INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 2, No 1, 2011 Copyright 2010 All rights reserved Integrated Publishing services Research article ISSN 0976 4399 Numerical investigations of Coandă lift on a double curvature super circulated ramp POLITEHNICA University Bucharest, Faculty of Aerospace Engineering Str. Gheorghe Polizu, nr. 1, sector 1, 011061, Bucharest, Romania. drvaleriu@gmail.com ABSTRACT The paper relies on Henri Coandă s observations of very thin flows over curved surfaces in the late 1930 s in which it became apparent that such an arrangement would yield more lift than the thrust of a jet having the same mass flow. Since then various experiments have been carried out culminating with the development of super circulation aircraft such as the Antonov An 71 and the Boeing YC 14. Those aircraft however do not fully take advantage of effect, relying mostly on diverting the fan flow downwards trough gapless flaps. In this paper we try to investigate numerically the lifting properties of thin jets, at various velocities in the subsonic regime. The method used is a 2D computational fluid dynamic, Reynolds averaged Navier Stokes with a k epsilon two equation viscosity model. The results obtained indicate that, indeed such thin flows generate higher lift than if the flow were to be directed downwards. Efficiency and effectiveness parameters have been defined in order to estimate the feasibility of further real life applications of this effect per se in aircraft wings or turbo machinery blades. The findings are encouraging however they still require experimental validations. Keywords: super circulation, Coandã effect, lenticular aerodyne, RANS, CFD Nomenclature is the momentum coefficient q is the dynamic pressure of the free stream c is the chord length is the mass flow is the injector velocity is the bukl averaged velocity of the injector jet is the lift obtained by super circulation A is the super circulated surface aria E is the effectiveness coefficient L is the loading factor η is the efficiency of the ramp is the efficiency increase 1. Introduction Ever since Henri Coandã s lenticular aerodyne first took flight in 1938 as a small scale test model it became apparent that not only he had discovered a new principle of flight but also a new principle of achieving thrust. The key of the lenticular aerodyne was the thin film jet that washed the curved ramp of the aircraft achieving lift by lowering the static pressure on Received on July 2011 published on September2011 241
theupper surface. The lift obtained in this manner is slightly higher than that obtained by directing the fluid downwards without a ramp.coandã (1936) shows the original patent obtained for a device for deflecting a stream of elastic fluid projected into an elastic fluid. Super circulation, in itself is a combination of the Venturi suction effect and Coandã effect, both of which must be considered for accurate modeling of the phenomenon. It is manifested by a drop in static pressure due to a combination of Coandã effect and the increase of the dynamic pressure. Previous studies indicating no drop in pressure on flows over flat surfaces, the effect being applicable only on curved surfaces. Thus far, the main applications derived from this principle were the Antonov An 71 and the Boeing experimental YC 14 aircraft. Both of them used thick jets equal to the size of their fan and almost no curvature on their upper surface, relying instead on deflection of the fan flow trough the Coandã effect downwards. This approach shows little understanding of Coandã s findings and their significance. Description of this complex effect has never been attempted trough parametric studies but by more pragmatic approaches such as the ones of (Aoyagi et al.,1973) and (Ernest B. Keen and William H. Mason, 2005) in which the layout of the YC 14 is varied as with a conventional non Coandã effect aircraft. In newer applications the effect has been studied for fluid flap systems for conventional aircraft. The momentum coefficient is defined trough the dynamic pressure of the free stream of air surrounding the object, the considered airfoil. In (E. M. Lee Rausch et al., 2006) such a flap system is described in which the thin Coandã flow is blown over a double curvature ramp in various embodiments, hence motivating our own approach of using a simple double curvature ramp. The main differences in our test is the large dimensions of the ramp and the functional role of it, i.e. to obtain lift rather than deflect the surrounding fluid as it is the case with the flap system from In (E. M. Lee Rausch et al., 2006). A parametric study was considered in this paper, in order to observe the behavior of a given super circulated surface in zero aerial velocity at different injector velocity outputs. The varied parameter was the velocity of the injected air stream. The main measured parameter being the static pressure on the upper side of the ramp. It needs to be said that the studied ramp is only for theoretical purposes and should not be thought of as an aeronautical application. The lessons learned by studying this simple, crude geometry will help generate a wide set of applications ranging from airfoils for aircraft and blades to jet nozzles. (1) 2. The Computational Fluid Dynamic layout Past studies, (Drãgan, 2011) have revealed that certain viscosity models although attractive due to their mathematical formulation such as the Reynolds 5 equation model (RSM) may prove erroneous when studying the Coandã effect. The same study shows preliminary calculations using the one equation Spallart Alamaras model which offered less errors however failed to predict flow detachment from the single curved ramp, in order for the S A model to accurately predict such cases it requires a curvature and rotation compensation, described in (Shur, M. L et al. 2000) however this model defeats the purpose of a quick converging single equation model. The only model that performed well was the two equation k omega. International Journal of Civil and Structural Engineering 242
In this case, the curvature is quite small and well within the known attached region described in the experimental study performed in (Neuendorf, R., Wygnanski, I, 1999), below 90 degrees, therefore little differences are to be expected between the k epsilon model used here and other two equations viscosity models. Although certain authors(thomas D. Economon, William E. Milholen II, 2008) obtained more optimistic results with the Menter SST than the k epsilon viscosity model, here we will focus on the latter since it requires fewer modeling constants making it more robust especially in the far field regions of the flow. A computational grid detail can be observed in Fig.1. Special care was given to refining the mesh around the curvature, refinements being set for every 0.001 radians. Also the boundary of the 2D domain is as far away as reasonably possible in order to minimize boundary effects that might influence the output results. Figure 1: A close up view of the mesh Boundary conditions were set at 3 bar, as the intended practical applications on low pressure compressor blades envisioned for further development dictates this pressure. The injected fluid is considered at the ambient 3 bar pressure, the only varied parameter being the velocity. As it will become apparent, the effect of the two radii ramp has been somewhat unexpected as the resultant of the super circulation lift obtained shifted its angle from one part of the ramp to the other, this can be interpreted as an indication that each ramp curvature attains an optimal lift only on a given velocity. Ramp proportions and sizes can be seen in Fig.2. All dimensions are given in millimeters. The simulation is considered to be a two dimensional one however, the actual model is a narrow three dimensional mesh with periodicity boundary conditions on the frontal plane. This is because turbulence a key component especially in this case is a three dimensional phenomenon, not a two dimensional one. International Journal of Civil and Structural Engineering 243
Figure 2: Dimensions and proportions for the solid geometry used 3. Modeling the Problem In the beginning, several key velocities were considered at 100, 150, 200, 250 and 300 m/sec. Integrated parameter plots indicated an anomaly at the 200 m/sec setting. This setting was found to be in correlation with a shift in lift resultant angle. This is the result of ramp double curvature. To ensure that the anomaly was not a computational error tests have been carried out on both sides of the three point saddle created by the 150, 200 and 250 m/sec velocities. Results with these further studies revealed that indeed the saddle formation was the result of a velocity geometric correlation effect and not a computational error. Maxima in lifting efficiency were observed at 175, 250 and 330 m/sec. The static velocity plot in Fig.3 corresponds to the 250 m/sec setting. Figure 3: Velocity plot for 250 m/s injector velocity setting Lifting efficiency is defined as the ratio between the lift obtained by super circulation and the ideal thrust calculated for the exhaust parameters of the injector, the mathematical expression is given by equation 2: (2) Since the flow considered was fully developed, i.e. the velocity distribution near the wall varied due to the wall friction, the bulk average velocities were considered for injector thrust International Journal of Civil and Structural Engineering 244
calculation. The initial velocity conditions have been corrected for velocity distribution at the nozzle boundary for better physical modeling. We can also define the efficiency increase as: (3) 4. Interpretation and data correlation Aside from the lifting efficiency parameter defined in Eq. (2), we also define the effectiveness parameter. Effectiveness considers four important sub parameters: injector thrust, super circulation lift efficiency, load factor and injector mass flow required for achieving this lift. The load factor is defined, classically by equation (4), as the product between the lift obtained by super circulation and the total super circulated area. The mass flow requirement is a very important aspect since the flow is taken from the core, or primary flow, of the turbine engine. Usually mass flows exceeds 2% of the total core flow cannot be tolerated since that can induce low engine efficiencies. A complete analysis must be made and, if the engine used is not specifically designed to have a surplus core airflow, a cycle and super circulation tradeoff analysis must be made for economical purposes. For the purposes of this paper however, the effectiveness parameter is sufficient for the preliminary parametric studies. Effectiveness is mathematically expressed in Eq.5. (4) Correlations were made between plots of lift efficiency with velocity and lift efficiency with injector mass flow, both having an almost identical profile which was to be expected, even in the compressible velocities of the testing. Figure 4 depicts the surplus lift obtained by super circulation as opposed to direct thrust in percent versus the injector velocity. (5) Figure 4: Efficiency increase, η 100 [%] Vs. injector velocity Another parameter that can be correlated with velocity is the angle of the total super circulation resultant force, which has an influence in lifting efficiency, generating the saddle International Journal of Civil and Structural Engineering 245
region. This shifting effect is to be expected even in ramps with only one curvature radius but it is more exacerbated in this, two radii, ramp setup. Figure 5: Efficiency times loading Vs. injector velocity A key observation is that the effectiveness to velocity plot is virtually linear excepting the saddle region which can be seen as a small abatement from the otherwise straight general slope. Figure 6: Effectiveness Vs. injector velocity Notable is that the plot of efficiency times load factor with velocity is not linear but almost parabolic in shape. Correlating these findings with the effectiveness plot can offer two leads for further optimization: 1. Maximising the effectiveness of a super circulation system 2. Maximising the resultant force (load factor times lift efficiency) very useful in critical flight conditions and an attractive parameter for military applications where economical solutions are often overshadowed by high performance outputs. International Journal of Civil and Structural Engineering 246
5. Conclusions Numerical investigations of Coandă lift on a double curvature super circulated ramp A super circulation parametric test of a very thin jet over a double curvature ramp has been devised and carried out. The CFD simulations were made at constant ambient pressure of 3 bar, static atmosphere, with far field velocity zero and by variation of injector velocity. Velocities ranged from 10 m/s to 330 m/s and included further refinements around the 150 m/s, 200m/s and 250 m/s settings. Findings have been synthesized in the following list: 1. In the case of very thin jets, super circulation provides higher lift than the thrust of the bare jet. This effect has previously been observed by Henri Coandã and is consistent with current findings that used RANS k epsilon turbulence model CFD simulations. 2. The effectiveness of the super circulated system, Eq (5)shows a linear dependency with injector velocity 3. The lift efficiency parameter, defined by Eq(2) varies quite rapidly with injector velocity until a maximum is reached at around 100m/s. Some small variations have been observed at 200 m/s, mostly due to lift resultant angle shifting with velocity. Hence it is apparent that after reaching the velocity at which the air becomes compressible, the efficiency virtually stagnates. 4.An efficiency times load factor to injector velocity plot has been made showing an almost parabolic profile. This opens the perspective for a different optimization criterion i.e. resultant force maximization rather than effectiveness maximization. 5.Injector flow deviation effect is largely identical, proportional to the injector velocity, in all cases. The deviation angle was practically unaffected even by high injector velocity variations from 10 m/s to 330m/s. Injector flow deviation can be estimated in each case as a function of ramp geometry, In other words it is independent at subsonic velocities and low curvatures of the velocity of the injector jet. 6. The double radius ramp exhibits a shift in the lift force orientation that depends on the velocity of the injected fluid. Although it is difficult to formulate a complete explanation for this phenomenon, it is likely that the fluid film thickness plays a significant role. In other words at low velocities, the first ramp section consumes the energy of the flow leaving the second section to have less lift. In the higher velocity cases, the fluid has enough energy to provide lift on both sections but since the second section is more curved it will provide more lift than the first physically can. Therefore we should expect the total lifting force to have a shifted orientation for various fluid velocities. 7. The thin fluid jet is accelerated when passing over the ramp Further work may include devising a hovering device such as a flying disk suggested by Coandã or fixed wing hybrid aircraft which would make use of the findings. The same principle can be retrofitted to rotary wings, compressor and fan blades to increase their load factor and increase thrust. Acknowledgement The work has been funded by the Sectorial Operational Programme Human Resources Development 2007 2013 of the Romanian Ministry of Labour, Family and Social Protection through the Financial Agreements POSDRU/88/1.5/S/60203 International Journal of Civil and Structural Engineering 247
6. References Numerical investigations of Coandă lift on a double curvature super circulated ramp 1. Coanda, H., (1936) Device for deflecting a stream of elastic fluid projected into an elastic fluid. US2, 052,869. 2. Aoyagi, Kiyoshi, Falarski, Michael D. and Koenig, David G, (1973), Wind Tunnel Investigation of a Large Scale Upper Surface Blown Flap Transport Model Having Two Engines. NASA TM X 62,296. 3. Ernest B. Keen and William H. Mason, A Conceptual Design Methodology for Predicting the Aerodynamics of Upper Surface Blowing on Airfoils and Wings, 23rd AIAA Applied Aerodynamics Conference 6 9 June 2005, Toronto, Ontario Canada AIAA 2005 5216. 4. E. M. Lee Rausch, V. N. Vatsa,C. L. Rumse, Computational Analysis of Dual Radius Circulation Control Airfoils, 36th AIAA Fluid Dynamics Conference, June 5 8, 2006, San Francisco, California 5. Valeriu Drãgan, (2011),A parametric study on ambient pressure effects on super circulation over a simple ramp, International Journal of Advanced Engineering Sciences and Technologies Journal, 5(1), pp 94 104. 6. Shur, M. L., Strelets, M. K., Travin, A. K., Spalart, P. R., Turbulence Modeling in Rotating and Curved Channels: Assessing the Spalart Shur Correction, AIAA Journal, 38(5), 2000, pp 784 792. 7. Neuendorf, R., Wygnanski, I., On a turbulent wall jet flowing over a circular cylinder, Journal of Fluid Mechanics, 381(1), 1999. 8. Thomas D. Economon, William E. Milholen II, Parametric Investigation of a 2 D Circulation Control Geometry, Configuration Aerodynamics Branch Research and Technology Directorate Submitted: August 7, 2008. International Journal of Civil and Structural Engineering 248