Reciprocating Compressors

RECIPROCATING COMPRESSORS

There are various compressor designs:

Rotary vane; Centrifugal & Axial flow (typically used on gas turbines); Lobe (Roots blowers), and Reciprocating.

The main advantages of the reciprocating compressor are that it can achieve high pressure ratios (but at comparatively low mass flow rates) and is relatively cheap.

It is a piston and cylinder device with (automatic) spring controlled inlet and exhaust valves. Delivery is usually to a receiver. The receiver is effectively a store of energy used to drive (eg) compressed air tools.

Delivery

TDC BDC

Inlet

Clearance vol.

Reciprocating compressors usually compress air but are also used in refrigeration where they compress a superheated vapour (to which the gas laws strictly do not apply).

In order to be practical there is a clearance between the piston crown and the top of the cylinder. Air 'trapped' in this clearance volume is never delivered, it expands as the piston moves

back and limits the volume of fresh air which can be induced to a value less than the swept volume.

The induced volume flow is an important purchasing parameter. It is called the "Free Air Delivery" (FAD), and it measures the capacity of a compressor in terms of the air flow it can handle. It is normally measured at standard sea level (SSL) atmospheric conditions and allows the capacities (size) of compressors to be compared.

N.B. The induced mass per cycle must equal the delivered

mass per cycle (continuity!), although the induced and

800 900 1000 4®1 Induction 1®2 Compression 2®3 Delivery 3®4 Expansion Cycle Analysis

The cycle may be analysed as two non-flow (compression and expansion) processes and two flow processes (delivery and induction)

PROCESS GROSS WORK p2V2 - p1V1 n-1 p2(V2-V3) p4V4 - p3V3 n-1 p1(V4-V1)

Note that we assume polytropic compression and expansion. This is because some degree of cooling is usually attempted for reasons we shall see later.

If no cooling were attempted n becomes g. On p-V co-ordinates:

2 3

The work per cycle is given by: å gross work

p2V2 - p1V1

n-1 p2(V2-V3) p

4V4 - p3V3

n-1 p1(V4-V1)

work per cycle = + + +

p4V4 - p1V1 n-1 p2V2 - p3V3 n-1 p1(V4-V1) p2(V2-V3) p1(V4-V1) n-1 p1(V4-V1) p2(V2-V3) n-1 p2(V2-V3) p1(V4-V1) {1+ } + p2(V2-V3){1+ } 1 n-1 1 n-1 but mass delivered = mass induced

p1(V1-V4) RT1 p2(V2-V3) RT2 = p2(V2-V3) p1(V1-V4) T2 T1 p1(V1-V4) { } [ -1] n n-1 T2T1

for a polytropic process : T2 T1 p2 p1 n-1 n = ( ) = rp n-1 n =

Noting that (V1-V4) is the induced volume (Vind), and p1 is the inlet pressure (pin) we may re-arrange and write:

work per cycle = p n in Vind { rp -1} n-1

n-1 n work per cycle =

+ + +

= but p1=p4 & p2=p3

work per cycle = + + +

=

\

0.9 1

Volumetric Efficiency

The reference conditions (p & T) at which the volumetric efficiency is measured should always be quoted (it would normally be SSL conditions).

[The concept of hvol applies also to reciprocating engines.] We have already noted that the induced volume is less than the swept volume. To enable this effect to be evaluated we define volumetric efficiency (hvol) as:

hvol = Induced volume Swept volume V1-V4 Vs = but p3V3 = p4V4 n n \ V4 = V3 rp 1 n

V3 is the clearance volume (Vc), and V1 = Vc + Vs hvol = Vc + Vs - Vc rp Vs 1 n \ hvol = 1 - ( rp - 1)Vc Vs 1 n

Volumetric Efficiency referred to SSL conditions.

In testing a compressor, the measured induced volume flow will be that of the actual test inlet conditions.

It is unlikely that these inlet conditions will be SSL.

We therefore need to refer our results to SSL conditions.

SSL _{Inlet >>}

Ts Ps

Ti Pi

The mass flow of gas must be the same both at SSL (s) conditions and at Inlet (i) conditions.

ms = mi psVs RTs piVi RTi = Vs pi Ts ps Ti = Vi

dividing both sides by Vswept

h

h

0 50 100 150 200 250 1 1.1 1.2 1.3 1.4 Compressor Efficiency

If we plot the specific work (kJ/kg delivered) against the polytropic index n we obtain:

w = RTin { rp -1} n n-1 n-1 n w kJ/kg n rp=4 rp=8 Is o th e rm a l c o m p re s s io n A d ia b a ti c c o m p re s s io n Polytropic

We can therefore define compressor efficiency as: Isothermal work per cycle Actual work per cycle

hiso =

If we recalculate the work input assuming isothermal compression [ W12 = p1V1 ln(p1/p2) etc] it is found that:

hiso =

Note that this efficiency is known as the isothermal efficiency. The degree of cooling possible during a single stage

compression process tends to be limited. It improves at low speeds but this limits compressor capacity.

One way of improving efficiency, especially at higher compression ratios and speeds, is to go to multistage

compression with cooling of the gas between each stage.

{ rp -1} n n-1 n-1 n ln rp

Multistage compression

To avoid unacceptable reductions in compressor capacity (RPM and volumetric efficiency) and to minimise power input with high compression ratios, multistaging with inter-cooling is used.

The number of stages will normally be between two and four.

Stage 1 Stage 2 Stage 3

in > > out

intercoolers

Each stage may be treated as a separate compressor,

however, with multistaging, all will normally rotate at the same speed.

The volumetric efficiency of the compressor as a whole is determined by the first stage.

Optimum stage pressure ratio

Assume we have two stages of compression with ideal intercooling and the same index of compression (and expansion) 'n' in each stage.

Total Work per cycle

= p1in V1ind { rp1 -1} n n-1 n-1 n _{+ p2in V2ind { rp2}n-1 n _-1} é ù ë û Since the mass induced by the first stage must be equal to the mass induced by the second stage:

p1in V1ind R Tin p2in V2ind R Tin = = p n 1in V1ind { rp1 -1} n-1 n-1 n _{+ { rp2 -1}}n-1 n é ù ë û Total Work per cycle

If p1 is the inlet pressure and p2 the final delivery pressure, let pi = the inter-stage pressure:

rp1 = pi

p1 rp2 = p

2 pi &

If we substitute the above in the expression for Total Work and differentiate wrt pi, we can find pifor minimum Total Work.

pi = [p1 p2]½ or rp1 = rp2 = p2

p1

( )

We could extend the same method to N stages with the result that, for minimum work input, the pressure ratio across each stage must be the same and equal to the Nth root of the overall pressure ratio.

rp(opt)= rp(overall) 1 N \ then whence