Trans RINA, Vol 156, Part B2, Intl J Small Craft Tech, Jul-Dec 2014
Table 5: Cavitation numbers
0.25 0.30 0.40 0.50 0.60 0.75 1.00 The results of testing are given in Table 6.
Table 6: Results of testing Ae /A0, P/D,
J KT j1 j2
t1 t2
... jn
... tn
KQ q1 q2 ... qn
Since there were twelve models and each of them was tested in nine different conditions of the environment (nine cavitation numbers from Table 5), this means that there are 108 tables of results. All tables do not contain the same number of the rows.
Mathematical models take the data from these tables. 6.3 (a) Koushan's Mathematical Model The general
tanh(C (Otanh(a (h (D X E )) )) ) G Y
i1
nm ii k,i
k 1 L k k k 2.50 Atm
Koushan obtained the constants for these expressions using artificial neural networks. The values of constants were published in [8]. Expressions for calculation of the coefficients are valid for the following
ranges of
independent variables 1.04 P/D 2.08, 0.48 Ae /A0 0.95, 0.25 1
J D
min 2
J D
min 0.538 0.129 P
for cavitating (15) and noncavitating (16) conditions. 6.3 (b) Modeling by Database
A computer database was created on the basis of data from Tables 4, 5 and 6. Program procedures enabled a simulation of tests in the cavitation tunnel. All graphics of functions are represented by spline functions.
form of Koushan's [8] mathematical expression for calculation of the coefficients KT and KQ is (14)
where Y may be KT or KQ depending on the set of constants used.
Independent X4=.
variables are: X1=J, X2=Ae/A0, X3=P/D,
6.4 COMPARISON OF MATHEMATICAL MODEL AND DATABASE
The results of testing of each model propeller from the series, for a given condition of the environment, are represented by one table. In Figure 5 these results are presented by points for the model propeller with the following ratios: Ae /A0=0.95, P/D=1.24 and =0.5. The curves presenting the dependence of KT on J and of KQ on J are obtained in two ways: by spline functions and by Koushan’s expression (14). The efficiency is calculated by the expression (11) and relates only to the spline functions. Koushan's curves are presented for the range of advance coefficient from J=0.5 to J=2.3. This is done to show how large the domains of the spline functions and the approximating mathematical functions are.
P (1.08 1.585 1.013) (15) (16)
0
10KQ KT
Figure 5: Model propeller with: Ae /A0=0.95, P/D=1.24 and =0.5 B-50 ©2014: The Royal Institution of Naval Architects
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