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The present study attempts to reduce secondary flow losses by application of streamwise endwall fence. After comprehensive analysis on selection of objective function for secondary flow loss reduction, coefficient of secondary kinetic energy (CSKE) is selected as the objective function in this study. A fence whose height varies linearly from the leading edge to the trailing edge and located in the middle of the flow passage produces least CSKE and is the optimum fence. The reduction in CSKE by the optimum fence is 27% compared to the baseline case. The geometry of the fence is new and is reported for the first time. Idea of this fence comes from the fact that the size of the passage vortex (which is the prime component of secondary flow) increases as it travels downstream, hence the height of fence should vary as the objective of fence is to block the passage vortex from crossing the passage and impinging on suction surface of the blade. Optimum fence reduced overturning and underturning of flow by more than 50% compared to the baseline case. Magnitude and spanwise penetration of the passage vortex were reduced considerably compared to the baseline case.

The term secondary flows refers to the three-dimensional vortical flow structures that develop in blade passages due to high turning of the flow and nonuniform inlet total pressure profiles. Primary flow is the flow which is responsible for the torque generation. Flow which is transverse to the primary flow direction is termed as secondary flow. The boundary layer flow along the endwall contains spanwise velocity gradients. When the boundary layer flow is turned, transverse velocity components are introduced. These secondary flows, created at the endwall and blade junction, extract energy from the fluid which would otherwise be used to rotate the blades or produce thrust. If these secondary flows can be weakened, more energy would be available for torque and thrust production.

Horseshoe vortex, corner vortex, tip vortex, endwall crossflow, and passage vortex are secondary flow components in the cascade. Among these, passage vortex is the primary source of loss. Streamwise endwall fences were employed by Kawai [

The aerodynamic and endwall heat transfer effects were presented by Camci and Rizzo [

Flow in a curved channel has no stagnation zone (except a very small zone near to fence), while flow in a turbine comprises of stagnation zone near to the leading edge of blade (also a small zone near the leading edge of fence). Computation of flow using isotropic eddy viscosity turbulence models suffers from a defect called

Present study attempts to reduce secondary flow losses by the application of streamwise endwall fences. An innovative design of fence is presented which is found to be more efficient than fence of height 1/3rd of inlet boundary layer thickness for the present turbine cascade. Selection of the objective function for computational optimization for secondary flow losses is addressed here.

Secondary flow loss reduction in a turbine can be achieved by leading edge modifications, endwall profiling,and by using streamwise endwall fences. For a given turbine cascade and for a particular secondary flow loss reduction technique, there could be many test cases to be tried to determine an optimum. Opting for experimental investigations is certainly a very accurate way of solving the problem but it is highly time-consuming and costly. CFD can predict correctly provided the objective function used in the computation is predicted correctly (at least qualitatively). Few of the quantities which were used as objective function by researchers in numerical study for secondary flow loss reduction are exit flow angle deviation, coefficient of secondary kinetic energy (CSKE), and secondary kinetic energy helicity (SKEH) or combination of these. Ideally the mass averaged total pressure loss coefficient should be taken as objective function, but its prediction by CFD is not accurate [

Ingram [

Comparison of

Experimental | ||

46.0 | 54.5 | |

21.5 | 30.2 | |

CFD | ||

48.9 | 38.6 | |

−1.0 | 6.7 |

Another quantity called Secondary Kinetic Energy Helicity (SKEH) is also used as an objective function for secondary flow loss reduction. The dot product of SKE (secondary kinetic energy) and helicity (

The secondary kinetic energy (SKE) at any measuring plane is caused by viscous effects and potential flow (inviscid flow) effect. Because of viscous effect, vortices are generated and vortices cannot be generated in an inviscid flow. In order to consider the SKE associated with vortical components of fluid only (which means excluding SKE caused by potential effects), the dot product of the SKE and helicity is used. Helicity is zero in potential flows (vorticity is zero); therefore, use of SKEH would exclude SKE associated with potential flow. However, SKEH does not exclude the SKE due to the potential field in the regions of vortical flow. This contribution will be small compared with the changes due to the vortical flow. SKEH was used as objective function by Corral and Gisbert [

Objective functions used for different secondary flow reduction techniques.

Investigator | Secondary flow loss reduction technique | Optimization parameter |
---|---|---|

Brennan et al. [ | Endwall profiling | SKEH |

Ingram [ | Endwall profiling | CSKE |

Corral and Gisbert [ | Endwall profiling | SKEH + an exponential function of inlet swirl angle |

Bagshaw et al. [ | Endwall profiling | SKEH |

Nagel and Baier [ | Endwall profiling | Weighted addition of various postprocessor results (averaged loss accounts for the major part) |

Duden et al. [ | Endwall and leading edge modification | Exit flow angle deviation and a secondary flow area with the least possible distance from the endwall |

Harvey et al. [ | Endwall profiling | Cross-passage static pressure gradient on endwall and exit flow angle deviation |

Pralsner et al. [ | Endwall profiling | Total pressure loss coefficient, SKE and TKE (turbulent kinetic energy) |

Ingram et al. [ | Endwall profiling | Exit flow angle deviation |

Germain et al. [ | Endwall profiling | Combination of total pressure loss coefficient and CSKE |

Schüpbach et al. [ | Endwall profiling | CSKE |

Moon and Koh [ | Streamwise endwall fence | Stream wise vorticity |

Details of the turbine blades employed in the present investigation are shown in Figure

Details of cascade.

Govardhan et al. [

A miniaturized five-hole probe having a head diameter of 0.0024 m was traversed at the exit of the cascade from midspan to the endwall at 26 locations covering more points in the endwall region. For each spanwise location, the probe was traversed in the pitchwise direction at more than 25 locations covering one blade spacing. The probe was used to measure the total pressure, static pressures, and the flow direction in mutually perpendicular planes (yaws and pitch planes). In all the experiments space-chord ratio was maintained constant at 0.79, and the tip clearance was varied from

For the present investigations fences are fixed normal to the endwall in streamwise direction. The curvature of the fence is the same as that of the blade camber line. The fence thickness,

Typical mesh and a view of the computational domain with blade and fence.

According to method of characteristics, flow angle, total pressure, and total temperature are used as boundary conditions at subsonic axial inlet. All solid walls are set with no slip condition and are adiabatic. At inlet experimentally measured total pressure profile for 0° incidence is specified with a turbulence intensity of 1% and integral length scale of 0.005 m. Experimentally measured inlet boundary layer thickness (

Computations are carried out for half the span height from the endwall by giving symmetry boundary condition for the midspan. Fluid interfaces are specified as periodic with nonconformal grids. ANSYS high-resolution discretization scheme was chosen for all calculations. For details regarding numerical scheme CFX manual [

Variation of

In the present investigations, SST [

As the mesh is very fine near to the solid walls, low Reynolds number formulation of the turbulence model is employed instead of wall function approach. The solver runs and calculates the

The exit measurements in computations as well as in experiments are taken at

Spanwise variation of pitchwise mass averaged exit flow angle (baseline case) at

Spanwise variation of pitchwise mass averaged nondimensional velocity ratios (baseline case) at

Spanwise variation of pitchwise mass averaged coefficient of secondary kinetic energy (baseline case) at

Spanwise variation of pitchwise mass averaged exit flow angle (fence of

Despite using SST [

In Figure

Comparison between computational and experimental results is also obtained for profile loss coefficient and is shown in Table

Profile loss coefficient.

Comparison of profile loss coefficients ( | |||
---|---|---|---|

CFD | Experimental | % Difference | |

Baseline case | 0.0334 | 0.0340 | 1.72 |

Fence of | 0.0337 | 0.0340 | 0.66 |

The difference between computed and experimental profile loss coefficient is 1.7% for the baseline case and 1% for fence of

Comparison of

Baseline case | Fence of | % change w.r.t the baseline case | |
---|---|---|---|

0.0023 | 0.0019 | −17% | |

0.0016 | 0.0011 | −28% | |

0.0492 | 0.0519 | 5.5% | |

0.0751 | 0.0648 | −14% |

The fences were attached normal to the endwalls and were of the same camber line and the same stagger angle as the blades. The distance and the height of the fences were independently varied. Measurements of CSKE were done at

Mass averaged CSKE for fences of different height placed at different locations.

S. no. | Fence location and fence height ( | % reduction in | |
---|---|---|---|

1 | 1/3, 1/6 | 0.002103 | −9.3 |

2 | |||

3 | 2/3, 1/6 | 0.002004 | −13.5 |

4 | 1/3, 1/3 | 0.002035 | −12.3 |

5 | |||

6 | 2/3, 1/3 | 0.001979 | −14.7 |

7 | 1/2, 2/5 | 0.001955 | −15.7 |

8 | 1/3, 2/3 | 0.00342 | 47.5 |

9 | 1/2, 2/3 | 0.002031 | −12.4 |

10 | 2/3, 2/3 | 0.001947 | −16.1 |

11 | 1/3, 1 | 0.00513 | 121.2 |

12 | 1/2, 1 | 0.002334 | 0.6 |

13 | 2/3, 1 | 0.00254 | 9.5 |

14 | 1/2, 4/3 | 0.002803 | 20.9 |

15 | |||

16 | — |

Contours of nondimensional streamwise vorticity

Baseline at

Baseline at

With optimum fence at

With optimum fence at

With fence of

With fence of

Since CSKE is indicative of secondary flow losses, let us examine the role of CSKE in reducing the total pressure loss coefficient. The total pressure loss coefficient is given by

In cases with streamwise endwall fences, it is observed that profile loss coefficient does not change much. Both experimental and numerical investigations indicate that there is negligible change in

Comparison of

Baseline case | Optimum fence | % change w.r.t the baseline case | |
---|---|---|---|

0.00231915 | 0.001674 | −27.8% | |

0.033424 | 0.0334549 | 0.09% | |

0.04921 | 0.0507523 | 3.1% |

The table also shows reduced

If the flow deflection is more than the geometrical deflection then flow overturning occurs, and if flow deflection is less compared to geometrical deflection then underturning occurs. The direction of rotation of passage vortex is such that, below its center (near to endwall), it increases the tangential velocity (

Pitchwise mass averaged exit flow angle for baseline and optimum fence cases at

Contours of exit flow angle at

Baseline

Optimum fence

The inception and transport of the passage vortex and its impact on the surface boundary layers can be interpreted from the distribution of wall shear stress and skin friction lines. Skin friction lines describe the flow immediately on the surface of a body. In a two-dimensional flow, boundary layer separation is characterized by a reverse flow or vanishing wall shear stress, but in case of a three-dimensional flow vanishing shear is not the binding criterion. In three dimensional flow separations wall shear can have value other than zero. A necessary condition for the occurrence of three dimensional flow separation is the convergence of skin friction lines onto a separation line. The flow gets lifted along that separation line. Figure

Contours of wall shear stress on the suction surface (with skin friction lines).

Baseline case

Optimum fence

Figure

Contours of wall shear stress on the endwall (with skin friction lines).

Baseline case

Optimum fence

Hunt [

Figure

Vortex isosurface using

Baseline case

Optimum fence

Variation of CSKE (at

Variation of Profile loss coefficient (at

Different turbulence models were used in the present investigations, and the quantitative difference in

The difference between CFD (SST transition) and experimental results is more in case of

In the present study, a range of engine relevant turbulence intensity levels is generated, and the resulting flow field is reported. This section assesses the effectiveness of fence at higher turbulence intensity levels. Higher turbulence intensity levels in gas turbines would typically increase the heat transfer rates on turbine blades and influence the boundary layer transition to a greater extent. On the suction surface of the airfoil the main effect of turbulence is to cause an earlier onset of transition to turbulent flow. From Figure

Variation of mass averaged CSKE at different turbulence intensity for optimum fence and unfenced case.

Variation of profile loss coefficient at different turbulence intensities for optimum and baseline cases.

If flow incidence is positive there will be increase in net flow deflection resulting in higher change in momentum, leading to increase in lift or blade loading. Similarly if flow incidence is negative, net flow deflection will be less leading to reduction in blade loading. Secondary flow in a turbine is dependent on net flow deflection of flow. This can be concluded from the transport vorticity equation which is obtained by forming the curl of the Navier-Stokes equation. In an intrinsic coordinate system the streamwise component can be written as follows:

If the viscous term is neglected, it follows that in the entrance region of a linear turbine cascade the rate of change of streamwise vorticity (

Variation of

From Figure

Variation of profile loss coefficient with incidence angle for the optimum and baseline cases.

A fence whose height varies linearly from

Axial chord (m)

Velocity (m/s)

Blade chord (m)

Axial velocity (m/s)

Radial velocity (m/s)

Tangential velocity (m/s)

Coefficient of secondary kinetic energy

Fence height (m)

Leading edge

Passage vortex

Pressure (N/m^{2})

Strain tensor (

Fence thickness (m)

Trailing vortex

Trailing edge

Turbulence intensity

Inlet loss coefficient

Distance from the pressure surface (m)

Profile loss coefficient

Total pressure loss coefficient.

Cascade inlet and outlet

Components in axial, pitchwise, spanwise, and streamwise directions

Index notations (1,2,3).

Pitchwise mass averaged quantity

Pitchwise and spanwise mass averaged quantity.

Flow angle measured from the axial direction (deg)

Inlet boundary layer thickness (m)

Tip gap height (m)

Vorticity (

Rotation tensor (