3 replies to this topic

[ARC]

Dears

can somebdoy tell me
1. If compression ratio is reduced what will be the effect on brake horse power.
2 What is the formula to calculate the BHP?
3. The clearance volume is constant for each compressor or it changes during operarion? it is always supplied by manufacturer or can be calculated from volumetric efficiency if known?



Regards
Amol

[Art Montemayor]

Amol:

1. If the compression ratio is reduced in a reciprocating compression stage, the corresponding required horsepower to compress the gas introduced is LESS than when the compression ratio was larger;

2. The formula to calculate the adiabatic work of compression in a reciprocating gas compressor is:

Theoretical Work of compression, hp = (144/33,000) (a) (P₁V₁) [(P₂/P₁)^b -1]

Where,

a = k/ (k-1)
k = Adiabatic exponent; ratio of specific heat at constant pressure to specific heat at constant volume
P₁ = suction pressure, psia
P₂ = discharge pressure, psia
V₁ = suction volume, cubic feet/min
b = 1/a

Another equation that can be used as a “quickie” estimate is:

Brake hp = (22) (ratio/stage) (number of stages) (MM cfd) (F)

Where,

MM cfd = Compressor capacity referred to 14.4 psia and suction temperature;
F = 1.0 for single stage; 1.08 for 2-stage; and, 1.10 for 3-stage machine;

This equation was developed for obtaining a quick and reasonable estimate for compressor horsepower. It was developed for slow speed (300 - 450 rpm) compressors handling gases with a specific gravity of 0.65 and having compression ratios above 2.5. It will also provide a rough estimate of horsepower for lower compression ratios and/or gases with a higher specific gravity, but it will be on the high side.

3. The clearance volume in a reciprocating compressor is normally constant for each compressor cylinder – not for each compressor. The clearance volume can be changed by using, for example, variable clearance pockets and thus obtain an excellent capacity control that also furnishes economic horsepower usage.

[ARC]

Dear ART

Thank you very much for your reply.

Still i have doubt. for a compressor if volumetric efficiency is known and no information related to clearance volume is known,how to calculate the percentage clearance volume and suction volume?

Regards
Amol

[Art Montemayor]

Amol;

You have, as yet, still not defined what type of compressor we are discussing here – nor the gas conditions you are compressing under. You force us to speculate or guess that it is a reciprocating type and I will assume as much.

A reciprocating compressor is a “pure” positive displacement type of machine and to understand what is meant by “volumetric efficiency” should be nothing more than common sense:

Volumetric Efficiency = (Gas Volume delivered / Total Gas Volume inside Compressor Cylinder) (100)

You should know – from the compressor’s manufacturer – the Gas Volume delivered. What is difficult to know is the total Gas Volume inside compressor cylinder. The Gas Volume delivered is also what you call the “suction volume” (what is sucked in must be delivered – if there is to be no accumulation).

Another way to express Volumetric Efficiency (VE) in a reciprocating machine is:

VE, % = 100 – C ( R^a -1) - L

Where,

C = the cylinder clearance, %
R = cylinder compression ratio
L = an empirical loss factor, %
a = 1/k
k = Specific heat at constant pressure / specific heat at constant volume

The term L is introduced to allow for the effect of such variables as internal leakage, gas friction, pressure drop through valves, inlet gas preheating, etc. This term is difficult to generalize. It may be 5% for a moderate pressure (50 psig), oil lubricated air compressor. It is probably higher for a Hydrogen compressor cylinder with a higher compression ratio and some valve leakage.

Inspection of the formula shows that the VE decreases:

1. As the clearance increases;
2. As the compression ratio increases; and,
3. As k decreases.

You ask: “how to calculate the percentage clearance volume and suction volume?”. The % clearance you speak of is, I presume, the Cylinder clearance volume. If so, then your answer is cited above. This is a very difficult figure to generate given that it must include the valve chambers exposed to the cylinder, the end clearances, etc.

Cylinder clearance cannot be completely eliminated. Normal clearance is the minimum obtainable in a given cylinder and will vary between 4 and approximately 15% for most standard cylinders. Some special low ratio cylinders have normal clearance much greater than this. Normal clearance does not include volume that may have been added for other purposes, such as capacity control.

Although clearance is of little importance to the average user (guarantees being made on actually delivered capacity), its effect on capacity should be understood because of the wide application of a variation in clearance for control and other purposes. There are many cases where extra clearance is added to a cylinder to:

1. Reduce capacity at fixed pressure conditions; and
2. Prevent driver overload under variable operating pressure conditions by reducing capacity as compression ratio changes.

If a compressor is designed for a given capacity at a given condition, the amount of normal clearance in cylinder or cylinders has no effect on power.

The suction volume, as explained before, is the delivered volume – since there is no accumulation in the compressor cylinder. You have not given us any other information – such as variable speed, clearance pockets, variable compression ratio, etc. Therefore, your compressor capacity (expressed as suction volume, discharge volume, or delivery volume) should be constant and equal to that guaranteed by the manufacturer for the application.

I believe this addresses both of your questions and helps you to understand the principles behind a positive displacement, reciprocating compressor - which is what I believe you are dealing with.