Effect of counter-rotating fan’s speed matching on stall inception and characteristics of tip clearance flow

4.3.1. Comparative of tip clearance flow field under different conditions

When the condition is $R2$:$R1=$ 1, the characteristics of tip clearance flow field are firstly analyzed at the design point and near-stall points, as shown in Fig. 8. The tip clearance flow streamline of Rotor 1 and Rotor 2 is displayed in Fig. 8(a), and the circumferential average absolute vorticity contour is presented in Fig. 8(b). The black and red lines in the figure represented tip streamlines at 0.2 h and 0.8 h, respectively: h is the tip clearance heights, 0 h is the blade tip and 1 h is the casing. And the absolute vorticity was defined as:

where, $\left|\xi \right|$ and $\omega$ represented the mode of absolute vorticity and rotational angular velocity, respectively. The larger value of absolute vorticity is, the higher strength of the clearance leakage vortex would be.

As known from the streamline diagram, tip leakage vortex is appeared in Rotor 1 and Rotor 2 under the design condition, with the vortex core in the form of concentrated vortex, which is appeared in the blade leading edge. Tip leakage vortex streamlines are rolled tightly and spirally. With flow reduce to near stall point, the streamline is changed apparently, the upstream incoming flow and leakage flow of Rotor 1 are rolled at the leading edge, and the fluids in stream wise direction are almost parallel with the leading edge of plane of blades, which is consistent with the research of Vo [19]. Meanwhile, the leading edge streamline of Rotor 1 is in diffusion shape, and the streamline of Rotor 2 spiral degree becomes weak. In addition, due to the relative motion between the rotor and casing, the tip leakage vortex is significantly influenced by the drag action of viscous force in wall boundary layer, which led to the nearly circumferential leakage streamline close to the wall, thus eventually resulting in the occurrence of secondary leakage.

As found from circumferential average contour of absolute vorticity, at the design point, the tip leakage vortex is appeared in the upstream and middle regions of chord length, while at the near-stall point, the tip leakage vortex is emerged in the blade leading edge, which is consistent with the above streamline result. The flow from the design point to the near-stall point, high vorticity region within the tip clearance is significantly increased along both radial and flow direction, while the vorticity within the casting area is not changed significantly. Therefore, the tip leakage vortex is the main reason of fan stall.

Fig. 8Behavior of the tip leakage flow at two representative operating points

a) Peak efficiency point

b) Near stall point

4.3.2. Analysis of tip clearance flow field under different speed ratios

To study the effect of speed ratio on tip clearance leakage flow, the flow characteristics of tip clearance flow field at near-stall point (Fig. 5, point B) under different speed ratios are studied as below.

The tip clearance flow streamlines under different speed ratios are shown in Fig. 9 and Fig. 10. The condition of $R2$:$R1<$ 1 (Rotor 1 of fixed speed and Rotor 2 of gradual decreasing speed) is shown in Fig. 9 and the condition of $R2$:$R1>$ 1 (Rotor 2 of fixed speed and Rotor 1 of gradual decreasing speed) is displayed in Fig. 10. Black and red lines in the figure represented tip streamlines at 0.2 h and 0.8 h, respectively. The static entropy contour and casting wall static pressure distribution at different speed ratios are shown in Fig. 11 and Fig. 12. The condition of $R2$:$R1<$ 1 is shown in Fig. 11 and $R2$:$R1>$ 1 is displayed in Fig. 12.

With the condition of $R2$:$R1<$ 1 in Fig. 9, the rotational speed of Rotor 1 is remained constant, and the leakage flow streamline is shown little changes on Rotor 1; meanwhile, the spiral degree of tip clearance streamline of Rotor 2 is reduced slightly along with the decreasing rotational speed of Rotor 2. As seen from the static entropy contour in Fig. 11, an obvious interface, including dramatic entropy gradient changes in the direction parallel with the leading edge plane, between high and low entropy values is existed in the leading edge of Rotor 1, which is the interface of mainstream and leakage flow. A similar interface is also appeared in the leading edge of Rotor 2, namely the interface of upstream incoming flow and tip leakage flow of Rotor 2. With the decreasing rotational speed of Rotor 2, no significant changes are shown in the interface of Rotor 1 leading edge, while the entropy gradient in the interface of leading edge of Rotor 2 is weakened gradually. When the condition is $R2$:$R1=$ 740:980, the entropy gradient of interface is relatively small, indicating a better balance reached between the mainstream momentum and tip leakage flow momentum of Rotor 2. As found from static pressure distribution in Fig. 11, an obvious pressure trough is appeared in the blade suction surface side. It was indicated from Furukawa’s research that the pressure trough of casting wall was corresponding to characteristics of the tip leakage vortex. The pressure trough of Rotor 1 declines rapidly in the stream wise direction, and that of Rotor 2 is very apparent in stream wise direction. Along with the reduction of rotational speed of Rotor 2, no obvious changes of pressure trough of Rotor 1 and Rotor 2 is shown in the leakage flow direction, thus indicating the insignificant changes regarding characteristics of tip leakage vortex.

Fig. 9Tip clearance flow at speed ratio R2:R1< 1: a) R1:R2= 980:900, b) R1:R2= 980:820, c) R1:R2= 980:740

Under the condition of $R2$:$R1>$ 1 in Fig. 10, the streamlines of Rotor 1 and Rotor 2 are changed significantly. When the rotational speed of Rotor 1 is declined, the originally diffused streamline at the leading edge of Rotor 1 is changed to the tight spiral, and the red streamline at the side of the wall is transferred from circumferential to the stream wise direction, thus indicating the improvement of flow field characteristics of Rotor 1; meanwhile, the streamline form of Rotor 2 is altered from the spiral to the diffusion due to the impact of speed ratio. The static entropy contour of Rotor 1 in Fig. 12 is changed significantly, and the reduced rotational speed of Rotor 1 caused the high-entropy gradient interface in its leading edge to move inside the channel; the entropy values in leading edge of Rotor 2 have always been existed. As found from static pressure distribution, if the rotational speed of Rotor 1 is reduced, the pressure trough on the wall of Rotor 1 is becoming clear gradually, and the angle between vortex core track and chord length is significantly reduced; and meanwhile, the pressure trough on the wall of Rotor 2 is attenuated gradually, and the angle between vortex core track and chord length is decreased slightly.

Fig. 10Tip clearance flow at speed ratio R2:R1> 1: a) R1:R2= 900:980, b) R1:R2= 820:980, c) R1:R2= 740:980

Fig. 11Static entropy contour and casting wall static pressure distribution at speed ratio R2:R1< 1: a) Near-stall point R1:R2= 980: 980, b) R1:R2= 980:900, c) R1:R2= 980:820, d) R1:R2= 980:740

Fig. 12Static entropy contour and casting wall static pressure distribution at speed ratio R2:R1> 1: a) Near-stall point R1:R2= 980: 980, b) R1:R2= 980:900, c) R1:R2= 980:820, d) R1:R2= 980:740

Therefore, the reduction of rotor speed can, firstly, weaken the viscous force in boundary layer suffered by tip leakage vortex of the rotor; secondly, reduce the high load on the rotor, thereby improving its tip leakage flow field. It is worth noting that characteristics impact of tip leakage vortex of counter-rotating fan can be significantly differed by the changes of rotational speeds of Rotor 1 and Rotor 2. Hence, characteristics of tip leakage vortex of counter-rotating fan are given further analysis.

4.3.3. Characteristics of tip leakage vortex under different speed ratios

The absolute vorticity contour under different speed ratios is shown in Fig. 13, and the distribution of total pressure loss coefficient in stream wise direction under different speed ratios is shown in Fig. 14, respectively. In the figure, the cross section (Plane 1, Plane 2, Plane 3, ...) is approximately perpendicular to the tip leakage vortex direction. LE indicates the leading edge of the blade and TE expresses the rear edge of the blade. The definition of absolute vorticity had been given in Eq. (1).

Fig. 13Stream wise absolute vorticity distributions on crossflow planes

a)$R2$:$R1<$ 1

b)$R2$:$R1>$ 1

Tip leakage vortex core is corresponding to the concentrated area of vorticity. With $R2$:$R1<$ 1 in Fig. 13(a), a clear concentrated area of vorticity can be seen in Plane 1 of the Rotor 1. However, affected by the strong viscous force in the boundary layer, the concentrated area of vorticity is diffused apparently and vigorously from Plane 2. That same was to that from Plane 3, 4, 5, 6. Since the mainstream is overflowed in the leading edge, a series of vortex patches with low absolute vorticity magnitude are appeared in the leading edge of the plane. Rotor 2 is changed simultaneously with Rotor 1. Regarding Rotor 2, though the absolute vorticity of tip leakage vortex is gradually weakened in the stream wise direction at the same time, the concentrated area of vorticity corresponded by vortex core can be clearly observed from Plane 1 to Plane 4. Along with the gradually decreasing rotational speeds of Rotor 2, small changes regarding the absolute vorticity characteristics are presented in Rotor 1 and Rotor 2, which is consistent with the above analysis in Fig. 9 and 11.

As can be seen from Fig. 13(b), at the condition of $R2$:$R1>$ 1, along with the decreasing rotational speed of Rotor 1, significant changes are appeared in the absolute vorticity contour of Rotor 1; a series of obvious concentrated area of vorticity are appeared in the blade passage; and the angle between vortex core track and chord length is decreased, which is corresponding to the static pressure distribution on the wall in Fig. 11. As indicated from the vorticity distribution contour of Rotor 2, when the speed ratio is changed to $R2$:$R1=$ 820:980 from $R2$:$R1=$ 900:980, the absolute vorticity distribution pattern is appeared abruptly in the blade passage of Rotor 2, and the concentrated area of vorticity is significantly diffused, which is no longer evident in Plane 4.

Total pressure loss coefficient in Fig. 14 is defined as:

wherein, $Pt$ represented local total pressure, the total pressure loss coefficient in the numerical range greater than zero is only shown in the figure.

Fig. 14Total pressure loss distribution on crossflow planes

a)$R2$:$R1<$ 1

b)$R2$:$R1>$ 1

At the condition of $R2$:$R1<$ 1 in Fig. 14(a), the total pressure loss of Rotor 1 is dramatic in the streamwise direction, whose scope is developed in the streamwise and radial directions until covering the entire blade passage. High loss region means the accumulation of low-energy fluid on the wall, and severe blocking effect is caused by greater high loss area, thus resulting in significant blocking impact of Rotor 1. And at the speed ratio of $R2$:$R1<$ 1, certain degree of total pressure losses is existed in the leading edge of plane of Rotor 2. With the decreasing rotational speed of Rotor 2, the total pressure losses of Rotor 1 and 2 are only relieved mildly. At the condition of $R2$:$R1=$ 980:740, the mixing phenomenon in Rotor 2 channel is apparent, which is corresponding to the smaller entropy gradient of Rotor 2 in Fig. 11.

At the condition of $R2$:$R1>$ 1 in Fig. 14(b), the scope and strength of total pressure losses on Rotor 1 are declined rapidly with the decreasing rotational speed of Rotor 1, while the scope and strength of total pressure losses in the entire tip area of Rotor 2 are increased. Therefore, the blocking effect of Rotor 1 can be improved by such speed ratio, which could, however, aggravate the blocking effect of Rotor 2.

Speed ratio plays an important influence on the characteristics of tip leakage vortex. And characteristics of tip leakage vortex can be varied through the individual change regarding rotational speeds of Rotor 1 or Rotor 2. Compared with the speed ratio of $R2$:$R1<$ 1, the tip leakage vortex at the speed ratio of $R2$:$R1>$ 1 is suffered from stronger impact. In the characteristic curve, it is expressed by the offsetting stall point towards points with small flow rate, showing greater amplitude. Moreover, a rotor with high rotational speed has more severe corresponding blocking degrees in the tip region under different speed ratios.