Simpson’s Rules

Basic assumption:

The curved portion of a figure forms part of a parabola

y=a₀+a₁x+a₂x²+a₃x³

and gives the area contained between 3 consecutive equally spaced ordinates.

Simpson’s  1^st rule

-is used to find area when there are odd number of evenly spaced ordinates.

- This is called “3 ordinate rule”

This rule can be generalized to any figure defined by an odd number of evenly spaced ordinates, by applying the First Rule to ordinates 0 to 2, 2 to 4, 4 to 6 and so on, and then summing the resulting answers.

This provides the rule for (n + 1) ordinates:

Simpson’s  2^nd  rule

-is used to find area when there are even number of evenly spaced ordinates.

The rule for four evenly spaced ordinates is:

It can be extended to cover 7, 10,13, etc., ordinates, becoming:

Simpson’s  3^rd  rule

-is a special case to find area between any 2 ordinates when 3 evenly spaced ordinates are known.

- This is called Simpson's 5, 8 minus 1 Rule.

Unlike other Simpson's rules, the 5, 8, -1 rule cannot be applied to moments.

A corresponding rule for moments, derived in the same way as those for areas,

is known as Simpson's 3, 10 minus 1 rule and gives the moment of the area bounded by y₀ & y₁ about y₀, as:

Reefer Compressor oil properties

-Good chemical stability

(little or no chemical reaction with refrigerant or materials)

-Good thermal stability

(should not form hard carbon deposits at hotspots in the compressor like valves or discharge ports)

-Low viscosity

(good fluidity at low temperatures)

-Low wax content

-Low pour point (temp at which the oil ceases to flow)

-Low floc point (temp at which wax content in L.O. separate from L.O & refrigerant)

-Moisture-free

(may cause corrosion)

Desirable properties of refrigerant

-Low boiling point (otherwise operation at high vacuum becomes a necessity)

-Low condensing pressure (avoids heavier plant and reduces leakage risk)

-High specific enthalpy of vaporization

-Low specific volume in vapour state (reduces size and increases efficiency)

-High critical temperature

-Non-corrosive & non solvent

-Stable  under working conditions

-Non-flammable & non explosive

-Immiscible with oil (oil separator is a must if miscible)

-Easy leak detection

-Non toxic

-Cheap, easily stored & obtained

Refrigerant used on my ship (Plz know the same for your ship)

R134A----->CF₃CH₂F----> 1,1,1,2-Tetra fluroethane

-does not contain chlorine atoms and thus does not attack the ozone layer.

-But it is a green house gas, may be subjected to future legislation.

Reefer System Safeties

-HP cut out

-LP cut out

-Differential pressure L.O. cut out

-Cylinder head relief valve

-Relief valve in condenser                                               

-Unloaders / capacity controllers

-Non-return shut-off valves

-Pressure & temperature sensors

-Oil separator

-Drier (removes moisture in the line)

-Motor overload trip

-Belt driven (slips at overload)

-Mechanical seal

Parameters to be checked in refrigeration rooms

-Suction pressure

-Discharge pressure

-L.O. pressure

Typical room temperatures (±2)

Veg room           (+5°C)

Fish room           (-18°C)

Meat room          (-20°C)

** During defrosting process (manual/automatic), higher temperature may be shown.

REFRIGERATION basics

Cooling – final temperature may not be lower than the surroundings.

e.g. cooling the coffee or tea in the room.

Refrigeration- final temperature is always lower than the surroundings.

e.g. cooling the water with ice cubes.

Gas cycle

-involves gas with sensible cooling and no phase change takes place.

Vapour cycle

-involves phase change from liquid to gas in evaporator and gas to liquid in condenser.

*Vapour compression uses mechanical compressors.

*Vapour absorption uses thermal compressors.

Why SUPER-LONG STROKE ?

Super-Long stroke advantages

- Low quality fuel can be burnt 

(since more time is available for fuel combustion).

- Slow rpm is possible

(-->so large diameter propeller can be used -->propeller efficiency increases.)

- More time for heat dissipation to cooling water.

-better scavenging

-higher compression ratio can be achieved.

(so more fuel can be burnt per stroke and more power developed)

-reduced exhaust temperature

-reduced fouling, smoke, NOx

-increased thermal efficiency   

(heat converted into useful work / total heat supplied)

-power to weight ratio is more.

Classification based on stroke/bore ratio (For Man B&W)

Short stroke             : 2.6-3.2

Long stroke              : 3.2-4.0

Super-Long stroke : 4.0-4.7

Ultra-Long stroke  : >4.7

CRITICAL SPEED RANGE

Critical Speed Range (or Barred range)

-is the range of speed at which resonance may occur.

-Resonance is a phenomenon experienced when the engine’s operating frequency coincides with the natural frequency of the hull which results in vibrations of higher amplitudes than normal which is very dangerous.

-The critical speed range should be passed as soon as possible.

-In order to avoid operation of the main engine in critical (or barred) speed range, a quick-pass function is provided.

If the bridge command is within these areas, the lamps for critical rpm limit on the bridge and in the engine control room will illuminate.

The system will,

-during acceleration, keep the engine running below the lower critical speed,

-during deceleration it will keep the engine running above the upper limit.

Indications of Critical speed range :

- More vibrations can be experienced.

- The lamps for critical rpm limit on the bridge and in the ECR will illuminate.

*The speed range is marked RED in all Manoeuvring Panels. (Bridge, ECR, Local)

*The critical speed range is also labeled adjacent to the Manoeuvring Panels or near the telegraphs.

Means to reduce the amplitude of vibrations:

-sectionalizing of the shafting and

-interposing special couplings between sections.

-using vibration absorbers fitted to the crankshaft.

Means to avoid resonance is to adjust:

-speed of the engine

-mass of the flywheel or

-engine’s firing order.