation for which all stresses were included has been performed for the near-peak efficiency flow condition using a time-marching finite-volume solver. The calculation proved to be in good agreement with the tangentially averaged 3D solution. Moreover, the relative importance of the perturbation and viscous stresses has been investigated. The influence of the viscous stresses on the meridional flow was not found important whereas the perturbation stresses were identified as significant contributors to the blade passage losses and to the spanwise mixing phenomenon. Furthermore, the relative effects of each perturbation term on the meridional flow prediction have been investigated for the near-peak efficiency case. The u′w′~, v′w′~, u′v′~ and u′u′~ stresses proved to exert a significant influence on the prediction of blade design key parameters such as flow angles and losses in the tip region, essentially.

A Numerical Analysis of the Three-Dimensional Viscous Flow in a Transonic Compressor Rotor and Comparison With Experiment

1987 ◽  
Vol 109 (1) ◽  
pp. 83-90 ◽  
Author(s):  
W. N. Dawes
Keyword(s):  
Boundary Layer ◽  
Numerical Analysis ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Flow ◽  
Tip Clearance ◽  
Navier Stokes ◽  
Viscous Effects ◽  
Transonic Compressor ◽  
Compressor Rotor

The numerical analysis of highly loaded transonic compressors continues to be of considerable interest. Although much progress has been made with inviscid analyses, viscous effects can be very significant, especially those associated with shock–boundary layer interactions. While inviscid analyses have been enhanced by the interactive inclusion of blade surf ace boundary layer calculations, it may be better in the long term to develop efficient algorithms to solve the full three-dimensional Navier–Stokes equations. Indeed, it seems that many phenomena of key interest, like tip clearance flows, may only be accessible to a Navier–Stokes solver. The present paper describes a computer program developed for solving the three-dimensional viscous compressible flow equations in turbomachine geometries. The code is applied to the study of the flowfield in an axial-flow transonic compressor rotor with an attempt to resolve the tip clearance flow. The predicted flow is compared with laser anemometry measurements and good agreement is found.

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 Extension of a Solution-Adaptive Three-Dimensional Navier–Stokes Solver Toward Geometries of Arbitrary Complexity

1993 ◽  
Vol 115 (2) ◽  
pp. 283-295 ◽  
Author(s):  
W. N. Dawes
Keyword(s):  
Guide Vane ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Centrifugal Impeller ◽  
Transonic Compressor ◽  
Compressor Rotor ◽  
Wide Range ◽  
Nozzle Guide Vane ◽  
Recent Developments ◽  
Nozzle Guide

This paper describes recent developments to a three-dimensional, unstructured mesh, solution-adaptive Navier–Stokes solver. By adopting a simple, pragmatic but systematic approach to mesh generation, the range of simulations that can be attempted is extended toward arbitrary geometries. The combined benefits of the approach result in a powerful analytical ability. Solutions for a wide range of flows are presented, including a transonic compressor rotor, a centrifugal impeller, a steam turbine nozzle guide vane with casing extraction belt, the internal coolant passage of a radial inflow turbine, and a turbine disk cavity flow.

scholarly journals Modeling of Tip Clearance Flows Through an Improved 3-D Pressure Correction Navier-Stokes Solver

1993 ◽  
Author(s):  
N. Lymberopoulos ◽  
K. Giannakoglou ◽  
I. Nikolaou ◽  
K. D. Papailiou ◽  
A. Tourlidakis ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Tip Clearance ◽  
Navier Stokes ◽  
Special Treatment ◽  
Pressure Correction ◽  
Compressor Rotor ◽  
Numerical Predictions ◽  
Correction Technique

Mechanical constraints dictate the existence of tip clearances in rotating cascades, resulting to a flow leakage through this clearance which considerably influences the efficiency and range of operation of the machine. Three-dimensional Navier-Stokes solvers are often used for the numerical study of compressor and turbine stages with tip-clearance. The quality of numerical predictions depends strongly on how accurately the blade tip region is modelled; in this respect the accurate modelling of tip region was one of the main goals of this work. In the present paper, a 3-D Navier-Stokes solver is suitably adapted so that the flat tip surface of a blade and its sharp edges could be accurately modelled, in order to improve the precision of the calculation in the tip region. The adapted code solves the fully elliptic, steady, Navier-Stokes equations through a space-marching algorithm and a pressure correction technique; the H-type topology is retained, even in cases with thick leading edges where a special treatment is introduced herein. The analysis is applied to two different cases, a linear cascade and a compressor rotor, and comparisons with experimental data are provided.

Aerodynamic Design Optimization of an Axial Flow Compressor Rotor

2002 ◽  
Author(s):  
Chan-Sol Ahn ◽  
Kwang-Yong Kim
Keyword(s):  
Design Optimization ◽  
Response Surface ◽  
Computing Time ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Axial Flow ◽  
Navier Stokes ◽  
Transonic Compressor ◽  
Compressor Rotor ◽  
Design Variables

Design optimization of a transonic compressor rotor (NASA rotor 37) using the response surface method and three-dimensional Navier-Stokes analysis has been carried out in this work. The Baldwin-Lomax turbulence model was used in the flow analysis. Three design variables were selected to optimize the stacking line of the blade. Data points for response evaluations were selected by D-optimal design, and linear programming method was used for the optimization on the response surface. As a main result of the optimization, adiabatic efficiency was successfully improved. It was found that the optimization process provides reliable design of a turbomachinery blade with reasonable computing time.

Three-Dimensional Flowfields Inside a Transonic Compressor With Swept Blades

1991 ◽  
Vol 113 (2) ◽  
pp. 241-250 ◽  
Author(s):  
C. Hah ◽  
A. J. Wennerstrom
Keyword(s):  
Turbulence Modeling ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Operating Conditions ◽  
Tip Clearance ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Tip Clearance Flow ◽  
Transonic Compressor ◽  
Improved Performance

The concept of swept blades for a transonic or supersonic compressor was reconsidered by Wennerstrom in the early 1980s. Several transonic rotors designed with swept blades have shown very good aerodynamic efficiency. The improved performance of the rotor is believed to be due to reduced shock strength near the shroud and better distribution of secondary flows. A three-dimensional flowfield inside a transonic rotor with swept blades is analyzed in detail experimentally and numerically. A Reynolds-averaged Navier–Stokes equation is solved for the flow inside the rotor. The numerical solution is based on a high-order upwinding relaxation scheme, and a two-equation turbulence model with a low Reynolds number modification is used for the turbulence modeling. To predict flows near the shroud properly, the tip-clearance flow also must be properly calculated. The numerical results at three different operating conditions agree well with the available experimental data and reveal various interesting aspects of shock structure inside the rotor.

scholarly journals Three-Dimensional Flowfields Inside a Transonic Compressor With Swept Blades

1990 ◽  
Author(s):  
C. Hah ◽  
A. J. Wennerstrom
Keyword(s):  
Turbulence Modeling ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Operating Conditions ◽  
Tip Clearance ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Tip Clearance Flow ◽  
Transonic Compressor ◽  
Improved Performance

The concept of swept blades for a transonic or supersonic compressor was reconsidered by Wennerstrom in the early 1980s. Several transonic rotors designed with swept blades have shown very good aerodynamic efficiency. The improved performance of the rotor is believed to be due to reduced shock strength near the shroud and better distribution of secondary flows. A three-dimensional flowfield inside a transonic rotor with swept blades is analyzed in detail experimentally and numerically. A Reynolds-averaged Navier-Stokes equation is solved for the flow inside the rotor. The numerical solution is based on a high-order upwinding relaxation scheme, and a two-equation turbulence model with a low Reynolds number modification is used for the turbulence modeling. To properly predict flows near the shroud, the tip-clearance flow also must be properly calculated. The numerical results at three different operating conditions agree well with the available experimental data and reveal various interesting aspects of shock structure inside the rotor.

Tip-Clearance and Secondary Flows in a Transonic Compressor Rotor

1999 ◽  
Vol 121 (4) ◽  
pp. 751-762 ◽  
Author(s):  
G. A. Gerolymos ◽  
I. Vallet
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Main Flow ◽  
Secondary Flows ◽  
Tip Clearance ◽  
Computational Method ◽  
Tip Vortex ◽  
Computational Results ◽  
Transonic Compressor ◽  
Compressor Rotor

The purpose of this paper is to investigate tip-clearance and secondary flows numerically in a transonic compressor rotor. The computational method used is based on the numerical integration of the Favre-Reynolds-averaged three-dimensional compressible Navier–Stokes equations, using the Launder–Sharma near-wall k–ε turbulence closure. In order to describe the flowfield through the tip and its interaction with the main flow accurately, a fine O-grid is used to discretize the tip-clearance gap. A patched O-grid is used to discretize locally the mixing-layer region created between the jetlike flow through the gap and the main flow. An H–O–H grid is used for the computation of the main flow. In order to substantiate the validity of the results, comparisons with experimental measurements are presented for the NASA_37 rotor near peak efficiency using three grids (of 106, 2 X 106, and 3 X 106 points, with 21, 31, and 41 radial stations within the gap, respectively). The Launder–Sharma k–ε model underestimates the hub corner stall present in this configuration. The computational results are then used to analyze the interblade-passage secondary flows, the flow within the tip-clearance gap, and the mixing downstream of the rotor. The computational results indicate the presence of an important leakage-interaction region where the leakage-vortex after crossing the passage shock-wave mixes with the pressure-side secondary flows. A second trailing-edge tip vortex is also clearly visible.

Toward Improved Throughflow Capability: The Use of Three-Dimensional Viscous Flow Solvers in a Multistage Environment

1992 ◽  
Vol 114 (1) ◽  
pp. 8-17 ◽  
Author(s):  
W. N. Dawes
Keyword(s):  
Experimental Evidence ◽  
Guide Vane ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Flow Properties ◽  
Transonic Compressor ◽  
Compressor Rotor ◽  
Blade Row ◽  
Nozzle Guide Vane ◽  
Nozzle Guide

A methodology is presented for simulating turbomachinery blade rows in a multistage environment by deploying a standard three-dimensional Navier–Stokes solver simultaneously on a number of blade rows. The principal assumptions are that the flow is steady relative to each blade row individually and that the rows can communicate via inter-row mixing planes. These mixing planes introduce circumferential averaging of flow properties but preserve quite general radial variations. Additionally, each blade can be simulated in three-dimensional or axisymmetrically (in the spirit of throughflow analysis) and a series of axisymmetric rows can be considered together with one three-dimensional row to provide, cheaply, a machine environment for that row. Two applications are presented: a transonic compressor rotor and a steam turbine nozzle guide vane simulated both isolated and as part of a stage. In both cases the behavior of the blade considered in isolation was different to when considered as part of a stage and in both cases was in much closer agreement with the experimental evidence.

An Investigation of the Effect of Cascade Area Ratios on Transonic Compressor Performance

1994 ◽  
Author(s):  
A. R. Wadia ◽  
W. W. Copenhaver
Keyword(s):  
High Speed ◽  
Three Dimensional ◽  
Area Ratio ◽  
Peak Efficiency ◽  
Trailing Edge ◽  
Transonic Compressor ◽  
Compressor Rotor ◽  
Wide Range ◽  
Boundary Layer Interaction ◽  
Compressor Performance

Transonic compressor rotor performance is highly sensitive to variations in cascade area ratios. This paper reports on the design, experimental evaluation and three-dimensional viscous analysis of four low aspect ratio transonic rotors that demonstrate the effects of cascade throat area, internal contraction and trailing edge effective camber on compressor performance. The cascade throat area study revealed that tight throat margins result in increased high speed efficiency with lower part speed performance. Stall line was also improved slightly over a wide range of speeds with a lower throat-to-upstream capture area ratio. Higher internal contraction, expressed as throat-to-mouth area ratio, also results in increased design point peak efficiency, but again costs performance at the lower speeds. Reducing the trailing edge effective camber expressed as throat-to-exit area ratio, results in an improvement in peak efficiency level without significantly lowering the stall line. Among all four rotors, the best high speed efficiency was obtained by the rotor with tight throat margin and highest internal contraction, but its efficiency was the lowest at part speed. The best compromise between high speed and part speed efficiency was achieved by the rotor with a large throat and a lower trailing edge effective camber. The differences in the shock structure and the shock boundary layer interaction of the four blades was analyzed using a three-dimensional viscous code. The analytical results are used to supplement the data and provide further insight into the detailed physics of the flow field.

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