Propeller efficiency at full scale : measurement system and mathematical model design

What is propeller efficiency at full scale? This question is asked equally by ship operators and by propeller and propulsion system manufacturers. The question reflects the need to measure propeller efficiency at full physical scale and during regular operation of the vessel. The question has a context: the ship operator wants to reduce the fuel consumption and forecast maintenance; and, the manufacturer wants to improve the design of the propeller and optimize the propulsion system. In this thesis, we work towards an answer by designing methods to determine propeller efficiency at full scale. In accordance to the hydrodynamics community, we define propeller efficiency as the ratio of the power produced to the power consumed. The power produced and the power consumed are the product of thrust and advance velocity, and, of torque and angular velocity, respectively. Thus, propeller efficiency at full physical scale requires full scale measurements of thrust, torque, angular velocity, and advance velocity. Up-to-date, thrust and advance velocity are thought to be the bottlenecks in estimating propeller efficiency at full scale. Recently, a prototype thrust sensor has been developed that seems to have solved the problem of propeller thrust measurements. The remaining bottleneck, the measurement of advance velocity, is a main topic of this thesis. The advance velocity cannot be directly measured on board of a vessel with the current sensor technology. We replace the advance velocity by ship’s speed-through-water up to a factor. This factor is known as the wake fraction. Since the speed-through-water is measurable at full scale, we need to find the wake fraction. For that we apply mathematical modeling in combination with full scale measurements during rigourously defined conditions. The method to determine propeller efficiency at full-scale relies on five principles: mathematical models, design of measurements, identification of parameters, statistical analysis of data, and identification of stationary states. Propeller efficiency at full scale can only be defined when the ship is in a stationary state; also in the practice of propeller model tests and CFD simulations the propeller efficiency is determined under stationary conditions. First, we developed a concept of stationarity of a process; it means that the trend is close to zero, and small oscillations about the trend are allowed. Second, we developed a method that automatically extracts the stationary excerpts from the full scale measurements. The mathematical models that we elaborate on in this thesis are inspired by the classical mathematical models for guidance and control of vessels. In this mathematical environment, relationships between advance velocity, thrust, torque, speed-through-water, and angular velocity are defined on basis of physical laws and empirically established relationships. The mathematical models introduce parameters that are unknown at full physical scale. One of these parameters is the wake fraction. For realistic values of parameters the model mimics the ship behavior. From the measurements we want to obtain the model parameters by estimation. For that, we construct a regression kind of method that minimizes the difference between the measurements data and the output of the mathematical model when we feed it by full scale measurements. Our measurement design includes the functional specification for a data collection system, a list of signals with details on sampling frequency and resolution, a design of propulsion tests, and processing of measurements. The result of that processing is the selection of stationary states and their characteristics. A central piece of the data collection system is the propeller thrust sensor. In fact, this thesis would not have been written as it is without the availability of the thrust sensor. The speed-through-water measured by the speed log is equally important. It is generally known that speed logs are not reliable. Thus, we had to focus on getting a reliable speed-through-water. For this purpose, we designed an algorithm that reconciles the speed-through-water with other measured navigation signals. The combination of mathematical models and propulsion test measurements yields the model parameters. The value of each model parameter is calculated by a mathematical algorithm that needs measurements of stationary or dynamic states as input. The mathematical models structure these algorithms. It is at this stage that the external factors come into play. External factors, for instance, wind, waves, and sea currents, are not explicitly modeled so that their influence is noticeable in the model parameters. For instance, the parameters of the ship resistance force account also for the wind-induced resistance. Consequently, the estimated propeller efficiency at full scale is influenced by the external factors. If our findings were put into practice, the best would be to create a ship-tailored lookup table of reference model parameters and reference propeller efficiency as function of external conditions that would represent the reference states. At predefined time intervals, the reference state would be updated by new propulsion tests. During ship operations the reference model parameters would be used to retrieve the propeller efficiency relative to the selected reference states. At sea, vessels have typical operational profiles that are concentrated at one or two predefined velocities. As a result, the relative propeller efficiency forms clusters of data points. Propeller efficiency is function of state variables connected to ship propulsion and external factors. Under the influence of the state variables the data clusters are more or less densely packed. We use statistical tools to analyze these data clusters. To evaluate the data clusters we introduce the concept of precision that, in our definition, is the normalized standard deviation of the data clusters. Filtering the data clusters based on propulsion state variables increase the precision, i.e., the clusters become more densely packed. The clusters of data points indicate that the external factors account for most of the variations in propeller efficiency. We expect that this is the de facto situation of propeller efficiency at sea. Thus, what is propeller efficiency at full scale? Propeller efficiency is an indicator with values between 0 and 1. This indicator is measured by a sensor: a mathematical algorithm structured by a mathematical model and fed with full-scale measurements. Under specified conditions, this sensor measures the propeller efficiency with high precision. The ship owners and the propeller and propulsion system manufacturers may use the full-scale propeller efficiency to compare different propeller designs at similar conditions, to track long-term changes in propeller efficiency for the maintenance forecast, to optimize fuel consumption as function of external conditions, or to plan the optimal route of the vessel