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

Transcription

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 Contents I. Introduction 7 II. Initial Study and Tests on the Wind Tunnel 9 1. General notes about wind tunnels and pressure measurement Introduction to LSWT Analysis of LSWT parts Test Chamber Contraction Settling Chamber Diffusers Corners Power Plant Pressure Measurement Sources of Uncertainty in Pressure Measurement Main Sources of Uncertainty Dirt in the Drill Holes Probe Situation Scanivalve Error Test With Flaps and Mesh Calibration Process Statistical Analysis Measurement Process in the Wind Tunnel Wind Tunnel Contraction Test Without Flap and Mesh Total Pressure Coefficient In Detail Study From the Contraction to Corner Test without Flaps Test with Flaps

3 III. Analysis of the Influence of Corner 1 on the Total Pressure Loss Pressure Loss in Corner 1. Estimation Methods Boundary Layer Effects Boundary Layer Thickness Boundary Layer Integral Equation Application of Boundary Layer Theory to Compressor Blades and Airfoil Cascade Airfoil Cascade Analysis Secondary Flow Introduction Wall Effects in Rectangular Ducts Diffuser Performance Conclusions Analysis of the influence of the guide vane cascade in Corner 1 total pressure loss Study of the parameters of a guide vane cascade Total pressure loss in guide vane cascade IV. Design of an easily constructable optimised guide vane Airfoil Selection Analysis of Flow Turning with a Parafoil cascade Design and Manufacturing Process PARAFOIL Introduction Software inputs & outputs Blade.parafoil Ises.parafoil Internal running of the code Manufacturing Process Materials Process Manufacturing Process Corner Assembly Conclusion and assessment of the Manufacturing Process V. Possible improvements for the proposed guide vane Introduction 70 3

4 11.Parafoil improvement Optimization process Improvements from the ¼-circle airfoil 75 VI. Wind tunnel tests with improved corner 1 and chamfers Introduction Tests in Corner General tests Conclusions 84 VII.Conclusions and Final Remarks 86 VIII.APPENDIX 89 4

5 List of Figures Typical Wind Tunnel Setup Probe and wall section Average of the calibration measures for different number of tests (4, 6, 8 & 10 tests) Average of the calibration tests Pressure coefficient at the exit of every element Pressure coefficient on the top view and the front view Pressure coefficients and total pressure coefficient for a meshless and flapless wind tunnel Accumulated Cp with and without flaps In detail study from the contraction until corner 1 without flaps In detail study from the contraction until corner 1 with flaps Boundary layer on a flat plate Airfoil Cascade Parameters Secondary Flow in Rectangular Ducts Wind Tunnel Section Modification Computer modelling for the guide vane cascade Camber influence in flow deflection Distance between airfoils effect Maximum thickness vs Camber º-flow-deflection airfoil: thickness and camber distribution, and airfoil circle curved plate guide vane º curved plate guide vane circle curved plates with 30-chord flap Result for elliptical and circumferential upper side Performance analysis of parabolic airfoil and curved plate Analysis of LE Radius Effects (12.5 Maximum Thickness) Analysis of Maximum Thickness Effects (0.5 LE Radius) Initial Angle Effect in Pressure Losses Relation between Lift Force and Flow Turning β vs Flow Turning

6 9.1.1.PARAFOIL Vane, Thickness and Camber Distribution Cuts on the PVC sheet Distances for supports placement Section of a manufactured upper side Coincidence between both leading edges Section of a fully assembled profile Parafoil geometry c p curve of Parafoil. The blue line represents the upper side and the red line the lower side Results for modified Parafoil Best specimen geometry vs Parafoil geometry Airfoil proposed in KTH article Total pressure loss in each element measured by parameter ξ Total c p curve in the wind tunnel Total pressure loss coefficient Improvement percentage in total pressure loss with Parafoil cascade 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

7 Part I. Introduction 7

8 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. 8

9 Part II. Initial Study and Tests on the Wind Tunnel 9

10 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 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 Analysis of LSWT parts 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. 10

11 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: ζ = 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: λ = 1/(1.8 log(re) 1.64) 2 (1.2.2) where Re is the Reynolds number based on the hydraulic diameter 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 16 sin(α/2) where λ is defined as: Settling Chamber } ( 1 1 ) { N 2 + λ 16 sin(β/2) } ( 1 1 ) N 2 (1.2.3) λ = 1/(1.8 log(re) 1.64) 2 (1.2.4) 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 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. 11

12 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 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 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 Ẇ. Once the test chamber cross-section surface S tc, and the desired operating speed V, are fixed, and the total pressure loss coefficient ζ has been calculated. These parameters are: p = 1 2 ρv 2 ζ (1.2.5) Q = V S T 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. 12

13 MAAJ The pattern of the probes remains the same for the whole tunnel. () stands for rear probe. Figure : Typical Wind Tunnel Setup. 13

14 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 Main Sources of Uncertainty 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. 14

15 Figure : 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. 15

16 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 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 Pressure value (Pa) Table : 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 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 P a applying a total error of +/- 0,08: P a (±0.0008) = ± 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 16

17 dynamic pressure in test chamber of p 0,T C p T C 370 P a 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. 17

18 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 : Average of the calibration measures for different number of tests (4, 6, 8 & 10 tests). 18

19 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 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 : Average of the calibration tests. However, a statistical analysis was performed in order to prove in a rigorous way the previous paragraph 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. 19

20 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 (3.2.1) Sample Average : x = 1 n xi (3.2.2) 1 Sample Standard Deviation : s = (xi x) n 1 2 (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 Interval = t n 1,1 α n, µ ɛ s x t n 1,1 α n, x + t s n 1,1 α 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. 20

21 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 Measurement Process in the Wind Tunnel 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). 21

22 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, C p = p p 1 2 ρu2 T 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 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 : Pressure coefficient at the exit of every element 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. 22

23 Figure : Pressure coefficient on the top view and the front view. 23

24 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 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, p 0 = p ρv 2 (4.0.1) 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 = v 1 A 1 = v 2 A 2 (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 Total Pressure Coefficient The total pressure coefficient behaves as expected. As it can be observed in figure 4.1.1, the total c p 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 24

25 the flow achieves the design speed, which implies that the coefficient remains constant in the test chamber. c p,total = p 0 p 1 (4.1.1) 2 ρu2 T C 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 : 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: 25

26 p ρu2 = const (4.1.2) The variation of the pressure coefficient for a section i is calculated as: C p,i = {C p,theoretical C p,experimental } i {C p,theoretical C p,experimental } i 1 (4.1.3) Representing the accumulated C p it can be observed that the presence of flaps reduces the total pressure loss. Figure : 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. 26

27 5. In Detail Study From the Contraction to Corner 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 : In detail study from the contraction until corner 1 without flaps. In conclusion, figure 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 27

28 can be taken as representative of the pressure coefficient 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 : 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. 28

29 Part III. Analysis of the Influence of Corner 1 on the Total Pressure Loss 29

30 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 Boundary Layer Effects 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 δ 1, momentum thickness δ 2, and energy dissipation thickness δ 3. 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 : Boundary layer on a flat plate. 30

31 ˆδ ˆδ ρuhw = ρw [(u U) + U]dy = ρw[ (u U)dy + (h + δ 1 )U] 0 with δ 1 = δ 0 (1 u U ) the drag force in x-direction is obtained from 0 using continuity: ˆ δ D = ṁu udṁ 0 Introducing the drag coefficient: D = ṁu ˆ δ 0 (U u)udy ˆ δ D C d = 1 2 ρu 2 Lw = 2 (1 u L 0 U ) u U dy where the integral is the momentum deficiency thickness: δ 2 = ˆ δ 0 (1 u U ) u U dy 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: δ 3 = ˆ δ 0 (1 u U )( u U )2 dy Now two parameters can be defined so as to relate the previous quantities: H 12 = δ 1 δ 2 ; H 32 = δ 3 δ 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 δ 2 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 x + v y = 0 31

32 ρ(u u x + v u y ) = p x + µ( 2 u x u y 2 ) ρ(u v x + v v y ) = p y + µ( 2 v x v y 2 ) If the Reynolds number is large enough, the shear layer must be very thin so that the following approximations are valid: p p y 0 which results in p = p(x) and x = dp 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 that: 2 u x 2 2 u y 2 with these approximations the previous system can be reduced to: u x + v y = 0 u u x + v u y U du dx + u µ 2 y 2 introducing the shear stress τ = µ u y equation: which leads to the Karman boundary layer dδ 2 dx + (2 + H 12) δ sdu Udx = τ w ρu 2 = 0.5C f this equation expresses the change of the momentum thickness δ 2 as a function of variable x and contains the form parameter H 12 and the friction factor C f are needed. Furthermore, the streamwise pressure gradient, which is expressed in terms of du dx must be known 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. 32

33 2. The working fluid is incompressible M< 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: with C p = p ρv 1 2 p 0 = 1 ṁ ˆ s as the mass averaged total pressure loss. o (p 01 p 02 )dṁ According to the assumptions listed above, the total pressure outside the boundary layer is: p 01 = p 02 = p ρv 2 2 The static pressure p 2 is constant inside the boundary layer within section 2. Replacing the differential mass flow dṁ = ρv 2 sinα 2 hds with the cascade height h = 1, the total pressure loss obtained is: s o 1 2 p 0 = ρ(v 2 2 v2 2 )ρv 2sinα 2 ds s o ρv 2sinα 2 ds taking into account the boundary layer quantities expressed in the previous section: δ 1, δ 2, δ 3, H 12 = δ 1 δ 2, H 32 = δ 3 δ 2 and substituting in the total pressure loss coefficient: C p = σ( δ 2 α 1 c )(sin2 sin 3 )( 1 + H 32 α 2 1 δ 2σH 12 c sinα 2 ) The dimensionless momentum thickness δ 2 c can be obtained either from the Von Karman s boundary layer equation or from experimental data 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: S = c d (6.3.1) 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. 33

34 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 : Airfoil Cascade Parameters. Parameters used in this analysis are described next: F low Deflexion Angle : φ = β 1 β 2 (6.3.2) Static P ressure : P 1, P 2 (6.3.3) T otal P ressure : P 01, P 02 (6.3.4) Dynamic P ressure at the Cascade Entrance : q = P 01 P 1 (6.3.5) Angle Relation : φ = i + θ + δ (6.3.6) Defining pressure losses as: 34

35 ω = P 01 P 02 q an analysis of corner losses will be carried out. (6.3.7) 6.4. Secondary Flow 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 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: 35

36 a) Secondary Flow Cells b) Axial Velocity Isovels Figure : 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 is very small ( U secondary U 0.01). 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: 36

37 Figure : 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 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 p ρv 2 = p 0 = const where p 0 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 C p defined as: C p = p e p i p 0i p i 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): or adding one-dimensional continuity: p 01 = p ρv 2 1 = p ρv 2 2 = p 02 C p,frictionless = 1 ( V 2 V 1 ) 2 37

38 Q = V 1 A 1 = V 2 A 2 combining both of the previous equations the pressure coefficient can be written in terms of the area ratio AR = A 2 /A 1, a basic parameter in diffuser design: C p,frictionless = 1 (AR) 2 For example, calculating the area ratio for diffuser 1, AR = Following the previous equation, this leads to C p,frictionless = However, calculating the pressure coefficient at the exit and entrance of diffuser 1, and taking the difference the result obtained is C p,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 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, H 12, C f 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. 38

39 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 = pisentropic 02 p 02 p 01 p 1 (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 p 02 p 01 = 1 since no external work is added an 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 1 4-circle curved plates with the following characteristics: Guide vane chord: c = 150mm Distance between vanes: d c =

40 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 p T C 0 p T C = 1 2 ρv 2 T C (7.0.2) 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 Q = v da = v da = v A = cte. (7.0.3) σ σ v T C A T C = v C1,inlet A C1,inlet = v C1,outlet A C1,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 p 0 = p ρv2 (7.0.5) 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 = 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 m 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 ω friction,vane = with a flow deflection angle of 81.4º. 40

41 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 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 1 4 -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 41

42 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: xt c = Maximum thickness: t c = 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 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 Figure : Computer modelling for the guide vane cascade. 42

43 Camber (θ) Flow rotation angle 80º 75º 90º 78.82º 100º 82.6º 110º 86.38º 120º 90.14º Table : 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 : 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 d c. The results can be seen in figure and table

44 Figure : Distance between airfoils effect. d c Flow deflection angle º º º º º º Table : Distance between airfoils effect. The lower the value of d c, the greater the flow deflection angle. This is mainly due to the fact that a low value of d c 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 and in figure 7.1.4, a greater thickness led to a smaller camber for the same deflection angle. 44

45 Maximum thickness () Camber (θ) Table : Maximum thickness vs Camber. Figure : 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. 45

46 Figure : 90º-flow-deflection airfoil: thickness and camber distribution, and airfoil 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 1 4-circle curved plates of the wind tunnel were studied with MISES, with a result of ω f,vane = and a deflection angle of 81.4º, as explained before. 46

47 Figure : 1 4-circle curved plate guide vane. Then, the 1 4-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 1 4-circle. With this modification the flow was deflected 90º with a pressure loss of ω f,vane = 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 1 4-circle curved plates case, the simulations did not show the existence of flow separation, so the pressure loss can be expressed as ω total = ω f,vane + ω collision,81.4º + ω f,wall = (7.2.1) Where ω f,vane = 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 ω collision + ω f,vane. With this condition, the new design will improve the current one. 47

48 Figure : 101º curved plate guide vane. There is an option to improve the 1 4-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 1 4 -circle curved plate chord, with a pressure loss of ω f,vane = As a result, it seems better to introduce a flap in a 1 4-circle curved plate rather than to lengthen it so that it covers a 101º angle, to get the flow deflected 90º. 48

49 Figure : 1 4-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 1 4-circle shaped lower side and a analytical curve for the upper side. 49

50 Part IV. Design of an easily constructable optimised guide vane 50

51 8. Airfoil Selection As explained in chapter 7, a 1 4-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 and Figure : Result for elliptical and circumferential upper side. Figure : Performance analysis of parabolic airfoil and curved plate. In comparison with the total pressure loss of the curved plates which were analysed 51

52 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 1 4-circle lower side at the leading edge in order to avoid sharp profiles in this part. The analysis parameters are defined below: Maximum T hickness () = T hickness (x /c = 50) 100 (8.0.1) c LE Radius () = LE Radius 100 (8.0.2) c P ressure Loss = ω = pisen 02 p 02 p 01 p 1 (8.0.3) F low deflection = θ 2 (8.0.4) F low deflection P arameter = tan(θ 2 ) (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 : Analysis of LE Radius Effects (12.5 Maximum Thickness). 52

53 There is an optimum value with 0.5 LE Radius. It can be appreciated that the minimum loss implies maximum flow deflection angle. The explanation of this point is shown below: The total pressure loss is closely related to the situation where flow detachment appears. The greater the part of the airfoil with flow separation is, the greater the total pressure loss is. Detachment implies that streamlines do not remain attached to the vane so, consequently, the flow deflection angle will be lower than in potential calculations and the decrease of this angle is directly proportional to the existing detachment. Figure : Analysis of Maximum Thickness Effects (0.5 LE Radius). Total pressure loss has a minimum in 12.5 while the flow deflection angle is directly proportional to the vane thickness. 53

54 Figure : Initial Angle Effect in Pressure Losses. The flow incidence angle is important in pressure loss since it is related with the position of the stagnation point in the vane. The optimum situation is a stagnation point located in the LE with no deviation neither to the upper side nor the lower side of the airfoil. According to this analysis, it seems that the defined geometry is reasonably good for the new guide vanes. This airfoil was given the name Parafoil and selected for manufacturing the cascade. This manufacturing process is detailed in chapter Analysis of Flow Turning with a Parafoil cascade It has been carried out an analysis of the main parameters in flow turning across a Parafoil airfoil cascade. The following variables have been taken from MISES: Flow turning c p distribution in a guide vane of the cascade This procedure has been carried out for different values of the cascade solidity. It can be appreciated that the solidity variation implies different stresses in guide vanes. Thus, the greater the cascade solidity is (more guide vanes in the same distance), the lower the stresses they withstand are since the overall lift force (for the same flow turning) is divided between more lift surfaces. 54

55 Also, different guide vanes have been tested with the same solidity value, obtaining different c l values in each vane. This coefficient has been obtained from the c p distribution given by MISES. In order to compare the different analysed cases, a new parameter was created. The overall lift force is defined as: C l,total = C l,vane S (8.1.1) where S is the cascade solidity defined as S = c d. This force is closely related to the flow turning. The greater the lift force is, the higher the flow turning angle is, as it can be seen in the next graph. Figure : Relation between Lift Force and Flow Turning. It can be appreciated that the trend of this graph is approximately linear, so the flow turning increases with the overall lift force of the cascade. Also, there is some dispersion in the map due to secondary order effects, which avoid a perfect linearity. Then, a new parameter is created: β = C l,total α 1 α 2 (8.1.2) where α 1 α 2 represents the flow turning in the cascade. In the analysed gap of values, there is a difference of 3 in the maximum and the minimum value of this parameter, which means β is approximately constant and implies, in a first approach, that C l,total is linear with the flow turning. 55

56 However, the next graph shows the relationship between flow turning and β for different solidity values and airfoil shapes. Figure : β vs Flow Turning. β parameter represents the C l,total efficiency in flow turning (β = C l,total α 1 α 2 ). Then, for the same flow turning, a minimum value of this parameter would be desirable (the same flow turning is achieved with less C l,total, that implies less C d and also less pressure losses). Thus, analysing the map above, the optimum points will be those which, with the same flow turning, have minimum β value. During this section, it has only been talked about the overall turning vane lift that, as it was seen, is directly related with the flow turning. However, C l distribution has a big importance in pressure losses since they depend on it. Two C l distributions with the same overall lift can introduce different pressure losses. Another fact to remark in the wind tunnel corner analysis is the way the flow turns. In the most simple case (with no guide vanes) the flow would bump the outer walls of the wind tunnel, creating a high pressure area which would cause the flow movement to the following wind tunnel part (where there is a favourable pressure gradient). In the analysed case, the objective is turning the flow with the cascade lift force. The aim is to avoid the flow bumps the tunnel wall, since it is very inefficient and it is related to high pressure losses. 56

57 9. Design and Manufacturing Process 9.1. PARAFOIL Introduction The study of the parameters that influence the performance of corner 1 guide vanes in flow deflection (section 8.1) enables us to create the geometry of the new airfoil for the wind tunnel. In order to facilitate the manufacturing process, as well as the computer modeling of the airfoil to conduct calculations with software MISES, a Matlab code was written containing the calculations to obtain the geometrical characteristics of the new airfoil. This code is PARAFOIL, and it consists of a script named PARAFOIL.m, and some functions that act as subroutines. These functions are listed below: 1. centroba.m 2. circunferencia.m 3. circunferenciaba.m 4. curvesp.m 5. desplazaba.m 6. desplazaparabola.m 7. detcentro.m 8. extint.m 9. extrados_points.m 10. interseccionba.m 11. offsetba.m 12. offsetcircunferencia.m 13. parabola3p.m This program is run from the Matlab interface. It gives back the files required by MISES to perform the airfoil cascade calculations,which are blade.parafoil, gridpar.parafoil and ises.parafoil, with the adequate format. It also generates in the workspace the variables that collect the camber and thickness distributions, as well as the points that define the geometry. 57

58 Software inputs & outputs When executing PARAFOIL from Matlab interface, the user is asked to introduce the value of thickness in x c = 0.5 and the leading edge circumference radius. With these inputs, the program returns as outputs the files blade, gridpar and ises for MISES, as well as the fabricacion file, which contains useful information for the manufacturing process. This process is detailed in section Blade.parafoil The file blade.parafoil is generated in MISES s bin folder. It contains the x,y-coordinates of the points that compose the geometry of the airfoil, arranged as MISES requires: the series of points starts in the leading edge, then goes across the upper side until the leading edge and finally goes across the lower side until the trailing edge. It also includes in its second line, the value of the following variables: 1. SINL is the initial S 1 = tan(β 1 ), the tangent of the inlet flow angle relative to the axial. direction. In this case S 1 = 1 since β 1 = 45º. 2. SOUT is the initial S 2 = tan(β 2 ). With the new panel-solver grid generator in ISET, SOUT is no longer used. For this reason S 2 can be given any value, for example S 2 = CHINL is the distance in m from the blade 1 leading edge to the grid inflow plane. For this airfoil cascade, CHINL = CHOUT is the distance in m from the blade 1 trailing edge to the grid outflow plane. In this case CHOUT = 1 5. PITCH is the distance between homologue points of the airfoils in the cascade. For a correct computer simulation, PITCH is given its real value, that is, P IT CH = (distance between airfoils in real wind tunnel is 65 mm; airfoil chord is 150 mm so d c = For MISES calculations, chord is unitary, so d = P IT CH = 0.433) Ises.parafoil Ises is the file that contains the values of the necessary variables for MISES to perform viscous calculations once the problem is solved using the panel method. This variables are, arranged as in MISES: GVAR(1) GVAR(2)... GVAR(N) GCON(1) GCON(2)... GCON(N) MINLin P1PTin SINLin XINL [ V1ATin ] <-- optional MOUTin P2PTin SOUTin XOUT [ V2ATin ] <-- optional MFRin HWRATin [ XSHKin MSHKin ] <-- optional REYNin NCRIT TRANS1 TRANS2 (TRANS1 TRANS2 for blade 2) ISMOM MCRIT MUCON 58

59 For this airfoil cascade the values of the variables are: E Line 1 is the list of integers GVAR(1)... GVAR(N) that, given in any order, specifies the global variables to be treated as formal unknowns in the overall Newton equation system. In this case the selected variables are the inlet flow slope (variable number 1), the grid exit slope (variable number 2), the inlet Mach number (variable number 15) and the grid exit static pressure (variable number 6). Line 2 is the list of integers GCON(1)... GCON(N) that, in any order, specifies the global constraints to be used to close the Newton equation system. For this problem the constrains are: 1. Drive inlet slope S1 to SINLin (constraint number 1) 2. Set trailing edge Kutta condition for all blades (constraint number 4) 3. Drive outlet pressure P2/Po1 to P2PTin (constraint number 18) 4. Drive inlet P0a to PSTr0 ( = 1/gamma ) (constraint number 6). Lines 3 and 4 specify the flow conditions in the inlet and outlet sections respectively. In particular, the specified inlet flow conditions for this problem are: 1. MINLin: inlet relative Mach number M 1. Even if the flow can be considered as incompressible (M 1 = 0), the exact value of inlet Mach number has been calculated from the speed in the inlet section of corner one and the room temperature, leading to M 1 = P1PTin: inlet static/inlet-total pressure ratio p 1 p 01 = This value has been calculated from inlet Mach number M 1 = and γ = SINLin: inlet relative flow slope S 1 = tan(β 1 ) = v 1 u 1 = 1. As said before, β 1 = 45º. 4. XINL: inlet-condition location m 1 = 0.1 Outlet flow conditions appear in line 4. These are calculated following the same procedure as in the previous line 1. MOUTin: outlet relative Mach number M 2 = P2PTin: outlet static/inlet-total pressure ratio p 2 p 01 =

60 3. SOUTin: outlet relative glow slope S 2 = tan(β 2 ) = v 2 u 2 = 0 4. XOUT: outlet-condition location m 2 = 1.3 Lines 6 and 7 present the information regarding Reynolds number, flow quality factors and transition points. 1. REYNin: Reynolds number in the inlet section. For this problem, Re in = , which is the Reynolds number in the inlet section of the corner 1 when the tunnel is working at maximum power. This is the working point that the redesign was done for. 2. NCRIT: if positive, it is the critical amplification factor ncrit for e n transition model; if negative, it is the freestream turbulence level (τ = NCRIT, in ) for modified Abu-Ghannam Shaw bypass transition model. In this case, this variable is given the value N CRIT = 9, so that it represents the amplification factor corresponding to medium flow quality in a wind tunnel. 3. TRANS1: side 1 surface transition trip m /chord location =1 4. TRANS2: side 2 surface transition trip m /chord location =1 Line 8 finally indicates the value of the following variables: 1. ISMOM = 1. It means that MISES uses S-momentum equation 2. MCRIT: critical Mach number in the definition of bulk viscosity. It is usually equal to 0.98 for weak shocks. In this case it is given the value MCRIT= MUCON: artificial dissipation coefficient (= 1.0 normally). A negative MUCON value disables 2nd-order dissipation. In this problem it is equal to Internal running of the code Once the input variables are given a value, calculation processes leading to the geometrical definition of the airfoil start. For these calculations, a 2-D cartesian coordinates system is used. While it is true that the resulting airfoil of the program has unitary chord, this fact has no relevance in MISES calculations since as long as Reynold number is the same both in simulation and all the results will be the same as in reality. First, according to the design constraint that the lower side of the airfoil must be a ¼-circle shape, a circumference arch is generated with origin in (0,0) and end in (1,0), covering a 90º angle. This constitutes the lower side of the new airfoil. The coordinates of the center of this arch, as well as its radium, are calculated. Variable tubos is a 3 x 2 matrix containing three values of the half airfoil thickness in different parts of it. Initially it was thought that the easiest way for manufacturing the airfoil was to put three sticks of circular shape in the lower side so that they act as spars for the airfoil and allow to place a plastic sheet above them, forming the upper side. Note that the circular spars would be tangent to lower side and upper side at the 60

61 same time. For this reason, the values contained in the second column of tubos are the radius of these spars, whose position is calculated lately. Finally it was decided to use rectangular shape spars with their height equal to the circular shape spars diameter and their length equal to 3 mm, in order to facilitate the manufacturing process, see section 9.2. The error committed when substituting the circular shape spars for rectangular shape spars is irrelevant but clearly facilitates the manufacturing process. The second of these values, which can be found on tubos (2,2), is the half of the maximum thickness of the airfoil. It is located in the 50 of the chord and it is introduced by the user through the first input. Once this value is know, the parabola that forms the upper side can be calculated since three points that it passes through are known (points (0,0), (1,0) and the vertex, calculated from tubos(2,2)). Once this parabola is calculated, the position where the other values of thickness contained in tubos are located in the airfoil are calculated. This process is explained below. Function parabola3p.m calculates the coefficients of a parabola passing by three points. This function uses the general formula for a parabola, ax 2 + bx + c + dy = 0 (9.1.1) where d = 1 in this case. In order to find coefficients a, b and c, it is necessary to solve the system of equations: x 2 1 x 1 1 x 2 2 x 2 1 x 2 3 x 3 1 a b c = y 1 y 2 y 3 (9.1.2) This system is then solved to give the value of the coefficients. Once the analytical expression of the parabola is known, the position of the center of the hypothetical circular shape spars can be calculated. This position corresponds to the intersection of the upper side and lower side curves displaced in the normal local direction of the point specified by the first column of tubos. Take, for instance, the first row of tubos. Tubos(1,1) indicates the x-coordinate of the point where the normal direction to lower side and upper side curves will be calculated. Once this directions are known, both curves are displaced in this direction in a quantity specified by tubos(1,2), which is the radius of the hypothetical circular shape spar. The curve that results from displacing each point of a parabola in the normal local direction is not a parabola. Function desplazaparabola.m creates a fourth-degree polynomial function that passes by 1000 points located near the point specified by tubos first column. In the case of the lower side, the curve resulting from displacing each point of a circumference arch in the local normal direction in a constant quantity is equal to increasing the radius of that angle. This is done by function offsetcircunferencia.m. The intersection of the previous curves gives the position of the center of the circular shape spar. Function detcentro.m performs that calculation. However, the coordinates of the center of the circular shape spars are not useful in terms of manufacturing, so the coordinates of the tangency point of the spar with the lower side is calculated. Then, 61

62 the length of the arch starting in the leading edge (or trailing edge in the case of the third spar) and finishing in the tangency point is calculated and given as an output in the fabricacion file. Note that the position of the central spar is already known and thus it is not calculated. The fabricacion file also contains the values of the radius of the spars. The same procedure is conducted for calculating the situation of the leading edge spar, as well as the position of the tangency point with the lower side from point (0,0). Function inteseccionba.m calculates the intersection of leading edge circumference with lower side and upper side. Once these points are known, the program generates the x and y coordinates of the points that define the geometry of the new airfoil arranged as in MISES. These coordinates are written in file blade.parafoil. After this, points from the lower side are separated from those of the upper side. The objective is to define the camber line and thickness line of the airfoil, which are outputs of this program. Both thickness and camber have a strong influence in the outlet conditions of the flow. These parameters are defined as: Camber(x) = z upperside(x) z lowerside (x) 2 + z lowerside (x) (9.1.3) T hickness(x) = z upperside (x) Camber(x) (9.1.4) Camber line corresponds to the medium line of the airfoil and has a great influence in flow deflection angle. Thickness represents the distance of the points that form the airfoil from the medium line and has a weaker influence in flow deflection than camber. However, total pressure loss depends on thickness distribution. Thickness and camber distributions appear as output variables in the workspace of Matlab inteface as it can be seen in the picture below. 62

63 Figure : PARAFOIL Vane, Thickness and Camber Distribution. This vane was used by Mises to generate the results analysed in chapter Manufacturing Process The objective of this section is to describe the manufacturing process which results in corner 1 with fully assembled modified guide vanes. The process is designed to be as simple as possible with an acceptable level of accuracy since simplicity during this process was established as a design criterion. The process explains how the upper part of each corner vane and the supports or spars are obtained by cutting different sheets of PVC, according to plans in appendix (the dimensions of the unfolded upper side as well as the position of the spars were obtained with program PARAFOIL). Then, spars are attached onto the surface of the upper part sheet in certain positions previously calculated. This attachment is done using PVC fast adhesive. Once the curing of the adhesive is finished, the upper side is folded and placed over the lower side 63

64 forcing the coincidence of the leading edge with its counterpart, fixing it with aluminium tape. The same process is repeated for the nine vanes Materials The list of materials used is: 1. PVC sheets: 2 units: One of 1 mm thickness Another of 3 mm thickness 2. PVC fast adhesive: Griffon PVC gel 250 ml 3. Generic solvent: Eco-Solv 1L. 1 unit 4. Brush 5. Cutter 6. Ruler and measuring tape 7. Aluminium tape: 2 units PVC is relatively low cost, its chemical resistance and workability have resulted in it being considered the best candidate for manufacturing the upper side of the new guide vanes. It can easily be cut with a normal cutter if the sheet is soft enough, which means sheets with the desired measures can be obtained from bigger plates with no difficulty. This leads to lower costs being able to buy large amounts of PVC if the modification is big enough. Moreover, PVC adhesives are very effective: in a curing time of ten minutes the adhesive used can withstand 16 atmospheres of pressure which is many more times than needed to resist the present forces. This implies avoiding the use of other fastening elements such as rivets or bolts and associated tools. Finally, the aluminium tape is used to fix the leading and trailing edges since it can be glued in a way that guarantees continuity and softness in both edges, avoiding again different fastening elements which might be difficult to add in a pre-assembled corner because of space matters Process Manufacturing Process 1. Take the PVC sheet and trace the unfolded dimensions of the upper side (173.27mm x 370mm x 10 units). Then cut following the trace using the cutter with the help of a cutting ruler. 64

65 Figure : Cuts on the PVC sheet. 2. Proceed equally with the 3mm thickness sheet to obtain the three different supports or spars. Because of the bigger thickness, a saw might be needed to cut the sheet as desired. 3. Once the supports are obtained, all the parts that assemble the vane are available. The next step is to clean the surface of the upper side sheet with the solvent in order to eliminate oily substances which could damage the adhesive. For this, use a brush and apply solvent generously over the surface. Wipe if necessary and wait for the solvent to dry. 4. Mark the distances on the upper side surface where the supports or spars are placed at. Do this with the help of a measuring tape or a pre-made assembly tool. These distances were calculated with the PARAFOIL routine. 65

66 Figure : Distances for supports placement. 5. Next, apply adhesive with the help of a brush. Apply it over the lower side of the support to glue and the area of the upper side surface where it will be glued. Apply pressure for a few minutes until the support can stand for itself. Proceed the same way for the rest. 6. Finally, let the adhesive cure. Although the adhesive is fast, one day of prudential time is advised. After this time has passed, the upper side with the supports attached to it are ready to be assembled onto the existing vane. Figure : Section of a manufactured upper side. 7. Proceed the same way for the rest of vanes Corner Assembly This process is in charge of finally attaching the upper side previously manufactured onto the existing vane already assembled in the corner. For this: 1. Make coincidence of both leading edges. Fix with Aluminium tape. 66

67 Figure : Coincidence between both leading edges. 2. Bend over and make coincidence between trailing edges. Check the suports make contact with the lower side. Fix with tape. 67

68 Figure : Section of a fully assembled profile. 3. Proceed the same way for the rest of corner vanes obtaining a completely modified corner Conclusion and assessment of the Manufacturing Process This process describes a method by which the corner vanes are completely modified obtaining the desired guide vanes cascade. If this cascade is accurate enough, the method could be considered accurate despite its simplicity. Finally, good results in experimental data of the modification would confirm its reliability and if calculation methods are correct. In terms of accuracy, all measurements conducted during the process entail an error of 0.5mm. This could lead to a maximum deviation of 0.5mm of the maximum thickness and overall length of the upper side sheet when cut. An accuracy test could be done by checking this when forcing the leading edges of the upper and lower side to coincide, and forcing the contact of the supports with the lower side, both trailing edges coincide. This would result in the fact that the final vane will be close enough to the one calculated. This test was conducted for every corner vane during assembly and negligible deviation was observed. Finally, as it will be shown in later sections, experimental results are satisfactory, which means that the modifications made correspond to those calculated theoretically. To sum up, it can be said that, with this method, the modifications are made with simplicity, accuracy, and low cost materials leading to good results. Moreover, is a versatile method since different geometries can be manufactured only by changing the length of the different supports, making it a general method. 68

69 Part V. Possible improvements for the proposed guide vane 69

70 10. Introduction Parafoil has been found as a simple solution for turning the flow at corner 1 that suits the imposed requirements in design. This requirements are: 1. Acceptable total pressure loss in the guide vane cascade, lower to that offered by the ¼-circle shaped guide vanes. 2. Use of the existing guide vanes of the wind tunnel as the lower side of the new guide vanes. 3. Easily constructable upper side geometry. This way, there is no need for a complex or expensive manufacturing process 4. Flow deflection angle of 90º in the cascade. For these reasons, it was decided to use Parafoil airfoils to construct the guide vanes of corner 1. Nevertheless, this solution may not be the best one in terms of total pressure loss due to the presence of constraints of design (the lower side could not be modified and the manufacturing process had to be facilitated), so it is proposed to evaluate how different the geometry of Parafoil is from that of minimum total pressure loss with a 90º flow deflection. In order to obtain that geometry, the previous design constraints have to be eliminated so that the solution range may be widen. Figure : Parafoil geometry. In order to find the geometry with minimum pressure loss, the inverse calculus tool of software MISES, subprogram EDP, can be used. Its function is to perform geometrical redesign of an existing airfoil from a modification in its c p curve (or in other parameters such as Mach number curve or pressure curve) introduced by the user. EDP requires the converged solution of the current case as an input. The modifications in the c p curve should be introduced progressively so that the new geometry is obtained after an iterative process. 70

71 11. Parafoil improvement A first approach to determine how good the Parafoil is in terms of total pressure loss is to compare it with the geometry that presents the minimum pressure loss and respects the constraint of a 90º circumference arch lower side. This can be achieved by introducing iteratively little modifications in the upper side c p curve through subprogram EDP, without modifying the lower side c p curve. It is necessary then to establish a criterion to modify the upper side c p curve, so that the total pressure loss are reduced but the flow deflection angle stays unaltered. According to Fluid Mechanics theory, the flow experiments a change in its momentum when passing through corner 1. In fact, inlet flow direction is perpendicular to outlet flow direction. This is a change in the momentum of the flow due to an external action. This action is a force produced as a reaction of the lift force that appears on the guide vane due to the flow. For this reason, a greater lift force produces a greater flow deflection angle. Besides, from an aerodynamic point of view, flow deflection is related to the intensity of vortex that appear when the flow passes around the guide vanes, and vortex are related to the value of lift coefficient, which reassures the previous reasoning. According to the previous lines, it seems clear that a constraint to be respected while modifying the c p curve is that the area that it covers (that is, the area between lower side and upper side curves) should remain constant. The c p distribution of Parafoil is based on an upper side curve that presents a suction peak in the leading edge, then reaches an approximate value of c p 0.8 near x c = 0.5 and finally increases its value to c p 0.1 in the trailing edge, where lower side and upper side speeds are equal. In this case, program calculacl.m detailed in appendix, gives a value of lift coefficient of c l = In the next modifications, efforts will be made in order to maintain the value of this coefficient near c l =

72 Figure : c p curve of Parafoil. The blue line represents the upper side and the red line the lower side. Total pressure loss in the guide vane cascade are caused by two different effects with similar importance: velocity and static pressure decrease of the flow. Both of them are caused by viscosity, since according to results provided by MISES, there is no flow separation in any point of the airfoil so there are no losses due to that phenomenon. Moreover, the parameter that controls the losses caused by viscosity is the Reynolds number. In this study, it remains constant since the redesign is done just for the point of operation corresponding to maximum power of the fans. Therefore, the c p curve of the upper side is modified to make it flatter, in order to reduce the total pressure loss. 72

73 12. Optimization process This process starts with the computer modeling of the Parafoil airfoil. Once its solution is converged, subprogram EDP is used to modify the c p distribution. There are two different ways to modify this distribution. The first one consists of introducing a series of new points in the c p graphic displayed on the PC screen with the cursor, so that the program recalculates the new curve that passes through them using a smoothing technique. This information is complemented by delimiting the part of the curve to be modified, as well as by imposing smoothing conditions in the common parts. The second options is to introduce the new values of the c p curve through a file with a predefined format for upper side and lower side, so that the program reads them. Once these values are introduced, they are written in file idat.xxx (the file that contains the solution of the problem). File ises.xxx lines 1 and 2 have to be modified by adding the global variables and global constraints 11 and 12. Then subprogram ises is run, so that the iterations to calculate the new geometry that fits the modifications in c p start. Note that, even if the required changes in c p curve are considerable, changes should be introduced gradually in order to lower the execution time and to guarantee the convergence. Besides, this allows the user to check the results from each modification and to decide what modification should be done next. The following table shows the obtained solutions by modifying the c p curve of the upper side. Specimen c l S 2 ω Original Version Version Version Version Table : Results for modified geometries of the airfoil. The obtained results fit the expectations. In the previous results, it does not seem to be a clear trend between c l value and flow deflection angle S 2 as it should according to previous reasoning. This is mainly due to the fact that the values are in a small range near one point, which is c l = 0.85 and S 2 = For this reason, an analysis with these data is not relevant and a further one was presented in section 8.1. In terms of total pressure loss optimization in the guide vane cascade, it seems clear that there is room for improvement up to a 10 by means of modifying only the upper 73

74 side. Thus, it might be concluded that the degree of approximation of the Parafoil, compared to the best specimen in terms of total pressure loss with a ¼-circle lower side and a 90º of flow deflection with a modified upper side is reasonably high. As well, it is not worthy to implement the resulting geometry of this optimization process because it would imply to complicate the manufacturing process for a slight performance improvement. Figure : Results for modified Parafoil. Figure : Best specimen geometry vs Parafoil geometry. 74

75 13. Improvements from the ¼-circle airfoil The ¼-circle shaped airfoils initially used in corner 1 can be subject to an iterative redesign process similar to that exposed in the previous chapter. In this case, this process will allow to find an optimum solution in terms of total pressure loss by means of eliminating the constraint of a given lower side geometry. That is, the most general optimum solution would be found. Although the manufacturing process would present a greater complexity, its geometry would allow to evaluate the degree of approximation of Parafoil to an airfoil with redesign criteria of minimum total pressure loss and 90º flow deflection. The reference [9] proposes a solution obtained by means of inverse iterative calculations starting from the a ¼-circle airfoil. In the case of the tunnel that the study was done for, as well as in this tunnel, corner 1 has a larger outlet section than inlet section. After corner 1, there is a 2-D diffuser (the expansion occurs in one plane). This type of diffusers are more sensitive to flow separation, and in case of flow separation the flow quality is poor, so it must be avoided. For this reason, the reference [9] proposes a design of the guide vanes centered in avoiding laminar bubbles, so that the flow arrives to the diffuser in the best conditions. With this design criterion, some conditions must be imposed for inverse calculations. These conditions are: 1. The channel that appears between two consecutive guide vanes presents a outlet area to inlet are ratio, Aout A in, equal to outlet area to inlet area ratio for the whole corner. This can be achieved by imposing the following condition in the inlet and outlet slopes of the flow: h 2 h 1 = cos α 2 cos α 1 (13.0.1) 2. Flow must be deflected 90º when passing through the cascade. This is an essential condition to prevent the flow collision in the walls of the corner. 3. Reasonably low total pressure loss. α 1 + α 2 = 90º (13.0.2) Note that these conditions, excepting the second one, are not the same as the ones used for the present project. In the case of the ETSIAE wind tunnel, the maximum importance has been given to minimising the total pressure loss as well as to facilitate the manufacturing process, putting aside the possible effects of flow separation that can 75

76 occur in diffuser 2. Therefore, it is expected that the resulting geometry (shown in figure ) may differ from that proposed in this text. Figure : Airfoil proposed in KTH article. In fact, that is what happens. The guide vane proposed by [9] presents a smaller maximum thickness and a extension in the shape of a flap. According to that text, total pressure loss of the guide vane cascade is ω = 0.041, which is greater than total pressure loss in Parafoil cascade. Moreover, the manufacturing of the KTH guide vane requires a more expensive and complex process. At this point, it would be interesting to study the result of imposing, along with the minimum total pressure loss and easy manufacturing process conditions, the criterion in which the outlet to inlet area ratio of the channel between consecutive airfoils is equal to the outlet to inlet area ratio of the corner. This point is proposed as a future work. 76

77 Part VI. Wind tunnel tests with improved corner 1 and chamfers 77

78 14. Introduction Corner 1 has been modified by means of redesign and construction of a new guide vane cascade. In order to check the variation in total pressure loss from the initial configuration, new tests were conducted in the modified wind tunnel. In them, the settling chamber did not include the mesh, so that the results can be comparable with the initial configuration. Two different tests were conducted. The first one consisted on measuring the new value of the total pressure loss in corner 1. The second one was done with the wind tunnel fully instrumented, so as to obtain the total pressure loss in each element of the wind tunnel and to analyse the global improvement introduced with the new guide vane cascade. 78

79 15. Tests in Corner 1 First, a test in corner 1 was conducted to calculate the total pressure loss. The procedure was the same as explained in previous chapters. The parameter to evaluate the total pressure loss is ω. It takes into account the variation in total pressure between the inlet (1) and outlet (2) sections of corner 1. ω = pisentropic 02 p 02 p 01 p 1 (15.0.1) For obtaining the value of this coefficient, the Scanivalve gives the value of static pressure in the probes that are placed in the sections. These data are given as an input to the code perdidas_esquina.m, which calculates the total pressure loss. Nine static pressure probes are placed both in the inlet and outlet sections of corner 1. A total pressure probe was placed in the test chamber, along with a static pressure probe, in order to obtain the value of velocity in that section. It is noteworthy that the tunnel presents another modification from the initial configuration: the chambers in contraction chamber, test chamber and diffuser 1. Their goal is to reduce the secondary flow that appear in the corners of transversal sections of the wind tunnel (see section 6.4). According to [1], two-dimensional diffusers are susceptible to flow separation when the opening angle is bigger than 3.5º. Chamfers in diffuser 1 increase this angle increasing the risk of flow separation, with the consequences of lower flow quality and greater total pressure loss. For this reason, some threads where placed in three walls of diffuser 1 as well as in the trailing edge of guide vanes in order to check whether flow separation exists. If this phenomenon occurs, the threads would go backwards since the velocity profile is negative when boundary layer is detached. The procedure to obtain the pressure data consists of three calibration tests and three maximum performance tests. With them, data for total pressure loss calculation can be obtained with a high enough confidence level, as the results of section 3.2 show. These data are used as inputs for the code perdidas_esquina.m. Static pressure in the inlet and outlet section of corner 1 is obtained as the average value of the pressure in the nine probes placed around each of them. Velocity in test chamber is calculated from the dynamic pressure in the section, obtained as 2(p T 0 C p v T C = T C ) (15.0.2) ρ Velocity in inlet and outlet sections of corner 1 are calculated by means of the continuity equation, that is, 79

80 ˆ Q = σ v da = v A = constant vt C A T C = v inlet C1 A inlet C1 = v outlet C1 A outlet C1 (15.0.3) Note that chamfers reduce the area of the inlet section of diffuser 1 and must be considered. With these values, it is possible to obtain the total pressure in both inlet and outlet sections of corner 1 as So that the value of ω can be now calculated as p 0 = p ρv2 (15.0.4) ω = p 01 p 02 p 01 p 1 (15.0.5) since p isentropic 02 = p 01. Several groups of three calibration test and three maximum performance test were conducted to obtain the value of ω. Its final value was obtained as the average value of the results of these group of tests. This led to ω = (15.0.6) During the tests, threads placed in chamfers of diffuser 1 and trailing edge of guide vanes in the cascade were observed. Those situated at the beginning of chamfers started to move roughly, revealing that the boundary layer is turbulent, and those in the final part of the chamfers (closer to the inlet section of corner 1) started to move backwards. This means that there is flow detachment near the inlet section of corner 1. Consequently, flow quality is lowered by chamfers, so it might be possible that the total pressure loss in corner 1 is affected by this phenomenon, leading to a poorer result. The code perdidas_esquinas.m was adapted to be used with data from the tests with the curved plate cascade without flaps in the airfoils nor mesh in the settling chamber. The result revealed that the total pressure loss in that case was ω = (15.0.7) The result with flaps in the airfoils and mesh in the settling chamber was ω = (15.0.8) Note that, in this case, chamfers were not included in the tunnel so the flow in the inlet section was not detached. 80

81 16. General tests Several tests were conducted with the tunnel fully instrumented, that is, with several probes in each section. The goal of these tests was to calculate the total pressure loss in each element as well as the global effects of the improvements. The results of the tests were static pressure data used as inputs for the code ensayos_finales.m. It calculates the total pressure loss in each element of the wind tunnel (diffusers 1, 2 and 3; corners 1, 2, 3 and 4; power plant, settling chamber, contraction chamber and test chamber), using the parameter ξ = pisentropic 02 p 02 p T 0 C p T C (16.0.1) Which is very similar to ω, but the total pressure loss is divided by the dynamic pressure in test chamber instead of dynamic pressure in the inlet section of each element. Note that in passive components (such as corners and diffusers), p isentropic 02 = p 01 because they do not introduce external work to the flow. In the case of the power plant, parameter ξ is defined as ξ P P = p 01 p 02 p T C 0 p T C (16.0.2) and represents the increase in total pressure respect to the dynamic pressure in test chamber that this component introduces. In this way, a negative value would mean that total pressure has been increased. The procedure to obtain the total pressure in each element from the static pressure measurements of the probes is the same as explained in chapter 15. This time, four probes were placed in each section. The code was also used to calculate total pressure loss in each element in the wind tunnel with the previous configuration, that is with a curved plate cascade with flaps and mesh in the settling chamber. This allows to establish a comparison between both cases and to decide whether the tunnel has improved its performance. Figure and table show the parameter ξ for each element, before and after the modifications were introduced. The following analysis can be done: 81

82 Figure : Total pressure loss in each element measured by parameter ξ. Element ξ (before improvements) ξ(after improvements) D C D C D PP D C C SC CC Table : Total pressure loss per element. Corner 1 has been clearly improved with the new guide vane cascade so that it presents lower total pressure loss. Besides, the performance of diffuser 2 has been improved as well probably because of the good flow quality in the outlet section of corner 1. However, diffuser 1 has worsened its performance. As seen during test, there is flow detachment in chamfers, which implies higher total pressure loss and poor flow quality. Also, due to the chamfers modification, the dynamic pressure at diffuser 1 entrance is higher (because of 82

83 entrance section reduction) and this fact implies higher pressure losses. Other elements of the wind tunnel have varied their performance slightly, except the power plant. As explained in section 1.2.6, the mission of the power plant is to compensate the total pressure loss that is produced in other elements in the wind tunnel. For this reason, the increase of total pressure that the fans introduce is a measure of the global total pressure loss of the wind tunnel. With the new cascade and the chamfers, the variation in total pressure loss introduced by the power plant has varied from ξ = to ξ = (ξ < 0 since it is a gain); that is, the total pressure loss of the wind tunnel respect to dynamic pressure in test chamber has decreased in a Figure shows the value of total c p per element in the wind tunnel, both in the initial configuration and in the improved configuration. Figure : Total c p curve in the wind tunnel. 83

84 17. Conclusions Tests in corner 1 revealed a great improvement in terms of total pressure loss respect to dynamic pressure at inlet section. It was reduced in a 37 respect to the previous configuration with flaps and mesh and a 33 respect to the configuration without flaps nor mesh, as shown in figures and This is a great result with a simple, cheap manufacturing process for the new guide vanes. Finally, it can be said that the total pressure loss in the wind tunnel respect to dynamic pressure in test chamber has been reduced in a 14 respect to the initial configuration. Figure : Total pressure loss coefficient. 84

85 Figure : Improvement percentage in total pressure loss with Parafoil cascade. 85