Combustion instability analysis in an ethylene-fueled scramjet combustor under various fuel penetration height conditions using an image-based nonlinear dimensionality reduction method

We present an alternative approach to generate gait motion at arbitrary speed for gait rehabilitation robots. The methodology utilizes Gaussian process dynamical model (GPDM), which is a nonlinear dimensionality reduction technique. GPDM consists of a dynamics in low-dimensional latent space and a mapping from the space to configuration space, and GPDM learning results in the low-dimensional representation of training data and parameters for the dynamics and mapping. We use second-order Markov process dynamics model, and hence given a pair of initial points, the dynamics generates a latent trajectory at arbitrary speed. We use linear regression to obtain the initial points. Mapping from the latent to configuration spaces constructs trajectories of walking motion. We verify the algorithm with motion capture data from 50 healthy subjects, who walked on a treadmill at 1, 2, and 3 km/h. We show examples and compare the original and interpolated trajectories to prove the efficacy of the algorithm.

Locally Linear Embedding (LLE) is a recently proposed algorithm for non-linear dimensionality reduction and manifold learning. However, it may not be optimal for classification problem. In this paper, an improved version of LLE, namely KFDA-LLE, is proposed using kernel Fisher discriminant analysis (KFDA) method, combined with SVM classifier for face recognition task. Firstly, the input training samples are projected into the low-dimensional space by LLE. Then KFDA is introduced for finding the optimal projection direction. Finally, SVM classifier is used for face recognition. Experimental results on face database demonstrate that the extended LLE method is more efficient and robust.

Current practice in Quantitative Structure Activity Relationship (QSAR) methods usually involves generating a great number of chemical descriptors and then cutting them back with variable selection techniques. Variable selection is an effective method to reduce the dimensionality but may discard some valuable information. This paper introduces Locally Linear Embedding (LLE), a local non-linear dimensionality reduction technique, that can statistically discover a low-dimensional representation of the chemical data. LLE is shown to create more stable representations than other non-linear dimensionality reduction algorithms, and to be capable of capturing non-linearity in chemical data.

We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized data points sampled with noise from a parameterized manifold, the local geometry of the manifold is learned by constructing an approximation for the tangent space at each data point, and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold. We also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases. We illustrate our algorithm using curves and surfaces both in two-dimensional/three-dimensional (2D/3D) Euclidean spaces and in higher-dimensional Euclidean spaces. We also address several theoretical and algorithmic issues for further research and improvements.

Diesel engines are a major source of nitrogen oxides, carbon dioxide, and particulate matter emissions. While biodiesel blends offer potential emission reductions, challenges remain in viscosity, flash point, cold weather performance, and combustion characteristics. This study examines the performance and emission behavior of biodiesel–diesel blends to enhance efficiency and reduce environmental impact. Multiscale entropy analysis was employed to assess combustion instability and complexity, focusing on the influence of fuel composition and engine speed at full load. Experimental investigations were conducted using biodiesel derived from tomato, papaya, and apricot, blended with diesel. The tested fuels included binary and ternary biodiesel–diesel blends with varying levels of complexity. Results indicate that at optimal operating conditions, biodiesel blends enhance energy and exergy efficiency while exhibiting higher carbon dioxide and nitrogen oxide emissions compared to pure diesel. Hydrocarbon emissions decreased under optimized conditions, while fuels with lower chemical complexity demonstrated improved torque output. Diesel, characterized by greater combustion complexity, resulted in lower exergy and useful work. These findings contribute to the understanding of biodiesel application in compression ignition engines, providing insights into performance optimization and emission control strategies. Keywords: Biodiesel blends; combustion stability; engine emissions; energy efficiency; exergy analysis.

Proper orthogonal decomposition and dynamic mode decomposition are evaluated for the study of self-excited longitudinal combustion instabilities in laboratory-scaled single-element gas turbine and rocket combustors. Since each proper orthogonal decomposition mode comprises multiple frequencies, specific modes of the pressure and heat release are not related, which makes the analysis more qualitative and less efficient for identifying physical mechanisms. On the other hand, dynamic mode decomposition analysis generates a global frequency spectrum in which each mode corresponds to a specific discrete frequency so that different dynamics can be correlated. In addition, proper orthogonal decomposition results are found to be inaccurate when only a limited amount of spatial information is provided in contrast with dynamic mode decomposition results, which provide more reliable results. Overall, dynamic mode decomposition analysis proves to be a robust and systematic method that can give consistent interpretations of the periodic physics underlying combustion instabilities.

Three-dimensional simulations of combustion instability can provide extremely valuable insight into the problem physics, but they represent an enormous investment in time and, thus, may preclude parametric studies that are practical with two-dimensional simulations. Three numerical simulations of an unstable laboratory rocket combustor were performed to assess the effect of grid resolution and dimensionality on the ability to predict and model combustion instability. Computations show that two-dimensional axisymmetric simulations using both coarse and fine grids are able to capture the amplitude of the first longitudinal mode within an order of magnitude of what was measured in the experiment. Whereas the three-dimensional calculation based on the coarse grid resolution shows excellent agreement with the experimental level of instability two-dimensional simulations are valuable in parametric evaluations in developing diagnostic methods and in increasing the efficiency of expensive three-dimensional simulations.

FDF-based combustion instability analysis for evolution of mode shapes and eigenfrequency in the multiple flame burner

Numerical study of combustion instability in liquid propellant rocket engine is presented in the paper. Time-depending two-dimensional Navier-Stokes equations were employed to describe the fluid flow in the combust chamber and solved by finite difference method with MacCormack scheme. Turbulent viscosity was taken into consideration by the subgrid scale turbulence model. Propellant spray was treated with a lagrangian tracking method and droplet source terms were incorporated into the gas phase calculation by PSIC method. Droplet initial conditions were determined by a stochastic spray model . Spray burning rate is calculated by the classic D2 vaporization law with Ranz-Marshall correlation. The coupling of pressure disturb and burning rate variation was described with Prime's twoparameter model. The actual axisymmetric combustor was transferred into equivalent annular geometry as the references do. Combustion instability analysis was performed by imposing a bomb pressure pulse on the computed steady flow field to trigger unstable combustion. By observing the pressure wave propagation , we can asses the damping capability of the engine.The computational analysis show that numerical schemes and physical models used to describe unstable combustion are the most important factors to the success of numerical study. d NOMENCLATURE a sound velocity b annular combustor width constant pressure spcific heat CP C,, drag coefficient d droplet diameter D mass diffusivity e total energy f frequency h enthalpy 1 L~ heat of evaporation f i transverse length of the annular combstor mass flux or evaporation rate M number of computational droplet NU Nusselt number pr Prantdl number Ice Reynolds number s source terms time T lempeerature X,Y coordinates p density h coductivity P I velocity components

Combined applications of analytic methods for detection of combustion instability triggering

Homogenous charge compression ignition (HCCI) combustion can significantly reduce automotive pollution and increase the thermal efficiency of the engine. However, combustion phasing control is a major challenge in HCCI engines due to severe cyclic combustion variations. This study investigates the cyclic combustion dynamics of the HCCI engine using nonlinear dynamic methods such as return maps, recurrence plots (RPs), and recurrence quantitative analysis (RQA). Combustion stability and cyclic variations of HCCI combustion parameters were investigated on a modified four-stroke diesel engine. The experiments were conducted by varying relative air-fuel ratios ([Formula: see text]) and intake air temperatures ([Formula: see text]) at two engine speeds. In-cylinder pressure data of 2000 consecutive engine combustion cycles is logged for each test condition. In this study, deterministic characteristics of combustion phasing (CA50) and crank angle position of maximum cylinder pressure ([Formula: see text]) are investigated and compared by employing nonlinear dynamical methods. Return maps revealed that [Formula: see text] is having distinct and more frequently observed deterministic characteristics in comparison to CA50. Patterns in RPs showed a more persistent and sudden change in the combustion dynamics at higher engine speeds. Recurrence plot-based analysis found the existence of deterministic features in the combustion dynamics irrespective of the operating conditions. It was found using RQA parameters that the deterministic nature becomes stronger with a decrease in [Formula: see text] and any deviation in intermediate values of [Formula: see text]. Additionally, RQA measures advocate that CA50 has more deterministic characteristics at higher engine speed while [Formula: see text] at lower engine speed. Strong coupling and synchronization between [Formula: see text] and CA50 is indicated by cross-recurrence plots and CPR index when engine operated with a comparatively richer mixture.

The pilot stage plays a crucial role in central-staged combustion technology. This study aimed to investigate the impact of the jet-type pilot stage on the flame structure and combustion instability in a novel strong coupled centrally staged swirl gas turbine combustor, using both experiments and large eddy simulations (LES). Nonlinear dynamic analyses of dynamic pressure, including phase and recurrence plots, were performed alongside a proper orthogonal decomposition of the dynamic flame structures. It is indicated that a richer pilot stage worsens the instability of the centrally staged combustion system. An increase in the equivalence ratio of the pilot stage leads to enhanced non-premixed combustion and a downstream shift in the heat release region. The transition results in the shift of flame shape from an attached V-shaped flame to an intermittent lifting U-shaped flame. The flame surface statistics from LES results including the strain rate and progress variable gradient of lean and rich pilot conditions were compared. Under richer pilot conditions, the lifting U-shaped flame demonstrates increased sensitivity to flow field fluctuations, intensifying vortex–flame interactions. This interaction causes the large-scale flame surface stretching and even extinction of the pilot stage flame, exacerbating combustion instability observed in this study. These insights offer a deeper understanding of the impact of the jet-type pilot stage on the novel multi-staged central combustion systems.

The cycling combustion instabilities in a diesel engine have been analyzed based on chaos theory. The objective was to investigate the dynamical characteristics of combustion in diesel engine. In this study, experiments were performed under the entire operating range of a diesel engine (the engine speed was changed from 600 to 1400 rpm and the engine load rate was from 0% to 100%), and acquired real-time series of in-cylinder combustion pressure using a piezoelectric transducer installed on the cylinder head. Several methods were applied to identify and quantitatively analyze the combustion process complexity in the diesel engine including delay-coordinate embedding, recurrence plot (RP), Recurrence Quantification Analysis, correlation dimension (CD), and the largest Lyapunov exponent (LLE) estimation. The results show that the combustion process exhibits some determinism. If LLE is positive, then the combustion system has a fractal dimension and CD is no more than 1.6 and within the diesel engine operating range. We have concluded that the combustion system of diesel engine is a low-dimensional chaotic system and the maximum values of CD and LLE occur at the lowest engine speed and load. This means that combustion system is more complex and sensitive to initial conditions and that poor combustion quality leads to the decrease of fuel economy and the increase of exhaust emissions.

We present a detailed study on the characterization of the degeneration process in combustion instability based on dynamical systems theory. We deal with combustion instability in a lean premixed-type gas-turbine model combustor, one of the fundamentally and practically important combustion systems. The dynamic behavior of combustion instability in close proximity to lean blowout is dominated by a stochastic process and transits to periodic oscillations created by thermoacoustic combustion oscillations via chaos with increasing equivalence ratio [Chaos 21, 013124 (2011); Chaos 22, 043128 (2012)]. Thermoacoustic combustion oscillations degenerate with a further increase in the equivalence ratio, and the dynamic behavior leads to chaotic fluctuations via quasiperiodic oscillations. The concept of dynamical systems theory presented here allows us to clarify the nonlinear characteristics hidden in complex combustion dynamics.

Spark-enhanced ignition and flame stabilization in an ethylene-fueled scramjet combustor with a rear-wall-expansion geometry