scholarly journals Interpretation of Adjoint Solutions for Turbomachinery Flows

2012 ◽  
Author(s):  
Sriram Shankaran ◽  
Andre Marta ◽  
Prem Venugopal ◽  
Brian Barr ◽  
Qiqi Wang
Keyword(s):  
Flow Field ◽  
Adjoint Equations ◽  
Flow Solver ◽  
Low Pressure Turbine ◽  
Compressor Rotor ◽  
Performance Metric ◽  
Physical Insight ◽  
End Wall ◽  
Adjoint Solutions ◽  
Design Guidance

While the mathematical derivation of the adjoint equations and their numerical implementation is well established, there is a scant discussion on the understanding of the adjoint solution by itself. As this is a field solution of similar resolution of the flow-field, there is a wealth of data that can be used for design guidance. This paper addressess this specific topic. In particular, we take representative cases from turbomachinery aerodynamic problems and use the adjoint solution to identify the “physical insight” it provides. We aim to tie the adjoint solution to the flow-field which has physical properties. Towards this end, we first look at three problems 1) a fan, 2) a compressor rotor and stator, 3) a low pressure turbine. In all three of them, we focus on changes related to geometry, but one can also realize the changes using other inputs to the flow solver (eg. boundary conditions). We show how the adjoint counter-part of the density, the velocity fields and the turbulence quantities can be used to provide insights into the nature of changes the designer can induce to cause improvement in the performance metric of interest. We also discuss how to use adjoint solutions for problems with constraints to further refine the changes. Finally, we use a problem where it is not immediately apparent what geometry changes need to be used for further evaluation with optimization algorithms. In this problem, we use the adjoint and flow solution on a turbine strut, to determine the kind of end-wall treatments that reduce the loss. These changes are then implemented to show that the loss is reduced by close to 8%.

End Wall Loss Reduction of High Lift Low Pressure Turbine Airfoils Using Profile Contouring—Part II: Validation

2014 ◽  
Vol 136 (8) ◽  
Author(s):  
Keith Sangston ◽  
Jesse Little ◽  
M. Eric Lyall ◽  
Rolf Sondergaard
Keyword(s):  
Flow Field ◽  
Low Pressure ◽  
Stereoscopic Particle Image Velocimetry ◽  
Loss Reduction ◽  
High Lift ◽  
Low Pressure Turbine ◽  
Wall Loss ◽  
Wall Flow ◽  
End Wall ◽  
Stagger Angle

The hypothesis, posed in Part I, that excessive end wall loss of high lift low pressure turbine (LPT) airfoils is due to the influence of high stagger angles on the end wall pressure distribution and not front loading is evaluated in a linear cascade at Re = 100,000 using both experimental and computational studies. A nominally high lift and high stagger angle front-loaded profile (L2F) with aspect ratio 3.5 is contoured at the end wall to reduce the stagger angle while maintaining the front loading. The contouring process effectively generates a fillet at the end wall, so the resulting airfoil is referred to as L2F-EF (end wall fillet). Although referred to as a fillet, this profile contouring process is novel in that it is designed to isolate the effect of stagger angle on end wall loss. Total pressure loss measurements downstream of the blade row indicate that the use of the lower stagger angle at the end wall reduces mixed out mass averaged end wall and passage losses approximately 23% and 10%, respectively. This is in good agreement with computational results used to design the contour which predict 18% and 7% loss reductions. The end wall flow field of the L2F and L2F-EF models is measured using stereoscopic particle image velocimetry (PIV) in the passage. These data are used to quantify changes in the end wall flow field due to the contouring. PIV results show that this loss reduction is characterized by reduced inlet boundary layer separation as well as a change in strength and location of the suction side horseshoe vortex (SHV) and passage vortex (PV). The end wall profile contouring also produces a reduction in all terms of the Reynolds stress tensor consistent with a decrease in deformation work and overall flow unsteadiness. These results confirm that the stagger angle has a significant effect on high-lift front-loaded LPT end wall loss. Low stagger profiling is successful in reducing end wall loss by limiting the development and migration of the low momentum fluid associated with the SHV and PV interaction.

Study of the Standard k-ε Model for Tip Leakage Flow in an Axial Compressor Rotor

2016 ◽  
Vol 33 (4) ◽  
Author(s):  
Yanfei Gao ◽  
Yangwei Liu ◽  
Luyang Zhong ◽  
Jiexuan Hou ◽  
Lipeng Lu
Keyword(s):  
Flow Field ◽  
Large Scale ◽  
Turbulent Viscosity ◽  
Axial Compressor ◽  
Leakage Flow ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Tip Leakage Flow ◽  
Tip Leakage ◽  
Compressor Rotor

AbstractThe standard k-ε model (SKE) and the Reynolds stress model (RSM) are employed to predict the tip leakage flow (TLF) in a low-speed large-scale axial compressor rotor. Then, a new research method is adopted to “freeze” the turbulent kinetic energy and dissipation rate of the flow field derived from the RSM, and obtain the turbulent viscosity using the Boussinesq hypothesis. The Reynolds stresses and mean flow field computed on the basis of the frozen viscosity are compared with the results of the SKE and the RSM. The flow field in the tip region based on the frozen viscosity is more similar to the results of the RSM than those of the SKE, although certain differences can be observed. This finding indicates that the non-equilibrium turbulence transport nature plays an important role in predicting the TLF, as well as the turbulence anisotropy.

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.

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.

Profiled End-Wall Design Using an Adjoint Navier-Stokes Solver

2006 ◽  
Author(s):  
Roque Corral ◽  
Fernando Gisbert
Keyword(s):  
Kinetic Energy ◽  
Cost Function ◽  
Unstructured Mesh ◽  
Low Pressure ◽  
Navier Stokes ◽  
Low Pressure Turbine ◽  
Gradient Based ◽  
Parallel Multigrid ◽  
End Wall ◽  
Discrete Formulation

A methodology to minimize blade secondary losses by modifying turbine end-walls is presented. The optimization is addressed using a gradient-based method, where the computation of the gradient is performed using an adjoint code and the secondary kinetic energy is used as a cost function. The adjoint code is implemented on the basis of the discrete formulation of a parallel multigrid unstructured mesh Navier-Stokes solver. The results of the optimization of two end-walls of a low pressure turbine row are shown.

Analysis of Transonic Bladerows With Non-Uniform Geometry Using Spectral Method

2020 ◽  
Author(s):  
Feng Wang ◽  
Luca di Mare
Keyword(s):  
Flow Field ◽  
Spectral Method ◽  
Computational Cost ◽  
Leading Edge ◽  
Wave Number ◽  
Efficient Tool ◽  
Flow Solver ◽  
Engine Order ◽  
Harmonic Flow ◽  
Good Agreement

Abstract Turbomachinery blade rows can have non-uniform geometries due to design intent, manufacture errors or wear. When predictions are sought for the effect of such non-uniformities, it is generally the case that whole assembly calculations are needed. A spectral method is used in this paper to approximate the flow fields of the whole assembly but with significantly less computation cost. The method projects the flow perturbations due to the geometry non-uniformity in an assembly in Fourier space, and only one passage is required to compute the flow perturbations corresponding to a certain wave-number of geometry variation. The performance of this method on transonic blade rows is demonstrated on a modern fan assembly. Low engine order and high engine order geometry non-uniformity (e.g. “saw-tooth” pattern) are examined. The non-linear coupling between the flow perturbations and the passage-averaged flow field is also demonstrated. Pressure variations on the blade surface and the potential flow field upstream of the leading edge from the proposed spectral method and the direct whole assembly solutions are compared. Good agreement is observed on both quasi-3D and full 3D cases. A lumped approach to compute deterministic fluxes is also proposed to further reduce the computational cost of the spectral method. The spectral method is formulated in such a way that it can be easily implemented into an existing harmonic flow solver by adding an extra source term, and can be potentially used as an efficient tool for aeromechanical and aeroacoustics design of turbomachinery blade rows.

The Impact of Manufacturing Variations on Performance of a Transonic Axial Compressor Rotor

2018 ◽  
Author(s):  
Marcus Lejon ◽  
Niklas Andersson ◽  
Lars Ellbrant ◽  
Hans Mårtensson
Keyword(s):  
Flow Field ◽  
Geometric Mean ◽  
Pressure Ratio ◽  
Axial Compressor ◽  
Mean Deviation ◽  
Design Intent ◽  
Compressor Rotor ◽  
Measuring Machine ◽  
The Mean ◽  
The Impact

In this paper, the impact of manufacturing variations on performance of an axial compressor rotor are evaluated at design rotational speed. The geometric variations from the design intent were obtained from an optical coordinate measuring machine and used to evaluate the impact of manufacturing variations on performance and the flow field in the rotor. The complete blisk is simulated using 3D CFD calculations, allowing for a detailed analysis of the impact of geometric variations on the flow. It is shown that the mean shift of the geometry from the design intent is responsible for the majority of the change in performance in terms of mass flow and total pressure ratio for this specific blisk. In terms of polytropic efficiency, the measured geometric scatter is shown to have a higher influence than the geometric mean deviation. The geometric scatter around the mean is shown to impact the pressure distribution along the leading edge and the shock position. Furthermore, a blisk is analyzed with one blade deviating substantially from the design intent, denoted as blade 0. It is shown that the impact of blade 0 on the flow is largely limited to the blade passages that it is directly a part of. The results presented in this paper also show that the impact of this blade on the flow field can be represented by a simulation including 3 blade passages. In terms of loss, using 5 blade passages is shown to give a close estimate for the relative change in loss for blade 0 and neighboring blades.

Effects of Cavity Purge Flow on Intermediate Turbine Duct Flowfield

2018 ◽  
Author(s):  
Jun Liu ◽  
Qiang Du ◽  
Guang Liu ◽  
Pei Wang ◽  
Hongrui Liu ◽  
...  
Keyword(s):  
Flow Field ◽  
Flow Rate ◽  
Design Criterion ◽  
Operating Conditions ◽  
Duct Flow ◽  
Intermediate Turbine Duct ◽  
Low Pressure Turbine ◽  
Cavity Structure ◽  
Flow Mechanisms ◽  
Purge Flow

To increase the power output without adding additional stages, ultra-high bypass ratio engine, which has larger diameter low pressure turbine, attracts more and more attention because of its huge advantage. This tendency will lead to aggressive (high diffusion) intermediate turbine duct design. Much work has been done to investigate flow mechanisms in this kind of duct as well as its design criterion with numerical and experimental methods. Usually intermediate turbine duct simplified from real engine structure was adopted with upstream and downstream blades. However, cavity purge mass flow exists to disturb the duct flow field in real engine to change its performance. Naturally, the wall vortex pairs would develop in different ways. In addition to that, purge flow rate changes at different engine representative operating conditions. This paper deals with the influence of turbine purge flow on the aerodynamic performance of an aggressive intermediate turbine duct. The objective is to reveal the physical mechanism of purge flow ejected from the wheel-space and its effects on the duct flow field. Ten cases with and without cavity are simulated simultaneously. On one hand, the influence of cavity structure without purge flow on the flow field inside duct could be discussed. On the other hand, the effect of purge flow rate on flow field could be analyzed to investigate the mechanisms at different engine operating conditions. According to this paper, cavity structure is beneficial for pressure loss. And the influence concentrates near hub and duct inlet.

The Unsteady Flow Field of a Purged High Pressure Turbine Based on Mode Detection

2017 ◽  
Author(s):  
S. Zerobin ◽  
S. Bauinger ◽  
A. Marn ◽  
A. Peters ◽  
F. Heitmeir ◽  
...  
Keyword(s):  
High Pressure ◽  
Flow Field ◽  
Unsteady Flow ◽  
Flow Behavior ◽  
Low Pressure ◽  
Pressure Probe ◽  
Special Focus ◽  
High Pressure Turbine ◽  
Low Pressure Turbine ◽  
Mode Detection

This paper presents an experimental study of the unsteady flow field downstream of a high pressure turbine with ejected purge flows, with a special focus on a flow field discussion using the mode detection approach according to the theory of Tyler and Sofrin. Measurements were carried out in a product-representative one and a half stage turbine test setup, which consists of a high-pressure turbine stage followed by an intermediate turbine center frame and a low-pressure turbine vane row. Four independent purge mass flows were injected through the forward and aft cavities of the unshrouded high-pressure turbine rotor. A fast-response pressure probe was used to acquire time-resolved data at the turbine center frame duct inlet and exit. The interactions between the stator, rotor, and turbine center frame duct are identified as spinning modes, propagating in azimuthal direction. Time-space diagrams illustrate the amplitude variation of the detected modes along the span. The composition of the unsteadiness and its major contributors are of interest to determine the role of unsteadiness in the turbine center frame duct loss generation mechanisms and to avoid high levels of blade vibrations in the low-pressure turbine which can in turn result in increased acoustic emissions. This work offers new insight into the unsteady flow behavior downstream of a purged high-pressure turbine and its propagation through an engine-representative turbine center frame duct configuration.

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