Journal of Thermal Science Vol.21, No.5 (2012) 474−482
DOI: 10.1007/s11630-012-0571-0
Article ID: 1003-2169(2012)05-0474-09
Numerical Simulation of Clocking Effect on Blade Unsteady Aerodynamic Force in Axial Turbine LI Wei, ZHU Xiao-cheng, OUYANG Hua, DU Zhao-hui Shanghai JiaoTong University, Shanghai, 200240, China © Science Press and Institute of Engineering Thermophysics, CAS and Springer-Verlag Berlin Heidelberg 2012
To give an insight into the clocking effect and its influence on the wake transportation and its interaction, the unsteady three-dimensional flow through a 1.5-stage axial low pressure turbine is simulated numerically by using a density-correction based, Reynolds-Averaged Navier-Stokes equations commercial CFD code. The 2nd stator clocking is applied over ten equal tangential positions. The results show that the harmonic blade number ratio is an important factor affecting the clocking effect. The clocking effect has very small influence on the turbine efficiency in this investigation. The difference between the maximum and minimum efficiency is about 0.1%. The maximum efficiency can be achieved when the 1st stator wake enters the 2nd stator passage near blade suction surface and its adjacent wake passes through the 2nd stator passage close to blade pressure surface. The minimum efficiency appears if the 1st stator wake impinges upon the leading edge of the 2nd stator and its adjacent wake of the 1st stator passes through the mid-channel in the 2nd stator. The wake convective transportation and the blade circulation variation due to its impingement on the subsequent blade are the main mechanism affecting the pressure variation in blade surface.
Keywords: Axial Turbine; Clocking Effect; Numerical Simulation
Introduction The flow in axial turbine is highly unsteady essentially. Rotor-stator interactions in multistage axial turbine cause inherently unsteady flow fields because of the viscous wakes and the potential effects of the blades. The pressure distribution on the blades changes considerably with time because of these aerodynamic interactions, so unsteady aerodynamic blade forces and moments are generated. If the frequency of the aerodynamic interaction matches with the natural frequency of blade, the critical blade vibration is excited. This will reduce the fatigue life and destroy the blade. So during the design process the unsteady effects due to the periodic wake should be considered. It is necessary for gas turbine designers to get
a better understanding of the unsteady wake through an axial turbine so as to bring the unsteady flow mechanisms into the design system. Recently numerous experimental and numerical studies have shown that clocking effect is another tool to increase the turbine aerodynamic performance in a moderate way. So the aim of this paper is to deliver a detailed insight into the knowledge of clocking effect on the blade aerodynamic response. Clocking is one way of influencing the flow field in multistage turbomachine by changing the relative circumferential position of stators or rotors with the same blade count of adjacent rows. An experimental/numerical investigation has been completed that indicated ±0.5% turbine stage efficiency increases can be attained through the second stator clocking effect in a two-stage low-
Received: May 2011 LI Wei: Post Doctoral Researcher www.springerlink.com
Li Wei et al.
Numerical Simulation of Clocking Effect on Blade Unsteady Aerodynamic Force in Axial Turbine
Nomenclature Ca axial chord (mm) CP static pressure coefficient D mean diameter (mm) H blade height (mm) Pt total pressure (Pa) p static pressure (Pa) number of blades/rotational N (r/min) NJ negative jet T rotor-passing period TKE turbulent kinetic energy t Time η efficiency
speed
pressure turbine [1-2]. Many studies show that the maximum turbine efficiencies can be achieved at the clocking position in which the wake generated by a stator/rotor blade impinges on the leading edge of the next stator/rotor blade [1-5]. Recently Sevn Konig [6] experimentally studied the clocking effect in a 1.5-stage axial low-pressure turbine. The results indicated that three main factors affecting the total pressure loss could be separated: the size of the separation bubble, the production of turbulent kinetic energy, and the strength of the periodic fluctuations downstream of Stator 2. The effect of clocking on the boundary layer behavior is studied [7]. In these above investigations much work is focused on the wake transportation, the effect of clocking on the unsteady aerodynamic blade force is less studied. Furthermore, the harmonic blade number ratio in these studies is an integer, such as 1 or 2, which is uncommon in real turbine of the aero-engine. So it is necessary to study the clocking effect on the blade aerodynamic force in the turbine with the harmonic blade number ratio of noninteger. The paper presents unsteady three-dimensional numerical simulation of the blade aerodynamic force in a realistic 1.5-stage LP axial turbine where the stator blade number ratio isn’t an integer.
SW TL V SS PS Subscript
stator wake tip leakage flow vortex suction side pressure side
max
maximum
min o l un 1
minimum outlet local unsteady inlet
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mass-weighted average exit Mach number of the 2nd stator is nearly 0.63 and the Reynolds number based on the axial chord and exit velocity of the 2nd stator is 268355. The rotor tip is unshrouded and the tip clearance height is 1.0% of the rotor blade height. The time-averaged static pressure coefficient distribution in the 50% span of three blades is shown in Fig. 1. The time-averaged static pressure coefficient in two of the 1st stator blades and four rotor blades changes little and the curves are nearly in superposition, while that in three of the 2nd stator blades changes strongly, which indicates that the 1st stator wake, the rotor wake, and the secondary vortex in the 1st stage transfer downstream differently in three of the 2nd stator passages. Each of the 2nd stator blades should be studied individually.
Turbine stage and CFD Numerical Method Turbine Stage The turbine in this paper is a 1.5 stage axial low pressure blades of a large bypass ratio turbofan engine. The cylindrical profile of the blades is taken from the rootsection of an aeronautic gas turbine blade. It can be seen in Tab. 1, where the geometrical parameters are given. The rotor under consideration has a small geometry while the stators have a relatively large geometry, which are the characteristics of large bypass ratio turbofan engine. The
Fig.1 The static pressure coefficient distribution in the 50% span of three sort of blades
CFD Numerical Method The presented simulations of the unsteady wake transport process were performed with the commercial CFD
476 Tab. 1
J. Therm. Sci., Vol.21, No.5, 2012 Test turbine geometry 1st Stator
Rotor
2nd Stator
Number of blades (N)
84
172
126
Axial chord (Ca/mm)
40
18
30
Blade height (H/mm)
63
76
90
Stagger angle (vs. axial)
27.5°
13.5°
26.5°
Mean diameter (D/mm)
707
730
750
Rotational speed (N/r/min) Inlet relative flow angle Solidity
0
5000
0
52°
−33°
55°
1.866
1.718
1.812
software CFX. The software solves the three-dimensional, unsteady, turbulent form of the Reynolds-Averaged Navier-Stokes equations. The CFX flow solver is an unstructured multiple element (hexa-, tetra-, wedge, pyramid) finite volume method. The fluid is assumed to behave as a perfect gas. Finite volume method is adopted todiscretize the equations. Conservation equations are obtained by integration over the element mesh. The spa-
tial discretization uses a second-order central differencing scheme. A fully implicit solution strategy is employed. Multi-grid acceleration is applied to the coupled solution of the governing equations. A domain decomposition method is employed that permits parallel processing. In a low pressure turbine the boundary layer transition often appears in the blade suction side, so the Shear Stress Transport turbulence model with Gamma transition model is employed. In addition, experimental data on the real turbine flow field in detail is very difficult to obtain in the aero-engine realistic operating conditions. We select the total performance of a certain single turbine stage and the outlet flow field in an axial linear turbine cascade is used to validate the software. The simulation results are compared with the total performance of a certain single turbine stage shown in Figs. 2(a)-(b) [8]. Figs. 2(c)-(d) respectively show the experimental data and the simulation result denoted by the total pressure loss coefficient in a linear turbine cascade. The profile data is taken from the Ref. [9]. The simulation results agree well with the ex-
Fig. 2 Comparison between the experimental data and the simulation results
Li Wei et al.
Numerical Simulation of Clocking Effect on Blade Unsteady Aerodynamic Force in Axial Turbine
perimental data both in total performance and in flow field details. The intensity and the orientation of tip leakage vortex, passage vortex, and blade wake are in good consistent, which shows the code can be used to simulate the turbine flow details. Grids and Boundary Conditions A scaling method [10] is adopted to reduce the numerical effort. The rotor blades are enlarged by a factor of (86/84) keeping the pitch-to-chord ratio the same. It is then assumed that there are only 84 rotor blades in the rotor row. This assumption makes it possible to perform a calculation with only two inlet stator blades, four rotor blades and three outlet stator blades. The mesh is generated using all hexa elements, employing an H-J mixed mesh topology, O-grid around the blade surface, one-toone node matching periodicity, hexa elements in the tip region, and mesh smoothing. The y+ value near wall is about 2 by splitting or merging the near wall grid to satisfy the requirement of the turbulence and transition model. The total mesh number of nearly 1500k, 1950k, and 2203k is calculated respectively. From the computational results we found that when the node number is larger than or equal to 1950k, the mesh number had little influence on the turbine efficiency. So the mesh number of 1950k is adopted in this paper. The time step used for this simulation was corresponding to 1/omega (rad/s). Eighty time steps are set in the rotor region. Ten minutes is needed in each time step in four-cell CPU with processor 3.0GHz. At least one thousand steps are computed to obtain a good simulation result where the periodic fluctuation is very obvious and the accuracy of turbine efficiency is within 0.01%. Nearly it costs a week to obtain a result. The inlet boundary is placed at one axial chord length in the blade root upstream of the leading edge of the 1st stator blade. The total temperature (1100K) and the total pressure (240 kPa) are specified along with the inlet flow angle and turbulence intensity level (5.0%). The exit boundary is located at two axial chord lengths in the blade root downstream of the trailing edge of the 2nd stator blade. The radial equilibrium outlet boundary condition with the specified gauge pressure of 200 kPa is given at the exit.
Results and Discussion Efficiency Variations The clocking effect is taken into account by changing the position of the 2nd stator to affect the relative position between the 1st and 2nd stator. The position of the 2nd stator is computed over one circumferential pitch in ten equal distances. The circumferential position of the 2nd stator is varied while keeping the 1st stator in their
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reference positions. The turbine efficiency η is calculated using the massaverage of the time-averaged total pressure and total temperature [5]. Efficiency variation Δη shows the clocking effects, which is computed by the efficiency subtracting a constant. Fig. 3 displays the variation in the overall efficiency as the 2nd stator is clocked over a ten equal circumferential distance equal to one pitch. The result clearly indicates the best and the worst configurations. The clocking effect has a small influence on the turbine efficiency as a whole. The efficiency variation is nearly 0.1%. The clocking position of minimum efficiency is in 2 Clp and that of maximum efficiency is in 5 Clp. In 2 Clp, the tangential position of the trailing edge point in the 1st stator is similar to that in the leading edge point in the 2nd stator. The efficiency curve from -5 Clp to 0 Clp shows a similar variation trend with that from 0 Clp to 5 Clp. This is due to the blade number ratio 2:3 between the 1st and the 2nd stator. Next we will compare and analyse the 1st stator wake transportation and its interaction with the downstream blade row in these two different clocking positions which are known as the minimum and the maximum configuration.
Fig. 3
Efficiency variation versus the 2nd stator clocking position (Clp)
Static Pressure Coefficient Distribution at 50% Span of the 2nd Stator The static pressure coefficient is defined as: Cp =
p1 − pl P1 − po
where p1, po, and pl are refer to the mass-averaged static pressure at the inlet, outlet, local location. P1 is the mass-averaged total pressure at the inlet. Generally, there are two main flow mechanisms affecting the periodic unsteady pressure distribution: the wake segments propagating along the blade surface, the potential effect of upstream and downstream passing
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blade. The circulation variation during the wake impingement is caused by the combined effect of these two mechanisms. In a particular turbine there is no general rule regarding which mechanism is the dominant one. The potential effect propagates upstream and downstream with the sonic speed and makes the blade surface pressure change nearly simultaneously. It decays quickly and its influence region is mainly near the blade leading edge and the trailing edge. The convective propagation of wake segments is embodied by the negative jet, so there is a deferred procedure from the leading edge to the trailing edge which is expressed by an oblique line in space-time diagram. The wake impinges on the subsequent blade leading edge, and changes the blade circulation. The upstream wake running into the leading edge in the downstream blade makes the flow angle and the approaching velocity change, so the blade circulation changes correspondingly. The impinging effect of the wake serves as a pressure wave travelling downstream along the blade surface. The sonic speed is higher than the flow velocity in this study, so the blade surface pressure changes nearly simultaneously by the wake impingement, which is shown by a horizontal line. From the pressure contour we can see which mechanism is dominant. Fig. 4 displays the Cp distribution at 50% span of the 2nd stator in the minimum configuration. The first and
the second row refer to pressure side and suction side. The left, the middle and the right column correspond to three different blades respectively. The central part shows the structure scheme. Each stator interacts with four rotor wakes in a time period, so four periodic fluctuations appear. In pressure side, the Cp distribution in the 1st and the 3rd blade pressure side take a characteristic of the wake convective transportation, while that in the 2nd blade exhibits the potential effect. In suction side, the characteristic of convective transportation is obvious on the 2nd blade surface. On the 1st and 3rd blade surface Cp variation is mainly due to the potential effect. Fig. 5 displays the Cp distribution at 50% span of the 2nd stator for the maximum configuration where we can see the wake convective transportation process. The potential effect is dominant in the 2nd blade suction side, while the Cp characteristics in the other blade surface are the obvious convective transportation. Although the Cp distribution in suction side indicates that the wake impingement on the blade leading edge changes the blade circulation and the pressure, the convex profile in the first half of blade suction side makes the wake contact with suction side at nearly 15% Ca firstly and then impinges on the leading edge. The negative jet causes the wake to flow from pressure side to suction side and the 1st stator wake segments accumulate on the blade suction side and move downstream, so the
Fig. 4 Unsteady static pressure coefficient distribution at 50% span of the 2nd stator, Minimum
Li Wei et al.
Numerical Simulation of Clocking Effect on Blade Unsteady Aerodynamic Force in Axial Turbine
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Fig. 5 Unsteady static pressure coefficient distribution at 50% span of the 2nd stator, Maximum
sudden change in the Cp distribution in suction side is not caused by the change of blade circulation, while the sudden change on the pressure side is brought about by the variation of blade circulation. Compared with Fig. 4, Fig. 5 does not show the features of wake impingement. The influence of the rotor wake in Fig. 4 is nearly the same as that in Fig. 5, so the difference is produced by the 1st stator wake. It is concluded: if the 1st stator wake impinges on the 2nd stator leading edge, the turbine efficiency decreases. Unsteady Static Pressure Coefficient Distribution at 50% Span of the 2nd Stator The static pressure is not a constant at a fixed location of the 2nd stator blade surface. The unsteady static pressure amplitude is used to compare the unsteadiness levels in minimum and maximum configuration. The unsteady static coefficient Cp,un is defined by C p ,un =
pmax − pmin pref
where pmax and pmin are the maximum and the minimum values in the instantaneous static pressure over one rotor-passing period. In this study, three of the 2nd stator blades are computed and each changes strongly, so the maximum and the minimum value in the static pressure are the averaged value of three blades surface in the same axial position. Fig. 6 displays the Cp,un distributions in the 2nd stator
blade for both the minimum and the maximum configurations. Each configuration corresponds to three different blade heights at 10%, 50%, and 90% span respectively. The results indicate that when the 2nd stator is optimally clocked the unsteadiness in the blade surface is lower than that in the minimum configuration position on the whole. The amplitude of the static pressure disturbances is the greatest when the 1st stator wake impinges on the 2nd stator leading edge, while a decrease occurs if the 1st stator wake enters the 2nd stator mid-channel. Although there is half of the 1st stator wake entering the 2nd stator mid-channel in the minimum configuration, the sum of the pressure fluctuation is larger than that in the maximum configuration. The pressure fluctuations are related to the wake tangential position. A relationship between the efficiency variation and the blade pressure unsteadiness can be established. In this investigation, analyzing unsteadiness levels near the 2nd stator blade surface may be an alternative method to detect the best and the worst clocking position. Wall Shear Stress Distribution at 50% Span of the 2nd Stator The Reynolds number is relative high and the levels of the 2nd stator suction side deceleration are slight, then the attached flow transition is induced by the wake. The freestream turbulence intensity is higher in LP turbines, which causes bypass transition. The 2nd stator blade is
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Fig. 6
Unsteady static pressure coefficient distribution for the 2nd stator at 10%, 50%, and 90% of the span
conventional and has medium load which can be seen from Fig. 1, so the laminar separation bubble in the 2nd stator suction side boundary layer doesn’t appear in this paper. The blade profile loss can be estimated from the surface wall stress distribution. Fig. 7 displays the wall stress space-time distribution at 50% span of the 2nd stator suction side, where the 1st and the 2nd row correspond to the minimum and the maximum configuration, respectively. The wall shear stresses for the maximum configuration are lower than that in the minimum configuration. The area-averaged wall shear stresses value in the maximum configuration is 183.49 Pa and that in the minimum configuration is 186.73 Pa. The wall stress in
Fig.7
the maximum configuration is smaller than that in the minimum configuration. Higher shear stress means higher frictional loss, so the frictional loss is higher in the minimum configuration. The transition point for the minimum configuration is closer to the leading edge compared with that for the maximum configuration, and the area covered by turbulent boundary layer in blade surface in the minimum configuration is larger. The dissipation factor in turbulent boundary layer is larger than that in laminar boundary layer, so the dissipation loss in the minimum configuration is large. It can be concluded that the influence of the 2nd stator clocking on the boundary layer development and the transition point is an
Unsteady wall strain stress distribution for the 2nd stator at 50% span
Li Wei et al.
Numerical Simulation of Clocking Effect on Blade Unsteady Aerodynamic Force in Axial Turbine
important factor which affects the aerodynamic loss. Aerodynamic Force Distribution at 50% Span of the 2nd Stator Taking the turbine rotation axis and the rotor rotation tangential direction as the reference frame to analyse the blade force, the blade force F can be resolved to axial force Fx and peripheral force Fy. The direction angle of blade aerodynamic forceγis defined as the included angle between the directions of the resultant force and the axis. Δh is the selected tiny blade height. The effect of boundary layer viscosity is neglected. The aerodynamic force is obtained by integrating the static pressure along the blade surface. The F, the γ, and the aerodynamic force coefficient CF can be calculated in the form. F (t ) = ( Fx (t ), Fy (t ))
Fy (t ) = −Δh ∫ p (t )dx
Fx (t ) = − Δh ∫ p (t ) dy
γ = arctan(Fx / Fy )
CF (t ) = F (t ) /( ρ × Vm2 × Δh × B / 2) where ρ , Vm , and B represent the averaged density, the averaged velocity and the chord length at the 50% span of the studied blade.
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Fig. 8 displays the CF and the γ distribution at 50% span of the 2nd stator where they represent characteristics of periodic fluctuation. The left and the right columns refer to the minimum and the maximum configurations respectively. The aerodynamic load in each blade is different. In each curve a trough and a peak exist. When the rotor trailing edge passes across the 2nd stator leading edge a peak appears. When the rotor trailing edge passing across the mainstream in the 2nd stator a trough appears. There are several extremes in a period due to the combined effect of the 1st stator wake and the rotor wake. On the whole the oscillation amplitude in the minimum configuration is larger than that in the maximum configuration. The larger of the change of the aerodynamic force and the direction angle γ in the minimum configuration, the less the blade fatigue life. It is because that the clocking effect changes the 1st stator wake transportation and the blade aerodynamic force distribution in the 2nd stator.
Conclusions (1) The clocking effect had a very small influence on the turbine efficiency in this investigation. The efficiency
Fig. 8 Unsteady aerodynamic load distribution at 50% span of the 2nd stator
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difference between the maximum and minimum configuration was nearly 0.1%. The pressure fluctuations in the blade surface of the 2nd stator had a connection with the turbine performance. The phase difference between the maximum and minimum configuration in the transportation of the 1st stator wake through the 2nd stator passage made the pressure change differently. The static pressure fluctuated strongly in minimum configuration compared with that in the maximum configuration. (2) The reason that the pressure distribution varies in the 2nd stator is embodied in the wake convective transportation and the blade circulation variation due to its impingement on the subsequent blade. In the minimum configuration, the pressure variation in the pressure side of two blades is brought about by the wake convective transportation and the pressure variation in the third blade is caused by the wake impingement. In the maximum configuration, the pressure variation in pressure side is mainly caused by the wake convective transportation. The pressure variation in suction side is complicated and mainly caused by the wake convective transportation. (3) The 2nd stator blade aerodynamic load coefficient and phase angle for the minimum configuration is larger than that for the maximum configuration. The blade aerodynamic load can be efficiently reduced and the blade life can be improved with properly chosen clocking position of the 2nd stator.
J. Therm. Sci., Vol.21, No.5, 2012
[2]
[3]
[4]
[5]
[6]
[7]
Acknowledgement
[8]
This investigation was supported by China Postdoctoral Science Foundation (Grant No. 20100470694) and Shanghai Postdoctoral Sustentation Fund, China (Grant No. 11R21413800).
[9]
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