ON TRIM EFFECTS George Tzabiras Laboratory for Ship and Marine - - PowerPoint PPT Presentation

Presentation at SNAME Greek Section November 13th, 2014

EXPERIMENTAL AND NUMERICAL STUDIES ON TRIM EFFECTS George Tzabiras

Laboratory for Ship and Marine Hydrodynamics (LSMH) School of Naval Architecture and Marine Engineering NATIONAL TECHNICAL UNIVERSITY OF ATHENS

• Trim optimization is directly related to the resistance minimization

and, therefore, to the overall efficiency of a ship. There are various

• ptions to face the problem.
• The scope of the present work is to study the influence of trim on the

hydrodynamic performance of various types ships. The studies are based on model experiments carried out in the Towing Tank of NTUA as well as on CFD calculations by methods developed at LSMH-NTUA.

CRUCIAL ISSUES

• Can we trust simple resistance tests (including dynamic sinkage and

trim) or we should face the real problem of self-propulsion?

• The optimum trim is realizable?
• Can we measure accurately the benefits of trim optimization
• What happens in rough seas?

Trim influence is associated to bow and stern flow conditions

Bulb influence on bow wave (trim by bow) Stern separation about immersed transom

PART I : TOWING TANK TESTS The problem of scaling Equal Froude numbers (V/(gL)1/2 ) at model and full scale but substantially different Reynolds numbers (VL/ν)

Froude Hypothesis (first scale problem)

Extrapolation of self-propulsion experiments (second scale problem)

 

/

M FM FS S S S A S S M S S

R C V effective horsepower E R C C S HP R V         

3 2

1 2

1 1    

R S S S P

t w EHP R V SHP   

The towing tank of LSMH,NTUA 90mx4.5mx3m

TOWING TANK TETS ON SIX MODELS IN ORDER TO IVESTIGATE THE TRIM INFLUENCE ON THE RESISTANCE

• BULK CARRIER
• PASSENGER SHIP SINGLE-SCREW
• ROPAX FERRY TWIN-SCREW
• SEMI-SWATH
• SAILING YACHT
• FISHING VESSEL

Convention for “theoretical” trim angles (+) trim by bow (-) trim by stern

BULK-CARRIER (L=183m, Δ=37,000t) Single screw, bulbous bow, wetted transom Full Load (T=10.15m) and Heavy Ballast (T=7.25m)conditions Model scale 1:35

Ship main particulars

________________________________________________ Particulars Condition _____________________________ B1 B2 B3 ________________________________________________ LWL [m] 183.295 187.320 183.785 BWL [m] 23.695 23.695 23.695 TM [m] 10.150 --------- ---------- Trim [deg] 0.000 -0.500 0.500 Δ [t] 37,177 37,177 37,177 W.S. [m2] 6,885 6,902 6,860 Bulb immer. YES NO YES Transom immer. YES YES NO ________________________________________________

Model resistance vs. Froude no. at T=10.15

0,5 1 1,5 2 2,5 0,050 0,070 0,090 0,110 0,130 0,150 0,170 0,190

Rm [Kp] Froude

Trim = 0.0 deg Trim = 0.5 deg by stern Trim = 0.5 deg by bow

Vs (knots) Fr. No. 5.88 0.072 8.82 0.108 10.78 0.132 12.66 0.155 13.72 0.168 14.71 0.180

Experiments in random sea-state show the same trends !!!

Resistance differences % at model scale (-) corresponds to “gain”

• 4
• 3
• 2
• 1

1 2 3 4 5 6 7 0,050 0,070 0,090 0,110 0,130 0,150 0,170 0,190

Rm [%] Froude

T=10.15m (Even Keel vs 0.5 deg by stern) T=10.15m (Even Keel vs 0.5 deg by bow)

Dynamic trim and heave (sinkage) at model scale

• 0.60
• 0.40
• 0.20

0.00 0.20 0.40 0.60 0.80 0.050 0.070 0.090 0.110 0.130 0.150 0.170 0.190 0.210

Total Trim [deg] Froude

T=7.25 m (Even Keel) T=7.25 m (0.5 deg by stern) T=7.25 m (0.5 deg by bow)

• 0.90
• 0.80
• 0.70
• 0.60
• 0.50
• 0.40
• 0.30
• 0.20
• 0.10

0.00 0.050 0.070 0.090 0.110 0.130 0.150 0.170 0.190 0.210

Heave [cm] Froude

T=7.25 m (Even Keel) T=7.25 m (0.5 deg by stern) T=7.25 m (0.5 deg by bow)

EHP vs. Froude no. (ship, T=10.15m))

1000 2000 3000 4000 5000 6000 0,050 0,070 0,090 0,110 0,130 0,150 0,170 0,190

EHP [PS] Froude

T=10.15m (Even Keel) T=10.15m (0.5 deg by stern) T=10.15m (0.5 deg by bow)

EHP differences % vs. Froude no. (ship)

• 6
• 4
• 2

2 4 6 8 10 0,050 0,070 0,090 0,110 0,130 0,150 0,170 0,190

ΕΗΡ[%] Froude

T=10.15m (Even Keel vs 0.5 deg by stern) T=10.15m (Even Keel vs 0.5 deg by bow)

Heavy Ballast Condition Ship T=7.25m

Model Characteristics Test conditions A1 A2 A3 A4 LWL m 5.11 5.362 5.082 5.024 LBULB m 5.116 5.361 5.096 5.09 BWL m 0.677 0.677 0.677 0.677 t deg 0.000

• 0.500

0.500 1.500 Δ mt 589.42 556.84 592.46 599.32 W.S. m2 4.669 4.677 4.676 4.696 Cb 0.820 0.808 0.824 0.834 Bulb immersion NO NO NO NO Transom immersion NO YES NO NO

Model Resistance vs. Froude no.

0,5 1 1,5 2 2,5 3 3,5 0,050 0,070 0,090 0,110 0,130 0,150 0,170 0,190 0,210 0,230 0,250

Rm [Kp] Froude

T=7.25 m (Even Keel) T=7.25 m (0.5 deg by stern) T=7.25 m (0.5 deg by bow) T=7.25 m (1.5 deg by bow)

Resistance differences % vs. Froude no. (model)

• 15
• 13
• 11
• 9
• 7
• 5
• 3
• 1

1 3 5 0,050 0,070 0,090 0,110 0,130 0,150 0,170 0,190 0,210 0,230 0,250

Rm [%] Froude

T=7.25 m (Even Keel vs 0.5 deg by stern) T=7.25 m (Even Keel vs 0.5 deg by bow) T=7.25 m (Even Keel vs 1.5 deg by bow)

Total trim and heave (sinkage) vs. Froude no. (model)

• 1,20
• 1,00
• 0,80
• 0,60
• 0,40
• 0,20

0,00 0,050 0,070 0,090 0,110 0,130 0,150 0,170 0,190 0,210

Heave [cm] Froude

T=7.25 m (Even Keel) T=7.25 m (0.5 deg by stern) T=7.25 m (0.5 deg by bow) T=7.25 m (1.5 deg by bow)

• 1,00
• 0,50

0,00 0,50 1,00 1,50 2,00 0,050 0,070 0,090 0,110 0,130 0,150 0,170 0,190 0,210

Total Trim [deg] Froude

T=7.25 m (Even Keel) T=7.25 m (0.5 deg by stern) T=7.25 m (0.5 deg by bow) T=7.25 m (1.5 deg by bow)

EHP vs. Froude number (ship, T=7.25m)

2000 4000 6000 8000 10000 12000 14000 0,050 0,070 0,090 0,110 0,130 0,150 0,170 0,190 0,210 0,230 0,250

EHP [PS] Froude

T=7.25 m (Even Keel) T=7.25 m (0.5 deg by stern) T=7.25 m (0.5 deg by bow) T=7.25 m (1.5 deg by bow)

EHP differences % vs. Froude no. (ship)

• 15
• 10
• 5

5 10 0,050 0,070 0,090 0,110 0,130 0,150 0,170 0,190 0,210 0,230 0,250

ΕΗΡ[%] Froude

T=7.25 m (Even Keel vs 0.5 deg by stern) T=7.25 m (Even Keel vs 0.5 deg by bow) T=7.25 m (Even Keel vs 1.5 deg by bow)

Passenger Ship Single screw, bulbous bow, wetted transom Scale 1:15 Lines plan Main particulars

Particulars Condition

A1 A2 A3 A4 A5 __________________________________________________ LWL [m] 55.155 55.050 52.500 53.595 56.550 BWL [m] 10.500 10.500 10.500 10.500 10.500 TM [m] 3.150 3.15 0 3.150 3.150 3.150 Trim [deg] 0.000 -0.500 -1.000 0.500 1.000 Δ [t] 1,135 1,135 1,135 1,135 1,135 W.S. [m2] 665,1 672,3 694,1 649,4 641,9

A1 A2 A3 A4 A5 Bulb immersion YES YES NO YES YES Transom immers. YES YES YES NO NO

Bow wave at low speed Bow wave at high speed

Model resistance vs. Froude number

1 1 2 2 3 3 4 4 5 5 0,100 0,150 0,200 0,250 0,300 0,350

Rm [Kp] Froude

Trim = 0.0 deg Trim = 0.5 deg by stern Trim = 1.0 deg by stern Trim = 0.5 deg by bow Trim = 1.0 deg by bow

Vs(Knots)

• Fr. No.

6.95 0.151 8.33 0.181 10.16 0.221 11.13 0.242 12.37 0.269 14.45 0.314

Resistance differences % (model)

• 15
• 10
• 5

5 10 15 20 0,100 0,150 0,200 0,250 0,300 0,350

Rm [%] Froude

T=3.15m (Even Keel vs 0.5 deg by stern) T=3.15m (Even Keel vs 1 deg by stern) T=3.15m (Even Keel vs 0.5 deg by bow) T=3.15m (Even Keel vs 1 deg by bow)

Total trim angle and heave vs. Froude number

• 1,50
• 1,00
• 0,50

0,00 0,50 1,00 1,50 0,150 0,200 0,250 0,300 0,350 0,400

Total Trim [deg] Froude

T=3.15 m (Even Keel) T=3.15 m (0.5 deg by stern) T=3.15 m (1 deg by stern) T=3.15 m (0.5 deg by bow) T=3.15 m (1 deg by bow)

• 1,80
• 1,60
• 1,40
• 1,20
• 1,00
• 0,80
• 0,60
• 0,40
• 0,20

0,00 0,150 0,200 0,250 0,300 0,350 0,400

Heave [cm] Froude

T=3.15 m (Even Keel) T=3.15 m (0.5 deg by stern) T=3.15 m (1 deg by stern) T=3.15 m (0.5 deg by bow) T=3.15 m (1 deg by bow)

EHP vs. Froude number (ship)

200 400 600 800 1000 1200 1400 0,100 0,150 0,200 0,250 0,300 0,350

EHP [PS] Froude

T=3.15 m (Even Keel) T=3.15 m (0.5 deg by stern) T=3.15 m (1 deg by stern) T=3.15 m (0.5 deg by bow) T=3.15 m (1 deg by bow)

EHP differences % vs. Froude number (ship)

• 15
• 10
• 5

5 10 15 20 0,100 0,150 0,200 0,250 0,300 0,350

EHP [%] Froude

T=3.15m (Even Keel vs 0.5 deg by stern) T=3.15m (Even Keel vs 1 deg by stern) T=3.15m (Even Keel vs 0.5 deg by bow) T=3.15m (Even Keel vs 1 deg by bow)

ROPAX PASSENGER-FERRY (Twin-screw, bulbous bow, wetted transom) Scale 1:35

Particulars Condition _______________________________ A1 A2 A3 A4 A5 LWL [m] 153.65 154.80 153.09 138.00 137.55 BWL [m] 22.60 22.60 22.60 22.60 22.60 TM [m] 4.00 ----- ----- ----- ----- Trim [deg] 0.00 -1.00 -2.00 1.00 2.00 Δ [t] 6832 7078 7797 6724 6738 W.S. [m2] 2748 2889 3187 2703 2706 Bulb NO NO NO NO NO immersion Transom NO YES YES NO NO immersion

Resistance vs. Froude number (model)

1 2 3 4 5 6 0,150 0,200 0,250 0,300 0,350 0,400

Rm [Kp] Froude

T=4.0 m (Even Keel) T=4.0 m (1 deg by stern) T=4.0 m (2 deg by stern) T=4.0 m (1 deg by bow) T=4.0 m (2 deg by bow) Vs (knots) Fr. no 12.36 0.164 16.5 0.219 20.72 0.275 24.87 0.330 26.9 0.357 28.94 0.384

Resistance differences % vs. Froude no.(model)

• 30
• 20
• 10

10 20 30 0,150 0,200 0,250 0,300 0,350 0,400

Rm [%] Froude

T=4.0m (Even Keel vs 1 deg by stern) T=4.0m (Even Keel vs 2 deg by stern) T=4.0m (Even Keel vs 1 deg by bow) T=4.0m (Even Keel vs 2 deg by bow)

Trim by stern Trim by bow

Heave, dynamic and total trim angle

• 0,60
• 0,40
• 0,20

0,00 0,20 0,40 0,150 0,200 0,250 0,300 0,350 0,400

Dynamic Trim [deg] Froude

Trim = 0.0 deg Trim = 1.0 deg by stern Trim = 2.0 deg by stern Trim = 1.0 deg by bow Trim = 2.0 deg by bow Froude no. Total Trim [deg] A1 A2 A3 A4 A5 A1 A2 A3 A4 A5 Even Keel t=1.0 deg by stern t=2.0 deg by stern t=1.0 deg by bow t=2.0 deg by bow Even Keel t=1.0 deg by stern t=2.0 deg by stern t=1.0 deg by bow t=2.0 deg by bow 0.164 0.158 0.158 0.165 0.169

• 0.063
• 1.044
• 2.026

0.978 2.008 0.219 0.211 0.212 0.220 0.225

• 0.138
• 1.018
• 2.048

0.978 2.027 0.275 0.265 0.264 0.276 0.282

• 0.239
• 0.979
• 2.080

0.906 1.992 0.330 0.317 0.318 0.332 0.339

• 0.167
• 0.955
• 2.109

0.574 1.869 0.357 0.343 0.345 0.360 0.367

• 0.192
• 0.998
• 2.176

0.567 1.636 0.384 0.370 0.372 0.387 0.394

• 0.300
• 1.143
• 2.356

0.463 1.121

• 3
• 2
• 2
• 1
• 1

0,150 0,200 0,250 0,300 0,350 0,400

Heave [cm] Froude

T=4.0 m (Even Keel) T=4.0 m (1 deg by stern) T=4.0 m (2 deg by stern) T=4.0 m (1 deg by bow) T=4.0 m (2 deg by bow)

EHP vs. Froude no. (ship)

5000 10000 15000 20000 25000 30000 35000 40000 0,150 0,200 0,250 0,300 0,350 0,400

EHP [PS] Froude

T=4.0 m (Even Keel) T=4.0 m (1 deg by stern) T=4.0 m (2 deg by stern) T=4.0 m (1 deg by bow) T=4.0 m (2 deg by bow)

EHP differences % vs. Froude no. (ship)

• 30
• 20
• 10

10 20 30 40 0,150 0,200 0,250 0,300 0,350 0,400

EHP [%] Froude

T=4.0m (Even Keel vs 1 deg by stern) T=4.0m (Even Keel vs 2 deg by stern) T=4.0m (Even Keel vs 1 deg by bow) T=4.0m (Even Keel vs 2 deg by bow)

SEMI-SWATH Passenger-ferry L=64m T=3.3m Scale 1:12

Main particulars Conditions B1 B2 B3 LWL m 64,568 64,830 68,968 BWL m 7,997 8,189 8,067 ΤΜ m 3,300 3,300 3,300 t deg

• 0.3
• 1.22

Δ mt 1025,00 1025,00 1025,00 W.S. m2 1039,28 1037,14 997,51

Model resistance vs. Froude no.

2 4 6 8 10 12 14 16 18 0,100 0,200 0,300 0,400 0,500 0,600 0,700 0,800

Rm [Kp] Froude

T=3.30 m (Even Keel) T=3.30 m (0.30m deg by stern) T=3.30 m (1.222 deg by stern) Vs(Knots) Fr. No. 6.03 0.164 12.05 0.246 16.02 0.327 17.05 0.348 17.98 0.367 19.01 0.388 19.99 0.408 24.01 0.490 28.03 0.572 30.04 0.613 31.02 0.633 31.99 0.653 33.03 0.674 34.00 0.694 34.99 0.714

Resistance differences % vs. Froude no. (model)

• 5

5 10 15 20 25 30 35 40 45 0,100 0,200 0,300 0,400 0,500 0,600 0,700 0,800

RM [%] Froude

T=3.30 m (Even Kee vs 0.30m by sternl) T=3.30 m (Even Keel vs 1.222 deg by stern)

Dynamic trim and heave vs. Froude no.

• 2
• 1,5
• 1
• 0,5

0,5 0,100 0,200 0,300 0,400 0,500 0,600 0,700 0,800

Dynamic Trim [deg] Froude

T=3.30 m (Even Keel) T=3.30 m (0.30m deg by stern) T=3.30 m (1.222 deg by stern)

• 2,5
• 2
• 1,5
• 1
• 0,5

0,5 0,100 0,200 0,300 0,400 0,500 0,600 0,700 0,800

Heave [cm] Froude

T=3.30 m (Even Keel) T=3.30 m (0.30m deg by stern) T=3.30 m (1.222 deg by stern)

EHP vs. Froude no. (ship)

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 0,100 0,200 0,300 0,400 0,500 0,600 0,700 0,800

EHP [PS] Froude

T=3.30 m (Even Keel) T=3.30 m (0.30m deg by stern) T=3.30 m (1.222 deg by stern)

EHP differences % vs. Froude no. (ship)

• 10

10 20 30 40 50 60 70 0,100 0,200 0,300 0,400 0,500 0,600 0,700 0,800

EHP[%] Froude

T=3.30 m (Even Kee vs 0.30m by sternl) T=3.30 m (Even Keel vs 1.222 deg by stern)

Sailing yacht L=15m, T=0.25m, Scale=1:4

Main Particulars Conditions Α1 Α2 Α3 LWL m 14,908 14,976 13,992 BWL m 14,908 14,976 13,992 ΤΜ m 0,252 0,252 0,252 t deg 0,000

• 1,000

1,000 Δ mt 103 103 103 W.S. m2 1,844 1,877 1,804

Resistance differences % vs. Froude no. (model)

Vs (Knots)

• Fr. No.

3.88 0.165 5.83 0.248 7.78 0.331 9.71 0.413

• 2
• 1

1 2 3 4 5 6 7 8 0,150 0,200 0,250 0,300 0,350 0,400

Rm [%] Froude

T=0,25m (Even Keel vs 1 deg by stern) T=0,25m (Even Keel vs 1,0 deg by bow)

Total trim angle vs. Froude no.

• 2,5
• 2
• 1,5
• 1
• 0,5

0,5 1 1,5 0,150 0,200 0,250 0,300 0,350 0,400

Total Trim [deg] Froude

T=0,25m (Even Keel) T=0,25m (1,0 deg by stern) T=0,25m (1.0 deg by bow)

EHP differences % at full scale

• 2

2 4 6 8 10 0,150 0,200 0,250 0,300 0,350 0,400

EHP [%] Froude

T=0,25m (Even Keel vs 1 deg by stern) T=0,25m (Even Keel vs 1,0 deg by bow)

Traditional fishing vessel PERAMA L=19.3m T=2.2m Scale=1:10

Main Particulars Tetsed conditions A1 A2 LWL m 19.330 19.300 LBULB m 0.000 0.000 BWL m 6.10 6.10 ΤΜ m 2.200 2.200 trim deg 0.0000

• 2.5000

Δ mt 104.70 104.11 W.S. m2 125.20 124.90 CB 0.394 0.396

Model resistance vs. Froude no.

0,5 1 1,5 2 2,5 3 3,5 0,090 0,140 0,190 0,240 0,290 0,340 0,390

Rm [Kp] Froude

T=2.20 m (Even Keel) T=2.20 m (2.5 deg by stern)

Resistance differences % vs. Froude no. at model scale

Vs/(Kn)

• Fr. No.

2.68 0.100 3.93 0.147 5.31 0.198 6.64 0.248 7.95 0.297 9.30 0.347 10.67 0.398

• 4
• 2

2 4 6 8 10 12 0,090 0,140 0,190 0,240 0,290 0,340 0,390

Rm [%] Froude

T=2.20 m (Even Keel vs 2.5 deg by stern)

Total trim angle and heave vs. Froude no.

• 3,7
• 3,2
• 2,7
• 2,2
• 1,7
• 1,2
• 0,7
• 0,2

0,3 0,090 0,140 0,190 0,240 0,290 0,340 0,390

Total Trim [deg] Froude

T=2.20 m (Even Keel) T=2.20 m (2.5 deg by stern)

• 3
• 2,5
• 2
• 1,5
• 1
• 0,5

0,090 0,140 0,190 0,240 0,290 0,340 0,390

Heave [cm] Froude

T=2.20 m (Even Keel) T=2.20 m (2.5 deg by stern)

Full scale EHP and EHP differences %

50 100 150 200 250 0,090 0,140 0,190 0,240 0,290 0,340 0,390

EHP [PS] Froude

T=2.20 m (Even Keel) T=2.20 m (2.5 deg by stern)

• 4
• 2

2 4 6 8 10 12 14 16 18 0,090 0,140 0,190 0,240 0,290 0,340 0,390

EHP [HP] Froude

T=2.20 m (Even Keel vs 2.5 deg by stern)

CFD shows the effect of scale and the propeller operation on stern separation about the traditional fishing vessel “PERAMA” Usual towing tank extrapolation (Froude) appears questionable

Self-propulsion parameters at two model speeds

Condition Vm [m/s] rpm Resistance Ro [kp] Thrust T [kp] Thrust deduction t Effective wake w EHP/SHP Even Keel 1.081 481 0.528 0.797 0.34 0.353 0.661 2.5 deg by stern 1.081 511 0.568 0.887 0.36 0.313 0.608 Condition Vm [m/s] rpm Resistance Ro [kp] Thrust T [kp] Thrust deduction t Effective wake w EHP/SHP Even Keel 1.508 799 1.714 2.530 0.32 0.294 0.568 2.5 deg by stern 1.508 824 1.720 2.894 0.41 0.330 0.519

PART II: COMPUTATIONAL FLUID DYNAMICS (CFD) advantages: fast and less expensive, no scale effects shortcomings: discretisation and modeling errors, difficult to simulate exactly the propeller

CFD is based on the transformation

• f the Navier-Stokes differential

equations to a set of non-linear algebraic equations that can be solved using high performance computers. Values for different variables are

• btained on grid nodes.

CFD shows that the scale effect on the formation of waves about a ship is practically meaningless. Therefore, the geometrical similarity is at least fulfilled when performing towing tank tests

CFD shows the propeller effect on the stern wave formation Whenever this effect is strong, SHP is influenced noticeably

CFD compares the formation of waves at steady forward speed between the potential and viscous flow solutions

TEST CASE : CHEMICAL PRODUCT CARRIER DWT=20,000mt L=150m, B=23.20m, D=13m, Prop. D=4.25m (CPP), SHP:6000KW Tested Conditions at Vs=14 Knots Full load FL1 (trimmed) Sea-trials FL2 (zero trim) Full load FL3 (zero trim) Heavy Ballast BL1 (trimmed) Heavy Ballast BL2 (zero trim)

Conditions of test cases at Vs=14knots. FL1 FL2 FL3 BL1 BL2 Displacement (KN) 25,980 23,105 25,980 15,982 15,982 Static trim angle (deg.) 0.584 0.080 0.080 1.413 0.080 Dynamic trim (deg) 0.601 0.043

• .119

1.433 0.004 (+ : trim by stern)

CFD calculations following a hybrid method (Free-surface by potential flow and N-S underneath) Propeller model : actuator disk Full load (FL1,FL3) and sea-trials (FL2) conditions

Resistance characteristics at full load, Vs=14knpots. FL1 FL2 FL3 CTx103 3.408 3,155 3.339 CFx103 1.552 1.534 1.530 CPx103 1.856 1.622 1.809 R(KN) 4,880 4,270 4,800 EHP(KW) 3,511 3,070 3,454 S wetted (m**2) 5,394 5,095 5,416 Self-propulsion characteristics at full load, Vs=14knpots. FL1 FL2 FL3 T(KN) 5,820 5,159 5,834 DHP(KW) 6,117 5,171 6,125 RPM 172 162 172 P/D 0.820 0.830 0.820

δEHP(1-2)=14% δEHP((3-1)=-1.6% δSHP(1-2)=18% δSHP((3-1)=-0.13%

Ballast condition at 14 Knots Trimmed and zero trim conditions

Resistance characteristics at ballast condition, Vs=14knots.

BL1 BL2 R(KN) 3,471 3,730 EHP(KW) 2,498 2,633 S wetted (m**2) 4,263 4,229 Self-propulsion characteristics at ballast codition, Vs=14knots. BL1 BL2 T(KN) 4,140 4,139 DHP(KW) 3,953 3,765 RPM 143 146 P/D 0.900 0.835

δEHP(2-1)=2.16% δSHP(2-1)=-4.75% (opposite trend than EHP)

Wave formation at the speed of 14 knots with and without trim Heavy ballast condition

Computations at full-load condition with trim at the reduced speed of 10knots (“low steaming”)

Resistance characteristics at full load, Vs=10knots. FL1 CTx103 2.965 CFx103 1.603 CPx103 1.362 R(KN) 2,157 EHP(KW) 1,108 S wetted (m**2) 5,372 Self-propulsion characteristics at full load, Vs=10knots. FL1 T(KN) 2,645 DHP(KW) 1,908 RPM 116 P/D 0.830

Noticeable result EHP(14)/EHP(10)≈ SHP(14)/SHP(10)

Wave patterns at the speeds of 14 and 10 Knots Full load condition

Predictions at “low steaming” cases in still and “rough” conditions (full load condition with trim)

Ship speed V=10 kn V=10Kn “rough” V=8Kn V=8Kn “rough” SHP(KW) 1900 2646 1075 1487 Increase 39% 38% EHP(KW) 1109 1432 623 802 Increase 29% 29% SHP/EHP 1.71 1.84 1.72 1.85

With the established SHP of 1900 KW the ship will achieve 8.7 Knots in “rough” conditions

• r, equivalently, will lose 1.3 Knots.

CONCLUSIONS

• The effect of trim on the hydrodynamic resistance depends on the ship type

(hull geometry), the speed and the loading condition.

• Unless there is strong evidence that EHP is directly related to SHP, self-

propulsion tests are required to find the real influence of trim on the fuel consumption.

• Experiments in towing tanks are accurate at model scale and may also provide

safe information for full scale ships as regards trim effects.

• CFD comprises a fast and substantially less expensive tool for trim
• ptimization, but the accuracy of results suffers due to numerical uncertainties

which may be of the same order as the expected benefit. References

G.D. Tzabiras, “Resistance and Self-propulsion simulations for a Series 60, CB=0.6 hull at model and full scale”, Ship Technology Research, 51, 2004, pp. 21-34

• G. Tzabiras and K. Kontogiannis, “An integrated method for predicting the hydrodynamic

performance of low-cB ships”, Computer-Aided Design Journal, 42, 2010, pp 985-1000

• M. Iakovatos, D. Liarokapis and G. Tzabiras, “Experimental investigation of the trim influence on

the resistance characteristics of six ship models”, IMAM-2013 Int. Conference, La Coruna, 2013, pp. 23-32

• G. Tzabiras and K. Psaras, “Numerical simulation of self-propulsion characteristics of a product

carrier at various speeds”, to be presented at HIPER14 Int. Conference