Abstract
This article describes a propeller design method for small scale inland ship models, which ensure the similarity of hull resistance and rudder forces between the full scale vessel and the manoeuvre test model.
Introduction
Although the inland waterway transportation is one of the safest, to enhance the safety of navigation always will be the responsibility of the research. The key question of safe navigation is the manoeuvrability of vessels. The requirements are given by the waterway parameters (water level, fairway width, curves, fords, bridge clearance, hydraulic engineering structures, etc), the meteorological conditions (wind direction and speed, precipitation, visibility, etc) and the actual traffic situation.
To know the manoeuvrability of a vessel is essential whether it is about ship design, the analysis of an accident, or training of the crew. The cheapest way to predict the motion of a ship is the computer simulation. For this several motion equation theories are available but every simulation needs to be validated by full scale or model manoeuvre tests. The full scale experiments are very expensive and often cannot be implemented (e.g.: follow-up analysis of an accident), that is why the manoeuvre tests by the ship models are highlighted.
This article describes a propeller design method for small scale inland ship models.
1. The importance of propeller design by small scale manoeuvre tests.
The importance of model propeller selection can be presented by a parameter sensitivity analysis of the ship motion equations. The semi-empirical motion equations – based on Newton’s II. law – determine the forces and torques acting on a ship according to the ship design practice.
According to an earlier parameter sensibility research [1] the longitudinal and transversal force-coefficients of the rudder (cKx, cKy), the lateral resistance coefficient of the hull (clat) and the longitudinal resistance of the hull (R’t) have the biggest effect
speed (ωz) of the vessel.
The hull resistance can be determined relatively precisely by model tank tests and experience based calculations [2]. But only calculations [3] with relative serious errors are still exist to determine the rudder force factors (cKx; cKy), or they can be deduced according to former experimental results.
In order to the rudder forces can be proportioned to the full scale rudder forces (and the model maneuvers shows the real ship maneuverability) the proportional propeller stream (velocity, pressure distribution, flow- and vortex lines, etc.) have to be established by the model of an inland ship. The reason is that the usual inland merchant vessels produce the rudder forces by the deflection of the propeller stream.
2. The similarity of full and model scale propellers
The similarity of the following ship and propeller parameters have to established by the model manoeuvre tests for rudder force analogy between full scale and model ship at the ship speed of manoeuvre (vman).
Paramter Full scale ship Model ship
For similarity of forces Ship speed by manoeuvre
Total resistance of hull
Thrust
For similarity of flow Effective wake fraction
Thrust deduction fraction
2.1 Similarity of forces
According to Froude’s similarity theory, the similarity of pressure and gravity forces of ship can be ensured if the Froude number of full and model scale ship is the same (2). In this case the residual resistances (RR) are similar and the residual force coefficients (cR) are equal.
(2)
In case the Froude No. is computed at full scale ship manoeuvre speed, the manoeuvre speed of model can be also calculated:
at the speed of manoeuvring. [2]
The resistance of full scale ship (RT) can be read off from the towing tank test results at the speed of manoeuvring. The total resistance coefficient (cT) can be computed, from which the residual resistance coefficient (cR) is determined by deduction of friction resistance coefficient (cF) (this can be appointed acc. to ITTC1957 formula or [4]):
(4)
Total resistance of the small scale model can be computed from the residual resistance coefficient and the friction resistance of the model (this also can be appointed acc. to ITTC1957 formula or [4]):
(5)
The needed thrust of the full scale ship can be read off form the self propelled test results. According to this the thrust deduction fraction is given:
(6) Because the propeller has to have the same pressure effect (proportional) on the smal scale model, the thrust deduction fraction of full scale ship has to be equal as the model. According to this the needed thrust of the model is given:
(7) The propeller of the small scale model has to be designed for this thrust.
2.2. Similarity of flow
The produced thrust and needed torque of the different propellers can be appointed by the open-water tests of propellers (towing test without any hull). The open-water characteristics of a propeller give the thrust and torque coefficient (kT and kQ) in function of advance number of propeller (J).
; ; (8)
By self propelled ship tests the research institute reports not only the characteristics of the vessel but the dimensions and open-water characteristics of the vessel’s propeller.
But the effect of the hull on the propeller stream has to take into account by the design of a propeller. Because the propeller works in a flow which is disturbed by the hull, the propeller produces the same thrust by different speed in self propelled and in open-water cases. The difference between the speed of the propeller in wake and in open water is defined by the effective (or Taylor) wake fraction (11).
The wake fraction of the full scale ship can be determined from the self propelled test
The advance number of propeller at the manoeuvre speed (Jman) is appointed from the open-water characteristics, and so the propeller speed of advance can be calculated:
(10)
The effective wake fraction is:
(11) The full scale wake fraction is not equal to the model wake fraction because the friction forces are different (Reynolds numbers are not equal). The friction caused wake fraction difference can be compensated according to [6] as follows.
The full scale speed of advance of propeller:
2
Where the speed loss coefficient after hull is:
2
And the axial induced velocity at propeller section from the momentum law:
2
The speed loss coefficient of the model can be determined with proportion of friction coefficient of the full scale ship and the model:
F MF
M c
c c
c = ⋅ (15)
The model axial induced velocity at propeller section from the momentum law:
2
The model speed of advance of propeller:
2
With the previously calculated speed of advance of model ship propeller (vAM) the advance number of propeller (JM) is given.
(19)
Conclusion
With the help of the above-described method those basic model propeller parameters can be defined, which ensure that the model propeller thrust and flow are similar to the full scale ship. By conventional inland ship rudders this also means the similarity of rudder forces.
But the method do not select a single model propeller, which performs the tasks.
Selecting the best propeller has a number of other factors and properties, for example the available motor of the model, propeller cavitations, strength of propeller, efficiency, etc. To select or design the optimal propeller will always depend on the current maneuver model.
Acknowledgement
The work reported in the paper has been developed in the framework of the project
„Talent care and cultivation in the scientific workshops of BME" project. This project is supported by the grant TÁMOP - 4.2.2.B-10/1--2010-0009
References
[1] Rohács, J., Hargitai, L. Cs.: „Inland waterway ship motion simulation and parameter sensibility of its motion equations”; Transport Means Conference 2007, Kaunas, 2007
[2] Kovács A. – Benedek Z.: Hajók elmélete (Theory of Ships)
[3] Hargitai, L. Cs.: „Passzív kormányrendszereken ébredő erők.” (Hydrodynamic forces on passive rudders);
Hajós Füzetek 4.szám, 2005
[4] Lap, A. J. W. – Manen, J. D. Van: „Fundamentals of Ship Resistance and Propulsion.” International Shipbuilding Progress, IV. Series, 1957
[5] Benedek, Z.: „Hajócsavar sorozatok kisminta-érési eredményei.”;Teaching aids; BME, Járműgépészeti intézet, 1988
[6] Benedek, Z.: „A Simple method to reduce scale effects on wake and thrust deduction fractions”; SORTA 2008 Conference, Pula, 2008