Transonic Regime Research Articles

Connecting transonic buffet with incompressible low-frequency oscillations on aerofoils

Self-sustained, low-frequency, coherent flow unsteadiness over rigid, stationary aerofoils in the transonic regime is referred to as transonic buffet. This study examines the role of shock waves in sustaining this transonic phenomenon and its relation to low-frequency oscillations (LFO) that occur in flow over aerofoils in the incompressible regime (Zaman et al., J. Fluid Mech., vol. 202, 1989, pp. 403–442). This is investigated by performing large-eddy simulations of the flow over a NACA0012 profile for a wide range of flow conditions under free-transition conditions. At low Reynolds numbers, zero incidence angle and sufficiently high free-stream Mach numbers, $M$ , transonic buffet occurs with shock waves present in the flow. However, when $M$ alone is lowered, self-sustained, periodic oscillations at a low frequency are observed even though shock waves are absent and the entire flow field remains subsonic at all times. At higher incidence angles, the oscillations are sustained at progressively lower $M$ and are present even at $M=0.3$ , where compressibility effects are low. A spectral proper orthogonal decomposition (SPOD) shows that the spatial structure of these oscillations is consistent for all cases. The SPOD modes are topologically similar, suggesting a connection between transonic buffet and LFO in the incompressible regime. Comparisons with other studies examining transonic buffet on various aerofoils, under forced-transition and fully turbulent conditions support this hypothesis. Future studies using tools of global linear stability analysis, especially at high free-stream Reynolds numbers are required to examine whether the underlying mechanisms of transonic buffet and incompressible LFO are the same.

Development of a steady-state computational fluid dynamics solver for transonic rotorcraft flows

The capability for solving compressible fluid flows in the rotating frame of reference is added to an existed open-source CFD solver, namely, HiSA solver. The new implementation is explained and validated using the experimental data of the Sikorsky S-76 rotor. A comparison is presented between the moving mesh results obtained from the original HiSA code and the single rotating frame results achieved through the new implementation. The comparison includes an analysis of torque and thrust values, as well as computational costs. The results imply that, for evaluating the performance of an isolated rotor or for shape optimization purposes at the transonic regime, the single rotating frame method, like the one introduced in the current work, can provide accurate results within an acceptable computational budget. Furthermore, the results show that, at least 25 revolutions are required for the transient analysis to reach an acceptable steady-state converged solution like the one obtained by the single rotating frame method.

Design Optimization of Blade Tip in Subsonic and Transonic Turbine Stages—Part I: Stage Design and Preliminary Tip Optimization

Abstract Rotor blade tip has significant influence on turbine stage aerodynamics and heat transfer. Most previous efforts have been based on low-speed cascade settings. However, more recent research on transonic blade tips exhibits distinctive flow features with qualitatively different performance sensitivities. These prompt two key issues of interest on the related flow conditioning. First, the contrast between a low-speed flow and a transonic regime highlights the less studied high-subsonic flow regime, closely relevant to many realistic turbine designs. Second, the relative casing movement and upstream inflow conditions, known to have non-negligible effects, indicate the need to examine a rotor blade tip in a realistic stator–rotor stage environment, which is also lacking. To elaborate the Mach number effect in the flow regimes of practical interest, we aim to examine a high subsonic stage in a direct and consistent comparison with a transonic one. To this end, a high subsonic stage (exit Mach number of 0.7) and a transonic (exit Mach number of 1.1) are designed at the same Reynolds number with a three-dimensional parameterization and meshing system. The tip squealer height is used as a representative parameter to investigate the sensitivity of the stage aerothermal performance. The multi-objective optimization using the Kriging surrogated model is employed to identify the Pareto fronts for the stage efficiency and the heat transfer. The comparison of the optimized results between these two stages shows distinctively different trends in the performance variation with the squealer height. The efficiency of the subsonic stage increases with the squealer height reaching a plateau. In contrast, the efficiency in the transonic stage first increases and then drops to the level comparable to that of a flat tip. Significantly, the present results indicate, for the first time, that the squealer tip in a transonic stage may not be as effective as in a subsonic stage. On the other hand, for heat transfer, sensitivity variations are more complex. The overall heat load and the local nonuniformity lead to qualitatively different sensitivities with the squealer height, as well as completely incomparable Pareto fronts. These observed heat transfer sensitivities raise the question on how to effectively conduct a combined aerodynamic and heat transfer performance design optimization. The authors subsequently resort further aerothermal physics analyses described in a companion paper as Part II of the two-part article. In Part II, the physical interpretation of the contrasting aero-efficiency sensitivities for the two stages, as well as a physical understanding leveraged selection of the objective function for such combined blade tip aerothermal optimization will be presented.

Overview of Computational Methods to Predict Flutter in Aircraft

Abstract Aeroelastic flutter is a dynamically complex phenomenon that has adverse and unstable effects on elastic structures. It is crucial to better predict the phenomenon of flutter within the scope of aircraft structures to improve the design of their wings. This review aims to establish fundamental guidelines for flutter analysis across subsonic, transonic, supersonic, and hypersonic flow regimes, providing a thorough overview of established analytical, numerical, and reduced-order models as applicable to each flow regime. The review will shed light on the limitations and missing components within the previous literature on these flow regimes by highlighting the challenges involved in simulating flutter. In addition, popular methods that employ the aforementioned analyses for optimizing wing structures under the effects of flutter—a subject currently garnering significant research attention—are also discussed. Our discussion offers new perspectives that encourage collaborative effort in the area of computational methods for flutter prediction and optimization.

Aerodynamic force by Lamb vector integrals in unsteady compressible flows

PurposeThis study aims to propose an aerodynamic force decomposition which, for the first time, allows for thrust/drag bookkeeping in two-dimensional viscous and unsteady flows. Lamb vector-based far-field methods are used at the scope, and the paper starts with extending recent steady compressible formulas to the unsteady regime.Design/methodology/approachExact vortical force formulas are derived considering inertial or non-inertial frames, viscous or inviscid flows, fixed or moving bodies. Numerical applications to a NACA0012 airfoil oscillating in pure plunging motion are illustrated, considering subsonic and transonic flow regimes. The total force accuracy and sensitivity to the control volume size is first analysed, then the axial force is decomposed and results are compared to the inviscid force (thrust) and to the steady force (drag).FindingsTwo total axial force decompositions in thrust and drag contributions are proposed, providing satisfactory results. An additional force decomposition is also formulated, which is independent of the arbitrary pole appearing in vortical formulas. Numerical inaccuracies encountered in inertial reference frames are eliminated, and the extended formulation also allows obtaining an accurate force prediction in presence of shock waves.Originality/valueNo thrust/drag bookkeeping methodology was actually available for oscillating airfoils in viscous and compressible flows.

Sinusoidally Pitching Foils in Transonic Flow: Insights into Flutter from Time Accurate Simulations

The impact of shock formation and vortex dynamics on airfoil flutter in the transonic regime is investigated through a series of two-dimensional time-accurate simulations of a sinusoidally pitching airfoil at a Reynolds number of 10,000. To gain insight into transonic flutter in the fully nonlinear regime, an energy-based approach that employs prescribed kinematics is utilized. Flutter stability boundaries are identified as a function of the Mach number and the reduced velocity, the latter of which is a surrogate for structural stiffness or flight speed. The results show a subcritical instability near Mach numbers of M∞=0.7 for a range of oscillation frequencies. Additionally, three shock-induced mechanisms are identified that influence the transfer of energy from the flow to the airfoil. The primary mechanism is flow separation triggered by the generation of a lambda shock. The influence of the lambda-shock dynamics on airfoil flow separation is determined for different Mach numbers, providing insight into the well-known “transonic dip” observed in flutter boundaries.

Robust shape optimization using artificial neural networks based surrogate modeling for an aircraft wing

Aerodynamic shape optimization is a very active area of research that faces the challenges of highly demanding Computational Fluid Dynamics (CFD) problems, optimization with Partial Differential Equations (PDEs) as constraints, and the appropriate treatment of uncertainties. This includes the development of robust design methodologies that are computationally efficient while maintaining the desired level of accuracy in the optimization process. This paper addresses aerodynamic shape optimization problems involving uncertain operating conditions. After a review of possible approaches to account for uncertainties, an Artificial Neural Network (ANN) model is used to approximate the aerodynamic coefficients when the operating conditions vary. Robust optimization problem-solving approaches based on deterministic measurements are used, inspired by the work of Deb [Deb K., Gupta H. Introducing robustness in multi-objective optimization. KanGAL Report 2004–2016, Kanpur Genetic Algorithms Laboratory, Indian Institute of Technology, Kanpur, India (2004)]. The first procedure is a direct extension of a technique used for single-objective optimization. The second is a more practical approach allowing a user to define the desired degree of robustness in a problem. These approaches have been tested and validated in the case of the optimization of an aircraft wing profile in the transonic regime considering two uncertain variables: the Mach number and the angle of incidence.

Data-driven reduced-order modeling for nonlinear aerodynamics using an autoencoder neural network

The design of commercial air transportation vehicles heavily relies on understanding and modeling fluid flows, which pose computational challenges due to their complexity and high degrees of freedom. To overcome these challenges, we propose a novel approach based on machine learning (ML) to construct reduced-order models (ROMs) using an autoencoder neural network coupled with a discrete empirical interpolation method (DEIM). This methodology combines the interpolation of nonlinear functions identified based on selected interpolation points using DEIM with an ML-based clustering algorithm that provides accurate predictions by spanning a low-dimensional subspace at a significantly lower computational cost. In this study, we demonstrate the effectiveness of our approach by the calculation of transonic flows over the National Advisory Committee of Aeronautics 0012 airfoil and the National Aeronautics and Space Administration Common Research Model wing. All the results confirm that the ROM captures high-dimensional parameter variations efficiently and accurately in transonic regimes, in which the nonlinearities are induced by shock waves, demonstrating the feasibility of the ROM for nonlinear aerodynamics problems with varying flow conditions.

Experimental and numerical study on RBCC engines performance in simultaneous and combustion cycle

The simultaneous mixing and combustion (SMC) cycle is a simple yet effective approach to augment the specific impulse of rocket-based combined cycle (RBCC) engines in ejector mode. However, the thrust performance of RBCC engines in the SMC cycle has not been adequately explored. This study investigates the effects of the flight Mach number, mixer shapes, and mixture ratio (MR) on the thrust performance of an axisymmetric kerosene-fueled RBCC engine. Ground free-suction experiments were conducted, employing a supersonic air ejector to simulate varying flight backpressures. Wall pressure distributions and axial thrusts were obtained. To eliminate undesirable interactions between MRs and backpressures inherent in experiments, numerical simulations were performed. The experimental results show that as flight Mach number increases, specific impulse improves rapidly, and specific impulse augmentation is achieved in the transonic regime. Simulations conducted at H4.0km/Mach0.88 with the expansion mixer reveal that as MR decreases, both mixing efficiency and combustion intensity increase. The balance between specific impulse gain from the secondary stream and loss from the primary stream is achieved at MR = 2.2, with the highest specific impulse being achieved at MR = 2.0. These insights provide valuable guidance for advancing the development of more efficient RBCC engines using the SMC cycle.

Numerical study on aerodynamic characteristics of the grid fins with different grid patterns

Grid fins are unconventional control surfaces configured by a grid of cells within an outer frame; this grid acts as multiple lifting surfaces, and the pattern of the cells strongly affects the grid fin's performance. In this study, three-dimensional simulations were performed using a computational fluid dynamic approach with a k–ω shear stress transport turbulence model to investigate the effect of grid patterns on fin aerodynamic characteristics. Three fin models were designed, including square, tri, and hexa grid patterns, to be more independently comparative; other parameters consisting of the outer frame's dimensions, internal web's thickness, chord length, dragging area, and grid cell area were kept similar between the models. The Mach numbers 0.7, 1.2, and 2.5 corresponding to subsonic, transonic, and supersonic regimes were investigated for varying angles of attack from −5° to 15° for each fin model. The aerodynamic efficiency of grid fins is appreciably improved by increasing the normal force coefficient (CN) while reducing the area force coefficient (CA) and hinge moment coefficient (CHM). The results underscore the hexa grid pattern's superiority, with CN increasing by 2.2% and CA decreasing by 1.92% compared to the square model (the original model) at Mach number 0.7. Especially, the hexa model exhibited a substantial decrease in CHM, with the largest difference being 56.8% compared to the square model at Mach 2.5.

Optimization of transonic low-Reynolds number airfoil based on genetic algorithm

A 2-D airfoil shape optimization in transonic low-Reynolds number regime is conducted. A Navier–Stokes flow solver with a transition model (k-ω SST γ-Reθ) is used to evaluate the fitness function. Single-point and multi-point formulations of the optimization results are compared. In addition, the effects of Mach number and angles of attack on aerodynamic characteristics of the optimized airfoils are investigated under low Reynolds number (Re = 17,000) and high-subsonic-flow ([Formula: see text]) conditions. The results show that the corresponding drag divergence Mach number curves of the conventional airfoil present almost a parallel shifting at the entire Mach number range. By contrast, the unconventional airfoil starts showing a significant drag reduction when Mach number is greater than 0.75. Besides, the maximum lift-to-drag ratio is highly influenced by the Mach number because of the formation, movement, type, and strength of a shock wave. In addition, the distinguishing difference in the conclusion between two airfoils is that the lift fluctuation of the conventional airfoil amplifies with the increase of the Mach number. However, the unconventional airfoil shows an opposite trend.

Experimental investigation on the turbulent wake flow in fully established transonic buffet conditions

The transonic flight regime is often dominated by transonic buffet, a highly unsteady and complex shock-wave/boundary-layer interaction involving major parts of the flow field. The phenomenon is associated with a large-amplitude periodic motion of the compression shock coupled with large-scale flow separation and intermittent re-attachment. Due to the resulting large-scale variation of the global flow topology, also the turbulent wake of the airfoil or wing is severely affected, and so are any aerodynamic devices downstream on which the wake impinges. To analyze and understand the turbulent structures and dynamics of the wake, we performed a comprehensive experimental study of the near wake of the supercritical OAT15A airfoil in transonic buffet conditions at a chord Reynolds number of 2×106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2\ imes 10^{6}$$\\end{document}. Velocity field measurements reveal severe global influences of the buffet mode on both the surface-bound flow field on the suction side of the airfoil and the wake. The flow is intermittently strongly separated, with a significant momentum deficit that extends far into the wake. The buffet motion induces severe disturbances and variations of the turbulent flow, as shown on the basis of phase-averaged turbulent quantities in terms of Reynolds shear stress and RMS-values. The spectral nature of downstream-convecting fluctuations and turbulent structures are analyzed using high-speed focusing schlieren sequences. Analyses of the power spectral density pertaining to the vortex shedding in the direct vicinity of the trailing edge indicate dominant frequencies one order of magnitude higher than those associated with shock buffet (Stc=O(1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$St_c=\\mathcal {O}({1})$$\\end{document}) vs. Stc=O(0.1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$St_c=\\mathcal {O}({0.1})$$\\end{document}). It is shown that the flapping motion of the shear layer is accompanied by the formation of a von Kármán-type vortex street of fluctuating strength. These wake structures and dynamics will impact any downstream aerodynamic devices affected by the wake. Our study, therefore, allows conclusions regarding the incoming flow of devices such as the tail plane.

State switching in the wake of a transverse circular cylinder in the transonic regime

The flow past a circular cylinder in a cross-flow configuration was investigated using a wind tunnel experiment across a range of Mach numbers M∞ from 0.30 to 0.85 and corresponding Reynolds numbers, based on diameter, ranging from 2×105 to 5×105. The boundary layer at the cylinder surface is either free or fixed turbulent using artificial tripping at azimuth 12.5°, 25°, and 50°. Measurements combine temporal recordings of the wall pressure and schlieren high-speed visualizations of the flow past and downstream of the cylinder. First, by attaching the tripping strips to the cylinder at the different azimuthal positions, the effect of the boundary layer state on the cylinder wake is found to be strong at subsonic speeds but much smaller in the transonic regime. Multiple flow states are observed depending on the value of M∞. Of particular interest was the narrow region between M∞=0.80 and =0.85, which yields three different states, namely the vortex shedding state, the parallel shear layer state, and the crossed shear layer state. By precisely managing back and forth travels in Mach number with the wind tunnel, it is found that the transitions between these states have a hysteresis behavior. This sub-critical behavior could explain the surprisingly variable threshold values between these different states reported in the literature.

Data-Driven Modeling for Transonic Aeroelastic Analysis

Aeroelasticity in the transonic regime is challenging because of the strongly nonlinear phenomena involved in the formation of shock waves and flow separation. In this work, we introduce a computationally efficient framework for accurate transonic aeroelastic analysis. We use dynamic mode decomposition with control to extract surrogate models from high-fidelity computational fluid dynamics (CFD) simulations. Instead of identifying models of the full flowfield or focusing on global performance indices, we directly predict the pressure distribution on the body surface. The learned surrogate models provide information about the system’s stability and can be used for control synthesis and response studies. Specific techniques are introduced to avoid spurious instabilities of the aerodynamic model. We use the high-fidelity CFD code SU2 to generate data and test our method on the benchmark supercritical wing. Our Python-based software is fully open source and will be included in the SU2 package to streamline the workflow from defining the high-fidelity aerodynamic model to creating a surrogate model for flutter analysis.

Investigation of a Near-Field Cylinder Wake in the Subsonic, Transonic, and Supersonic Regimes

The near wake of a circular cylinder in a high-Reynolds-number regime is investigated using the particle image velocimetry technique for an inflow Mach number spanning 0.3 to 2. The mean flow and turbulent kinetic energy field for different Mach number cases are presented. Furthermore, the influence of the Reynolds and Mach number effects is examined based on the mean separation point along the cylinder surface, which is extracted from complementary schlieren visualization measurements, and the literature. The wake width for the supersonic inflow case is found to be an order of magnitude smaller physically than the subsonic case with an identical cylinder diameter. Additionally, the swirl strength criterion is used to identify the eddies present within the wake, and the eddy size and convection velocity are characterized based on the spatiotemporal correlations. The result suggests that the mean wake features for the subsonic and supersonic cases are very different. Moreover, the interaction of eddies generated at the cylinder’s top and bottom shear layers leads to the large-scale features present in the wake, and the differing paths followed by the eddies between the subsonic and supersonic cases are responsible for the variation in the observed wake width.

Multidisciplinary Design Optimization of Transonic Wings with Boundary-Layer Suction

A quasi-three-dimensional aerodynamic solver is developed for the aerodynamic analysis of wings in a transonic regime that is able to capture the effect of BLS in hybrid laminar flow control (HLFC) application or transition to turbulent flow for natural laminar flow (NLF). The tool provides accurate results, but without the high computational cost of high-fidelity tools. The solver combines the use of an Euler flow solver characterized by an integral boundary-layer method and linear stability analysis using a approximation for transition prediction. In particular, a conical transformation is adopted, including the determination of the shock-wave position. The solver is implemented in a multidisciplinary design optimization (MDO) framework, including wing weight estimation and aircraft performance analysis. The framework consists of different modules: aerodynamics, structure, suction system analysis, and performance evaluation. Using a genetic algorithm and considering HLFC technology, wing MDO has been performed to find the optimum wing planform and airfoil shape. A backward-swept wing (BSW) aircraft, developed inside the Cluster of Excellence–Sustainable and Energy Efficient Aviation (A) is studied. Novel technologies such as active flow control, limited maximum load factors due to load alleviation, and novel materials allow a fuel weight reduction of 6%.

Evolutionary generative design of supercritical airfoils: an automated approach driven by small data

Supercritical airfoils are critical components in the design of commercial wide-body aircraft wings due to their ability to enhance aerodynamic performance in transonic flow regimes. However, traditional design methods for supercritical airfoils can be time-consuming and require significant manual effort, not to mention the high cost associated with computational fluid dynamics analysis. To address these challenges, this paper introduces a highly automated approach for supercritical airfoil design, called Evolutionary Generative Design (EvoGD). The EvoGD approach is based on the framework of Evolutionary Computation and employs a series of sophisticated data-driven generative models incorporated with physical information to iteratively refine initial airfoil shapes, resulting in improved aerodynamic performances and reduced constraint violations. Moreover, to speed up the evaluation of the generated airfoils, a series of accurate and efficient data-driven predictors are utilized. The efficacy of the EvoGD approach was demonstrated through experiments on a dataset of 501 supercritical airfoils, including one baseline design and 500 randomly perturbed airfoils. On average, the generated airfoils showed improved performance in terms of buffet lift coefficient, cruise lift-to-drag ratio, and thickness by 5%, 4%, and 1%, respectively. The best generated airfoil outperformed the baseline design in terms of critical buffet lift coefficient and cruise lift-to-drag ratio by 7.1% and 6.4%, respectively. The entire design process was completed in less than an hour on a personal computer, highlighting the high efficiency and scalability of the EvoGD approach.

Manipulating near-wall flow instability and transport characteristics by the airfoil probe: Investigation on a transonic compressor cascade

The flow field exhibits complex features, such as shock waves, wakes, and end wall vortices in a transonic cascade. Installation of airfoil probes exacerbates the multi-scale and unsteady behavior of the internal passage flow. Apart from inducing measurement errors, it also generates extra flow loss inevitably and further affects the measuring accuracy. This paper investigates the impact of airfoil probes on a transonic compressor cascade's unsteady behavior and transport characteristics. Using high-fidelity numerical simulations, the influence of pipe layouts on the flow field of instrumented blades is visualized, revealing highly radial asymmetry. Loss analysis uncovers entropy transport induced by the streamwise vortices, primarily manifested by large-scale angular deformation at the outlet. The vortex structures in the wake region are dominated by momentum transport, displaying regional evolution and momentary equilibrium. The vortex expansion plays a leading role in the global vortex transport process, which is strengthened by the presence of the probes. Spatiotemporal analysis of the unsteady flow field can reveal some features overlooked by conventional fluid mechanics analysis. Using proper orthogonal decomposition, wake vortex pairs' high-frequency oscillations and shedding behaviors are captured in adjacent modes for the first time. The proposed approach can provide a theoretical basis for in-depth investigations of instrumented blade flow fields at the transonic regime. Furthermore, corresponding research can promote the refinement of instrument design by enabling experimentalists to understand the effects of intrusive instruments on transonic flow fields.

Ground Vibration Test Based Flutter Prediction for a Combat Aircraft

This paper compares the flutter characteristics of a combat aircraft predicted using experimental modal parameters from ground vibration tests with the results obtained by flight flutter tests. An equivalent finite element model representing the test points in ground vibration tests has been developed and further refined to obtain a finite element model with fine mesh encompassing the entire lifting surface areas. Infinite plate interpolation scheme has been used to extrapolate the eigenvectors for the refined model. A Direct Matrix Abstraction Program (DMAP) written in NASTRAN replaces the generated mass normalized eigenvalues and vectors of the refined model from a dynamic analysis in NASTRAN, with the experimentally obtained eigenvalues and extrapolated eigenvectors. Flutter analysis has been carried out with the replaced experimental modal parameters in subsonic, transonic and supersonic regimes using flutter modules in NASTRAN and ZAERO software. The results obtained using this procedure have been compared with the flight flutter test results. The dispersion in the damping and frequency results obtained from computations and the flight flutter tests were within acceptable limits showing a good correlation.

Numerical model of predicting surge boundaries in high-speed centrifugal compressors

A numerical model of the whole compression system is established in this paper. The introduction of the Laval nozzle and opening boundary methods adaptively simulate the physical fluctuating boundary conditions during the surge without any artificial hypothesis. Based on the model, the steady simulation method has the capacity to well predict the low-order systematical oscillations during the surge by monitoring flow parameters on several representative surfaces. The surge boundaries of a high-speed centrifugal compressor, including the mild surge and the deep surge, are predicted based on the current numerical model in different flow regimes. The discrepancies of the mild surge boundary between experimental data and numerical predictions are within 5% in the transonic regime, but within 0.5% in the subsonic and supersonic regimes. The sensitivities of the mild surge to the throttle opening degree differ much in different flow regimes: the highest is in the transonic regime and the lowest is in the supersonic regime. In the supersonic regime, there exist various mild surges in a wide range of throttle opening degrees and an unstable equilibrium point (UEP) which is the most typical characteristic of the two-regime surge. To the best knowledge of the authors, it is the first time that all the oscillation characteristics of various mild surges and the existence of UEP in the supersonic regime are well predicted by one numerical method.