**2. Definition of inlet distortion parameters**

The total pressure distortion, total temperature distortion, and swirl distortion parameters selected in the numerical simulation are as follows.

1.Steady-state circumferential-distortion parameter Δ*σ*<sup>0</sup> is selected as the total pressure distortion parameter. The index is the relative difference between the average total pressure recovery coefficient on the air interface plane (AIP) and the average total pressure recovery coefficient in the low-pressure zone. The low-pressure zone refers to the circumference range where the total pressure is less than the average total pressure on the AIP. The total pressure recovery coefficient is the ratio of the measured total pressure to the total pressure of undisturbed airflow before the inlet. The parameter is obtained by

$$
\Delta \overline{\sigma}\_0 = 1 - \frac{\sigma\_0}{\sigma\_{av}} \tag{1}
$$

where *σ*<sup>0</sup> is the average total pressure recovery coefficient in the low-pressure region; *σ*av the face-average total pressure recovery coefficient at the AIP.

1.Relative increase of average surface temperature *δT2*FAV is selected as the total temperature distortion parameter. It numerically represents the temperaturedistortion amplitude. The parameter is obtained by Eq. (2).

$$
\delta T\_{\text{2FAV}} = \frac{\Delta T\_{\text{2FAV}}}{T\_0} \tag{2}
$$

where Δ*T2*FAV = *T2*FAV-*T0* is the increase of the face-average total temperature, K; *T2*FAV the face-average total temperature, K; *T0* the total temperature of the external test environment, K.

2. *τ*<sup>87</sup> is selected as the swirl distortion parameter. According to the preliminary calculation results, the inlet vortex is mainly the bulk swirl under the swirl distortion. *τ*<sup>87</sup> is the average *τ*<sup>87</sup> value, which can represent overall vortex (bulk swirl) strength; *τ*<sup>87</sup> is the ratio of the tangential component velocity at a radius of 0.87 *R*max to the axial flow rate. *τ*<sup>87</sup> is the tangent of airflow tangential angle *δ* and is often directly expressed by the airflow tangential angle. **Figure 2** shows the installation of the *τ*<sup>87</sup> detector and defines the tangential angle of airflow [15].

The parameter is obtained by

$$
\tau\_{87} = \frac{\upsilon\_l}{u} = \tan \delta \approx \delta \tag{3}
$$

where *u* is the axial velocity, m/s; *vt* the tangential velocity, m/s;

*πc=Wa*,*<sup>c</sup>* � �

2

3. Stability margin. We choose the stability margin evaluated at a constant corrected rotor speed (see Eq. (4)).

3

**Figure 2.** *Definition of* τ*<sup>87</sup> [15]. (a) Installation of the* τ*<sup>87</sup> detector. (b) Definition of the airflow tangential angle.*

*The Influences of Combined Distortions on Fan Performance DOI: http://dx.doi.org/10.5772/intechopen.109209*

**Figure 3.** *Stability margin definition.*

where *Su* is the stability-limit point, and *o* the operating point. The stability margin loss is obtained by

$$
\Delta \text{SM}\_{\text{Su},i} = \text{SM}\_{\text{Su},\rho} - \text{SM}\_{\text{Su},w} \tag{5}
$$

where *Su, w* is distorted flow, and *Su, o* is undistorted flow (clean flow). **Figure 3** shows the parameters in the definition of the stability margin loss.
