A Numerical Method for Computing Double Integrals with Variable Upper Limits

We propose and justify a numerical method for computing the double integral with variable upper limits that leads to the variableness of the region of integration. Imposition of simple variables as functions for upper limits provides the form of triangles of integration region and variable in the external limit of integral leads to a continuous set of similar triangles. A variable grid is overlaid on the integration region. We consider three cases of changes of the grid for the division of the integration region into elementary volumes. The first is only the size of the imposed grid changes with the change of variable of the external upper limit. The second case is the number of division elements changes with the change of the external upper limit variable. In the third case, the grid size and the number of division elements change after fixing their multiplication. In these cases, the formulas for computing double integrals are obtained based on the application of cubatures in the internal region of integration and performing triangulation division along the variable boundary. The error of the method is determined by expanding the double integral into the Taylor series using Barrow’s theorem. Test of efficiency and reliability of the obtained formulas of the numerical method for three cases of ways of the division of integration region is carried out on examples of the double integration of sufficiently simple functions. Analysis of the obtained results shows that the smallest absolute and relative errors are obtained in the case of an increase of the number of division elements changes when the increase of variable of the external upper limit and the grid size is fixed.

Two Dimensional Analysis and Optimization of Hybrid MDCD-TENO Schemes

In this article, a quasi-linear semi-discrete analysis of shock capturing schemes in two dimensional wavenumber space is proposed. Using the dispersion relation of the two dimensional advection and linearized Euler equations, the spectral properties of a spatial scheme can be quantified in two dimensional wavenumber space. A hybrid scheme (HYB-MDCD-TENO6) which combines the merits of the minimum dispersion and controllable dissipation (MDCD) scheme with the targeted essentially non-oscillatory (TENO) scheme was developed and tested. Using the two dimensional analysis framework, the scheme was spectrally optimized in such a way that the linear part of the scheme can be separately optimized for its dispersion and dissipation properties. In order to compare its performance against existing schemes, the proposed scheme as well as the baseline schemes were tested against a series of benchmark test cases. It was found that the HYB-MDCD-TENO6 scheme provides similar or better resolution as compared to the baseline TENO6 schemes for the same grid size.

A simple machine learning based framework for processing the inline inspection data of subsea pipelines

This paper presents a simple machine learning based framework for diagnosing the inline inspection data (ILI) of subsea pipelines. ILI data are obtained by intelligent pigging devices operating along subsea pipelines. The wall thickness (WT) and standoff distance (SO) are collected by the sensors installed on the pigging, which are normally in the format of 2D arrays. There are many uncertainties for the ILI data collected from the offshore survey. An attempt was made to apply the machine learning method to diagnose the uncertainties. A convolutional neural network (CNN) is used, the ILI data are discretized and processed in 64x64 grid size. Fabricated training datasets were made for training the machine learning model since the ground truth information (actual corroded wall thickness) is hardly known in this case. The trained model was successfully. It is demonstrated that certain corrosion patterns have been recognized by the trained model. Comparisons were performed between the new method and traditional methods with case studies on real ILI data. The validity of the methodology was discussed.

High-Fidelity Energy Deposition Ignition Model Coupled With Flame Propagation Models at Engine-Like Flow Conditions

With the heightened pressure on car manufacturers to increase the efficiency and reduce the carbon emissions of their fleets, more challenging engine operation has become a viable option. Highly dilute, boosted, and stratified charge, among others, promise engine efficiency gains and emissions reductions. At such demanding engine conditions, the spark-ignition process is a key factor for the flame initiation propagation and the combustion event. From a computational standpoint, there exists multiple spark-ignition models that perform well under conventional conditions but are not truly predictive under strenuous engine operation modes, where the underlying physics needs to be expanded. In this paper, a hybrid Lagrangian-Eulerian spark-ignition (LESI) model is coupled with different turbulence models, grid sizes, and combustion models. The ignition model, previously developed, relies on coupling Eulerian energy deposition with a Lagrangian particle evolution of the spark channel, at every time-step. The spark channel is attached to the electrodes and allowed to elongate at a speed derived from the flow velocity. The LESI model is used to simulate spark ignition in a non-quiescent crossflow environment at engine-like conditions, using CONVERGE commercial CFD solver. The results highlight the consistency, robustness, and versatility of the model in a range of engine-like setups, from typical with RANS and a larger grid size to high fidelity with LES and a finer grid size. The flame kernel growth is then evaluated against schlieren images from an optical constant volume ignition chamber with a focus on the performance of flame propagation models, such as G-equation and thickened flame model, versus the baseline well-stirred reactor model. Finally, future development details are discussed.

A Modeling Study of Rainbands Upstream from Western Japan during the Approach of Typhoon Tokage (2004)

During 19–20 October 2004, a series of spectacular arc-shaped rainbands developed south or southeast of southwestern Japan when Typhoon Tokage (TY0423) approached the region from the southwest. As the typhoon moved closer and the upstream Froude number (Fr) continued to increase, these rainbands first remained quasi-stationary but eventually retreated backward. Using the Nagoya University Cloud-Resolving Storm Simulator (CReSS) at 1-km grid size, these rainbands were successfully simulated, and their behavior during the transition period from a relatively low-Fr to a high-Fr regime was investigated and compared with idealized two-dimensional (2D) model results from theoretical studies. In the present case, the rainbands were found to develop along a low-level frontal convergence zone between the southerly flow associated with the typhoon and the northerly flow from the Sea of Japan. The northeasterly winds accelerated through gaps between topography and fed the offshore flow at the backside of the rainbands, producing a strong resistance that allowed the rainbands to remain stationary under significantly higher Fr values (at least 1.2) than predicted by 2D simulations (of about 0.3–0.5) for the retreat to occur in conditionally unstable flow with a convective available potential energy of about 1300 J kg−1. Typically ≤ 500 m in depth with a potential temperature (θ) deficit of 2–4 K across the rainband, the cooler offshore flow was also found to be enhanced by evaporative cooling as in some other events. The cooling effect helped the rainbands to hold their position until Fr of the upstream flow became too large, and the rainband with stronger cooling behind was able to withstand a higher Fr before retreat. Once the retreat started, the offshore layer became thinner and the θ deficit also reduced, and the rainbands were washed back by the strengthening upcoming flow.

Million node fracture: size matters?

Transmissivity of self-affine fractures was computed numerically as a function of the grid size. One-million-node fractures (1024 × 1024 nodes) with fractal dimensions of 2.2–2.6 were cut into successively smaller fractures (“generations”), and transmissivities computed. The number of fractures in each generation was increased by a factor of 4. Considerable scatter in transmissivity was observed for smaller grid sizes. Average transmissivity of the fractures in the generation decreased with the grid size, without approaching any asymptotic value, which indicates no representative elementary volume (REV). This happened despite the average mean aperture being the same in each generation. The results indicate that it is not possible to estimate the transmissivity of a large fracture by cutting it into smaller fractures, running flow simulations on those and averaging the results. The decrease in transmissivity with the grid size was found to be due to an increase in the flow tortuosity.

IWC Analysis of Turbulent Plume Fires

Plumes fires are characterized by a turbulent nature with a large number of different scales. LES is used to solve the largest structures and to model the smallest ones. Grid size and time steps become decisive to place a limit between solved and modelled turbulence. A spectral analysis, both in frequency and wavenumber domain of the specific turbulent kinetic energy is an instrument to check for the information investigated. Unfortunately, the spectra in the wavenumber domain can be difficult to achieve adequately, because the specific turbulent kinetic energy values should be available in many points. This issue can be overcome by identifying a correlation law between frequencies and wavenumbers. An approach to identify this correlation law can be to adopt the IWC method. Here, for a test case of a turbulent reacting plume of burning propane, specific turbulent kinetic energy is analysed both in frequency and wavenumber and a correlation law between them is identified by using the IWC method. A study has been performed to evaluate the grid dependency of the specific turbulent kinetic energy spectra, by assessing the extension of the Kolmogorov power law region. The correlation results are discussed and compared with the Taylor’s hypothesis.