# Main characteristics of a compressor. Throughput and power

**Contents:**

Compressors, like other sophisticated technical units, have a huge number of wide-ranging characteristics. However, a number of characteristics may be distinguished which are basic for the unit. Those values determine the scope of application of a compressor and make the basis for the calculations and selection of compressor equipment for a specific task. Other characteristics are secondary and mostly dependent on the primary values. Secondary characteristics also affect the design, operation and overall efficiency of a compressor, but to a much lesser degree.

Primary values determine the operational conditions of a compressor as well as compressed gas flow figures that may be achieved with this compressor. What is convenient is that based on a limited set of parameters it is possible to determine the scope of application of a compressor or, alternatively, determine the units suitable for this task. The choice may be based on a single principle parameter or on a set of several ones depending on the requirements to the compressor.

A compressor’s applicability is mostly influenced by the following characteristics:

- operating pressure;
- throughput;
- power.

Undoubtedly, other characteristics, such as: overall size, weight, exit gas temperature, noise, etc. may also have a significant impact on the calculations and resulting choice of a compressor, however, throughput and operating pressure are the key parameters underlying the selection of a suitable unit. For example, if high-pressure air feed is required for a certain application, but with a relatively low flow rate, this screens out immediately low-pressure compressors, such as centrifugal and liquid ring types. Trying to achieve the required operating pressure on such compressors will either be impossible or economically infeasible. At the same time high-pressure compressors are by definition more suitable for such conditions. A more precise selection depends on various secondary characteristics and results of technical and economic analysis. Piston compressors would be much cheaper in terms of capital expenditures, while screw-type compressors could give a better air purity, but all of them would meet the requirements to key characteristics.

Usually the buyer does not, and quite often cannot, have full data on the compressor parameters required. Only the basic requirements to be met by the compressor may be available: gas volume and pressure, connected power restrictions. In other words, operating pressure, throughput and consumed power. Apparently this basic set of requirements may be revised and supplemented with such characteristics as corrosion and chemical resistance of parts, noise level, feed rate consistency, etc. Based on these data several compressors may be chosen and designed, each of them capable to perform the task at hand. They could differ in some minor details, which make it possible for the buyer to select the most optimal unit, where any of the secondary characteristics, such as, for example, electric power consumption (in case of a compressor unit with electric motor) or maintenance costs may be a determining factor.

Though the above characteristics may be considered basic, there are some parameters that have a comparable impact while selecting a compressor. Thus, chemical and physical composition of gas may have a decisive influence, since the compressor’s ability to handle such media determines not only its efficiency, but the possibility of operation as such. Plus, if parts are manufactured from materials resistant to chemicals or wear, the unit may become several times more expensive. In other cases the requirements to the exiting compressed gas may be of critical importance, such as gas purity, feed consistency, temperature, instead of just throughput and pressure. For example, in food industry, there are stricter requirements to cleanliness of media and substances, so it is essentially inadmissible to use oil lubrication of screws in a screw compressor, if there is a possibility of lubricant getting into the gas stream, while other values may not have any impact on the final decision on application. The difference of such significant, but secondary characteristics from the primary ones, is that the degree of their impact varies from case to case, while operating pressure, throughput and power are always important.

## Compressor operating pressure

This characteristic may be called fundamental, since it represents the core function of a compressor - gas compression, which results in boosting its pressure. The pressure generated by a compressor is usually measured in Pascals (Pa), bars (bar) or atmospheres (atm), but also such units as millimetres of mercury column (mm Hg), kilogram-force per square centimetre (kgf/cm^{2}) or pounds per square inch (psi) may be used. Pascals and bars are the most common units correlating as follows: 1 bar = 0.1 MPa. Besides, operating pressure may be divided into gage pressure (P_{gage}) and absolute pressure (P_{abs}). They differ by the atmospheric pressure value (P_{atm}) and correlate as follows Р_{gage} = Р_{abs} - Р_{atm}.

When choosing a compressor one should remember that the pressure generated by the unit is gradually going down on its way to equipment or instrumentation. Pressure drop may occur both along the entire gas line and at so called local constraints: valves, line bends, flaps, etc. The compressor’s operating pressure should cover all the losses on the way to the consumers and comply with target specifications at the exit.

In some cases compressed gas delivery conditions may be of critical importance. Thus, piston compressors, due to their design, create a pulsating compressed gas flow, while screw compressors compress the media uniformly, without any time fluctuations. In such cases as, for example, spraying of paints and varnishes, consistent feed is critical for proper operation. There are different ways of suppressing compressor pressure surges. Thus, piston compressors may have several chambers with operating cycles time-shifted against each other, which partially smooths out the total flow. However, quite often a device called “receiver” is used, i.e. a vessel accumulating compressed gas delivered by the compressor, which almost fully eliminates exit gas pressure fluctuations.

Depending on the pressure generated compressors are divided into the following units:

- vacuum (negative pressure 0.05 MPa);
- low pressure (from 0.15 to 1.2 MPa);
- medium pressure (from 1.2 to 10 MPa);
- high pressure (from 10 to 100 MPa);
- ultra-high pressure (over 100 MPa).

## Compressor throughput

Compressor throughput means gas volume delivered per time unit. It is usually measured in m³/min, l/min, m³/h, etc. Compressor throughput may be specified both for a suction line and discharge line, and those values are not equal, since in the process of combustion gas changes its volume. For inlet throughput standard conditions are usually assumed, i.e. atmospheric pressure and 20°C temperature. Specification of a compressor throughput may be determined by perception convenience depending on the unit’s field of application. Gas flow rate recalculation from inlet to outlet conditions may be done using special formulae. Besides, throughput recalculation may be required, if gas has a different temperature.

As a function of throughput compressors are divided into:

- high throughput units (over 100 m³/min);
- medium throughput units (from 10 to 100 m³/min);
- low throughput units (below 10 m3/min).

**Throughput of a piston compressor**

The throughput of a specific compressor depends mostly on its geometry and type. A piston compressor is the simplest and most indicative in this case, since its throughput is directly dependent on the size of its working chamber. Throughput can be represented as the working chamber volume multiplied by the number of piston strokes per unit of time, or, if we invoke the geometry of piston parts, as a cylinder cross-section area (F) multiplied by the piston stroke (S) and shaft rotation rate (n). However, this is only possible in an ideal case. In reality, due to the design of the valves, cylinder itself and piston, gas is not displaced completely from the working chamber. Some part of it remains and the respective space occupied by it is called dead space. This is done on purpose, to avoid piston hitting the end of the chamber, which could result in compressor failure.

Let's designate the volume displaced by the piston as V_{p}, then the dead space may be expressed as V_{d}=V-V_{p}, where V is the working chamber volume. To account for the dead space the respective coefficient is used ε=(V-V_{p})/V_{p}. That is the dead space may also be determined from the formula V_{d}=ε∙V_{p}.

The gas occupying the dead space also has an impact on the suction of a new portion of gas, since this process will not start before the remaining gas expands to a certain value, while the piston goes a certain distance, so the suction will be incomplete as compared to the ideal case. To account for this effect a volumetric efficiency parameter is introduced calculated according to the formula λ_{v}=V_{a}/V_{p}, where V_{a} is the actual gas volume transferred by suction pressure. The coefficient itself may be determined as follows:

λ_{v} = 1 - ε∙((p_{2}/p_{1})^{1/m} - 1)

where:

λ_{v} – volumetric efficiency;

ε – dead space coefficient;

p_{1} – inlet pressure, Pa;

p_{2} – outlet pressure, Pa;

m – polytropic coefficient.

Thus, the throughput of a single-action piston compressor is determined from the formula:

V_{p} = λ_{v}∙F∙S∙n

If a double-action piston is used, the throughput cannot be calculated as a simple doubling of throughput of a single working chamber. Some adjustment is necessary, since one of the chambers will be partially occupied by the piston rod, so its throughput will be less than that of the rod-less chamber. The adjusted formula looks as follows:

V_{p2} = λ_{v}∙(2∙F - f)∙S∙n

where:

V_{p2} – double-action piston pump throughput;

f – rod cross-section area.

**Throughput of a screw compressor**

Volumetric capacity of such a compressor may be represented as the overall volume of spaces limited by the screws and casing, driven out per time unit. Ideally, when there are no losses or leakages, theoretic throughput of a screw compressor (with two screws) may be calculated as follows:

Q_{t} = l∙m_{1}∙n_{1}∙f_{1} + l∙m_{2}∙n_{2}∙f_{2}

where:

Q_{t} – theoretical throughput of a screw compressor, m³/s;

l – screw length, m;

m_{1} – number of lobes of the driving screw;

n_{1} – rotation rate of the driving screw, s^{-1};

f_{1} – driving screw recess area, m^{2};

m_{2} – number of lobes of the idle screw;

n_{2} – rotation rate of the idle screw, s^{-1};

f_{2} – idle screw recess area, m^{2}.

Considering that the equation m_{1}∙n_{1} = m_{2}∙n_{2} = m∙n is usually satisfied, the theoretical throughput formula for a screw compressor may be represented as:

Q_{t} = l∙m∙n∙(f_{1}+f_{2})

The actual flow rate turns out to be less than theoretical one, which is a natural phenomenon. The influence of different leakages inside the compressor and gas leakages into the atmosphere through seals has a certain effect. Mathematically this is taken into account in the delivery rate, so the actual throughput will equal:

Q_{a} = Q_{t}∙η_{d} - Q_{l}

Q_{a} – actual throughput;

Q_{l} – leakages through seals;

η_{d} – delivery rate.

**Throughput of a centrifugal compressor**

Media pumping principle in a centrifugal compressor is identical to that of a centrifugal pump, the only difference being that compressed gas is reduced in volume, which results in higher density. For such compressors throughput is usually calculated at the inlet at normal conditions, which is convenient for operation. The initial value of this parameter, as well as the outlet pressure, are usually preset before the calculation, after which the geometry of wheel elements is calculated. For example, the formula correlating the throughput of a centrifugal compressor and the inlet section of a wheel is as follows:

Q = (π/4)·v_{in}·(d²_{2}-d²_{1})

where:

Q – throughput of a centrifugal compressor, m³/s;

v_{in} – gas flow rate at the inlet, m/s;

d_{1} – outer diameter of the wheel hub, m;

d_{2} – minimum diameter of cover disk, m;

## Compressor power

In general, power, according to a standard definition, is relation of energy consumed within a certain period to the duration of this period. With regard to a compressor, this is a product of gas flow rate multiplied by compression energy. Such power is called theoretical and is calculated as follows:

N_{t} = (Q∙ρ∙A)/1,000

where:

N_{t} – theoretical power, kW;

Q – throughput, m³/min;

ρ – gas density, kg/m³;

A – theoretical gas compression energy, J/kg.

However, it is worth noting that theoretical power differs from that which has to be connected to the compressor for its operation and the power that needs to be generated by the motor connected to the compressor. This is a result of power loss, which is numerically described by a set of efficiency ratios. The compression process occurring in a compressor has its own efficiency indicator (depending on the process), and a part of connected power is lost for mechanical transmission.

**Power of a piston compressor**

Power calculation for piston compressors compressing to 10 MPa maximum, may be done accurately according to the formulae, where gas is assumed to be ideal. However, for compressors with a higher maximum compression pressure (over 10 MPa), calculations are influenced by the fact that the handled gas is not ideal. The key difference of ideal gas from not ideal one (actual) lies in an assumption that gas molecules do not interact, while in actual gas there is such interaction, which may have a significant influence on gas behaviour. The theoretical power formula taking these factors into account, looks as follows:

N_{t} = (Q∙ρ∙(i_{2}-i_{1})) / 1,000

where:

N_{t} – theoretical power, kW;

Q – compressor throughput, m³/s;

ρ – gas density, kg/m³;

i_{1} – gas enthalpy before compression, J/kg;

i_{2} – gas enthalpy after compression, J/kg.

The formula above is designed for a single-stage compressor. If compression is performed in several stages, then the delta of enthalpies (i_{2}-i_{1}) in the formula should be replaced by the sum of such deltas at each stage. If the compression energy is the same for each stage, the equation looks as follows:

N_{t} = (Q∙ρ∙n∙(i_{2}-i_{1})) / 1,000

where:

n – number of stages;

i_{1}, i_{2 }– initial and final enthalpies of the first stage, J/kg.

As represented in the figure, the power of the first stage is N_{1}=(Q∙ρ∙n∙(i_{2}-i_{1}))/1,000, second stage N_{2}=(Q∙ρ∙n∙(i_{3}-i_{2}))/1,000, and third stage N_{3}=(Q∙ρ∙n∙(i_{4}-i_{3}))/1,000. Let’s assume that the delta of enthalpies is the same at each stage, i.e. (i_{2}-i_{1})=(i_{3}-i_{2})=(i_{4}-i_{3}). Considering that the total number of stages is (n=3), we get:

N_{tot} = N_{1} + N_{2} + N_{3} = (Q∙ρ∙n∙(i_{2}-i_{1}))/1,000 + (Q∙ρ∙n∙(i_{3}-i_{2}))/1,000 + (Q∙ρ∙n∙(i_{4}-i_{3}))/1,000 = 3∙(Q∙ρ∙(i_{2}-i_{1}))/1,000

**Power of a screw compressor **

When gas is passing through the screw compressor, continuous power losses occur in different ways. Since the screws are not ideal in shape and size, gas continuously backflows from cavity to cavity from discharge side to the suction side, which partially accounts for those losses. Besides, gas energy is lost to friction against the screws and casing, to impacts, etc. For these reasons the actual power consumed for gas compression in the unit happens to be larger than the theoretical one required for the same gas to be compressed under ideal conditions. Such power is called indicative and may be determined as follows:

N_{i} = (k∙Q)/1,000 ∙ [p_{s}∙(ε^{m-1}-m)/(1-m) + p_{d}∙(1/ε)]

where:

N_{i} – screw compressor power (indicative), kW;

k – adjustment coefficient (from 1.05 to 1.18 depending on the unit size);

Q – throughput at input conditions, m³/s;

p_{s} – suction pressure, Pa;

p_{d} – discharge pressure, Pa;

ε – compression degree (geometry);

m – polytropic coefficient.

In all the rest the calculation of the full power of the entire compressor unit consisting of a compressor proper, a motor and transmission, is the same as for the other types of compressors. The power of the compressor itself is increased from the indicative one by the value of mechanical losses in its operation. Some part of power is lost to transmission, some - in the motor itself. These losses are accounted for by introducing the respective efficiency ratios.

**Power of a centrifugal compressor**

Gas flow passing through a centrifugal compressor loses part of its energy to hydraulic losses. These losses are described by hydraulic efficiency (η_{h}), which correlates the theoretical power (N_{t}), which would be needed for gas compression under ideal conditions, and the indicative power (N_{i}):

N_{i} = N_{t}/η_{h}

Besides, due to inevitable gas leakages from the working space the actual gas flow rate eventually differs from the theoretical one, which also results in additional power losses characterized by volumetric efficiency (η_{v}). The useful power (N_{u}), which should be transmitted to the impeller for gas compression will be equal to:

N_{u} = N_{i}/η_{v}

Useful power may also be calculated based on the measured actual compressor parameters according to the formula:

N_{u} = V_{a}∙H_{a}∙p

where:

N_{u} – useful power, W;

V_{a} – actual flow rate, m³/s;

H_{a} – actual head, m;

p – average pressure before and after compression, usually taken as the arithmetic average, Pa.

The total compressor power, which should be transmitted to the shaft, is called shaft power and may be calculated from the indicative power adjusted for mechanical losses in the compressor:

N_{s} = N_{i}/η_{m}

where:

N_{s} – compressor shaft power, W;

η_{m} – mechanical efficiency.

Considering all the losses the full efficiency (η_{f}) of a centrifugal compressor is expressed as follows:

η_{f} = η_{h}∙η_{v}∙η_{m}

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