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Hydrodynamic Forces and Moments

The value RAP is calculated using formula

RAP = kAP (α AP ,CT ) PAP [1− t(δ AP )],

where kAP – the coefficient depending on the propeller load and inflow angle, PAP

– the propeller thrust, t(δ AP ) – thrust deduction fraction.

Propeller thrust is calculated according to the propeller type as follows:

PAP = ρ n2D4KT (J,P / D) ,

where n – the propeller rotation frequency, D – the propeller diameter, KT – the propeller load coefficient, J – the propeller advance coefficient.

The calculation of the inflow velocity and force on the azimuth thrusters is fulfilled taking into account the values of wake scaling factor at all needed angles of device deflection.

The azimuth thrusters control effect is its angle of turn.

Vane Propellers

The mathematical model allows to calculate the thrust value and lateral force value developed by the vane propellers. Size and position of devise are tacked into account

They are as follows:

•propeller diameter at blades’ axes DVSP ,

•blades number ZVSP ,

•blade length lVSP ,

•blade-area ratio AVSP / AVSP 0 .

The value of blade-area ratio (a vane propeller characteristic) is calculated using formula:

AVSP / AVSP 0 = bVSP ZVSP ,

DVSP

where bVSP – the propeller blade chord, ZVSP – the number of propeller blades.

The formulas for forces calculation are as follows:

FxVSP = CxVSP 0.5 ρ VVSP2 FP [1− t(δVSP )]

FyVSP = CyVSP 0.5 ρVVSP2 FP [1− t(δVSP )] ,

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Hydrodynamic Forces and Moments

where CxVSP and Cy VSP – the thrust and lateral force coefficients in body axis, VVSP – blade velocity, FP – the hydraulic section area, t(δVSP ) – thrust deduction fraction, δVSP – the control center deflection angle1.

CxVSP and Cy VSP are defined as follows: non-dimensional propeller thrust

CxVSP = KxVSP (eVSP , αVSP ,JVSP ) cos βVSP + Ky VSP (eVSP , αVSP ,JVSP ) sin βVSP

non-dimensional lateral force

Cy VSP = Ky VSP (eVSP , αVSP ,JVSP ) cos βVSP + KxVSP (eVSP , αVSP ,JVSP ) sin βVSP where

Kx and Ky – non-dimensional values of longitudinal and lateral force components in body axes defined in the database, eVSP – the vane propeller eccentricity, αVSP –

the eccentricity angle in body axes, βVSP – the local drift angle.

Control center angle in flow axes is calculated as the sum of two angles: the control center deflection angle in body axis and local drift angle taking into account wake scaling factor.

αVSP = δVSP + βVSP

The advance coefficient of vane propeller is calculated as the ratio of the inflow

velocity and blade velocity: JVSP = VpVSP

VVSP

where VpVSP – the inflow velocity.

Roll and trim moments as well as the yaw moment due to the vane propeller operation are defined taking into account their position on the ship.

Vane propeller control effects the blades deflection angle and vane propeller frequency.

1 blade velocity. blade velocity is defined by formula: VVSP = 2π n RVSP (n – vane propeller frequency, RVSP – the vane propeller radius at blades axes)

Hydraulic section area. Hydraulic section area FP is calculated by formula FP = l DVSP , (l – the blade length, DVSP = 2RVSP is the vane propeller diameter at blades axes).

Thrust and lateral force coefficients. Thrust and lateral force coefficients are defined depending on the propeller eccentricity eVSP , control center deflection angle αVSP in flow

axis and propeller advance coefficient JVSP .

40 NAVI-TRAINER 4000. Mathematical Models. Technical Description.

Engine Model With Remote Control System

Thursters

Mathematical model describes the tunnel-type thruster: stern or bow thrusters installed as a group (1 to 3).

The thrust is provided by an impeller situated inside a pipe located perpendicularly to the ship centreplane.

Impeller thrust value depends on the thruster characteristics (output section diameter DTHR , impeller characteristics) as well as on the relative water velocity and

flow velocity at the thruster output section Vlq /VTHR . The force location depends on the thruster position on the hull.

The lateral force and yaw moment generated by thruster are calculated using formula:

lateral force

FyTHR = FyTHR 0fy THR (β ,VTHR ,Vlq ) ,

yaw moment

MzTHR = Fy THR 0fmTHR (β ,uTHR ,V )xTHR ,

where Fy THR 0 – the thrust at zero ship velocity, fy THR and fmTHR – coefficients obtaining the hull form influence on the thrust value.

Roll moment, trim moments and yaw moment due to thrust are depended on the thruster position.

The thruster control effects the impeller rotation frequency or impeller pitch.

ENGINE MODEL WITH REMOTE CONTROL SYSTEM

Engine control is performed using engine telegraph. The signal is sent to the engine remote control system and provides certain mode of fuel feed to the engine depending on the received command. As result, the engine rotation frequency changes, which provides the requested thrust.

Mathematical model allows to simulate main engines of the following types:

•Low-speed and medium-speed reversible engines, which start and reverse is done by compressed air;

•Non-reversible medium-speed and high-speed engines, which reverse is achieved by a reversing clutch, and the rotation transfer to the propeller is performed through a reduction gear.

Engine

Engine mathematical model is based on the engine dynamics on rotation frequency.

2πJe n&e = Q(ne ,h) + Qf (ne ) + Qp (n,V,f1) + Qc (ne )

where Q is the engine torque that depends on the operation mode, Qf is the friction moment of the rotating engine parts, Qc is the compression moment in the engine, Qp is the moment at propeller shaft, Je is the reduced inertia moment of all the

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Engine Model With Remote Control System

rotating masses relatively to the propeller axis, h is the position of the fuel-control device (fuel rack), ne – engine RPM, n is the propeller shaft RPM.

Engine torque Q equals moment Qe (n,h) defined basing on the engine partial characteristics (when running on fuel) or its torque QA(ne,PA ) at engine start or reverse.

The friction moment of the engine rotating parts Qf is calculated using formula

Qf = − A neb , where А and b are coefficients depending on the engine characteristics.

Propeller moment Qp is calculated depending on the propeller diameter, rotation

frequency and moment coefficient that is defined in accordance with propeller effect curves, and is reduced to the engine output shaft.

The inertia moment of the rotating parts relatively to the propeller axis Je is

calculated as the sum of moments of all the rotating parts in the engine, inertia moment of the propeller and propeller added mass.

Engine operation mode is set using the main engine remote control system (ME RCS). The ME RCS structure depends on the engine and propeller types.

Engine diagrams with different remote control systems are illustrated on the figures below.

Remote Control Systems

Low RPM Engine with FPP

Main Engine remote control system provides engine start, stop and reverse, changes in engine operation mode during vessel movement and RPM control.

Fig. 6. Engine Diagram with ME RCS for a FPP Type Vessel

42 NAVI-TRAINER 4000. Mathematical Models. Technical Description.

Engine Model With Remote Control System

Engine Start, Stop, Reverse

Engine Start, Stop and Reverse model for reverse engines using compressed air. Engine start model is based on the calculation of torque QA(ne,PA ) created by the

pressed air. Value РА defines the startup air pressure calculated using the equation

P&A = qc − qstart ,

where qc and qstart are the pressure change speed at compressor operation and at startup. For reverse engines, at least 12 sequential startups are provided.

Engine Control Modelling

Engine control modeling is accomplished using special software that defines the fuel duty. The engine control diagram for a FPP type vessel is illustrated below:

Fig. 7. Engine Control Diagram for a FPP Type Vessel

Legend: Н is the engine telegraph position, h is the current fuel rack, h is the set fuel rack position, h& is the speed of fuel rack position change, U is the index specifying the RCS program (“normal”, “emergency”, “warm up”).

RPM Regulator

An all modes, PI RPM regulator has a restrictive characteristic. The regulator mathematical model is defined by equation:

h = K ne + K∫ ∫(ne − ne )dt ,

where ne is the current engine RPM, ne is the set engine RPM, h is the fuel rack

deviation from the set value. The model also considers the condition that the change made to the fuel rack height when adjusting the propeller RPM should not exceed the set value:

h ≤ hlim .

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Engine Model With Remote Control System

Low/Medium RPM Engine with CPP

Beside the engine start, stop and operation mode change during the vessel movement, the ME remote control system on a CPP type vessel provides propeller pitch control. See Fig. 8.

Fig. 8. Engine Diagram with ME RCS for a CPP Type Vessel.

RCS for CPP type vessel implements two modes:

“fixed RPM” mode (propeller pitch is set using the engine telegraph lever),

“combo” mode (propeller pitch and RPM are set using the engine telegraph lever in accordance with the combinative diagram).

Propeller Pitch Adjusting Mechanism

See Fig. 9. Legend: Н is the engine telegraph lever position, P is the propeller pitch, P is the set propeller pitch, P& is the pitch change rate, U is the index defining the engine operation mode.

Fig. 9. Engine Control Diagram for a CPP Type Vessel

44 NAVI-TRAINER 4000. Mathematical Models. Technical Description.

Engine Model With Remote Control System

Medium/High RPM Engine with Reverse-Reduction Gear and FPP

The RCS for a vessel with Reverse-reduction gear controls the RPM and shaft rotation direction via a clutch and a reduction gear controlled via engine telegraph. See

Fig. 10. Engine Diagram with ME RCS for a Vessel with Reverse Reduction Gear

The propeller RPM value depends on the engine RPM according to the following formula:

n = rneUc .

where r is the reduction gear ratio, ne is the engine RPM, Uc is the index defining the clutch operation mode (forward/aft/disconnected).

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Control Driving Gear

CONTROL DRIVING GEAR

Steering Gear

Steering gears are used for rudder and nozzle turnover of different types. Steering gear control is performed using the steering wheel (FFU control) or remote control buttons (simple control).

The steering gear contains 1 to 3 pumps with permanent or alternate discharge rate. The steering gear control diagram is illustrated on Fig. 11.

Fig. 11. Steering Gear Control Diagram

Steering gear mathematical model defines the rudder angle change depending on the pump discharge rate. The Rudder angle equation is as follows:

JR δ&&R = MSG (δ ,δ ,i) + MR (δ R ,ω z ,V,CT ) ,

where i is the number of operating pumps.

When moving in normal mode, the rudder stock moment is considered to be equal to

the steering gear moment, i.e. MSG (δ ,δ ,i ) = MR (δ R ,ωz,V,CT ) , and rudder angle is calculated from formula:

δ& = f (δ ,δ ,i ) .

The mathematical model considers the rudder angle restriction defined by the rudder structure, and the rudder turnover maximal speed.

Maximal rudder turnover speed is defined by the number of operating pumps. Also, the steering gear model allows considering:

Rudder turnover slowdown due to pressure decrease in the hydro-system;

Pump failure

Control circuit failure (set rudder angle not worked off.

Steering gear power supply failure

46 NAVI-TRAINER 4000. Mathematical Models. Technical Description.

Control Driving Gear

Rudder wedging

In case of steering gear power supply failure, the rudder is positioned stream-wise. The rudder movement equation is:

JR δ&&R = MR (δ R ,ω z ,V,CT ) .

Tunnel Type Thruster Gear

Tunnel type thruster gear control is performed either by changing the impeller RPM, or by changing the pitch (depending on the thruster structure).

Thruster mode change command is sent from the vessel control panel by changing the thruster lever position.

The thruster RCS provides permanent rate for changing control values (impeller RPM or impeller pitch). The FFU thruster control diagram is illustrated on Fig. 12.

Fig. 12. FFU Thruster Control Diagram

Vane Propeller Gear

Vane propeller gear is controlled by changing the longitudinal and lateral eccentricities.

The vane propeller gear mode change command is sent from the vane propeller control panel by separate changes to the lever position defining the longitudinal eccentricity value and steering gear turnover defining the lateral eccentricity value. In case of two vane propellers, lateral eccentricity control is done synchronously.

Vane propeller RCS provides constant eccentricity change rate. FFU control diagram is similar to the one illustrated on Fig. 11.

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Control Driving Gear

Waterjet Gear

Waterjet gear is controlled by changing the vane position and reverse rudder structure angle.

Waterjet gear mode change command is sent from the waterjet control panel by separate changes done to the vanes position lever and steering wheel turnover defining the reverse rudder position angle. In case of two waterjets, reverse rudders are controlled synchronously by a joystick system (see Fig. 13).

Fig. 13. Joystick System Control Panel

A two-coordinate joystick is designed for waterjet thrust specification (direction and value) in “port” mode and reverse rudder structure angle specification and waterjet RPM in “normal” mode. A set of buttons in the central part of the control panel is designed for turning the joystick system on/off and changing its operation modes. Indicators above the know are designed for displaying the sector, in which the know is currently in.

The knob is designed for waterjet torque direction and value in “port” mode and for waterjet rudder angle limiters in “normal” mode.

Waterjet RCS provides permanent rate for changing control parameters. FFU diagram is similar to the one illustrated on Fig. 11.

Nozzle Gear

Nozzle gear control is accomplished by changing the nozzle shaft RPM and angle.

Nozzle mode change command is sent from the nozzle control panel from a twocoordinate joystick, which scales display the angle and propeller thrust. In case of two nozzles, control is done synchronously.

Waterjet RCS provides constant rate for changing control parameters (RPM and angle).

FFU control diagram is identical to the one illustrated on Fig. 11.

48 NAVI-TRAINER 4000. Mathematical Models. Technical Description.