Proceedings of the ASME 2017 Fluids Engineering Division Summer Meeting FEDSM2017 July 30-August 3, 2017, Waikoloa, Hawaii, USA FEDSM2017-69271 A CRITICAL COMPARISON OF NUMERICAL AND EXPERIMENTAL RESULTS FOR THE EXAMINATION OF A CASCADE CONSISTING OF NACA 65-010 1 % PROFILES Andreas Baum∗, Constantin Berger, Christian Landfester, Martin Böhle Institute of Fluid Mechanics and Fluid Machinery University of Kaiserslautern, Germany Email: [email protected] ABSTRACT Numerical and experimental investigations through different spans of the rotor are a common approach in turbo machinery design. As the aerodynamic quality of rotor blades is crucial for turbo machinery’s efficiency, mass-averaged loss coefficients ζ¯ NOMENCLATURE b c1 c2 D DF e H i l ki, j M N ptot,1 ptot,2 Re t t/l x y z β1 β2 ∆β γ Γ δ δ ζ and turning angles ∆β̄ are of particular interest. Using the example of commonly used NACA-65 profiles, a comparison between the results obtained by those methods should investigate whether Computational Fluid Dynamics (CFD) applying the Transition SST turbulence model delivers sufficiently accurate results regarding both 2D and 3D modeling approaches. The comparison is supplemented by the singularity method based on the potential theory as well as historical data provided by NACA. While CFD produced a noticeable offset for some angle configurations, the 2D results of ∆β̄ were in good agreement for singularity method, historical data and experimental investigations on the center line of the cascade supporting the validity of the measurement. Although significant deviations were also found for ζ¯ , it can be stated that CFD reproduced the qualitative course sufficiently for both variables considered. A similar picture emerges from the 3D comparison: Despite noticeable deviations in quantitative terms, a good correspondence was found for both variables regarding local and mass-averaged values. KEYWORDS: compressor blade cascade, loss coefficient, corner stall / separation, NACA-65, secondary flow, five-hole probe measurements, turbulence modeling ∗ Address all correspondence to this author. 1 Width of the blade Velocity upstream of the cascade Velocity downstream of the cascade Diffusion parameter Diffusion factor Maximal thickness of the blade De Haller criterion Incidence angle Chord length of the blade Coupling coefficient between points i and j Mach number Number of points on the contour of the blade Total pressure upstream of the cascade Total pressure downstream of the cascade Reynolds number Time Spacing ratio Cartesian coordinate Cartesian coordinate Cartesian coordinate Inflow angle Outflow angle Turning angle Vorticity per length Circulation Deviation angle Boundary layer thickness Loss coefficient Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/28/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use η λ µ ϕ φ ρ σ Dynamic viscosity Stagger angle Axial velocity ratio Camber angle Velocity potential Density Solidity c2 c1 β2 δ c∞ φ = 40° c2 camber line β2 β∞ t chord line λ β1 i c1 β1 cm INTRODUCTION m 00 m 1 l= For ecological and economical reasons, turbo machines have to cover wider loading ranges whilst guaranteeing efficient operation. Under part- and overload conditions wall-induced flow phenomena like corner stall (resp. corner separation) and, hence, blocking effects intensify. As those effects massively affect both loss emergence and flow deflection, this issue has to be addressed by research and development in order to allow efficient and stable operation. Multiple variations and approaches in blade and cascade design were meant to deal with separation and secondary flow effects, e.g. side-slotted blades or sheets, variations of NACA profiles etc. [1–3]. Other cascade studies were conducted for different operating conditions, like transonic flows [4]. Beside experimental examinations, these issues were addressed by numerical studies investigating the outcome and validity of different modeling approaches, e.g. the turbulence model [5]. Using the example of commonly used NACA-65 profiles, the present study concentrates on a critical comparison between numerical and experimental methods in order to investigate whether CFD delivers sufficiently accurate results for the specific test design. A valid model would not only allow swift and equally extensive parameter variation for future research, but also a profound investigation of near wall flow phenomena. The comparison is supplemented by the singularity method based on the potential theory as well as historical data provided by NACA [6]. For the purpose of further comparison and validation, separation and blocking indicators are applied, e.g. two diffusion factors (according to Lei [7] and Lieblein [8]), the Wilson’s de Haller criterion and the axial velocity ratio. Moreover, this study is intended to provide detailed and systematic data for a broad range of parameter variations, e.g. spacing ratios, inflow and stagger angles. Beside general insights into the influence of these parameters on losses and turning angles, this study is meant to examine wall-induced 3D losses in both measurement and simulation. Last but not least, it is part of a research series which will examine and compare the current blades with simple circular-arc sheet blades regarding 2D and 3D losses. FIGURE 1. Nomenclature cascade flow TEST DESIGN The cascade consists of blades with a NACA-65 equivalent circular arc camber line and a NACA 65-010 thickness distribution. The relative thickness amounts 8 %. Its trailing edge has been thickened by 1 % of the chord line length l. The geometry and kinematic relations of the cascade are shown in Fig.1. The incidence angle i is defined as the angle between the inlet velocity vector c1 and the tangent to the camber line. It is defined i = β1 − λ − ϕ 2 (1) The geometric specifications of the examined cascade as well as the test parameters are given in Tab.1. The examination was conducted for three spacing ratios t/l = {0.5, 1.0, 1.5} and two stagger angles λ1 = 30◦ and λ2 = 40◦ . All investigations were performed for a Reynolds number Re = 4 · 105 . 2D calculations and line measurements at the cascade’s center line were carried out for imin = −25◦ and imax = 12.5◦ representing both heavy part and over load scenarios. For the investigation of near wall phenomena caused by secondary flow and its influence on losses, 3D calculations and field measurements were conducted for three selected incidence angles, i.e. the optimal incidence and the outermost angles of the operational range, where losses rise sharply. 2 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/28/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use TABLE 1. Geometric specifications and test parameters honeycomb Prandtl probe Side channel compressor ② measuring traverse ṁ SC2 Parameter Value Unit ρ 1.196 kg/m3 η 1.847 · 10−5 kg/(m·s) l 0.1 m b 0.2 m e 0.08 ϕ 40 ◦ c1 61.3 m/s Re 4 · 105 M 0.18 ṁ ṁ SC1 ① inﬂow inlet nozzle acceleration two stage cone axial compressor FIGURE 2. Side channel compressor test section Measurement setup ∆z = 2 · 10−3 m and ∆y = 10−3 m were chosen for the field measurements. The number of samples was reduced to 10 with an interval of ∆t = 0.1 s. A schematic depiction of the measurement setup is given in Fig.2. CFD SETUP For the discretization of the control areas, ANSYS ICEM CFD (v15) was used. As the flow can be considered to be periodic between the spacings of the cascade, the control area was limited to a single spacing for the benefit of less calculation effort. By means of a block structured grid, the 2D control area was divided into three sections. Two H-grids for the in- and outlet ensure a less distorted mesh with an optimized number of cells. For a sufficient refinement of the near wall cells, an O-grid was used around the blade. The 3D meshes have been generated by extruding the 2D meshes. By means of a mesh independence study, a sufficient number of cells was determined counting 5.5 · 105 for the 2D mesh with t/l = 1 and 5.5 · 107 for the corresponding 3D + mesh. With y+ min ≈ 0.01 and ymax ≈ 3, it was further taken care that the meshes meet the requirements of Menters [10] Transition SST turbulence model which was used for a precise calculation of the laminar-turbulent transition [11]. The calculations were carried out with ANSYS FLUENT (v15). The 3D flow region, its boundary conditions and characteristic dimensions are shown in Fig.3. The velocity inlet and the measure plane were placed in a distance of l/2 in front of the leading edge and −l/2 behind the trailing edge of the blade. The outflow was set one chord-length behind the blade. Assuming symmetric flow referred to the center line, a symmetry condition was set at a blade width of b/2. Based on a free flow measurement, an user-defined function for the velocity inlet was implemented utilizing the 1/7 potential law and, therefore, reproducing the specific inflow conditions of the test section. It is given by MEASUREMENT SETUP An in-house cascade wind tunnel has been used for the measurements, cf. [9]. It consists of an inlet nozzle according to standard DIN 1952 (inner diameter 0.71 m, length 1.575 m), a frequency controlled two stage axial compressor (diameter 0.6 m, performance 18.5 kW per stage), a honeycomb grid (length 0.16 m, comb distance 9 · 10−3 m, thickness 2 · 10−4 m) to produce an unimpeded stream behind the compressor, an acceleration nozzle (length 1.5 m, inlet diameter 0.71 m, outflow cross section 0.5 × 0.2 m), a smoothing segment (length 0.6 m) and a test section. Two frequency controlled side channel compressors are installed in front of the test section to suction the upper and lower boundary layer of the smoothing section. They are also used to avoid blocking and to realize periodic inflow conditions. By means of a Prandtl probe at the center of the inflow’s cross section, the reference values for total and static pressure are measured. The test section is pivoted to realize different inflow angles. The measurements of loss coefficients and turning angles were carried out at a distance of l/2 behind the trailing edge using a calibrated five-hole-probe. The probe has a length of 0.25 m and a diameter of 2 · 10−3 m. For the acquisition and processing of raw measurement data, an in-house developed measuring box is used containing AMSYS pressure sensors with a measurement error of ±1. (%FS)RT and a programmable Arduino Mega 2560 microcontroller. To ensure safe operation, field measurements were carried out up to a distance of 4 · 10−3 m from the side wall. The aluminum-milled NACA-65 blades can be considered to be hydraulically smooth. A step size of ∆z = 5 · 10−4 m was chosen for line measurements. To compensate fluctuations of the axial compressors as well as the pressure sensors, 20 samples with an interval of ∆t = 0.1 s are measured and averaged in each measurement point. Step sizes of y c1 (y) = c1 · ( )8/71 δ if y ≤ δ (2) The simulations were conducted at an isotropic turbulence intensity of 2 %. This value has been determined by hot-wire mea- 3 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/28/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use periodic 1 and symmetry 1 n−1 cz,i = ∑ 2t j=0 wall (blade) velocity inlet 2Π t (x − x j ) 2Π 2Π t (x − x j ) − cos t cosh ! sinh (z − z j ) γ j ∆s j (4) Adding the kinematic boundary condition leads to the linear equation for the contour integral: M ∑ k(i, j)γ(s j )∆(s j ) = 2 · (ẋi cos(βi ) + z˙i sin(βi )) measuring plane (5) j=1 outflow with: wall z x y periodic 2 FIGURE 3. 2Π Π z˙i · sinh 2Π t (xi − x j ) − ẋi · sin t (zi − z j ) ki, j = (6) 2Π Π t · N cosh 2Π t (xi − x j ) − cos t (zi − z j ) + zi · t·N Control volume CFD calculations if i 6= j and surements at the wind tunnel. The SIMPLEC-algorithm with a skewness correction of 1 has been used. The equations of motion for pressure, momentum and viscosity have been spatially discretized with the Second Order Upwind method, while for the gradient calculation the ”Least Square Cell based” method has been chosen. For solution controls, the settings were set to default. As it may not be sufficient to judge convergence only by examining the residuals, it was additionally evaluated by monitoring the drag coefficients and the mass-averaged total pressure on the measuring plane. The post-processing and evaluation of the obtained data were performed with ANSYS CFD-Post (v15) and Matlab 2016a. ki, j = 1 + 1 (ẋi · ẍi ) − (z˙i · z¨i ) Π 2N ẋi 2 + z˙i 2 · z˙i · t·N (7) if i = j respectively. Based on the velocity triangles and the coherences for c∞,x , c∞,z and tan βi , the outflow angle can be calculated by: β2 = arctan tan β1 + Γ t · cos β1 (8) where the circulation Γ is described by: n−1 Γ≈ POTENTIAL THEORY The calculations for the potential theory are based on the Martensen Method (cf. e.g. [12]) using singularities to model the flow around the blade surfaces. The potential flow at a given point results from the superposition of a translational flow c∞ and the vortex distribution on the contour of the blade. Therefore, the components of the velocity ci in a point i can be calculated by: 1 n−1 cx,i = − ∑ 2t j=0 sin cosh 2Π t ∑ γ j · ∆s j (9) j=0 2Π t (z − z j ) (x − x j ) − cos AERODYNAMIC QUALITY The aerodynamic quality of a cascade is characterized by its losses: ! 2Π t The Kutta condition wit γ j=n−1 = 0 was imposed. (z − z j ) γ j ∆s j ζ (y, z) = (3) 4 ptot,1 − ptot,2 (y, z) ρ 2 2 c1 (10) Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/28/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Mass-averaging For comparison and evaluation purposes, it is useful to mass-average loss coefficients and turning angles as conclusions on the overall performance can only be drawn from a limited extent from local values. Therefore, an integration was carried out over one spacing t/l and, based on the symmetric flow conditions, half of the blade width b . This leads to c ζ (y, z) · c2,x (y, z)dzdy z 1 R y=b/2 R z+t c2,x z y=0 c1 (y, z)dzdy Separation and stall criteria To signify the occurrence of stall, and measure the aerodynamic load of a three dimensional flow, the diffusion parameter in reference to Lei et al. [7] is used. It assumes separation for: 1 1− D= σ cos β1 cos λ − ϕ2 !2 · (i + ϕ) ≥ 0.4 ± 0.05 (13) R y=b/2 R z+t ζ= β2 = arctan y=0 R y=b/2 R z+t c2,z z c1 Another measurement is Wilson’s de Haller criterion [14]. It is defined as the velocity ratio in front of and behind the cascade and implies stall if: c2,x c1 (y, z)dzdy 2 (y, z) · R y=b/2 R z+t c2,x z y=0 c1 (y, z) y=0 (11) H= (12) c2 (y)min < 0.7 c1 (14) dzdy For two dimensional flows, Lieblein’s Diffusion factor [8] is a typical measurement to forecast separation. Therefore, the bound for the beginning of separation is exceeded if: For two dimensional investigations, the dependence of the horizontal axis y disappears. cos β1 1 cos β1 DF = 1 − + · (tan β1 − tan β2 ) > 0.6 (15) cos β2 σ 2 Correction of loss coefficients The evaluation of a free field measurement revealed that loss coefficients decline from the center line reaching negative values up to a point where side-wall related effects set in. It can be assumed that this decline has to be attributed not to flow physics, but to measurement restrictions as the reference pressure is measured on a fixed centered position in front of the test section. Therefore, a local correction of the measured loss coefficients is applied which based on the measured loss coefficients of the free field. Assuming that losses have to be zero within the free stream of the free field, the free field loss coefficients are mass-averaged in z-direction and added to the corresponding local values of the final measurements. To prevent a distortion of near wall losses, the correction value at the border line between free stream and boundary layer is perpetuated up to the side wall. To get a comprehension about the blockage due to the increase in boundary layer thickness, secondary flow effects and recirculation of the primary flow, the axial velocity ratio is taken into account. It is defined as µ(y, z) = c2,x c2 · cos β2 (y, z) · cos γ(y, z) = c1,x c1 · cos β1 (16) 2D RESULTS Beside some general observations regarding the dependence of ζ¯ and ∆β̄ on t/l and λ , this section is dedicated to the comparison between the line measurements and the corresponding 2D calculations. It can be noticed that ζ¯CFD and ζ¯EXP are in best agreement for the medium spacing ratio t/l = 1. While ζ¯CFD is surpassed by ζ¯EXP for t/l = 0.5, the CFD results exceed the experimental values for t/l = 1.5. Regarding the turning angles ∆β̄ , the following picture emerges: A better accordance is generally found for higher spacing ratios and smaller stagger angles within the incidence angle range of linear dependency. When leaving the interval of linear dependency, growing separation presumably leads to a smaller incline of β̄ . This effect is significantly overvalued by CFD resulting in a pronounced deviation between the experimental and numerical results. As smaller spacing ratios provide a better flow guidance, the operating range becomes broader for smaller t/l. Since better guidance is attended by Secondary flow 3D losses are highly influenced by secondary flow phenomena like corner stall, i.e. a simultaneous back flow on the side wall and the suction side of the blade due to an imbalance of pressure- and dynamic forces. It evokes secondary flow phenomena, which are highly responsible for the losses in turbo machinery. Secondary flow is defined as the deviation between the local- and potential flow (characterized by ∆φ = 0) [13]. According to comparable parameters the primary flow is defined by mass averaging the flow in the nearly frictionless region outside the wake for both CFD calculations and experimental investigations. 5 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/28/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use FIGURE 4. Results for ζ¯ and ∆β̄ for line measurements higher losses, the loss curve shifts upwards for smaller t/l and ζ¯min moves towards smaller incidence angles. However, this correlation cannot be derived from the computational results where losses rises for higher t/l. Within the incidence angle range of linear dependency, the occurring deviations between the experimental and numerical results seem to have a nearly constant offset which leads to the conclusion of a systematic bias. For interpretation, the course of the axial velocity ratio is exemplary shown for t/l = 1 in Tab.2. Due to the highest blocking effect occurs in the homogeneous flow field, the maximum value of µ is characteristic. As monitored, an increase of i causes an acceleration of the axial flow component. Therefore, a separation is prevented, leading to both a higher deflection and a decrease in losses. In contrast, the 2D CFD results show a constant velocity upstream and downstream of the blade. For an additional validation the experimental results are compared with values obtained from the described singularity method as well as a formula apparatus from Aungier [15] based on the results made by Bullock and Johnson [6]. In Tab.3 several 6 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/28/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use TABLE 2. Maximal axial velocity ratio for σ = 1 in dependence of i TABLE 3. i/◦ i/◦ 30 µmax −20 0.98 −15 0.99 −10 0.98 1.10 −5 1.04 1.21 0 1.12 1.38 5 1.27 1.60 two problems: in some cases it emerged from convergence issues during the numerical simulation and in others it was restricted by the measuring method, or more precise, by leaving the calibration range of the five-hole probe. Due to the correction procedure described in ’Correction of loss coefficients’, the 2D results were also affected. The adaptation of the loss coefficient led to a systematic shifting of the data points. Subsequently, the results for t/l = {1, 1.5} approximated the CFD values and, however, for t/l = 0.5 the results diverged. 40 µmax 3D RESULTS Additionally to the line measurements covering the whole operating range, several field measurements were conducted to examine and compare the influence of wall-induced flow phenomena on the emergence and distribution of losses. Due to limited space for extensive diagrams, the medium spacing ratio t/l = 1 was taken for representation of loss distribution and secondary flow, depicted in Fig.5 and Fig.6. The chosen incidence angles are i = {−15◦ , −5◦ , 5◦ }. First, the distribution of the loss coefficients on the measuring plane is compared between measurement and calculation. Beside this comparison, general observations regarding the cause of the specific loss distribution are described. In the second step, a closer look is taken at the secondary flow and its influence on loss emergence. Comparison of turning angles for σ = 1, λ = 30◦ ∆β exp /◦ ∆β Sing /◦ ∆β NACA /◦ ∆NACA /% ∆Sing rel rel /% −20 9.3 11.9 11.7 25.9 28.5 −15 14.4 16.8 16.3 13.2 16.5 −10 19.6 21.6 20.9 6.3 10.2 −5 24.2 26.5 25.4 4.6 9.1 0 28.4 31.3 29.8 5.0 10.1 5 31.7 36.0 34.2 7.6 13.5 Losses and turning angles 2D related losses, i.e. a clearly separated wake and a large free-flow area, can be seen for both measurement and calculation expanding from the center line in direction to side wall. Depending on the inflow conditions, wallinduced 3D losses set in. With increasing incidence angles, the influence of those losses rises as the effects of corner stall occurring on the side wall and the suction side of the blade increase. As this effect is directly linked to secondary flow and corner stall, its cause is described in the following section. Moreover, it can be clearly seen that the wake is bend upwards – especially for i = {−15◦ , −5◦ }. The comparison shows a sufficient agreement for smaller incidence angles. Although the deviations in the loss distribution rise, there is still a good accordance in qualitative terms for higher incidence angles, i.e. the underlying flow phenomena are sufficiently represented in the calculation. It can be assumed that the increasing deviations between CFD and measurement for larger incidence angles have to be attributed to the changes in thickness of the side wall’s boundary layer in the experiment and, therefore, deviation from the UDF. This guess is also confirmed by the column by column mass averaged flow parameters, shown in the lower row of Fig.5. The mass-averaged losses of the measurement show a pronounced decrease on the way to the side wall which has no representation in the calculation. In fact, the course of mass-averaged values for ∆β are exemplary compared and the relative deviations are given. It is apparent that for uncritical inflow angles (−10◦ ≤ i ≤ 5◦ ) the deviations are small, especially for NACA results. For high overload regions, a pressure sided flow separation occurs for the experimental investigations. For regions of partload, the results show again an earlier separation compared to the NACA data. In contrast, the singularity method cannot represent the phenomenon of flow separation leading to higher calculated turning angles ∆β than achievable in the experiment. Within the linear dependency of the turning angles, the deviation does not significantly exceed 10 % for both methods. Beside that, there is a nearly constant offset, which can be considered to be an acceptable result. A comparison of the applicability for DF shows different results for CFD and experimental investigations. While a reasonably good agreement for the flow prediction by means of CFD can be recognized, the experimental results differ considerably. Therefore, the flow stays attached for values significant larger than DF = 0.6. In some cases the amount of data points was limited due to the possibility to obtain valid results. This limitation is based on 7 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/28/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 3D FIGURE 5. SS SS PS EXP PS PS PS SS CFD PS EXP SS EXP i = 5° CFD PS CFD SS i = -5° SS i = -15° 2D Comparison of 3D results for λ = 30◦ losses is even opposed for i = 5◦ . Even though losses clearly increases at close distance to the side wall for every incidence angle, there is only a good accordance in qualitative terms for i = −15◦ . To compare the differences more in detail, again, the changes of µ are taken into account. For experimental data, µ rises from the center line to the inset of the boundary layer. This increase has an influence on separation and 3D flow phenomena resulting in lower losses. In contrast, due to idealized boundary conditions the blocking effect is much smaller for CFD leading to a nearly constant course of µ. Similar to the 2D results, steeper inflow angles lead to an increase of µ for experimental investigations, and so, to a worse agreement between experiments and 8 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/28/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use TABLE 4. Comparison of 2D and corner stall induced losses for σ = 1 and λ = 30◦ TABLE 5. Values of D and H EXP for σ = 1 and λ = 30◦ . i/◦ D H EXP i/◦ ζ 2D /% ζ CS /% −15 0.1344 0.696 −15 3.12 2.03 −5 0.2959 0.573 −5 2.91 4.02 5 0.5190 0.628 5 4.52 4.83 is just reached, the experimental investigation shows only a small area of higher losses. CFD. The same holds true for 2D and 3D simulations regarding the agreement of the results at the center line. In general, the 2D CFD investigations overestimate the losses at the center line due to an exclusion of 3D flow phenomena. The overestimation of losses are positively correlated to β1 . A better agreement was achieved for the mass-averaged turning angles: In both measurement and calculation ∆β̄ decreases in direction to the side wall before it sharply increases and even exceeds the center line’s value in direct proximity to the side wall. This effect has to be attributed to near wall secondary flows resulting in an extend curvature of the streamlines as described below. For all three incidence angles the measured turning angles exceed the calculated ones as the evaluation of the 2D findings has already indicated. The systematic deviation increases with rising incidence angles reaching up to 10◦ . To quantify the influence of corner stall, the 3D losses are considered separately. Therefore, the corner stall influenced area is detected as the loss region exceeding ζ at the center line. Additionally, the mass averaged 2D losses are deducted. For the exemplary shown results, a comparison of 2D losses and losses induced through corner stall is given in Tab.4. In accordance with the course of losses, the influence of corner stall is reflected in an increase in ζ CS . Especially in regions near the 2D design point, the losses induced by corner stall reach approximately 60 % of the total losses. Secondary flow Due to secondary flow, a circulation sets in transporting low-loss fluid along the pressure side towards the side wall. On the suction side the high-loss boundary layer of the side wall is carried away and intermixes with the main flow. Although these opposing flows mutually weaken each other behind the trailing edge (with an increase of friction losses), this circulation still persists on the measurement plane bending the wake upwards and expanding the area of high losses on the suction side. This process is highly influenced by the inflow conditions: Increasing incidence angles trigger higher pressure gradients between the suction and pressure side. Higher pressure gradients foster the curvature of the near wall streamlines. This intensifies, in turn, secondary flow due to continuity requirements (cf. [16]). For high incidence angles, such as i = 5◦ , these secondary flows transport considerable parts of near wall fluid expanding highloss areas up to one quarter of the blades’ width. Regarding the secondary flow under qualitative aspects, the accordance between experiment and CFD is good. The circulation area is precisely depicted and consistent. In both measurement and calculation, the level of secondary flow clearly increases with smaller distances to the side wall. In contrast to the measurement, the calculation shows a strong secondary flow pointing downwards from the pressure side of the adjacent blade. Moreover, the calculated secondary flow on the left edge of the highloss area heads in south-west direction while the measured secondary flow points almost horizontally to the blade’s center line. Separation and corner stall Alike for two-dimensional investigations, a comparison between literature parameters and the investigation results is considered. The values for D and H EXP are exemplary shown for t/l = 1 and λ = 30◦ in Tab.5. As mentioned before, all investigations show typical corner stall phenomena, while D predicts the formation only for an incidence angle of i = 5◦ . This discrepancy can be explained by the thickness distribution of the side-wall boundary layer, as this parameter highly influences the occurrence of corner stall. Since it is not considered in the diffusion parameter, the prediction of corner stall formation is delayed. In contrast, the results are totally in accordance with the de Haller criterion. While for small incidence angles the boundary condition for corner stall occurrence CONCLUSION For a cascade, consisting of NACA-65 blades, experimental and numerical findings for three spacing ratios and two stagger angles were compared with regard to its losses and turning angles. Additionally, the prediction of the occurrence of separation for both 2D and 3D flows was examined. It can be stated that prediction of the real flow behavior by means of CFD is only useful in qualitative terms, while for precise findings an experimental investigation is indispensable. A forecast of the turning angles for 2D consideration using the sin- 9 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/28/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 0.5 0.9 0.75 0.98 REFERENCES [1] Ma, W., 2012. “Experimental investigation of corner stall in a linear compressor cascade”. Phd thesis, Ecole Centrale de Lyon. [2] Roche, R. F., and Thomas, L. R., 1954. “The effects of slotted blade tips on the secondary flow in a compressor cascade”. [3] Beselt, C., 2016. “Experimental investigation of secondary flow phenomena in a compressor stator cascade”. PhD thesis, Technische Universität Berlin. [4] Weber, A., Schreiber, H. A., Fuchs, R., and Steinert, W., 2002. “3-D Transonic Flow in a Compressor Cascade With Shock-Induced Corner Stall”. ASME Journal of Turbomachinery, pp. 358–366. [5] Liu, Y., J. L. H. Y., 2016. “Numerical study of corner separation in a linear compressor cascade using various turbulence models”. Chinese Journal of Aeronautics, 29(3), pp. 639–652. [6] Bullock, R. O., J. I. A., 1965. Aerodynamic Design of Axial-Flow Compressors. Tech. rep., NASA, Washington, 7. An optional note. [7] Lei, V.-M., Spakovszky, Z., and Greitzer, E., 2008. “A criterion for axial compressor hub-corner stall”. Journal of Turbomachinery, 130(3). [8] Abbott, Ira. A., v. D. A. E. S. L. S. j., 1945. Summary of Airfoil Data. Tech. rep., National Advisory Committee for Aeronautics. [9] Böhle, M., T. F. “Three-dimensional near wall flow phenomena of a tandem cascade”. 10th European Conference on Turbomachinery Fluid dynamics & Thermodynamics, 2013, pp. 1–12. [10] Menter, F. R. “Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications”. pp. 1598–1605. [11] ANSYS, 2013. Ansys fluent theory guide. release 15.0. [12] Lewis, R. I., 1996. Turbomachinery Performance Analysis. Butterworth-Heinemann. [13] Detra, R. W., 1953. “The Secondary Flow in Curved Pipes”. Dissertation, The Swiss Federal Institute of Technology, Zurich. [14] Wilson, D. G., T. K., 2014. The Design of High-Efficiency Turbomachinery and Gas Turbines, 2. edition ed. The MIT Press. [15] Aungier, R. H., 2003. Axial-Flow Compressors - A Strategy for Aerodynamic Design and Analysis. ASME Press. [16] Frey, T., 2014. “Numerische und experimentelle Untersuchungen der 3D-Grenzschichtströmung in Wandnähe hochumlenkender Tandem-Gitter”. PhD thesis. C2 / C1 0.1 1 z/t CFD 0.5 0 1 z/t EXP 0.5 0 0.5 y/b FIGURE 6. Secondary flow for i = −5◦ and λ = 30◦ gularity method as well as the historical NACA data is in good accordance to the experimental results. Hence, the validity of the measurement was guaranteed. It has been shown that the prediction for flow separation by means of Lieblein’s diffusion factor and Lei’s diffusion parameters differs significantly from the experimental results. In contrast, DF corresponds to the results made by CFD, while D shows qualitatively the same difference as for the experimental investigations. Merely, the de Haller criterion is in a good agreement with both types of investigations. To get a comprehensive prediction of 3D flow separation, Lei’s diffusion factor needs to be extended by a parameter involving the boundary layer thickness, which has to be addressed by future research. 10 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/28/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use

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