QUASI-STEADY MODEL EXPERIMENTS ON HYBRID PROPULSION ARRANGEMENTS

Jan Holtrop and Patrick Hooijmans (MARIN, Wageningen, The Netherlands)

Several past ITTC committees dealing with powering performance and propulsors have advocated the load-variation test as a valuable addition to the more usual speed-variation test. This load-variation test is even essential in complex propulsors and it can certainly not be dispensed with when hybrid propulsion concepts are studied by model experiments. At MARIN the load-variation test for one test speed has become a standard addition to every propulsion experiment and, indeed, the information about the effects of the varying load is analysed to enhance consistency and accuracy.

At MARIN it was investigated whether the usual test procedure could be simplified and the load-variation test can be fully dispensed with by carrying out propulsion experiments in a quasi-steady manner. In the quasi-steady method described here, a gradual variation of the rotative speed of the propeller(s) is imposed, while the forward speed of the ship model is kept constant. Thus, the load of the propellers continuously changes during the measurement run.

The following figures show the variation of the rotation rate N, the thrust T and the resulting variation of the longitudinal towing force F as recorded for a certain case during one typical measuring run.

The next series of figures show for the same test case the relationship between the towing force F and the thrust T, the thrust coefficient KT as a function of the apparent advance coefficient JV and the torque coefficient KQ in relation to KT.

An essential assumption of quasi-steady experiments is that each instantaneous condition encountered during the quasi-steady test is representative for the corresponding steady condition. By means of regression analysis of the recorded data, which are first converted to physical units, the coefficients of a pre-defined numerical model of the propulsion characteristics are determined. From this numerical model, which has been extended by a scheme for the extrapolation of the model data to prototype values, a prediction of the full-scale propulsion properties can be made for any specified method of extrapolation.

The advantage of the quasi-steady method is the time saving element and the straightforward analysis of the test data which is to be made while the carriage is being returned to its starting position. In the analysis the loading effects are fully accounted for and the complete analysis enables next test conditions being selected effectively. It is essential to implement a proper interpretation of the transducer calibrations, including multy-channel, non-linear cross-talk contributions and, in some cases, the geometric projection of some of the measured entities.

For hybrid concepts an independent variation of the load of the two different sets of propulsors is accomplished simultaneously in such a manner that all possible combinations of the load of the two sets of propulsors are covered. Here, the generation of the load-variation effects is a two-dimensional problem because interaction between the propulsors potentially plays a certain role. Once the load-variations have been applied independently a dedicated analysis and an extrapolation to the full scale is to be made in which scale effect corrections of different magnitude can be applied to the individual propulsors and the different wakes.

The numerical model used for a hybrid propulsion concept, which is considered to consist of two propulsor groups 1 and 2, is the same as that which is used in the conventional, steady propulsion experiments. In this numerical model the sum of the thrust components in propulsor group T1 and those in group T2 are related linearly to the towing force F for each constant speed:

F = a + b Σ T1 + c Σ T2 ……………………………………………………………..……(1)

where a, b and c are coefficients to be determined from each measuring run in the experiment. The coefficient a is the towing force at zero thrust, FT=0, and b and c are the “true thrust deduction factors" t*1 minus one, and t*2 minus one, respectively. Notice that

TF*t ∂∂+= 1

and that the true thrust deduction fraction t* is equal to the classical thrust deduction fraction t if the resistance of the ship model Rm would be equal to the towing force at zero total thrust FT=0. In practice, this is not true. FT=0/Rm is approximately 1.02 and, hence, the classical thrust deduction fraction t is always larger than t* and t depends on the loading of the propulsor.

Next, for each propulsor, the thrust and torque coefficients, KT and KQ, are related to the apparent advance coefficients Jv1 and Jv2 of the two propulsor groups involving linear and, optionally, quadratic terms:

KT (KQ) = d + e Jv1 + f Jv2 + g Jv1 Jv2 + quadratic terms ……………………………….(2)

Additional thrust components (e.g. pod unit thrusts, nozzle thrust, etc) can be included similarly. It is noted that the measured torque is corrected for the inertia torque induced by the changes of the rotative speed. However, these inertia torque effects in the usual model tests are quite small when compared to the hydrodynamic torque. In the analysis of twin-screw ships an assumption has to be made about the distribution of the thrusts over the propulsors. For twin-screw ships several options exist: • The starboard propulsor is considered representative for both the full-scale propellers which are

considered symmetric, • the port propeller is representative, or • perfect symmetry is assumed to be present in the full-scale propellers, while this is only so by

approximation if a pair of model propellers is tested and port and starboard data are averaged.

Once the regression coefficients a-g have been established after each run the following analysis procedure is followed to find the full-scale operational condition:

The scale effect on the resistance is expressed as a towing force on model scale FD. This towing force FD includes the form factor, hull roughness effects and scale effects on the passive propulsor components, if any. FD should be applied as a forward force to the ship model in the propulsion experiment to achieve the loading condition commonly referred to as the “self-propulsion point of ship”.

The total model thrust is calculated from (1) for F=FD where in hybrid concepts an (initial) assumption about the thrust-loading ratio of the two groups of propulsors has to be made. By iteration this thrust ratio can be adjusted later to satisfy any specified distribution of the power or the rotation rates over the various propulsor components or to satisfy a prescribed output of one of the two components. This is also relevant for contra-rotating propellers coupled by a gearing as front and aft propeller react differently on the wake and propeller scale effects. Anyhow, assuming Froude scaling for the time and supposing the absence of scale effect on the true thrust deduction, the full-scale thrust for a ship speed of

Vs = Vm λ1/2 becomes: Ts = Tm λ3 ρs / ρm, where Tm is the model thrust at the "self-propulsion point of ship".

The non-dimensional thrust-loading coefficient KT/Jv2, based on the apparent advance coefficient, is

then calculated using the full-scale thrust and the ship’s speed. Relationship (2) holds essentially for the model scale as scale effects on the wake fractions and the propeller performance have not yet been introduced. Relationship (2) between the thrust coefficient and the apparent advance coefficient is then made valid for the ship scale by entering the scale effects on the entrance velocity (wake) and the propeller performance. In [1] it is explained in detail how this is done by substitution in the polynomials. By solving (2), after conversion to the full scale, Jv1 and Jv2 are found. From Jv1 and Jv2 the rotative speed of the propellers are known. From substitution of Jv1 and Jv2 in the scaled-up expressions for the torque coefficients the propulsive powers are found. Finally, assumed shaft and gearbox losses provide the power to be supplied to the propulsion system. As mentioned, a reconsideration of the initial thrust load ratio matches the final solution to a specified distribution of the power, or to a certain ratio between the rotation rates, or a to a specified power output of one of the propulsor components.

An experimental verification programme has been carried out at MARIN to see if the quasi-steady method of propulsion testing provides the same results as the conventional method using the steady test procedure. To this end, some tests were carried out in the Depressurised Towing Tank (1996) and a series of ten experiments were made in the Deep Water Towing Tank of MARIN (2000 and 2001). The quasi-steady tests were done with the same equipment right after the regular tests. A variety of types of ship models of non-hybrid propulsion arrangements were investigated. These were single-screw ships and symmetric twin-screw ships, one of which propelled by pods. The conclusions of these quasi-steady verification tests are such that discrepancies with the results of the regular tests remained within a band width of 2 per cent. Moreover, speed-wise undulations, as found on resistance curves, reproduced better in the quasi-steady test results than in the traditionally obtained results. Data smoothing of test results can possibly be further minimised because quasi-steady testing seems to give more consistent results.

Such a type of quasi-steady measurements needs a well functioning captive measuring system. From the analyses it appeared that the scatter in the towing force F was clearly larger than that of the other signals. This conclusion is not new. Therefore, continuous efforts are being made to further improve the quality of the captive measurements with the objective to reduce the scatter of the towing force. Software to apply the quasi-steady type of measurements and the on-line analysis on a routine basis is under preparation.

The quasi-steady method appears a preferred alternative over the steady propulsion experiment. A clear advantage of the quasi-steady method is that the additional load-variation test can be fully dispensed with and that a substantially smaller number of test runs are needed, thus leading potentially to an important time saving in model propulsion experiments. Another advantage of the quasi-steady method is that from each individual measurement a prediction for the full scale can be made in which the propeller loading effects are fully included.

[1] Holtrop, J., “Extrapolation of Propulsion Tests for Ships with Appendages and Complex Propulsors”, Marine Technology, July 2001.

Discussor To Group Discussion A1

Prof. Jerzy Matusiak, Helsinki University of Technology, Finland

Mr. Jan Holtrop, MARIN, The Netherlands

Subject of contribution to discussion

You call your method “Quasi-Steady Model”. I see from the figures of your presentations a relatively fast decrease of propeller revolutions. Aren’t you concerned the unsteadiness of the flow of model stern? How save can you be that your assumption of flow steadiness is fulfilled?

Discussor To Group Discussion A1

Prof. Michael Schmiechen, Germany

Mr. Jan Holtrop, MARIN, The Netherlands

In listening to the very interesting presentation four questions or rather remarks came to my mind:

In some methods for evaluating the powering performance at the narrow service conditions (Abkowitz, Kracht) a wide range of test conditions, including the condition of zero thrust, is required to provide the data necessary. Am I right to assume that this is not the case in the method presented?

In the ‘hybrid’ model the inertial term is missing. So the question arises: Is the inertia being treated statistically, assumed to vanish in the average? Some forty years ago in a Japanese study it has been shown, that even very small accelerations, less than a thousand of a g, may easily upset the momentum balance. And I have observed that taking averages or, even worse, relying on ill-defined averages provided by somebody else may be ‘exactly’ the wrong thing to do. Traditional methods usually rely on steady conditions and thus these have to be ‘established’ or constructed!

Concerning the thrust deduction ‘axiom’ adopted, also used by Kracht, I have very strong theoretical reservations, which I have discussed in detail in a paper to be found on my website. The thrust deduction fraction does depend on propeller loading and on scale. The differences may appear very small in the first place, but due to the differentiating nature of our analysis the final results differ quite considerably.

Finally, I am of course very happy that, after all, quasisteady testing has been successfully implemented and shown to provide ‘useful’ results, exactly as I have promised for nearly two decades now.