# The Investigation of a New End Wall Contouring Method for Axial Compressors
## 4 Experiment on the Axial Compressor Test Rig
### The Baseline Compressor Stage and the Design of End Wall Contouring
(**a**) Total pressure ratio of the stage; (**b**) Total temperature ratio; (**c**) Efficiency of the stage; (**d**) Total pressure recovery coefficient of the stator (the values of the overall performance are not shown here for confidential reasons. The figure shows only the normalized mass flow rate and the unit of the vertical axis). Figure 15: The circumferential averaged loss coefficient of the stator at 70% design speed. (**a**) \(\overline{m}\) = 0.89; (**b**) \(\overline{m}\) = 0.77. At the LM point, the effect of end wall contouring on the loss coefficient extends significantly from the blade top to the full-span region. Figure 15b shows that the loss coefficient reduces by 0.01-0.03 above 0.85_span_, increases by 0.01-0.03 from 0.7_span_ to 0.85_span_, and increases up to 0.023 from 0.6_span_ to the hub. The variation of loss coefficiency from 0.7_span_ to the blade tip region should be affected by the end wall contouring. Although part of this region increases the loss coefficient, this still shows more benefit than case c3 in the cascade: the loss coefficient close to the end wall reduces (Figure 15b), and the core region of low \(\sigma\) at 0.75_span_ is slightly relieved (Figure 16d). However, the range from 0.6_span_ to the hub is beyond the end wall contouring's direct influence. In Figure 16d, the corresponding region shows a heavier wake in the end wall contouring case, indicating a greater blade profile loss than the baseline stator. Thus, the increase of loss below 0.6_span_ should be associated with the spanwise variation of the throughflow under the same mass flow rate. It should be the end wall contouring that relieves the blockage due to corner separation on the top side of the blade passage, thereby reducing the mass flow rate of the lower span range. As a result, the lower part of the passage is more throttled than ever, thus generating a higher loss in return. The above study generally verifies the effect of end wall contouring on the control of corner separation and its contribution to the compressor's performance. However, it is still uncertain whether the control of secondary flow that leads to these improvements is  
Figure 16: The two-dimensional distribution of total pressure recovery coefficient at the outlet plane of the stator: (**a**) baseline, \(\overline{m}=0.89\); (**b**) end wall contouring, \(\overline{m}=0.89\); (**c**) baseline, \(\overline{m}=0.77\); (**d**) end wall contouring, \(\overline{m}=0.77\). consistent with the design intent shown by the variables in Table 4. This is further verified below with the testing result from the end wall pressure taps. It is known that near the end wall region, the boundary layer motion should obey the N-S equation, i.e.,  
\[\frac{\partial\mathbf{V}}{\partial t}+\mathbf{V}\
abla\mathbf{V}=-\frac{1}{\rho}\
abla p+\tau \tag{11}\]  
Suppose the end wall contouring surface has a relatively slight waviness to the scale of the chord length, and the flow is constant; in this case, the N-S equation on the end wall surface before and after the end wall contouring can be subtracted to obtain  
\[\mathbf{V}_{\text{EWC}}\
abla\mathbf{V}_{\text{EWC}}-\mathbf{V}_{\text{baseline}}\
abla\bm {V}_{\text{baseline}}=-\frac{1}{\rho}\
abla(P_{\text{EWC}}-P_{\text{baseline}})+ \tau_{\text{EWC}}-\tau_{\text{baseline}} \tag{12}\]  
where the subscripts \"EWC\" and \"baseline\" represent the aerodynamic parameters before and after using the end wall contouring, and their subtraction result thus represents the variation of the parameters at the corresponding position on the S1 flow surface. The left side is the variation of the acceleration due to the end wall contouring, which directly changes the secondary flow on the end wall surface. Thus, the variation of pressure gradient on the right side of Equation (12) should be the primary cause for the left-side items, and thus the end wall secondary flow and corner separation.