Chapter 4 Estimation of wing loading and thrust loading - 8 Lecture 16 Topics

Transcription

1 hater 4 Estimation of wing loading and thrust loading - 8 Lecture 16 Toics Selection of roeller diameter for a chosen alication Examle Procedure for obtaining THP for given h, V, BHP and W Selection of roeller diameter for a chosen alication A roeller is selected to give the best efficiency during a chosen flight condition which is generally the cruising flight for transort airlanes. Some comanies may use their own roellers. However, design fabrication and testing of roeller are comlicated technical tasks. Hence, the general ractice is to use the standard roellers and the charts corresonding to them. As a first ste, the number of blades of the roeller is decided deending on the amount of ower to be absorbed by the roeller. The ower absorbed by a roeller deends mainly on three geometric features of the roeller viz. diameter, solidity ratio last two quantities are defined as follows. Solidity ratio at a radius r = σ (r) = Nc b πr σ r and activity factor (AF). The (4.13) 3 Activity factor = AF = N r/r c/ddr/r b 1,, (4.131) where, N b = Number of blades in the roeller. = hord of the blade section at radius r. R = radius of the roeller (d/). d = diameter of the roeller. Det. of Aerosace Engg., Indian Institute of Technology, Madras 1

2 The multilying factor (1,/16) is inserted so that the AF er blade has a convenient magnitude (8 to ). The two bladed roellers are used on the general aviation aircraft and for engines with ower rating uto kw. They are simler, lighter and cheeer than roellers with 3 or more blades. However, the two bladed roellers would become too large for higher ower ratings. The Mach number, corresonding to the resultant velocity at roeller ti, may exceed critical Mach number of the blade resulting in lowering of roeller efficiency. According to Ref.1.19, chater 1 and Ref.1.15, chater 3, the three bladed roellers are referred for engines with rating between to 5 kw. Four bladed roellers are used for engines with higher ratings. Early version of ATR 7 airlanes had 4 bladed roellers. The resent versions have 6 bladed advanced roellers. (see subsection ) At the resent stage of reliminary design rocess, the number of blades can be chosen from trends indicated by the data collection. The designer of a new airlane generally chooses the diameter of the roeller using the design chart (e.g. Fig.4.15c) aroriate to the roeller. onsider a four bladed roeller. Following stes are used to select the diameter of a roeller. (a) hoose a level flight condition i.e. altitude ( h c ) and seed ( V c ). (b) Obtain lift coefficient ( L ) in this flight using : L = W/.5ρ V S. Obtain the corresonding D from the drag olar of the c airlane. (c) Obtain THP required during the flight using : THP =.5ρ V 3 S /1 (d) Assume η between.8 to.85 deending on likely maximum value of η. (e) Obtain BHP = THP/ η. Then RPM (N) which will give this ower outut at the chosen h c with low BSF is known from the engine curves e.g. Fig.4.1. alculate n = N/6. (f) alculate 1/5 = V ρ /Pn. S D Det. of Aerosace Engg., Indian Institute of Technology, Madras

3 (g) From the design chart like Fig.4.15c, obtain the value of J on the dotted line, corresonding to the value of S in ste (f). Also obtain the value of β from the same curve. Obtain the value of η from the uer art of the design chart. (h) Since V, n and J are known, obtain roeller diameter using : d = V/n J (i) If the value of η obtained in ste (g) is significantly different from the value of η assumed in ste (d), then iterate by using the value of η obtained in ste (g). Finally round-off the roeller diameter to nearby standard value. Remark : The choice of the arameters of the roeller like, diameter, itch, blade size are also influenced by factors like noise level of the roeller, ground clearance, and natural frequency of the blade. Refer chater 6 of Ref.3.4. Examle 4.19 For the sixty seater turboro airlane considered in examle 4.16, obtain the diameter of the roeller from the consideration of cruise at V cr = 5 kmh and h cr = 4.5 km. Assume that the roeller has RPM of 1 and is a constant seed roeller. Solution : From examle 4.16 we note the following. W/S = 357 N/m, D = S = m L, W = 8757 N, Further, V cr = 5 kmh = m/s at h cr of 4.5 km, ρ =.7768 kg/m 3 q W/S L = ρv Hence, 357 L = = D = x.4764 =.341 Det. of Aerosace Engg., Indian Institute of Technology, Madras 3

4 THP required = 1 ρ V 3 SD 1 3 = = 1851 kw Since, the airlane has two engines, THP er engine = 1851/ = 95.5 kw Note : As regards the roeller, the actual airlane may have an advanced six bladed roeller. Such roellers are currently manufactured by M/S Ratier Figeac, Avenue Ratier, 461 Figeac, France. The roeller charts for this roeller do not seem to be available in oen literature. For the sake of this examle, the stes to obtain the diameter of the roeller are illustrated using roeller charts given in Figs.4.15a to d. From Fig.4.15a, the maximum efficiency can be taken as.85. onsequently, BHP er engine is 95.5/.85 = kw = 1888 W N = 1 or n = 1/6 = rs Hence, s = V 1/5 ρ/pn = /1888 1/5 =.47 From design chart in Fig.4.15c, corresonding to s =.47, the values of o β = 39.5 and J = 1.76 from lower art of the figure and η =.84 from the uer art of figure are obtained. Hence, roeller diameter = d = V Jn = = 3.95 m The value of η is obtained as.84 instead of the assumed value of.85 Hence, BHP required er engine = 95.5 = kw.84 onsequently, s 1/5 = /1118 =.466. Within the accuracy of grahs, J = 1.76 is obtained. Hence, roeller diameter = d = 3.95 m. Remarks : (i) It is interesting to note that ATR 7 has a roeller of diameter 3.93 m. Det. of Aerosace Engg., Indian Institute of Technology, Madras 4

5 (ii) Examle 4.4 of Ref.3.3 illustrates the rocedure to obtain diameter of roeller for a general aviation aircraft Procedure for obtaining THP for given h, V, BHP and N For calculating the erformance of the airlane, the thrust horse ower (THP) is needed at different values of engine RPM(N), break horse ower (BHP), flight seed (V) and flight altitude (h). In this context the following may be noted. (a) The engine outut (BHP) deends on the altitude, the flight seed and the throttle setting. (b) The roeller absorbs the engine ower and delivers THP; THP = η (c) The roeller efficiency deends, in general, on BHP, V, N and β. (d) The three quantities viz. d, V and n can be combined as advance ratio (J = V/nd). (e) Once η is known : THP = η x BHP and T = THP 1 / V. BHP The stes required to obtain η deend on the tye of roeller viz. variable itch roeller, constant seed roeller and fixed itch roeller. The stes in the three cases are resented below. I) Variable itch roeller In this tye of roeller the itch of the roeller is changed during the flight so that the maximum value of η is obtained in various hases of flight. The stes are as follows. (a)obtain the ambient density ρ for the chosen altitude. Also obtain the engine BHP at chosen V and N. 3 5 (b)obtain = P/ ρ n d ; P is BHP in watts P (c)obtain J = V/nd (d)alculate = J/ S 1/5 P Det. of Aerosace Engg., Indian Institute of Technology, Madras 5

6 (e)from the design chart for the chosen roeller (e.g. Fig.4.15c for a four bladed roeller), obtain β which will give maximum efficiency. Obtain corresonding η. onsequently, THP = η x BHP and T = THP x 1 / V ; note V (f) To get the thrust (T) at V =, obtain BHP of engine at V = at the chosen altitude and RPM. alculate. From Fig.4.15b obtain T and β at this value of P and J =. Having known T, the thrust (T) is given by : T = 4 ρ n d T II) onstant seed roeller The variable itch roellers were introduced in 193 s. However, it was noticed that as the ilot changed the itch of the roeller, the engine torque changed and consequently the engine RPM deviated from its otimum value. This rendered, the erformance of the engine-roeller combination, somewhat sub-otimal. To overcome this roblem, the constant seed roeller was introduced. In this case, a governor mechanism alters the fuel flow rate so that the required THP is obtained even as rm remains same. The value of β is adjusted to give maximum ossible η. The stes to obtain η are the same as mentioned in the revious case. III) Fixed itch roeller From Fig.4.15b it is observed that a fixed itch roeller has a definite value of P for a chosen value of advance ratio (J). onsequently, the roeller can absorb only a certain amount of ower for a given value of J. Thus, when the flight seed changes, the ower absorbed by the roeller also changes. However, for the engine-roeller combination to be in equilibrium i.e. run at a constant r..m, the ower absorbed by the roeller and that roduced by the engine must be the same. This would render the roblem of determining ower outut as a trial and error rocedure. However, it is observed that the fixed itch roellers are used in general aviation aircraft which use iston engines. The torque of a iston engine remains nearly constant over a wide range of r..m s. Using this fact, the torque coefficient ( Q ) and torque seed coefficient (Q s ) are Det. of Aerosace Engg., Indian Institute of Technology, Madras 6

7 deduced in Ref.1.5, chater 16, from the data on P & T. Further a rocedure is suggested therein to obtain η at different flight seeds. Herein, the rocedure suggested in the Aendix of Ref.4.8 is resented. It is assumed that the roeller is designed for a certain seed, altitude, rm and ower absorbed. Let, V = design seed (m/s) N = design rm ; n = N / 6 BHP = BHP of the engine under design condition (kw) d = diameter of roeller (m) J = Advance ratios under design condition = V / n d β = design blade angle; this angle is fixed η = efficiency of roeller under design condition The stes, to obtain the THP at different flight seeds, are as follows. 1.Obtain from the roeller charts, T and P corresonding to J and β. These values are denoted by TO and PO..hoose values of J from to a suitable value at regular intervals. Obtain from the relevant roeller charts, the values of T and P at these values of J s and the constant value of β. 3.alculate J/J, T / P and P / P from values obtained in ste. 4.alculate: T = ηbhp 1 / V and (4.13) K = T PO/ TO (4.131) 5.The assumtion of constant torque (Q ) gives that N and P are related. Note: Q =P /πn This yields: N = N PO P (4.13) Det. of Aerosace Engg., Indian Institute of Technology, Madras 7

8 J N V=V J N P T T and T=T =K T P P (4.133) (4.134) onsequently, THP = TV/1 and BHP = THP/ η Remarks: (i) Examle 4.5 in Ref.3.3 can be referred to for an illustration of the rocedure. (ii) Sometimes the manufacturer of the roeller may give an estimated variation of η vs J which can be used at various flight seeds and altitudes. Such a variation is used in Aendix A of Ref.3.3 for estimation of the erformance of a general aviation aircraft (Pier herokee PA 8-18). Det. of Aerosace Engg., Indian Institute of Technology, Madras 8