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Exposure of a spherical human skull substitute to free-field blast conditions 将球形人类头骨替代品暴露在自由场爆炸条件下
IF 1.8 4区 工程技术 Q3 MECHANICS Pub Date : 2025-10-14 DOI: 10.1007/s00193-025-01248-y
N. Elster, J. Boutillier, P. Magnan, S. De Mezzo, P. Naz, R. Willinger, C. Deck

On the battlefield, soldiers may be injured by the detonation of explosive charges, particularly to the head. Several injury mechanisms have been proposed in the literature to explain the observed brain lesions, and numerous experiments, such as post-mortem studies, have been carried out to investigate those hypotheses. In the current study, a new skull substitute has been developed and its mechanical behaviour has been evaluated under free-field blast conditions. Instrumentation included accelerometers, strain gauges, and pressure sensors mounted in multiple positions. The substitute was embedded on a rigid mount and subjected to the detonation of 21 explosive charges. The proposed experimental campaign included seven free-field scenarios with incident pressures ranging from 75 to 200 kPa and two blast durations of 1.2 ms and 2.0 ms. The time analysis of signals revealed an “ipsi-contralateral” effect for internal pressures, i.e., an overpressure at the ipsilateral site concomitant to a depressure at the contralateral site. A slight underestimation of the first peaks versus incident pressures was also observed when compared with the literature on post-mortem human subjects. For shell strains, an overestimation of the maximum values and the first peak values versus incident pressures was attested compared to the bibliographic data. According to the current findings, the newly designed skull substitute produces results in line with post-mortem human subjects in terms of first peak strain and peak internal pressure trends. The described methodology could be applied to develop new head substitutes and, in the future, investigate injury mechanisms.

在战场上,士兵可能会因炸药的爆炸而受伤,尤其是头部。文献中提出了几种损伤机制来解释观察到的脑损伤,并进行了许多实验,如死后研究,以调查这些假设。在目前的研究中,开发了一种新的颅骨替代品,并对其在自由场爆炸条件下的力学行为进行了评估。仪器包括安装在多个位置的加速度计、应变计和压力传感器。替代物被嵌在一个坚硬的底座上,经受21个炸药的爆炸。拟议的实验活动包括7个自由场场景,入射压力范围为75至200 kPa,两次爆炸持续时间为1.2 ms和2.0 ms。信号的时间分析揭示了内压的“同侧-对侧”效应,即同侧部位的超压伴随对侧部位的降压。与死后人类受试者的文献相比,还观察到对第一个峰值与事件压力的轻微低估。对于壳应变,与文献数据相比,证明了最大值和第一峰值与入射压力的高估。根据目前的研究结果,新设计的颅骨替代物在首次峰值应变和峰值内压趋势方面产生的结果与死后人类受试者一致。所描述的方法可以应用于开发新的头部替代品,并在未来研究损伤机制。
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引用次数: 0
Shock wave propagation along a straight street 冲击波沿直街传播
IF 1.8 4区 工程技术 Q3 MECHANICS Pub Date : 2025-09-25 DOI: 10.1007/s00193-025-01250-4
Y. Marchal, I. Sochet, E. Lapébie, K. Atlassi, A. Faugaret, N. Billois

This study is motivated by concerns for the safety of goods and people, as well as the need to provide individuals with the means to prevent and protect against accidental risks and terrorist threats. The research is one of the tasks in the ANR research project (mathrm{URB(EX)}^{{3}}), which aims at developing a fast-running, breakthrough model for blast consequences in urban configurations. The objective is to characterize the propagation of a shock wave along a straight street using experimental and numerical approaches. The shock wave results from the detonation of a gaseous explosive charge. The experiments are carried out at laboratory scale by applying the laws of similarity. Shock waves are studied using pressure profiles recorded by regularly distributed pressure sensors. Visualization is also used to illustrate various shock wave interactions between the two walls. The explosive charge is placed on the central axis of a street between two parallel walls. The shock wave propagation is analysed in terms of street width and height. It is demonstrated that the shock wave changes its propagation mode from 3D to 2D. It is also shown that several planar shock waves are correlated with the junction of two Mach stems. This study reveals secondary shock waves, as well as multiple shock waves, which can lead to a certain complexity in interpreting the measured pressure signals. The 3D to 2D mode transition zone is determined for each configuration, and an empirical law is established based on the different experimental results obtained. The law considers three parameters, namely the diameter of the explosive charge and the dimensions of the street (height and width).

这项研究的动机是对货物和人员安全的关注,以及需要为个人提供预防和保护意外风险和恐怖主义威胁的手段。这项研究是ANR研究项目(mathrm{URB(EX)}^{{3}})的任务之一,该项目旨在为城市结构中的爆炸后果开发一个快速运行的突破性模型。目的是利用实验和数值方法来描述冲击波沿直线街道的传播特性。冲击波是由气体炸药爆炸产生的。这些实验是应用相似定律在实验室规模上进行的。冲击波的研究采用了由规则分布的压力传感器记录的压力曲线。可视化还用于说明两面墙之间的各种冲击波相互作用。炸药被放置在两堵平行墙之间街道的中轴线上。根据街道的宽度和高度对冲击波传播进行了分析。结果表明,激波的传播方式由三维转变为二维。研究还表明,几个平面激波与两个马赫干的连接处有关。该研究揭示了二次激波以及多重激波,这可能导致对测量压力信号的解释具有一定的复杂性。确定了每种构型的三维到二维模态过渡区,并根据不同的实验结果建立了经验规律。法律考虑了三个参数,即炸药的直径和街道的尺寸(高度和宽度)。
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引用次数: 0
Selected topics from the 26th International Symposium on Military Aspects of Blast and Shock, Wollongong, Australia, December 3–8, 2023 2023年12月3日至8日,澳大利亚卧龙岗,第26届爆炸与冲击军事国际研讨会选题
IF 1.8 4区 工程技术 Q3 MECHANICS Pub Date : 2025-09-15 DOI: 10.1007/s00193-025-01251-3
D. L. Frost
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引用次数: 0
Blast and fragmentation modelling in urban environments using Rapid City Planner 使用Rapid City Planner在城市环境中建立爆炸和碎片模型
IF 1.8 4区 工程技术 Q3 MECHANICS Pub Date : 2025-08-06 DOI: 10.1007/s00193-025-01232-6
S. D. Ryan, N. J. McCormick, R. C. Ripley

It is important to understand the effects of explosions to ensure the safety of civilians and military personnel. Rapid City Planner (RCP) is a comprehensive software tool for predicting the effects of conventional and improvised explosive devices with geographic information system-based outcomes for munition safety, building/structure damage, protection of assets, and human vulnerability in real cities. Modelling cased explosives requires the consideration of casing fragmentation, which is modelled in RCP using three different methods having a different level of detail. The present study focuses on introducing and validating one of the methods, namely the fast primary fragmentation method. The fast fragmentation solver is used to simulate casing breakup of steel-cased cylindrical charges with various TNT- and RDX-based explosives. The predicted velocities were within less than one percent of theoretical Gurney velocities, and the fragment size distributions compared well with experimental data for each explosive. A TNT-filled artillery shell trial was used to validate the fast fragmentation solver in terms of polar distributions of initial fragment speed and number, as well as the spatial spread of fragment throw in a free-field environment. The RCP hydrocode solver is used to assess the equivalent bare charge model used by the fast fragmentation approach. The detailed and fast-modelling approaches produced similar peak overpressures, but underpredicted impulses, at standoff distances between 5 and 10 m (mid-to-far field range). The failure strain and fragment size distribution are shown to have little effect on the blast wave, whereas both would have a significant impact on subsequent fragment effects. Finally, a full-scale scenario was modelled in RCP to show blast and primary fragmentation effects in a coastal urban environment, including a demonstration of urban blast effects from blast pressure and primary fragment trajectories outcomes.

重要的是要了解爆炸的影响,以确保平民和军事人员的安全。快速城市规划(RCP)是一个综合性的软件工具,用于预测常规和简易爆炸装置的影响,并提供基于地理信息系统的结果,用于实际城市中的弹药安全、建筑/结构损坏、资产保护和人员脆弱性。对套管炸药进行建模需要考虑套管破片问题,在RCP中使用三种不同的方法对其进行建模,这些方法具有不同的详细程度。本研究重点介绍并验证了其中一种方法,即快速初级破碎法。利用快速破片求解器模拟了不同TNT和rdx炸药对钢壳圆柱装药破壳的影响。预测速度与理论格尼速度相差不到百分之一,而且每一种炸药的破片尺寸分布与实验数据比较良好。利用tnt填充炮弹试验,从破片初始速度和破片数量的极性分布以及破片抛掷的空间扩散等方面验证了快速破片求解器在自由场环境下的有效性。利用RCP氢码求解器对快速破片法所用的等效裸荷模型进行了求解。详细和快速的建模方法产生了类似的峰值超压,但在5到10米(中远场范围)之间的距离上,脉冲预测不足。破坏应变和破片尺寸分布对爆震波影响不大,但对后续破片效应影响较大。最后,在RCP中模拟了一个全尺寸场景,以显示沿海城市环境中的爆炸和初级破片效应,包括爆炸压力和初级破片轨迹结果的城市爆炸效应演示。
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引用次数: 0
Design of a novel nozzle for rocket engines with full flow at sea level 海平面全流火箭发动机新型喷管设计
IF 1.8 4区 工程技术 Q3 MECHANICS Pub Date : 2025-06-29 DOI: 10.1007/s00193-025-01236-2
Y. Z. Liu, Z. Wang, P. Li

To prevent flow separation under overexpanded conditions in traditional large-area-ratio nozzles of rocket engines at sea level, the method of characteristics for wall pressure control is adopted. This method, which is based on thrust-optimized contours, can be implemented to redesign the latter half of a divergent contour to ensure that the wall pressure of the new contour is not less than the critical separation pressure of 0.03 MPa. The newly generated nozzle is named the full-flow nozzle. Then, the design method is verified by simulations, and the performance of full-flow nozzles is evaluated. The results show that the method of wall pressure control can achieve the intended purpose, and the newly generated contour ensures that the nozzle is not only in the full-flow state at sea level but also able to withstand combustion chamber or ambient pressure fluctuations. The combustion chamber pressure is 8.5 MPa, and the specific heat ratio of hot gas is 1.144. Compared with the thrust-optimized contour with an area ratio of 40, in which the flow tends to separate at sea level, the full-flow nozzle can increase the area ratio to 60. Thus, the vacuum specific impulse can be increased by approximately 5.24 s. Compared with the thrust-optimized contour nozzle with an area ratio of 60, the vacuum specific impulse of the full-flow nozzle with an equal area ratio is decreased by 1.57 s.

传统的火箭发动机大面积比喷管在海平面上为防止过膨胀工况下的流动分离,采用了壁压特性控制方法。该方法基于推力优化轮廓,可实现对发散轮廓后半部分的重新设计,确保新轮廓的壁压不小于0.03 MPa的临界分离压力。新生成的喷嘴被命名为全流喷嘴。然后,通过仿真验证了设计方法,并对全流喷管的性能进行了评价。结果表明,壁面压力控制方法可以达到预期目的,新生成的轮廓保证了喷管在海平面上既处于满流状态,又能承受燃烧室或环境压力波动。燃烧室压力为8.5 MPa,热气体比热比为1.144。与面积比为40的推力优化轮廓相比,水流在海平面上趋于分离,全流喷管可以将面积比提高到60。因此,真空比脉冲可增加约5.24秒。与面积比为60的推力优化轮廓喷管相比,等面积比全流喷管的真空比冲减小了1.57 s。
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引用次数: 0
One-dimensional model predictions for the detonation diffraction critical tube diameter 爆轰衍射临界管径的一维模型预测
IF 1.8 4区 工程技术 Q3 MECHANICS Pub Date : 2025-06-27 DOI: 10.1007/s00193-025-01235-3
J. Klein, J. R. Klein, O. Samimi-Abianeh

Detonation diffraction leads to either successful transmission of the detonation or quenching wherein the propagation mechanism is attenuated. The transmission behavior is governed by competing effects of energy release, curvature, and unsteadiness. There is a potentially unique critical diameter that will determine the diffraction outcome for every combustible mixture composition at each set of initial conditions. The critical diffraction diameter has been correlated to several detonation parameters to date; however, these correlations all have limitations. Analytical or quasi-analytical solutions to the diffraction problem, specifically those able to predict the critical diameter, are scarce. The present work develops several critical diameter models by uniting previous work on diffraction phenomena and the critical initiation energy problem. Curvature, decay rate, and energy-based models are established, and their critical diameter predictions are compared against a wide range of experimental critical diameter data. While detonation diffraction is a complex multifaceted phenomenon, a curvature-based one-dimensional model in this work is shown to accurately reproduce empirical critical diameter behavior at relatively low computational cost.

爆轰衍射要么导致爆轰的成功传递,要么导致淬灭,其中传播机制被衰减。传输行为受能量释放、曲率和非稳定性的相互竞争影响。存在一个可能唯一的临界直径,它将决定每种可燃混合物组成在每组初始条件下的衍射结果。迄今为止,临界衍射直径已与几个爆轰参数相关联;然而,这些相关性都有局限性。衍射问题的解析解或准解析解,特别是那些能够预测临界直径的解,很少。本文结合前人关于衍射现象和临界起爆能问题的研究,建立了几个临界直径模型。建立了基于曲率、衰减率和能量的模型,并将它们的临界直径预测与广泛的实验临界直径数据进行了比较。虽然爆轰衍射是一个复杂的多面现象,但在这项工作中,基于曲率的一维模型被证明可以以相对较低的计算成本准确地再现经验临界直径行为。
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引用次数: 0
A practical numerical simulation approach for explosions in large-scale complex urban environments 大型复杂城市环境爆炸的实用数值模拟方法
IF 1.8 4区 工程技术 Q3 MECHANICS Pub Date : 2025-06-26 DOI: 10.1007/s00193-025-01234-4
Z. L. Hu, L. L. Ma, H. Wu, Q. Fang

In recent years, terrorist attacks and accidental explosions in urban environments have occurred frequently, causing severe damage, even collapse, of building structures, and have become a major concern of modern society. The need to design and evaluate the blast resistance of building structures is rising markedly. The utmost requirement is the determination of blast loads acting on building structures, i.e., the reflected overpressure of blast waves. To better keep the balance between computational efficiency and prediction accuracy of complex blast wave propagation and its interactions with buildings, a practical numerical simulation approach integrating multiple existing techniques including the multi-stage method, graded mesh, mapping, and un-refinement technique is proposed based on ANSYS/AUTODYN. Firstly, the propagation of blast waves is simplified into three stages, i.e., propagation in the free air from the explosion center to ground zero, propagation after the ground reflection, and interaction with building structures. These three stages are modeled by 1D uniform meshes and 2D/3D graded meshes with increasing mesh sizes. Then, the mapping technique, including mesh un-refinement, is adopted to transfer the predicted results at the previous stage into the next stage. The corresponding meshing strategy against the scaled distances Z ((Z = R / root 3 of {W}), where R is the distance between the detonation point and the target surface, W is the equivalent charge weight of TNT) for each stage is recommended through mesh sensitivity analyses. Finally, the proposed approach and mesh sizes are validated against four series of explosive tests for a single house, an intersection, and two city blocks by comparing with both the overpressures and impulses of blast waves. Additionally, two solvers, i.e., Euler FCT and Euler multi-material, are compared. The former solver is recommended due to its greater efficiency and accuracy. The present work could provide a helpful reference for the blast-resistant design and evaluation of urban building structures.

近年来,城市环境中的恐怖袭击和意外爆炸事件频发,造成建筑结构严重损坏甚至倒塌,已成为现代社会关注的主要问题。建筑结构抗震设计与评价的需求日益增加。最大的要求是确定作用在建筑结构上的爆炸荷载,即爆炸波的反射超压。为了更好地平衡复杂冲击波传播及其与建筑物相互作用的计算效率和预测精度,基于ANSYS/AUTODYN,提出了一种综合多阶段法、梯度网格法、映射法、非细化技术等多种现有技术的实用数值模拟方法。首先,将爆炸波的传播过程简化为三个阶段,即从爆炸中心到地面零点的自由空气传播阶段、经过地面反射后的传播阶段和与建筑结构的相互作用阶段。这三个阶段分别采用一维均匀网格和二维/三维渐变网格模型,网格尺寸逐渐增大。然后,采用映射技术,包括网格不细化,将前一阶段的预测结果传递到下一阶段。通过网格敏感性分析,推荐每段对应距离Z ((Z = R / root 3 of {W}), R为爆点与目标表面之间的距离,W为TNT当量装药重量)的网格策略。最后,通过比较爆炸冲击波的超压和脉冲,在单个房屋、十字路口和两个城市街区的四组爆炸试验中验证了所提出的方法和网格尺寸。并对Euler FCT和Euler multi-material两种求解方法进行了比较。建议采用前一种求解方法,因为它具有更高的效率和准确性。本研究可为城市建筑结构的抗震设计和评价提供有益的参考。
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引用次数: 0
Experimental and numerical studies of a near-field blast loading model for cylindrical charges 圆柱装药近场爆炸载荷模型的实验与数值研究
IF 1.8 4区 工程技术 Q3 MECHANICS Pub Date : 2025-06-25 DOI: 10.1007/s00193-025-01229-1
S.-L. Liang, J. Yu, L. Chen

In the current practice of blast-resistant design, blast loads are determined by the Kingery and Bulmash charts in accordance with a database of free-air blasts of spherical charges and surface bursts of hemispherical charges initiated at the center. However, most charges are closer to cylinders in geometry. In addition, charge shapes and initiation configurations significantly affect blast loads under a near-field blast scenario. Therefore, it is imperative to develop a near-field blast loading model for cylindrical charges that can account for the effects of both charge shape and initiation configuration in blast-resistant design. Compared with incident blast loads, reflected blast loads are more relevant because the latter can be directly used for blast-resistant design. Accordingly, in this paper, experimental and numerical studies were performed to develop a near-field blast loading model for cylindrical charges in terms of the peak reflected overpressure and the maximum reflected impulse. Two series of tests were conducted with either one-end-initiated or both-end-initiated cylindrical charges to obtain reflected blast loads with different scaled distances. It was found that the spatial distribution of blast loads along the axial direction of the charges was extremely non-uniform. Then, high-efficiency numerical models were built using 2D to 3D mapping techniques. After being validated against experimental results, numerical models were employed to simulate the blast loads generated by cylindrical charges with different length-to-diameter ratios and initiation configurations (one-end, center, and both-end initiations) with scaled distances ranging from 0.2 to 1.0 m/kg(^{mathrm {1/3}}). To develop the blast loading model, the peak reflected overpressure and the maximum reflected impulse at the center of a rigid reflection surface were firstly determined by curve fitting as the benchmark blast loads, which were expressed as functions of scaled distance and length-to-diameter ratio, and then the benchmark blast loads were used to normalize the blast loads at different locations. Accordingly, the spatial distribution of blast loads can be described with the benchmark blast loads and a spatial load distribution function, in which the latter is determined by surface fitting of extensive numerical results. The results indicate that the blast loading model developed is able to predict the blast load with considerable accuracy.

在目前的防爆设计实践中,爆炸载荷由Kingery和Bulmash图根据球形装药的自由空气爆炸和在中心起爆的半球形装药的表面爆炸数据库确定。然而,大多数电荷在几何上更接近圆柱体。此外,在近场爆炸情况下,装药形状和起爆结构显著影响爆炸载荷。因此,在抗爆设计中,建立一个考虑装药形状和起爆形态影响的圆柱装药近场爆炸载荷模型势在必行。与入射爆炸载荷相比,反射爆炸载荷更重要,因为后者可以直接用于抗爆设计。因此,本文通过实验和数值研究,建立了圆柱装药的峰值反射超压和最大反射冲量的近场爆炸加载模型。采用一端起爆和两端起爆的圆柱形装药进行了两组试验,以获得不同比例距离下的反射爆炸载荷。结果表明,爆炸载荷沿装药轴向的空间分布极不均匀。然后,利用二维到三维映射技术建立了高效的数值模型。在与实验结果进行对比验证后,采用数值模型模拟了不同长径比和起爆构型(一端起爆、中心起爆和两端起爆)的圆柱形装药产生的爆炸载荷,比例距离为0.2 ~ 1.0 m/kg (^{mathrm {1/3}})。为了建立爆炸载荷模型,首先通过曲线拟合确定刚性反射面中心的反射超压峰值和最大反射冲量作为基准爆炸载荷,并将其表示为缩放距离和长径比的函数,然后利用基准爆炸载荷对不同位置的爆炸载荷进行归一化。因此,爆炸载荷的空间分布可以用基准爆炸载荷和空间载荷分布函数来描述,其中空间载荷分布函数是通过对大量数值结果的曲面拟合来确定的。结果表明,所建立的爆炸荷载模型能够较准确地预测爆炸荷载。
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引用次数: 0
Soil-filled perimeter walls under blast 爆破下的填土外墙
IF 1.8 4区 工程技术 Q3 MECHANICS Pub Date : 2025-06-18 DOI: 10.1007/s00193-025-01223-7
M. L. Ruiz-Ripoll, C. Roller, H. Dirlewanger, A. Stolz

Soil-filled gabion systems can be used in many civil applications such as retaining walls against flooding and erosion or shoreline protection. In addition, the gabion systems provide good resistance in high dynamic loading scenarios such as blast events. These systems allow for a modular setup of easy-to-use perimeter walls with variable height and cross section, application as a gravity wall, and use of local filling material. The latter is the subject of the present paper. Depending on aggregate size and morphology, size distribution, and humidity, soil materials exhibit different material properties such as compaction parameters, cohesion, and the angle of friction among others. Each of these parameters directly affects the structure’s response under highly dynamic conditions. To understand the influence of varying soil parameters at varying loading conditions and thus to predict the structure’s behavior precisely, the authors investigated soil-filled perimeter walls experimentally and using hydrocode simulations. Since the soil’s properties primarily influence the wall’s behavior—at the resistance side—an extensive laboratory test campaign was required to characterize different soils. The experimental data serve for the derivation of dynamic material models and are complemented by numerical simulations. Furthermore, this paper describes the execution of near-field detonation and shock tube tests of soil-filled perimeter walls to analyze their load-bearing behavior under blast load. The experiments are evaluated with regard to the failure mechanism as well as the blast mitigation. Additionally, the blast mitigation effect is numerically investigated and the results are compared to the experiments.

填土格宾网系统可用于许多民用应用,如挡土墙,防止洪水和侵蚀或海岸线保护。此外,格宾笼系统在高动态载荷情况下(如爆炸事件)具有良好的抗冲击性。这些系统允许模块化设置易于使用的周墙,具有可变高度和横截面,应用于重力墙,并使用当地填充材料。后者是本文的主题。根据骨料粒度和形态、粒度分布和湿度的不同,土壤材料表现出不同的材料特性,如压实参数、黏聚力和摩擦角等。这些参数中的每一个都直接影响结构在高动力条件下的响应。为了了解不同荷载条件下不同土壤参数的影响,从而准确预测结构的行为,作者通过实验和hydrocode模拟研究了填土周墙。由于土壤的性质主要影响墙的行为(在阻力方面),因此需要进行大量的实验室测试来表征不同土壤的特征。实验数据可用于动态材料模型的推导,并可通过数值模拟加以补充。此外,本文还介绍了填土周墙近场爆轰和激波管试验的实施情况,以分析其在爆炸荷载作用下的承载性能。从破坏机理和爆破缓解两方面对试验进行了评价。此外,还对爆破减缓效果进行了数值研究,并与实验结果进行了比较。
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引用次数: 0
A parametric analysis of streamwise vortices on a compression ramp at Mach 4 马赫数为4的压缩坡道上流向涡的参数分析
IF 1.8 4区 工程技术 Q3 MECHANICS Pub Date : 2025-06-17 DOI: 10.1007/s00193-025-01239-z
K. Dixit, R. R. Kumar, N. R. Vadlamani, N. Tsuboi

Large-eddy simulations are conducted to investigate supersonic flow over a compression ramp at a free stream Mach number of 4.0 and a unit Reynolds number of (4.56 times 10^{6}) per meter. Two ramp angles of (15^circ ) and (18^circ ) are considered along with three different ramp positions (P1, P2, and P3) from the plate leading edge, with the plate length increasing progressively from P1 to P3. Simulations reveal that with an increase in the plate length and ramp angle, the separation point shifts downstream, accompanied by an extended separation length. Furthermore, with an increase in the ramp angle and plate length, a higher Görtler number is observed upstream of the reattachment indicating a greater likelihood of Görtler instability. In particular, no streamwise vortices were observed for the 15P1 and 15P2 cases, while for the 18P3 case, increased instability resulted in the breakdown of streamwise vortices, driving the transition to turbulence. The wavelength of streamwise streaks decreased by approximately (15%) as the plate length increased by (approx 80%) from 18P1 to 18P3. Unsteady analysis revealed the role of spanwise secondary instabilities over these vortices, that trigger turbulent spots that propagate at a speed of (approx 0.6 U_{infty }). The peak value of the Stanton number is found to be (approx ) 15–27% higher than the time and span-averaged value for the 15P3 and 18P3 cases, highlighting a strong effect of downwash due to streamwise vortices on the wall heating rate distribution. The unsteady data also reveal a negative correlation between the flow reattachment location and the Stanton number close to the reattachment point. An earlier reattachment is shown to increase the Stanton number and vice versa resulting in a (approx 40%) variation compared to the time-averaged value. The results from this study underscore the critical influence of plate length on the formation of streamwise vortices, with significant implications for wall heating rate distribution and flow transition dynamics.

在自由流马赫数为4.0、单位雷诺数为(4.56 times 10^{6}) / m时,对压缩坡道上的超声速流动进行了大涡模拟。考虑了两个斜坡角(15^circ )和(18^circ )以及三个不同的斜坡位置(P1, P2和P3),从板前缘,板的长度逐渐增加,从P1到P3。仿真结果表明,随着平板长度和斜坡角的增大,分离点向下游移动,分离长度也随之延长。此外,随着斜坡角和钢板长度的增加,在再附着的上游观察到更高的Görtler数,表明更有可能发生Görtler不稳定。特别是在15P1和15P2中没有观测到流向涡,而在18P3中,不稳定性的增加导致了流向涡的破坏,推动了向湍流的过渡。从18P1到18P3,随着板长增加(approx 80%),流向条纹的波长大约减少(15%)。非定常分析揭示了这些涡旋上沿展向的次级不稳定性的作用,它触发了以(approx 0.6 U_{infty })速度传播的湍流点。斯坦顿数的峰值为(approx ) 15-27% higher than the time and span-averaged value for the 15P3 and 18P3 cases, highlighting a strong effect of downwash due to streamwise vortices on the wall heating rate distribution. The unsteady data also reveal a negative correlation between the flow reattachment location and the Stanton number close to the reattachment point. An earlier reattachment is shown to increase the Stanton number and vice versa resulting in a (approx 40%) variation compared to the time-averaged value. The results from this study underscore the critical influence of plate length on the formation of streamwise vortices, with significant implications for wall heating rate distribution and flow transition dynamics.
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Shock Waves
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