### 11.1.3. Computing Speedlines for a Machine

Most turbomachinery simulations examine the machine performance across a range of operating points. A speedline involves varying the mass flow rate from choke to stall at a fixed rotational speed. This is often accomplished by varying the exit mass flow rate or exit pressure while maintaining a constant, stationary frame total temperature and pressure at the inlet. If total conditions are not maintained at the inlet, the resulting inlet mass flow rate must be corrected to a standard reference condition.

Performance along a speedline is typically measured in terms of a pressure ratio and an efficiency. A full performance map is obtained by examining the performance across a range of rotation rates; that is, multiple speedlines. A plot containing multiple speedlines is called the performance map of the machine. Computing speedlines and performance maps requires many individual computations (one per mass flow), therefore it is desirable to automate the process.

Depending on the machine type, you can use the following boundary conditions to effectively compute speedlines:

- For low speed compressors and turbines (subsonic), liquid pumps: Specify Total Pressure and Temperature at the inlet and a Mass Flow Rate condition or a Exit Corrected Mass Flow Rate condition at the outlet. This enables you to easily vary the mass flow across the full speedline while maintaining stationary inlet total conditions. For compressors, the specification of the mass flow rate at the outlet is essential towards the low flow end of a speedline where the machine pressure ratio is insensitive to the mass flow rate. For this reason, you should not specify a Static Pressure condition at the outlet boundary for these machines.

- For high speed turbines and compressors (transonic): In these machines, the mass flow through the system is limited by a choked condition. If the specified exit mass flow exceeds the choke flow rate, the net mass downstream of the choke condition will decrease until it reaches zero density, causing the solver to fail. It is therefore important to avoid an exit mass flow near choke.

  Similarly, at lower mass flow rates, close to stall, the pressure ratio is either constant or decreasing. A pressure specified outlet is generally unstable in this regime because there are multiple mass flow rates that may satisfy the outlet condition. Therefore a pressure boundary condition should be avoided in this range.

  This presents a problem with running speedlines using pressure and mass flow conditions, because neither boundary condition can be used across the entire speedline.

  While the exit pressure and mass flow rate may be asymptotic over portions of a speedline, the exit corrected mass flow remains non-asymptotic and is therefore applicable across the entire operating range. Thus, it is recommended that you use the Exit Corrected Mass Flow Rate outlet boundary condition for running speedlines.

Some advantages of using the Exit Corrected Mass Flow Rate outlet boundary condition are:

- It allows you to specify the exit corrected mass flow, which is a function of the outlet mass flow rate, total conditions, and a user-supplied reference condition.

- It makes it possible to automate the speedline analysis by enabling you to specify one boundary condition type that functions well across the entire speedline.

- It improves stability when a run is started with poor initial conditions, allowing for the use of a much larger timescale factor, so that all runs can be started from a simple or automatic initial guess. This allows points along the speedline to be computed independently rather than using each existing solution to initialize the next.

- Typically in compressor operations, a fixed value of Exit Corrected Mass Flow Rate represents a fixed running or “op” line. As a result, you could keep the Exit Corrected Mass Flow Rate boundary condition fixed and vary the rotational speed to generate the compressor performance along an op line. This is useful when comparing designs.

For more details on the mathematical treatment of exit corrected mass flow rate as an outlet boundary condition, see Exit Corrected Mass Flow Rate in the CFX-Solver Theory Guide.

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