Which of the following are the two common types of compressors used in turbine engines?

The two common types of compressors used in turbine engines are axial and centrifugal flow compressors.

Axial compressors function by drawing air in through a series of rotating blades arranged in stages. The design allows for efficient compression of air along a straight line, maintaining high airflow and pressure ratios, which makes them suitable for high-speed applications typically found in jet engines. Their design allows for a compact engine layout, which is crucial for aerodynamics and overall performance.

Centrifugal flow compressors, on the other hand, operate by flinging air outward from the center of a rotating impeller. This increases the air's velocity and, consequently, its pressure as it moves through a diffuser. These compressors are typically used in smaller engines or auxiliary power units due to their robustness and ability to handle varied operating conditions.

While other compressor types mentioned in the options might be used in specific applications or for particular designs, axial and centrifugal flow compressors are indeed the primary types utilized in most turbine engines, which makes this answer appropriate.