Improved hybrid model for transitional separated flows over a rough compressor blade
Introduction
The aerodynamic property of compressors is very important for turbofan engine performance [1], and the corresponding boundary layer transition method is a hot research topic in fluid mechanics [2]. As known, the flow around a compressor is very complex due to the blade leading edge shape, suction side curvature, strong pressure gradients, high-turbulence-intensity level, high-temperature and high-pressure flow conditions. The typical flow phenomenon is the laminar separation bubble (LSB) induced transition and reattachment process of turbulent separation over a smooth wall with a high-turbulence-intensity inflow [3]. In fact, there is micron-sized distributed roughness on the surface of the compressor, which can significantly affect the boundary layer transition and the separated flow pattern after the transition [4], [5], [6]. To simulate it accurately, many methods have been proposed. Reynolds-averaged-Navier-Stokes (RANS) method is usually used in engineering with high computational efficiency [7], [8], [9], [10], [11], but it has a weak ability to predict massively separated flows. Direct-numerical-simulation (DNS) and large-eddy-simulation (LES) methods have high simulation accuracy but cost too much in engineering applications. Therefore, scholars developed the hybrid RANS/LES method with a reasonable computational cost [12], [13] to simulate and analyze the transitional separated flow around the compressor.
In the 1990s, the very-large-eddy-simulation (VLES) method was first proposed by Speziale [14], [15], which is a unified simulation approach enabling a seamless evolution from RANS to LES and finally approaching DNS depending on the numerical resolution. Subsequently, Fasel et al. [16], [17] improved it and developed the flow simulation methodology (FSM). After that, according to the idea of FSM, several hybrid models have been proposed [18], [19]. Han et al. [20], [21], [22] proposed improved variants of the VLES method based on the standard model and Wilcox's model, which have been applied to combustion and heat transfer simulations [23] and achieve accurate and reliable prediction results. In 2018, Li et al. [24] transplanted the VLES method to Menter's shear-stress-transport (SST) model and made corresponding modifications, which performs well in the simulation of separated flow around the airfoil and cylinder.
However, similar to most hybrid RANS/LES methods, VLES is still developed for fully turbulent flow and cannot predict laminar-turbulence transition. Since the transition phenomenon before turbulence is very important for the accurate simulation of turbulent flow, it is necessary to couple the VLES method with the RANS-based transition model. In recent years, some researchers have done a lot of work on this point. Sørensen et al. [25] and Qiao et al. [26] combined the transition model with the detached-eddy-simulation (DES) and delayed-DES (DDES) model, yielding more accurate results around the airfoil and cylinder than the DES and DDES alone. To capture the boundary layer transition process and the unsteady flow perturbation structures in the wake region, You and Kwon [27] implemented the transition model to Menter's scale-adaptive-simulation (SAS) model [28]. Based on the hybrid RANS/LES framework proposed by Germano [29], [30] and Sánchez-Rocha and Menon [31], the local dynamic kinetic energy model is combined with the transition model by Hodara and Smith [32], which can capture the flow characteristics of the massively separated boundary layer after the transition. Coder and Ortiz-Melendez [33] developed a new hybrid method for predicting transitional turbulence flows with the combination of the Spalart-Allmaras (SA) turbulence model and the amplification factor transport (AFT) transition model, showing better agreement with the experimental data in several classical flow cases. Xiao et al. [34] developed a novel hybrid model based on the three-equation RANS closure model [35], which performs well to simulate the hypersonic flow at a high angle of attack past the Orion capsule. In 2021, Kim and Kwon [36] coupled the crossflow transition model with the improved DDES (IDDES) method. For flows around the 6:1 inclined prolate spheroid, the predictions are in good agreement with the experiment and improved results on the rear end surface of the prolate spheroid are presented. The adaptive DES model was proposed by Yin & Durbin [37], [38] to simulate the transition flow in the V103 linear compressor. The model responds well to freestream turbulence and can successfully capture the transition process. Subsequently, Bader & Durbin [39] modifies the coefficient according to the structural function of Vreman. The model is validated by flat plate cases with bypass and separation-induced transition. Similar to Han's study on heat transfer through VLES [23], Lee and Shih [40] employed the SAS model to study the effects of heat load on the unsteady flow and heat transfer in the entrance region of a cooling duct with a staggered array of pin fins and developed novel correlations that account for the effects of heat loads on averaged Nusselt number in the entrance and post-entrance regions. Recently, Zhang and Shih [41], [42] proposed a new idea to deal with the information exchange at the LES-RANS interface and eliminating the instabilities at the LES-to-RANS interface, which is crucial for solving the weaknesses of the zonal hybrid LES-RANS method.
In a word, these hybrid models only consider boundary layer transitions and turbulent separations over smooth walls. However, surface roughness always has an important impact on the boundary layer transition prediction and turbulent flow simulation [1], [4], [5], [43], [44], [45]. This paper presents an effective modeling strategy for the laminar, roughness-induced-transition, and attached turbulence/massively separated flows that couples the VLES model [24] and a transition model [46] considering roughness effects. A new hybrid function is developed in this paper to suppress the inaccuracy of the hybrid function in the bottom region of the post-transition turbulence region [47].
Section snippets
Transition model
The transition model proposed by Zhang et al. [46] is employed herein as the baseline. It is developed for the bypass and laminar-separation-bubble (LSB)-induced transition and distributed surface roughness effects have been taken into account by constructing a transport equation for the roughness amplification factor . The transport equations for the intermittency factor γ [48], [49], [50], [51], [52], [53], [54], [55] and take the form
Results and discussions
At low Reynolds numbers, the boundary layer on the suction side of a highly loaded blade is prone to separation. Subsequently, the laminar separated shear layer transitions to turbulent flow and quickly reattaches. The separation bubbles formed during this process change the effective shape of the blade, thereby reducing the performance of the blade and increasing the loss. In addition, the deposits and erosion can result in modified blade shapes and increase the surface roughness, which
Conclusion
In this paper, based on the hybrid RANS/LES method framework, the rough transition model and the VLES are carried out by shielding the turning-on region of the VLES mode in the laminar boundary layer, limiting the freestream turbulence intensity decay, and constructing the laminar separation bubble transition influence function, resulting in a new γ--VLES model that can simulate and analyze the roughness effects on the transitional and separated flow.
However, due to the construction of the
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work is supported by the National Natural Science Foundation of China (Grant No. 12102361) and the Fundamental Research Funds for the Central Universities (Grant No. G2021KY05101). The work was carried out at National Supercomputer Center in Tianjin, and the calculations were performed on TianHe-1(A).
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