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Interaction of wake disturbance with compressible transitional boundary layers in a low-pressure turbine cascade under rotor-stator interaction
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Energy Procedia Procedia 00 160(2017) (2019)000–000 68–75 Energy www.elsevier.com/locate/procedia
2nd International Conference on Energy and Power, ICEP2018, 13–15 December 2018, 2nd International Conference on Energy and Power, ICEP2018, 13–15 December 2018, Sydney, Australia Sydney, Australia
Interaction of wake disturbance with compressible transitional Interaction disturbance compressible transitional The of 15thwake International Symposiumwith on District Heating and Cooling boundary layers in a low-pressure turbine cascade under rotor-stator boundary layers in a low-pressure turbine cascade under rotor-stator Assessing the feasibilityinteraction of using the heat demand-outdoor interaction temperature a long-term district demand Kazuofunction Matsuuraa,*for , Kotaro Matsuib, Naoki Tanibheat ,Takashi Gotob forecast b Kazuo Matsuuraaa,*, Kotaro Matsui , Naoki Tanib,Takashic Gotob a,b,c a b Ehime University, 3 Bunkyo-cho, Matsuyama, Ehime, 790-8577, Japan I. Andrić *, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière , O. Le Correc a
a IHI Corporation, 229, Tonogaya, Mizuho-machi, Nishitama-gun, Tokyo, 190-1297, Ehime University, 3 Bunkyo-cho, Matsuyama, Ehime, 790-8577, Japan Japan b a IHI Corporation, 229,Policy Tonogaya, Mizuho-machi, Nishitama-gun, Tokyo, 190-1297, IN+ Center for Innovation, Technology and Research - Instituto Superior Técnico, Av. Rovisco PaisJapan 1, 1049-001 Lisbon, Portugal b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France b
Abstract Abstract Transition-process-resolving numerical simulations of compressible transitional flows subjected to rotor-stator interaction in a Abstract turbine cascade numerical low-pressure were performed. Casesofofcompressible small and large Strouhalflows numbers (St) oftoblade passage, and with in anda Transition-process-resolving simulations transitional subjected rotor-stator interaction without isotropic free-stream (IFST) Cases are compared. geometry T106, and theofcomputations areand conducted at low-pressure turbine cascade turbulence were performed. of small Cascade and large Strouhalisnumbers (St) blade passage, with and District heating networks are commonly addressed in the literature as oneonofsixth-order theT106, mostand effective solutions decreasing the its design point condition. Aturbulence higher-order finite method compact differencefor and tenth-order without isotropic free-stream (IFST) aredifference compared. Cascadebased geometry is the computations are conducted at greenhouse gas emissions from theStbuilding sector. These systems require investments which are returned through the and heat filtering employed. Variation in and thefinite intensity of IFST changes thehigh frequency of turbulence inflow, the and convection its designis point condition. A higher-order difference method based on sixth-order compact difference tenth-order sales. Due to turbulence, the changed climate conditions building renovation heat demand in inflow, the future could result decrease, propagation of and the interaction of and disturbance boundary layers in the blade passage. Thethechanges in filtering is employed. Variation in St and the intensity of IFSTwith changes thepolicies, frequency of turbulence convection and prolonging the investment return period. different pressure fluctuation in the the passage. Because pressurewith fluctuation canlayers convey information away from the passage, is propagation of turbulence, and interaction of disturbance boundary in the blade passage. The changes resultit in The mainpressure offluctuation thisdiagnosing paper in is the to boundary assess thelayer feasibility of usingfluctuation theblade heat demand – outdoor temperature forpassage, heat demand expected toscope be used for states around the indirectly away from the passage. different passage. Because pressure can convey information awayfunction from the it is forecast.toThe district Alvalade,boundary located layer in Lisbon was used as a away case study. The district is consisted of 665 expected be used for of diagnosing states (Portugal), around the blade indirectly from the passage. buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district © 2018 The Authors. Published by Elsevier Ltd. © 2019 The Authors. by Ltd. renovation scenarios were developed (shallow, deep). To estimate the error, obtained heat demand values were This is an open accessPublished article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) © 2018 The Authors. Published by Elsevier Elsevier Ltd. intermediate, This is an open access the CC license (https://creativecommons.org/licenses/by-nc-nd/4.0/) compared with resultsarticle fromunder aunder dynamic heatBY-NC-ND demand previously developed by theConference authors. on Energy and Selection peer-review responsibility of themodel, scientific committee of theand 2ndvalidated International This is an and open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Energy and The results showed that when only weather change is scientific considered, the margin of error could be acceptable for some applications Power, ICEP2018. Selection and peer-review under responsibility of the committee of the 2nd International Conference on Energy and Power, ICEP2018. (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation Power, ICEP2018. scenarios,Compressible the error value to 59.5% (depending the weather andflows; renovation scenarios combination considered). Keywords: flow;increased Large-eddyup simulation/direct numericalon simulation; Cascade Laminar-turbulent transition; Turbine The valueCompressible of slope coefficient increased on averagenumerical within the range of 3.8%flows; up toLaminar-turbulent 8% per decade,transition; that corresponds Keywords: flow; Large-eddy simulation/direct simulation; Cascade Turbine to the decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the 1.renovation Introduction scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and 1.coupled Introduction improve the accuracy of heat demandofestimations. The aerodynamic performance a cascade has a great influence on energy conversion efficiency in aeronautical
The aerodynamic performance of a cascade has a great influence on energy conversion efficiency in aeronautical
© 2017 The Authors. by Elsevier fax:+81-89-927-9720. Ltd. * Corresponding author.Published Tel.:+81-89-927-9720; Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and * E-mail Corresponding Tel.:+81-89-927-9720; fax:+81-89-927-9720. address:author. [email protected] Cooling. E-mail address: [email protected]
Keywords:©Heat Forecast; Climatebychange 1876-6102 2018demand; The Authors. Published Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) 1876-6102 © 2018 The Authors. Published by Elsevier Ltd. Selection under responsibility of the scientific of the 2nd International Conference on Energy and Power, ICEP2018. This is an and openpeer-review access article under the CC BY-NC-ND licensecommittee (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Energy and Power, ICEP2018. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Energy and Power, ICEP2018. 10.1016/j.egypro.2019.02.120
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as well as industrial gas turbines, which has prompted extensive research on cascade flows. In particular, accurate prediction of and detailed investigation into compressible low-Reynolds number cascade flows are crucial to improve the efficiency of aeronautical low-pressure turbines that operate at 2-5% below the designed efficiency at altitude [1], and therefore, further research on low-Reynolds number cascade flows seems necessary. In lowpressure turbines, the Reynolds number based on the chord length and the throat exit velocity becomes as small as on the order of 104-105 due to a decrease in density, resulting in an increase in kinematic viscosity. The boundary layer on the blade in such a turbine thus becomes transitional and unsteadiness of the cascade flows becomes evident. At the same time, the boundary layers are affected by the strong freestream turbulence (FST) with about 520% intensity that originates in the combustion chamber or wakes of the upstream blade rows. Recently, numerical methods that solve the Navier-Stokes equation as directly as possible have been developed and applied to the prediction of transitional flows. These methods are capable of directly treating the temporal evolution of flow disturbances and the frequency contents of freestream disturbances that are vital in the transitional processes. Direct numerical simulation (DNS) and Large-Eddy Simulation (LES) of transitional flows in a low-pressure turbine were performed by several researchers [2-9], and physical aspects of the flows have been revealed gradually. Progresses are summarized in some review papers [10, 11]. Concerning the computations without FST, Raverdy et al. [5] calculated transitional separated flows in a cascade with Reynolds number of 1.6×105 by a compressible numerical method where LES is coupled with a two dimensional computation. They analyzed the transition process focusing on the unsteady characteristics of the laminar separation bubble and reported the existence of coupling between the separation bubble and the vortex shedding from the trailing edge (TE). Concerning the computations with FST, Wu and Durbin [2] conducted an incompressible DNS on bypass transition caused by the influences of periodic upstream wakes. They investigated the process of turbulent spot production due to the interaction of the wakes with the blade boundary layer and the vortical structures that are created by the passage of wakes in a cascade. Kalitzin et al. [3] investigated the effects of different types of inlet disturbances on the boundary layer transition near a blade surface. For a turbulence-free inlet condition, natural transition occurs near the TE on the suction side of the blade. For grid turbulence and wake inlet conditions, bypass transition occurs further upstream, triggered by the convection of the inlet disturbances to the boundary layer of the blade. Wang et al. [12] proposed an overset grid approach coupling multicopies of a massively-parallel unstructured compressible LES solver for turbomachinery applications. The method has been applied to rotor-stator interaction for QinetiQ MT1 high-pressure transonic experimental turbine. Cui et al. [13] investigated contrasting flow physics in different zones of a high-lift low pressure turbine cascade T106A under the influence of different inflow boundary conditions. They considered (a) the effect of wakes at low and high turbulence intensity on the flow at mid-span and (b) the impact of the state of the incoming boundary layer on endwall flow features. Although information on the physical process has been growing, it is not relatively understood how flow fields including pressure fields are globally modified due to the interaction of the boundary layer on a blade with incoming disturbances. Recently, Matsuura et al. [14] conducted transition-process-resolving numerical simulations with different types of inflow turbulence. They compared cases of no FST, isotropic FST of 5% and wakes from an upstream cylinder. They found that FST qualitatively affects the global pressure fluctuations, which become a medium to convey boundary-layer information away from the cascade. In this study, we extend our previous study and investigate the effects of freestream and wake disturbances on the compressible transitional flow fields under rotor-stator interaction in a low-pressure turbine cascade. Interrelationship among the path of the free-stream/wake turbulence, the state of the blade’s boundary layer and the global pressure fluctuation is investigated. 2. Numerical method The governing equations are the unsteady three-dimensional fully compressible Navier-Stokes equations in general coordinates (ξ, η, ζ). The perfect gas law closes the system of the equations. Viscosity is evaluated by Sutherland’s formula and a constant Prandtl number of Pr = 0.72 is assumed. The equations are solved by a finitedifference method. Spatial derivatives that appear in the metrics, convective and viscous terms are evaluated using the sixth-order tridiagonal compact scheme [15]. Near boundaries, the fourth-order one-sided and classical Padé schemes are used on the boundaries and at one point internal to them. Time-dependent solutions to the governing
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3
equations are obtained using the third-order explicit Runge-Kutta scheme. In addition to the above-mentioned spatial discretization and time integration, a tenth-order implicit filtering [16] shown below is introduced to suppress numerical instabilities that arise from central differencing in the compact scheme.
α f φi −1 + φi += α f φi +1
5
an
∑ 2 (φ n =0
i+n
+ φi − n ), i ∈ {6, ,imax − 5}.
(1)
Here, ϕ denotes a conservative quantity and φ a filtered quantity at each grid point. Regarding coefficients an (n=0,…,5), the values in [16] are used in this study. Near boundaries, an implicit filter of a decreased order, i.e., 2nd-order for i=2 and imax-1, 4th-order for i=3 and imax-2, 6th-order for i=4 and imax-3 and 8th-order for i=5 and imax-4, is used. The parameter af except for i=2 and imax-1, is set to be 0.46. At i=2 and imax- 1, af of 0.33 is used. Not only the accuracy of the filter but also the values of af have a considerable influence both on the accuracy and on the stability of the calculation. In this study, the above value is used in order to keep the stability of the computation while maintaining high-accuracy of the computational results. The present numerical method has also been well validated for the prediction of transitional and turbulent subsonic flows [7,14,17]. 3. Cascade flow computation In the computation of the stator-rotor interaction, the stator geometry is a cylinder, and the rotor geometry is T106 [18]. Wake disturbances shed from the upstream cylinder flow into the downstream rotor cascade. The diameter of the cylinder is assumed to be 2 mm. Figure 1 shows the computational grid system. It consists of the “cylinder region" and the “blade region", which are non-conforming at the interface. In this study, the blade region moves in the pitchwise direction relative to the cylinder region. The interface is located 0.5C upstream of the leading edge (LE), while the outflow boundary is located 1C downstream of the TE. The spanwise length of the grid is 0.1C in all cases. The design point data for T106 are presented in Table 1. Computational cases are summarized in Table 2. Three cases are considered in total, and the computational conditions are approximately unified so as to realize the design point condition for the rotor on its attached frame. The Strouhal number of blade passage is defined by St=fbpC/uin. Here, fbp is the blade passing frequency and uin is the relative inflow velocity to the blade. In Case C, compared with Cases A and B, isotropic turbulence of 6% intensity is introduced in the free-stream in addition to cylinder wakes. The details of generating inflow turbulence are explained in [7]. A characteristic interface condition is used between the cylinder and the blade region. While the baseline method is proposed in Kim and Lee [19] and Deng et al. [20], we extended it to the nonconforming situation using the 4th-order Lagrange interpolation in our previous study [14]. Body-fitted meshes of H-type topology represented by (ξ, η, ζ) are used, where ξ, η and ζ represent the streamwise, pitchwise and spanwise directions, respectively. Because the present cascade is two-dimensional, the cross section of the blade does not change in the ζ direction.
Fig. 1. Computational grid system (every 10 grid lines are shown).
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Table 1. Cascade design data [18], Subscript “th” : theoretical isentropic flow. Inlet total pressure Inlet total temperature
Free-stream condition Pt,1 Tt,1
47,540 Pa 312.9 K
p2
37,930 Pa
Outlet static pressure
Design point condition Isentropic outlet Mach #
Ma2,th
0.59
Isentropic outlet Reynolds #
Re2,th
5.0×105
Inlet flow angle
β1
127.7º
Outlet flow angle
β2
26.8º
Geometry Chord length
C
100 mm
Pitch/chord ratio
l/C
0.799
Table 2. Computational cases, IST: Isotropic turbulence. Case
The speed of rotor movement, m/s
St
FST
A
20
0.264
Cylinder wake, no IST
B
60
0.792
Cylinder wake, no IST
C
60
0.792
Cylinder wake, IST
The ζ direction corresponds to the z direction in the Cartesian coordinate system. At the inlet boundary of the cylinder region, the velocity and static temperature are prescribed, and the static pressure is extrapolated from the interior. The velocity and static temperature are determined from our previous computations on this system [12]. Periodicity is assumed for the spanwise (ζ, z) and pitchwise (η) directions. At the outflow, wave reflections are reduced by a non-reflecting characteristic boundary condition [21]. The no slip boundary condition together with an adiabatic wall condition is used on the walls. The numbers of grid points are 147×150×40 and 1440×250×40 for the cylinder and rotor regions, respectively. Grid resolutions are about Δξ+<15 and Δζ+<30 in the streamwise and spanwise directions, respectively near the 60%90% chord length position, and about Δξ+<10 and Δζ+<20, respectively, near the 80% chord length position where critical phenomena such as separation or transition are expected to occur. In the pitchwise direction, Δηmin+<2.3 near the 60%-90% chord length position and Δηmin+<1.0 near the 80% chord length position. These wall units are based on the local friction velocity. Streamwise mesh widths are made fine to treat the mesh interface condition accurately. In the blade region shown in Fig. 1, mesh widths in the region between the mesh interface and the LE are important for accurate convection of cylinder wakes. The maximum grid widths are set to 7.74×10-3C and 1.24×10-3C in the streamwise and pitchwise directions, respectively. The initial condition of Case A is a resultant flow field of our previous computation with the stationary blade [14]. The initial condition for the other cases is a resultant flow field of Case A. The time step for time integration is Δt=1.86×10-5C/a0,n in all cases. Here, a0,in is the sound speed at the inlet.
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4. Results and discussion a
b
c
d
e
f
Fig. 2. Vortical structures are visualized by the iso-surfaces of the second invariance of the velocity gradient tensor Q*=5. (a) Case A, t*=0.372; (b) Case A, t*=3.68; (c) Case B, t*=0.372; (d) Case B, t*=2.97; (e) Case C, t*=2.93; (f) Case C, t*=3.53. Here, quantities with ‘*’ are nondimensionalized by C and a0,in. The color on the iso-surfaces is local Mach number that is shown in the legend placed in the upper right. The color on the innermost z=constant plane shows the divergence of velocity. a
b
c
Fig. 3. Space-time plot of pressure fluctuation around the rotor blade. (a) Case A; (b) Case B; (c) Case C. Here, pressure fluctuation p’ is nondimensionalized by the density ρ0,in and the sound speed a0,in at the blade inlet.
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Fig. 4. Fractional energies of the top five dominant POD modes. a
b
c
d
e
f
g
h
i
j
k
l
Fig. 5. Time histories of the POD coefficients and eigenfuctions for the top three dominant modes. (a) Case A, time histories of the coefficients; (b) Case A, eigenfunction of the 1st mode; (c) Case A; eigenfunction of the 2nd mode; (d) Case A, eigenfunction of the 3rd mode; (e) Case B, time histories of the coefficients; (f) Case B, eigenfunction of the 1st mode; (g) Case B, eigenfunction of the 2nd mode; (h) Case B, eigenfunction of the 3rd mode; (i) Case C, time histories of the coefficients; (j) Case C, eigenfunction of the 1st mode; (k) Case C, eigenfunction of the 2nd mode; (l) Case C, eigenfunction of the 3rd mode.
Figure 2 shows vortical structures and sound propagation for all cases, and Fig. 3 shows the space-time plots of pressure fluctuation around the rotor blade. In Case A, the frequency of the wake inflow to the blade passage is small because St is small. When wakes impinge on the pressure side (PS) of the blade, turbulence is generated along the PS downstream of the impingement location as shown in Fig. 2(a). After some movement of the blade relative to the cylinder, the wakes go through the middle of the passage without contacting with the blade surface. Separation occurs near the TE of the rotor blade when wakes do not disturb the boundary layer of the suction side (SS), which is confirmed by the train of the discrete spanwise vortices in ξ direction near the TE. In Case B, the frequency of the wake inflow is larger than that of Case A. Both ends of a wake trajectory inside the passage attach to the blade surfaces. The free-stream region of the wake trajectory convects faster than the wall region. The sweeping of the ends of a wake trajectory along the blade surfaces induces turbulence in the boundary layers, and the turbulence convects and propagates along the blade. In particular, the convection and propagation of turbulence suppress separation near the TE. The intermittency/cycle of the suppression depends on the frequency of the wake inflow. This intermittency is also confirmed in Fig. 3(b). In Case C, FST continuously affects the boundary layer of the blade, and additionally LE separation occurs due to the fluctuation of inflow angle to the blade. As found in Fig. 2(c), boundary layer separation near the TE is continuously suppressed by the continuous forcing, the sweeping of
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both ends of a wake trajectory along the blade, the convection and propagation of turbulence from the LE, and the interaction of the free-stream regions of wake trajectories with the boundary layer. The FST induces larger flow oscillation compared with Cases A and B as found from Fig. 3(c). Thus, different types of FST induce different types of flow oscillation in the passage. In order to extract dominant variation of pressure fluctuation, a snapshot proper orthogonal decomposition analysis (SPOD) [22] is conducted. The details of the analysis are described in [7]. One snapshot is pressure distribution in the entire blade region. Snapshots are collected every 2000Δt, and 100 snapshots are used for the analysis. Figure 4 shows the fractional energy of the top five dominant POD modes, and Fig. 5 shows the time histories of the POD coefficients and eigenfunctions for the first three dominant modes for all cases. In all cases, the first modes occupy around 27%-38%. In Case A, the effects of the periodic wake impingement on the rotor blade appear as mode 1, and the periodic shedding of vortices in the separated region near the TE appear as modes 2 and 3. In Case B, mode 1 is similar to that in Case A. On the other hand, it is considered that the effects of the sweeping of both ends of a wake trajectory are included in modes 2 and 3. In Case C, large pressure oscillation occurs as in Fig. 3(c). This oscillation is due to pressure difference between the near-throat region on the PS and the near TE region on the SS as found in the eigenfunction of the mode 1 shown in Fig. 5(c). The boundary layer separation near the LE induced by the incoming FST also induces pressure fluctuation in the passage, and appears as mode 2 as found from the pressure distribution in its eigenfunction. A blade passage has its own property of flow oscillation. In addition, its global pressure fluctuation is made unique by the frequency of FST inflow, the convection and propagation of turbulence, and the interaction of the disturbance with boundary layers in the passage. Because pressure fluctuation can convey information away from the passage, it is expected to be used for diagnosing boundary layer states around the blade away from the passage. 5. Conclusions In order to investigate boundary-layer dynamics and flow oscillation due to the interaction of the boundary layers around a rotor blade with incoming disturbances, the transition-process-resolving numerical simulations of compressible transitional flows subjected to rotor-stator interaction in the low-pressure turbine cascade were performed. The cases of small and large St of blade passage, and with and without isotropic FST were compared. The investigated cascade geometry is T106, and the computations were conducted at its design point condition. The sixth-order compact difference and 10th-order filtering are employed. The variation in St and the intensity of the isotropic FST changes the frequency of turbulence inflow, the convection and propagation of turbulence, and the interaction of the disturbance with boundary layers in the passage. The change modifies global pressure fluctuation in the passage. The dominant variation of the pressure fluctuation was analysed by the SPOD. Because pressure fluctuation can convey information away from the passage, it is found that it may be used for diagnosing boundary layer states around the blade indirectly away from the passage. Acknowledgements The present study is financially supported by IHI Corporation under a collaborative research project between Ehime University, Japan and IHI Corporation. Computations are conducted using supercomputer systems of Japan Aerospace Exploration Agency (JAXA-JSS2), the Institute of Statistical Mathematics, and the University of Tokyo. References [1] Mayle, R.E. “The role of laminar-turbulent transition in gas turbine engines.” Transactions of the ASME, Journal of Turbomachinery 113(1991): 509-537. [2] Wu, X., and P.A. Durbin. “Evidence of longitudinal vortices evolved from distorted wakes in a turbine passage.” Journal of Fluid Mechanics 446(2001): 199-228. [3] Kalitzin, G., X. Wu, and P.A. Durbin. “DNS of fully turbulent flow in a LPT passage.” International Journal of Heat and Fluid Flow 24(2003): 636-644.
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[4] Michelassi, V., J.G. Wissink, J. Fröhlich, and W. Rodi. “Large-eddy simulation of flow around low-pressure turbine blade with incoming wakes.” AIAA Journal 41(11)(2003): 2143-2156. [5] Raverdy, B., I. Mary, and P. Sagaut. “High-resolution large-eddy simulation of flow around low-pressure turbine blade.” AIAA Journal 41(3)(2003): 390-397. [6] Wissink, J.G. “DNS of separating, low Reynolds number flow in a turbine cascade with incoming wakes.” International Journal Heat and Fluid Flow 24(2003): 626-635. [7] Matsuura, K, and C. Kato. “Large-eddy simulation of compressible transitional flows in a low-pressure turbine cascade.” AIAA Journal 45(2)(2007): 442-457. [8] Sandberg, R.D., V. Michelassi, R. Pichler, L. Chen, and R. Johnstone. “Compressible direct numerical simulation of low-pressure turbinespart I: methodology.” Transactions of the ASME, Journal of Turbomachinery 137(2015): 051011-1-10. [9] Michelassi, V., L. Chen, R. Pichler, and R.D. Sandberg. “Compressible direct numerical simulation of low-pressure turbines-part II: effect of inflow disturbances.” Transactions of the ASME, Journal of Turbomachinery 137(2015): 071005-1-12. [10] Tucker, P.G. “Computation of unsteady turbomachinery flows: part 1-progress and challenges.” Progress in Aerospace Sciences 47(2011): 522-545. [11] Tucker, P.G. “Computation of unsteady turbomachinery flows: part 2-LES and hybrids.” Progress in Aerospace Sciences 47(2011): 546-569. [12] Wang, G., F. Duchaine, D. Papadogiannis, I. Duran, S. Moreau, and L.Y.M. Gicquel. “An overset grid method for large eddy simulation of turbomachinery stages.” Journal of Computational Physics 274(2014): 333–355. [13] Cui, J, V.N. Rao, and P.G. Tucker. “Numerical investigation of contrasting flow physics in different zones of a high-lift low pressure turbine blade.” Proceedings of ASME Turbo Expo 2015, GT2015:1–14. [14] Matsuura, K, K. Matsui, and N. Tani. “Effects of free-stream turbulence on the global pressure fluctuation of compressible transitional flows in a low-pressure turbine cascade.” International Journal of Numerical Methods for Heat and Fluid Flow 28(5)(2018): 1-16. [15] Lele, S.K. “Compact finite difference schemes with spectral-like resolution.” Journal of Computational Physics 103(1992): 16-42. [16] Gaitonde, D.V., and M.R. Visbal. “Padé-type higher-order boundary filters for the Navier-Stokes equations.” AIAA Journal 38(11)(2000): 2103-2112. [17] Matsuura, K, and M. Nakano. “A throttling mechanism sustaining a hole tone feedback system at very low Mach numbers.” Journal of Fluid Mechanics 710(2012): 569-605. [18] Hoheisel, H. “Test Cases for Computation of Internal Flows in Aero Engine Components”, in L. Fottner (ed), AR-275, AGARD, (1990): 112123. [19] Kim, J., and D.J. Lee. “Generalized characteristic boundary conditions for computational aeroacoustics, Part 2.” AIAA Journal 42(1)(2004): 47-55. [20] Deng, X., M. Mao, G. Tu, Y. Zhang, and H. Zhang. “Extending weighted compact nonlinear schemes to complex grids with characteristicbased interface conditions.” AIAA Journal 48(12)(2010): 2840-2851. [21] Kim, J, and D.J. Lee. “Generalized characteristic boundary conditions for computational aeroacoustics.” AIAA Journal 38(11)(2000): 20402049. [22] Sirovich, L., and J.D. Rodriguez. “Coherent structures and chaos: a model problem.” Physics Letters A 120(5)(1987): 211-214.
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2nd International Conference on Energy and Power, ICEP2018, 13–15 December 2018, 2nd International Conference on Energy and Power, ICEP2018, 13–15 December 2018, Sydney, Australia Sydney, Australia
Interaction of wake disturbance with compressible transitional Interaction disturbance compressible transitional The of 15thwake International Symposiumwith on District Heating and Cooling boundary layers in a low-pressure turbine cascade under rotor-stator boundary layers in a low-pressure turbine cascade under rotor-stator Assessing the feasibilityinteraction of using the heat demand-outdoor interaction temperature a long-term district demand Kazuofunction Matsuuraa,*for , Kotaro Matsuib, Naoki Tanibheat ,Takashi Gotob forecast b Kazuo Matsuuraaa,*, Kotaro Matsui , Naoki Tanib,Takashic Gotob a,b,c a b Ehime University, 3 Bunkyo-cho, Matsuyama, Ehime, 790-8577, Japan I. Andrić *, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière , O. Le Correc a
a IHI Corporation, 229, Tonogaya, Mizuho-machi, Nishitama-gun, Tokyo, 190-1297, Ehime University, 3 Bunkyo-cho, Matsuyama, Ehime, 790-8577, Japan Japan b a IHI Corporation, 229,Policy Tonogaya, Mizuho-machi, Nishitama-gun, Tokyo, 190-1297, IN+ Center for Innovation, Technology and Research - Instituto Superior Técnico, Av. Rovisco PaisJapan 1, 1049-001 Lisbon, Portugal b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France b
Abstract Abstract Transition-process-resolving numerical simulations of compressible transitional flows subjected to rotor-stator interaction in a Abstract turbine cascade numerical low-pressure were performed. Casesofofcompressible small and large Strouhalflows numbers (St) oftoblade passage, and with in anda Transition-process-resolving simulations transitional subjected rotor-stator interaction without isotropic free-stream (IFST) Cases are compared. geometry T106, and theofcomputations areand conducted at low-pressure turbine cascade turbulence were performed. of small Cascade and large Strouhalisnumbers (St) blade passage, with and District heating networks are commonly addressed in the literature as oneonofsixth-order theT106, mostand effective solutions decreasing the its design point condition. Aturbulence higher-order finite method compact differencefor and tenth-order without isotropic free-stream (IFST) aredifference compared. Cascadebased geometry is the computations are conducted at greenhouse gas emissions from theStbuilding sector. These systems require investments which are returned through the and heat filtering employed. Variation in and thefinite intensity of IFST changes thehigh frequency of turbulence inflow, the and convection its designis point condition. A higher-order difference method based on sixth-order compact difference tenth-order sales. Due to turbulence, the changed climate conditions building renovation heat demand in inflow, the future could result decrease, propagation of and the interaction of and disturbance boundary layers in the blade passage. Thethechanges in filtering is employed. Variation in St and the intensity of IFSTwith changes thepolicies, frequency of turbulence convection and prolonging the investment return period. different pressure fluctuation in the the passage. Because pressurewith fluctuation canlayers convey information away from the passage, is propagation of turbulence, and interaction of disturbance boundary in the blade passage. The changes resultit in The mainpressure offluctuation thisdiagnosing paper in is the to boundary assess thelayer feasibility of usingfluctuation theblade heat demand – outdoor temperature forpassage, heat demand expected toscope be used for states around the indirectly away from the passage. different passage. Because pressure can convey information awayfunction from the it is forecast.toThe district Alvalade,boundary located layer in Lisbon was used as a away case study. The district is consisted of 665 expected be used for of diagnosing states (Portugal), around the blade indirectly from the passage. buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district © 2018 The Authors. Published by Elsevier Ltd. © 2019 The Authors. by Ltd. renovation scenarios were developed (shallow, deep). To estimate the error, obtained heat demand values were This is an open accessPublished article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) © 2018 The Authors. Published by Elsevier Elsevier Ltd. intermediate, This is an open access the CC license (https://creativecommons.org/licenses/by-nc-nd/4.0/) compared with resultsarticle fromunder aunder dynamic heatBY-NC-ND demand previously developed by theConference authors. on Energy and Selection peer-review responsibility of themodel, scientific committee of theand 2ndvalidated International This is an and open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Energy and The results showed that when only weather change is scientific considered, the margin of error could be acceptable for some applications Power, ICEP2018. Selection and peer-review under responsibility of the committee of the 2nd International Conference on Energy and Power, ICEP2018. (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation Power, ICEP2018. scenarios,Compressible the error value to 59.5% (depending the weather andflows; renovation scenarios combination considered). Keywords: flow;increased Large-eddyup simulation/direct numericalon simulation; Cascade Laminar-turbulent transition; Turbine The valueCompressible of slope coefficient increased on averagenumerical within the range of 3.8%flows; up toLaminar-turbulent 8% per decade,transition; that corresponds Keywords: flow; Large-eddy simulation/direct simulation; Cascade Turbine to the decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the 1.renovation Introduction scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and 1.coupled Introduction improve the accuracy of heat demandofestimations. The aerodynamic performance a cascade has a great influence on energy conversion efficiency in aeronautical
The aerodynamic performance of a cascade has a great influence on energy conversion efficiency in aeronautical
© 2017 The Authors. by Elsevier fax:+81-89-927-9720. Ltd. * Corresponding author.Published Tel.:+81-89-927-9720; Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and * E-mail Corresponding Tel.:+81-89-927-9720; fax:+81-89-927-9720. address:author. [email protected] Cooling. E-mail address: [email protected]
Keywords:©Heat Forecast; Climatebychange 1876-6102 2018demand; The Authors. Published Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) 1876-6102 © 2018 The Authors. Published by Elsevier Ltd. Selection under responsibility of the scientific of the 2nd International Conference on Energy and Power, ICEP2018. This is an and openpeer-review access article under the CC BY-NC-ND licensecommittee (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Energy and Power, ICEP2018. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Energy and Power, ICEP2018. 10.1016/j.egypro.2019.02.120
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as well as industrial gas turbines, which has prompted extensive research on cascade flows. In particular, accurate prediction of and detailed investigation into compressible low-Reynolds number cascade flows are crucial to improve the efficiency of aeronautical low-pressure turbines that operate at 2-5% below the designed efficiency at altitude [1], and therefore, further research on low-Reynolds number cascade flows seems necessary. In lowpressure turbines, the Reynolds number based on the chord length and the throat exit velocity becomes as small as on the order of 104-105 due to a decrease in density, resulting in an increase in kinematic viscosity. The boundary layer on the blade in such a turbine thus becomes transitional and unsteadiness of the cascade flows becomes evident. At the same time, the boundary layers are affected by the strong freestream turbulence (FST) with about 520% intensity that originates in the combustion chamber or wakes of the upstream blade rows. Recently, numerical methods that solve the Navier-Stokes equation as directly as possible have been developed and applied to the prediction of transitional flows. These methods are capable of directly treating the temporal evolution of flow disturbances and the frequency contents of freestream disturbances that are vital in the transitional processes. Direct numerical simulation (DNS) and Large-Eddy Simulation (LES) of transitional flows in a low-pressure turbine were performed by several researchers [2-9], and physical aspects of the flows have been revealed gradually. Progresses are summarized in some review papers [10, 11]. Concerning the computations without FST, Raverdy et al. [5] calculated transitional separated flows in a cascade with Reynolds number of 1.6×105 by a compressible numerical method where LES is coupled with a two dimensional computation. They analyzed the transition process focusing on the unsteady characteristics of the laminar separation bubble and reported the existence of coupling between the separation bubble and the vortex shedding from the trailing edge (TE). Concerning the computations with FST, Wu and Durbin [2] conducted an incompressible DNS on bypass transition caused by the influences of periodic upstream wakes. They investigated the process of turbulent spot production due to the interaction of the wakes with the blade boundary layer and the vortical structures that are created by the passage of wakes in a cascade. Kalitzin et al. [3] investigated the effects of different types of inlet disturbances on the boundary layer transition near a blade surface. For a turbulence-free inlet condition, natural transition occurs near the TE on the suction side of the blade. For grid turbulence and wake inlet conditions, bypass transition occurs further upstream, triggered by the convection of the inlet disturbances to the boundary layer of the blade. Wang et al. [12] proposed an overset grid approach coupling multicopies of a massively-parallel unstructured compressible LES solver for turbomachinery applications. The method has been applied to rotor-stator interaction for QinetiQ MT1 high-pressure transonic experimental turbine. Cui et al. [13] investigated contrasting flow physics in different zones of a high-lift low pressure turbine cascade T106A under the influence of different inflow boundary conditions. They considered (a) the effect of wakes at low and high turbulence intensity on the flow at mid-span and (b) the impact of the state of the incoming boundary layer on endwall flow features. Although information on the physical process has been growing, it is not relatively understood how flow fields including pressure fields are globally modified due to the interaction of the boundary layer on a blade with incoming disturbances. Recently, Matsuura et al. [14] conducted transition-process-resolving numerical simulations with different types of inflow turbulence. They compared cases of no FST, isotropic FST of 5% and wakes from an upstream cylinder. They found that FST qualitatively affects the global pressure fluctuations, which become a medium to convey boundary-layer information away from the cascade. In this study, we extend our previous study and investigate the effects of freestream and wake disturbances on the compressible transitional flow fields under rotor-stator interaction in a low-pressure turbine cascade. Interrelationship among the path of the free-stream/wake turbulence, the state of the blade’s boundary layer and the global pressure fluctuation is investigated. 2. Numerical method The governing equations are the unsteady three-dimensional fully compressible Navier-Stokes equations in general coordinates (ξ, η, ζ). The perfect gas law closes the system of the equations. Viscosity is evaluated by Sutherland’s formula and a constant Prandtl number of Pr = 0.72 is assumed. The equations are solved by a finitedifference method. Spatial derivatives that appear in the metrics, convective and viscous terms are evaluated using the sixth-order tridiagonal compact scheme [15]. Near boundaries, the fourth-order one-sided and classical Padé schemes are used on the boundaries and at one point internal to them. Time-dependent solutions to the governing
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3
equations are obtained using the third-order explicit Runge-Kutta scheme. In addition to the above-mentioned spatial discretization and time integration, a tenth-order implicit filtering [16] shown below is introduced to suppress numerical instabilities that arise from central differencing in the compact scheme.
α f φi −1 + φi += α f φi +1
5
an
∑ 2 (φ n =0
i+n
+ φi − n ), i ∈ {6, ,imax − 5}.
(1)
Here, ϕ denotes a conservative quantity and φ a filtered quantity at each grid point. Regarding coefficients an (n=0,…,5), the values in [16] are used in this study. Near boundaries, an implicit filter of a decreased order, i.e., 2nd-order for i=2 and imax-1, 4th-order for i=3 and imax-2, 6th-order for i=4 and imax-3 and 8th-order for i=5 and imax-4, is used. The parameter af except for i=2 and imax-1, is set to be 0.46. At i=2 and imax- 1, af of 0.33 is used. Not only the accuracy of the filter but also the values of af have a considerable influence both on the accuracy and on the stability of the calculation. In this study, the above value is used in order to keep the stability of the computation while maintaining high-accuracy of the computational results. The present numerical method has also been well validated for the prediction of transitional and turbulent subsonic flows [7,14,17]. 3. Cascade flow computation In the computation of the stator-rotor interaction, the stator geometry is a cylinder, and the rotor geometry is T106 [18]. Wake disturbances shed from the upstream cylinder flow into the downstream rotor cascade. The diameter of the cylinder is assumed to be 2 mm. Figure 1 shows the computational grid system. It consists of the “cylinder region" and the “blade region", which are non-conforming at the interface. In this study, the blade region moves in the pitchwise direction relative to the cylinder region. The interface is located 0.5C upstream of the leading edge (LE), while the outflow boundary is located 1C downstream of the TE. The spanwise length of the grid is 0.1C in all cases. The design point data for T106 are presented in Table 1. Computational cases are summarized in Table 2. Three cases are considered in total, and the computational conditions are approximately unified so as to realize the design point condition for the rotor on its attached frame. The Strouhal number of blade passage is defined by St=fbpC/uin. Here, fbp is the blade passing frequency and uin is the relative inflow velocity to the blade. In Case C, compared with Cases A and B, isotropic turbulence of 6% intensity is introduced in the free-stream in addition to cylinder wakes. The details of generating inflow turbulence are explained in [7]. A characteristic interface condition is used between the cylinder and the blade region. While the baseline method is proposed in Kim and Lee [19] and Deng et al. [20], we extended it to the nonconforming situation using the 4th-order Lagrange interpolation in our previous study [14]. Body-fitted meshes of H-type topology represented by (ξ, η, ζ) are used, where ξ, η and ζ represent the streamwise, pitchwise and spanwise directions, respectively. Because the present cascade is two-dimensional, the cross section of the blade does not change in the ζ direction.
Fig. 1. Computational grid system (every 10 grid lines are shown).
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Table 1. Cascade design data [18], Subscript “th” : theoretical isentropic flow. Inlet total pressure Inlet total temperature
Free-stream condition Pt,1 Tt,1
47,540 Pa 312.9 K
p2
37,930 Pa
Outlet static pressure
Design point condition Isentropic outlet Mach #
Ma2,th
0.59
Isentropic outlet Reynolds #
Re2,th
5.0×105
Inlet flow angle
β1
127.7º
Outlet flow angle
β2
26.8º
Geometry Chord length
C
100 mm
Pitch/chord ratio
l/C
0.799
Table 2. Computational cases, IST: Isotropic turbulence. Case
The speed of rotor movement, m/s
St
FST
A
20
0.264
Cylinder wake, no IST
B
60
0.792
Cylinder wake, no IST
C
60
0.792
Cylinder wake, IST
The ζ direction corresponds to the z direction in the Cartesian coordinate system. At the inlet boundary of the cylinder region, the velocity and static temperature are prescribed, and the static pressure is extrapolated from the interior. The velocity and static temperature are determined from our previous computations on this system [12]. Periodicity is assumed for the spanwise (ζ, z) and pitchwise (η) directions. At the outflow, wave reflections are reduced by a non-reflecting characteristic boundary condition [21]. The no slip boundary condition together with an adiabatic wall condition is used on the walls. The numbers of grid points are 147×150×40 and 1440×250×40 for the cylinder and rotor regions, respectively. Grid resolutions are about Δξ+<15 and Δζ+<30 in the streamwise and spanwise directions, respectively near the 60%90% chord length position, and about Δξ+<10 and Δζ+<20, respectively, near the 80% chord length position where critical phenomena such as separation or transition are expected to occur. In the pitchwise direction, Δηmin+<2.3 near the 60%-90% chord length position and Δηmin+<1.0 near the 80% chord length position. These wall units are based on the local friction velocity. Streamwise mesh widths are made fine to treat the mesh interface condition accurately. In the blade region shown in Fig. 1, mesh widths in the region between the mesh interface and the LE are important for accurate convection of cylinder wakes. The maximum grid widths are set to 7.74×10-3C and 1.24×10-3C in the streamwise and pitchwise directions, respectively. The initial condition of Case A is a resultant flow field of our previous computation with the stationary blade [14]. The initial condition for the other cases is a resultant flow field of Case A. The time step for time integration is Δt=1.86×10-5C/a0,n in all cases. Here, a0,in is the sound speed at the inlet.
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4. Results and discussion a
b
c
d
e
f
Fig. 2. Vortical structures are visualized by the iso-surfaces of the second invariance of the velocity gradient tensor Q*=5. (a) Case A, t*=0.372; (b) Case A, t*=3.68; (c) Case B, t*=0.372; (d) Case B, t*=2.97; (e) Case C, t*=2.93; (f) Case C, t*=3.53. Here, quantities with ‘*’ are nondimensionalized by C and a0,in. The color on the iso-surfaces is local Mach number that is shown in the legend placed in the upper right. The color on the innermost z=constant plane shows the divergence of velocity. a
b
c
Fig. 3. Space-time plot of pressure fluctuation around the rotor blade. (a) Case A; (b) Case B; (c) Case C. Here, pressure fluctuation p’ is nondimensionalized by the density ρ0,in and the sound speed a0,in at the blade inlet.
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Fig. 4. Fractional energies of the top five dominant POD modes. a
b
c
d
e
f
g
h
i
j
k
l
Fig. 5. Time histories of the POD coefficients and eigenfuctions for the top three dominant modes. (a) Case A, time histories of the coefficients; (b) Case A, eigenfunction of the 1st mode; (c) Case A; eigenfunction of the 2nd mode; (d) Case A, eigenfunction of the 3rd mode; (e) Case B, time histories of the coefficients; (f) Case B, eigenfunction of the 1st mode; (g) Case B, eigenfunction of the 2nd mode; (h) Case B, eigenfunction of the 3rd mode; (i) Case C, time histories of the coefficients; (j) Case C, eigenfunction of the 1st mode; (k) Case C, eigenfunction of the 2nd mode; (l) Case C, eigenfunction of the 3rd mode.
Figure 2 shows vortical structures and sound propagation for all cases, and Fig. 3 shows the space-time plots of pressure fluctuation around the rotor blade. In Case A, the frequency of the wake inflow to the blade passage is small because St is small. When wakes impinge on the pressure side (PS) of the blade, turbulence is generated along the PS downstream of the impingement location as shown in Fig. 2(a). After some movement of the blade relative to the cylinder, the wakes go through the middle of the passage without contacting with the blade surface. Separation occurs near the TE of the rotor blade when wakes do not disturb the boundary layer of the suction side (SS), which is confirmed by the train of the discrete spanwise vortices in ξ direction near the TE. In Case B, the frequency of the wake inflow is larger than that of Case A. Both ends of a wake trajectory inside the passage attach to the blade surfaces. The free-stream region of the wake trajectory convects faster than the wall region. The sweeping of the ends of a wake trajectory along the blade surfaces induces turbulence in the boundary layers, and the turbulence convects and propagates along the blade. In particular, the convection and propagation of turbulence suppress separation near the TE. The intermittency/cycle of the suppression depends on the frequency of the wake inflow. This intermittency is also confirmed in Fig. 3(b). In Case C, FST continuously affects the boundary layer of the blade, and additionally LE separation occurs due to the fluctuation of inflow angle to the blade. As found in Fig. 2(c), boundary layer separation near the TE is continuously suppressed by the continuous forcing, the sweeping of
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both ends of a wake trajectory along the blade, the convection and propagation of turbulence from the LE, and the interaction of the free-stream regions of wake trajectories with the boundary layer. The FST induces larger flow oscillation compared with Cases A and B as found from Fig. 3(c). Thus, different types of FST induce different types of flow oscillation in the passage. In order to extract dominant variation of pressure fluctuation, a snapshot proper orthogonal decomposition analysis (SPOD) [22] is conducted. The details of the analysis are described in [7]. One snapshot is pressure distribution in the entire blade region. Snapshots are collected every 2000Δt, and 100 snapshots are used for the analysis. Figure 4 shows the fractional energy of the top five dominant POD modes, and Fig. 5 shows the time histories of the POD coefficients and eigenfunctions for the first three dominant modes for all cases. In all cases, the first modes occupy around 27%-38%. In Case A, the effects of the periodic wake impingement on the rotor blade appear as mode 1, and the periodic shedding of vortices in the separated region near the TE appear as modes 2 and 3. In Case B, mode 1 is similar to that in Case A. On the other hand, it is considered that the effects of the sweeping of both ends of a wake trajectory are included in modes 2 and 3. In Case C, large pressure oscillation occurs as in Fig. 3(c). This oscillation is due to pressure difference between the near-throat region on the PS and the near TE region on the SS as found in the eigenfunction of the mode 1 shown in Fig. 5(c). The boundary layer separation near the LE induced by the incoming FST also induces pressure fluctuation in the passage, and appears as mode 2 as found from the pressure distribution in its eigenfunction. A blade passage has its own property of flow oscillation. In addition, its global pressure fluctuation is made unique by the frequency of FST inflow, the convection and propagation of turbulence, and the interaction of the disturbance with boundary layers in the passage. Because pressure fluctuation can convey information away from the passage, it is expected to be used for diagnosing boundary layer states around the blade away from the passage. 5. Conclusions In order to investigate boundary-layer dynamics and flow oscillation due to the interaction of the boundary layers around a rotor blade with incoming disturbances, the transition-process-resolving numerical simulations of compressible transitional flows subjected to rotor-stator interaction in the low-pressure turbine cascade were performed. The cases of small and large St of blade passage, and with and without isotropic FST were compared. The investigated cascade geometry is T106, and the computations were conducted at its design point condition. The sixth-order compact difference and 10th-order filtering are employed. The variation in St and the intensity of the isotropic FST changes the frequency of turbulence inflow, the convection and propagation of turbulence, and the interaction of the disturbance with boundary layers in the passage. The change modifies global pressure fluctuation in the passage. The dominant variation of the pressure fluctuation was analysed by the SPOD. Because pressure fluctuation can convey information away from the passage, it is found that it may be used for diagnosing boundary layer states around the blade indirectly away from the passage. Acknowledgements The present study is financially supported by IHI Corporation under a collaborative research project between Ehime University, Japan and IHI Corporation. Computations are conducted using supercomputer systems of Japan Aerospace Exploration Agency (JAXA-JSS2), the Institute of Statistical Mathematics, and the University of Tokyo. References [1] Mayle, R.E. “The role of laminar-turbulent transition in gas turbine engines.” Transactions of the ASME, Journal of Turbomachinery 113(1991): 509-537. [2] Wu, X., and P.A. Durbin. “Evidence of longitudinal vortices evolved from distorted wakes in a turbine passage.” Journal of Fluid Mechanics 446(2001): 199-228. [3] Kalitzin, G., X. Wu, and P.A. Durbin. “DNS of fully turbulent flow in a LPT passage.” International Journal of Heat and Fluid Flow 24(2003): 636-644.
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