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In today's world, compressor operation can occur over all the four quadrants of the Head vs. Flow plot. It can occur in both axial and centrifugal compressors if the direction of flow or the sign of the pressure difference across the compressor reverses. In normal working conditions, the operating point stays inside the classical portion of the performance map, with positive flow (from impeller inlet to outlet), compression ratio higher than unity and positive torque (rotor is absorbing power). In case of failures of some parts of the system, emergency operations such ESD or transient operating conditions in general flow rate, pressure difference between inlet and outlet sections or speed can assume opposite values. Under such conditions, both compressor equipment (in particular impeller blades) and all other system devices experience unusual loading levels. Shaft torque may reverse in case of negative rotation.
This article contains excerpts from the paper, “Four quadrant centrifugal compressor performance” presented at the 2016 Turbomachinery Symposium by Elisabetta Belardini, Dante Tommaso Rubino, Libero Tapinassi and Marco Pelella of GE Oil & Gas.
The term four quadrant operation is used to indicate all the possible operating condition of a rotating machine. Deep choke (fourth quadrant) and deep surge with reverse flow (second quadrant) represent important four quadrant operations. The first is characterized by direct flow and rotation but reverse pressure and is likely to occur during compressor start up. In deep choke unusual high mass flow is forced across the machine due to the high inlet pressure and axial thrust across bearings may overcome capacity.
Second quadrant is characterized by direct speed and pressure with reverse flow: gas is driven backward by an overwhelming discharge pressure typical during ESD or valve failures causing unusual blade and equipment loading. Fourth and second quadrant characteristics have been experimentally investigated for a centrifugal compressor stage and, after a brief introduction about the four quadrant operating map, the results are presented.
In normal working conditions the operating point stays inside the portion of the performance map called normal operating map delimited by the surge and choke lines. Normal operating conditions are characterized by positive flow (from impeller inlet to outlet), compression ratio higher than unity and positive torque (rotor is absorbing power). Speed rotation is ranging from about 60% up to 110% of the nominal value (blue lines in figure 1). In transient operating conditions, flow rate, pressure ratio between inlet and outlet sections or speed can vary outside the normal operating map. Different areas can be identified in the four quadrant operating map of the compressor.
Deep Choke/Fourth quadrant: direct speed, direct flow, reverse pressure
In Figure, the area located on the right of the choke line is characterized by a pressure coefficient decreasing to zero (deep choke) or even negative values (4th quadrant) for progressively increasing flow coefficients. Fourth quadrant is characterized by a downstream pressure lower or equal to the upstream, while speed rotation and flow are still in the same direction of design conditions. Deep choke area is likely to be entered by the compressor during start-up when one or more of last stages can operate in 4th quadrant. The proper understanding of the basic physics at right of the choke line, in particular for power absorption is mainly important for the sizing of start-up devices.
Deep Surge/Second quadrant: direct speed, reverse flow, direct pressure
The area of the performance map on the left of the surge line in Figure can be divided in two sections: the first is characterized by positive flow with positive slope in 1st quadrant. This region is generally unstable considering the standard volumes involved in typical systems and the operating points reside in this region for very small periods of time.
The second area (2nd quadrant) is characterized by negative flow and negative slope in the pressure coefficient versus flow plane and is characterized by a stable behavior. This region is usually referred to as second quadrant, characterized by positive rotation, negative flow and positive speed. The physics of second quadrant is used for the simulation of ESD and the sizing of surge avoidance and control devices.
During transient operations rotational speed can be inverted with respect to the design direction. Examples are present in literature and in the authors direct field experience. This situation may occur for instance during emergency stop of the train: in this situation the rotor is subject to extremely rapid deceleration reaching zero speed before the complete equalization of pressure. The residual pressure difference between compressor discharge and suction may accelerate the train in reverse rotation. Speed inversion can happen with both direct and reverse flow. The valve-like characteristic of the compressor at zero rotation and both positive and negative flow is called limit line and can be used to identify in performance map the positive and negative rotation regions.