Effects of the Duct Angle and Propeller Location on the Hydrodynamic Characteristics of the Ducted Propeller

Resumen Efectos del ángulo de ducto y ubicación de la hélice en las características hidrodinámicas de la hélice con ducto Date Received: April 17th 2017 Fecha de recepción: Abril 17 de 2017 Date Accepted: October 13th 2017 Fecha de aceptación: Octubre 13 de 2017 Effects of the Duct Angle and Propeller Location on the Hydrodynamic Characteristics of the Ducted Propeller DOI: https://doi.org/10.25043/19098642.162 Ship Science & Technology Vol. 11 n.° 22 (41-48) January 2018 Cartagena (Colombia) 1 Department of Maritime Engineering, Amirkabir University of Technology, Tehran, Iran. Email: Chamanara.m68@aut.ac.ir 2 Department of Maritime Engineering, Amirkabir University of Technology, Tehran, Iran. Email: gasemi@aut.ac.ir 3 Department of Maritime Engineering, Amirkabir University of Technology, Tehran, Iran. Email: fadavie@aut.ac.ir 4 Department of Maritime Engineering, Amirkabir University of Technology, Tehran, Iran. Email: marefghassemi@gmail.com

In recent year, considerable eff orts have been made to improve the propulsive effi ciency of the propeller on the ships.One of these propulsors is called a ducted propeller found as widespread application.Th e duct is generally used to obtain augment thrust, but it is also used to minimize cavitation and underwater noise or to protect the propeller from damage.Th ere are two types of duct, the fi rst type is called an acceleration duct or Kort nozzle and the second type is a deceleration duct.Fig. 1 shows both types of the ducted propeller.Th e Acceleration duct has a fl at surface on the outside of the curve in the inner area.Th e outer surface is high-pressure surface and the inner surface is low-pressure surface (or suction).Th e suction allows more current to be directed into the duct and thus increase the fl ow rate.Th e increased infl ow velocity causes a decrease in the thrust and torque of the propeller.At the same time, a circulation develops around the duct section resulting in an inward directed force which has a forward component, the duct thrust.Th e duct also has a drag directed aft.Th e effi ciency of the ducted propeller is therefore greater than of the open propeller (Ghose, Kogarn, 2004).
In recent years, computational fl uid dynamics (CFD) have been extensively used for the analysis of marine propellers.Due to the complex shape, fl ow turbulence, fl ow separation and the possibility of cavitation, the analysis of marine propellers is a diffi cult task; however, some works have been done in the fi eld of ducted propellers.For example, (Taketani et al., 2009) presented the advanced design method of a ducted propeller which has high bollard pull performance.A nozzle section shape and a propeller have been designed according to a parametric study of the numerical simulation in order to have higher performance than a conventional ducted propeller.Th e optimum arrangement between nozzle and propeller combination is also studied.Th e open water tests are carried out in a towing tank of Akishima Laboratories.(Tadeusz et al., 2009) have completed the design for ducted propellers using the new computer systems.In this paper, the performance of the fi ve diff erent ducts are compared and the result show that in most cases only the 19A duct was considered, and that this duct was designed for low speed and high bollard pull conditions.(Celik et al., 2010(Celik et al., , 2011) ) presented a design methodology for the operation of ducted propellers in a non-uniform wake fi eld.Th ey also presented an investigation of optimum duct geometry for a passenger ferry.Th e numerical eff ect of duct shape on the propeller performance was presented by (Caldas et al., 2010).(Baltazar et al., 2012) predicted the thrust and torque of a ducted propeller using a panel method to improve the accuracy of the calculated shape of wake panels and the fl ow behavior in the tip gap region.Th e numerical analysis employed to the ducted propeller performance under open water test condition (Yu et al., 2013).Th ey also investigated the open water performance of the Ka-series propellers at various pitch and expanded area ratios in combination with the 19A duct by employing the panel method PAN-MARE and the RANSE code ANSYS-CFX.(Krzysztof et al., 2014) presented four diff erent geometries ducts to get better thrust characteristics in medium and high advance velocity ratio.(Xueming et al., 2015) analyzed the hydrodynamic performance of the ducted propeller by diff erent turbulent models.Th ey presented the pressure distribution on the propeller surfaces, the pressure and the velocity vector distribution of the fl ow fi eld around the ducted propeller.Th ey showed that the Reynolds stress model (RSM) is better that the k-ε standard model.The hydro-acoustic characteristics of the ship propeller in uniform and non-uniform flow were determined by (Gorji et al., 2016).(Majdfar et al., 2015 and2017) presented the numerical results of the hydrodynamic characteristics of a ducted propeller operating in oblique flow.Hydrodynamic characteristics of the Kort-nozzle propeller by different turbulence models carried out by (Chamanara and Ghassemi, 2016).

Introduction
Various studies have been done on a ducted propeller, but analyzing a ducted propeller by using different turbulence models and comparing them with each other, studying the effects of propeller position along the duct and duct angle relative to propeller on hydrodynamic characteristics have not been studied.In this paper, a Kaplan propeller with a 19A duct is used for CFD analysis.First, 19A duct data, especially data on the beginning and end of the duct which do not find in any references, are provided to model the duct geometry.Then, the ducted propeller is analyzed by using three different turbulence models including k-ε standard, k-ω SST and RSM and the results are compared with experimental data.Furthermore, the effects of the propeller position along the duct on hydrodynamic characteristics are investigated and the position in which the maximum thrust is produced will be determined.Finally, the effects of duct angle relative to propeller on hydrodynamic characteristics are studied.
In the present study, it is assumed that the fluid is incompressible.The governing equations consist of the mass and momentum conservations.Using the Reynolds averaging approach, the Navier-Stokes equations can be stated as: where is the Reynolds stresses.
In many important engineering flows, we deal with rotating or swivel flows.Rotating flows occur in turbo machinery, mixing tanks, marine propellers and a variety of other systems.Equations ( 1) and ( 2) are solved in a stationary coordinate system but sometimes it is useful to be solved in a moving coordinate system.When we are looking at moving parts from the stationary coordinate system, the flow zones result in a stability problem, but with a choice of rotating reference frame around the moving parts, the stability problem is solved.For simple problems, if we do not have any stationary zone, the single rotating reference frame (SRF) method can be used.For complex geometries, using the SRF is not possible.In this case, the problem is divided into several zones and two methods of MPM and MRF can be applied.The MPM method, despite being more accurate, due to the inclusion of interactions between the stationary and moving zones, requires a high computational time.In this paper, the MRF method is used, because not only does it need low computational time but it also has acceptable accuracy levels.
The ducts are mostly used with 19A and 37 in ships with the Kaplan propeller.So, here we employed Kaplan propeller with a 19A duct for the analysis.
The main dimensions of the ducted propeller are shown in Table 1.The duct section is shown in Fig. 2. The three dimensional 19A duct model with a Kaplan propeller is created using CATIA software as shown in Fig. 3 Governing equations Geometric Modeling Th e method of tetra/mixed type is used for mesh generation in ICEM software.Th e maximum size of mesh elements is 0.2 and to make better meshing in the curved parts (such as the leading edge) it is necessary to enable curvature/proximity based refi nement option and to set the minimum size limit at 0.00175.Th e blade section is an airfoil with a sharp edge so in order to preserve the airfoil form after the mesh generation, it is necessary to set the edge criterion value in the volume meshing parameters tab to 0.08.Th e split wall option of a rotating zone in the partial mesh setup should be checked to create an interface between the rotating and stationary zones.

Solver settings and boundary conditions
We used the MRF method which means that the computational domain is divided into two zones.
Th e zone around the propeller is a rotational area and the other is a stationary area.Th e velocity inlet is changed to fi nd the diff erent advance coeffi cient.
Th e infl ow and outfl ow boundaries were set to velocity inlet and pressure outlet boundary conditions, respectively.Th e far fi eld boundary was taken as the wall.Th e boundary conditions are shown in Fig. 5.
Calculations are carried out by the "Fluent software" to solve the three-dimensional viscous incompressible fl ow.Th e steady state pressurebased solver in a segregated mode was implemented using the MRF technique.
To fi nd a proper turbulence model, the k-ε standard model, which has been used in most articles for ducted propeller analysis, is applied fi rst.Th en the results of this model are validated against the experimental results.In the next stage, the k-ω SST and RSM turbulence models are used and the

Mesh Generation and setting the boundary condition
Th e computational domain is required to be discretized to convert the partial diff erential equations into a series of algebraic equations.Th e ICEM software is used for mesh generation.Fig. 4 shows the computational domain of the ducted propeller.Th e upstream part is considered to be 3D (where D is diameter of the propeller) from the mid-point of the chord of the root section.Th e downstream part is considered at a distance of 6D.
In radial direction, the domain is considered at a distance of 1.5D from the axis of the hub.results of these three models are compared.As a result of this comparison, the k-ω SST turbulence model is used as an appropriate model for investigating the effects of propeller position along the duct and also the effects of duct angle relative to propeller on hydrodynamic characteristics.

Independence of the mesh
The number of mesh elements is checked to match the numerical results.In general, the mesh size should be small enough so that the results are not changed by increasing the number of elements.Finally, we observed that if the number of elements is equal to 2.5 million, the results will be independent of the mesh number.

Hydrodynamic characteristics
The open water characteristics of a propeller are usually given in terms of the advance coefficient and open water efficiency Those coefficients are defined as follows: Assuming constant rotational speed, advance velocity is changed until the advance coefficient of 0 to 1 is found and then, the hydrodynamic characteristics (K T , K Q , ƞ ) are calculated.
Firstly, we use the k-ε standard model for the analysis of ducted propeller.The trust coefficient, torque coefficient and efficiency are calculated and validated against the experimental.Table 2 is compared the calculated results and experimental data of Other turbulent models like the k-ω SST, k-ε standard and RSM are also employed.Table 3 compares the relative error of calculated efficiency with experimental data for three turbulent models.
As can be seen, the relative error for RSM model is smaller than the two other models.The maximum relative error is less than 6%.The k-ω SST model is better than k-ε standard model.The y+ value for all models is less than 30.It should be mentioned that very fine meshes are needed near the blades to achieve the less y+.

Results and discussion
(3)

Effect of the propeller location
Here, the propeller is moved to the outlet direction as a percent of the duct length (LD%).The results of the thrust and torque are determined at various locations (0<LD%<7%).The thrust, torque and the percentage of the thrust is shown in Table 4.It is concluded that when LD is 3% the thrust increases about 2.148%.For other advance coefficients (when the LD% is 3), the results are given in Table 5.When

Effect of duct angle
Another important point is the effect of the duct angle.The gap between the blade tip and the inner surface of the duct is 3 mm (0.001D where D is the propeller diameter) and a rotational zone is defined at this distance, so the duct or propeller cannot easily be rotated due to the duct angle.The maximum possible rotation of the duct relative to the propeller is 2 degrees counter-clockwise (CCW).Fig. 7 shows the duct angle with the propeller.
The results of the thrust and torque and their incremental are presented in Table 6.Thrust and torque are increased about 3 and 3.35% respectively.Efficiency is diminished about 0.25%.
the advance coefficient is 0.797 the efficiency is increased by approximately 1.05%.In this study, a Kaplan propeller with 19A duct was numerically analyzed using RANS solver.
Th ree turbulent models were studied, and the eff ect of propeller location and duct angles were investigated.Based on the results, the following conclusions may be drawn: • Th e ducted propeller was analyzed with three k-ε standard, k-ω SST and RSM models and the results were compared with experimental data.Th e error percentages showed that the RSM model has a lower error level compared to two other turbulent models.
• Th e propeller location is aff ected by the thrust and torque.According to our results, the best location is found when the LD is 3%, because of the higher thrust obtained.

Fig
Fig. 6.Comparison of open water characteristic with three turbulence models

Table 1 .
Main dimensions of the propeller and duct Effects of the Duct Angle and Propeller Location on the Hydrodynamic Characteristics of the Ducted Propeller Ship Science & Technology -Vol.11 -n.° 22 -(41-48) January 2018 -Cartagena (Colombia)

Table 3 .
Comparison of the relative error of calculated efficiency with experimental data

Table 2 .
Comparison of calculated results and experimental data of K T , K Q & ƞ 0 with k-ε standard model Effects of the Duct Angle and Propeller Location on the Hydrodynamic Characteristics of the Ducted Propeller Ship Science & Technology -Vol.11 -n.° 22 -(41-48) January 2018 -Cartagena (Colombia)

Table 4 .
Increase of thrust with moving propeller

•
Th e eff ect of the duct angle by 2 degrees shows that effi ciency decreases about 0.25% although thrust and torques are increased.

Table 6 .
Increase or decrease of the hydrodynamic characteristic with rotation propeller ConclusionsReferences Eff ects of the Duct Angle and Propeller Location on the Hydrodynamic Characteristics of the Ducted Propeller Ship Science & Technology -Vol.11 -n.° 22 -(41-48) January 2018 -Cartagena (Colombia)