Optimisation of a Low-Speed Wind Tunnel. Analysis and Redesign of Corner Vanes.

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(1)Optimisation of a Low-Speed Wind Tunnel. Analysis and Redesign of Corner Vanes.. May 2014. Luis López de Vega Francisco Javier Maldonado Fernández Pedro Muñoz Botas.

(2) MAAJ. Contents I.. Introduction. 7. II. Initial Study and Tests on the Wind Tunnel 1. General notes about wind tunnels 1.1. Introduction to LSWT . . . . 1.2. Analysis of LSWT parts . . . 1.2.1. Test Chamber . . . . . 1.2.2. Contraction . . . . . . 1.2.3. Settling Chamber . . . 1.2.4. Diffusers . . . . . . . . 1.2.5. Corners . . . . . . . . 1.2.6. Power Plant . . . . . . 1.3. Pressure Measurement . . . .. and pressure measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2. Sources of Uncertainty in Pressure Measurement 2.1. Main Sources of Uncertainty . . . . . . . . . . 2.1.1. Dirt in the Drill Holes . . . . . . . . . 2.1.2. Probe Situation . . . . . . . . . . . . . 2.1.3. Scanivalve Error . . . . . . . . . . . . 3. Test 3.1. 3.2. 3.3.. With Flaps and Mesh Calibration Process . . . . . Statistical Analysis . . . . . Measurement Process in the 3.3.1. Wind Tunnel . . . . 3.3.2. Contraction . . . . .. 9. . . . . . . . . . . . . . . . . Wind Tunnel . . . . . . . . . . . . . . . .. . . . . .. . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. 10 10 10 10 11 11 11 12 12 12. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. 14 14 14 16 16. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. 18 18 19 21 21 22. 4. Test Without Flap and Mesh 24 4.1. Total Pressure Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5. In Detail Study From the Contraction to Corner 1 27 5.1. Test without Flaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.2. Test with Flaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 2. ©UPM.

(3) MAAJ III. Analysis of the Influence of Corner 1 on the Total Pressure Loss 6. Pressure Loss in Corner 1. Estimation Methods 6.1. Boundary Layer Effects . . . . . . . . . . . . . . . . . . . . . . . 6.1.1. Boundary Layer Thickness . . . . . . . . . . . . . . . . . 6.1.2. Boundary Layer Integral Equation . . . . . . . . . . . . . 6.2. Application of Boundary Layer Theory to Compressor Blades and Cascade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3. Airfoil Cascade Analysis . . . . . . . . . . . . . . . . . . . . . . . 6.4. Secondary Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.2. Wall Effects in Rectangular Ducts . . . . . . . . . . . . . 6.5. Diffuser Performance . . . . . . . . . . . . . . . . . . . . . . . . . 6.6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 29. 30 . . . . . 30 . . . . . 30 . . . . . 31 Airfoil . . . . . 32 . . . . . 33 . . . . . 35 . . . . . 35 . . . . . 35 . . . . . 37 . . . . . 38. 7. Analysis of the influence of the guide vane cascade in Corner 1 total pressure loss 39 7.1. Study of the parameters of a guide vane cascade . . . . . . . . . . . . . . 41 7.2. Total pressure loss in guide vane cascade . . . . . . . . . . . . . . . . . . . 46. IV. Design of an easily constructable optimised guide vane. 50. 8. Airfoil Selection 51 8.1. Analysis of Flow Turning with a Parafoil cascade . . . . . . . . . . . . . . 54 9. Design and Manufacturing Process 9.1. PARAFOIL . . . . . . . . . . . . . . . . 9.1.1. Introduction . . . . . . . . . . . 9.1.2. Software inputs & outputs . . . . 9.1.2.1. Blade.parafoil . . . . . 9.1.2.2. Ises.parafoil . . . . . . . 9.1.3. Internal running of the code . . . 9.2. Manufacturing Process . . . . . . . . . . 9.2.1. Materials . . . . . . . . . . . . . 9.2.2. Process . . . . . . . . . . . . . . 9.2.2.1. Manufacturing Process 9.2.2.2. Corner Assembly . . . . 9.2.3. Conclusion and assessment of the. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Manufacturing Process. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. 57 57 57 58 58 58 60 63 64 64 64 66 68. V. Possible improvements for the proposed guide vane. 69. 10.Introduction. 70. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 3. ©UPM.

(4) MAAJ 11.Parafoil improvement. 71. 12.Optimization process. 73. 13.Improvements from the ¼-circle airfoil. 75. VI. Wind tunnel tests with improved corner 1 and chamfers. 77. 14.Introduction. 78. 15.Tests in Corner 1. 79. 16.General tests. 81. 17.Conclusions. 84. VII.Conclusions and Final Remarks. 86. VIII.APPENDIX. 89. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 4. ©UPM.

(5) MAAJ. List of Figures 1.3.1.Typical Wind Tunnel Setup. . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1.1.Probe and wall section. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.1.1.Average of the calibration measures for different number & 10 tests). . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2.Average of the calibration tests. . . . . . . . . . . . . . . 3.3.1.Pressure coefficient at the exit of every element. . . . . . 3.3.2.Pressure coefficient on the top view and the front view.. of tests (4, 6, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 8 . . . .. . . . .. 18 19 22 23. 4.1.1.Pressure coefficients and total pressure coefficient for a meshless and flapless wind tunnel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.1.2.Accumulated Cp with and without flaps. . . . . . . . . . . . . . . . . . . . 26 5.1.1.In detail study from the contraction until corner 1 without flaps. . . . . . 27 5.2.1.In detail study from the contraction until corner 1 with flaps. . . . . . . . 28 6.1.1.Boundary layer on a flat plate. . . . . 6.3.1.Airfoil Cascade Parameters. . . . . . . 6.4.1.Secondary Flow in Rectangular Ducts. 6.4.2.Wind Tunnel Section Modification. . .. . . . .. . . . .. 30 34 36 37. 7.1.1.Computer modelling for the guide vane cascade. . . . . . . . . . 7.1.2.Camber influence in flow deflection. . . . . . . . . . . . . . . . . . 7.1.3.Distance between airfoils effect. . . . . . . . . . . . . . . . . . . . 7.1.4.Maximum thickness vs Camber. . . . . . . . . . . . . . . . . . . . 7.1.5.90º-flow-deflection airfoil: thickness and camber distribution, and 7.2.1. 14 -circle curved plate guide vane. . . . . . . . . . . . . . . . . . . 7.2.2.101º curved plate guide vane. . . . . . . . . . . . . . . . . . . . . 7.2.3. 14 -circle curved plates with 30%-chord flap. . . . . . . . . . . . .. . . . . . . . . . . . . . . . . airfoil. . . . . . . . . . . . .. . . . . . . . .. 42 43 44 45 46 47 48 49. 8.0.1.Result for elliptical and circumferential upper side. . . . . . 8.0.2.Performance analysis of parabolic airfoil and curved plate. . 8.0.3.Analysis of LE Radius Effects (12.5% Maximum Thickness). 8.0.4.Analysis of Maximum Thickness Effects (0.5% LE Radius). 8.0.5.Initial Angle Effect in Pressure Losses. . . . . . . . . . . . . 8.1.1.Relation between Lift Force and Flow Turning. . . . . . . . 8.1.2.β vs Flow Turning. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . .. . . . . . . .. 51 51 52 53 54 55 56. Aero-MAAJ. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 5. . . . .. . . . .. . . . . . . .. . . . .. . . . . . . .. . . . .. . . . . . . .. . . . .. . . . .. . . . . . . .. . . . .. . . . . . . .. . . . . . . .. ©UPM.

(6) MAAJ 9.1.1.PARAFOIL Vane, Thickness and Camber Distribution. 9.2.1.Cuts on the PVC sheet. . . . . . . . . . . . . . . . . . . 9.2.2.Distances for supports placement. . . . . . . . . . . . . . 9.2.3.Section of a manufactured upper side. . . . . . . . . . . 9.2.4.Coincidence between both leading edges. . . . . . . . . . 9.2.5.Section of a fully assembled profile. . . . . . . . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. 63 65 66 66 67 68. 10.0.1. Parafoil geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 11.0.1. cp curve of Parafoil. The blue line represents the upper side and the red line the lower side. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 12.0.1. Results for modified Parafoil. . . . . . . . . . . . . . . . . . . . . . . . . . 74 12.0.2. Best specimen geometry vs Parafoil geometry. . . . . . . . . . . . . . . . . 74 13.0.1. Airfoil proposed in KTH article. . . . . . . . . . . . . . . . . . . . . . . . 76 16.0.1. Total pressure loss in each element measured by parameter ξ. . . . . . . . 82 16.0.2. Total cp curve in the wind tunnel. . . . . . . . . . . . . . . . . . . . . . . 83 17.0.1. Total pressure loss coefficient. . . . . . . . . . . . . . . . . . . . . . . . . . 84 17.0.2. Improvement percentage in total pressure loss with Parafoil cascade. . . . 85 17.0.3. Total pressure increment in power plant vs Test chamber velocity. The intersection between the fan operation curve and and wind tunnel total pressure loss curve gives the velocity in test chamber, which clearly depends on the fan efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . 88. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 6. ©UPM.

(7) MAAJ. Part I.. Introduction. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 7. ©UPM.

(8) MAAJ This paper includes the experimental study, analysis, redesign and subsequent test of the parts of a closed circuit, low speed wind tunnel which are relevant in terms of total pressure loss. The objective is to lower the energy consumption of this system for given conditions in test chamber, so as to reduce the operational costs. In order to achieve this objective, several tasks were performed as the text shows in its different parts. For these tasks, the ETSIAE wind tunnel was used, although the results of this work can be extrapolated to any wind tunnel with the same characteristics. Part II presents a theoretical previous study of the general running of a closed circuit, low speed wind tunnel, as well as the followed procedure to conduct experimental tests for obtaining the total pressure loss in its parts. Results from these tests and their analysis are included in this part. In part III, the analysis of the influence of corner 1 on the pressure loss takes place. As it is said in this part, corner 1 has great importance in the total pressure loss of the wind tunnel. Therefore, it is the first part that should be modified in order to improve the performances of the wind tunnel. During part IV, an optimised guide vane is designed in order to reduce the pressure loss in corner 1 of the wind tunnel. Software MISES is used to achieve this goal by means of selecting the optimum guide vane. In order to introduce the new guide vane in wind tunnels with affordable costs, the easily constructable criterion is kept during design. For this reason, the guide vane will consist of simple aerodynamic contours. Part V includes some possible improvements for the proposed guide vane, in order to evaluate if there is room for improvement in its design. Finally, part VI includes the tests that were conducted in the wind tunnel with the new guide vane cascade and the analysis of their results, in order to asses whether the proposed design fulfills the requirement of lowering the total pressure loss in the wind tunnel. Part VII gathers the main ideas resulting from the whole work.. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 8. ©UPM.

(9) MAAJ. Part II.. Initial Study and Tests on the Wind Tunnel. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 9. ©UPM.

(10) MAAJ. 1. General notes about wind tunnels and pressure measurement This part describes the process of instrumentation, measurement, and result analysis conducted on a low speed wind tunnel. The objective of this process is to determine the global pressure loss, as well as to analyse the contribution of the different elements to this loss in order to improve the performances of the wind tunnel. To begin with, a brief explanation of closed-circuit Low Speed Wind Tunnels (LSWT) is detailed next.. 1.1. Introduction to LSWT Wind Tunnels are devices which allows to study the interaction between objects and the flow around them. They generate a flow at a desired speed to study the phenomena that take place when this flow passes around the studied object. The main requirements of Low Speed Wind Tunnels are low turbulence levels and flow uniformity in test chamber, along with acceptable economic costs in operation. As it is shown in picture 1.3.1, this type of wind tunnels has 6 main parts: • Diffusers • Corners • Settling Chamber • Contraction • Power Plant • Test Chamber The most important parts in LSWT are Settling Chamber, Contraction, Corner 1 and Diffuser 1, due to their influence in flow uniformity and turbulence levels. The characteristics of every part of a LSWT are analyzed in the next section.. 1.2. Analysis of LSWT parts 1.2.1. Test Chamber It is the part of the wind tunnel in which the model is tested. Its size defines the overall wind tunnel dimension. This dimension and the maximum operating speed define the model’s size, along with the operational Reynolds number.. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 10. ©UPM.

(11) MAAJ This size use to be about 10% of the total test chamber size (in terms of chamber section), in order to avoid non linear corrections. Because of operational issues, it is also important that the static pressure coincides with the ambient pressure. Then, it is advisable to open the test chamber before diffuser 1 about 1% of the whole test chamber length. According to Idel’Cik (1969)[11], the pressure loss coefficient, related to the dynamic pressure in the test section is given by the expression: λ·L (1.2.1) DH where L is the length of the test chamber, DH the hydraulic diameter and λ a coefficient given by the expression: ζ=. λ = 1/(1.8·log(Re) − 1.64)2. (1.2.2). where Re is the Reynolds number based on the hydraulic diameter.. 1.2.2. Contraction It is the most critical part of a wind tunnel, due to its great influence in flow quality reducing axial and transversal fluctuations. It is defined by the parameter N (contraction ratio), which represents the quotient between the initial and final area of this element. As N increases, better flow quality is obtained in the test chamber. According to Idel´Cik (1969)[11], the pressure loss coefficient related to the dynamic pressure in the narrow section, is given by the expression: . ζ=. λ 1 · 1− 2 16·sin(α/2) N . . . . +. λ 1 · 1− 2 16·sin(β/2) N . . . (1.2.3). where λ is defined as: λ = 1/(1.8·log(Re) − 1.64)2. (1.2.4). 1.2.3. Settling Chamber In case of low quality flow requirements, it consists on a simple straight section. If a greater flow quality and lower levels of turbulence are required, honeycombs or screens can be introduced. Honeycombs are used to reduce cross turbulence while screens are used to reduce axial turbulence. These elements increase the total pressure loss in the wind tunnel that, for high N values, can be considered insignificant.. 1.2.4. Diffusers The main function of diffusers is to recover the static pressure in order to higher the wind tunnel efficiency. It is very important to avoid detachment on them, due to the adverse pressure gradient.. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 11. ©UPM.

(12) MAAJ Thus, in case of detachment in diffuser 1, pressure irregularities would go downstream to the test chamber. This could lead to velocity and pressure non-uniformities there. Due to this fact, the semi-opening diffuser angle has to be limited. It has been proven that semi-opening angles smaller than 3.5º do not lead to detachment. Besides, the lower dynamic pressure at corner 1 entrance, the lower pressure losses at it.. 1.2.5. Corners Their main function is to turn the flow. It is important to introduce turning vanes or guide vanes on them in order to reduce pressure losses and improve the flow quality. They will be analysed in deep during this report by studying corner 1.. 1.2.6. Power Plant The main objective of the power plant is to maintain the flow in the test chamber at constant speed, compensating pressure losses and dissipation. The parameters that . specify it are the pressure increment ∆p, the volumetric flow Q, and the power W . Once the test chamber cross-section surface Stc , and the desired operating speed V , are fixed, and the total pressure loss coefficient ζ has been calculated. These parameters are: 1 ∆p = ρV 2 ζ 2. (1.2.5). Q = V ·ST C. (1.2.6). .. W = ∆p·Q·η. (1.2.7). 1.3. Pressure Measurement For the instrumentation process, probes are placed in different sections of interest. These probes are connected to the Scanivalve pressure measurement device by silicon tubes. Received data is processed by software RadLink which is provided by the manufacturer. In order to study the individual contribution to the pressure loss of each element, several tests with different tunnel configurations were conducted. Firstly, preliminary tests were conducted in order to check the correct setup of the instruments, which are the Scanivalve device, the probes and software Radlink. These instruments give the value of manometric static pressure in every probe placed in the wind tunnel. Once this first step is finished, calibrations and tests take place. The manometric static pressure measurements are then turned dimensionless with respect to dynamic pressure in the test chamber. The procedure remains the same for the different configurations.. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 12. ©UPM.

(13) MAAJ. The pattern of the probes remains the same for the whole tunnel. () stands for rear probe. Figure 1.3.1.: Typical Wind Tunnel Setup.. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 13. ©UPM.

(14) MAAJ. 2. Sources of Uncertainty in Pressure Measurement In every experiment, the analysis of sources of uncertainty plays an important role in the accuracy of the obtained results. This analysis is based on the characteristics of each experiment, being these the physical phenomena involved, hardware and software used for data acquisition and analysis, as well as the models and treatment applied to the data. In this section these sources are analysed based on troubles found during the experiment in order to identify areas of improvement and to know how reliable the obtained data are. The experiment consists of placing probes in certain key sections through drill holes, which are connected to the pressure measurement device (Scanivalve) by silicon tubes. During this experiment and before any main test, a trial was carried out so as to check the correct performance of the hardware as well as the software setup. It was often found that some probes gave invalid values from one test to another, but it was solved when they were cleaned. Moreover, the quality of the drill holes can also interfere with the obtained pressure value, since it controls the level with respect the inner surface of the section at which probes are placed. In addition to these sources, it is also mandatory to consider the inherent error of the Scanivalve. Accumulated dirt, the quality of the drill holes, the actual positioning of the probes within the section and the error associated to the Scanivalve are considered to be the main sources of uncertainty.. 2.1. Main Sources of Uncertainty 2.1.1. Dirt in the Drill Holes The following picture is a sketch of a typical probe inserted in a double radius drill hole, being the smallest radius of 1mm.. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 14. ©UPM.

(15) MAAJ. Figure 2.1.1.: Probe and wall section. With a radius of 1mm, it can be appreciated that a negligible amount of dirt will cause blockage or alteration of the pressure value. The experience shows that this problem is frequent. As mentioned above, a trial test was always carried out before a final one as a general check method. It was in these tests where this problem was identified and solved. One of the main sources of dirt is the one already present inside the tunnel. When running a test, this dirt, mainly dust, tends to accumulate in the drill holes. With only a small amount of dust the probe gets blocked. The solution to this problem is to disassemble the probe and unblock it with the help of an aluminium wire.. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 15. ©UPM.

(16) MAAJ Another source of dirt would be the drill hole itself. After the drill bit is removed from the hole when drilling, some drilling waste remains. If the drill hole is not cleaned correctly this waste will block the probe. The problem is solved by cleaning the drill hole with the help of the drill bit and with proper drilling techniques.. 2.1.2. Probe Situation Due to the fact that the Scanivalve is limited to 64 probes, the resolution of the obtained data in each section is limited unless a very in detail study is conducted; although it would still be limited. However, for the pursued purpose, which is to estimate global pressure losses, this resolution shows to be enough. According to this, some precautions should be taken. During the tests it was found that some local flow behaviour can alter significantly the pressure values. For example, at the exit section of the power plant, one of the probes at the outer surface showed an unusual value compared to its homologues at the section. After checking the state of the probe and the drill hole, this phenomenon was attributed to tridimensional effects caused by the fan matrix. Probe number 21 22 23 24. Pressure value (Pa) 206 242 308 381. Table 2.1.1.: Power Plant Pressure Values for a fully-instrumented wind tunnel test. Another important aspect concerning probe positioning is the relative level of the probe with the wall surface inside the tunnel. If the probe is introduced more than it should an expansion occurs at the tip of the probe giving misleading values.. 2.1.3. Scanivalve Error One of the main problems found when measuring, concerning accuracy, is the scale accuracy problem. The Scanivalve is a pressure measurement device able to measure manometric pressures from 0 to 5 PSI. According to the ZOC 33/64 Px user manual, which can be found in the Scanivalve web page, the full scale accuracy is +/- 0,08%. The conversion of 1 PSI to Pa is: 1 P SI ' 6894.7573 P a applying a total error of +/- 0,08%: 6894.7573 P a·(±0.0008) = ±5.5158 P a It must be taken into account that, when measuring manometric pressures in a wind tunnel where the test chamber maximum speed is about 25 m s , which is equivalent to a. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 16. ©UPM.

(17) MAAJ dynamic pressure in test chamber of p0,T C − pT C w 370 P a w 0.0534 P SI, the resulting value is very little in comparison with the Scanivalve measurement range, so errors in appreciation may appear during these measurements. The situation is even more adverse when trying to measure an ambient pressure, that is, 0 Pa. This makes necessary to conduct some calibration tests before the main tests, so as to set the measured “zero value” for each probe.. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 17. ©UPM.

(18) MAAJ. 3. Test With Flaps and Mesh 3.1. Calibration Process In this process, static pressure measurements for zero test chamber speed were conducted. The aim of this is to obtain a statistical value of the measurement error of the Scanivalve since manometric pressure in this case should be zero. Ten tests were conducted for obtaining the pressure at the 64 probes that the Scanivalve is able to handle, which are divided in four probes per section (that is, the virtual surfaces limiting the different components of the wind tunnel). Thus, the measurement process of Scanivalve consists of 100 measures per probe taken every second, and each one of them is the average of 10 measures in the same probe. In order to check whether the error of the measurement process was convergent with the number of measures or it was a random error, the average pressure value in each probe (that is, the average deviation from the real value, which is zero, or the error in pressure measuring) was analysed for various number of tests. The average error in each probe for a given number of tests proved to be constant as it can be seen in the following figures (4, 6, 8 & 10 tests).. Figure 3.1.1.: Average of the calibration measures for different number of tests (4, 6, 8 & 10 tests).. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 18. ©UPM.

(19) MAAJ During the tests it was observed that probes 33, 34 and 36, which are placed at the entrance of the settling chamber, showed an excessive measure of the static pressure (−30 P a,30 P a and−120 P a respectively) taking into account the design speed in the test chamber (u ∼ 25 m s , that is q v 350 P a). As a possible explanation it was assumed that this could be the consequence of unexpected contact between the mesh and the probe. This problem was solved by repositioning the probes at a larger distance from the mesh. To sum up, it can be said, after analysing these results, that the error of the measurement remains constant and it is not aleatory, which implies that increasing the number of tests will not reduce this measurement error.. Figure 3.1.2.: Average of the calibration tests. However, a statistical analysis was performed in order to prove in a rigorous way the previous paragraph.. 3.2. Statistical Analysis In this section, an analysis of the confidence in pressure measurement in the wind tunnel is presented. The first problem was to find out the appropriate number of measurements that were necessary to take in the wind tunnel, in order to ensure that the measured value was close to the real value and it did not have dispersion. To determine this number, different number of measurements were performed and their average was calculated. These tests consisted of groups of 3, 4, 6, 8 and 10 measurements, noticing that there were no important differences in the average of each group. Then, in a first approach and in order to maximise the efficiency of the measurement process, three measurements group was taking as the final measurement value.. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 19. ©UPM.

(20) MAAJ In order to prove this option is suitable, a statistical calculation of confidence intervals was carried out: Taking into account the theory of Statistics, the start point is a random population sample in which the average and standard deviation are unknown. Then, the following variables are defined: Sample Size : n Sample Average : x =. 1X xi n s. Sample Standard Deviation : s =. (3.2.1) (3.2.2). 1 X (xi − x)2 n−1. (3.2.3). Now, it is possible to define an interval in which the population average would be found with a certain confidence. To achieve this goal, it is necessary to use the statistical distribution t-student because the standard deviation of the population is unknown (in the case it was known, normal distribution would be used). Thus, the confidence interval is defined, with a confidence level “1 − α” and for a sample size “n”, as: s s s Interval = tn−1,1−α , µ x − tn−1,1−α , x + tn−1,1−α n n n . . (3.2.4). To determine the t-student parameter value, it is necessary to know three parameters: • Sample Standard Deviation: s • Sample Size: n • Confidence Level: 1 − α The first two parameters are known after simple calculations of the measured values while the third can be a starting point or it can be calculated if the confidence interval length is known. The measurement results after 10 tests are shown in the appendix “Statistical Data”. It can be appreciated that, in some probes, the standard deviation value is too high compared to the average value. There are three main reasons to explain this fact: 1. Some probes got wrong values, were improperly positioned or were faulty. 2. Some probes of Scanivalve were not used and they were more exposed to external parameters which can cause the appearance of random errors and create dispersion. 3. According to the manufacturer, the Scanivalve error for every measurement is ±5.5 P a so, for pressure values which are closed to ambient pressure (0 Pa), Scanivalve measurements do not have confidence.. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 20. ©UPM.

(21) MAAJ This fact implies great interval lengths in the measurements and it is the reason why these probes will be discarded in the following analysis. Thus, a confidence interval will be set up and it will show the degree of dispersion in the wind tunnel measurements. Four confidence levels will be fixed: 90%, 95%, 98% and 99%. These values represent the probability of the population average value can be found in the interval defined by these confidence levels. Thus, the 90% confidence interval will be smaller than 99% one, since the last one has to ensure a bigger probability of finding the real population average value. Now, the confidence intervals are divided by their corresponding average value in order to determine their relative length. This parameter will give information about the results dispersion. These results are shown in the appendix “Statistical Data”. As it was previously said, the higher the confidence level is, the greater the interval is. After analysing the different probes, it can be say that: 1. With a confidence level of 95%, the confidence interval limits, in which the population average will be found, will not differ in more than 1% of the sample average. 2. With a confidence level of 99%, the confidence interval limits, in which the population average will be found, will not differ in more than 1.5% of the sample average. Analysing these results, it can be observed that the different measurements have no dispersion and they are stable. Then, to optimise the measurement process, it would be desirable to make less measurements but having the confidence of reaching good results. Thus, the three measurements group is analysed. Firstly, the difference between the 10 measurements and 3 measurements average is calculated. As it can be observed, this difference is smaller than the 99% interval length, so the three measurements group can be considered an acceptable measurement. This fact is proved in the appendix “Statistical Data”. The difference between 3 and 10 measurements group is about 1% of the corresponding average value so, for an average pressure value in the wind tunnel of 150 Pa, it represents 1.5 Pa. This value can be considered totally insignificant since it is lower than the Scanivalve error and the dispersion in this measurement interval is too high. In conclusion, it is acceptable to perform only three measurements in order to have confidence in the obtained values.. 3.3. Measurement Process in the Wind Tunnel 3.3.1. Wind Tunnel With the tunnel running at full speed, measurements are taken at the selected sections from diffuser 1 until the stagnation chamber. After this, the process is reproduced for the contraction since this element deserves more in detail measurements due to its position at the entrance of the test chamber (possible loss of the flow quality).. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 21. ©UPM.

(22) MAAJ The process is similar to the calibration one, that is, average values are calculated for several tests (4, 6, 8 & 10 tests). As expected, the error continued to be constant similarly to the calibration process. The results are expressed in terms of pressure coefficient referred to the dynamic pressure in the test chamber, Cp =. p − p∞ 1 2 2 ρuT C. (3.3.1). Four graphs are obtained from the test. Each graph corresponds to a different line of probes being these classified in front face probes and rear face probes. Within these faces there are also inner and outer probes according to figure 1.3.1. It can be observed that the 4 coefficients behave quite similar before the power plant. After the power plant an unusual spike appears at the rear face outer probe. As it was said before, this might be caused by non symmetrical velocity components produced by the fan matrix and secondary flows.. Figure 3.3.1.: Pressure coefficient at the exit of every element.. 3.3.2. Contraction Measurements in the contraction are made both on the front side and the top side of the contraction. The number of probes and measurements is different due to the spacing between the probes, so the distribution is also different. This is done with the aim of increasing the number of data points assuming that the flow behaves in a similar way on both surfaces.. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 22. ©UPM.

(23) MAAJ. Figure 3.3.2.: Pressure coefficient on the top view and the front view.. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 23. ©UPM.

(24) MAAJ. 4. Test Without Flap and Mesh For this test, the flaps on the corner guide vanes were removed as well as the settling chamber mesh. The objective of this test is to check the degree of approximation to the theoretical method presented by [1] which is calculated without flaps nor mesh. In order to compare the loss coefficient with that of the reference, it is needed to obtain the pressure coefficient in each element divided by the dynamic pressure calculated, using the average speed in the middle section of the element. Figure 4.1.1 shows the results obtained for the previous test. One way to check that the measurements and calculations are correct is to present the total pressure coefficient instead of the static pressure coefficient. The reason is that the behaviour of this coefficient can be expected and compared to the conducted calculations. It must be said that an error is introduced when calculating the value of the total pressure in a section from the value of the static pressure in four probes situated in the wall of that section. As it is know, 1 p0 = p + ρV 2 (4.0.1) 2 Where p is the average value of the static pressure in the section and the value of the velocity in the section is unknown, so that it is calculated by means of the continuity equation, that is Q = v1 ·A1 = v2 ·A2. (4.0.2). This procedure to calculate the total pressure in a section supposes that flow is onedirectional, which is an approximation instead of an experimentally obtained value.. 4.1. Total Pressure Coefficient The total pressure coefficient behaves as expected. As it can be observed in figure 4.1.1, the total cp decreases until it reaches the power plant section. After this section the coefficient rises from 0.6 until 0.9 approximately. After the pressure increase due to the effect of the power plant, the coefficient rises slowly and reaches the value of 1.0 at the entrance of the contraction. This rise in the value of the coefficient can be explained by considering that the pressure needs a characteristic time to uniform (the probes are located in the wind tunnel walls and they do not appreciate the phenomenon until the flow harmonises). Finally, the flow reaches the test chamber with a pressure coefficient of 1.0 at the exit of the contraction, where the pressure is equal to ambient pressure and. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 24. ©UPM.

(25) MAAJ the flow achieves the design speed, which implies that the coefficient remains constant in the test chamber. cp,total =. p0 − p∞ 1 2 2 ρuT C. (4.1.1). The total pressure loss measured during the tests is slightly inferior to that of the fast method presented by [1]. This is because this method assumes flow conditions that increase the loss coefficient.. Figure 4.1.1.: Pressure coefficients and total pressure coefficient for a meshless and flapless wind tunnel. An estimation of the pressure loss can be calculated by comparing a theoretical calculation conducted with Bernoulli’s equation and the experimental coefficient. Assuming steady, irrotational flow and the average speed:. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 25. ©UPM.

(26) MAAJ 1 p + ρu2 = const 2 The variation of the pressure coefficient for a section i is calculated as:. 4Cp,i = {Cp,theoretical − Cp,experimental }i − {Cp,theoretical − Cp,experimental }i−1. (4.1.2). (4.1.3). Representing the accumulated 4Cp it can be observed that the presence of flaps reduces the total pressure loss.. Figure 4.1.2.: Accumulated Cp with and without flaps. Once the general behaviour of the wind tunnel is studied, it is convenient to proceed with an in depth study of the most critical parts in the wind tunnel: the contraction, corner 1 and diffuser 1. The contraction section is where longitudinal pressure perturbations are dumped, thus is the main responsible for the quality of the flow in the test chamber. Corner 1 and diffuser 1 are the sections where the most important total pressure loss takes place.. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 26. ©UPM.

(27) MAAJ. 5. In Detail Study From the Contraction to Corner 1 5.1. Test without Flaps In this test, the probes in each section were increased in number. The objective of this test is to obtain more accurate measurements, and compare them with the ones obtained in the complete wind tunnel test. Therefore, the main trend of the pressure coefficient can be confirmed if this coefficient shows to behave the same way.. Figure 5.1.1.: In detail study from the contraction until corner 1 without flaps. In conclusion, figure 5.1.1 shows a similar behaviour comparing to the previous tests, which suggests that data collected during the initial test represents the main trend of the pressure evolution. Thus, a simpler measurement with a reduced number of probes. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 27. ©UPM.

(28) MAAJ can be taken as representative of the pressure coefficient.. 5.2. Test with Flaps The objective is to see how the presence of flaps in the corner uniforms the pressure distribution in the corner section by diminishing the turbulence level generated by the corner effect. The procedure during this test is similar to the one without flaps, except that the flaps where assembled onto the corner vanes.. Figure 5.2.1.: In detail study from the contraction until corner 1 with flaps. It was observed that the probes at the inner part of the corner measured similar pressure values than those on the outer surface. This suggests that the flaps reduce the corner effect helping to deflect the flow. On one hand, the presence of flaps increases the pressure loss due to the increase of the friction surface. On the other hand, the flaps improve the quality of the upstream flow into diffuser 1 and might also affect the test chamber if the damped pressure perturbation is intense enough. This can also be seen in figure 4.1.2, which shows that the presence of flaps reduces the pressure loss by diminishing the turbulence level in the corner.. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 28. ©UPM.

(29) MAAJ. Part III.. Analysis of the Influence of Corner 1 on the Total Pressure Loss. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 29. ©UPM.

(30) MAAJ. 6. Pressure Loss in Corner 1. Estimation Methods The fact that the corner 1 is the major pressure loss contributor justifies a more in depth study of the physics involved in the pressure loss process. This study is going to be centered in boundary layer effects and secondary flows in diffusers and cascades. The previous flow phenomena have been chosen to explain the total pressure loss since secondary flows appear in every section of the tunnel due to the rectangular-shaped section and at the hub of every corner vane, and the boundary layer produces flow separation in diffusers and corners as well as friction at the guide vanes.. 6.1. Boundary Layer Effects 6.1.1. Boundary Layer Thickness In order to calculate the total pressure losses within a cascade caused by viscous effects, the boundary layer calculation method can be applied. This viscous flow is described by the Navier-Stokes equations applied to this layer, and once it is known, the total pressure loss coefficient at the cascade can be determined. Before discussing the boundary layer integral equation some important layer quantities are going to be introduced. According to the reference [7], this quantities are the displacement thickness δ1 , momentum thickness δ2 , and energy dissipation thickness δ3 . However the relevant quantities for this method, as it will be explained later, are the displacement thickness and the momentum thickness. The displacement thickness is obtained by applying the continuity condition to the boundary layer flow:. Figure 6.1.1.: Boundary layer on a flat plate.. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 30. ©UPM.

(31) MAAJ ˆδ [(u − U ) + U ]dy = ρw[. ρU hw = ρw ´δ. ˆδ. 0. (u − U )dy + (h + δ1 )U ] 0. with δ1 = 0 (1 − Uu ) the drag force in x-direction is obtained from ˆ. δ. D = ṁU −. udṁ 0. using continuity: ˆ. δ. (U − u)udy. D = ṁU − 0. Introducing the drag coefficient: D 2 Cd = 1 2 = L 2 ρU Lw. ˆ. δ. (1 − 0. u u ) dy U U. where the integral is the momentum deficiency thickness: ˆ. δ. (1 −. δ2 =. 0. u u ) dy U U. Thus, the drag coefficient is directly proportional to the momentum thickness. This implies that this magnitude can be expected to be present when obtaining a method for the total pressure loss calculations. In similar manner the energy dissipation thickness is defined as: ˆ δ3 =. δ. (1 − 0. u u 2 )( ) dy U U. Now two parameters can be defined so as to relate the previous quantities: H12 =. δ1 δ3 ; H32 = δ2 δ2. 6.1.2. Boundary Layer Integral Equation In this section Karman’s boundary layer integral equation is presented. This equation states a problem in terms of friction (shear stress) and velocity gradient (pressure gradient) that when solved for the momentum thickness δ2 allows to estimate the pressure loss coefficient presented in the next section. Considering two-dimensional incompressible viscous flow within the boundary layer of a flat surface, the equations of continuity and momentum in x- and y- direction are: ∂u ∂v + =0 ∂x ∂y. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 31. ©UPM.

(32) MAAJ ∂u ∂u ∂p ∂2u ∂2u +v )=− + µ( 2 + 2 ) ∂x ∂y ∂x ∂x ∂y 2 ∂2v ∂v ∂p ∂ v ∂v +v )=− + µ( 2 + 2 ) ρ(u ∂x ∂y ∂y ∂x ∂y. ρ(u. If the Reynolds number is large enough, the shear layer must be very thin so that the following approximations are valid: ∂p ∂p dp ∂y ' 0 which results in p = p(x) and ∂x = dx This change of static pressure can be obtained by applying the Bernoulli equation outside the boundary layer due to the traversal variation of the pressure in the boundary layer is negligible: ∂p dU = −ρU ∂x dx This requires that the distribution of U (x) outside the boundary layer is known and 2 2 that: ∂∂xu2 ∂∂yu2 with these approximations the previous system can be reduced to: ∂u ∂v + =0 ∂x ∂y ∂u ∂u dU ∂2u u +v 'U +µ 2 ∂x ∂y dx ∂y introducing the shear stress τ = µ ∂u ∂y which leads to the Karman boundary layer equation: dδ2 δs dU τw + (2 + H12 ) = = 0.5Cf dx U dx ρU 2 this equation expresses the change of the momentum thickness δ2 as a function of variable x and contains the form parameter H12 and the friction factor Cf are needed. Furthermore, the streamwise pressure gradient, which is expressed in terms of dU dx must be known.. 6.2. Application of Boundary Layer Theory to Compressor Blades and Airfoil Cascade With the expression obtained is now possible to calculate the airfoil cascade losses. It has been assumed that: 1. Outside the boundary layer, the pressure is constant; thus the pressure loss happens inside the boundary layer.. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 32. ©UPM.

(33) MAAJ 2. The working fluid is incompressible M<0.3. 3. Outside the boundary layer at the exit, the static pressure and the flow angle are constant. The total pressure loss coefficient has the following expression: Cp =. ∆p0 1 2 2 ρV1. with ˆ 1 s (p01 − p02 )dṁ ṁ o as the mass averaged total pressure loss. ∆p0 =. According to the assumptions listed above, the total pressure outside the boundary layer is: 1 p01 = p02 = p2 + ρV22 2 The static pressure p2 is constant inside the boundary layer within section 2. Replacing the differential mass flow dṁ = ρv2 sinα2 hds with the cascade height h = 1, the total pressure loss obtained is: ´s 1 ρ(V 2 − v22 )ρv2 sinα2 ds ∆p0 = o 2 ´ s2 o ρv2 sinα2 ds taking into account the boundary layer quantities expressed in the previous section: δ1 , δ2 , δ3 , H12 = δδ21 , H32 = δδ32 and substituting in the total pressure loss coefficient: Cp = σ(. δ2 sin2 α1 1 + H32 )( )( ) σH12 3 c sin α2 1 − δc2sinα 2. δ2 c. can be obtained either from the Von KarThe dimensionless momentum thickness man’s boundary layer equation or from experimental data.. 6.3. Airfoil Cascade Analysis Pressure loss analysis in the wind tunnel corners has to be carried out using airfoil cascade theory, since interaction between guide vanes makes isolated airfoil analysis not suitable. Solidity is an important parameter in this analysis. It is defined as: c (6.3.1) d where c represents the airfoil chord and d the distance between vanes. This parameter shows the importance of performing an airfoil cascade analysis instead of an isolated airfoil analysis. Thus, the greater the value of solidity for a fixed chord is, the more suitable the airfoil cascade analysis is. S=. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 33. ©UPM.

(34) MAAJ One disadvantage of performing this kind of analysis is the fact that this method does not take into account secondary flows, which appear in 3D cases. However, for the wind tunnel corner analysis, 2D-flow hypothesis can be suitable. An scheme of the airfoil cascade analysis is shown below:. Figure 6.3.1.: Airfoil Cascade Parameters. Parameters used in this analysis are described next: F low Def lexion Angle : φ = β1 − β2. (6.3.2). Static P ressure : P1 , P2. (6.3.3). T otal P ressure : P01 , P02. (6.3.4). Dynamic P ressure at the Cascade Entrance : q = P01 − P1. (6.3.5). Angle Relation : φ = i + θ + δ. (6.3.6). Defining pressure losses as:. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 34. ©UPM.

(35) MAAJ ω=. P01 − P02 q. (6.3.7). an analysis of corner losses will be carried out.. 6.4. Secondary Flow 6.4.1. Introduction Secondary flows are fluid dynamic effects which appear when a flow moves inside a duct. They can be recognised as streamlines which do not follow the main flow direction and cause distortion in velocity vectors. This implies a worse flow quality and higher levels of turbulence, specially in rectangular ducts, where the wall effects are more intense than in circular ones.. 6.4.2. Wall Effects in Rectangular Ducts Wall effects are greater on a rectangular duct than they are on a circular duct because: • There is a bigger wall surface: The ratio of the stack wall perimeter to the total stack cross sectional area is greater on a rectangular duct than on a circular stack. Therefore, the region influenced by wall effects is greater on a rectangular duct. The more wall surface, the more wall effects. • Wall effects are more intense in the corners of the sections: Wall effects on rectangular ducts would also be expected to play a more important role on a rectangular duct because of the impact of the corners. In the corners, the velocity drop off is greater because the flow is impacted by viscous shear stresses from velocity gradients in two planes. In rectangular ducts, secondary flows are produced due to gradients of the Reynolds stresses, propagating flow cells that move inward along the corner bisectors. This phenomenon can be appreciated in the following pictures:. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 35. ©UPM.

(36) MAAJ. a) Secondary Flow Cells. b) Axial Velocity Isovels. Figure 6.4.1.: Secondary Flow in Rectangular Ducts. While the secondary flows can, like viscous shear, contribute to a degradation of axial momentum, its impact in that regard is not significant since the secondary flow vector U is very small ( secondary ≤ 0.01). U A more significant impact of the secondary flow is its distortion of corner and near wall isovels (lines of constant velocity) as shown in Figure 2b. The secondary flow tends to sweep the isovels toward the corners. As it drives the mean flow toward the corners, the secondary flow also serves to relocate the impact of the more intense wall effects away from the corners, tending to push out the isovels along the wall and make the velocity contours more similar around the entire cross-section. For this reason, the wind tunnel sections were modified in order to minimise the negative effects of secondary flows and lessen their presence. This change is shown in the pictures below:. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 36. ©UPM.

(37) MAAJ. Figure 6.4.2.: Wind Tunnel Section Modification. As it can be seen, the original section has been reduced. However, the secondary flow effects will be lessen due to 90º corners removal and also a better quality flow will be obtained.. 6.5. Diffuser Performance A diffuser is a device created to reduce velocity in the wind tunnel in order to recover the static pressure head of the flow. Neglecting losses and gravity effects, the incompressible Bernoulli equation predicts that 1 p + ρV 2 = p0 = const 2 where p0 is the stagnation pressure which the fluid would achieve if the fluid were slowed to rest without losses. The basic output of a diffuser is the pressure recovery coefficient Cp defined as: Cp =. pe − pi p0i − pi. Where e stands for the exit section and i for the inlet section. Consider a typical diffuser. Applying Bernoulli’s equation between the entrance (1) and exit (2): 1 1 p01 = p1 + ρV12 = p2 + ρV22 = p02 2 2 or Cp,f rictionless = 1 − (. V2 2 ) V1. adding one-dimensional continuity:. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 37. ©UPM.

(38) MAAJ Q = V1 A1 = V2 A2 combining both of the previous equations the pressure coefficient can be written in terms of the area ratio AR = A2 /A1 , a basic parameter in diffuser design: Cp,f rictionless = 1 − (AR)−2 For example, calculating the area ratio for diffuser 1, AR = 1.38. Following the previous equation, this leads to Cp,f rictionless = 0.47. However, calculating the pressure coefficient at the exit and entrance of diffuser 1, and taking the difference the result obtained is Cp,real = 0.3. The basic reason for this discrepancy is flow separation and boundary layer effects. The increasing pressure in the diffuser is an unfavourable pressure gradient, which causes the boundary layer to transition into turbulent flow increasing friction resistance. Moreover, if the diffuser angle is too large, flow separation would appear, contributing to lower the pressure recovery coefficient. Also, it is important to remark that flow separation at the end of diffuser 1, could lead to a bad quality inlet flow in corner 1, which represents more pressure losses in this corner along with perturbations that could move backwards to the test chamber.. 6.6. Conclusions In order to calculate pressure losses in Corner 1, boundary layer method would be ideal, and is described as an accurate method by the reference [7]. It provides a semiempirical method to obtain an accurate total pressure loss coefficient. The momentum thickness can be obtained solving the Karman’s integral equation. For this problem dU dx , H12 , Cf are needed and are obtained experimentally. However, there are no available means at the moment in the laboratory to conduct such measurements, that is why a different pressure loss estimation method, in which airfoil cascade theory is used, is described in the next chapter.. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 38. ©UPM.

(39) MAAJ. 7. Analysis of the influence of the guide vane cascade in Corner 1 total pressure loss The aim of this chapter is to calculate the total pressure loss in corner 1 from the previously collected data in order to set the loss reference to be improved by modifying the design of the guide vane cascade, as well as to analyse the influence of various design parameters of airfoils that form the guide vanes of the cascade in its performance. Software MISES was used with this purpose. The variable used to measure the total pressure loss between two different sections is ω, which is defined as ω=. − p02 pisentropic 02 p01 − p1. (7.0.1). where 01 represents the inlet section and 02 the outlet section of the corner. That is, it compares the outlet total pressure in the ideal case with that of the real case, divided by the dynamic pressure in the inlet section. Note that, in a guide vane cascade acting as a stator, in the ideal case pp02 = 1 since no external work is added an 01 there is no friction, so ω = 0. Several effects are responsible for the pressure loss in corner 1: • Viscous friction in guide vanes • Viscous friction in walls of the corner • Flow separation in guide vanes (if it exists) • Collision of the flow into the wall when the guide vanes do not deflect it properly To eliminate the pressure loss due to collision of the flow into corner 1 walls, it is necessary that the guide vanes achieve to deflect the flow 90º, so that the flow turns because of the lift forces that appear in the guide vanes instead of the boundary condition imposed by the wall. Firstly, the experimental value of ω was calculated from experimental data previously gathered. The initial configuration of the ETSIAE wind tunnel presented corner 1 guide vanes designed as 14 -circle curved plates with the following characteristics: • Guide vane chord: c = 150mm • Distance between vanes:. Aero-MAAJ. d c. = 0.433. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 39. ©UPM.

(40) MAAJ • Thickness: t = 1mm In order to calculate the total pressure loss in corner 1, experiments and subsequent data analysis were conducted. Nine probes were placed in the inlet and outlet sections of corner 1 in order to measure the static pressure in both sections. Dynamic pressure in test chamber was measured as well with a total pressure probe and a static pressure probe. The experiment was conducted without mesh in the settling chamber nor flaps in the guide vanes. Once the results of the experiments were obtained, program analisis_esquina.m was used. This program uses as inputs data from Radlink software corresponding to calibrations and tests. Static pressure in inlet and outlet sections are calculated as the average value of the static pressure of the nine probes. Then, velocity in test chamber is calculated from dynamic and static pressure data in that section as 1 pT0 C − pT C = ρVT2C (7.0.2) 2 According to the continuity equation, flow remains constant when passing through different sections if no sources or leakages exist, as it occurs in a closed wind tunnel. For this reason, if flow is considered one dimensional, ˆ ˆ → − (7.0.3) Q= v ·dA = v· dA = v·A = cte. σ. σ. v T C ·AT C = v C1,inlet ·AC1,inlet = v C1,outlet ·AC1,outlet. (7.0.4). With the value of average velocity in each section, the total pressure can be calculated for inlet and outlet corner 1 section as 1 p0 = p + ρv 2 (7.0.5) 2 Note that these calculations constitute an approximation to the real value. The previous process is implemented in code analisis_esquina.m. This program gave a result for the total pressure losses ω = 0.1466. This value is then set as a reference to evaluate the improvements to be obtained through modifications. This value of the total pressure loss is due to several contributions as explained above. Flow collision in corner walls and flow separation in guide vanes can be avoided with a correct redesign of guide vanes, and friction in guide vanes can be reduced with redesign as well. It is important to realise that MISES only takes into account friction in guide vanes when calculating the total pressure loss in the cascade. A computer modelling of the airfoils in the cascade was introduced in MISES in order to calculate ω coefficient in the cascade due to friction in guide vanes. File blade.circ90 presents the coordinates of the points that form a 90º degree circumference arch in the m0 − θ plane. File ises.circ90 presents the necessary information for subprogram ises to perform viscous calculations. After some iterations, the program gave a result of ωf riction,vane = 0.0317 with a flow deflection angle of 81.4º.. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 40. ©UPM.

(41) MAAJ These results give some ideas about how to raise the redesign of guide vanes. Since the objective is to lower the total pressure loss of corner 1, as well as to maintain an acceptable flow quality downstream corner 1, the new guide vanes have to meet the following requirements: 1. Flow deflection between inlet section and outlet section of 90º to prevent flow collision into corner walls. 2. No flow separation. Flow detachment causes poor flow quality since it introduces transversal components of velocity. 3. Low viscous friction in guide vanes. Some additional criteria should be considered as well in order to find a low cost option. 1. The geometry of the airfoil should be easy to manufacture, that is, it should not require expensive machines, complex processes or expensive materials. 2. The previous condition may be easily fitted if the curved plates of the wind tunnel are used as the lower side of the new airfoils. This means as well that the number of guide vanes of the cascade remains constant. Even if this design constraint is quite strong, good results can be achieved. Software MISES is used as a design tool in order to reach these goals. The design process will consist of a previous studies of the parameters that influence the performance of a guide vane, the geometrical definition of the new airfoil from the conclusions of this study and finally the analysis of its performance, as well as the analysis of the existence of possible room for improvements without no design constraints.. 7.1. Study of the parameters of a guide vane cascade The previous analysis revealed that it is necessary to eliminate the collision of the flow into corner 1 wall so as to lower the total pressure loss in this section. The 14 -circle shaped airfoils are not suitable for this, since they cannot turn the flow 90º but only 81.4º. In order to learn how diverse parameters of an airfoil influence the flow deflection angle, some of them where considered for a study: 1. Thickness distribution 2. Maximum thickness and its position 3. Camber distribution 4. Maximum camber and its position 5. Leading edge radius 6. Trailing edge shape. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 41. ©UPM.

(42) MAAJ 7. Separation between guide vanes According to linear potential theory, the geometry of an airfoil can be considered as the superposition of camber, thickness and angle of attack. If an airfoil cascade is considered, the separation between airfoils must be considered as well. In order to get a first idea of how these parameters affect the flow deflection angle, an analysis process was conducted, consisting of determining the deflection angle of the flow for a varying camber distribution, thickness distribution and separation between airfoils, while the rest of the parameters remain constant. Subprogram ISET of software MISES was used for this purpose. Firstly, the influence of the camber was analysed. An arbitrary thickness distribution was used during the analysis. Its characteristics are: 1. Maximum thickness position: 2. Maximum thickness:. t c. xt c. = 0.45. = 0.18. 3. Distance between airfoils in the cascade:. d c. = 0.8. Several camber distributions were added to this thickness distribution to generate different airfoils. These camber distributions were created as the arc of circumference characterised by their central angle. The resulting geometry constituted the input for ISET, which performs potential calculations. The inlet angle of the flow was fixed to 45º so as to simulate the layout of the guide vanes in the tunnel, as shown in figure 7.1.1 corresponding to a 120º circumference arch camber distribution. The deflection angle of the flow was obtained from the outlet angle calculated by ISET. Results can be found on table 7.1.1.. Figure 7.1.1.: Computer modelling for the guide vane cascade.. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 42. ©UPM.

(43) MAAJ Camber (θ) 80º 90º 100º 110º 120º. Flow rotation angle 75º 78.82º 82.6º 86.38º 90.14º. Table 7.1.1.: Influence of the camber in flow deflection. The graphical representation of the previous results (figure 7.1.2), highlighted that the deflection of the flow increases linearly as the camber parameter θ does in potential calculations. According to potential theory, the effect of the camber is to increase the lift coefficient of an airfoil. Since a greater lift force causes a greater deflection, the previous results are reasonable.. Figure 7.1.2.: Camber influence in flow deflection.. The influence of separation between airfoils was analysed as well. For a 90º camber distribution and the previous thickness distribution, potential calculations were conducted to determine the flow deflection angle versus the parameter dc . The results can be seen in figure 7.1.3 and table 7.1.2.. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 43. ©UPM.

(44) MAAJ. Figure 7.1.3.: Distance between airfoils effect. d c. 0.4 0.6 0.8 1 1.2 1.4. Flow deflection angle 86.1º 82.4º 78.8º 75.8º 71.8º 68.4º. Table 7.1.2.: Distance between airfoils effect. The lower the value of dc , the greater the flow deflection angle. This is mainly due to the fact that a low value of dc implies that there are more guide vanes in the cascade, so a greater force will be produced to turn the flow. Nevertheless, the total pressure loss may increase as well due to the fact there are more friction surfaces. A further analysis is presented in section 7.2. Thickness influence was studied using a different procedure: the camber distribution was calculated for each thickness maximum value in order to get 90º of flow deflection. Thickness distribution was not modified but its maximum value, and camber distribution was parametrised as a circumference arc, as explained previously. As shown in table 7.1.3 and in figure 7.1.4, a greater thickness led to a smaller camber for the same deflection angle.. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 44. ©UPM.

(45) MAAJ Maximum thickness (%) 10 15 20 25 40. Camber (θ) 124.48 121.55 118.81 115.99 111.13. Table 7.1.3.: Maximum thickness vs Camber.. Figure 7.1.4.: Maximum thickness vs Camber. The effect of thickness is not as important as camber effect in lift coefficient, however it must be taken into account because of its influence in pressure field in the airfoil as well as in stall. In the particular case of a flow deflection of 90º, the resulting airfoil presented the following geometry.. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 45. ©UPM.

(46) MAAJ. Figure 7.1.5.: 90º-flow-deflection airfoil: thickness and camber distribution, and airfoil.. 7.2. Total pressure loss in guide vane cascade As the previous results show, camber, thickness and distance between guide vanes determine the performance of the guide vane cascade in terms of flow deflection angle. Moreover, these parameters also determine the total pressure loss in the cascade. In this part, the total pressure loss coefficient is calculated for different solutions for a flow deflection of 90º. Firstly, the 41 -circle curved plates of the wind tunnel were studied with MISES, with a result of ωf,vane = 0.0317 and a deflection angle of 81.4º, as explained before.. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 46. ©UPM.

(47) MAAJ. Figure 7.2.1.: 41 -circle curved plate guide vane. Then, the 14 -circle curved plates were modified in MISES in order to get the flow deflected 90º. Since a greater camber makes the flow to be deflected a greater angle, the curved plates were lengthened so that they covered an angle of 101º instead of 90º of 41 -circle. With this modification the flow was deflected 90º with a pressure loss of ωf,vane = 0.0505. As explained before, in general the total pressure loss that appears in corner 1 can be originated by different effects: viscous friction in the airfoil, viscous friction in the walls, collision of the flow into the wall when the flow is not deflected 90º and flow separation. In the 41 -circle curved plates case, the simulations did not show the existence of flow separation, so the pressure loss can be expressed as ωtotal = ωf,vane + ωcollision,81.4º + ωf,wall = 0.1466. (7.2.1). Where ωf,vane = 0.0317. In a first approximation the total pressure loss due to friction in the walls of corner 1 can be considered constant when Reynolds number does not vary, so the goal is that the new airfoil lowers the pressure loss to a smaller quantity than ω ≤ ωcollision + ωf,vane . With this condition, the new design will improve the current one.. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 47. ©UPM.

(48) MAAJ. Figure 7.2.2.: 101º curved plate guide vane. There is an option to improve the 41 -circle curved plates performance by adding a flap so that the flow is deflected a greater angle. However, this flap introduces additional pressure loss due to viscous friction, so there is an optimum flap length, which is the smallest one that allows a 90º flow deflection. This optimum length was found to be 30% of the 14 -circle curved plate chord, with a pressure loss of ωf,vane = 0.0477. As a result, it seems better to introduce a flap in a 14 -circle curved plate rather than to lengthen it so that it covers a 101º angle, to get the flow deflected 90º.. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 48. ©UPM.

(49) MAAJ. Figure 7.2.3.: 41 -circle curved plates with 30%-chord flap. In this study a sharp leading edge was used. Although this may work in theory, it can lead to unexpected performances in practice when the flow is not unidirectional. Indeed, if transversely velocities exist, the stagnation point may be displaced to the upper side or the lower side of the airfoil, causing greater loss than predicted. For this reason, the new airfoil design should include a leading edge radius to avoid this problem. The easy manufacturing criterion, along with the condition that the existing airfoils will form the lower side of the new guide vanes (this is also influenced by the idea that the flow deflection is mainly influenced by the shape of the lower side), leads to design an airfoil composed by a 14 -circle shaped lower side and a analytical curve for the upper side.. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 49. ©UPM.

(50) MAAJ. Part IV.. Design of an easily constructable optimised guide vane. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 50. ©UPM.

(51) MAAJ. 8. Airfoil Selection As explained in chapter 7, a 41 -circle contour was selected for the lower side in order to deflect the flow properly, so the optimised design of the guide vane is focused on the upper side. Different analytical curves such as circumference, parabola and ellipse were tested as upper side contours. Several numerical simulations conducted with MISES shown that a parabolic upper side offered the best performances in terms of total pressure loss and flow detachment for a flow deflection angle of approximately 90º, as it can be seen in figures 8.0.1 and 8.0.2.. Figure 8.0.1.: Result for elliptical and circumferential upper side.. Figure 8.0.2.: Performance analysis of parabolic airfoil and curved plate. In comparison with the total pressure loss of the curved plates which were analysed. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 51. ©UPM.

(52) MAAJ in chapter 7, a parabolic contour reduces in 43% the total pressure loss with the same flow deflection. This guide vane has two main design parameters: Maximum Thickness: The position of maximum thickness is located in 50% of the chord since it obtains good results and facilitates the manufacturing process. Leading Edge Radius: It joins the parabolic upper side and the 41 -circle lower side at the leading edge in order to avoid sharp profiles in this part. The analysis parameters are defined below: M aximum T hickness (%) = LE Radius (%) =. T hickness (x/c = 50%) ·100 c. (8.0.1). LE Radius ·100 c. (8.0.2). P ressure Loss = ω =. pisen 02 − p02 p01 − p1. (8.0.3). F low def lection = θ2. (8.0.4). F low def lection P arameter = − tan(θ2 ). (8.0.5). Next, an analysis of LE Radius and Maximum Thickness parameters and their effects in the pressure loss and flow deflection is presented.. Figure 8.0.3.: Analysis of LE Radius Effects (12.5% Maximum Thickness).. Aero-MAAJ. Aero-MAAJ UNIVERSIDAD POLITÉCNICA DE MADRID Plaza Cardenal Cisneros Nº3 28040 MADRID, SPAIN www.aero-maaj.etsiae.upm.es 52. ©UPM.