Propeller design calculation.doc

Propeller design calculationHere we describe the steps in a simple propeller design calculation, using lifting line theory. A table with an example is given afterwards. This corresponds to chapter 5.1 in Minsaas “Propeller Theory”, but be aware that the example in chapter 5.1 have several numerical errors, and the different lines in the example table dont necessarily come in order of calculation.The propeller design calculation consists of three steps:1. Calculation of thrust and torque2. Check of risk of cavitation3. Determination of camber and pitch distributionCalculation of thrust and torque1. Select propeller diameter and RPM. A Bp-d diagram or experience might be used.2. Select blade section thickness and camber distribution, using for instance tabulated data in books such Abbott & von Doenhoff “Theory of wing sections”3. Design radial chord length distribution c(r)4. Design radial thickness distribution t(r)5. Find radial wake distribution w(r) from model tests or from empirical data6. Design circulation distribution. The following generic type of distribution is frequently used: . In this case, the design is about selecting values of k, a, and m. 7. Calculate mean induced tangential velocity UT at all radii: 8. Solve to find mean axial induced velocity UA at all radii9. Find mean hydrodynamic angle of attack bi at all radii: 10. Find correction factors for finite number of blade to determine values of UT and UA at the blades. Two alternative methods:a. Goldstein factors (used in the example below)b. Induction factors11. Calculate , , and : 12. Calculate the resulting total velocity at each radius: 13. Calculate the lift of each section: 14. Calculate the corresponding lift coefficient: 15. Calculate the drag coefficient of each section: 16. Calculate the drag of each section: 17. Calculate total thrust of each section: 18. Calculate torque of each section: 19. Integrate (sum up) to find total thrust and torque20. Are the thrust according to required thrust?a. No: Go to step 6 and adjust the circulation distribution. Change of RPM or diameter, is also possible.b. Yes: Proceed to cavitation checkExample calculation Circulation distribution parameters:k=20a=0.1m=0.4A spreadsheet containing the formulas and numbers behind this calculation is available on the subject web pagesMain input data:Vs18knotsT1080kNRPM150n=2.5HzD6mxboss0.2rboss0.6mz4bladesWater Density1025kg/m3Kin.viscosity1.19E-06m2/sCalculation of thrust and torque:x=r/R0.2040.2840.3640.4440.5240.6040.6840.7640.8440.924r0.6120.8521.0921.3321.5721.8122.0522.2922.5322.772xx0.0050.1050.2050.3050.4050.5050.6050.7050.8050.905w0.1490.1370.1290.1230.1180.1130.1100.1070.1040.102t0.2190.1980.1780.1580.1380.1180.0970.0770.0570.037c1.2871.4881.6361.7381.7951.8041.7571.6421.4351.07G3.4711.7215.2117.5819.1720.0220.0619.1417.0313.15VA7.8827.9928.0688.1268.1728.2108.2428.2708.2948.316UTmean0.9032.1882.2172.1001.9411.7591.5561.3291.0700.755UAmean0.9882.8553.6044.1014.4324.6134.6354.4714.0673.274bi42.43537.46931.59727.11623.64820.86918.55616.55514.74612.983C(x,z,bi)1110.9970.9930.9840.9640.9240.8410.66UT0.9032.1882.2172.1061.9551.7871.6141.4381.2731.144UA0.9882.8553.6044.1144.4644.6884.8084.8384.8364.960bi42.4437.4731.6027.1323.6920.9518.7116.8515.3114.10V m/s12.41415.48318.83722.32725.89729.52033.18036.86740.57644.306Lift N/m44191185934293683402246508889605893682192723201708294596990CL0.1090.2540.2470.2260.2060.1880.1720.1580.1460.139Rn1.35E+071.94E+072.60E+073.27E+073.92E+074.49E+074.91E+075.10E+074.90E+073.99E+07CF2.85E-032.68E-032.56E-032.47E-032.40E-032.35E-032.32E-032.30E-032.32E-032.39E-03CD7.64E-036.79E-036.23E-035.83E-035.53E-035.31E-035.14E-035.04E-035.00E-035.11E-03dr0.2520.240.240.240.240.240.240.240.240.228dD N783119217792485327741074894553058125018dTD N5287259321133131614681570160315341223dQDNm35480616552946471869509512121311419413491dT N7691346925910284781110528134335153500164510162426130789dQ Nm495223935419836159181846101151117304127468127823105425Resulting performance:Thrust1042.4kNTorque793.5kNmPower12464kWVs18knotsRPM150KT0.126KQ0.0159JA0.544h0.682Cavitation checkTo check for cavitation, we need to estimate the local velocity at each blade section (radius). To do so, we need to select thickness and velocity distributions. Mostly, standard profiles for which properties are known are selected. For the example, we have chosen NACA a08 camber distribution and NACA 16 thickness distribution. Other data we need are:Draugt to propeller shaft: 7 mWater vapour pressure: pv=1500 PaAtmospheric pressure pa=101325 PaCalculation procedure:1. Calculate cavitation number: 2. Calculate velocity due to thickness: , where value for is taken from the table in Appendix I in Abbott & Doenhoff. 3. Calculate velocity due to camber: where the value for is taken from the table in Appendix II in Abbott & Doenhoff.4. Calculate total max velocity at the suction side of each section: 5. Check for cavitation. If then we will get cavitation. Often, a margin is introduced, for instance: Example of cavitation check:s2.0771.3160.8760.6140.4490.3400.2650.2110.1720.141v/V1.1941.1521.1241.1041.0881.0751.0631.0541.0451.039Dv/V0.0300.0710.0690.0630.0570.0520.0480.0440.0410.039Vx15.20018.93022.46926.05029.65533.26736.85840.46144.06547.763(Vx/V)2-10.4990.4950.4230.3610.3110.2700.2340.2040.1790.162Cavitation?NoNoNoNoNoNoNoNoYesYesDetermination of camber and pitch distributionThe point here is correction of the geometry for the fact that the propeller blade sections arent foil sections alone in linear motion, but operate in vicinity of other blades in a helical motion. This can be taken into account directly by lifting surface calculations, but can also be taken into account in an approximate manner, as described in Minsaas “Propeller Theory” chapter 6.1. For the purpose of this example, we use the following correction formulas:Camber correction factor: Correction factor for angle of attack: Correction factor for effect of thickness: The basis for the calculation is that the propeller blade sections are designed to lift purely by camber. It is fairly straight forward to modify the procedure to allow for a combination of angle of attack and camber. Calculation procedure:1. Calculate max camber of each radius: where is the max camber value found in the tabulated data for NACA a08 camber profile.2. Calculate correction of ideal angle of attack due to 3-D effects: 3. Calculate correction of ideal angle of attack due to thickness effects: 4. Calculate resulting geometric pitch distribution: Example calculation of camber and pitch distribution:kc1.6681.6141.5571.5091.4831.4941.5531.6751.8732.159ka1.01241.03341.07041.12781.21011.32171.46721.65111.87782.1518kt7.7606.9316.3805.8065.2284.6494.0553.4282.7331.872f/c0.01180.02670.02500.02220.01990.01830.01740.01720.01780.0195ai30.16950.40460.40680.39340.38430.38270.38870.40190.42290.4594at1.32050.92220.69420.52780.40200.30410.22390.16080.10860.0647P/D0.61730.71730.73410.74340.74920.75260.75360.75290.75220.7576