Computational Analysis of Flow Field Variation with Grooved Probes in Transonic Axial Compressor ^†

Abstract

This study aims to enhance total pressure probe performance in transonic axial compressors using passive flow control via circular grooves. Simulations in ANSYS CFX were performed on six probe configurations, one smooth baseline and five with groove depths of 0.1 to 0.5 mm, across Mach numbers 0.3 to 0.86. The 0.1 mm grooved probe showed optimal results, reducing the drag coefficient from 15.23 to 14.33 and the lift from 0.0169 to 0.0042. A spanwise analysis from the hub to tip (55–95%) confirmed improved flow uniformity, while a streamwise analysis (zones 0–2) showed steadier downstream pressure and reduced wake-induced distortion. The 0.1 mm groove also minimized the shock strength and flow separation near blade tips. Results confirm that micro-grooving at 0.1 mm significantly stabilizes measurements and enhances aerodynamic efficiency, offering a practical optimization strategy for high-speed compressor applications.

1. Introduction

Transonic axial compressors are a key component in modern power generation and propulsion systems and are subject to intricate aerodynamics where slight perturbations of flow can alter performance [1]. There is a high demand for the precision measurement of the total pressure for enhancing compressor efficiency. With an increase in the number of probes, the frontal blockage effect is heightened, causing a significant decrease in the mass flow rate and performance [2], particularly under near-stall [3] and choke regimes.

An increased probe penetration depth into the flow enhances the Mach number around the probe, thus resulting in aggravated wake turbulence and enhanced aerodynamic losses [4]. Near full submersion, the formation of a radial vortex flow [5] behind the probe considerably decreases the overall pressure ratio and compressor efficiency. Research indicates that reducing the size of the probe and meticulously choosing the probe position [2] can counteract these negative consequences while still making precise flow measurement possible. Probes situated nearer the leading edge of the rotor tend to cause more aerodynamic interference in that they affect the incoming flow and shockwaves produced by the rotor more deeply [6]. Probes located more downstream or nearer mid-span areas are less likely to significantly impact flow stability [7], maintaining precise data acquisition for performance assessments [8].

Probe intrusion into the flow has the potential to change the stall margin, leading to early stall inception and decreased operating stability [9]. The effect is specifically strong under near-stall conditions [10], as the blockage effect is more extreme, and minor aerodynamic changes can have drastic effects. Experiments have demonstrated that probe support can alter the tip leakage [11] vortex structure, which influences the pressure rise distribution and changes the response of the compressor to changing flow conditions [12]. For certain situations, probes have been found to create localized flow separation, which results in a greater possibility of flow instability and a reduction in performance. Probes enable the detailed analysis of the flow behavior, turbulence intensity, and shockwave interactions, providing valuable insights into the complex aerodynamics of high-speed compressors [13]. Hole probe [14] configurations and advanced pressure sensors make it possible to acquire more accurate data, allowing researchers to conduct flow phenomena research with a higher accuracy and resolution. Numerical and experimental studies [15] have been instrumental in the development of our knowledge of probe effects in transonic axial compressors.

Computational Fluid Dynamics (CFD) simulations have been extensively utilized to study probe-induced flow disturbances, wake structures, and aerodynamic losses [16] under different operating conditions. Numerical models [17], however, need to be validated against experimental data to provide accurate and reliable results. The probe measurement accuracy [18] depends not only on the probe design but also upon the calibration step and the capacity to compensate for flow disturbances caused by the probe itself. Experiments have established that measurement errors brought about by proximity effects near walls [19], flow deviations caused by probes, and turbulent fluctuations should be considered meticulously when post-processing probe data, such as with sophisticated calibration methods such as dynamic response analysis [20]. In addition, the probe data interpretation must involve extensive knowledge of aerodynamic principles and flow physics so that the resulting measurements best represent the true compressor performance [21]. Overall, this review highlights the significance of probe insertion in transonic axial compressor performance with the positive as well as the negative aspects of aerodynamic measurement techniques [22].

Probes offer indispensable data for characterizing flow behavior and designing optimum compressor geometry [23] while also creating aerodynamic disturbances affecting performance, stability, and efficiency. Probes with a larger size, positioning, and immersion depth determine their effect in significant ways, with an increased depth of immersion and probe size causing higher aerodynamic losses [24]. Furthermore, probes tend to alter the stall margins, wake structures, and shockwave interactions, directly affecting the general stability of the compressor [25]. Despite these issues, improvements in probe technology, calibration techniques, and measurement practices increasingly enhance the precision and accuracy of aerodynamic diagnostics.

The rectangular model performed best, improving the stall margin by 6.17% (to 19.44%), with just a 0.2% decrease in adiabatic efficiency (to 88.11%). Grooves located at 18–38% of the blade chord were the most efficient in suppressing the tip leakage vortex and improving compressor stability while reducing efficiency loss [26]. Six circumferential groove configurations on NASA Rotor 37 were numerically investigated utilizing 3D RANS simulations. Rectangular grooves with a 0.556 mm tip clearance increased the stall margin by 4.4% while decreasing adiabatic efficiency by just 0.9%. A larger tip spacing (0.756 mm) resulted in reduced efficiency and performance advantages [27]. Single circumferential casing grooves were investigated to increase the axial compressor stall margin with a minimal efficiency loss. The groove models improved the stall margin by 6.62% and 4.45% with efficiency reductions of only 0.79% and 1.08%, confirming their efficacy for stability enhancement [28]

The main objective of this study is to examine the aerodynamic behavior of grooved probes, with a particular emphasis on shallow groove configurations, in transonic axial compressor environments. This research aims to assess how the groove geometry influences the flow attachment, shear layer stabilization, and vortex shedding, thereby affecting the total pressure measurement accuracy and overall aerodynamic performance. Special attention is given to optimizing the groove depth to achieve a balance between enhanced flow control and the potential drawbacks of increased drag and turbulence.

2. Problem Formulation

This study is based on the well-established NASA Rotor 37 axial compressor model, which is widely recognized in transonic compressor research due to its comprehensive experimental dataset and CFD validation. The selected Mach number range (0.3–0.86) encompasses both subsonic and transonic regimes, enabling a detailed investigation of the shockwave formation, flow separation, and boundary layer behavior. The spanwise analysis is focused on 55% to 95% of the blade span, where critical flow features like tip leakage and shock–boundary layer interactions are most prominent. The rotor has 36 blades, a hub-to-tip radius ratio of 0.7, and a blade aspect ratio of 1.19. The rotational speed is set to 17,188.9 rpm in accordance with the original Rotor 37 specifications. All geometric and flow parameters are chosen to ensure the realistic simulation of the transonic axial compressor behavior. The key target parameters evaluated include the total pressure recovery, static and total pressure distribution, shear layer reattachment, vortex shedding, wake behavior, shock interaction, stall margin, and lift/drag coefficients. These allow a comprehensive aerodynamic assessment under varying flow conditions.

3. Computational Setup and Boundary Conditions

Six total pressure probes, including a smooth baseline and five with circular grooves (0.1–0.5 mm), were modeled to study their aerodynamic impact in a transonic axial compressor. The grooves acted as passive flow control features to reduce the wake and improve the boundary layer behavior. A fine mesh (2.25–2.75 million elements) with inflation layers captured near-wall flow features, while the extended domain minimized boundary effects as shown in Figure 1. Groove depths were selected to balance aerodynamic performance and structural integrity. Shallow grooves aided reattachment and reduced turbulence, while deeper ones tested potential adverse effects. All probes had 38 grooves with a width that was twice the depth; other dimensions remained constant to isolate the effect of the groove depth.

A mesh independence study was performed using five mesh sizes (0.2–2 million nodes) to evaluate the convergence of the lift and drag coefficients. Results (

Table 1. Lift and drag coefficients corresponding to different mesh sizing.

Sr. No.	Mesh Size	Lift Coefficient	Drag Coefficient
1	0.2 million	1.79 × 103	0.10948
2	0.5 million	0.02179	0.13686
3	1 million	0.035902	0.15098
4	1.5 million	0.041789	0.161001
5	2 million	0.0424	0.16225

, Figure 2) showed that the accuracy improved with the mesh refinement, with 2 million nodes identified as optimal. The further refinement had a minimal impact, ensuring the efficient use of resources without compromising accuracy.

This study included a rotor–stator setup to assess the impact of the probe geometry on compressor performance. A 60° sector with six rotor blades ensured accurate periodic conditions. The rotor and stator were modeled separately and then coupled via an interface (Figure 3), with the probe mounted in the stator to analyze its aerodynamic influence.

The meshing strategy was divided into two phases: a stator mesh with 2.5 million nodes, refined to enhance the resolution near the probe, and a rotor blade mesh generated in the turbo-grid module, ensuring accurate wake capturing near the leading and trailing edges. Special refinement layers were added at distances of 1 mm, 1.5 mm, and 2 mm (Figure 4) to guide the mesh generation and maintain a balance between the resolution and computational efficiency.

Boundary conditions were set using a pressure variation: the inlet pressure of 1 atm and outlet pressure was gradually reduced to reach stall. This enabled the analysis of flow instabilities and compressor behavior near critical limits. A frozen rotor interface preserves steady-state interactions between the rotor and stator, balancing accuracy and efficiency. The rotor was assigned a rotational speed of 17188.7 RPM (

Table 2. Design parameters of axial compressor.

Sr No.	Design Parameters	Value
1	Design mass flowrate (kg/s)	20.19
2	Rotational speed (r/min)	17,188.9
3	Total pressure ratio	2.016
4	Inlet hub–tip ratio	0.7
5	Blade aspect ratio	1.19
6	Tip relative inlet Mach number	1.48
7	Hub relative inlet Mach number	1.13
8	Tip solidity	1.29
9	Number of rotor blades	36

), with the stator remaining stationary. This setup allowed for the evaluation of wake effects, pressure losses, and probe-induced disturbances in the transonic flow.

4. Mathematical Modeling

The flow was modeled using the continuity, Navier–Stokes, and energy equations to capture the mass, momentum, and energy conservation. Turbulence was simulated using the SST k-ω model for probe cases and the k-ε model for the rotor–stator interaction. Allequations were solved in ANSYS CFX 18.1 under steady-state conditions to analyze the shockwaves, flow separation, and wake behavior in the transonic regime. The SST k-ω model was used for simulations involving standalone probes due to its accuracy in capturing near-wall effects and boundary layer behavior. For full rotor–stator simulations, the standard k-ε model was employed for its computational efficiency and stability under large-scale turbulence, while the SST model combines both k-ω and k-ε formulations.

The governing equations used in this study are based on the fundamental principles of fluid dynamics. First, the continuity equation ensures mass conservation and is given as

$${\displaystyle \frac{\partial \rho }{\partial t}}+\nabla \left(\rho V\right)=0$$

(1)

To describe the motion of the fluid, the Navier–Stokes momentum equation is applied [29], which accounts for the effects of pressure, viscous stresses, and body forces:

$${\displaystyle \frac{\partial (\partial V)}{\partial t}}+\nabla \left(\rho VV\right)=-\nabla P+\nabla \tau +\rho g$$

(2)

The energy conservation equation considers internal energy, pressure work, heat conduction, and viscous dissipation:

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho e\right)+\nabla \left[\left(\rho e+P\right)V\right]=\nabla \left(k\nabla T\right)+\mathsf{\Phi }$$

(3)

Two turbulence models were used based on simulation domains:

The SST k-ω model, suitable for resolving boundary layers and flow separation, was used in all grooved and simple probe analyses. It combines k-ω near walls and k-ε in the free-stream region via a blending function.

Turbulent kinetic energy (k) for k-ω:

$${\displaystyle \frac{\partial \left(\rho k\right)}{\partial t}}+{\displaystyle \frac{\partial \left(\rho u_{j}k\right)}{\partial x_j}}=P_k-B^{\ast }\rho k\omega +{\displaystyle \frac{\partial }{\partial x_j}}\left[\left(\mu +{\sigma }_k{\mu }_t\right){\displaystyle \frac{\partial k}{\partial x_j}}\right]$$

(4)

Specific dissipation rate ($\omega$) equation:

$${\displaystyle \frac{\partial \left(\rho \omega \right)}{\partial t}}+\nabla \left(\rho \omega V\right)=\alpha {\displaystyle \frac{\omega }{k}}{P}_k-\beta \rho {\omega }^2+{\displaystyle \frac{\partial }{\partial x_j}}\left[\left(\mu +{\sigma }_{\omega }{\mu }_t\right){\displaystyle \frac{\partial \omega }{\partial x_j}}\right]$$

(5)

The k-ε model was used for full rotor–stator simulations due to its robustness for large rotating flows.

Turbulent kinetic energy (k) for k-ε:

$${\displaystyle \frac{\partial \left(\rho k\right)}{\partial t}}+{\displaystyle \frac{\partial \left(\rho u_{j}k\right)}{\partial x_j}}=P_k-\rho \mathsf{\epsilon }+{\displaystyle \frac{\partial }{\partial x_j}}\left[\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_k}}\right){\displaystyle \frac{\partial k}{\partial x_j}}\right]$$

(6)

Turbulent dissipation rate (ε):

$${\displaystyle \frac{\partial \left(\rho \mathsf{\epsilon }\right)}{\partial t}}+{\displaystyle \frac{\partial \left(\rho u_j\mathsf{\epsilon }\right)}{\partial x_j}}=C_{1\mathsf{\epsilon }}{\displaystyle \frac{\mathsf{\epsilon }}{k}}{P}_k-C_{2\mathsf{\epsilon }}\rho {\displaystyle \frac{{\mathsf{\epsilon }}^2}{k}}+{\displaystyle \frac{\partial }{\partial x_j}}\left[\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_{\mathsf{\epsilon }}}}\right){\displaystyle \frac{\partial \omega }{\partial x_j}}\right]$$

(7)

To quantify losses due to shock waves, the normal shock loss coefficient is defined as:

$${\xi }_{\mathcal{S}}=1-{\left({\displaystyle \frac{P_{02}}{P_{01}}}\right)}^{{\displaystyle \frac{\gamma -1}{\gamma }}}$$

(8)

The overall performance of the compressor is assessed using isentropic efficiency, which compares the actual and ideal enthalpy rise:

$${\eta }_C={\displaystyle \frac{(\frac{T_{03}}{T_{01}}-1)}{{\left(\frac{P_{03}}{P_{01}}\right)}^{\frac{\gamma -1}{\gamma }}-1}}$$

(9)

Finally, to evaluate the compressor’s operational stability, the stall margin (SM) is computed as a function of mass flow rates at stall and operating conditions:

$$\mathrm{Stall} \mathrm{Margin} (\%)=({\displaystyle \frac{{\mathrm{q}}_{\mathrm{N}}}{{\mathrm{q}}_{\mathrm{S}}}}\times {\displaystyle \frac{{\mathsf{\pi }}_{\mathrm{S}}}{{\mathsf{\pi }}_{\mathrm{N}}}}-1) \ast 100$$

(10)

5. Numerical Solution Procedure

Simulations were performed in ANSYS CFX 18.1 using a pressure-based, steady-state solver under compressible flow conditions. Air was modeled as an ideal gas at an inlet total pressure of 101325 Pa and temperature of 288 K, with gradually reduced outlet pressure to simulate near-stall conditions. A frozen rotor interface coupled the rotor and stator domains. A structured hexahedral mesh (2.25–2.75 million elements) was used, refined near walls and grooves. Mesh independence was confirmed beyond 1.5 million elements. A physical time scale of 1 × 10⁻⁶ s ensured the shock and vortex resolution. The SST k-ω model was used for probe-only cases, and the standard k-ε model was used for full compressor simulations. Convergence was achieved when residuals dropped below 10⁻⁵ and physical quantities (lift, drag, pressure) stabilized over 1000 iterations. Validation against NASA Rotor 37 showed a <3% deviation in the pressure ratio and efficiency.

6. Validation

Numerical results were validated by comparing the pressure ratio and isentropic efficiency with experimental data, as shown in Figure 5a,b. All probe configurations, including the simple and grooved designs (0.1–0.5 mm), followed similar trends across normalized mass flow rates. In the pressure ratio comparison, simulations slightly overpredicted values compared to experiments, especially near stall, but the overall agreement remained acceptable. The 0.1 mm grooved probe showed the highest pressure ratio in the low-flow region. For isentropic efficiency, grooved probes with 0.17 mm and 0.25 mm depths, particularly, matched experimental data more closely than the simple probe, which consistently underperformed. Simulations predicted slightly higher efficiency, likely due to modeling simplifications.

7. Results

The primary target parameters in this study are the total pressure recovery, shear layer reattachment distance (Figure 6), vortex shedding behavior, wake region stability, drag and lift coefficients, and stall margin. These were selected to evaluate the aerodynamic performance and measurement accuracy of different probe configurations in a transonic axial compressor environment. Secondary parameters include shockwave strength, flow separation zones, and Stable Operating Range (SOR), which help assess overall flow stability and compressor efficiency. The 0.1 mm groove depth was identified as optimal, offering the best balance of wake stability, reduced vortex shedding, shock control, and shear layer reattachment (

Table 3. Lift and drag coefficients of different probe configurations.

Sr No.	Probe Characteristics	Lift Coefficient Cl	Drag Coefficient Cd
1	Simple Probe	0.0169	0.154036
2	Probe with Groove Depth of 0.1 mm	0.00424065	0.13278
3	Probe with Groove Depth of 0.17 mm	0.0207507	0.17431
4	Probe with Groove Depth of 0.25 mm	0.0388891	0.18603
5	Probe with Groove Depth of 0.375 mm	0.0320908	0.20410
6	Probe with Groove Depth of 0.5 mm	0.14581	0.293690

). The 0.17 mm and 0.25 mm grooves also performed well, especially at intermediate Mach numbers (0.44–0.72), improving the reattachment and reducing the wake size. However, their effectiveness dropped at Mach 0.86 (due to stronger shocks) and Mach 0.3 (due to weaker boundary layer energization). In contrast, the smooth probe and grooves ≥0.375 mm were less effective in controlling the wake and turbulence.

8. Stall Margin

The simple probe has a stall margin of 9.73%, while adding 0.1 mm grooves increases it to 10.15%, indicating improved flow stability. This enhancement is likely due to earlier boundary layer reattachment and reduced flow separation, which help delay the stall. As the groove depth increases beyond 0.1 mm, the stall margin steadily declines dropping to 9.64% (0.17 mm), 9.03% (0.25 mm), 7.89% (0.375 mm), and 6.07% (0.5 mm) (Figure 7). This indicates that while shallow grooves enhance stability, deeper grooves disrupt flow, causing earlier separation and reduced stall margins.

9. Stable Operating Range

The Stable Operating Range (SOR) is quantitatively defined as the range of mass flow rates between near-stall and peak efficiency operating conditions over which aerodynamic stability is maintained without flow reversal or stall onset. It is computed using differences in normalized flow and pressure ratios between stable and unstable conditions.

The simple probe has a Stable Operating Range (SOR) of 5.25, while the 0.1 mm grooved probe increases it to 5.74, the highest among all cases. This indicates an enhanced airflow stability and greater resistance to stalls or surges with the 0.1 mm groove depth. As the groove depth increases beyond 0.1 mm, the Stable Operating Range (SOR) declines: 4.67 (0.17 mm), 4.27 (0.25 mm), 3.84 (0.375 mm), and 3.40 (0.5 mm). This (Figure 8) reflects a narrower stable range and reduced aerodynamic performance with deeper grooves.

10. Forces

At Rotor

The probe with a 0.5 mm groove depth experiences the highest aerodynamic forces up to 170 N axially, 109 N radially, and 81 N tangentially, indicating a significant energy loss and reduced efficiency. Similarly, the 0.375 mm and 0.25 mm probes show elevated force levels, particularly in the axial and tangential directions, pointing to inefficient aerodynamic behavior. In contrast, the 0.1 mm grooved probe exhibits notably lower forces in all directions, suggesting reduced aerodynamic stress and better overall efficiency (Figure 9).

11. Conclusions

This study investigated the aerodynamic performance of total pressure probes with varying groove depths in a transonic axial flow compressor. Using CFD simulations, probes with circular grooves (0.1 mm to 0.5 mm) and a simple ungrooved probe were analyzed under near-stall and peak efficiency conditions. The flow behavior was assessed in circumferential, spanwise, and streamwise directions to evaluate the Mach number distribution, pressure recovery, shock control, and boundary layer reattachment. The simulations used steady-state analysis with turbulence modeling to capture flow features around the rotor blades. Key conclusions include the following:

• The 0.1 mm grooved probe consistently delivered the best aerodynamic performance, with lower Mach numbers, early boundary layer reattachment, and improved flow stability across all regions.
• The simple (ungrooved) probe exhibited high Mach numbers, delayed reattachment, strong vortex shedding, and poor shock control, leading to significant total pressure losses.
• The 0.5 mm groove introduced excessive turbulence, resulting in flow instability, poor pressure recovery, and impaired reattachment in both spanwise and streamwise directions.
• Circumferentially, the 0.1 mm groove achieved the highest pressure recovery between 10° and 50°, indicating an efficient velocity-to-pressure conversion, while the simple probe had the lowest.
• In the spanwise direction, the 0.1 mm probe delayed the stall near blade tips (55–95%), whereas the 0.5 mm groove increased the risk of shock and reverse flow.
• Overall, deeper grooves (0.375 mm and 0.5 mm) degraded performance, while the 0.1 mm groove proved to be the most efficient design for minimizing losses and enhancing compressor stability.