Newbie question about performance curve

[ali_g]

Hello,

I am a mature student and I’m trying to get to grips with a refrigeration problem I've been given.
I would much prefer an explanation than an outright answer.
But failing that, I might be able to reverse engineer an answer.

Bear in mind that this is a university apparatus so looks nothing like a refrigerator, here goes...
I am required to find electrical power of the electric motor (W_elec) using the equation W_elec = I_c x V x P_f.
Where I_c is the current measured at the compressor and V is the supply voltage.
Knowing this, I need to find the power factor (P_f) so I can draw a performance curve graph of motor shaft power v power factor.
I do not have access to the motor or an energy monitor; all results MUST be calculated.

I think I’m required to figure out how much energy it transferred into the refrigerant but don’t know how to go about it.
I have 4 enthalpy readings and 2 pressure readings that I have added to an enthalpy chart (refrigerant R134a).

I have details for the compressor;
Bore = 40mm; stroke = 30mm; total swept volume = 75.5x10^-6 m^3 ; pulley ratio between compressor & motor = 3.17; torque arm radius = 0.165m.
Compressor friction force = 5N

I have recorded and calculated many values:
Motor Shaft Power
Heat transfer rate to Cooling Water
Evaporator Heat Input
Energy transferred into refrigerant by compressor
Heat transfer rate from condenser to surroundings
Heat transfer rate into evaporator
Coefficient of Performance (COP) of refrigerator unit based on indicated power
Coefficient of Performance (COP) of refrigerator unit based on motor power
Volumetric efficiency of compressor



Still have to find:

Coefficient of Performance (COP) of refrigerator unit based on electrical input power (need electric power of motor)

Isentropic efficiency of compressor (need to find h_ (2^’) from enthalpy chart)

But have no idea where to go from here.

Any help will be much appreciated.

Thanks in advance.

[mad fridgie]

You have circular calculation, you either need to know your moter shaft power (power factor for calculation) or your Isentropic efficiency to work out what shaft power is required.
and of course each of these will change if refrigerant working conditions change.

[ali_g]

Smashing, thanks for the help.
I have checked out my graph and have determined that my isentropic efficiency is 81%.

Please pardon my ignorance but...
I understand that the Power Factor (PF) = true power / apparent power but I just cant figure out the necessary info to calculate it.

I have recorded data as follows:

Refrigerant inlet temperature to compressor T1 ºC
Refrigerant inlet temperature to condenser T2 ºC
Refrigerant inlet temperature to expansion valve T3 ºC
Refrigerant inlet temperature to evaporator T4 ºC
Water inlet temperature to condenser T5 ºC
Water outlet temperature from condenser T6 ºC
Evaporating pressure p1 kN/m2 (gauge)
Condensing pressure p2 kN/m2 (gauge)
Refrigerant flow rate mr g/s
Water flow rate mw g/s
Brake force Fb N
Compressor speed Nc rpm
Compressor current Ic A
Supply voltage V V
Evaporator voltage VE V
Evaporator current IE A

So I have to assume I can calculate it but I don’t know how to go about it.

Is there a default equation that I can use?

Thanks again in advance for any pointers given.

[DTLarca]

Average velocity is the distance between the final position coordinates and the initial all over time. Average speed is overall distance traveled all over time. The ratio of the first to the second is what I haven't noticed being mentioned here yet?