Trans RINA, Vol 156, Part B2, Intl J Small Craft Tech, Jul-Dec 2014
of operating conditions, i.e. the cavitation number, is represented in a table (see Table 3). There are relations between these tables indicating how the data from Table 6 are related to the data from Table 2 and Table 3, more exactly, which graphic belongs to the propeller that operated under certain environmental conditions. In the area of programming, a series of mutually-connected tables makes a relational database.
This database can be represented by multidimensional matrices containing the data from the tables. The indexes of matrices serve to make connections between the tables.
This way of describing the data makes it possible for the results of tests of some propeller series to be presented in a computer program. Matrices with written data are an integral part of this program. In the beginning of the program, a program procedure reads the data from each respective matrix. On the basis of these data, one interpolating spline function is made for each model propeller and
for each propeller, which represent
relation to J (or KQ to J). The coefficients are stored in other multidimensional matrices. In this way, the whole family of graphics is described by spline functions, which are stored in the computer memory. This means that the results of the model propeller series tests have their own program (computer) record.
Now it is possible, with the help of written program procedures, at any time to simulate by computer the complete testing procedure of the model propeller series. This means that we may choose any model propeller and the conditions of environment where this model operated, i.e. the cavitation number, and obtain results of these tests: the dependence of KT on J and the dependence of KQ on J for some .
The use of the tables containing basic and accurate data, creating connections between them and using spline functions to present the dependence is done to obtain accurate and reliable results. The accuracy is maintained because the spline functions interpolate the points of measurements (KT, J) and
(KQ, J). In making
mathematical models of experimental tests by functions fT and fQ, accuracy is sacrificed and, consequently, unreliability is increased.
According to the database, it can be observed how geometrical changes of the model propeller and changes in the conditions of environment, the cavitation number, affect the amount of thrust and efficiency, i.e. the changes in the law of dependence of KT on J and of KQ on J. These changes can be monitored in three separate procedures and analyzed:
how the dependence of KT on J (and of KQ on J) of a model propeller changes when it operates in an environment that changes its condition;
how the dependence of KT on J (and of KQ on J) changes when the pitch of a model propeller is changed but the condition of environment is not changed; and
how the dependence of KT on J (and of KQ on J) changes when the expanded area of a model propeller is
changed but the pitch and the condition of the environment are not changed.
Each of these procedures produces a family of graphics whose parameter is a quantity that changes. The law according to which KT is changed in relation to J (or KQ to J) by some parameter is the law according to which the first graphic of the family turns into the last one. It can be said that this law is a "genetic code" according to which the first graphic passes through phases and transforms into the last graphic of the family. This law of change is
defined by the process
operating condition of the the law of change of KT in
of interpolation.
Interpolation is always done by the spline function. The respective laws of change of the dependence of KT on J (and of KQ on J) are examined separately and one does not affect another.
With the functions fT and fQ , all laws according to which the changes occur, occur simultaneously and affect each other.
An example of mathematical modeling of the results of experimental tests of a model propeller series using the functions fT and fQ and of the modeling by database will be shown on the Newton-Rader propeller series. Published results from this series are presented by tables, meaning that all mathematical models use the same data, i.e. the graphics are not arbitrarily digitized.
6.3 NEWTON-RADER SERIES
The Newton-Rader series is used for designing the propellers for high-speed craft. The series consisted of twelve three-blade model propellers. All tests were carried out in the cavitation tunnel. Test results are published in the paper [7].
The series was created by systematical changes of the geometric quantities Ae and P of the basic model. The changes are described in Table 4.
Table 4: Geometrical quantities of models Ae /A0
P/D
0.48 0.71 0.95
1.05 1.05 1.04
1.26 1.25 1.24
1.67 1.66 1.65
2.08 2.06 2.04
Each of the models was tested in the environment whose conditions are presented by the cavitation numbers given in Table 5.
©2014: The Royal Institution of Naval Architects
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