Influence of hydrodynamic retarder blade angle on vortex structure

The internal flow of the hydrodynamic retarder cavity is a complex three-dimensional turbulent flow, and the evolution of vortices in its internal two-phase flow field is closely related to the generation of braking torque and the dissipation of kinetic energy. In this study, a periodic flow channel model is used to investigate the influence of different blade angles on vortex structure characteristics. The vortex structure identification method with Q criterion is employed to compare and analyze the distribution and development of the vortex structure. Particle image velocimetry (PIV) tests are conducted to observe the evolution of the vortex structure inside the retarder and validate the simulation analysis. Results show that the increase of the vortex structure scale, intensity, and transformation speed caused by the increase of the blade angle, which affects the energy dissipation and transfer of the flow field and explains the reason for the change of the braking torque. This provides a theoretical basis for the study of the braking performance mechanism and design optimization of the hydrodynamic retarder.


Introduction
With the growing popularity of transportation tools, there is an increasing focus on the safety and stability of vehicle braking systems [1].Among the important components, the retarder plays a crucial role in ensuring the safety performance of the entire braking system.As a continuous braking auxiliary device, hydrodynamic retarders enable vehicles to maintain a constant speed during long downhill stretches and quickly decelerate and stop in emergency braking situations [2].However, during operation, the hydrodynamic retarder is often partially filled with liquid, leading to a complex gasliquid two-phase flow phenomenon in the cavity [3].This phenomenon is accompanied by the generation and dissipation of different scales of vortex structures, and the blade angle is a crucial factor that affects the internal flow field characteristics and braking performance of the hydrodynamic retarder.
In recent years, scholars have delved into the correlation between the blade of hydrodynamic retarders and the internal flow field characteristics of the cavity.A few examples of this include Chen et al. [4] study, which explored the impact of various blade angles on hydrodynamic retarders, and analyzed the cavity flow and secondary vortex flow.Mu et al. [5] optimized the blade shape and blade top arc for double-cycle circular hydrodynamic retarders, analyzing the impact of different blades on braking torque and the internal flow field.Qiang et al. [6] also optimized the blade angle of and compared the velocity, pressure, and turbulent energy of the cavity under different blade.Li et al. [7] simulated the turbulent field using the scale-resolved simulation method, analyzing the distribution of vortex structure inside the cavity of hydrodynamic retarders.Yang et al. [8] optimized the blade angel and the number of inlet and outlet of hydrodynamic retarders, comparing the turbulent energy and vortex distribution of the internal flow field before and after the optimization.While there has been some progress in the study of vortex structure inside retarders, there is still relatively little research on the effect of blade angle on vortex structure and the mechanism of its impact on braking torque.Liu et al. [9] compared the prediction results of vortex structure distribution in torque converters using different models.Yasunori et al. [10] analyzed the distribution law of vortex structure in torque converters under different speed ratios, but these research methods are less frequently applied to hydrodynamic retarders.
This paper presents a simulation model of a hydrodynamic retarder and investigates the impact of blade angles on the internal flow field.By utilizing the Q criterion, the vortex structure is identified, and the influence of blade angle on the distribution of the vortex structure within the internal flow field is analyzed.This study aims to provide an explanation for the intrinsic reasons for the change of braking performance and offer theoretical support for the optimization of retarder performance.

Numerical Calculation Model
During the braking process, the hydrodynamic retarder operates in a partially fluid-filled state where the working medium in the cavity is composed of two phases -oil and air.Based on the air-liquid stratification model, it is assumed that a density difference exists between the two phases, resulting in stratified flow within the retarder cavity due to the centrifugal force.This phenomenon occurs in the partial fluid filling condition, where the oil and air are separated into distinct layers.The basic set of equations for two-phase flow is founded on the continuous medium theory, which upholds the fundamental physical laws such as conservation of mass, momentum, and energy.This paper considers the gas-liquid two-phase flow in the retarder to be isothermal, and thus, does not account for the energy equation of the flow.
The hydrodynamic retarder's rotor and stator have been extracted for simulation purposes.The blades are uniformly distributed in terms of periods, and a period model that includes the inlet and outlet runners is used for the simulation, as illustrated in Figure 1.The model undergoes preprocessing using non-structural tetrahedral meshing, with a mesh base size of 1.5mm and a total mesh size of approximately 150,000.The SST turbulence model was chosen to predict the turbulence characteristics within the hydrodynamic retarder.As for the gas-liquid two-phase flow characteristics, we utilized the nonhomogeneous model known as the "Eulerian-Eulerian multiphase flow".The working medium used in this model is a mixture of oil and air, with the oil-liquid phase defined as the main phase.This approach allowed us to better understand the behavior of the oil and air mixture in the hydrodynamic retarder, as well as predict the associated turbulence characteristics.These steps ensure accurate and reliable results for the simulation.
The above model was utilized to simulate the steady-state operating conditions of the hydrodynamic retarder.Furthermore, the braking torque corresponding to different rotor speeds was computed under the fully charged condition.The computed outcomes were then compared with the test data, as depicted in Figure 2. The simulation findings demonstrated consistency with the test data, and both speed and braking torque were quadratic functions, which was in line with the theoretical analysis.The discrepancy between the simulation and test was less than 10%, thus validating the established numerical calculation model as rational.

Vortex Structure Distribution in Internal Flow Field
The Q-criterion discriminant method is a widely used approach for identifying vortex structures among various available methods [11].This method involves decomposing the velocity gradient tensor of the fluid into a symmetric and an anti-symmetric tensor, and then comparing the magnitudes of these tensors using the Q criterion equation to determine the existence of vortex structures.One advantage of this method is that it allows for pressure extremes to be located on the boundary, while ensuring that pressure minima are within the region.This feature makes it suitable for discriminating vortices in the flow field of a retarder [12].The Q criterion equation is as follows: ( ) Where e ik is the symmetric tensor and Ω ik is the anti-symmetric tensor.
The simulation was conducted using the periodic flow channel model to obtain the velocity distribution of the cavity flow field under different filling rates.To visualize the flow field inside the rotor and stator, the Q-equivalent surface was used to color the flow field, as illustrated in Figures 3  and 4. The simulation results indicate that the turbulent flow in the hydrodynamic retarder is a combination of vortices of various scales.The oil is accelerated by the rotation of the rotor into the stator, creating a large-scale vortex structure and acquiring energy.The oil in the stator then flows back to the rotor, forming a circular flow, which develops and disintegrates the large-scale vortex structure, transferring energy to the small-scale vortices.The small-scale vortex is predominantly determined by the fluid viscous force, generating heat energy through viscous dissipation and completing the energy conversion.Upon comparing Q-equivalent surfaces at varying filling rates, it was observed that at low filling rates, the internal flow field was rife with small-scale vortex structures, and transverse vortices were more prominent in the center of the stator blades.With increasing filling rates, the scale of the vortex structure in the internal flow field gradually increased, thereby augmenting the impact of oil on the blade.Large-scale vortex structures had more energy, and the energy dissipated by their development and breaking was higher.Thus, as the filling rate rose, the energy dissipation of the vortex structure in the internal flow field increased gradually, leading to an increase in the braking torque of the hydrodynamic retarder.By examining the vortex structure distribution of the internal flow field, the paper provides a macroscopic perspective on the mechanism of the generation of braking torque by the hydrodynamic retarder.

Effect of Blade Angle on Vortex Structure
To investigate the impact of the blade angle on vortex structure, the angle of the rotor blade was maintained at 45°, while the angles of the stator blade were varied to 40°, 45°, and 50°, respectively.The numerical simulation model is established, and the simulation results are shown in Figures 5 and 6   As depicted in Figure 5, the vortex structure in the stator exhibits a larger scale near the outer ring of the circulation circle and a smaller scale near the inner ring.Furthermore, as the blade angle in the stator increases, the oil flow rate on the Q-equivalent surface gradually increases.In Figure 6, a largescale vortex structure near the suction surface of the rotor blade is observed, indicating that oil enters the flow channel from this location.The oil then flows from the suction surface to the pressure surface of the blade, where the large-scale vortex structure transforms into smaller-scale structures until it eventually disappears.Similarly, with an increase in the blade angle of the stator, the oil flow rate on the Q-equivalent surface also gradually increases.Additionally, the vortex structure scale on the blade pressure surface near the oil inlet location gradually increases.The CFD simulation results reveal that the suction surface, middle surface, and pressure surface in both stator and rotor have been extracted.Q equivalence surface clouds are drawn, and the flow velocity vectors are labeled.As illustrated in Figure 7, the Q value is higher in the stator near the outer ring of the circulation circle.Moving from the suction surface to the pressure surface, the high Q value region gradually shifts towards the inner ring of the circulation circle, indicating the vortex structure's movement from the outer ring to the center.Comparing Figure 7 and Figure 8, it is evident that the oil flow trend in the inner flow channel is consistent under different blade angles of the stator, flowing in from the outside of the circulation circle and out from the inside.Moreover, as the blade angle of the stator increases, the range of the high Q value region expands, and the intensity of the vortex structure grows, moving closer to the center.
Figure 9 shows that the high Q value region is distributed from the suction surface to the pressure surface in the flow channel of the rotor, indicating that the vortex structure moves from the center of the circulation circle to the outer ring before disappearing.A comparison of Figures 9 and 10 reveals that the oil movement trend is the same in the rotor flow channel, regardless of the blade angles.The flow always moves from the inside of the circulation circle to the outside, and the flow velocity of the outer ring of the circulation circle is higher than that of the inner ring due to the centrifugal effect.Additionally, it was observed that the larger the blade angle of the stator, the larger the range of high Q value region, which improves the energy conversion speed of the flow field as evidenced by the change in the vortex structure from the suction surface to the pressure surface.Upon comparing the flow field within the stator and rotor, it was observed that the overall Q value within the stator is higher than that within rotor under the same blade angle.This suggests that FMIA-2023 Journal of Physics: Conference Series 2599 (2023) 012026 IOP Publishing doi:10.1088/1742-6596/2599/1/0120267 the strength of the vortex structure within the stator is greater than that within the rotor.By closely observing the oil flow and vortex structure during movement, it was found that the oil flows inwards from the inside and outwards from the outside of the circulating circle in the rotor, while the vortex structure moves from the center of the circulating circle towards the outer ring.In contrast, in the stator, the oil flows inwards from the outside and outwards from the inside of the circulating circle, while the vortex structure moves from the outer ring of the circulating circle towards the center.Based on these observations, the direction of rotation and development of the vortex structure in the both of stator and rotor were determined, as depicted in Figure 11.The simulation analysis reveals that the braking torque of the hydrodynamic retarder increases with an increase in the blade angle of the stator.This corresponds to an increase in the scale of the vortex structure and the oil flow rate within it.Therefore, it can be concluded that the vortex structure scale, intensity, and conversion speed are positively correlated with the braking torque in the hydrodynamic retarder.

Internal flow field observation test
Particle Image Velocimetry (PIV) is employed to observe and analyze the internal flow field during hydrodynamic retarder testing.The PIV test system comprises a laser section generation system and an image acquisition system.As the direct producer of braking torque, the rotor and stator of retarders frequently experience substantial loads on their blades.To safely observe the internal oil flow, the single runner opening scheme of the stator is adopted.This involves wire cutting the wall between two adjacent blades in the stator to reject the metal material, followed by in-situ replacement with Plexiglas.By transforming the test tooling and preparing the equipment, the installation, connection, and commissioning of the whole test bench were completed.Thus, the test platform for observing the flow field in the hydrodynamic retarder system was ultimately established, as shown in Figure 12.
To obtain a particle velocity vector map of the internal flow field of the hydrodynamic retarder, a high-speed camera is used when the retarder is running smoothly.The images captured by the camera are processed using a mutual correlation algorithm.The resulting map is illustrated in Figure 13, which depicts the distribution of the high-speed flow region in the upper area of the single runner, specifically, the outside of the stator.This region forms a discernible vortex structure.In Figure 13 (b), the vortex structure of the outside of the stator is observed to move toward the inside, consistent with simulation analysis.In Figure 13 (c), the outside of the stator shows the vortex structure again, and the transformation of the large-scale vortex structure into a small-scale vortex structure can be observed.Finally, the velocity field distribution in Figure 13 (d   The evolution of the velocity field distribution in the PIV test during this time interval indicates that the distribution of vortex structures inside the cavity exhibits a periodic change pattern, consistent with the simulation analysis.This demonstrates the accuracy of the simulation results.Moreover, the distribution of the retarder vortex structure is verified through the experimental test, which reveals the flow characteristics within the retarder.

Conclusion
The periodic flow channel model of the hydrodynamic retarder has been successfully established, and the steady-state simulation calculation has provided valuable insights into the flow characteristics of the retarder cavity fluid under different parameters.This model has enabled us to analyze the vortex structure of the flow field more effectively and has laid the foundation for further research in this area.
Using the Q criterion vortex structure identification method, we have been able to extract and compare the vortex structure of the internal flow field under different fluid filling rate conditions.Our analysis of the distribution and evolution of the vortex structure has shed light on the mechanism of braking torque generation of the hydrodynamic retarder from a macroscopic perspective.
Moreover, our analysis of the influence of different blade angles on the braking torque of the hydrodynamic retarder has revealed that the vortex structure distribution is affected by the blade angle.Specifically, we found a positive correlation between the vortex structure scale, vortex intensity, vortex structure conversion speed, and braking torque.
Finally, the PIV test has demonstrated the accuracy of our simulation analysis by enabling us to observe the vortex structure evolution inside the retarder cavity.This finding further underscores the importance of our study in improving our understanding of hydrodynamic retarders' performance.
In conclusion, our study has established a sound foundation for further research into the vortex structure of hydrodynamic retarder.The insights gained from our analysis have provided valuable technical support for the development of more efficient and effective hydrodynamic retarders.

1 .
(a) Front view (b) Front view Figure Periodic flow passages model of hydrodynamic retarder.

Figure 2 .
Figure 2. Comparison of simulation results and experimental data.

Figure 6 .
Iso-surface of Q criterion in flow field of rotor under different blade angle.

Figure 7 .
Iso-surface of Q criterion and velocity vector in stator when as=40°.(a) Suction surface (b) Middle surface (c) Pressure surface Figure 8. Iso-surface of Q criterion and velocity vector in stator when as=50°.(a) Suction surface (b) Middle surface (c) Pressure surface Figure 9. Iso-surface of Q criterion and velocity vector in rotor when as=40°.

Figure 10 .
Iso-surface of Q criterion and velocity vector in rotor when as=50°.

Figure 11 .
Figure 11.Vortex structure in the flow field.
) is consistent with that shown in Figure13 (b).

Figure 12 .
Figure 12.PIV internal flow field observation test bench.

Figure 13 .
PIV internal flow field observation results.