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Posted: February 28th, 2022
Influence of Trim Optimization on Ship Performance and Fuel Consumption
An investigation into the effects of trimming optimization on ship performance and fuel consumption
In recent years, as a result of rising fuel costs and environmental concerns, technology has focused heavily on achieving vessel optimum trim in order to increase power savings while simultaneously reducing greenhouse gas emissions. For the purpose of validating and investigating trim optimization, a simplified ship model was replicated using Ansys Fluent. In this paper, various tests for predicting trim optimization are presented, and the results are compared among themselves as well as with the literature. It is demonstrated that using Computational Fluid Dynamic (CFD) analytical methods as an effective design tool in the marine field can significantly reduce the time and cost of studies compared to relying on physical model tests during the preliminary ship design stage.
Drag Reduction, Trim Optimization, Numerical Simulation, Computational Fluid Dynamics, Fuel Consumption, Ansys Fluent are all terms that are used in the aerospace industry.
1. Greetings and introductions
The speed of computers has increased exponentially in recent years, and more sophisticated RANS codes have been developed to handle increasingly complex problems. It is now possible to run simulations that are more realistic. All of these advancements have been thoroughly documented in the proceedings of several international conferences on the applications of computational fluid dynamics techniques to ship flows. Since 1990, these conferences have been held on an annual basis. Most notable are those held in Tokyo , Gothenburg , and Tokyo  in 1994, 2000, and 2005, respectively. Recent studies presented in the proceedings of the ‘Symposium on Naval Hydrodynamics’ have revealed some remarkable information about the application of CFD codes to naval ships and submarines. This symposium, sponsored by the United States Office of Naval Research (ONR), was first held in 1956 and has since grown in popularity. Among the recent advances in specialized CFD codes for the flow simulation around naval hulls is the work of Burg et al. [5, which was presented at the 24th Symposium on Naval Hydrodynamics] which provides some examples of how these codes have evolved. Burg’s study made use of a three-dimensional unstructured, paralyzed CFD code named U2NCLE, which was developed by the Computational Simulation and Design Centre at Mississippi State University to simulate the free surface flow around a fully-appended model of a United States naval ship, according to the researchers. The results obtained through the use of this code accurately represented the turbulent flow and vortices generated by the bulbous bow and the tips of the propulsors and rudders. It was also discovered that it was possible to accurately model the propulsor rotation. A nonlinear free surface algorithm was used to successfully simulate the wave shapes of the near-field. A RANS code similar to the CFDShip-Iowa code, which was developed at the University of Iowa’s Institute of Hydraulic Research (IIHR) with funding provided by the Department of Energy (DOE), can be used as an example of another RANS code. This code was created specifically to solve problems involving the surface-ship interface and marine propeller flow, among other things. The prediction of resistance, which includes friction and pressure drag prediction, wave profiles, sea keeping using a code that allows for six degrees of freedom, and manoeuvring are all examples of general applications in naval hydrodynamics. CFDShip-Iowa code’s performance was recently compared to the performance of two commercial CFD codes, according to Wilson et al. . Fluent, developed by Fluent Inc., and Comet, developed by CD-Adapco, were used to predict the generation of waves by ships in order to improve ship navigation. It was discovered that each of the codes has distinct advantages and disadvantages when compared to the other, and that each code has its own set of specific parameters that must be taken into consideration when attempting to obtain accurate solutions for surface ship wave fields. When considering complex geometries with appendages and propulsors, it was discovered that commercial solvers may offer advantages due to their ability to use unstructured create meshes that contain unstructured and hybrid grids, in addition to their ability to use unstructured create meshes with unstructured and hybrid grids. Both codes, Fluent and Comet, demonstrated the benefits of allowing solution-based grid adaption techniques to provide finer grid resolution in critical regions of the grid, which was demonstrated by both codes. When an interface region is considered, as in this case, it can be extremely useful, and it may therefore provide a more detailed and computationally efficient way to provide accurate results of free surface prediction problems in the vicinity of surface ship hulls than is currently available. Ship trim optimization operations are widely regarded as one of the most cost-effective methods of improving ship performance while also lowering fuel consumption costs. In such an operation, there is no requirement for shape modification or power upgrade to be performed. It is possible to achieve this by developing a proper loading plan and implementing an efficient ballasting and de-ballasting process. Trim optimization is not regarded as being as important as other conventional power performance testing procedures from an operational standpoint. Nonetheless, it has been demonstrated that trim optimization can keep potential savings intact. Additionally, depending on the type of ship and its operation, trim optimization could result in a return on investment of one to six months depending on the situation. Hansen and Freund in 2010  described the influence of depth water on gains and demonstrated that these conclusions were correct. When testing a towing tank model or running a computational fluid dynamic (CFD) simulation, trim optimization test procedures can be used. In 2013, Hansen and Hochkirch  demonstrated possible power gains by using CFD tests and provided some CFD method comparisons with tests performed at both the model and full-scale levels. It was discovered that both methods were in reasonably good agreement when it came to the tendency of power requirement in relation to trim. Force Technology, a leading consultant in trim optimization, demonstrated that it is possible to save up to 15 percent on fuel under specific work conditions using trim optimization techniques. These savings can amount to as much as 2 percent or 3 percent of the total fleet operating costs. Force Technology has conducted extensive research campaigns to better understand the physical effects that can be used to reduce propulsive power. In 2012 , Lemb Larsen et al. presented an analysis of the origin factors in resistance and propulsive fields, as well as the influence of these factors on the power requirement. Despite the fact that resistance is the primary source of power gain, overall performance can be influenced by variations in the propulsive coefficients, which should be taken into consideration as well.  In this paper, operational constraints that should be considered in shipping, such as slamming or green water, strength and stability, manoeuvrability, and overall safety, were not taken into account. The optimization of the trim was the primary focus of the research.
2. International Maritime Organization (IMO): Ship Energy Efficiency Management Plan
The issues of energy and the environment have recently received extensive attention from researchers all over the world. Energy-efficient transportation vehicles, such as ships and airplanes, are the focus of this initiative.. The global temperature has risen by approximately 2°C above the pre-industrial level in recent years, and it is expected to cause widespread devastation on a global scale in the future. Only by reducing global greenhouse gas emissions will we be able to solve this problem. In the absence of proactive measures, future scenarios show that levels of carbon dioxide emissions from shipping could double by 2050 if current trends continue. As demonstrated by Kim, Hizir, Tuan, Day, and Incecik in 2017, the European Union (EU) and the United Nations Framework Convention on Climate Change (UNFCCC) are putting forth significant effort to bring global emissions under control. The International Maritime Organization (IMO) is currently in charge of establishing GHG commands for international shipping through the use of industrial, operational, and market-based policy tools, among other things. It appears that the International Maritime Organization’s regulations on CO2 emissions from shipping will continue to evolve in the coming years. As a result, as demonstrated by Kim, Hizir, Tuan, Day, and Incecik in 2017, fuel prices have been steadily rising and are expected to continue to rise in the future. Several ship operators are promoting the idea that ship performance should be monitored and controlled in order to maintain constant routine maintenance and maximize fuel consumption efficiencies. Every day presents an opportunity to improve speed, find the safest route, and ensure that the ship is sailing at the best draft and trim, which is tuned to keep the ship on course as safely and efficiently as possible. These efforts are directly aligned with the objectives of the recently published International Maritime Organization (IMO) Guideline on Ship Energy Efficiency Management Plans, a framework that captures the corporate commitment to energy conservation. The following are the most important factors that should be considered for energy conservation on ships currently in service: 1. Acceleration of the ship’s speed 2. Weather Routing – Energy Efficient Route Selection in a Safe Environment 3. The Roughness of the Hull and Its Influence on Resistance 4. Trim/Draft Optimization (Optimization) Trim Optimization was thoroughly investigated in this report in order to identify the most optimal points for a ship’s simplified geometry.
3. Trim Optimization (also known as trimming optimization)
Trim is defined as the difference between the draught at the AP and the FP difference, as defined by the following expression: Trim is equal to TA –TF. When the value is positive, the results are trimmed to the right. Furthermore, when the ship is trimmed, both the displacement and the speed remain constant. In this case, there is no additional ballast added, and power consumption only varies if resistance varies with the trim. Generally speaking, the goal of trim optimization is to reduce the amount of power required for a given ship’s displacement and velocity. Reduced propulsive power (PD) caused by trimming a ship’s trim can have physical consequences, as shown below, due to changes in hull resistance () and total propulsive efficiency (). PD is equal to RT.VD. As previously stated, the ship’s speed (V) remains constant. As a result, it can be concluded that the goal is to reduce resistance while simultaneously increasing overall efficiency.
3.1 Resistance to Change is Minimized
According to ITTC standards, ship resistance in still water is written as RT=1/2.V2.S.CT (rotating water resistance). Changes in ship resistance can be represented by changes in wetted surface area (S) and total resistance coefficient (CT). In order to achieve a trim gain, it is necessary to decrease both parameters. A ship’s wetted surface is calculated for a ship at rest, with no dynamic sinkage or trim factors taken into consideration. Trim is responsible for the variation in wetted surface because of the large flat stern area and the fact that it is relatively small. It has the potential to reach 0.5 percent of the even keel wetted surface, and it causes the total resistance to vary as a result of the linear proportionality of the wetted surface. All of the previously mentioned parameters can be reduced in order to achieve the desired total resistance coefficient. The following expression can be used to describe it in detail: CT is equal to CR+1+k. CF0+CA With the exception of ships with significant variations in draught, the allowance coefficient (CA) remains constant. The friction resistance coefficient (CF0) for the flow along the hull can vary with the Reynolds number (Re): CF0=0.075(log10Re-2) for the flow along the hull. 2 Where Re is the Reynolds number, which can be calculated as Re=V.Lwlv. From friction resistance coefficient and Reynolds number, it can be deduced that friction resistance coefficient is a function of the water line length ( Lwl), and this relation is inversely proportional. Although water line length can vary 5% from the even keel condition, inverse proportionality results by increase or decrease propulsive power of 0.5%. This effect comparing with overall possible savings is negligible. Form factor, ( 1+k), is often kept invariable at each draught to optimize the experimental program cost in the towing tank. In practice, there is no influence giving by this factor on the resistance changes for different trimmed conditions. Residual resistance coefficient ( CR) is often the parameter most affected by the ship trim. It was seen before that residual resistance coefficient at trimmed conditions can rise up to 150% from even keel condition values. That is reflected in power requirement changes up to 20%.
3.2 Increase of Total Propulsive Efficiency
Propulsive efficiency is the product result between the hull efficiency ( ηH), the open water propeller efficiency ( ηo) and the relative rotating efficiency ( ηrr). ηD=ηH.ηo.ηrr When the ship is trimmed none of these parameters are constant. Hull efficiency is a function of the thrust deduction ( t) and the effective wake fraction ( w). ηH=1-t1-w It is obvious that the thrust deduction decreases and effective wake fraction increases to achieve a gain trimming. Thrust deduction is a function of the propeller thrust ( T) and the hull resistance. t=T-RTT Also, it is known that hull resistance varies when the ship is trimmed and it causes that propeller thrust changes as the speed stays constant. Nevertheless, hull resistance is not constant. Thrust deduction changes as the trim changes and sometimes a peak, when propeller submergence decreases until arrive to a critical level, as it can be observed. The peaks localization depends on the dynamic sinkage and stern wave. Thrust deduction changings can produce values up to 15%. That means propulsive power changes up to 3%. However, the thrust deduction changes should be relatives to effective wake changes. Effective wake fraction is related to the ship velocity and the propeller inflow velocity (VA). w=V-VAV If the ship speed keeps constant, the effective wake fraction changes can only be related to the propeller inflow velocity. As mentioned before, the effective wake fraction increases for bow condition of trimming and decreases for stern condition of trimming. Wake fraction increasing for bow trims can catch up to 20% and the stern trims decreasing can rise up to 10%: Wake fraction differences can results in a power gain up to 2%. Propeller open water efficiency depends on the advancing ratio ( J), on the water inflow velocity of the propeller ( VA) and on the revolutions ( η). J=VAn.D Where Dis the propeller diameter. As concluded, propeller inflow velocity is affected by the trim. Since open water curve for the propeller efficiency is inclined for the actual ratio of advancing, with minor changes in the advance ratio result in a propulsive power changings. These changes can vary up to 2% of the even keel power demand. Relative rotating efficiency is described as the relation between the open water propeller torque coefficient (KQow) and the propeller torque coefficient behind the ship (KQship). ηrr=KQOWKQship It can be reach up to 2% from even keel condition and influencing the power requirement.
4. Experimental Data
There exist extensive database for CFD validation models. Some tests were done by the Resistance Committee of the 22nd International Towing Tank Conference to create this data base . The focus was on modern ship forms. Forms as tanker (KVLCC2), container ship (KCS), and surface combatant (DTMB 5415) were recommended for use. These results were shown at the workshop of Gothenburg 2000 on CFD for ship hydrodynamics  and other conferences. The bare hull trim results of this study were compared with the results of Olivieri et al.  and a combined effort between Istituto Nazionale per Studi ed Esperienze di Architettura Navale (INSEAN, Italian ship model basin ) and the Iowa Institute of Hydraulic Research (IIHR) to show experimental towing tank data and then compare to the CFD results. The CFD results used for compare appended model were the existing towing tank results performed by David Taylor Naval Ship Research and Development Centre . This model has fixed pitch shafts and struts and is designated Model 5415-1.
5. CFD Model
Computational Fluid Dynamics or CFD is a computational tool developed for studying the behaviour of the fluid flows in many different fields. It is impressive how the computer performance in this era gives us the possibility to recreate fluid flow models perfectly reals and the possibility of examining different equipment designs or compare performance under different operating conditions.
5.5 The Physics Models
5.5.1 K-Epsilon Turbulent Model
The K-Epsilon (k-ε) model is one of the most common turbulence models. The K-Epsilon turbulent model is a two-equation model known to be an eddy viscosity mode. Eddy viscosity models use the approach of a turbulent viscosity to model the Reynold stress tensor as a mean flow quantities function. In the K-Epsilon model additional transport equations are solved for the turbulent kinetic energy k and its dissipation rate ε to enable the turbulent viscosity derivation. The model transport equation for k is derived from the exact equation, while the model transport equation for ε is obtained using physical reasoning to its mathematically exact counterpart. In the procedure of the K-Epsilon model derivation, the flow is assumed as fully turbulent, and the effects of molecular viscosity are negligible. The standard K-Epsilon model is therefore valid only for fully turbulent flows.
5.5.2 Eulerian Multiphase
Eulerian multiphase model is required to create and manage the two Eulerian phases of the simulations with free surface models, where a phase has a distinct physical substance. The two phases for this models are water and air, each defined to have constant density and dynamic viscosity adjusted according to the tank average temperature. This model is not required for the models that do not use free surfaces (where the inlet fluid is water), which is gain defined to have constant density adjusted to the experiment temperatures used to validate the CFD simulation. In the Eulerian Multiphase model, the different phases are treated mathematically as interpenetrating continua. As the volume phase cannot be occupied by other phase, the concept of phasic volume fraction has to be introduced. The volume fraction parameter is assumed to be a continuous function of space and time. All volume fraction addition has to be equal to the unit. The conservation equations for each phase are derivate to obtain a package of equation with similar structure for all phases. These equations are closed by giving constitutive relationships that are found from empirical information. For the case of granular flows, the application of kinetic theory is necessary.
5.5.3 Volume of Fluid (VOF)
As already known the Volume of Fluid approach is used in combination with the RANS solver to determine the localization of the free surface. In this method this location is captured implicitly by determining the boundary between the water and the air long to the computational domain. An extra conservation variable is introduced and determines the proportion of water in the particular mesh cell with a value of one assigned for full and zero for empty. For the simulations where is no free surface, where there only on fluid, this model is no longer selected.
5.6 Geometry and Gird
The simplified geometry was considered as a hydrofoil which is a lifting surfaces, or foil, which operates in water. It can be seem similar in appearance and purpose to an aerofoil used by airplanes. Figure 2. Hydrofoil geometry. The characteristics of the hydrofoil are the following:
Hydrofoil (aerofoil adapted geometry) type: NACA0020 (Symmetrical)
Hydrofoil Chord: 63 mm
Hydrofoil Wing Span: 49mm
The geometry for this study was created in Cartesian coordinates. The geometry consisted of a simplified ship with six surface boundaries: inlet (for inflow), outlet (for out pressure), wall flow (wall), airflow (wall), symmetry1 (symmetry) and symetry2 (symmetry). The pre-processing of the surface and initial meshing was done in Ansys ICEMCFD software and subsequently the surface was imported into CFD code Ansys Fluent. The mesh contains approximately 38.000 cells. A structured mesh was used to this study. The ship surface was first meshed using quadrilateral elements. A volume forward of the bow was then created by projecting the outline of the bow surface towards the inlet. The mesh of this volume was created from the projection surface mesh on the bow matching portion. Once the surface mesh is created and physics models are selected, the next is to create the volume mesh. Volume controls are utilized to make the mesh more efficient and more effective as well. A volumetric control is used to specify the mesh properties as density for the surfaces and volume type meshes for the mesh generation. These controls work with volume shapes in the software. The volume shapes are a pretty well approximation of a geometry figure that can be used to specify a volumetric control for the surface or volume mesh refinement or coarsening during the meshing process. Volume shapes are created to achieve more computationally demanding and computationally important spaces of the mesh. The space around the bow, the stern and the free surface, and the space around the free surface as well, up to the height of the generated waves. The global goal of these volumetric controls, these spaces covered by the volume shapes, is specifically to have a more refined mesh. The driving factor which is in charge to the mesh refinement process and to maintain a balance between having satisfactory results and resting the computational cost as low as possible. The geometry was meshed with tetrahedral cells of defined global size, as shown in Figure 1 The mesh is finer at the more complex areas of the ship surface in order to capture the extra details and to more accurately represent them. The dimensions of the block that defines the volume mesh region. Figure 3. Mesh plot The dimension of the entire domain was chose with regard to accuracy of the results. The dimension was limited as much as possible because of the computational cost or simulation time. The length dimension behind the ship stem is longer than that forward from the bow to get more details on the waves generated by the ship. The dimensions of the block for the simulations with a free surface were initially similar in size to the ones of the simulations without a free surface. Nevertheless, as pressure concentrations were found at the ship boundaries, they were gradually increased to better represent the fluid flow and improve the accuracy of the results.
5.6.1 Mesh Evaluation
For the mesh evaluation two scalar and dimensionless parameters were used to evaluate the generated mesh. These parameters were wall y+ and the convective Courant number. The convective Courant number is only used in implicit unsteady models, thus this parameter was used to validate the model. Boundary layer needs a high mesh resolution in the near-wall region. The normalized wall distance parameter y+ was used to check the quality of the mesh near the walls and within the boundary layer. This parameter is defined as: y+=Twρ.yν Where Twis the shear stress at the wall, ρ is the local density, y is the normal distance of the cell centroid from the wall and ν is the local kinematic viscosity. Potential errors appear with large values of y+. If it is used a high y+ wall treatment, it is generally prudent to have y+ values between 30 and 50. Moreover, there are some cells that will inevitably have a small value of y+. Most values of y+ below 100 are considered as reasonable. The lowest y+ wall treatment requires the entire mesh to have values of y+ approximately of 1 or less. In this study, the all y+ wall treatment is used because it is the most general and all values of y+ are fixed to be below 100. Convective Courant number is defined as: Convective Courant number = Vdtdx That means to evaluate the mesh with the chosen time step. Convective Courant number depends on the velocity V, the time step dt, and the interval length or length of the cells dx. This ratio of the time step and the time required for a fluid particle to travel the cell length with its local speed. For each cell this parameter is calculated and it gives an indication of how fast the fluid is going through the computational cells defined before. As it can be deduced for a finer mesh drives the Courant number at higher values, a smaller time step drives it at lower values, and a higher velocity drives it up. Implicit solvers are usually stable at maximum values in the range 10-100 locally, but with a mean value of about 1. The Courant-Friedrich-Lewy condition states that the Courant number should be less than or equal to unity. Generally, this parameter arrives to values less than 1 and it is expected to give models that run faster and with greater stability.
5.7 Assumptions and Boundary Conditions
The work conditions of the simulation were the same that those in the Gothenburg 2000 workshop. The model attitude respecting to the coordinate axes was set according to the experimentally measured sinkage and trim values before creating the mesh. The coordinate system origin is located at the middle ship intersection of the water free surface and the centre plane. The open channel boundary condition was used to specify the inlet and outlet boundary condition. As has already said before, the boundary condition gives the particular solution of the general governing equation to any flow. Furthermore, these numerical solutions of the Navier-Stokes equations must give a compelling numerical representation of the proper boundary conditions. It was considered a no-slip wall boundary condition at all the walls (wall-flow and airflow and. The no-slip wall boundary condition represents the proper physical condition for a viscous flow, where the relative velocity between the boundary surface and the fluid immediately at the surface is assumed to be zero. The velocity of the flow at the surface is zero if the surface is stationary with the flow moving past it as it was defined in this case. At the inlet, it was prescribed a constant velocity that corresponds to the Froude number at which the simulation was run. The direction of the velocity that means the direction, at which the flow moves, is that of the x-axis direction. To understand, it moves perpendicular to the inlet boundary surface and toward the outlet. This inlet velocity condition is suitable for an incompressible flow. It is often utilized in combination with a pressure outlet boundary condition at the outlet flow, as it was employed in this study. The pressure outlet boundary condition is the flow outlet boundary at the outlet pressure defined. The pressure was specified to be the hydrostatic pressure of the flow with the reference pressure is the atmospheric pressure at sea level. Also, for the symmetry boundary conditions it was assumed a symmetry condition. A symmetry plane boundary condition is better used for the physical geometry with an interest and the expected pattern of the flow has mirror symmetry. A surface is defined as a symmetry plane boundary condition if it is the imaginary plane of symmetry in a simulation that would be physically symmetrical if modelled in its entirety. This solution for a symmetry plane boundary is identical to a solution that would be obtained if the mesh was replayed about the symmetry plane but in the other half of the domain. In this study, the simulations presented have an imaginary plane of symmetry where this boundary case condition was appropriate to be used. A zero-shear slip wall in viscous flows can be also modelled by a symmetry boundary condition. It was found that this condition works well and it was also used at the side, bottom and top boundaries of the simulations without a free surface. For these boundaries in the simulation with a free surface the velocity inlet boundary condition provided better performance results. The velocity imposed was the same in magnitude and direction as at inlet boundary condition. According to the real model physic, the numerical model develops a laminar regime all along the pipe and a laminar model was selected to solve the governing equations for this case. Also, the fluid was supposed incompressible, isothermal and fully developed.
6. Model Simulation
An implicit steady-state cell based solution procedure was used to solve the governing equation in this study. The SIMPLE algorithm was used for the pressure-velocity coupling and a PRESTO scheme was imposed to result the pressure interpolation. A 2nd order upwind scheme was choose for the solution of the momentum equations and the modified HRIC scheme for the solution of the volume fraction equation. The relaxation factors were typically set to 0.2 and the standard K-Epsilon turbulence model with equilibrium wall functions was used to simulate turbulent flow regime. The y+ values for the wall adjacent cells over the solid geometry were in the range of 80 and 100. That allows being comfortable within the guidelines for the use of the wall function approach. Before running the simulation, it is very important to know that Ansys determines to stop the simulation taking in consideration the iteration number and convergent limit that were specified. It means that once the maximum iteration number is reached or the convergence limit is satisfied the computation is terminated. It was imposed for every calculation a convergence limit of 10E-6 for each monitor and a maximum iteration number of 1495. Figure 4. Convergence plot (stopped at 1495 iteration). Simulation initial convergence was found to be considerably enhanced. It was due to the initialization procedure that it has to be careful attended. It is recommended that the primary phase is set to the lower density fluid, as in this case it was the air. The specific operating density should be set to that of the primary phase and the reference pressure location has to be set to the region of the primary phase. Also it is necessary and helpful to initialize the entire water domain with the correct hydrostatic pressure profile and to initialize both phase domains at the same velocity.
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