Sizing of a displacement air compressor

Using the generic pilot and a specific driver

Introduction
Loading the cooled displacement compressor model
Using the generic pilot
Off-design calculations
Using a specific driver
Conclusion

Introduction

In this guided exploration (DTNN-3) on positive displacement compressors, we detail the calculation and sizing of a piston compressor used to supply a compressed air storage tank.

Note that a second guided exploration (DTNN-1) deals with the determination of the surface of a heat exchanger and its behavior in off-design conditions.

Functionally, compressors are devices used to increase the pressure of fluids passing through them.

They are used for many industrial applications, for refrigeration, air conditioning, transportation of natural gas ...

Technologically speaking, compressors can be grouped into two main classes:

Positive displacement compressors, in which the fluid is trapped in a closed volume which is reduced gradually to achieve compression;
And dynamic compressors, which use a different principle: the compression is obtained by converting pressure into kinetic energy imparted to the fluid by moving blades.

For further explanations, we suggest you refer to the page of the Thermoptim-UNIT portal which deals with positive displacement compressors.

Special mention should be made of air compressors, used as a source of power in public works and construction and in factories, pneumatic tools having many benefits. The example presented here focuses on this type of device.

The example we are dealing with here is intended to diagnose the problems and show how they can be resolved without the overall system being too complicated. For specialists, it will seem a bit simplistic, but for beginners it is already quite difficult to treat completely.

Typology of problems posed and associated difficulties

The study of the compressors in an energy system has very different levels of difficulty depending on the objectives that we pursue.

The most basic approach is to calculate the outlet temperature when the compression ratio and isentropic efficiency are known. If the flow-rate involved is also known, the compression work can be deduced directly.

The inverse problem is solved also simply: knowing the compressor inlet and outlet states, you can determine the isentropic efficiency of the device.

To go further and determine the isentropic efficiency and the flow through a given displacement machine, we have to perform more complicated calculations, requiring a thorough knowledge of compressor operation.

We will call technological design calculations for determining the displacement of a compressor knowing the laws giving its volumetric and isentropic efficiencies.

This is by the way a general problem in energy systems studies: as long as one is satisfied to carry out cycle studies without trying to size the geometry of the components, the calculations are much simpler than when one wishes to closely analyze their internal behavior.

Once the displacement determined, allowing to geometrically characterize the compressor, another problem remains to be treated: that of its behavior when operating conditions differ from those used in the design.

We call this problem the study of its off-design behavior.

It can be a higher level of complexity than the technological design, because it may require solving large systems of nonlinear equations when several components are coupled together.

This is a relatively complex problem that you should understand before you can use it. It is presented in this page of the Thermoptim-UNIT portal, which we strongly recommend that you read before anything else.

When trying to accurately represent the behavior of a given compressor, it is necessary to characterize it by:

Its displacement;
The law of volumetric efficiency;
The law of isentropic efficiency.

The theory shows that the main factor on which these quantities depend is the compression ratio Pref/Pasp, ratio of the discharge pressure to the suction pressure.

rendement volumétrique

Generally, a first order polynomial law is enough to represent the evolution of the volumetric efficiency as a function of the compression ratio.

To properly represent the isentropic efficiency eta, we need more parameters. The law we will retain uses 5:

rendement isentropique

To size a compressor, it is necessary to know these laws.

Identification of their parameters can usually be made on the basis of data provided by the manufacturer.

Implementation in Thermoptim

Versions 2.7 and 2.8 of Thermoptim allow technological sizing and off-design studies. For this, they introduce screens complementary to those which allow the usual phenomenological modeling to be carried out.

They define the geometric characteristics representative of the different technologies used, as well as the parameters necessary for calculating their performance. For a given component, they obviously depend on the type of technology chosen.

The calculations are carried out in extensions of the core of the software package, and in particular in programs called pilots or drivers of Thermoptim.

They are so called because they take control of the software by driving it to perform specific operations not available in the core screens.

There are many types of pilots. Two categories of pilots make it possible to carry out technological sizing studies, generic pilots and specific pilots.

The former are by nature multipurpose but can only perform simple calculations, while the latter, defined specifically for a particular model, can perform much more complex operations.

Glossary

Adiabatic

Evolution without heat exchange with the surroundings

Reversible adiabatic

Adiabatic evolution without heat exchange with the surroundings and without friction losses

Heat

Transfer of thermal energy from one system to another when there is a temperature difference between them

Latent heat of change of state

Energy that must be supplied or withdrawn when a phase change takes place

Coefficient of performance (COP)

Generalization for the refrigeration cycles of the concept of efficiency

Cogeneration

Combined production of thermal energy and mechanical energy or electricity

Non stoichiometric combustion

Combustion with excess or lack of air.

Stoichiometric combustion

Combustion without excess or lack of air where all available oxygen is completely consumed.

Hermetic compressor

Compressor whose engine is directly cooled and lubricated by the thermodynamic fluid, which eliminates the need for oil

Scroll compressor

Compressor formed of two cylindrical spirals, one fixed, the other mobile, of identical shape, which roll by sliding one on the other, enclosing gas pockets of variable volume

Condensation

Evolution of a substance from the gaseous to the liquid state

Counter-flow

Thermodynamically efficient exchanger flow configuration

Composite curves

Set of two curves representing on the one hand the cumulative energy availability of a heat exchanger network as a function of temperature, and on the other hand, that of energy needs.

Cycle

Series of processes which bring a fluid to its initial state

Combined cycle

Integration into a single unit of mechanical power production of two complementary technologies in terms of temperature level, generally gas turbines and steam plants.

Brayton cycle

Motor cycle of a gas turbine composed of isentropic compression, isobaric heating, isentropic expansion, and isobaric cooling

Reverse Brayton cycle

Refrigeration cycle composed of isentropic compression, isobaric cooling, isentropic expansion, and isobaric heating

Carnot cycle

Motor cycle composed of isentropic compression, isothermal heating, isentropic expansion, and isothermal cooling

Hirn cycle

Rankine cycle with superheating

Rankine cycle

Motor cycle of a steam plant composed of isentropic compression, isobaric heating in two stages (heating in the liquid state, vaporization), isentropic expansion, and isobaric cooling

Motor cycle

Cycle converting heat into work

Refrigeration cycle

Cycle allowing to extract heat at low temperature or to raise the temperature level of a fluid thanks to a supply of mechanical energy

(h, ln(P)) chart

Thermodynamic chart with enthalpy on the abscissa and pressure on the ordinate, generally with a logarithmic scale.

Entropic chart

Thermodynamic chart with entropy on the abscissa and temperature on the ordinate.

Psychrometric chart

Thermodynamic chart including the dry temperature t on the abscissa and the specific humidity w on the ordinate.

Diffuser

Organ allowing the conversion of the kinetic energy of a fluid into pressure

Economizer

Heat exchanger for heating a fluid in the liquid state

Efficiency

Ratio of the useful energy effect on the purchased energy involved

Efficiency of a heat exchanger

Ratio of the greatest temperature increase within the fluids to the difference between the inlet temperatures of the two fluids

Ejector

Organ allowing the aspiration of a fluid thanks to the enthalpy of a motive fluid

Internal energy

Sum of kinetic energies (comparable to the thermal agitation of particles) and potential energies of microscopic interactions (chemical bonds, nuclear interactions) of the particles constituting a system

Purchased energy

sum of all the energies provided to the cycle coming from outside

Useful energy

Net balance of useful energies of the cycle, that is to say the absolute value of the algebraic sum of the energies produced and consumed within it participating in the useful energy effect

Enthalpy

Generalization to open systems of internal energy for closed systems.

Environment

All that is external to the system under consideration and with which it interacts

State of a system

The concept of a state of a system represents the minimum information necessary to determine its future behavior.

Reference evolution

Evolution corresponding to the functioning of components which would be perfect, for which a well-chosen variable or state function remains constant and to which we know how to associate a simple evolution equation

Excess air

Air in excess of the stoichiometric reaction.

Air factor

Multiplicative factor of the quantity of air in a non-stoichiometric reaction as compared with the stoichiometric one, equal to the inverse of the richness.

Flash

Evaporation of a fluid by isethalpic throttling from the liquid state

Working fluid

Fluid used in a thermal machine and undergoing various evolutions or processes

Path function

Quantity which depends not only on the initial and final states of the system, but also on the way in which evolution takes place.

State function

A state function is a quantity whose value depends only on the state of the system, and not on its history.

Mass fraction

Ratio of the mass of a constituent to the total mass of a mixture

Molar fraction

Ratio of the number of moles of a constituent to the total number of moles in a mixture

Fusion

Process which undergoes a substance from solid to liquid

Ideal gas

Fluid model where it is assumed that the size of the molecules and the interactions between them are negligible. Its internal energy and enthalpy only depend on temperature.

Perfect gas

Ideal gas with constant thermal capacities

Steam generator

Heat exchanger producing vapor from a pressurized liquid

Relative humidity

Ratio of the partial pressure of water vapor to its saturated vapor pressure.

Specific (or absolute) humidity

Ratio of the mass of water contained in a given volume of wet mixture to the mass of dry gas contained in this same given volume.

Thermal irreversibilities

Irreversibilities due to temperature heterogeneity arise from the difference in temperature which must in practice exist between two substances when they exchange heat.

Isenthalpic

Evolution during which the enthalpy remains constant

Isobaric

Evolution during which the pressure remains constant

Isothermal

Evolution during which the temperature remains constant

Isoquality

Evolution during which the vapor quality remains constant

Isenthalpic throttling

Adiabatic process without work.

Saturating pressure law

Relation which gives the saturation pressure of a fluid as a function of temperature

Oxycombustion

Combustion carried out with pure oxygen or a mixture of oxygen O₂ and carbon dioxide CO ₂ as oxydizer

Exchanger pinch

Minimum temperature difference between the two fluids which pass through a heat exchanger.

Critical point

State where the pure vapor phase has the same properties as the pure liquid phase. It is characterized by the critical pressure and the critical temperature

Heating value

Enthalpy released by a combustion reaction.

Partial pressure

Pressure that a constituent would exert if it occupied alone the volume V of a mixture, its temperature being equal to that of the mixture.

Pressurizer

Component of a Pressurized Water nuclear Reactor (PWR) used to maintain the pressure in the primary circuit

Extraction

Fraction of the main flow of fluid which is extracted in order to ensure a preheating of the fluid before entering the economizer

Efficiency

Ratio of the useful energy effect on the purchased energy provided

Carnot efficiency

Efficiency of an ideal thermal machine describing a cycle between two heat sources

Isentropic efficiency

Used to characterize the performance of compressors and turbines that are not perfect, so that compression and expansion follow non-reversible adiabatic processes

Polytropic efficiency

Infinitesimal isentropic efficiency

Richness

Ratio of the number of moles of fuel contained in a given quantity of mixture, to the number of moles of fuel contained in the stoichiometric mixture, equal to the inverse of the air factor.

Reheat

Refers to a cycle in which the partially expanded fluid is warmed up before further expansion

Regeneration

Use of some of the heat available after expansion of a fluid to preheat it

Sublimation

Process which a substance undergoes from the solid state to the gaseous state

Supercritical

State of a fluid whose pressure is greater than its critical pressure

Superheater

Heat exchanger for heating a vapor to a temperature higher than that of vaporization

Open and closed systems

A thermodynamic system designates a quantity of material isolable from its environment by a fictitious or real border. This system is said to be closed if it does not exchange matter with the surroundings across its borders; otherwise it is sayd open.

Separator

Organ used to separate a fluid in liquid-vapor equilibrium by dividing its flow into two parts, one corresponding to the liquid, and the other to the vapor

Temperature

Measurement of the degree of agitation of the molecules of a fluid: the more they are agitated, the higher its temperature

Quenching temperature

Temperature at which unburned gases were frozen during certain combustion reactions, and therefore the one that must be used in the law of mass action to calculate Kp and find the composition of the burnt gases.

Thermocoupler

Mechanism that complements heat exchangers by allowing components other than exchange processes to connect to one or more exchange processes to represent thermal couplings

Quality of a two-phase mixture of a pure substance

Ratio of vapor mass to total mass (vapor + liquid)

Irreversible process

A process is said to be irreversible in the following two cases:

the reverse process cannot be carried out without profound modification of the equipment (mixing, combustion, etc.);
it contains a cause of irreversibility of the friction or viscosity type.

Reversible process

We call reversible process between two states of equilibrium 1 and 2 a fictitious evolution which has the following two properties:

it is sufficiently slow in all respects (velocities, exchanges of heat and matter…) so that we can assimilate it to a continuous series of equilibrium states;
it constitutes the common limit of two families of real processes, one of which leads from 1 to 2, and the other from 2 to 1.

Useful work

Work produced by the moving walls of a machine operating in an open system

Aeroderivative gas turbine

gas turbines derived from aviation, variant of a turbojet engine

Nozzle

Organ allowing the conversion into kinetic energy of the enthalpy of a fluid

Vaporization

Process which a substance undergoes from the liquid state to the gaseous state

Vaporizer

Heat exchanger for vaporizing a fluid

State variables

Set of physical quantities (or thermodynamic properties) (temperatures, pressures, etc.) necessary and sufficient to completely characterize a system at a given instant.