Impacts of Inlet Circumferential Distortions on the Aerodynamic Performance of a Transonic Axial Compressor

Abstract

Distortion, such as total pressure distortion, is a common phenomenon at the inlet of an axial compressor. Nonuniform inflow can greatly affect the aerodynamic performance and the stability of the compressor. In this paper, a sinusoidal distortion model is used at the inlet. Then, a series of unsteady computational fluid dynamics (CFD) simulations with a full-annulus model is conducted. Three kinds of the total pressure distortions, such as circumferentially covering 60, 120, and 180-degs sectors above 70% span of the blade at the inlet section, are adopted. Based on the results, how the rotating stall cells can be induced and developed under the different inlet conditions is understood during the stall process. It is found that the secondary stall cell is more easily triggered when the circumferential range of total pressure distortion is increased. Meanwhile, the influence of the rotating distortion on the compressor performance is also studied and a dangerous distortion rotating speed is observed.

1. Introduction

As it can lead to serious deterioration of compressor performance, the distortions on inlet conditions are not neglected for the design of highly loaded compressors. The total pressure distortion on circumferential distribution is one of the most common inlet conditions, so a large number of experiments have been conducted to explore the relationship between distortions and compressor performance since the 1950s [1,2,3,4]. Most of the experiments were focused on investigating the influence of the distortions on the compressor stall, due to the importance of the compressor stability to compressor operation and some valuable conclusions were obtained. Fortin and Moffatt [5] conducted an experimental investigation with a full-scale model of an engine compressor. It was found that the distorted inflow had little effect on the rotating stall at low rotor speeds. However, at higher rotor speeds, there was a tendency toward more stall cells being produced under the stall conditions when the distortion angle and strength were increased. Spakovszky et al. [6,7] also employed an experimental method to investigate the stall inception pattern with radial and circumferential inlet distortions, respectively. Longley et al. [8] investigated the influence of the inlet rotating distortions on the stability of multistage compressors and found that the stall margin greatly decreased when the distortion speed was as much as 50 percent of the rotor speed.

With the increase of computational technology, the CFD method has provided an alternative route for the distortion research since the 1990s and some laborious and costly experiments were replaced by efficient and economical numerical simulations. In the beginning, numerical simulations were used to study the effects of distortion on the aerodynamic loss only [9,10,11]. Hah et al. [9] numerically studied the effects of the circumferential distortions on the flow field in a transonic compressor rotor. The results suggested that the inlet total pressure distortion could increase the aerodynamic losses due to the increase of strong interaction between the passage shock and the blade boundary layer. Moreover, many researchers began to use unsteady calculations to study the influences of distortion on the compressor stall [12,13,14]. All works proved that the distorted inflows could induce the rotating stall and reduce the compressor stability based on the numerical results, which was also proven by the experimental results.

In general, most researchers focused on analyzing the distortion under some specified states or at some typical working points. Very few published materials thoroughly studied the influence of the distortions during a whole stall process and deeply explored the mechanism of producing the second stall cell. Thus, the main aim of this paper was to analyze the difference in the compressor performance with and without the distortions during the stall process especially and try to explain why the second stall cell can be identified in the distorted flow field. To achieve these aims, the inlet distortion pattern was introduced by a mathematical formula because it is convenient to be implemented and suitable to develop the parametric analysis. Meanwhile, a transonic rotor, NASA Rotor 67, was selected as the numerical model. The compressor performance and flow fields under different inlet conditions were compared in detail at every stall stage. Furthermore, the characteristics of the rotating distortion are also discussed.

2. Numerical Method

2.1. Distortion Model

In this paper, a sinusoidal total pressure distortion model was adopted. In addition to the model being easy to be understood and profitable for developing further parametric analysis, the distorted total pressure distribution based on the model agrees well with the experimental results [15,16]. The definition of the model is found as the following [17].

$$p_T=p_T^{UNI}-\Delta p\left(\sin \left({\omega }_{1}t+{\phi }_k+\alpha \right)+1\right)$$

(1)

$$\Delta p=\frac{\gamma }{2}{p}_T^{UNI}\left(\sin ({\phi }_j+\beta )+1\right)$$

(2)

$${\phi }_k=\left\{\begin{array}{l}0 0<\theta <{\theta }_1 \mathrm{or} {\theta }_2<\theta <2\pi \\ \frac{\theta -{\theta }_1}{{\theta }_2-{\theta }_1}2\pi {\theta }_1<\theta <{\theta }_2\end{array}\right.$$

(3)

$${\phi }_j=\left\{\begin{array}{l}0 0\le \lambda \le {\lambda }_1\\ \frac{\lambda -{\lambda }_1}{{\lambda }_2-{\lambda }_1}\pi {\lambda }_1<\lambda \le {\lambda }_2\\ \pi {\lambda }_2<\lambda \le 1\end{array}\right.$$

(4)

$$\lambda =\frac{r-r_{hub}}{r_{tip}-r_{hub}}, \alpha =\beta =-\frac{\pi }{2}$$

(5)

where $p_T^{UNI}$ is the inlet total pressure with uniform distribution and ${\omega }_1$ the distortion rotating speed. $\gamma$ is a coefficient to control the strength of distortion. ${\phi }_k$ is a relative circumferential phase angle and $\theta$ the circumferential angle. The distorted domain in the circumferential direction is determined by ${\theta }_1$ and ${\theta }_2$. ${\phi }_j$ is a relative radial phase angle and $\lambda$ is the relative height in the radial direction. The distorted domain in the radial direction is determined by ${\lambda }_1$ and ${\lambda }_2$. Furthermore, $\alpha$ and $\beta$ are the initial phase angle.

The research focused on the parametric study of the circumferential range of inlet total pressure distortions in the performance of a transonic rotor. Thus, three kinds of pressure distortion at the inlet were adopted. Some important coefficients are listed in

Table 1. Coefficients of static distortions.

Test Cases	Distortion Speed (RPM)	Strength γ	Circumferential Range Angle (degree)	Radial Position λ1/λ2
UNI	\	\	\	\
D60_10	0	0.1	60	0.7/1
D120_10	0	0.1	120	0.7/1
D180_10	0	0.1	180	0.7/1

. In the table, UNI refers to the inlet condition with the uniform incidence flow, while D60_10, D120_10, and D180_10 are distorted inflow, in which the distorted domains in the circumferential direction are 60, 120, and 180 degrees, respectively. These three kinds of distorted inlet total pressure contours as well as the uniform total pressure distribution are shown in Figure 1. The computational domains and the boundary conditions of the cases with the distorted inflow were the same as those with uniform inflow, except the total pressure distribution at the inlet boundary. Under the uniform inflow condition, the total pressure at inlet was as much as a constant value $p_T^{UNI}$. When the inflow was distorted, the inlet total pressure was uneven in space and controlled by Equation (1).

2.2. Compressor Model

NASA Rotor 67 was chosen as the numerical model [18]. The rotor row had 22 blades and was rotated at a speed of 16,043 rpm. The tip clearance of the rotor was as much as 1.1 percent of the blade chord at the tip section. More detailed parameters of the rotor can be referred to in the technical paper [18]. The sketch of the numerical calculation region is shown in Figure 2. As shown in the figure, in order to reduce the influence of the rotor row on the inlet and the outlet boundaries, the simulation region was extended in both the upstream and the downstream directions. The inlet boundary and the outlet boundary were set on the section of Stations 1 and 4, respectively. In addition, the numerical results obtained from the section of Stations 2 and 3, which were both considered positions for the measurement in the experiments [18], were used to estimate the overall performance.

2.3. Computational Scheme

In this study, a commercial software CFX-Solver was used to solve the unsteady Reynolds-averaged Navier–Stokes equations with the help of SST k-ω turbulence model [19,20]. The second-order backward Euler scheme and the high-resolution scheme were adopted to discretize the temporal term and the convection terms, respectively. The physical time step was set as one ninetieth of the blade passing period (BPP), referring to the paper [21], to capture the stall inception under the low flow rate conditions. Total temperature and total pressure were set at the inlet, static pressure at the outlet. A nozzle, downstream of the duct, which was designed based on the suggestion of Zhang [22], was adopted in the current work as shown in Figure 3. The nozzle area was decreased gradually by 1 percent of the full open outlet area to obtain the performance lines. When the nozzle area was reduced to some extent, the changing of the aerodynamic parameters over time were not stable, and the stall process could be observed.

2.4. Grid Strategy

In this study, the simulations were conducted in a full annulus model. The mesh topology of a single passage was O4H and the butterfly topology was adopted in the tip clearance, which are as the same as those referred to [23]. The distance between the solid boundary and the first layer meshes was 0.001 mm. The grid independence verification was performed by using four gird strategies, namely 7.2 × 10⁶, 13.8 × 10⁶, 27.2 × 10⁶, and 40.6 × 10⁶ nodes, respectively. The grid independence results are compared in Figure 4. It was found that Grid 3 is sufficient to provide accurate simulation in this case. Thus, Grid 3 with 307 axial, 1210 tangential, and 73 radial points was adopted in this paper.

2.5. Validation

In order to prove the feasibility of the numerical method, comparisons of adiabatic efficiency and total pressure ratio between the experimental data [18] and the numerical results are shown in Figure 5 under some working points. The performance characteristics obtained from CFD were based on the time averaged results of the last revolution of the rotor. The flow rates were all normalized by the experimental choke flow rate. With the comparisons of the performance lines, it was found that the numerical efficiency was slightly lower than that of the experiment, and the deviation of the peak efficiency was 1.31% approximately. Meanwhile, the total pressure ratio obtained from CFD was also lower than that from the experiment.

Furthermore, the spanwise distributions of some important aerodynamic parameters are shown in Figure 6 at near peak efficiency point (PE) and near stall point (NS) on the section of Station 3 marked in Figure 2. As described in the figure, the difference between the CFD and the experimental results [18] was somewhat large at the NS point near the blade top region, and the max difference of the total pressure ratio was about 3.9%, 2.59% for the total temperature ratio, and 3.41% for the efficiency. However, the trends of the distributions along the span are similar to each other.

The distributions of relative Mach number on section of the span 90% at the NS point are shown in Figure 7. It was found in the figure that the calculated position of the captured shock wave was almost the same as that obtained from the experiments [18].

In general, the difference between CFD results and experimental data was acceptable, and a series of CFD results was suitable for the following analysis.

3. Results and Discussion

3.1. Overall Performance

The performance lines under the conditions of the uniform and three kinds of distorted inflows, predicted by the unsteady CFD method with the full-anulus model, are depicted in Figure 8. The mass flow rates were all normalized by the choke flow rate of the experiment without distortion and the stall processes were obtained in these simulations. As shown in the figure, when the inflow was distorted, the choke flow was decreased due to a drop of the inlet mass-averaged total pressure. Meanwhile, the efficiency and the total pressure ratio deteriorated since the distortion can increase the aerodynamic loss and decrease the blade load. As expected, when the range of distortion was increased, the performance was degraded further. In the figure, the stall processes are estimated and marked by the red curves and the stall margins are calculated according to the followed definition by the using of the data at the PE and the NS points.

$$\mathrm{Stall} \mathrm{margin}=\frac{m_{PE}}{m_{NS}}\cdot \frac{{\Pi }_{NS}}{{\Pi }_{PE}}-1$$

(6)

Compared with the uniform inflow, the stall margins in cases D60_10, D120_10, and D180_10 were decreased by 0.964%, 1.928%, and 2.819%, respectively. When the inflow was distorted, the axial velocity of the inflow was decreased effectively and the incidence angle was increased thereafter. Then, the flowing separation in the affected blade passages became more serious, and the stall was more easily induced at the bigger flow rate.

3.2. Impacts on Stall Process

As mentioned above, inlet distortion can give rise to extra aerodynamic loss and lead to the decreasing of compressor stability. In order to understand the impact of the distorted inflow on the stall process further, the unsteady flowing around the blade tip region, which is believed to play one of the most critical roles during the stall process, is discussed in this section.

It is on the section of span 95% that the static pressure over time at monitor points in front of the blade leading edge is described in Figure 9. There were five monitor points, which were rotated together with the rotor and arranged at the same relative location in five passages. At the beginning, under the low flow rate condition, one stall cell could be observed in four revolutions (revs) in all cases. However, with time, the situation became obviously different. For the UNI case, only one stall cell could be found in the whole process as shown in Figure 9a. However, when the inlet flow was distorted, more stall cells could be observed during the stall process. As shown in Figure 9b of the case of D60_10, the second stall cell marked by a green circle in the figure was being formed after 18.5 revs. For the case of D120_10, the second stall cell was generated earlier and the stall cell as well as the former produced cell became relative stable after 13.1 revs. When the impacting range of the distortion was increased to 180 degrees, two stall cells could be found obviously after 3.5 revs.

According to the forming and the developing of the stall cells around the blade tip region, the stall process can be divided into several stages as depicted in the figure. When the inflow is uniform, there are only two stages for the stall process. One is the stall formation stage, at which the stall cell is being formed. The other one is the one stall cell stage, at which only one stall cell exists in the flow field. In the case of D60_10, the stall process is divided into three stages. In addition to the first two stages similar to that with the uniform inflow, the stall process goes into the two stall cells evolution stage after about 18 revs, at which point two inception stall cells can be observed but their strength and relative positions are not stable and changed continuously. When the inflow is distorted in the case of D120_10, the stall process moves directly into the two stall cells evolution stage after the stall formation stage and the one stall cell stage is overlooked. Thereafter, the state of two stall cells becomes relatively stable and the process enters the third stage, the two stall cells stage. For the case of D180_10, two stable stall cells can be discovered after the stall formation stage and the stall process is divided into two stages only, namely the stall formation stage and the two stall cells stage. Thus, different distorted inflow can give rise to the different distinguishing of the stall stages.

3.3. Formation Process of the Initial Stall Cell

In order to explore the production and the propagation of the stall cells further, the detail flow field needed to be provided and analyzed at several typical working points. The changing of the normalized outlet flow rate during the stall process is shown in Figure 10. In every case, it was based on the above stage analysis of the stall process, such that five typical working points were selected for the following discussion. In the figure, these points are marked by the orange dots on every curve and named as A, B, C, D, and E, respectively.

The instantaneous contours of the axial velocity normalized by the blade tip speed, U_tip, at span 95% are shown in Figure 11. When the inflow was uniform, the small-scale backflow could be observed in each passage at 2 revs. With the decreasing of the flow rate, the region of the backflow in the passage was enlarged further and the difference of the velocity distributions among the passages became obvious at 3.3 revs. When the compressor was operated at 4 revs, it was found that a large-scale backflow squared with dashed lines in the figure was observed, by which almost 10 passages were occupied. As time passed to 20 revs, this backflow became a stable stall cell and was propagated circumferentially. When the inflow was nonuniform, it was due to the influence of the distortions that the small-scale backflow did not appear in every passage but only in several passages at the very beginning. Moreover, these backflows could evolve quickly into a flow cell at 3.3 revs, 2.7 revs, and 2 revs in the cases of D60_10, D120_10, and D180_10, respectively. If the flow cell was affected by the nonuniform flow continually, it was quickly developed to the stall cell.

In order to study the producing mechanisms of the stall cell further, the contours of the instantaneous vortical structure by Q-Criterion at span 95% are shown in Figure 12. When the inflow was uniform, the spilled flow being moved to the adjacent passage at the leading edge of every blade could almost be observed at 2 revs. When the compressor was operated at 3.3 revs, the spillages became more serious. As mentioned above, thereafter, a flow cell was observed and several passages were occupied by the cell at 4 revs. The available through-flow area was decreased substantially, and more fluid was forced to pass through the neighboring passages. At last, the flow cell developed to a stall cell. When the inflow was distorted, because of the decrease of the axial velocity of main flow in the effected region of distortion, the spillage was generated more easily and more seriously. This spilled flow could block the passage near the leading edge of the blade and lead to the backflows around the trailing edge as shown in the regions, such as A, B, and C marked by the red circles in the figure. Furthermore, in some cases a part of the backflow moved back through the passage and even spilled out from the leading edge of the adjacent blade, which can damage the flow field further, as shown in region B. Thus, compared with the uniform inflow, the stall cell was more easily produced with the distorted inflow. Once the stall cell formed, a group of vortexes, named GV circled by black dashed lines, could be observed. The vortexes were stirred in the different passages, stretched circumferentially, and pushed to the core of the stall cell. Serious separations could be found along the trajectory of the vortexes. It is believed that the GV is one of the most important characteristics of a stall cell and its behavior should be understood in depth.

3.4. Propagation of the Stall Cells

The principle of the propagating of the stall cells can be simply explained by reference [24]. The explanation sketch is shown in Figure 13a, and some related contours in case D60_10 at 12 revs during the stall process are shown in Figure 13b to understand the stall cell propagation. The region occupied by a GV can be divided into two parts, such as Region A and B. It was observed that the core of the stall cell was in Region B, since the vorticity was the strongest and the pressure was the lowest in this area circled by red lines in the figure. It was due to the lowest pressure in the cell core that a large number of vortexes were drawn into the area, which could induce further separation. The more serious the separation is, the more obvious the blockage effect is. Therefore, a part of the main flow was forced to pass through the neighboring right and left passages as shown in Figure 13a. Therefore, the incidence angles to the left passages decreased, while the angles to the right passages increased. In addition, because of the decrease of the incidence angle, the flow fields in the left passages recovered to the stable state and the vorticity in this area weakened gradually as described by Region A shown in Figure 13b. At the same time, new vortexes started to be produced in the right passages due to the increase of the incidence angles and the consequent deterioration of the flow field. Then, the circumferential propagation of the stall cell was realized, and its direction was opposite to the blade rotating direction in the rotating coordinate system.

3.5. Formation Process of the Second Stall Cell

In order to find out how the second stall cell is produced, the flow fields at four moments in case D60_10 are presented in Figure 14. When Region A was influenced by the distorted area, the vortexes in this region became stronger due to the velocity distortion and the propagation of the stall cell was interrupted. Then, a new core was generated gradually and became larger and larger, due to being continuously affected by distortion as shown in Figure 14c,d, circled by red lines. When the distortion range increased, there is no doubt that the new core was earlier and faster in forming and expanding. If the vorticity of the new core is strong enough, a new stall cell is induced in this area. As indicated by black dashed lines in Figure 14d, there were two serious separation zones in the flow field and a new stall cell was produced in the zone 1. Now, there are two stall cells in the flow field, and a part of fluid was blocked and forced to the neighboring passages, as shown in Figure 15. Then, flow 1 related to the second stall cell and flow 2 related to the initial stall cell were produced, and, because the tangential component of the relative velocity of these two flows were opposite, two stall cells were pushed away from each other until their relative position remained stable. Thereafter, the two stall cells were circumferentially propagated altogether with the same propagation speed.

The producing process of the second stall cell can also be analyzed with the help of the pressure distribution. The pressure contours and distributions near the leading edge of blade (position marked by black dashed lines in the figure) on the section of span 95% for the case of D60_10 are shown in Figure 16. It is in Figure 16a,b that the low pressure region can be observed. The region responded to the core of the initial stall cell and enlarged gradually, being continuously affected by the distortion. When the region expanded to a certain extent, a new low-pressure region appeared at a circumferential distance (about 30 degrees) from the core of the initial stall cell as shown in Figure 16c. This distance can help the new core not to be integrated into the initial stall cell immediately and the stall process is in the third stage, the two stall cells evolution stage. Finally, the new low-pressure region became larger and larger, and developed into a new stall cell gradually as shown in Figure 16d–f.

As mentioned above, when the distortion is stronger, the stall process and the distinguished stages are different. Thus, it is necessary to discuss the formation process of the second stall cell in the case with larger distortion. The pressure contours and distributions near the leading edge of blade on the section of span 95% for the case of D120_10 are shown in Figure 17. As shown in Figure 17b, a new low-pressure core was quickly formed in a circumferential distance of 40 degrees away from the initial one at only 4 revs before the initial one became strong. Then, because of the repulsive force induced by these two cores, the distance between these two became greater. Meanwhile, because there were two low pressure cores, the separation in the responded passages became more serious and the stall process was in the two stall cells evolution stage as shown in Figure 17c–f. Finally, these two low-pressure cores evolved into two strong and stable stall cells, and the strength and the propagating speed of these two stall cells reached the same level as shown in Figure 17g,h. Then, the stall process was in the two stall cells stage. When the circumferential range of the distortion was increased to 180 degrees, it is believed that the new core was observed earlier.

3.6. Rotating Distortion

As listed in Table 1, the distortion rotating speed of the cases discussed above was zero. However, in practical applications, the distortion with a rotating speed is usually experienced. Therefore, in the next section, the main effort is focused on the analyzing the effects of the rotating distortion on the compressor performance.

All distortion parameters are listed in the

Table 2. Coefficients of distortion rotating speed.

Test Cases	Distortion Speed (ωDIS/ωr)	Strength γ	Circumferential Range Angle (Degree)	Radial Position λ1/λ2
D120_30_0	0	0.3	120	0.7/1
D120_30_N1	−1	0.3	120	0.7/1
D120_30_N0.5	−0.5	0.3	120	0.7/1
D120_30_P0.25	0.25	0.3	120	0.7/1
D120_30_P0.5	0.5	0.3	120	0.7/1
D120_30_P0.75	0.75	0.3	120	0.7/1
D120_30_P1	1	0.3	120	0.7/1

. In the table, ${\omega }_r$ is the rotating speed of the rotor row. When the direction of the distortion rotating speed was the same as that of the rotating speed of the rotor, the direction was named as positive direction. In the converse case, it was named negative direction. The distortion rotating speed of the case of D120_30_N1 was −${\omega }_r$, while it was −0.5${\omega }_r$ for the case of D120_30_N0.5, 0.25${\omega }_r$ for D120_30_P0.25, 0.5${\omega }_r$ for D120_30_P0.5, 0.75${\omega }_r$ for D120_30_P0.75, and ${\omega }_r$ for D120_30_P1.

The influence of the rotating distortion on the compressor performance is shown in Figure 18. Compared with the static distortion, the efficiency seemed to be insensitive to the rotating of the distortion, which changed little. However, the pressure ratio increased a little with the increasing of the distortion rotating speed at the low flow rate points. Furthermore, the performance lines of the compressor shifted to the range of the low flow rate.

The comparison of the peak efficiency with the different distortion rotating speed is shown in Figure 19a. It was found in the figure that the efficiency was the highest when the speed was zero. Whether the direction of the speed was positive or negative, the efficiency decreased due to the increase of the aerodynamic loss caused by the rotated distortion region. Nonetheless, the decrease was so small that it was lower than 0.148%. In addition, the comparison of the stall margin is shown in Figure 19b. When the distortion was rotated in the reverse direction, the stall margin increased a little, but the direction of the speed was positive, such that the margin decreased sharply. When the speed was 0.75${\omega }_r$, the margin reached the lowest point, as little as 3.37%, which is only half of that of the static distortion. It was considered that there is a dangerous distortion rotating speed, which is about 0.75${\omega }_r$. The results agreed well with the conclusions from Ref. [25]. However, they are contradictory to the research works [8], in which two dangerous distortion rotating speed were observed during the stall process. The dangerous distortion rotating speed is very important to the operation stability of a compressor, so the research on it will be discussed in future works.

4. Conclusions

In this paper, a total pressure distortion model was applied to NASA Rotor 67. The effects of the distortion with different circumferential ranges on the performance and the stall process were discussed. Several valuable conclusions are summarized as follows.

▪

It was due to the distorted inflow that the decreasing of the choke flow, the efficiency, and the total pressure ratio were observed. Moreover, the performance deteriorated further when the influence range of distortion increased. Furthermore, compared with the uniform inflow, the stall margins in D60_10, D120_10, and D180_10 cases decreased by 0.964%, 1.928%, and 2.819%, respectively.

▪

Based on the analysis during the stall process, it was found that only one stall cell was produced with uniform inflow within 21 revs. Meanwhile, GV could also be found in the flow field, which is believed to be one of the most important characteristics of a stall cell.

▪

Under the distorted inlet conditions, a new vortex core was produced. When the vorticity of the core was strong enough, a secondary stall cell was formed around the core. The new stall cell could be produced earlier and faster with the increasing of the distorted region. Because of the repulsive interaction between two stall cells, the circumferential distance between the cells became larger and larger until their relative position remained stable.

▪

The stall margin was clearly influenced by the rotating distortion. It was noted that the margin decreased sharply when the distortion rotating speed was positive and as much as 0.75${\omega }_r$.