Performance Evaluation of Transonic Axial Flow Compressor under Distorted Conditions by Groove Casing Technique with Tip Injection and Surface Roughness Effects

The aerodynamic performance and pressure ratio of modern aircraft engine compressor are degrading due to unsteady flow distorted aerodynamic loads and complex phenomena in the blade tip. This paper attempts to improve the performance of modern axial flow transonic compressor stage under distorted flow conditions by incorporating the combination of groove casing, tip injection technique with surface roughness effects. This is performed for the Mach number ranging between 0.8 and 1.3. The obtained numerical results are compared with experimental studies and found to be in good agreement. Through the numerical analysis, the compressor stage flow interaction with the shock waves as well as vortex formation and boundary layer separation is studied in detail. While evaluating the performance of the axial flow compressor, more emphasis is given to the flow properties like pressure, density, temperature, velocity, etc. The performance improvement is observed at a particular Mach number for a specified aerodynamic flow property.


Introduction
Compressor is a dynamic component and is considered to be one of the crucial parts of the aircraft engine. It affects the performance of the overall engine significantly. The performance of the engine depends on the pressure ratio it is designed to build. The aircrafts had to use higher thrust force during takeoff, high cruising and sudden acceleration, sudden pull-ups, and so on. All modern transonic aircraft engines are using high loaded axial flow compressors, but they are not able to give maximum performance and high-pressure ratio because of its airflow blockage between the stage blades. The flow blockage is mainly caused due to distorted effect, and flow blockage calculations are studied [1]. Compressor operating at higher Mach speed (i.e., transonic speed 0.8 to 1.3) causes high aerodynamic loading; therefore, maintaining high efficiency within the safe margin is quite a difficult task [2]. From the literature survey, it is observed that 'rotating stall' is more near the tip portion of the rotor blade, which is caused due to distorted effect. Distortion is about studying stall and its behavior in the rotor and its implications on the stability of rotor under non-uniform inlet entry conditions. Therefore, it is very much required to understand separation, vortex flow, and stall. Steady flow simulations of distorted flow fields clearly show how wave-type discontinuities are established all along the blade. Therefore, in order to increase the performance range and pressure rise, a thorough understanding of flow through the rotor and its response to changing operating conditions should be made so that the designed modifications to reduce the impacts on the compressor are brought in thus ensuring reliability, where the life of machine is increased. In this regard, numerical simulations come very much handy in reducing cost, saving time, machine, manpower, labor, and risk. Unlike in experimental work, where knowing every detail in the domain of interest would be practically not possible, simulations help in understanding the flow's behavior and its influence on the rotor at the desired location.
The flow blockage unsteadiness can be calculated by two well-known techniques-active control technique and passive control technique. By conducting the systematic literature review, it is clear that flow leakage can be controlled by most sophisticated methods like wall bleeding and tip injection methods. However, the wall bleeding and tip injection techniques come under active techniques, where blade unsteadiness can be referred [3,4]. Several researchers [5][6][7][8][9][10][11][12] focused more on rotor blade unsteady flow parameters to improve efficiency of the compressor, but rotor flow was restricted to subsonic region and non-distorted conditions. In this work, emphasis has been given to 'groove casing' technique and 'tip injection' technique in order to improve the efficiency at transonic flow conditions under distorted conditions. Lu et al. [6] performed the tip clearance gap through stepped groove under transonic conditions. Through his paper, it was clear that for higher range of mass flow rate of air this technique was not able to bring up the required higher-pressure ratios. Later few more researchers [13][14][15] found that vibration was caused due to the unsteady and heavy turbulence flow formation on the blade passages.
Hoying et al. [16] and Huu Duc et al. [17] tried to find out the movement of flow leakage in only concentration of spike stall inception. The tip leakage movement may not be the same for all variety of transonic flow compressors; it is only particular to small loading capacity of compressor. Later few authors also attempted to work by linking flow blockage and rotation stall tip leakage under various groove casing treatments in order to improve performance of transonic flow conditions [17,18]. Numerical simulations are conducted by various authors [19][20][21] to study the effect of tip injection on the stability of a high-speed compressor rotor, which is an effective technique to improve stability. The best improvement in stall margin and overall performance is obtained when the injector is placed at the leading edge of the blade. The analysis shows that the characteristics of the total pressure ratio and the compressor stall margin are highly dependent on the axial injector position while also being inversely related to each other. The results concluded that tip injector at stator can greatly increase the performance of the compressor. Wei Wang et al. [22] and Mingcong Luo et al. [23] studied the performance of a transonic axial flow compressor stage and investigated the unsteady effects of discrete tip injection and the effects of the size of the tip injector on the performance of the compressor. By controlling the size of the tip injector, injection efficiency can be achieved which correlates to improve flow stability. (Flow behavior across the component is laminar and good aerodynamic streamlined way throughout the flow region.) The results show that a combination of an increased rate of injection, velocity, and decreased size of droplet translates to the decreased size of the shockwave and tip leakage vortex.
Xiaoyong Zhou et al. [24] and Cong-Truong Dinh et al. [25] conducted numerical simulations on NASA rotor 67 and rotor 37 to find the recirculation effect and to estimate the flow properties at different four positions. It is concluded through the simulations that recirculation in the slots has more prominence in improving the stall margin and efficiency improved with the combination of groove and tip injection technique when compared to only the groove casing technique. Keyvan Shaabani Lakeh et al. [26] conducted a numerical analysis on a compressor model to study the fouling mechanism and its effect on the gas-particle behavior over a compressor blade. From simulations, it was observed that at the pressure side of the blade, fouling films are formed and the same results were validated with the experimental studies. Experiments were conducted [27][28][29] to study the effect of leading-edge roughness on the state of the boundary layer of a wind turbine blade section using multiple hot-film sensors and CFD software. The results showed that surface roughness moved the transition point toward the leading edge and caused early trailing edge turbulent separation, which resulted in reducing the effectiveness of the airfoil. It was clear that the velocity profile on the smooth blade boundary layer was plumper than a rough surface.
Mulleners et al. [30] and Poursaeidi et al. [31] conducted experiments to investigate the impact of surface roughness on a turbulent blade wake using a linear cascade wind tunnel. The experimental results show that if the surface roughness increases, wake growth rate also increases because of increased development and density of vortices structure on the edges of the wake. The complete rotor and stator blades erosion was estimated depending on the trajectories of quartz and sand. It was found that the erosion was more on the leading edge and hub of the stator blade. Therefore, it is clear that at higher erosion angle, maximum erosion is possible on the leading edge of the blades. Xudong Shi et al. [32] and Nicola Aldi et al. [33] conducted an investigation on the axial flow compressor to study the effect of surface roughness on its aerodynamic performance. The results show a significant decrement in the performance of the compressor's efficiency and pressure ratio. For lower mass flow rates, stator blades have a larger degradation in performance. Mach number increases while the bow shock moves away from the blade's leading edge. Variable surface roughness can provide more realistic results of the degradation in performance. The pressure ratio was decreased by decreasing the flow rate in the stage.
After the successful completion of the systematic literature, it is clear that most of the researchers have worked on the casing treatment only for general conditions of the transonic flow compressors. However, working on the high loaded (i.e., with a greater mass flow rate of the air) and complete unsteady flow under distorted conditions is not investigated. Hence, an attempt is made to enhance the performance of axial flow compressor under distorted high loaded unsteady flow conditions using the combined passive technique of groove casing treatment and active technique of tip injection. Compressor fouling caused by surface roughness is a prominent loss in transonic axial flow compressors, which decreases the mass flow rate and compression ratio. Emphasis has also been given to the combination of groove casing, tip injection, and surface roughness technique to improve the efficiency at transonic flow conditions under distorted conditions.

Methodology Computational Approach
To solve the given transonic flow conditions, well-established Navier-Stokes equations could be written in the following standard equations.
Time required to solve Eq. (1) turbulence model is more. Therefore, to reduce the computational time and improve accuracy of solutions by using lesser memory the Reynolds averaged Navier-Stokes (RANS) equations are used to study the transonic axial flow compressor. For better understanding, the RANS equation is decomposed into two parts: a time averaged component part and a turbulent fluctuation part. Like a quantity of A can be decomposed as: Upon solving Eq. (1) using Eq. (7) reveals the momentum equation with constant density [34,36]. Equation (8) is like matching to Eq. (1) except the term − u � i u � . Technically speaking, this term is the stress tensor and is represented in Eq. (9). To make the complete flow converge ij needs to be modeled. Looking at the history through the literature, Boussinesq's eddy viscosity concept [34] proposed solution to model the term ij . Equation (10) describes the model solution for stress tensor ij . This equation also represents the turbulent nature flow modeled through v t and k under transonic flow conditions. In this research paper, these turbulent models v t and k play a vital role in solving distorted phenomena across the compressor rotor. ANSYS tool was selected to solve these equations, and it allows complete three-dimensional flow from grid generation to visualization. In the complete ANSYS compressor rotor simulations, air is considered as a real gas. Thermodynamically the equation of state is given in Eq. (11). For the same simulations, the enthalpy of rotor is given in Eq. (12) The transonic axial flow compressor stage with groove casing and tip injection techniques performance parameters calculations is used in this paper. The performance parameters are total pressure ratio, stage adiabatic efficiency, stall margin, stable range extension (SRE) given through Eq. (13)-(16) [25]: To compute the compressor stage simulations, the convergence criteria were set to 10 -06 , and to chock the injector, it was operated at pressure 'P inj ' as given by Eq. (17) [19].
where Modeling NASA rotor 37 geometrical details were considered to model the axial flow compressor stage. The same geometrical model was taken to conduct the numerical simulations of groove casing technique with tip injection and surface roughness effects. Complete rotor 37 geometrical data are reported in reference [21]. The designed specifications of an axial flow compressor are represented in Table 1. The complete modeling of rotor blades and blade tip clearance is shown in Figs. 1 and 2.
In order to find out the tip leakage around rotor circumferential direction, a grooved type casing treatment is performed around the rotor blades. The geometry of the solid part model used in tip injection case was edited using Space-Claim to design the grooves. Width of the groove was set to 2 mm, which is 7.26% of the rotor tip axial chord. The depth was also chosen to be 2 mm. Thus, the ratio of depth to width of the groove is 1:1. Then, the flow path and export points were generated in geometrical modeling under workbench [1] as shown in Fig. 3. For surface roughness analysis, two solid part models, viz. baseline and combined tip injection with groove casing, were used to analyze the effect of surface roughness and no  other model was created. In the module, roughness option was selected for the blade. The sand grain roughness distribution over the blade obtained is shown in Fig. 4.

Meshing
The geometrical model was later exported to Turbogrid for meshing. There the number of blade sets was specified for the rotor and stator, respectively. With the topology suspended, the rotor blade tip clearance was set to 0.63% of rotor tip chord, i.e., 0.356 mm. The inlet for the rotor and outlet for the stator was set at 50% of the length and the outlet for the rotor and inlet for the stator was set at 20% of the length, respectively. While performing high-speed (i.e., Transonic) turbulent flow simulations, it is very much essential that one should understand first grid node off the wall ( y wall ) within limited range. This is because formation of boundary layer viscous flow is accompanied with high gradients near the rotor walls. y + value defined for viscous flow in terms of y wall is given below to solve the transonic flow conditions: In Eq. (19) y + 1 is rotor blade first node off the wall variable. In the flow domain, this variable is actually a local Reynolds number. At high-speed transonic flow conditions for k − turbulence model, it is considered that the Reynolds number normally ranges from less than one. In general, for the Spalart-Allmaras the value ranges from 1 to 5 [36]. In this equation u is the friction velocity. Since the flow of air is real and viscous, the term u friction velocity can also be defined in terms of wall shear stress wall as shown in Eq. (20): For Reynolds number using 1/7th velocity profile, the term wall can be expressed in terms of coefficient of friction ( C f ) as shown in Eq. (21): There is one method which is available to calculate the y wall by using Blasius equation with order terms neglected as shown in Eq. (22). For conducting the simulations on rotor blade with groove casing, both the methods are used to calculate the y wall which comes out to be less than one (0.0045).
The full annulus axial flow compressor meshing is also shown in Fig 5. Near the blade tip region and at groove casing portion, high-quality mesh y + values of solid walls around the full annulus are maintained. To solve the governing equations like continuity equation, momentum equation, and energy equations precisely, the value of y + is maintained less than one. The complete axial flow compressor flow model was Fig. 3 Modeling of groove Casing After generating mesh for both blades, mesh was transferred to CFX for analysis. The mesh grid for Rotor 37 with groove casing is shown in Fig. 6.
To conduct the surface roughness analysis, for meshing, the respective geometrical models were exported to Turbogrid where the number of blade sets were specified for the rotor and stator. With the topology suspended, the same parameters of baseline analysis and tip injection with groove casing combined were used for blade tip clearance, inlet and outlet conditions. The size of the mesh was taken from the grid independency check. After generating mesh for both blades, they were transferred to CFX for analysis.

Boundary Conditions
The popular commercial numerical analysis ANSYS fluent solver was used for solving this groove casing treatment on axial flow compressor rotor blade. To solve the Navier stokes equations in the ANSYS flow solver 3D time accurate option was selected. In order to reduce the computational time for solving the diffusion solution second-order discretization-upwind scheme has been selected. Since the flow is running in distorted phenomena under transonic flow conditions the flow must be unsteady, in the flow process implicit-second order scheme was selected. The value of convergence criterion maintained throughout the flow analysis was 0.000001 to meet the residual values of governing equations. Within 1000 iterations of accumulated time steps, the solution converged. Throughout the compressor rotor, full annulus ANSYS CFD code was used to solve threedimensional Reynolds-averaged Navier-Stokes (RANS) equations. Additive multigrid approach was selected to resolve compressible flow around the blade passages. Just like baseline analysis of axial flow compressor under distorted conditions, even in groove casing treatment also the algebraic multigrid method was used to calculate advection parameters. Further, third-order high-resolution scheme was selected for simulation of unsteady flow. The simulations are completely run with clean off-design calculations based on multiple frame of reference results. The complete flow described the Mach speed ranges from 0.8 to 1.3 for better rotating spike stall alleviation suppression.
In post-processing the contour plots, inlet-outlet graphs and animations were obtained to analyze the numerical data by the solver as shown in Fig. 7. Near chocked condition the relative static pressure (P rel.static ) maintained was from zero pascals in the flow till it reaches rotating stall conditions. Angular velocity is also defined as per the standard NASA report for the transonic compressor rotor 37 blades [18]. The compressor full annulus rotor blade speed was maintained as 17,188.7 rpm. Table 2 represents the boundary conditions.   For surface roughness analysis, the analysis was set up in CFX-pre. Using Turbo-mode, the flow analysis was defined for the blades in their respective passages. Blades of rotors and stators were set to possess surface roughness of 40 µm. The remaining parameters used were same as that used in baseline analysis and tip injection combined with groove casing analysis, respectively [32,33]. Simulation results are validated with the experimental data [35].

Combination of Tip Injection Groove Casing Analysis
Numerical analysis is carried out for the axial flow compressor under transonic flow conditions. Compressor stage numerical simulations are performed similarly to Cong-Truong Dinhet et al. [25]. This is performed for the Mach number ranging between 0.8 and 1.3. Obtained results are compared with baseline numerical results. While evaluating the performance of the axial flow compressor, flow properties like pressure, density, temperature, velocity, etc. are considered. The performance improvement is observed at a particular Mach number for a specified aerodynamic flow property. These results are discussed in detail herewith.
PRESSURE: At Mach 1.3, 12.54% increase in pressure is observed after groove casing. Larger oblique shock waves and trailing edge vortex are formed for rotor blade of grooved casing. At the incident of the rotor blade, which is rotating at 17,188 rpm, a bow shock is formed at the leading edge as shown in Figs. 8 and 9. This is because a high-speed flow stream interacted with the leading edge of the rotor blade, and due to high turbulence flow, separation is formed at the trailing edge of the stator blade mid-span. It is also observed that at rotor exit, the pressure is suddenly increased due to better streamline flow in tip injection combined with groove casing technique. This phenomenon is observed more clearly in three-dimensional pressure contour plot of tip injection combined with grooved casing full annulus view as shown in Fig. 10.
TEMPERATURE: At Mach 1.1, 0.43% of temperature is increased after groove casing. Temperature is low at the leading edge of blade with smooth casing. Compared to baseline analysis, it is observed that for tip injection combined with groove casing technique the temperature is increased drastically after the rotor flow, because the rotor tip flow vortex is guided toward the entry of stator leading edge and also groove casing makes the complete flow field to pass it to the next consecutive blade as shown in Figs. 11 and 12.
DENSITY: At Mach 0.9, 4.40% of density is increased after groove casing. Less variation in density across the stage is observed, and it is shown in Figs. 13 and 14. Because of the reason that the numerical simulations are conducted with and without groove casing combined with tip injection techniques under the same Mach conditions, less variation   in density across the stage is observed. However, the density levels are increased with groove casing combined with tip injection due to improved aerodynamic flow behavior on the compressor stage.
TURBULENCE: At Mach 1.2, 15.38% of turbulence is decreased after grooved casing. The turbulence on rotor and stator blade is lower when subjected to grooved casing. Figures 15 and 16 represent an abrupt increase in turbulence, which is obtained at the mid span of the blade and extends to the tip clearance at the shroud. This is because the distortion phenomenon is prevailing as the high turbulence flow over the rotor to the stator blade. Incorporating the groove casing combined with tip injection the flow disturbances reduced drastically and hence the flow distortion is minimized. In baseline analysis, it was observed that tip leakage flows fail to pass through the compressor blade passage and that results in vortex breakup and formation of passage blockages occurs. When the compressor operates at higher mass flow rates in transonic flow conditions, these flow blockages increase in size and eventually lead the compressor to stall.     there is an increase in good aerodynamic flow variation observed after groove casing technique. This is 8.79% more compared to the smooth casing technique. Less Mach number variation was observed in smooth casing. It was also observed that due to the flow separation at the trailing edge of the blade the Mach number dropped sharply as shown in Figs. 17 and 18. This is due to the reason that groove casing combined with the tip injection flow makes aerodynamic stream across the compressor rotor. At the rotor blade, leading edge flow velocity is drastically reduced. In the case of baseline analysis, near stator suction surface mid-chord location leakage flow rolls up to form a vortex and separates the flow from more than half of the stator tip chord. It is evident that combination of groove casing and tip injection increases the compressor flow stability by separating the tip leakage flow, thus cutting off the supply to the blockage growth. This flow phenomenon was clearly observed (indicated with the circle and arrow), and it leads to improve the flow stability in compressor stage.
VELOCITY: At Mach number 0.8 flow conditions, there is a decrease in aerodynamic flow variation observed after groove casing technique. This is 1.71% less compared to the smooth casing technique. Large tip vortices at the leading edge and less flow separation at trailing edge of rotor blade for groove casing were observed. Figures 19 and 20 represent the velocity, which remains uniform in the inlet section but faces sudden drop due to the formation of the shock wave at the rotor. It is observed that by combining the groove casing and tip injection technique aerodynamic flow behavior of stage was improved. Flow separation streamlines are developed at the rotor suction surface mid-chord location due to the interaction of the boundary layer and passage shock. It is apparent that due to the better aerodynamics flow behavior flow separation region (indicated with the circle and arrow)    Figure 21 and Table 3 represent the Mach number for rotor total pressure ratio with smooth casing vs combined tip injection and groove casing analysis. Due to the combination of groove casing with tip injection technique, an improved pressure ratio difference was observed at Mach number 1.3 in the compressor stage. In addition, similar performance improvement was observed at Mach number 0.8 of the compressor stage flow simulation. Because of the high-speed distorted boundary flow interaction between the rotor and stator, the pressure ratio is not much significant at other Mach numbers. Figure 22 and Table 4 represent the Mach number for stage total pressure ratio with smooth casing vs combined tip injection and groove casing analysis. It was observed that   the stage pressure improvement at Mach number 1.3 was due to adding the groove casing on compressor blades. Table 5 represents the surface roughness flow simulation on the compressor stage both rotor and stator blades with a smooth surface and rough surface 40 µm. The baseline model was subjected to 40 µm roughness as given by Xudong Shi et al. [32]. Simulations are performed for 30, 40, 50 and 60 µm different rough surface values. It is observed that due to the distortion effect, the intensity of turbulence is more on the 40 µm rough surface than the smooth surface. Figure 23 illustrates the compressor stage complete annulus view pressure flow contour for the combination of tip    Fig. 24 and Table 6, it is observed that combining groove casing with tip injection there is an improved pressure ratio in the compressor stage at Mach number 1.3. From Fig. 25, it is noticed that numerical results are well matched with baseline analysis results and also with baseline surface roughness results. It is clear that the pressure ratio is improved due to the surface roughness with the combination of tip injection with groove casing techniques and is shown in Fig. 26 at Mach number 1.3; the pressure ratio is also increased due to the combination of tip injection with groove casing technique. Figure 27 provides a comparison of the percentage improvement between the baseline numerical results with groove casing, tip injection, and surface roughness combination numerical analysis results at all Mach numbers. When the compressor is operating at transonic flow conditions with Mach numbers ranging from 0.8 to 1.3, the compressor naturally exhibits distorted flow behavior. Because of the high momentum of the fluid moving from the rotor to the stator blades, the compressor's aerodynamic performance changes unevenly, which further impacts the pressure ratio of the stage's.
This analysis uses both active and passive techniques, as well as the compressor surface roughness technique, to maintain the best pressure ratio in the compressor stage. Surprisingly, the combination of groove casing (passive technique) and tip injection (active technique) at Mach numbers 0.8 and 1.3 showed the greatest pressure percentage improvement when compared to baseline analysis. Because of distorted flow effects, the pressure percentage improvement from 0.9 to 1.2 is not as significant.
Further analysis was carried out with the combination of groove casing, tip injection with surface roughness of 40 µm. Since the flow is close to supersonic flow conditions,

Conclusions
To improve the performance of the transonic axial flow compressor under distorted conditions, initially, the baseline model is solved numerically with the combination of groove casing with tip injection technique. The effect of groove casing on Mach number is increased and hence the highest change stage pressure ratio of 2.21 was obtained at Mach 1.3, which is 12.54% greater than the baseline values. Through the surface roughness analysis, it is clear that surface roughness accounts for the largest loss in an axial compressor, and hence, it is vital to analyze its effects. The numerical results are well matched with the reference values which showed a maximum of 7.4% decrease in stage pressure ratio at Mach 1.2. Also 2.7% decrease in stage pressure ratio was observed at Mach number 1.3. Flow contours show an increase in boundary layer thickness at the surface as well as at tip leakage vortex. Further, the model used in the analysis with the combination of groove casing and tip injection was modified for blade surface roughness of 40 µm. A comparison with the original results showed a decrease in pressure 0.87-12.7% for Mach numbers 0.8-1.3, respectively. The rough blade surface has a distortion effect on the flow path, which increases the shock wall at the leading edge and tip vortices at the trailing edge.

Conflict of interest
The present work is a numerical experimentation that is carried out using the licensed version of ANSYS. There is no conflict of interest either financially or technically with anybody.
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