MODEL EXPERIMENT- AN INSIGHT TO EXPLORE RESISTANCE

When any new-building order reaches the designer and consequently the shipyard, the owner mentions a list of soft information about the ship among which speed is a crucial parameter and there are a lot of liquidated damages associated with it. Now for a designer to finalize the ship speed and the engine power, he requires to find out the resistance and propulsion characteristics after deciding the hull form of the ship. These hull resistance and propulsive characteristics of a vessel are determined by performing model experiments on a scaled down model of the vessel. 

Resistance model experiment is performed for the following reasons:

•                 To obtain the desired ship resistance in a scaled down model and extrapolating the value to full scale.
•                To determine the flow pattern and flow induced vibration in a ship model scale so that in model stage corrections in hull form or alignment of hull appendages can be made to ensure streamline flow around the hull.
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The flow around the model hull is observed using:

•       Wool tuft test
•       Paint flow test

In both the tests the path lines of the fluid are traced and they are compared with streamline flow.

Wool tuft test showing path lines of flow around hull (Courtesy: Google Images)

Paint flow test depicting flow around the hull (Courtesy: Google images) 

 

REQUISITE OF A RESISTANCE MODEL EXPERIMENT

Resistance model experiments are based on 3 similarities between ship and model for extrapolation of model data to actual ship scale. The similarities are as follows:

Geometrical similarities- 

According to Froude Law of Similarity the vessel and the model should be geometrically similar. That is the linear dimensions of the ship should be proportional to the linear dimensions of the model. This constant is called scale factor.   

              Scale factor(λ)= linear dimension of actual ship/ linear dimension of model      

   

Similarly all the area ratios are proportional to (λ²) and the volume ratios like displacement are in the ratio of (λ³).

 Kinematic similarity- 

This similarity is also based on Froude Law of Similarity and states that  the model should be operated in a towing tank with corresponding speeds related as shown.

                      Corresponding speed =  Speed of ship/ (λ)^(.5)

   

Dynamic similarity- 

This similarity relates the fluid dynamics associated with the ship. This similarity states that the wave pattern around the model and actual ship hull should be the same. Residuary resistance of a ship is a function of the wave dynamics associated with the ship. Actually in practice when we maintain geometrical similarity and we are dealing with potential flows the dynamic similarity is automatically maintained. 

PROCEDURE OF A RESISTANCE MODEL EXPERIMENT

In a model experiment, geometrically similar model is manufactured of wood or wax and bamboo composites or FRP or even PVC foam. The size of the model depends on the scale factor used. The model cannot be manufactured to exact perfection as geometrically similar to the actual ship due to efficiency of machinery and manufacturing process, where minute errors are inevitable.  Thus, a tolerance of 2 mm and 1 mm is allowed for length and breadth respectively.            

Wooden and FRP model of a resistance test (Courtesy: Google Images)

                               

A larger model is always preferred since it is easier to manufacture and is more accurate. But the length of the model is restricted on the tank dimensions to avoid blockage effect. 

According to ITTC, to avoid blockage effect the following measures need to be pertained to:

1. L_m  <  d
2.  L_m  <  *w
3.  A_Xm < *A_c

Where,

              L_m = Length of the model

              A_{Xm =} Area of midship of the model

              A_{c =} Cross-sectional area of the towing tank

              d = Depth of the towing tank

                            w= Width of the towing tank

Blockage effect is primarily related to the wave making resistance. Thus for slow speed vessels where the wave making phenomenon is low enough to ignore, the blockage effect can be overlooked.

The models after manufacture is then ballasted to its required draft line and trim conditions. The draft of the model is generally kept according to the load water line (LWL) of the designed vessel. The model is then fixed to a carriage provided in the towing tank. The carriage is operated electrically or hydraulically which tows the model ahead at certain predetermined speeds. The carriage is fitted with a resistance dynamometer to measure the towing force required to tow the ship. The resistance dynamometer is attached to the model using pillars. These pillars are fixed but the pillars allow the model to heave and trim so as to maintain dynamic similarity.

Model experiment for resistance conducted in a carriage (Courtesy: Google images)

It is known that different components of the resistance sums up to total resistance that act on the vessel opposite to the direction of the model velocity. This total resistance acts on the centre of force of the total resistance and it is assumed to be at half draft above the keel or slightly lower than that. The model is towed from that point such that no moment is created that would trim the vessel leading to augment of the model resistance. Generally for merchant vessels with Froude Number (Fn) <0.3, this assumption holds true. But for high speed vessels, especially for planning crafts, where there is a lift of hull due to hydrodynamic forces there the towing force is applied further down to reduce trimming of the model.

PROBLEMS DURING A RESISTANCE MODEL EXPERIMENT

1. One of the primary problems encountered during model experiment is augmenting of the resistance of model due to blockage effect. This phenomenon can be avoided by following the ITTC rules for model and tank dimensions mentioned earlier.
   
2. One of the main problems of model experiments is Laminar flow around the model. We know for a ship 

Reynolds Number (Rn) = .

                Where,

                                v = Velocity of ship.

                                L = Length of ship.

                                ν = Coefficient of kinematic viscosity of water. 

Assuming coefficient of kinematic viscosity of sea water and fresh water (generally used in model experiment) to be the same. There since,

Lm/Ls=1/λ

Vm/Vs= 1/(λ)^(.5)

So,

Rnm/Rns=1/(λ)^(3/2)  . Where the symbols have their usual meanings

Thus Reynolds Number similarity of the model not being maintained, laminar flow prevails around the model than the turbulent flow that prevails for the actual vessel. Also considering boundary layer formation around the bow of the actual vessel laminar flow prevails which after some length become turbulent. But model length being small, only laminar flow prevails around it.

As shown by Blausius and Prandtl-Von Karman, for laminar flow the coefficient of frictional resistance (C_F) is less in comparison to turbulent flow and there is a decrease in extrapolated resistance value for actual ship.

Difference in coefficient of frictional resistance for laminar and turbulent flow (Courtesy. - Google images)

Response turbulence simulators like trip wire, sand strips, studs, etc. are fitted along the fore part of the ship at 5% of LOA or sometimes at 5% and 10% of LOA to stimulate turbulent flow around the model hull. 

It should be considered that the turbulence stimulators do not add to excess of appendage drag to the model. For this an alternative came up to stimulate turbulence in the towing tank in front of the model using turbulence stimulators attached to the carriage. Thus there will be no attachment of the stimulators with the model hull and appendage drag is omitted.

Due to laminar flow around the hull the C_T vs. Rn graph is obtained incorrect. At low speeds where coefficient of residuary resistance (C_R) is negligible often coefficient of residuary resistance (C_T) line goes below C_F line which is obtained from the ITTC formula

 C_{F =} (1+k)*0.075/(logRn-2)^(2)

At that point it is inferred that the flow around the model is laminar and turbulence has to be stimulated.

METHOD OF EXTRAPOLATION OF A RESISTANCE MODEL TEST RESULTS TO FULL SCALE

1.                         From the design parameters we know the Length of model (L_m), Displacement of the model (Δ_m) and the Wetted surface area of model (S_m).
2.          .      From the carriage dynamometer readings we measure the Velocity of the model (preset) and the total resistance of the model (R_Tm). 
3.            The particular dimensions and the velocities of the ship and the corresponding model are used to find out the Reynolds number of the ship and the model (Rn_s and Rn_m). This Reynolds number information is used to calculate the coefficient of frictional resistance for the ship and the model (C_Fs and C_Fm). 
4.           .       Then the Frictional resistance of the model is calculated and deducted from the measured total resistance of the model to find out the residuary resistance of the model. This residuary resistance is extrapolated to the actual ship scale according to Froude’s Law of similarity. The frictional resistance of the ship is calculated according to the ITTC formula
                                R_F = (1+k)*0.075/(logRn-2)^(2)* .5*(ρ_SW*v_s²* S_s).
5.                         The total resistance of the ship is thus obtained by summing the frictional resistance, residuary resistance, Appendage resistance, Air resistance and Correlation allowance.  Correlation allowance is an augment of the total resistance of the actual vessel based on the fact that the surface smoothness of model (25 micro m) is more than that of the actual ship (150 µm). So model experiences less resistance than the actual ship. Air drag and correlation allowance is calculated based on the given formulas
   R_AA = C_D* *(ρ_Air)*A_T*V_R²        

Thus the total resistance is:

R_TS =  (Sapp+Ss)/Ss*(R_F + Correlation allowance) + R_R + C_AA

This resistance value is used to calculate the effective power of the vessel given by the formula:

P_E = RTS * V_S

                                                                                                          

INTERESTING FACTS ABOUT RESISTANCE MODEL EXPERIMENTS

By definition the resistance if a ship is calculated with a constant ship speed. Had the ship being accelerating an extra force would act on the ship due to fluid dynamics called the ‘added mass force’. In the model experiment when the model accelerates to attain certain preset speed there is an augment of the resistance value due to this ‘added mass force’. Thus resistance value is only measured after a steady speed is attained. That’s why towing tanks are made long enough such that the first few metres required to tow the model to a constant speed can be ignored and these extra effects can be ignored in computing the final resistance. 

TYPICAL RESISTANCE DATA GRAPHS OBTAINED FROM MODEL EXPERIMENTS

Typical graph for coefficients of model resistance for a 450 t Oil Tanker (Copyright: NSDRC, Visakhapatnam)

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Typical graph for coefficients of ship resistance for a 450 t Oil Tanker (Copyright: NSDRC, Visakhapatnam)

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Typical graph for ship’s effective power vs. ship speed for a 450 t Oil Tanker (Courtesy, NSDRC, Visakhapatnam)

Symbols Index:

λ	Scale factor for model
ρAir	Density of air
ρSW	Density of sea water
ΡFW	Density of fresh water
Lm	Length of the model
Ls	Length of the ship
d	Depth of the towing tank
w	Width of the towing tank
AXm	Area of midship of the model
Ac	Cross-sectional area of the towing tank
	Velocity
L	Length
	Coefficient of kinematic viscosity of water
vm	Velocity of model
vs	Velocity of ship
Rnm	Reynolds number of model
Rns	Reynolds number of ship
CT	Coefficient of total resistance
CR	Coefficient of residuary resistance
CF	Coefficient of frictional resistance
k	Form factor of the model
Δm	Displacement of model
Sm	Wetted Surface area of model
Ss	Wetted Surface area of ship
Sapp	Wetted Surface area of appendage
Fns	Froude number of ship
Fnm	Froude number of model
CD	Coefficient of air drag
AT	Equivalent transverse area of ship exposed to wind
VR	Relative velocity of the wind with respect to ship
PE	Effective power

          

           Article By: Rijay Majee