Navier–Stokes Solutions of Unsteady Flow in a Compressor Rotor

1986 ◽  
Vol 108 (2) ◽  
pp. 206-215 ◽  
Author(s):  
J. N. Scott ◽  
W. L. Hankey
Keyword(s):  
Unsteady Flow ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Numerical Procedure ◽  
Navier Stokes ◽  
Suction Surface ◽  
Blade Passage ◽  
Radial Location ◽  
Transonic Compressor ◽  
Compressor Rotor

In order to achieve more accurate predictions of unsteady flow in a transonic compressor rotor an existing numerical approach has been modified by incorporating a turbulence model. The computations are performed by solving the complete time-dependent compressible Navier–Stokes equations using MacCormack’s explicit finite difference algorithm. These equations are solved for the flow through two adjacent rotor blades at a streamsurface near the blade tip subjected to the wakes emitted from upstream stators. At this radial location the flow enters the blade passage at an absolute Mach number of 0.66. The high blade curvature at this radial location produces a large region of separated flow on the suction surface with laminar flow. To more accurately resolve the features of this flow separation the Baldwin–Lomax algebraic eddy-viscosity turbulence model is incorporated into the numerical procedure in regions near the blade surface. The unsteady flow features are represented at the inflow boundary through the use of characteristic variables involving the upstream and downstream running Riemann invariants and the entropy variation expressed in terms of the total pressure profile. At the outflow boundary the concept of a “second throat” or choke point is implemented in conjunction with supersonic outflow conditions. The results are compared with numerical results obtained without the use of a turbulence model (laminar) for a single blade passage. Improved agreement with limited experimental data is also noted.

scholarly journals Navier-Stokes Solutions of Unsteady Flow in a Compressor Rotor

1986 ◽  
Author(s):  
James N. Scott ◽  
Wilbur L. Hankey
Keyword(s):  
Unsteady Flow ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Numerical Procedure ◽  
Navier Stokes ◽  
Suction Surface ◽  
Blade Passage ◽  
Radial Location ◽  
Transonic Compressor ◽  
Compressor Rotor

In order to achieve more accurate predictions of unsteady flow in a transonic compressor rotor an existing numerical approach has been modified by incorporating a turbulence model. The computations are performed by solving the complete time-dependent compressible Navier-Stokes equations using MacCormack’s explicit finite difference algorithm. These equations are solved for the flow through two adjacent rotor blades at a stream surface near the blade tip subjected to the wakes emitted from upstream stators. At this radial location the flow enters the blade passage at an absolute Mach number of 0.66. The high blade curvature at this radial location produces a large region of separated flow on the suction surface with laminar flow. To more accurately resolve the features of this flow separation the Baldwin-Lomax algebraic eddy-viscosity turbulence model is incorporated into the numerical procedure in regions, near the blade surface. The unsteady flow features are represented at the inflow boundary through the use of characteristic variables involving the upstream and downstream running Riemann invariants and the entropy variation expressed in terms of the total pressure profile. At the outflow boundary the concept of a “second throat” or choke point is implemented in conjunction with supersonic outflow conditions. The results are compared with numerical results obtained without the use of a turbulence model (laminar) for a single blade passage. Improved agreement with limited experimental data is also noted.

Simulating Periodic Unsteady Flows Using Cubic-Spline Based Time Collocation Method

2013 ◽  
Author(s):  
Pengcheng Du ◽  
Fangfei Ning
Keyword(s):  
Collocation Method ◽  
Stokes Equations ◽  
Differential Quadrature Method ◽  
Unsteady Flows ◽  
Cubic Spline ◽  
Navier Stokes ◽  
Transonic Compressor ◽  
Compressor Rotor ◽  
Time Marching ◽  
Flow Variables

Time periodical unsteady flows are typical in turbomachinery. Simulating such flows using conventional time marching approach is most accurate but extremely time consuming. In order to achieve a better balance between accuracy and computational expenses, a cubic-spline based time collocation method is proposed. In this method, the time derivatives in the Navier-Stokes equations are obtained by using the differential quadrature method, in which the periodical flow variables are approximated by cubic-splines. Thus, the computation of a time-periodical flow is substituted by several coupled quasi-steady flow computations at sampled instants. The proposed method is then validated against several typical turbomachinery periodical unsteady flows, i.e., transonic compressor rotor flows under circumferential inlet distortions, single stage rotor-stator interactions and IGV-rotor interactions. The results show that the proposed cubic-spline based time collocation method with appropriate time sampling can well resolve the dominant unsteady effects, whilst the computational expenses are kept much less than the traditional time-marching simulation. More importantly, this paper provides a framework on the basis of time collocation method in which one may choose more compatible test functions for the concerned specific unsteady flows so that the better modeling of the flows can be expected.

The Effect of Reynolds Number on Transonic Compressor Blade Rotor Section

2012 ◽  
Author(s):  
A. Shahrabi Farahani ◽  
H. Beheshti Amiri ◽  
H. Khazaei ◽  
A. Madadi ◽  
A. Fathi
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Pressure Ratio ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Blade Passage ◽  
Axial Compressors ◽  
Choked Flow ◽  
Transonic Compressor ◽  
Boundary Layer Interaction

To achieve at a more precise designing procedure in axial-compressors as well as a higher pressure ratio value, a comprehensive understanding on the flow aerodynamics and the governing phenomena is required. Existence of these complicated phenomena e.g., simultaneous production of supersonic and subsonic flows, shock-boundary layer interaction, unique incidence phenomenon, etc, makes it difficult to analyze the flow in the transonic compressors. One of the methods which is useful in the modeling of the phenomena occur in the compressors is investigating the flow in the blade to blade passage. In this paper, employing the simultaneous solution of the full Navier-Stokes equations (using the Roe-FDS numerical method) and turbulence equations (using the K–w (SST) model) the flow has been simulated in the blade to blade passage of a transonic compressor. In the following, in order to comparison the predicted results with experimental data, required adjustments and conditions have been taken into account. After passing through the first transonic compressor stages, the flow becomes remarkably compressed. In such conditions, the Reynolds number considerably changes compared to the inflow Reynolds number. In the present work, it is intended to numerically investigate the effects of the inflow Reynolds number on the unique incidence, flow losses, deviation angle, and also shock position changes, in three different important states of “Minimum loss” and “Choked flow” in started conditions and “Stall operation” in unstarted conditions.

Simulating Periodic Unsteady Flows Using a Cubic-Spline-Based Time Collocation Method

2013 ◽  
Vol 136 (4) ◽  
Author(s):  
Pengcheng Du ◽  
Fangfei Ning
Keyword(s):  
Collocation Method ◽  
Stokes Equations ◽  
Differential Quadrature Method ◽  
Unsteady Flows ◽  
Cubic Spline ◽  
Navier Stokes ◽  
Transonic Compressor ◽  
Compressor Rotor ◽  
Time Marching ◽  
Flow Variables

Time-periodical unsteady flows are typical in turbomachinery. Simulating such flows using a conventional time marching approach is the most accurate but is extremely time consuming. In order to achieve a better balance between accuracy and computational expenses, a cubic-spline-based time collocation method is proposed. In this method, the time derivatives in the Navier–Stokes equations are obtained by using the differential quadrature method, in which the periodical flow variables are approximated by cubic splines. Thus, the computation of a time-periodical flow is substituted by several coupled quasi-steady flow computations at sampled instants. The proposed method is then validated against several typical turbomachinery periodical unsteady flows, i.e., transonic compressor rotor flows under circumferential inlet distortions, single stage rotor–stator interactions, and IGV–rotor interactions. The results show that the proposed cubic-spline-based time collocation method with appropriate time sampling can well resolve the dominant unsteady effects, while the computational expenses are kept much less than the traditional time-marching simulation. More importantly, this paper provides a framework on the basis of a time collocation method in which one may choose more compatible test functions for the concerned specific unsteady flows so that better modeling of the flows can be expected.

Computation of Off-Design Flows in a Transonic Compressor Rotor

1986 ◽  
Vol 108 (1) ◽  
pp. 144-150 ◽  
Author(s):  
W. N. Dawes
Keyword(s):  
Stokes Equations ◽  
Current Paper ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Navier Stokes Equations ◽  
Interactive Method ◽  
Transonic Compressor ◽  
Compressor Rotor ◽  
Supersonic Inlet ◽  
Maximum Benefit

Recent years have seen increasing efforts to develop efficient solvers for the compressible Navier–Stokes equations. For maximum benefit to be derived from this effort, these Navier–Stokes solvers must be capable of dealing with off-design flows as readily and accurately as the on-design cases. The current paper outlines an efficient implicit algorithm developed recently by the author for solving the compressible Navier–Stokes equations in turbomachinery blade-blade flows. The Navier–Stokes solver is applied to the study of a transonic compressor rotor with supersonic inlet velocities for three cases, one on-design and two off-design. The results are compared with experimental measurements and with the predictions of a viscous-inviscid interactive method.

Development of Hub Corner Stall and Its Influence on the Performance of Axial Compressor Blade Rows

1999 ◽  
Vol 121 (1) ◽  
pp. 67-77 ◽  
Author(s):  
C. Hah ◽  
J. Loellbach
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Flow Direction ◽  
Three Dimensional ◽  
Suction Side ◽  
Compressor Blade ◽  
Suction Surface ◽  
Simple Diffusion ◽  
Transonic Compressor ◽  
Compressor Rotor

A detailed investigation has been performed to study hub corner stall phenomena in compressor blade rows. Three-dimensional flows in a subsonic annular compressor stator and in a transonic compressor rotor have been analyzed numerically by solving the Reynolds-averaged Navier–Stokes equations. The numerical results and the existing experimental data are interrogated to understand the mechanism of compressor hub corner stall. Both the measurements and the numerical solutions for the stator indicate that a strong twisterlike vortex is formed near the rear part of the blade suction surface. Low-momentum fluid inside the hub boundary layer is transported toward the suction side of the blade by this vortex. On the blade suction surface near the hub, this vortex forces fluid to move against the main flow direction and a limiting stream surface is formed near the hub. The formation of this vortex is the main mechanism of hub corner stall. When the aerodynamic loading is increased, the vortex initiates further upstream, which results in a larger corner stall region. For the transonic compressor rotor studied in this paper, the numerical solution indicates that a mild hub corner stall exists at 100 percent rotor speed. The hub corner stall, however, disappears at the reduced blade loading, which occurs at 60 percent rotor design speed. The present study demonstrates that hub corner stall is caused by a three-dimensional vortex system and that it does not seem to be correlated with a simple diffusion factor for the blade row.

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.

Development of Hub Corner Stall and its Influence on the Performance of Axial Compressor Blade Rows

1997 ◽  
Author(s):  
Chunill Hah ◽  
James Loellbach
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Flow Direction ◽  
Three Dimensional ◽  
Suction Side ◽  
Compressor Blade ◽  
Suction Surface ◽  
Simple Diffusion ◽  
Transonic Compressor ◽  
Compressor Rotor

A detailed investigation has been performed to study hub corner stall phenomena in compressor blade rows. Three-dimensional flows in a subsonic annular compressor stator and in a transonic compressor rotor have been analyzed numerically by solving the Reynolds-averaged Navier-Stokes equations. The numerical results and the existing experimental data are interrogated to understand the mechanism of compressor hub corner stall. Both the measurements and the numerical solutions indicate that a strong twister-like vortex is formed near the rear part of the blade suction surface. Low momentum fluid inside the hub boundary layer is transported toward the suction side of the blade by this vortex. On the blade suction surface near the hub, this vortex forces fluid to move against the main flow direction and a limiting stream surface is formed near the hub. The formation of this vortex is the main mechanism of hub corner stall. When the aerodynamic loading is increased, the vortex initiates further upstream, which results in a larger corner stall region. For the transonic compressor rotor studied in this paper, the numerical solution and the measured data indicate that a mild hub corner stall exists at 100 percent rotor speed. The hub corner stall, however, disappears at the reduced blade loading which occurs at 60 percent rotor design speed. The present study demonstrates that hub corner stall is caused by a three-dimensional vortex system and that it does not seem to be correlated with a simple diffusion factor for the blade row.

Effects of Inlet Distortion on the Flow Field in a Transonic Compressor Rotor

1996 ◽  
Author(s):  
Chunill Hah ◽  
Douglas C. Rabe ◽  
Thomas J. Sullivan ◽  
Aspi R. Wadia
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Viscous Flow ◽  
Total Pressure ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Aerodynamic Loss ◽  
Transonic Compressor ◽  
Inlet Distortion ◽  
Compressor Rotor

The effects of circumferential distortions in inlet total pressure on the flow field in a low-aspect-ratio, high-speed, high-pressure-ratio, transonic compressor rotor are investigated in this paper. The flow field was studied experimentally and numerically with and without inlet total pressure distortion. Total pressure distortion was created by screens mounted upstream from the rotor inlet. Circumferential distortions of 8 periods per revolution were investigated at two different rotor speeds. The unsteady blade surface pressures were measured with miniature pressure transducers mounted in the blade. The flow fields with and without inlet total pressure distortion were analyzed numerically by solving steady and unsteady forms of the Reynolds-averaged Navier-Stokes equations. Steady three-dimensional viscous flow calculations were performed for the flow without inlet distortion while unsteady three-dimensional viscous flow calculations were used for the flow with inlet distortion. For the time-accurate calculation, circumferential and radial variations of the inlet total pressure were used as a time-dependent inflow boundary condition. A second-order implicit scheme was used for the time integration. The experimental measurements and the numerical analysis are highly complementary for this study because of the extreme complexity of the flow field. The current investigation shows that inlet flow distortions travel through the rotor blade passage and are convected into the following stator. At a high rotor speed where the flow is transonic, the passage shock was found to oscillate by as much as 20% of the blade chord, and very strong interactions between the unsteady passage shock and the blade boundary layer were observed. This interaction increases the effective blockage of the passage, resulting in an increased aerodynamic loss and a reduced stall margin. The strong interaction between the passage shock and the blade boundary layer increases the peak aerodynamic loss by about one percent.

Simulation of the Transitional Flow in a Low Pressure Gas Turbine Cascade With a High-Order Discontinuous Galerkin Method

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
A. Ghidoni ◽  
A. Colombo ◽  
S. Rebay ◽  
F. Bassi
Keyword(s):  
Discontinuous Galerkin ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Time Integration ◽  
High Order ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Implicit Time ◽  
Turbine Cascade ◽  
High Reynolds

In the last decade, discontinuous Galerkin (DG) methods have been the subject of extensive research efforts because of their excellent performance in the high-order accurate discretization of advection-diffusion problems on general unstructured grids, and are nowadays finding use in several different applications. In this paper, the potential offered by a high-order accurate DG space discretization method with implicit time integration for the solution of the Reynolds-averaged Navier–Stokes equations coupled with the k-ω turbulence model is investigated in the numerical simulation of the turbulent flow through the well-known T106A turbine cascade. The numerical results demonstrate that, by exploiting high order accurate DG schemes, it is possible to compute accurate simulations of this flow on very coarse grids, with both the high-Reynolds and low-Reynolds number versions of the k-ω turbulence model.

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