Layer Model Research Articles

Lyapunov-Stable Deep Equilibrium Models

Deep equilibrium (DEQ) models have emerged as a promising class of implicit layer models, which abandon traditional depth by solving for the fixed points of a single nonlinear layer. Despite their success, the stability of the fixed points for these models remains poorly understood. By considering DEQ models as nonlinear dynamic systems, we propose a robust DEQ model named LyaDEQ with guaranteed provable stability via Lyapunov theory. The crux of our method is ensuring the Lyapunov stability of the DEQ model's fixed points, which enables the proposed model to resist minor initial perturbations. To avoid poor adversarial defense due to Lyapunov-stable fixed points being located near each other, we orthogonalize the layers after the Lyapunov stability module to separate different fixed points. We evaluate LyaDEQ models under well-known adversarial attacks, and experimental results demonstrate significant improvement in robustness. Furthermore, we show that the LyaDEQ model can be combined with other defense methods, such as adversarial training, to achieve even better adversarial robustness.

The existence and nonlinear stability of stationary solutions to outflow problem for a reduced gravity two and a half layer model

The main concern of this paper is to study large-time behavior of solutions for an outflow problem to the reduced gravity two and a half layer model in a half space. We establish the existence of stationary solutions and further obtain the large time asymptotic stability of small-amplitude stationary solutions provided that the initial perturbation is sufficiently small. Moreover, we obtain the convergence rate of the solution toward the stationary solution in some weighted Sobolev spaces only for the supersonic case. The proof is based on the basic energy method. A key point for the proof of convergence rates is to capture the positivity of the temporal energy dissipation functional and boundary terms with suitable space weight functions either algebraic or exponential depending on whether or not the incoming far-field velocity satisfy some additional conditions.

Effect of Rim Seal Geometry on Rotationally-Driven Ingestion

Abstract This study investigates turbine rim seal geometry effects within the rotationally-driven ingestion regime. Computations were performed with a wall-resolved unsteady Reynolds-averaged Navier–Stokes (URANS) model and a large-eddy simulation (LES) model including near-wall boundary layer modeling, that is, wall-modeled LES (WMLES). Use of simplified rim sealing models is proposed as an efficient method of ranking seal designs and investigating sensitivity to seal geometry. Four rim seal configurations, two chute seals, an axial seal and a radial seal which are representative of those used in gas turbines and in previous research were investigated. Furthermore, hybrid seals combining geometric characteristics from both the chute and radial seal were considered. Significant sensitivities of sealing performance to turbulence modeling are identified, but URANS and WMLES show similar trends in ranking of seal performance, and these are consistent with previous experimental work. The addition of an outer radial clearance section to a chute seal is effective in reducing ingestion levels.

A review on natural fiber composites: Polymer matrices, fiber surface treatments, fabrication methods, properties, and applications

AbstractHigh performance and durability are essential for goods to satisfy the needs of the expanding worldwide market. Wood plastic composites (WPCs) are materials made from a combination of wood, polymers, and additives. WPCs can be extruded, injected, compressed, or thermoformed. Presently, WPCs are manufactured using sophisticated processes including as laser sintering, fused layer modeling, and additive manufacturing. Properly managing the melt temperature and pressure is crucial in the manufacturing process of WPCs to ensure effective polymer incorporation. Natural fibers have distinct benefits for polymer composites, but they also have some serious drawbacks, like lower strength properties—especially lower impact strength than synthetic fibers—poor compatibility with hydrophobic polymers, poorer dimensional stability and moisture absorption due to hydroxly groups, a maximum processing temperature that is limited, thermal degradation above 200–220°C, and lower biological durability. The modification of the surface of the fibers improves the mentioned disadvantages of the natural fibers. High‐quality WPCs require the application of chemical or physical treatment to the wood fibers. This extensive review focused on the modification techniques applied to the surface of wood, manufacturing processes, and properties and applications of WPCs.Highlights Modification methods used in surface treatment of natural fibers was explained. Properties and recent applications of wood polymer composites were given. Optimum requirements of natural fibers and polymer matrices are given. Fabrication methods of natural fiber composites are extensively given.

Machine learning surrogates for surface complexation model of uranium sorption to oxides

The safety assessments of the geological storage of spent nuclear fuel require understanding the underground radionuclide mobility in case of a leakage from multi-barrier canisters. Uranium, the most common radionuclide in non-reprocessed spent nuclear fuels, is immobile in reduced form (U(IV) and highly mobile in an oxidized state (U(VI)). The latter form is considered one of the most dangerous environmental threats in the safety assessments of spent nuclear fuel repositories. The sorption of uranium to mineral surfaces surrounding the repository limits their mobility. We quantify uranium sorption using surface complexation models (SCMs). Unfortunately, numerical SCM solvers often encounter convergence problems due to the complex nature of convoluted equations and correlations between model parameters. This study explored two machine learning surrogates for the 2-pK Triple Layer Model of uranium retention by oxide surfaces if released as U(IV) in the oxidizing conditions: random forest regressor and deep neural networks. Our surrogate models, particularly DNN, accurately reproduce SCM model predictions at a fraction of the computational cost without any convergence issues. The safety assessment of spent fuel repositories, specifically the migration of leaked radioactive waste, will benefit from having ultrafast AI/ML surrogates for the computationally expensive sorption models that can be easily incorporated into larger-scale contaminant migration models. One such model is presented here.

Extension, development, and evaluation of the representation of the OH-initiated dimethyl sulfide (DMS) oxidation mechanism in the Master Chemical Mechanism (MCM) v3.3.1 framework

Abstract. Understanding dimethyl sulfide (DMS) oxidation can help us constrain its contribution to Earth's radiative balance. Following the discovery of hydroperoxymethyl thioformate (HPMTF) as a DMS oxidation product, a range of new experimental chamber studies have since improved our knowledge of the oxidation mechanism of DMS and delivered detailed chemical mechanisms. However, these mechanisms have not undergone formal intercomparisons to evaluate their performance. This study aimed to synthesise the recent experimental studies and develop a new, near-explicit, DMS mechanism, through a thorough literature review. A simple box model was then used with the mechanism to simulate a series of chamber experiments and evaluated through comparison with four published mechanisms. Our modelling shows that the mechanism developed in this work outperformed the other mechanisms on average when compared to the experimental chamber data, having the lowest fractional gross error for 8 out of the 14 DMS oxidation products studied. A box model of a marine boundary layer was also run, demonstrating that the deviations in the mechanisms seen when comparing them against chamber data are also prominent under more atmospherically relevant conditions. Although this work demonstrates the need for further experimental work, the mechanism developed in this work has been evaluated against a range of experiments, which validate the mechanism and reduce the bias from individual experiments. Our mechanism provides a good basis for a near-explicit DMS oxidation mechanism that would include other initiation reactions (e.g. halogens) and can be used to compare the performance of reduced mechanisms used in global models.

Multiscale optimization on polymer-based rejuvenators for the efficient recycling of aged high-viscosity modified asphalt: Molecular dynamics simulation and experimental analysis

With the depletion of fossil fuels, the advancement of efficient pavement recycling technology has garnered widespread attention, which contributes to the promotion of sustainable economic and environmental development. The polymers in polymer-based composite rejuvenators (PBCRs) are the key to restoring the performance of aged high-viscosity modified asphalt (HVMA). To optimize the polymers in PBCRs, this study investigates the rejuvenation effect and interface diffusion mechanism of various PBCRs using molecular dynamics simulation and experimental analysis. First, four PBCRs with different polymer components were designed, and their impact on the performance of weather-aged HVMA were examined using the rheological test, low-temperature force ductility test, crack resistance test, and aging resistance test. Subsequently, the rejuvenation effects of four PBCRs were ranked using the comprehensive performance radar chart. Finally, molecular models and layer models of weather-aged HVMA and four PBCRs were constructed, and the diffusion fusion process and interaction mechanism were analyzed using the molecular dynamics simulation. The findings indicate that PBCRs can rebuild the polymer network structure, partially restore the rheology, elastic recovery, and low-temperature ductility of aged HVMA. Additionally, PBCRs significantly reduce the crack potential of aged HVMA and ensure satisfactory aging resistance. Molecular dynamics simulation shows that due to the differences in their molecular structures, the diffusion ability of PBCRs is ranked as follows: crumb rubber rejuvenator (CR + R) > SBR rejuvenator (SBR + R) > SBS rejuvenator (SBS + R) > HVM rejuvenator (HVM + R). In summary, SBS + R proves most effective in regulating asphalt components and rebuilding the polymer network structure, but its interfacial diffusion ability is inferior to CR + R and SBR + R. CR + R has the highest diffusion coefficient, but its rejuvenation effect is not ideal. HVM + R is slightly less effective at rejuvenation than SBS + R, but has the worst diffusion capacity. The rejuvenation effect and diffusion ability of SBR + R are both not ideal. This study has significant implications for optimizing the polymers in PBCRs and promoting the efficient rejuvenation and eco-friendly sustainable development of HVMA.

Multi-machine benchmark of the self-consistent 1D scrape-off layer model DIV1D from stagnation point to target with SOLPS-ITER

This paper extends a 1D dynamic physics-based model of the scrape-off layer (SOL) plasma, DIV1D, to include the core SOL and possibly a second target. The extended model is benchmarked on 1D mapped SOLPS-ITER simulations to find input settings for DIV1D that allow it to describe SOL plasmas from upstream to target—calibrating it on a scenario and device basis. The benchmark shows a quantitative match between DIV1D and 1D mapped SOLPS-ITER profiles for the heat flux, electron temperature, and electron density within roughly 50% on: (1) the Tokamak Configuration Variable (TCV) for a gas puff scan; (2) a single SOLPS-ITER simulation of the Upgraded Mega Ampere Spherical Tokamak; and (3) the Upgraded Axially Symmetric Divertor EXperiment in Garching Tokamak (AUG) for a simultaneous scan in heating power and gas puff. Once calibrated, DIV1D self-consistently describes dependencies of the SOL solution on core fluxes and external neutral gas densities for a density scan on TCV whereas a varying SOL width is used in DIV1D for AUG to match a simultaneous change in power and density. The ability to calibrate DIV1D on a scenario and device basis is enabled by accounting for cross field transport with an effective flux expansion factor and by allowing neutrals to be exchanged between SOL and adjacent domains.

Deep neural network surrogate for surface complexation model of metal oxide/electrolyte interface

HypothesisSurface Complexation Models (SCM) are one of the most successful geochemical thermodynamics models of the speciation and charging of the mineral/electrolyte interface. However, finding unique and transferable SCM parameter values by fitting experimental data using existing numerical solvers is often challenging. We hypothesized that SCM surrogates built using Artificial Intelligence algorithms provide an alternative strategy for determining model parameter values and thus offer an ultrafast prediction of electrical double layer characteristics of metal oxide/electrolyte interface. ExperimentsWe generated synthetic datasets of surface charge and electrokinetic potential as a function of pH, ionic strength, varying site densities, acidity, and ion-affinities of mineral surfaces using the 2-pK Triple Layer Model - one of the most used generic SCM. We explored a wide range of types of mineral surfaces using random walks in the parameter space. Next, we trained and validated two AI surrogates using our synthetic SCM data. FindingsWe showed that AI-SCM surrogates for oxide/electrolyte interfaces are possible and cost-effective. They allow ultrafast and accurate SCM parametrization using synthetic data. AI-SCM can predict thermodynamic parameters from just a few titration data points, such as ion affinities and proton binding constants. What is more, the computational strategy we presented here to surrogate geochemical models by pre-trained AI architectures is more universal and can be applied to other geochemical/thermodynamic models – replacing the computationally expensive solvers with trained AI, thus minimizing computing costs and speeding up data analysis.

Anisotropic turbulence modeling of the atmospheric surface layer: Validation of novel model settings and comparison with traditional two-equation models in flows over complex terrain

For atmospheric flows, the limitations of the eddy viscosity assumption are even more critical in cases involving complex terrain and features, where secondary strains are influential. Reynolds Stress Models (RSMs) can account for these effects, but their numerical stiffness and crucially the lack of established guidelines for modelers regarding the appropriate boundary conditions and model settings, as exist for eddy-viscosity models (EVMs), have led to limited adoption. In order to circumvent the shortcomings of EVMs, the focus has been directed at large eddy simulations (LES), which have greater computational requirements that can be prohibitive. Thus, this work aims to extend the traditional methodology that has been applied to adapt EVMs to atmospheric flows to an RSM that incorporates near-ground effects. This results in suggestions for new model constants and novel boundary conditions, which can easily be adapted according to local atmospheric parameters and employed by modelers. The performance of the proposed RSM is compared with four distinct EVMs through real-life cases representing two distinct complex terrain configurations. The results showed that the RSM indeed outperformed the EVMs, and it was found that only its anisotropic formulation could capture more complex flow features that were observed experimentally.

Neural network and thermodynamic optimization of magnetized hybrid nanofluid dissipative radiative convective flow with energy activation

This article, motivated by hybrid magnetic coating manufacturing developments, utilizes a neural network-based computational program to study the dynamics of hybrid magnetic nanofluids with entropy generation. A new physico-chemo-mathematical model has been presented to simulate the hybrid magnetic nano-coating flow along a stretching surface to a porous medium with viscous heating. A Rosseland flux model is used for radiation heat transfer and Darcy’s model for the isotropic porous medium. The stretching sheet is porous, and wall suction or injection are possible. A robust neural network has been deployed to optimize the physical parameters controlling the transport characteristics of hybrid nanofluids. Specifically, two hybrid nanoparticle combinations are addressed, namely graphite oxide (GO)-molybdenum disulfide ( Mo S 2 ) and copper (Cu)-silicon dioxide ( Si O 2 ), both with engine oil as the base fluid. The dimensional boundary layer model is transformed via suitable scaling variables from a partial differential system into a dimensionless non-linear coupled ordinary differential system. The transformed boundary value problem is solved numerically with the BVP4C subroutine in the symbolic software MATLAB, which achieves exceptional accuracy. Validation with previous simpler studies is conducted and a good correlation is obtained. The neural network optimization analysis incorporates Bayesian regularization as the training algorithm. The Bejan entropy generation minimization (EGM) analysis shows that with increasing radiation parameter R d , both entropy generation rate and Bejan number are increased. Furthermore, an elevation in Brinkman number Br leads to an upsurge in entropy generation rate and a downtrend in the Bejan number. The numerical solution of the boundary value problem reveals that with an increment in nanoparticle solid volume fraction φ 2 , magnetic parameter M , inverse permeability parameter ϵ , surface injection parameter ( s < 0 ) , Eckert number Ec and radiation parameter R d and with a decrement in suction parameter ( s > 0 ) and Prandtl number Pr , there is a strong enhancement in temperature magnitude and thermal boundary layer thickness. With greater nanoparticle solid volume fraction φ 2 , magnetic parameter M , inverse permeability parameter ϵ , suction parameter s and a reduction in thermal buoyancy parameter λ , strong flow deceleration is induced, and momentum boundary layer thickness is increased. The skin friction coefficient is substantially boosted with lower values of magnetic parameter M , inverse permeability parameter ϵ , suction parameter s and higher values of thermal buoyancy parameter λ . There is a significant decrement also computed in Nusselt number with a greater radiation parameter R d . The simulations provide a good benchmark for future extensions that may consider non-Newtonian behavior.

Conduction mechanism analysis and modeling of different gas diffusion layers for PEMFC to improve their bulk conductivities via microstructure design

Increasing the conductivity of gas diffusion layers (GDLs) is an important way to improve the output performance of polymer electrolyte membrane fuel cells (PEMFCs). However, the complex porous fiber structures of GDLs significantly enhances the difficulty of quantitatively altering their conductivity which is determined by the carbon fibers and the conduction characteristics between fibers. In addition, the microstructures of various types of GDLs are different. Thus, it is a considerable challenge to explore the conductive mechanisms of these porous materials and optimize their structures to reduce their bulk resistances. In this work, a mathematical graph theory model that applies to the through-plane (T-P) bulk resistance prediction of two types of commonly used GDLs, carbon paper and carbon felt, is established to explain their different micro conduction mechanisms in depth. In addition to the number of fiber contact points, their distribution, as well as the resistance of the carbon fibers, are all important factors affecting the T-P conductivity. Optimizing fiber density and fiber diameter can significantly improve the T-P conductivity of carbon paper. In comparison, making the structure of carbon felt more compact so that the distribution of its contact points in the T-P direction can be more uniform will be more effective for the reduction of its T-P bulk resistance. Meanwhile, the T-P bulk resistance of carbon paper can also be effectively improved by optimizing the content and distribution of the binders. A method to decline the bulk resistance of carbon paper by aggregating the binders in the in-plane (IP) direction is proposed. The simulation results show that it can reduce the T-P bulk resistance of carbon paper by about 19.9% at a compressive stress of 1.5 MPa. This study provides further guidance for optimizing the structural designs of GDLs to optimize their conduction performance.

Lidar Observations of the Fe Layer in the Mesopause and Lower Thermosphere over Beijing (40.5° N, 116.0° E) and Mohe (53.5° N, 122.4° E)

Lidar observations of metal layers play a significant role in research on the chemistry and dynamics of the mesosphere and lower thermosphere. This work reports on Fe lidar observations conducted in Beijing and Mohe. Utilizing the same laser emission system, a 1064 nm seed laser was injected into an Nd: YAG laser to generate a single longitudinal-mode pulse 532 nm laser, which pumped a dye laser to produce a 572 nm laser. The 572 nm laser and the remaining 1064 nm fundamental frequency laser passed through a sum–frequency module to generate a 372 nm laser to detect the Fe layer. According to a total of 52.6 h of observations for 10 nights in Beijing, the Fe layer has an average column density of 1.24 × 1010 cm−2, an RMS width of 4.4 km and a centroid altitude of 89.4 km. In Mohe, observed for 16 nights and a total of 91.5 h, the Fe layer has an average column density of 1.08 × 1010 cm−2, an RMS width of 4.6 km and a centroid altitude of 89.5 km. The probability of the occurrence of sporadic Fe layers was 42.4% in Beijing and 29.4% in Mohe. Compared to simultaneously observed Na layers, the occurrence probabilities of sporadic Fe layers were higher than those of sporadic Na layers in both stations. Based on the two cases observed in Beijing, it is conjectured that the formation mechanism of sporadic metal layers above approximately 100 km has a more significant influence on sporadic Fe layers than on sporadic Na layers. The lower thermospheric Fe layers with densities significantly larger than those of the main layer were observed during two nights in Mohe. This work contributes to the refinement of the global distribution of Fe layers and provides abundant observational data for the modeling and study of the metal layers.

Virtual simulation of weld morphology for V-groove multi-layer welding

In order to study the virtual simulation of weld morphology for V-groove multi-layer welding, the prediction of characteristic parameters for weld morphology was realized by constructing the neural network models between the characteristic parameters and process parameters of different layers. At the same time, the virtual models of different layers were established according to the characteristic parameters of weld morphology and the structure parameters of V-groove. Combined with the prediction model and the virtual model, the process parameters were associated with the weld morphology, and the virtual simulation of weld morphology was realized. In the process of establishing the virtual model, first of all, the virtual model of root weld is established. Then, the virtual model of filling layer is established based on the root layer, and the virtual model of weaving layer is established based on the filling layer. Finally, validation experiments were carried out to verify the accuracy of the model. Verification results show that the prediction model can effectively predict the characteristic parameters of each layer, and the average relative errors of melting depth and width were less than 8%. The virtual simulation morphology has a high consistency with the actual morphology, and the average relative error of cross section area was less than 10%.

Constant charge method or constant potential method: Which is better for molecular modeling of electrical double layers?

In molecular modeling of electrical double layers (EDLs), the constant charge method (CCM) is prized for its computational efficiency but cannot maintain electrode equipotentiality like the more resource-intensive constant potential method (CPM), potentially leading to inaccuracies. In certain scenarios, CCM can yield results identical to CPM. However, there are no clear guidelines to determine when CCM is sufficient and when CPM is required. Here, we conduct a series of molecular simulations across various electrodes and electrolytes to present a comprehensive comparison between CCM and CPM under different charging modes. Results reveal that CCM approximates CPM effectively in capturing equilibrium EDL and current-driven dynamics in open electrode systems featuring ionic liquids or regular concentration aqueous electrolytes, while CPM is indispensable in scenarios involving organic and highly concentrated aqueous electrolytes, nanoconfinement effects, and voltage-driven dynamics. This work helps to select appropriate methods for modeling EDL systems, prioritizing accuracy while considering computational efficiency.

Hybrid RANS/LES modeling of hypersonic turbulent boundary layers with cold walls

Various strategies for hybrid RANS/LES modeling of hypersonic turbulent boundary layers subjected to strong wall-cooling are developed and analyzed. By defining a turbulent thermal length scale, the eddy viscosity and diffusivity of the hybrid model are calculated by the same formula, ℓ2ω. This allows a similar blending of the length scales and the development of analogous dynamic models for turbulent stress and heat flux. The dynamic procedure is applied to heat transfer by equating norms, rather than invoking least-squares with a lower bound, which improves robustness. The shielding function, as used in detached eddy simulations models, is revised to prevent a spurious early switch from the RANS to the LES mode. This revision significantly improves the accuracy of hybrid models on coarse grids. Finally, the proposed models are tested and validated for Mach numbers between 2.5 and 14, and wall-to-recovery temperature ratios between 0.18 and 1.

Link Prediction Based on Feature Mapping and Bi-Directional Convolution

A considerable amount of research on link prediction has recently been driven by missing relationships between knowledge graph entities and the problem of the incompleteness of knowledge graphs. Some recent studies have shown that convolutional neural networks based on knowledge embeddings are highly expressive and have good performance in link prediction. However, we found that the convolutional neural network (CNN)-based models do not handle the link between relations and entities well. For this reason, this paper proposes a link prediction model (LPM) based on feature mapping and bi-directional convolution. For the modeling of the task, an encoding layer–mapping layer–decoding layer structure is used. Among these layers, the encoding layer adopts a graph attention network to encode multi-hop triad information and obtains richer encoding of entities and relationships. The mapping layer can realize the mapping transformation between entities and relations and project the entity encoding in the space of relation encoding to capture the subtle connection between entities and relations. The decoding layer adopts bidirectional convolution to merge and decode the triples in a sequential inverse order, which makes the decoding layer model more advantageous in prediction. In addition, the decoding layer also adopts the r-drop training method to effectively reduce the distribution error generated by training between models and enhance the robustness of the model. Our experiments demonstrated the effectiveness of mapping relations, bidirectional convolution, and r-drop, and the accuracy of the proposed model showed significant improvements for each evaluation metric on two datasets, WN18RR and FB15k-237.

Verifying turbulence models in the atmospheric boundary layer by acoustical means

The impacts of turbulence on sound propagation in the atmospheric boundary layer (ABL) are important in many practical applications such as acoustic source localization, sonic boom propagation, and auralization of flying aircraft. However, turbulence impacts can vary dramatically in response to changing meteorological conditions. To address this issue, a turbulence spectral model has been introduced that captures the complexities of turbulence generation by wind shear, buoyancy instabilities, and ground blocking in the ABL. An experiment on vertical and slanted sound propagation through the ABL was conducted to verify the model. Various statistical characteristics of sound signals, including variances of the log-amplitude and phase fluctuations, coherences, and signal probability distributions were measured and compared to theoretical predictions. The dependence of the statistics on meteorological conditions was found to be accurately predicted in conditions of well-developed turbulence, as occurs in windy conditions and the daytime. Predictions in conditions of weak and intermittent turbulence, as often occur at night and around sunrise and sunset, remain challenging.

A comprehensive review on the modeling of tropical cyclone boundary layer wind field

Tropical cyclone (TC) wind field models are becoming increasingly sophisticated and complex. This review systematically discusses a range of models capable of simulating TCs in terms of modifications or simplifications of the governing equation, the Navier–Stokes equations, as a starting point. The discussion focuses on linear models, which include slab models, height-resolving models, and numerical simulation methods, respectively. The linear model offers quick calculations and insights into physical mechanisms, while slab models have limitations in capturing important processes and site conditions. The height-resolving model is widely used for Monte Carlo simulations, providing realistic three-dimensional wind structures. Nonlinear simulations yield reliable results for typhoon trajectory prediction, although they require specific boundary and initial conditions. Integration of nonlinear simulation with artificial intelligence and machine learning shows promise for faster typhoon prediction. However, challenges remain in terms of data training for machine learning models. Future advancements in these areas have the potential to enhance hazard assessment and weather forecasting.

Forced ignition modeling of methane-ethylene mixtures in scramjet combustors

To propose a design guideline for a scramjet combustor at low cost, an ignition model for a scramjet combustor is required. Therefore, the overall aim of this study was to propose an ignition model that could be used to estimate the forced ignition limits within a cavity. In this study, we developed two forced ignition models (FIMs): the forced ignition model in the recirculating zone (FIMR) and the forced ignition model in the shear layer (FIMS). We evaluated the forced ignition limits using a micro-rocket torch within a scramjet combustor. The validated results of the FIMs indicated that the modified FIMR incorporating cavity refresh time (defined as the time required for complete replacement of all gases in the cavity) was the most appropriate method for calculating the forced ignition limit within the recirculation zone. However, in the case of Φ2.0 + 50 % He torch, the modified FIMR could not precisely estimate the forced ignition limit, showing that further modification to the present prediction model was necessary. The forced ignition process in the cavity was investigated using OH* chemiluminescence images, which indicated that the fuel mixture ignited in the shear layer; therefore, it was necessary to investigate ignition not only within the recirculation zone but also in the shear layer. In the case of Φ2.0 + 50 % He torch, the forced ignition limit could not be predicted by the FIMR, but it could be predicted by the FIMS. These results demonstrate that the FIMS provides improved prediction accuracy for the forced ignition limit in the scramjet combustors.