Aerodynamic analysis of a propeller by vortex lattice method

Propellers with different shaped blades are used in many applications like fans, ships, wind turbines, aircrafts and helicopters. In this study, aerodynamic performance of a propeller is analysed numerically by using vortex lattice method. A FORTRAN based computer program is developed for this project. Propeller geometry information, propeller advance ratio and propeller blade section characteristics is used as program input for numerical calculation. There are many studies in literature which used computational fluid dynamics (CFD) methods, experimental methods and vortex lattice method (VLM) in order to calculate propeller performance in fans, ships, wind turbines, aircrafts and helicopters. There are numerical methods like momentum method, blade element method and Prandtl lifting line method in propeller theory. These methods are also used in literature for propeller calculations. According to studies in literature, thrust and tork values calculated by blade element method are generally %10 greater than values calculated by experimental methods.This difference is resulted from constraint of this method on considering effects of trailing vortices and blade vibration effects on propeller performance. There are also studies in literature comparing blade element method and CFD method. Blade element method and CFD thrust, tork and efficiency results are very similiar to each other and distribution graphics behave in a similiar way. CFD method shows tip loss caused by tip vortices better than blade element method. Because of this, there is a significant reduction in CFD profile's tip region. CFD methods can offer better opportunities for fan performance development rather than old design and analysis technics. CFD programs solve Navier-Stokes Equations for whole flow region. Programs written by VLM method can only calculate velocity and pressure on required location. In slender blades, successful results can be obtained by VLM method by using less computer force. Vortex lattice method helps selecting appropriate blade geometry from different blade geometries and helps rapid pre-design. There are many studies in literature which used vortex lattice method (VLM), in order to calculate propeller performance in ship, aircraft and helicopter propellers. However, there are few studies in literature which are analysing fluid flow around axial fans. Vortex lattice method is selected by researchers because it helps getting rapid and accurate results for propeller design. The weakness of the method is that lifting element is only considered as a camber curve and neglects thickness. Because of this assumption, VLM method can't consider viscose effets. In vortex lattice model which is build up for propeller, blades are divided into panels along span and chord. Flow around propeller can be modelled by horse shoe vortices on every panel. Vortex strenghts are problem's unknown parameters. In this method, horse shoe vortex strengths on blades opposite to each other are same. So, calculating vortex strenghts on one of the blades is enough, it is not necessary to calculate for other blades. Solution of equation system can be done by using surface boundary condition. Surface boundary condition assumes that flow's component vertical to boundary is equal to zero. Aerodynamic forces can be calculated from vortex strenghts calculated by Joukowsky lifting law. Trailing vortices behind 3D blade's wake is propagating in blade's moving frame. In propellers, trailing vortices are propagating behind propeller by helical trajectories on wake at the effect of revolving and advancing movements of propeller. Root vortex is extending along rotor axis lineerly. Going far from propeller, wake vortex straitens and similarity in geometry breaks. In this case it is supposed to be damped in far regions from propeller. Helix wake behind a propeller generated by vortex sheet which is built up by trailing vortices can be modelled by several wake methods. Wake methods can be divided into two basic methods, steady and transient methods. Prescribed wake model is a steady method which describes wake as a function. Free wake model is a transient method which includes rolling on blade tip and calculates wake vortex coordinates iteratively. In this study, free wake model isn't preferred because it needs long computational time and there is a little role on accuracy of the results. Prescribed wake model is selected in order to obtain wake vortex coordinates. Total thrust and moment on a propeller can be calculated if propeller blade geometry, blade section characteristics, propeller advance velocity, rotation velocity and density of air is given. By using these values propeller performance parameters (thrust coefficient, moment coefficient and efficiency) can be calcuated. Program results are validated by using different blade profils. Propeller results are validated by using a test propeller with known geometry and performance. Prandtl lifting line and blade element-momentum based programs which are developed before are used for validation of VLM based study results. Validation studies for propeller blades are performed by using lifting line method program (MAYwingPLL). In first application, uniform sheet shaped blade and blade which has a imaginary profile without camber with a smaller lifting curve slope is analysed. According to results of a profile without camber, lifting coefficient values calculated in different angles of attack with lifting line method and vortex lattice method are similiar to each other. Numerically calculated values are compared with analytically calculated values taken from literature. Lifting coefficient values calculated analytically for sheet shaped blade and a blade which has a imaginary profile, are greater than numerically calculated values because lift in 3D blade is smaller than lift in 3D blade in same angle of attack. Because 3D blade has an induced drag component added to lift which doesn't exist in 2D blade. In second application, camber is added to imaginary profile in order to see effect of camber in numerical method results.Lifting coefficients that are calculated by lifting line method has changed under the effect of profile camber. Lifting coefficients that are calculated by lifting line method are greater than lifting coefficients that are calculated by vortex lattice method. In third application, real blade profile data which includes non-lineer region data of an airfoil is used. NACA 4412 is chosen as a blade section profile. In results which are calculated by two methods (lifting line theory and vortex lattice method), lifting coefficients in lineer region is increasing lineerly similiar to lifting coefficients in literature. There isn't any reduction in slope of lifting curves of two methods in blade profile's non-lineer region because viscose effects are not included. In last blade test study, numerical results are compared with experimental study results in order to examine success of the method. NACA 4415 profile is chosen as rectangular blade section profile. In this application, calculations are made for rectangular blade with aspect ratio values 6, 9 and 12. Results are given compared with 3D experimental results given by Ostowari and Naik. When aspect ratio value is small (AR=6), vortex lattice method results are converging to experimental results between angle of attack interval 0°<α<10°. However harmonization between results isn't enough because flow passing above blade is assumed to be 2D in vortex lattice method. In this aspect ratio, 3D effects are stronger and using section profile values causes mistakes. When aspect ratio value is greater (AR=9 and AR=12), experimental and numerical results are consistent with each other. This study shows that when aspect ratio value is big enough, vortex lattice method is a reliable method. Test propeller with known geometry and performance parameters is selected for propeller application. Clark Y profile is used for test propeller blade profile. MAYpropBEM program is used for validation of results of vortex lattice method program for propeller. This program is used for propeller design and analysis. It is based on momentum and blade element methods. First of all, propeller in required conditions is designed with BEM program. Using this propeller geometry in design conditions, propeller performance is calculated in different advance ratio values. Thrust coefficients values which are calculated by vortex lattice method and blade element methods are compared. Results of two methods are consistent with each other around design advance ratio (Jprop= 0,467). In different advance ratios, variation of thrust coefficient values are also consistent with each other. Moment coefficient values calculated for different advance ratios by vortex lattice and blade element methods are consistent with each other. Efficiency values calculated by VLM method are greater than efficiency values calculated by BEM method in same advance ratios. Because VLM method doesn't consider viscous effects. However, this study can be extended by finding new propeller geometries and experimental studies from literature . Also VLM studies can be compared with other CFD studies or Numerical method studies solved with other methods in literature. New experimental studies can also be used for comparing with VLM studies.