Comparative Study of Numerical Simulation Methods for Flow Characteristics in Inlet/Isolator Configuration

JIN Yao¹,²*, LIAO Fei²
¹ School of Building Services Science and Engineering, Xi'an University of Architecture and Technology, Xi'an 710055, China
² School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China

Abstract

Focusing on shock-boundary layer interaction phenomena in inlet/isolator configurations, this study systematically compares the capabilities of shock-relation based methods, Euler methods, RANS methods, and DDES methods in predicting shock-train structures and wall pressure fluctuations. Blind-to-blind validation is performed using limited wind tunnel experimental data (schlieren images and high-frequency pressure measurements) to reveal the stringent modeling requirements of scale-resolving approaches (such as DDES) for accurately capturing shock-train unsteadiness and fluctuation intensity. The results demonstrate that DDES achieves significantly higher fidelity than RANS for key unsteady features, including wave structures, separation bubble size, shock-train oscillation characteristics, and the amplitude and frequency of pressure fluctuations. Building upon this foundation, DDES is employed to investigate shock-train oscillation modes and pressure fluctuation intensity under varying blockage ratios (adjusted through wedge-height-to-channel-height ratio h/H). At high blockage conditions (h/H = 0.3), a large-scale subsonic recirculation zone forms within the isolator, with the shock train oscillating longitudinally at approximately 110 Hz and pressure fluctuation intensities reaching 180 dB. In the unblocked state (h/H = 0), the dominant flow mechanism involves high-frequency coupling between turbulent boundary layers and the shock train, where boundary layer fluctuation frequencies are one to two orders of magnitude higher than shock-foot oscillation frequencies, yielding pressure fluctuation intensities of 156 dB.

Keywords: supersonic inlet; isolator; shock wave/boundary layer interaction; shock-train oscillation; wall pressure fluctuation; delayed detached-eddy simulation (DDES)

Funding: National Natural Science Foundation of China (12102360); China Postdoctoral Science Foundation (BX2021246)

Corresponding Author: JIN Yao, Lecturer, E-mail: jinyao@xauat.edu.cn

1. Introduction

The scramjet engine represents the core propulsion system for hypersonic vehicles, comprising an inlet, isolator, combustor, and nozzle. The inlet captures and efficiently compresses atmospheric air, while the isolator further decelerates and pressurizes the high-speed flow and isolates the dynamic high back-pressure effects from the combustor. The compressed high-temperature, high-pressure flow then enters the combustor for thorough mixing and combustion before expanding and accelerating through the nozzle to generate thrust. A critical requirement for efficient scramjet operation is maintaining stable and orderly flow conditions within the inlet/isolator configuration [1].

Highly integrated airframe/engine design characterizes typical hypersonic vehicle configurations, where the shock system at the inlet entrance exhibits strong internal/external flow coupling with the vehicle forebody shock system [2]. This coupled flow field contains unsteady flow features including turbulent boundary layers, shock/expansion wave systems, shear layers, and separation bubbles. Shock/boundary layer interaction phenomena in the viscous boundary layer of the isolator manifest as shock trains that can self-sustain oscillations within unsteady turbulent boundary layer fluctuations. The combined effects of turbulent boundary layers, separation bubbles, and shock oscillations create a complex multi-physics dynamic loading environment involving forces, heat, and acoustics [4-6], which can catastrophically lead to thrust loss, inlet surge, structural fatigue, avionics damage, or even vehicle disintegration. This environment is highly sensitive to disturbances including freestream Mach number [7], inlet boundary layer characteristics [8], incident shock strength [9], sidewall effects [10], and combustor unsteady pressure [11].

With rapid advances in high-performance computing and compressible computational fluid dynamics algorithms, integrated numerical simulations of inlet/isolator internal/external flow coupling have progressed toward high accuracy, high resolution, and refined prediction capabilities. Current numerical methods fall into three categories: shock-relation methods, low-fidelity numerical methods [12], and high-fidelity numerical methods [13]. Shock-relation methods primarily employ shock-expansion theory to predict flow field wave structures, offering high computational efficiency but neglecting viscous boundary layer effects and friction drag prediction. Low-fidelity methods mainly refer to Reynolds-Averaged Navier-Stokes (RANS) approaches, which exhibit strong numerical stability and low resource consumption, dominating scramjet flow simulations for decades [12]. However, RANS methods are limited in predicting complex unsteady phenomena such as shock oscillations, flow separation, and shear layer evolution, making accurate prediction of complex dynamic loading intensity and frequency difficult. Researchers have increasingly employed high-fidelity scale-resolving methods [13-15] (including Direct Numerical Simulation (DNS), Large Eddy Simulation (LES), and Delayed Detached-Eddy Simulation (DDES)) to predict unsteady flow phenomena and complex pressure fluctuation loads in inlet/isolator configurations.

One mechanism driving shock-train oscillation in isolators is unsteady pressure disturbances from the combustor. Previous numerical studies have often applied time-varying excitations at the computational domain outlet to create the combustor's dynamic loading environment, as demonstrated by Gnani et al. [14], Ram et al. [15], and Xie et al. [16]. While simple to implement, such numerical boundary conditions differ significantly from actual wind tunnel configurations, hindering precise back-to-back validation with experimental results. In wind tunnel experiments [17-20], adjustable-height blocks placed downstream of the isolator are typically used to throttle the channel area and create unsteady back-pressure environments [21-22]. However, experimental techniques are limited in providing high-resolution measurements of three-dimensional flow fields, offering only limited flow details. Therefore, constructing geometric models consistent with experimental conditions and considering the real effects of blockage elements is essential.

This study investigates the predictive capabilities of numerical simulation methods for wave characteristics and fluctuating loading environments in inlet/isolator configurations. For a classic two-dimensional inlet configuration, we systematically compare shock-relation, Euler, RANS, and DDES methods, conducting blind-to-blind comparisons between numerical results and wind tunnel schlieren images and pressure fluctuation measurements. This reveals the limitations of low-fidelity methods in predicting shock-train dynamic behavior and demonstrates the necessity of high-fidelity scale-resolving simulations. Based on this foundation, we further explore the influence of isolator blockage ratio (adjusted through internal blockage height) on shock-train oscillation characteristics and fluctuating loads, providing reference and guidance for predicting dynamic acoustic loads within inlet/isolator configurations.

2. Inlet Geometry Model

The two-dimensional supersonic inlet consists of a cowl surface, multi-stage compression ramps, a constant-area isolator, and a downstream wedge-shaped blockage element. Key geometric parameters are illustrated in Figure 1. The leading edge of the first compression ramp (L1) is located at (-356.92 mm, -75.33 mm), the ramp inflection point (L2) at (-216.57 mm, -58.03 mm), the ramp shoulder point (S) at (0 mm, 0 mm), and the cowl lip at (-57.50 mm, 30.00 mm). The isolator height H is 30 mm. The design Mach number is 4, following shock-on-lip design principles where the two-stage oblique shocks from the external compression surface intersect at point C (-61.91 mm, 30.0 mm) ahead of the lip. A wedge-shaped blockage element placed downstream of the channel provides throttling. The distance from the wedge leading edge to the shoulder point L is 292.5 mm, with a wedge base length of 25 mm, leading-edge angle of 45°, and variable wedge height h. Adjusting h simulates combustor unsteady back-pressure, enabling investigation of dynamic high back-pressure effects on shock-train position, intensity, and oscillation characteristics. The relative height h/H represents the throttling coefficient (or blockage ratio). In this study, absolute wedge heights of 0 mm, 3 mm, and 9 mm correspond to relative heights h/H of 0, 0.1, and 0.3, respectively. At the design Mach number (M = 4), the freestream total pressure is 101.325 kPa, total temperature is 288.15 K, the Reynolds number based on 1 m is 6.5×10⁶, static pressure is 0.633 kPa, static temperature is 72.15 K, and density is 0.031 kg/m³.

3. Numerical Setup

Simulations are conducted using an in-house developed compressible-flow, full-Mach-number-range, high-order finite-difference solver. The solver employs a geometric conservation high-order cell-centered finite-difference method [23] to discretize the Navier-Stokes equations on arbitrary curvilinear grids. It possesses high-resolution capabilities for complex turbulent flows [23-25] and supports various numerical methods including Euler, RANS, DDES, LES, and DNS for full-Mach-number-range simulations.

For validation, the GK-01 two-dimensional inlet [26] with an inlet Mach number of 7 is selected. Three grids are designed for grid convergence verification: a coarse grid with 40,000 cells, a medium grid with 100,000 cells, and a fine grid with 200,000 cells. The pressure coefficient distribution along the isolator is shown in Figure 2, where medium and fine grid results are nearly identical and show good agreement with experimental data [26]. Based on the fine grid distribution from this validation case, the grid for the current two-dimensional inlet is designed with approximately 500,000 cells, as shown in Figure 3. The two-dimensional grid is extruded in the spanwise direction to create a three-dimensional grid with a spanwise width of 30 mm and 25 uniformly distributed grid points, employing periodic boundary conditions. The resulting three-dimensional grid contains approximately 12.5 million cells. In subsequent discussions, Euler and RANS simulations are steady two-dimensional simulations based on the 2D grid, while DDES simulations are unsteady three-dimensional simulations based on the 3D grid.

For temporal discretization, unsteady simulations employ a dual-time-stepping algorithm with second-order backward differencing for physical time and an Alternating Direction Implicit (ADI) algorithm for pseudo-time advancement. Steady simulations use implicit time marching based on pseudo-time. The pseudo-time step is determined by stability criteria with a Courant number of 10,000, ensuring residual reduction by three orders of magnitude. The physical time step is selected based on flow characteristics to resolve unsteady phenomena.

3. Results and Discussion

3.1 Wave System Analysis Based on Shock Relations

The majority of the narrow isolator channel in supersonic inlets belongs to the supersonic mainstream region. Oblique shock relations determine the wave system positions and flow parameters upstream and downstream of shocks in the inlet section (Table 1). Based on these relations, Figure 4 clearly shows that the two-stage oblique shocks from the compression ramps converge at point C ahead of the lip, with the lip shock impinging downstream of the shoulder point S and subsequently forming a series of reflected shocks within the isolator.

3.2 Wave System Analysis Based on Euler Simulation

Euler simulations neglect viscous boundary layer effects, focusing solely on wave structures and positions in the supersonic mainstream region. The Mach number contour for the inlet section at M = 4 is shown in Figure 5, revealing a small triangular supersonic expansion fan region downstream of the shoulder point S—a typical inviscid Euler simulation feature. Comparing Figures 4 and 5 shows excellent agreement between the shock system obtained from oblique shock relations and that from Euler simulation. For high-throttling conditions (h/H = 0.4), a detached bow shock forms on the compression surface with subsonic spillage downstream (Figure 6).

3.3 Wave System Analysis Based on RANS Simulation

Real flow conditions involve viscous effects in near-wall regions. Therefore, RANS simulations are performed considering near-wall viscous effects and high-Reynolds-number turbulence, using the Spalart-Allmaras one-equation model to close the eddy viscosity terms. RANS simulation of the inlet configuration yields the time-averaged Mach number contour shown in Figure 7(b).

Comparing RANS results (Figure 7(b)) with Euler results (Figure 5) reveals similar shock positions, shock convergence points, and lip shock impingement locations downstream of the shoulder. However, the key difference lies in the flow pattern after lip shock impingement at the shoulder region. Specifically, Euler simulation shows flow acceleration past shoulder point S, forming a supersonic expansion fan, because viscous boundary layer effects are neglected and the shoulder experiences only a favorable pressure gradient. In contrast, RANS simulation shows a small separation bubble at shoulder S with subsonic flow, because the extremely thin viscous boundary layer between the supersonic mainstream and the wall causes shocks to terminate at the sonic line within the boundary layer. The subsonic region below the sonic line allows upstream-propagating acoustic feedback loops [27], forming self-sustaining boundary layer separation bubbles.

By adjusting the throttling coefficient h/H, RANS simulations are conducted at M = 4 for various blockage ratios, with density gradient contours shown in Figure 8. White regions indicate strong density gradients corresponding to shock discontinuities, expansion waves, and strong shear layers. Focusing on the wave system near the downstream blockage reveals that the wedge acts similarly to a continuous forward and backward step. The forward step creates a compression-corner separation bubble, while the backward step forms a recirculation zone. As wedge height increases, the bow shock ahead of the wedge strengthens and the separation region behind the wedge enlarges. Additionally, when the shock induced by the forward step intensifies and impinges on the upper wall, it generates a second reflected shock. If this second reflected shock is sufficiently strong, it induces a secondary separation bubble and separation shock on the upper wall. After the supersonic mainstream passes the backward step, a compression shock redirects the flow to align with the inlet mainstream direction.

Analysis of blockage effects on isolator shock-train characteristics in Figure 8 indicates that when h/H ≤ 0.2, the local wave system remains relatively stable. However, when h/H = 0.3, the wedge's local wave system becomes unstable, forming an upstream-propagating shock train within the isolator. Therefore, this study defines h/H = 0 and 0.1 as low-blockage cases, and h/H = 0.3 as a high-blockage case.

3.4 Wave System Analysis Based on DDES Simulation

In Section 3.3, all flow fluctuations in the inlet are modeled, with no fluctuation information for the shoulder separation bubble, shock-expansion wave system, or turbulent boundary layer. This section presents DDES simulations to capture unsteady turbulent boundary layer and shock-train oscillation characteristics.

Figure 9(a) shows the instantaneous flow pattern in the inlet entrance region. Compared with Figures 5 and 7, DDES wave systems differ significantly from Euler and RANS results. For reference, Figure 9(b) presents experimental schlieren results. In Figure 9(b), a distinct dark schlieren line is observed entering the lip interior. At the design Mach number, external compression surface shocks should always intersect ahead of the lip (at point C). Therefore, this dark schlieren line is inferred to be a virtual wall rather than an external compression ramp shock. Observing Figure 9(b) reveals that the shock foot of the lip shock terminates in the upper half of the supersonic mainstream channel without reaching the lower wall, indicating a subsonic region in the lower channel area. The presence of a subsonic region implies local separation. Comprehensive analysis thus indicates that the deep schlieren line entering the lip is a virtual wall separating the supersonic mainstream from the subsonic separation bubble, creating a new throat. Since the DDES result in Figure 9(a) generally matches the experimental schlieren in Figure 9(b), DDES demonstrates high fidelity in capturing wave system characteristics.

Detailed analysis of DDES-simulated inlet flow features is presented in Figure 10. The large-scale separation (recirculation region) on the lower compression surface acts like a virtual wall, deflecting the supersonic mainstream and inducing a separation shock on the ramp compression surface, causing partial supersonic spillage and flow distortion. The separation region in the entrance section dynamically adjusts its size and position to achieve equilibrium among freestream dynamic pressure, internal channel pressure, and supersonic spillage mass flow. Figure 10(b) also shows that the reattachment shock downstream of the separation reattachment point on the lower wall has very high intensity. Consequently, after the reattachment shock impinges on the upper wall, it excites a secondary separation bubble and similar wave structures on the upper wall. Theoretically, each oblique shock impingement on a solid wall creates a small separation bubble due to local adverse pressure gradients. However, as shock reflections increase within the channel, shock intensity gradually weakens, and these small local separation bubbles diminish and eventually disappear.

For quantitative validation, Figure 11 presents the time-averaged pressure distribution along the isolator upper wall. DDES predictions show good agreement with wind tunnel experiments [21] in magnitude, further confirming DDES reliability.

The cause of the large-scale separation bubble in the inlet entrance section (Figure 10) is investigated using classical inlet starting theory. Based on empirical formulas from Kantrowitz [28] and Van Wie [29] for predicting inlet starting limits, Figure 12 is constructed. The current inlet has a geometric contraction ratio (CR) of 3.511 (at design Mach number 4) and an internal contraction ratio (ICR) of 1.463 (throat Mach number 3.01). According to the starting limit theory in Figure 12, the inlet operates in the "dual-solution region," where non-unique states of started or unstarted conditions are possible. Excessive geometric contraction prevents captured flow from effectively entering the throat, causing separation on the compression surface. However, since the mainstream region remains supersonic, the unstart phenomenon is only local—hence termed partial unstart or soft unstart.

Based on the analysis in Figures 9-12, DDES simulation provides the highest credibility in capturing inlet wave system characteristics. Therefore, DDES is employed to investigate wave system evolution with varying blockage ratios.

By adjusting the throttling coefficient h/H, wave system evolution within the isolator is observed (Figure 13). The separation bubble position on the compression surface remains relatively stable across different blockage ratios, so the focus is on isolator flow. Longitudinal comparison of blockage region wave systems in Figure 13 yields the following conclusions: (1) When h/H = 0, the channel is dominated by interactions between the oblique shock train and turbulent boundary layer, with each shock foot undergoing self-excited oscillation. Oscillation patterns are similar, with intensity closely related to incident shock strength and turbulent boundary layer evolution. (2) When h/H = 0.1, disturbances propagate upstream from near the wedge, but weak back-pressure limits upstream propagation to local regions. Shock feet in the oblique shock train not directly affected by the wedge continue self-excited oscillation. (3) When h/H = 0.3, disturbance information propagates further upstream, enlarging the separation region ahead of the blockage. The shock train attached to this separation region is pushed toward the lip, exhibiting pronounced periodic large-amplitude oscillation characteristics (Appendix A).

4. Analysis of Pressure Fluctuation Frequency and Intensity in Isolator

This section analyzes the influence of throttling coefficient h/H on dynamic pressure fluctuation characteristics in the isolator. Pressure sensors are placed on the upper wall in numerical simulations at locations matching those in wind tunnel experiments. Spectral analysis identifies pressure fluctuation amplitudes and frequencies, revealing fluctuation characteristics and their connection to instantaneous flow structures.

4.1 Frequency Analysis of Pressure Fluctuations

4.1.1 Low-Frequency Fluctuation Analysis

We first analyze pressure fluctuation characteristics at sensors near the wedge. Figures 14(a), (b), and (c) present time histories of pressure fluctuations at sensors A, B, and C for three blockage conditions. Sensor coordinates are indicated by solid circles in Figure 14(a). Spectral analysis of sensor B is shown in Figure 15.

Comparing pressure fluctuation amplitudes on the vertical axes of Figures 14(a)-(c) reveals that fluctuation intensity increases significantly with blockage ratio. To establish connections between fluctuation frequency/intensity at different sensors and instantaneous flow evolution, Figure 14 also shows instantaneous flow fields at three characteristic times "t1," "t2," and "t3." At h/H = 0, sensors exhibit only low-amplitude, high-frequency fluctuations without obvious low-frequency components. Instantaneous contours show relatively stable shock-foot positions with only weak displacement and oscillation, indicating that shock-foot oscillation frequency is directly related to turbulent boundary layer fluctuation frequency. At h/H = 0.1 and 0.3, sensors show pronounced low-frequency oscillation characteristics: approximately 215 Hz at h/H = 0.1 and about 110 Hz at h/H = 0.3. Instantaneous contours reveal that shock oscillation originates from periodic shrinking and expansion of the separation region at the wedge's forward compression corner. Notably, at h/H = 0.3, high-pressure gas near the wedge can push the shock train almost completely to the lip, replacing channel flow with low-subsonic flow. This results in higher pressure fluctuation intensity and, as the shock train moves substantially forward to the lip, the separation shock foot on the lower compression surface also moves longitudinally. Figures 14 and 15 show that as blockage ratio increases from 0.1 to 0.3, shock oscillation frequency decreases from 215 Hz to 110 Hz, indicating that pressure fluctuation intensity increases with h/H while frequency shifts progressively lower. In wind tunnel experiments at h/H = 0.3, the periodic low-frequency oscillation frequency is 116 Hz [21], closely matching the DDES prediction of 110 Hz and further validating DDES reliability and necessity.

4.1.2 Mid/High-Frequency Fluctuation Analysis

This section analyzes pressure fluctuation characteristics at sensors near the isolator throat. Sensors D, E, F, and G are selected on the upper wall near the cowl lip (Figure 16(a)). Sensors D and F are located in strong shock-boundary layer interaction regions (shock-foot zones), while E and G are within turbulent boundary layers at some distance from shock feet.

Root-mean-square pressure fluctuation amplitudes (Cprms) are calculated as 0.0823 and 0.0885 for sensors D and F, and 0.0224 and 0.0167 for sensors E and G, respectively. Clearly, pressure fluctuation intensities at D and F are 4-5 times higher than at E and G. The time axis in Figure 16(a) shows that D and F have significantly lower dominant frequencies than E and G, typically associated with instantaneous mass ingestion and ejection dynamics within separation bubbles in shock-foot regions.

Spectral analysis of pressure fluctuations at sensors F and G (Figure 16(b)) reveals that sensor F oscillates at approximately 2,400 Hz (termed medium-amplitude, medium-frequency fluctuation), while sensor G exhibits dominant frequencies between 9,500-26,500 Hz (termed small-scale, high-frequency fluctuation). Since sensor F is located at the shock foot, its 2,400 Hz medium-frequency fluctuation correlates with self-excited oscillation of shock-boundary layer interaction. Sensor G, located within the turbulent boundary layer, shows 9,500-26,500 Hz small-amplitude, high-frequency fluctuations associated with unsteady turbulent structure evolution within the boundary layer. Sensor F's fluctuation frequency is about one order of magnitude lower than sensor G's, indicating that shock-foot oscillation frequencies are one to two orders of magnitude lower than turbulent boundary layer fluctuation frequencies—consistent with numerous studies on low-frequency oscillations induced by oblique shock-boundary layer interaction [27,30-32].

In summary, Sections 4.1 and 4.2 demonstrate three distinct frequency bands of fluctuation loads in the isolator: high, medium, and low frequency. Their corresponding frequency magnitudes and primary flow features are summarized in Table 2.

4.2 Intensity Analysis of Pressure Fluctuations

This section analyzes total fluctuation load intensity at different sensors in the channel. Pressure fluctuations are collected from upper wall sensors, and root-mean-square pressure (prms) and total load intensity (sound pressure level, SPL) are calculated as:

$$
p_{rms} = \sqrt{\frac{1}{N}\sum_{n=1}^{N}(p(n) - \bar{p})^2}
$$

$$
SPL = 20\log_{10}\left(\frac{p_{rms}}{p_{ref}}\right)
$$

where p(n) is pressure at time n, $\bar{p}$ is time-averaged pressure, and $p_{ref} = 2 \times 10^{-5}$ Pa. Figure 17 shows the streamwise distribution of SPL on the upper wall, with numerical simulations showing acceptable agreement with experiments [21]. Comparing different blockage cases reveals that at low blockage (h/H = 0), fluctuation intensity is approximately 156 dB, while at high blockage (h/H = 0.3), intensity reaches 180 dB. Pressure fluctuation intensity increases with blockage ratio.

4.3 Effects of High-Intensity, Broadband Pressure Fluctuations

Based on Figures 15-17, high-intensity, broadband pressure fluctuations exist in the isolator, affecting lightweight thin-walled structures in three ways: (1) Low-frequency, high-amplitude loads (~10² Hz) caused by channel-wide blockage and large-scale recirculation from dynamic high back-pressure, often accompanied by massive flow separation. These low-frequency fluctuations can approach structural natural frequencies, causing resonant fatigue, while also significantly degrading inlet compression performance and causing periodic thrust fluctuations that may lead to inlet flameout. (2) Mid-frequency, medium-amplitude loads (~10³ Hz) occurring near shock feet when reflected shock trains are present. The adverse pressure gradient creates local high pressure, thickens boundary layers, increases friction drag, intensifies local thermal loads, and causes structural thermal stress variations. (3) High-frequency, low-amplitude loads (~10⁴ Hz) primarily from pressure fluctuations within high-speed turbulent boundary layers. While small in amplitude, these high-frequency fluctuations increase boundary layer turbulence intensity, excite high-frequency structural acoustic vibration, and directly affect combustion stability.

5. Conclusions

This study investigates the capabilities of shock-relation, Euler, RANS, and DDES methods in capturing shock-train structures and unsteady oscillation characteristics in a two-dimensional inlet/isolator configuration. Results show that inlet wave systems are highly sensitive to numerical methods, with DDES predictions matching experiments most closely. Key conclusions include:

1. Interactions among shocks, expansion waves, and turbulent boundary layers in the isolator create rich multi-wave structures. The primary difference between RANS and Euler simulations lies in the shoulder region: Euler produces a supersonic expansion fan, while RANS generates a small separation bubble. The distinction between DDES and RANS is in the position and size of the shoulder separation bubble—RANS produces a small bubble confined to the shoulder, while DDES yields a large bubble extending to the forebody compression surface. Comparison with experiments confirms that DDES provides the most accurate wave system characteristics.

2. The shock train dynamically adjusts its intensity and position to achieve equilibrium between freestream dynamic pressure and high back-pressure in the wedge region. Changing blockage ratio significantly affects shock-train morphology. At no blockage (h/H = 0), the isolator is dominated by shock-train/turbulent boundary layer interaction. At low blockage (h/H = 0.1), high back-pressure only causes local recirculation without affecting the compression surface separation bubble. At high blockage (h/H = 0.3), wedge-induced recirculation moves upstream and merges with the compression surface separation bubble, creating a large subsonic region extending to the lip and causing severe low-frequency shock-train oscillation in the isolator mainstream.

3. DDES-predicted pressure fluctuation characteristics in the isolator contain three components: (a) High-frequency, low-amplitude fluctuations (~10⁴ Hz) from unsteady turbulent boundary layer pulsations; (b) Mid-frequency, medium-amplitude fluctuations (~10³ Hz) at shock feet from shock-boundary layer interactions; (c) Low-frequency, large-amplitude fluctuations (~10² Hz) from separation region contraction/expansion caused by wedge blockage.

The fluctuating load environment in scramjet isolators significantly affects total pressure loss, propulsion efficiency, structural force/heat/acoustic fatigue, and combustion stability. High-fidelity numerical simulations can identify pulsating load environments in inlets in detail, enabling understanding and control of these high-intensity dynamic loads. This work provides methodological guidance for accurately predicting flow structure evolution and fluctuating loads in hypersonic vehicle inlet/isolator configurations.

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Supplementary animations demonstrate the evolution of internal wave structures within the isolator under different blockage height conditions.