Reconstructing shock front of unstable detonations based on multi-layer perceptron

Abstract

The dynamics of frontal and transverse shocks in gaseous detonation waves is a complex phenomenon bringing many difficulties to both numerical and experimental research. Advanced laseroptical visualization of detonation structure may provide certain information of its reactive front, but the corresponding lead shock needs to be reconstructed building the complete flow field. Using the Multi-Layer Perceptron (MLP) approach, we propose in this study a shock front reconstruction method which can predict evolution of the lead shock wavefront from the state of the reactive front. The method is verified through the numerical results of one-and two-dimensional unstable detonations based on the reactive Euler equations with a one-step irreversible chemical reaction model. Resultsshow that the accuracy of the proposed method depends on the activation energy of the reactive mixture, which influences prominently the cellular detonation instability and hence, the distortion of the lead shock surface. To select the input variables for training and evaluate their influence on the effectiveness of the proposed method, five groups, one with six variables and the other with four variables, are tested and analyzed in the MLP model. The trained MLP is tested in the cases with different activation energies, demonstrates the inspiring generalization capability. This paper offers a universal framework for predicting detonation frontal evolution and provides a novel way to interpret numerical and experimental results of detonation waves.

A reconstruction method of detonation wave surface based on convolutional neural network

“…About 10 grids per L1/2 is used for the following simulations of cellular detonations, which is sufficient to simulate the unstable structures for the activation energy Ea considered in this work. A resolution study on the same results was previously conducted and reported in [31], indicating that this mesh scale is fine enough to reconstruct the Numerical results show that the detonation will become unstable and the lead shock front will be more distorted when the activation energy increases to 20. According to our recent study [31],…”

“…A resolution study on the same results was previously conducted and reported in [31], indicating that this mesh scale is fine enough to reconstruct the Numerical results show that the detonation will become unstable and the lead shock front will be more distorted when the activation energy increases to 20. According to our recent study [31],…”

“…Moreover, only the red circle on the reactive front (black dashed line in Fig. 1(c)) is fed as inputs into the multi-layer perceptron in [31], neglecting the effects of the neighboring reactive front on the lead shock. In order to consider the influence of 2D transverse waves on the lead shock, more spatial features on the reactive front should be provided to the neural network.…”

“…Due to the input dimension is too large, it is difficult for the traditional MLP method [31] to take the 2D spatial feature of reactive front into account, which may hinder the further optimization of reconstruction results with MLP approach. For CNN, the convolution combined with the pooling operation is an effective method of feature extraction and dimensionality reduction, which makes it feasible to input more spatial features into the neural networks.…”

“…The method is based on feedforward artificial neural network (ANN) or the MLP (Multi-Layer Perceptron), but POD (Proper Orthogonal Decomposition) modal analysis is used to extract the features of the flow fields, which in turn becomes involved and requires big data to be accumulated for increasing accuracy. Another preliminary work [31] uses only MLP to construct the detonation surface, demonstrating the MLP performs much better than classic regression methods. However, due to the large number of parameters, the traditional MLP approach is hard to cover the two-dimensional characteristics of the flow field for more accurate reconstruction.…”