Compressor map

A compressor map is a chart which shows the performance of a turbomachinery compressor. This type of compressor is used in gas turbine engines, for supercharging reciprocating engines and for industrial processes, where it is known as a dynamic compressor. A map is created from compressor rig test results or predicted by a special computer program. Alternatively the map of a similar compressor can be suitably scaled. This article is an overview of compressor maps and their different applications and also has detailed explanations of maps for a fan and intermediate and high-pressure compressors from a three-shaft aero-engine as specific examples.
Compressor maps are an integral part of predicting the performance of gas turbine and turbocharged engines, both at design and off-design conditions. They also serve a critical purpose in selecting the correct compressors for industrial processes. 
Fans and turbines also have operating maps, although the latter are significantly different in appearance to that of compressors.
Compressor design.
A compressor map shows the operating range of a compressor and how well it works within its operating range. Two fundamental requirements for the gas flowing through a compressor explain why it works best at a design condition and not so well at other conditions, known as off-design. First, the exit area has to be smaller than the inlet area because the compressed gas has a higher density. The exit area is sized to pass the specific volume at the design condition. Second, all the rotor and stator blades in an axial compressor, and impeller inducer and diffuser vanes in a centrifugal compressor, are angled to meet approaching air head-on at the design condition to minimize incidence losses. Incidence losses reduce the efficiency of compression. Satisfactory operation of the compressor relies on controlling the angle at which the gas approaches rotating and stationary blades to within an acceptable range. Deviating from the optimum first results in increased losses/reduced efficiency then either stalling or sonic velocity/choking which occur in the blade passages at opposite ends of an axial compressor at the same time. They also occur in a centrifugal compressor at entry to the impeller and in the diffuser.
The compressor design point will be in an area of high efficiency whether the compressor is part of a gas turbine engine or whether it is used for pumping air into a blast furnace. However the compressor has to provide suitable performance at other operating conditions imposed on it which means a high efficiency is required over a wider range of operation. In the case of a gas turbine engine it must permit the engine to be started readily and accelerated rapidly to the design speed which means operating at lower speeds than the design speed. At speeds and flows away from the design point the compressor flow area reduction is not appropriate for the actual density rise. A NACA report illustrates pictorially the difference in contraction required at the design condition and at low speed. At lower speeds, for example, the gas hasn't been compressed enough to exit the compressor without adversely affecting the blade angles of attack through the compressor. Away from the design point the middle stages of an axial compressor continue to operate at about the optimum angle of attack but the front stages deviate one way, towards stall, and the rear stages in the opposite direction towards choke. The deviation was acceptable up to a design pressure ratio of about 5:1, producing only a loss in efficiency. At higher design pressure ratios prevention of rotating stall, which occurs at low corrected speeds, and choking was required with the introduction of inlet guide vanes which partially closed at low speeds, or by removing air part-way along the compressor at low speeds. Rows of variable stators or split compressors, which allowed the front stages to speed up and the rear to slow down relative to each other, would also be introduced for the same reason. When pressure ratios reached about 12:1 compressors would incorporate more than one of these features together.
Fixes for rotating stall.
Early examples of different solutions to alleviate rotating stall in the front stages include the Rolls-Royce Avon with variable inlet guide vanes and interstage bleed, the General Electric J79 with variable inlet guide vanes and variable stators, the Bristol Olympus with split compressor and the Pratt & Whitney J57 with split compressor and intercompressor bleed. Compressor bleed up to this point had been only necessary for starting and accelerating beyond low corrected speeds where its loss to thrust production, from dumping overboard, was not important.
A further development was permanent compressor bleed routed back into the engine where it contributed to thrust. The Rolls-Royce Conway had a split compressor with intercompressor bleed to the jetpipe. A split compressor with this bypass arrangement allowed the highest pressure ratio of any Rolls-Royce engine, at that time, without the need for variable inlet guide vanes or interstage bleed. It was better known as an arrangement for better propulsive efficiency, a bypass engine. The Pratt & Whitney J58 used interstage overboard bleed for starting and accelerating through low corrected speeds but since it returned to these speeds at high mach numbers the bleed was opened again but this time routed to the jetpipe where it cooled the afterburner and nozzle. This cooling contributed indirectly to thrust in allowing more fuel to be burned in the afterburner. A similar arrangement, but using a split compressor with intercompressor bleed to the jetpipe, was later known as a 'leaky' turbojet, a bypass engine with only enough bypass for cooling the afterburner and nozzle.
Compressor map.
Compressors pump gas for a wide variety of applications each of which has its own flow resistance which the compressor has to meet to keep the gas flowing. A map shows the pumping characteristics for the complete range of flows and pressure requirements for its application. The map may be produced by driving the compressor with an electric motor with the flow resistance selected artificially using a variable area throttle valve. The compressor may also be mapped if it is part of a gas generator with a valve at the turbine exit. Campbell shows a General Electric J79 compressor mapped in this way.
Dimensional Analysis.
Compressor performance changes, day to day, with changes in the ambient pressure and temperature. Woolenweber shows the change in performance of a turbocharger compressor when the inlet temperature varies between 70 and 100 deg F. In the case of aircraft compressors, inlet pressure and temperature also change with altitude and airspeed. The presentation of different performance for every combination of inlet temperature and pressure would be unmanageable but it is possible to collapse it all onto a single map, which is applicable to a wide range of inlet conditions, using dimensional analysis. In dimensional analysis individual quantities such as rotor speed, mass flow and delivery pressure are each grouped with other relevant quantities in such a way that the groups have no dimensions but still have a physical meaning. For example rotor speed formula_1, inlet temperature formula_2, compressor diameter formula_3 and gas properties formula_4 and formula_5 are grouped together as dimensionless formula_6 which is equivalent to the blade mach number.
Parameter groups which are used as the basis for gas turbine engine compressor maps are total-pressure ratio (Pexit/Pinlet), formula_7, formula_6 and efficiency. formula_6, for example, is simplified below while still being representative of mach number. Maps for other applications use head or discharge pressure and volume flow.
For a particular compressor and gas the flow and speed groups are simplified, by deleting the terms which are constant for a particular compressor and application, namely compressor dimensions and gas properties formula_3, formula_11, formula_5 and . They are named pseudo-non-dimensional parameters formula_13 and formula_14.
A final step is to give the pseudo-non-dimensional parameters standard units for mass flow and speed and more recognizable numerical values by applying pressure and temperature ratio correction factors, also derived as part of the dimensional analysis.
The corrected parameters are formula_15 and formula_16. They have the same units as the original observed values and are corrected to agreed standard conditions, the International Standard Atmosphere at sea level (ISA SL). Alternatively they may be shown relative to the design value where the design value is specified as either 100% or 1.0.
The fuel burned in a gas turbine engine sets the compressor running line and also has to be used in 'non-dimensional' form to show its affect on engine operation.<ref>Propulsion and Power An Exploration of Gas Turbine Performance Modelling, Kurzke and Halliwell 2018, 