Acta Polytechnica https://doi.org/10.14311/AP.2024.64.0350 Acta Polytechnica 64(4):350–359, 2024 © 2024 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague EXPERIMENTAL INVESTIGATION OF AN ENTROPY PRODUCTION IN A LINEAR BLADE CASCADE Erik Flídr Czech Aerospace Research Centre, Laboratory of High-Speed Aerodynamics, Beranových 130, 199 00 Prague, Czech Republic correspondence: flidr@vzlu.cz Abstract. The vortical structures in turbomachinery are crucial phenomena that significantly impact the machine’s efficiency. Therefore, investigating them is essential for a better understanding of the machine’s operation. The presented paper focuses on an experimental investigation of entropy production in a linear blade cascade composed of prismatic blades for two pitch-to-chord ratios, t/c = 0.6, and 0.9. The effects of the inlet flow angle, α1 = −20°, 5°, 30°, and outlet isentropic Reynolds number, Re2,is = (0.8, 1.2, 2.5, and 4.5) × 105, are examined based on pressure measurements. Entropy production is evaluated as a balance of fluxes through the inlet and outlet boundaries of the control volume. The paper provides a detailed discussion of the local distribution of entropy production and vorticity in the flow field, as well as their evolution with the tested parameters. The correlations between the integral values of entropy production and the tested parameters are also given. Keywords: Entropy production, linear blade cascade, experimental research. 1. Introduction To the author’s knowledge, Einstein’s pioneering work [1] was the first present the evolution of sec- ondary vorticity based on physical explanations. Since then, several authors have studied this phenomenon theoretically, for example, [2–9] or [10]. Initially, theo- retical analysis required the curvature of the flow path and viscous fluid flow for the generation of vorticity, as shown by Dean [2]. Hawthorne [3] took a differ- ent approach, using fluid kinematics to derive the generation of secondary vorticity in curved channels. Subsequent work by Hawtrhone [4] connected theo- retical descriptions with blade cascades in a simple manner. Marris’s work showed that the curvature of the flow path is not necessary for secondary vorticity genera- tion (see [5]). Even a rotating reference frame has been studied in [8]. Lastly, intrinsic coordinates were used to describe this phenomenon in [10], where the impact of the individual terms in the Navier-Stokes equation on secondary vorticity was analysed, even for com- pressible fluids. The important results of these works for this study can be summarised as follows: Viscous forces are connected with the generation of vorticity in fluid flow in the end-wall boundary layers. This vortic- ity is then responsible for the generation of secondary vorticity in the curved channels and in their corners. The more curved the channel, the higher the centrifu- gal forces acting in the fluid, and therefore, stronger secondary vorticity is expected. Another parameter is the Reynolds number that causes vortex diffusion, and consequently different velocity gradients. Although the theoretical description is powerful, the full picture of the vortices in blade cascades is beyond the capability of theoretical predictions. The separa- tion of the inlet boundary layer in front of the cascade was observed in [11] as a place where the pressure at the end wall reached its maximal value. In this place, the so-called horseshoe vortex formed. Based on this experimental data, Langston in [12] formulated his secondary flow model, which was then modified several times, see e.g. [13], where the wrapping of the vortices was observed. Later, in [14], a more detailed model de- veloped based on smoke visualisation experiments was presented. Several unknown vortices were found, and their interactions were studied in the cascade. This research resulted in defining the newest secondary flow model (according to the author’s knowledge). The flow through a linear blade cascade is affected by many variables. The ideal case, when the blade worked under design conditions, was investigated by [15] and by [16]. The main goal of these works was to investigate the effect of the inlet boundary layer on the development of the secondary flow at the cascade outlet at different distances from the trailing edges of the blades. It has been shown that with increasing distance from the trailing edges, vortical structures migrate from the end wall towards the blade midspan. The effect of the inlet boundary layer on the secondary flow was as follows: With a thicker inlet boundary layer, stronger vortical structures are generated, and as a consequence, the kinetic energy dissipation at the cascade outlet is larger. The effects of the blade geometry and the state of the inlet boundary layer were investigated in [17]. This topic was studied in [18] from the unsteady point of view, where the evolution of Reynolds stress at the cascade outlet was measured at several positions 350 https://doi.org/10.14311/AP.2024.64.0350 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en vol. 64 no. 4/2024 Entropy production in a linear blade cascade and the mixing of wake with vortical structures was described. The effect of the inlet flow angle was investigated in [19–21], where the increasing inlet flow angle re- sulted in stronger vortical structures and their shifting towards the blade mid-span due to the larger centrifu- gal forces. Variation of Reynolds number and its impact on the flow were explored as well in [19, 21]. It was shown in [18] that with increasing Mach num- ber, the secondary losses decreased significantly. This can be explained by the increasing ratio of inertial to centrifugal forces in the cascade, where the inertial forces acted against the generation of vortical struc- tures. Moreover, the interaction between the vortical structures and the shock waves affected the results in the cases where the wave was present. The comprehensive review of the topic was then published in [22] and more recently the newer findings were summarised in [23]. Note that the theoretical works focused on the mech- anisms responsible for the generation of the vortical structures, and experimental works cited above fo- cused on the evaluation of the dissipation of kinetic energy in the cascades. Although there are some pa- pers where the entropy production in the cascade has been mentioned, see e.g. [24, 25], a comprehensive study of the entropy production due to the vortical structures in the blade cascade has, to the best of the authors’ knowledge, not yet been carried out. There- fore, this work aims to perform this type of research to fill such a gap in the present literature. 2. Experimental apparatus, setup, and methods 2.1. Apparatus 2.1.1. Wind tunnel The experiments were conducted in the VZLU Lab- oratory of High-Speed Aerodynamics, using a low- pressure, closed-loop wind tunnel (WT). The airflow was driven by a twelve-stage radial compressor, pro- pelled by a 1.3 MW electric DC motor. The Mach number and Reynolds number can be set indepen- dently. Mach number can be changed by the rota- tional speed of the compressor, while the Reynolds number can be set by the change of the pressure in the tunnel by a set of vacuum pumps. To reduce air humidity, a condensation dryer was positioned behind the compressor, followed by a settling chamber in front of the test section. The latter was equipped with a screen to minimise fluctuation components of the velocity. At the test section inlet, a pair of semi-shaped nozzles was placed in front of the cascade, determining the inlet flow angle. The cascade itself was mounted between two acrylic windows within the WT. The test section’s width was 100 mm. Two tailboards were positioned behind the first and the last blade of the (a). Preston probe used for the measurement of the inlet flow field. (b). Pyramid five-hole pressure probe. Figure 1. Pressure probes. cascade. The pressure in the WT was regulated by a set of vacuum pumps located at the cascade outlet. 2.1.2. Pressure probes The inlet flow field was measured using the Preston probe positioned 30 mm upstream of the cascade, with the outer diameter of the pressure tap dp = 0.4 mm and a ratio of inner to outer diameter of the probe d/dp = 0.5. The probe was designed to measure the entire inlet flow field and was equipped with two identical pressure taps, as shown in Figure 1a. The outlet flow field was measured by the pyramid five-hole pressure probe positioned 10 mm behind the cascade. The probe was manufactured from the tubes of the same diameter as the Preston tube, i.e. dp = 0.4 with a ratio of d/dp = 0.5. The geometry of the probe is shown in Figure 1b. 2.1.3. Blade cascade Two cascade configurations defined by different pitch to chord ratios (t/c = 0.6 and 0.9), were investigated. These pitches modelled both the hub and tip sections of the real turbine wheel of the high-pressure part of the machine. The cascade schematic, including the definition of a coordinate system and the entire control volume, is shown in Figure 2. The cascades were assembled from prismatic blades with the same geometry for both configurations. Individual blades were assembled between two acrylic WT windows. The blade chord was c = 50 mm, the axial chord was cax = 36 mm, and the blade height was the same as the width of the WT test section, i.e. h = 100 mm. The thickness of the blade trailing edges was ε = 1 mm. The periodicity of the flow was ensured by a large number of blades in cascades (11 for t/c = 0.9 and 14 for t/c = 0.6) and by the presence of tailboards. 351 Erik Flídr Acta Polytechnica Figure 2. Control volume, with the cascade coordi- nate system definition. 2.1.4. Data acquisition and measurement uncertainty Individual pressure signals were measured by the dif- ferential pressure transducers Druck with a reading ac- curacy of 0.1 % (rdg). These analogue voltage signals were then conditioned by the DEWETRON system and sampled by the A/D card (National Instruments PCI-6259 A/D card: 16-Bit, 1 MS s−1 (Multichannel), 1.25 MS s−1 (1-Channel), 32 Analogue Inputs). One measured point takes 3 seconds with a sampling rate of 1000 Hz. The low-pass filter of 100 Hz was used. The obtained data were then averaged. The barometric pressure was measured by the Druck DPI 145 digital pressure transducer with the precision of pb = (pb ± 15) Pa. The stagnation temperature, as well as air humidity, was measured at the settling chamber by means of Sensorika Humistar HTP-1 hygrometer with accuracy T = T ± 0.3 K and RH = RH ± 2 %. Uncertainties of measured quantities were evaluated with respect to the measurement chain and according to [26]. The outlet isentropic Mach number was set with the uncertainty of M2,is = 0.40±0.01. The outlet isentropic Reynolds number was set with the uncer- tainty of Re2,is = (4.500 ± 0.225)×105. Local entropy production was then evaluated with the uncertainty of p = (132.134 ± 21.046) J (K s m2)−1. Note, that all of these values represent the worst cases. Uncertain- ties were based on 95 % confidence level (±2 standard deviation). 2.2. Setup 2.2.1. Inlet flow field measurement The inlet flow fields were measured for constant in- let flow angle α1 = 5° because the inlet bound- ary layers were insensitive to the variation of this parameter. The measurements were performed for four levels of isentropic Reynolds number (Reis = (0.80, 1.25, 2.50 and 4.50) × 105) and for a constant value of outlet isentropic Mach number M2,is = 0.4. The inlet boundary layers were then measured at three positions z (at the blade channel centre and in front of the leading edges of the neighboring blades) to provide a better understanding of the inlet flow field. These measurements were subsequently averaged. 2.2.2. Outlet flow field measurement The outlet flow fields were measured for the same val- ues of isentropic Reynolds number and Mach number as in the case of the inlet flow fields. The effect of the inlet flow angle was studied for α1 = −20°, 5° and 30°, with nominal inlet flow angle α1 = 5°. 2.3. Used methods The air was considered a perfect gas, and heat transfer was not taken into account; thus, an adiabatic flow approach was used to evaluate the measured data. 2.3.1. Measurements in the Shear Flow and the Boundary Layers Measurements with the pressure probes in shear flows and close to the wall were corrected for the virtual shift of the probe position and blockage effects. The correction for the probe positions, originally proposed by [27] and later modified by [28], was extended in a subsequent work by [29]. This final correction was employed in the following form: ∆z = ϵdp = 0.15 tanh ( 4 √ β ) − ϵw, (1) where ϵw = A ( z dp − 3 ) + B ( z dp − 3 ) [ 0.15 tanh ( 4 √ β )] , (2) and where: β = dp 2u du dz . (3) Here, u is the velocity and A = 0.174 and B = −1.25 are constants. Near wall correction was used up to y/δ = 3, as was suggested by [29]. 2.3.2. Outlet flow field evaluation The velocity vector field was obtained from the mea- sured pressures thanks to the calibration of the five- hole pressure probe. The y components of the vorticity vector were then directly calculated from the velocity as: ωy = u (i+1),j x − u (i−1),j x z(i+1),j − z(i−1),j − u i,(j+1) z − u i,(j−1) z xi,(j+1) − xi,(j−1) , (4) where ux and uz are the velocity components in the x and z direction, respectively. The rest of the com- ponents of the vorticity vector were calculated from Crocco’s theorem written in the form: ϵijkujωk = 1 ϱ ∂ip0, (5) 352 vol. 64 no. 4/2024 Entropy production in a linear blade cascade t/c Re2,is × 10−5 Rey × 10−5 δ∗ θ H1,2[mm] [mm] 0.6 4.50 13.2 1.3 0.5 2.43 2.50 7.4 1.0 0.4 2.32 1.25 3.5 0.7 0.5 1.35 0.80 2.6 0.5 0.4 1.42 0.9 4.50 14.8 1.2 0.5 2.51 2.50 8.3 1.0 0.4 2.48 1.25 4.1 0.8 0.6 1.32 0.80 2.7 0.7 0.5 1.43 Table 1. Inlet boundary layers parameters where ϵijk is the Levi-Civita alternating tensor and p0 is the stagnation pressure. The local distribution of the entropy production is obtained as a difference between the entropy flux through the inlet and outlet control volume boundaries: p = Jout − Jin = ϱ2u2ys2 − ϱ1u1ys1, (6) where s stands for the entropy and ϱ is the fluid density. The density upstream of the cascade was considered constant, as the flow Mach number was lower than M < 0.09. However, at the cascade outlet, the flow Mach number was M2,is = 0.4. Therefore, the density distribution was calculated at individual measurement points using the perfect gas law and known static pressure and temperature. Note, that the fluxes across the boundaries ∂A and ∂B give no contribution to the entropy production thanks to the periodic boundary conditions. The averaged outlet flow field was evaluated based on the data reduction method briefly described in [21]. The averaged entropy productions in the individual z positions were evaluated as: ⟨p⟩ = ⟨Jout⟩ − Jin = ⟨ϱ2⟩ 〈 u2y 〉 ⟨s2⟩ − ϱ1u1ys1. (7) Supposing the superposition of the two-dimensional flow at the cascade mid-span (z = h/2) and the end- wall flows, the entropy production caused by these end-wall flows was obtained as: ⟨pew⟩z = ⟨p⟩z ⟨p⟩z= h 2 . (8) The total entropy production in the outlet flow field was then obtained by integration over the entire cascade outlet: P = h 2t h/2∫ 0 2t∫ 0 pdxdz, (9) where t stands for the blade pitch. The overall entropy production in the end-wall region was calculated as: Pnw = P − Pms. (10) Figure 3. Normalised Local distribution of the en- tropy production for t/c = 0.9. Figure 4. Integral entropy production for both stud- ied cascades. 3. Results and discussion 3.1. Inlet flow field The inlet flow field was investigated in detail in [30]. It was found that the inlet boundary layers behaved as boundary layers evolved on the flat plate and were laminar for Re2,is = (0.8 and 1.2) × 105 and turbulent for Re2,is = (2.5 and 4.5) × 105. The parameters of the inlet boundary layers are summarised in Table 1. Normalised local distribution of the entropy produc- tion across the WT test section for t/c = 0.9 is shown in Figure 3 and normalised integral values of the en- tropy productions for all studied cases are then given in Figure 4. The normalisation was performed using the maximal value of entropy production obtained from all tested cases. As expected, an increase in Reynolds number led to a higher entropy production in the inlet bound- ary layers, attributed to the growing boundary layer 353 Erik Flídr Acta Polytechnica Figure 5. Pressure coefficient distribution for t/c = 0.6 and α1 = 5°. thickness. Moreover, in the turbulent boundary layers, higher velocity gradients were observed in this region. The dependency of the integral entropy production on the Reynolds number Rey was approximated by the second order polynomial function with coefficients: a = 0.3640, b = 0.0993, and c = −0.0038. These data suggest a potential universal relationship between the entropy production in the boundary layer on a flat plate and Reynolds number Rey, a topic to be inves- tigated in future studies. This basic evaluation of the inlet flow field gave the inlet boundary condition for the calculation of the balance Equation (6). 3.2. Blade pressure distribution Figure 5 illustrates an example of the pressure coeffi- cient distribution on the blade surfaces for t/c = 0.6 with the nominal inlet flow angle. Flow separation be- came evident from s/c ≈ 0.65 up to the trailing edge of the blade. While this phenomenon was consistently observed for all tested inlet flow angles of the cascade with a pitch-to-chord ratio t/c = 0.6, it was not found in the other tested cascade with t/c = 0.9. This result will be further discussed in Section 3.3. The distribution of the pressure coefficient on the blade surface for t/c = 0.9 is depicted in Figure 6. Surprisingly, no separation occurred in this case, de- spite the larger diffusion factor for this pitch-to-chord ratio. 3.3. Outlet flow field 3.3.1. Local entropy production To illustrate the local distribution of entropy pro- duction at the cascade outlet for the tested case t/c = 0.9, inlet flow angle α1 = 30°, and Reynolds number Re2,is = 2.5 × 105, refer to Figure 7. The contour lines depict the distribution of the stream- wise vorticity, while the colours illustrate the nor- Figure 6. Pressure coefficient distribution for t/c = 0.9 and α1 = 5°. Figure 7. Distribution of the normalised local en- tropy production at the cascade outlet with con- tours of the vorticity for t/c = 0.9, α1 = 30°, and Re2,is = 2.5 × 105. malised local entropy production1. Individual vor- tices were identified and highlighted behind one blade. Wakes are evident at the cascade midspan, where the entropy generation is higher. However, the majority of the entropy is generated in the end- wall region between the individual vortices. This 1The highest value of local entropy production from all tested cases was taken as the normalisation factor. Since the presented case did not reach this extreme, the value p = 1 is not included in Figure 7. 354 vol. 64 no. 4/2024 Entropy production in a linear blade cascade observation is attributed to the highest velocity gradients in this region, as evident from the en- tropy production equation (the derivation is pro- vided in [31] or, in general curvilinear coordinates, in [32]): p = −∂ip + λ (∂iui)2 + 2µ∂iuj∂jui, (11) where the pressure gradients as well as the com- pressibility effects represented by the velocity diver- gence were negligible compared to velocity gradi- ents. 3.3.2. Averaged entropy production caused by the end-wall flows Averaged entropy productions for different inlet flow angles and the cascade configuration t/c = 0.9 are presented in Figures 8–10. These values were nor- malised by the entropy production at the cascade mid-span to assess the impact of the end-wall flows. It is important to note that, in the case of α1 = −20°, entropy production peaks were not identified due to their occurrence in regions where the probe was unable to perform measurements. The increase in the inlet flow angle resulted in the shift of the entropy production peak from the end-wall region towards the blade midspan, from the precisely unknown position for α1 = −20° up to z/h ≈ 0.12 for α1 = 30°. This is caused by the larger centrifugal forces acting in the cascade due to the higher flow turn- ing. This larger force generates the higher secondary vorticity in the blade channel, as was theoretically shown by [4], which moves with the vortices. In ad- dition, there is also a clear increase in the entropy production with increasing α1. The reason for this observation is the same as for the peak shift, i.e., the higher centrifugal forces that are responsible for the generation of the stronger vortices. Focusing on the evolution with Reynolds number shows that with increasing Re2,is, the entropy produc- tion grows as well. This is caused by the topology of the vortical structures. The higher inertial forces were responsible for smaller vortices diffusion, there- fore, larger velocity gradients occurred between the vortices, which is in agreement with the theoretical prediction of Equation (11). 3.3.3. Integral entropy production in the blade cascade Figure 11 shows the normalised integral entropy pro- ductions for both studied cases as a function of Reynolds number. The maximal value of the entropy production from all cases was chosen to normalise the evaluated data. It can be concluded, that the maximum entropy was observed for the case with t/c = 0.6, α1 = 30°, and Re2,is = 4.5 × 105. The occurrence of maximum entropy in this case was ex- pected. The small differences between individual cases on this pitch-to-chord ratio t/c = 0.6 were interesting and not expected. These little variances were caused Figure 8. Averaged normalised entropy production in the end-wall region for t/c = 0.9 and α1 = −20°. Figure 9. Averaged normalised entropy production in the end-wall region for t/c = 0.9 and α1 = 5°. Figure 10. Averaged normalised entropy production in the end-wall region for t/c = 0.9 and α1 = 30°. 355 Erik Flídr Acta Polytechnica Figure 11. Integral entropy production for both tested cases plotted as a function of Reynolds num- ber. Cascade t/c a b × 105 0.6 0.114 0.186 0.112 0.197 0.109 0.197 0.9 0.069 0.093 0.090 0.100 0.095 0.137 Table 2. Constants for approximation of integral entropy production in linear blade cascade. by the boundary layer separation on the suction sur- faces for all studied inlet flow angles. The majority of the entropy was generated in the separation region, overshadowing the effects of vortices in the end wall region. Significant variations between individual inlet flow angles were observed in the case of t/c = 0.9, where entropy production increases with increasing α1. En- tropy production for this case was considerably lower compared to the case of t/c = 0.6. In general, a linear dependency between the entropy production and this similarity criterion exists within the studied range of Reynolds numbers. The correla- tion parameters for the linear fits are summarised in Table 2. The normalised entropy production caused by vortical structures in the blade cascades was eval- uated using Equation (10). Specifically, the mid-span value of the overall entropy production was subtracted (a). Normalised near-wall entropy production for t/c = 0.6. (b). Normalised near-wall entropy production for t/c = 0.9. Figure 12. Normalised near-wall entropy production. and then divided by the maximal entropy production from all tested cases. Results of this approach are plot- ted in Figures 12a and 12b, respectively. First-order polynomial functions were used to approximate the data for all cases under investigation. The coefficients obtained from these approximations are summarided in Table 3. In both cases, the entropy production associated with vortical structures increased similarly with the Reynolds number. In the case of the cascade configuration with t/c = 0.6, the effect of the inlet flow angle on the entropy production was influenced by flow separation, as is evident from the points in Figure 12a. In this case, the data could not be approximated as effectively (using a linear approximation) compared to the other tested cascades, primarily due to the frequently mentioned flow separation. The interaction of the vortical structures with this separation caused that the assumption about the superposition of the 2D flow at the blade mid-span and the end wall flow was not quite right. 356 vol. 64 no. 4/2024 Entropy production in a linear blade cascade Cascade t/c a b 0.6 −0.006 0.021 −0.0398 0.0437 −0.0178 0.0321 0.9 0.0111 0.0033 0.0106 0.0181 0.0104 0.0372 Table 3. Coefficients for approximation of near-wall entropy production in linear blade cascade. 4. Conclusion The experimental research on entropy production in a linear blade cascade was conducted for two dif- ferent pitch-to-chord ratios under a constant out- let isentropic Mach number of 0.4. The study involved four different levels of Reynolds number (0.8, 1.2, 2.5, and 4.5) × 105 and three inlet flow an- gles: −20°, 5°, and 30°. The inlet entropy flux was assessed as the boundary condition at the inlet. It was demonstrated that a cor- relation exists between the entropy production in the boundary layer and the Reynolds number, modelled by a second-order polynomial function. The local distribution of parameters in the outlet flow field revealed the relationship between the po- sitions of the vortices and entropy production. The majority of entropy production took place between the vortices, where the velocity gradients were the largest. Increasing the inlet flow angle intensified the vor- tical structures and caused their shift from the end wall towards the blade mid-span, driven by the larger centrifugal forces resulting from the higher flow turn- ing. While the variation in Reynolds number did not significantly impact the distribution of vortical struc- tures and entropy production, an increase in Reynolds number led to the magnification of entropy produc- tion. This effect resulted from less diffused vortical structures, leading to larger velocity gradients within the individual vortices and between them. The pitch-to-chord ratio affected both the distribu- tion and strength of the vortical structures, as well as the amount of entropy production. For t/c = 0.6, the vortices were more shifted toward the blade mid-span and exhibited greater strength due to the larger cen- trifugal forces, resulting from the narrower channel. Finally, correlations were established between the overall entropy productions in the outlet flow field, as well as the relationships between the entropy produc- tion caused by the vortical structures and Reynolds number. These correlations take the form of first-order polynomial functions. Future work should focus on investigating the effects of flow separation on the suction side of the blade and its impact on the data evaluation procedure. It has been demonstrated that in cases where the separation did not occur (t/c = 0.9), the assumption of superpo- sition of the 2D flow at the blade midspan and the vortical motion in the end wall region is valid. How- ever, in cases where separation occurred (t/c = 0.6), this approach was not entirely appropriate for the evaluation. Therefore, a more suitable method should be developed to ensure an accurate data evaluation. List of symbols A, B empirical constants c blade chord [mm] cax axial blade chord [mm] cp pressure coefficient d probe diameter h blade height [mm] H1,2 shape parameter J flux through the boundary of the control volume M Mach number p pressure p local entropy production P integral entropy production Re Reynolds number t cascade pitch [mm] u flow velocity [m s−1] V control volume [m3] x, y, z Cartesian coordinates [m] α inlet flow angle [°] δ∗ displacement boundary layer thickness [mm] ε trailing edge thickness [mm] θ momentum boundary layer thickness [mm] ⟨•⟩ averaged parameter rdg reading value fs full scale Subscripts: 1 cascade inlet 2 cascade outlet b barometric ew cascade end-wall is isentropic ms mid-span nw end-wall x, y, z in the circumferential, axial, and radial directions Acknowledgements The work was not supported by any project, only by the author’s curiosity. Declaration: The spell check for this paper was conducted using Chat- GPT 3.5. References [1] C. Yogananda, A. 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Acta Polytechnica 63(2):103–110, 2023. https://doi.org/10.14311/AP.2023.63.0103 359 https://doi.org/10.14311/TPFM.2018.011 https://doi.org/10.1007/s11012-015-0284-z https://doi.org/10.14311/AP.2023.63.0103 Acta Polytechnica 64(4):350–359, 2024 1 Introduction 2 Experimental apparatus, setup, and methods 2.1 Apparatus 2.1.1 Wind tunnel 2.1.2 Pressure probes 2.1.3 Blade cascade 2.1.4 Data acquisition and measurement uncertainty 2.2 Setup 2.2.1 Inlet flow field measurement 2.2.2 Outlet flow field measurement 2.3 Used methods 2.3.1 Measurements in the Shear Flow and the Boundary Layers 2.3.2 Outlet flow field evaluation 3 Results and discussion 3.1 Inlet flow field 3.2 Blade pressure distribution 3.3 Outlet flow field 3.3.1 Local entropy production 3.3.2 Averaged entropy production caused by the end-wall flows 3.3.3 Integral entropy production in the blade cascade 4 Conclusion List of symbols Acknowledgements References