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We solve the Euler equations in one and two dimensions using a central compact scheme coupled with an AUSM+ algorithm. The compact scheme is used in the form of a cell-face interpolation scheme to create the left- and right-states of the primitive variables required by the AUSM+ based solver. We invoke a TVD limiter to locally apply smaller stencil low-order dissipative formulae near shocks. No extra high-order artificial dissipation is added to stabilize the computation. A number of one and two dimensional test cases has been solved to show the effectiveness of this approach.

Crustal thickness and Poisson's ratios were estimated at 13 broadband seismological stations established in a profile along the Kali river valley, Kumaon (Central) Himalaya. The seismological profile extends from the Indo-Gangetic plain (IGP) in the south to the Higher Himalaya in the north, passing through the Sub and Lesser Himalaya. The Receiver Function (RF) method has been adopted to investigate the crustal structure beneath the profile. Time domain iterative deconvolution method has been adopted for RF computation. The H-k stacking method has been adopted to analyze the RFs for obtaining average crustal thickness and Poisson’s ratio (σ) of the crust beneath each station. The study reveals that the crustal thickness beneath the IGP is ∼38 km which gradually increases up to ∼41 km at the northernmost station located in the Higher Himalaya. The values of σ vary from 0.23 to 0.28. The value of σ is low in the Sub-Himalaya and outer Lesser Himalaya suggesting more of a felsic composition of crust. A Significantly high value of σ (∼0.28) is observed in the Dharchula region of the Chiplakot Crystalline belt which is coincident with a large number of micro-to-moderate magnitude earthquakes forming a cluster at shallow to mid-crustal depths. The high Poisson’s ratio is possibly due to the presence of fluids/partial melts at mid-crustal depth. The presence of fluids influences the rheological property and controls the mechanical and shear strength of crustal rocks producing a cluster of seismicity observed beneath the Dharchula region.

Controlled cooling rate is essential in steel production in order to obtain the desired grades for specific mechanical properties. Optimal control of cooling process parameters is important to obtain the desired cooling rate. The system level uncertainty around the cooling process, the model form error around the generative model for the cooling process as well as the measurement noise make the problem of optimal cooling even more challenging. Machine learning approaches have been used in the recent past to solve optimization and optimal control problems. The present study sets out to design an optimal and robust cooling rate controller using a data-driven approach within a machine learning framework which accounts for the uncertainties inherent in the system. A Gaussian process regression model is developed to predict the cooling rate using temperate-time data and two simulated latent parameters with a suitable confidence interval. The experiments have been undertaken on a laboratory scale Run Out Table setup. The results show the suitability of the proposed approach to obtain a robust response surface of the cooling rate with the process parameters.

A shock-accelerated Refrigerant-22 bubble is computed using third-, fifth- and ninth-order accurate upwind schemes and a fifth-order accurate Weighted Essentially Non-Oscillatory (WENO) scheme by solving the Navier–Stokes equations. A third-order accurate four-stage Runge–Kutta scheme is used for time integration. The Mach 1.22 shock excites Richtmyer–Meshkov instability at the bubble-air interface, and the resulting small-scale vortices are resolved well by the high-resolution schemes due to their low numerical dissipation. Initial wave patterns and bubble shape match with existing experimental and numerical results. Differences become visible between the results of the different schemes at later times when the interfacial vortices grow into localized turbulent mixing zones. A central jet appears after the departure of the refracted shock from the bubble as a transmitted shock. The appearance of this jet confirms that lack of gas viscosity in earlier Euler simulations was not the reason behind its magnified appearance compared to experiments. The computations have been carried out upto 1539.22 µs after the shock first touches the upstream bubble-air interface. Results for such long time duration are not available in existing literature, to the best of our knowledge. Earlier simulation of this problem was carried out by solving the Euler equations. By solving the Navier–Stokes equations, we do not ignore gas viscosity, the effect of which might be significant at the late stages of the evolving bubble. The fifth-order WENO consistently predicts less mixing compared to the fifth-order upwind scheme. Enstrophy predicted by different schemes start varying significantly from each other after the refracted shock emerges from the downstream bubble-air interface. Difference in enstrophy between the ninth- and third-order schemes is found to be as high as 30% near the end of the simulation time (about 1539 µs). Higher-order schemes show more small-scale vortices embedded within the large-scale structures, and between the two fifth-order schemes, the WENO shows less proliferation of small eddies. The presented results indicate that the ninth-order scheme can be a fairly good choice for long time computation of shock-deformed R22 bubbles, and that the standard Jiang-Shu fifth WENO scheme can visibly and significantly deviate from the plain fifth-order upwind scheme in such long time integration problems.

Advanced non-destructive monitoring scheme is necessary for modern-day lightweight composite structures used in aerospace industry, due to their susceptibility to barely visible damages from minor impact loads. Acoustic emission (AE) based monitoring of these structures has received significant attention in the past few years primarily due to their possibility of use in operating structures under service loads. However, localization and characterization of damages using AE is still an open area of research. The exploration of the space of signal features collected by a distributed sensor network and its reliable mapping to damage metrics (such as location, nature, intensity) is still far from conclusive. This problem becomes more critical for composite structures with complex features/geometry where the localized effects of discontinuity in geometric or mechanical properties do not make it appropriate to rely on simple signal features (such as time difference of arrival, peak amplitude, etc.) to identify damage. In this work, the AE signal features (which are spatially and temporally correlated) have been mapped to the damage properties empirically with a training dataset using metamodeling techniques. This is used in the online monitoring phase to infer the probabilistic description of the acoustic emission source within a hierarchical Bayesian inference framework. The methodology is tested on a carbon fibre composite panel with stiffeners that is subjected to impact and dynamic fatigue loading. The study presents a generalized machine learning-based automated AE damage detection methodology which both localizes and characterizes damage under varying operational loads.

The viscous shock tube problem is studied using two different solvers, 5th order WENO solver and a 13th order hybrid scheme. The possibility to reach a grid-convergent solution for the Reynolds number Re = 2500 is investigated and an analysis of shock wave / boundary layer interaction details and flow dynamics inside the viscous shock tube is presented. Specific features and accuracy of the used solvers are discussed.The viscous shock tube problem is studied using two different solvers, 5th order WENO solver and a 13th order hybrid scheme. The possibility to reach a grid-convergent solution for the Reynolds number Re = 2500 is investigated and an analysis of shock wave / boundary layer interaction details and flow dynamics inside the viscous shock tube is presented. Specific features and accuracy of the used solvers are discussed.

The interaction of a reflected shock with the boundary layer inside the shock tubes is an important engineering problem. Studies related to shock wave mitigation and attenuation are performed inside the shock tubes. A proper understanding of the flow behind the reflected shock and the separated zone involving multiple vortical structures is highly essential for estimating the effectiveness of the shock wave mitigation/ attenuation. Such complex flows consist of Lambda shock, shear layer originating from the triple point, multiple shocklets, Mach stems, and vortices. Experimentally the shock structures are obtained through optical techniques. The vortices present in the compressible flow can be obtained through numerical simulations. The complex flows consisting of the above- mentioned features have been simulated numerically so far for the Reynolds numbers up to 1000 [ Zhou G, Xu K, Liu F. Grid-converged solution and analysis of the unsteady viscous flow in a two-dimensional shock tube. Phys Fluids 2018;30(016102):1-21.]. In the present investigation, the shock-wave boundary-layer interaction is simulated for the Reynolds numbers of 1000 and 2500 using a 13th order hybrid scheme to discern the distinct flow features. First, the solver [Kundu A, De S. Navier-Stokes simulation of shock-heavy bubble interaction: Comparison of upwind and WENO schemes. Comput Fluids 2017;157:131-145.] was validated with the benchmark wall density data for a Reynolds number of 1000. Next, the simulations were performed using 50 and 109.5 million cells for the Reynolds number of 2500. The density gradients, vorticity, wall density, and Fourier spectra were used for comparing the flow field for the Reynolds numbers of interest. The Lambda shock, Kelvin-Helmholtz (K-H) vortices in the shear layer, shocklets, the height of lambda shock, and Mach stems were obtained using a grid-mesh of 109.5 million cells. It is observed that the number of vortices generated inside the separated flow region increased with the increase in Reynolds number from 1000 to 2500. Furthermore, the triple point height and the number of K-H vortices generated at the shear layer also increase with an increase in Reynolds number. The present simulations revealed the formation of vortices close to the wall at a Reynolds number of 2500. Such flow structures have an important role in shock / blast wave mitigation and the associated aeroacoustics.

We present a methodology for application of compact schemes for unsteady compressible flow problems involving strong shocks and vortices. A compact interpolation formula is combined with a solver based on the ‘convective upwind and split pressure’ (CUSP) scheme [32] in conjunction with a limiter to restrict the numerical fluxes at the cell faces. The interpolation scheme is derived in a manner so that its use in a first derivative calculation results in high accuracy in the wave number space. This is established by the modified wavenumber and the numerical group velocity of the scheme. Use of compact schemes in compressible flow with shocks has mostly been limited to shocks at lower Mach number range. We test our solver by computing a Mach 7 shock interacting with a strong vortex. Results from the lower resolution version of the solver match well with existing data from an ENO scheme based solver. The high resolution scheme shows the break-up of the vortex into smaller vortices in great details, including roll-up of Kelvin–Helmholtz instability generated small scale vortices from slip lines. The presented method can be seamlessly integrated into existing finite volume or finite difference compressible solvers when such high resolution capability is required.

The world economy is presently confronting an era of energy crisis as it primarily depends upon the conventional energy resources for meeting its demand that accounts for 80% of the energy expenditure[1]. Gradual depletion of conventional fossil fuel reserves, ambiguous fluctuations in its prices and the ever-increasing greenhouse gas emissions have intensified research on the scope for renewable fuels from alternative feedstocks towards mitigation of acute energy crisis. Recently biodiesel has withdrawn eminent interest as a vehicular fuel as it can be synthesized from a large variety of raw materials[2]. The present investigation emphasizes the optimization of acid esterification of non-edible castor (Ricinus communis) oil towards preparation of biodiesel under the influence of four process parameters viz. reaction time (0 to 4 h), reaction temperature (40 to 80 0 C), catalyst concentration (0.25 to 3.25 w/w) and molar ratio of methanol to oil (1:1 to 20:1). The effect of each parameter on the conversion of fatty acids into FAME has been discussed. Optimal conditions during which the FFA was reduced from 4.038 to 1.076 % were: 1 % w/w conc. H2SO4, 15:1 molar ratio of methanol to oil, reaction temperature 50 0 C and reaction time 2.09 h. Among all the process variables, reaction temperature exhibited the most significant effect. Kinetic study of the optimized process parameters was performed. The experimental results were found to fit pseudo first order kinetics. These results were further fitted into the Arrhenius equation to determine the effect of temperature on rate constants. Activation energy and frequency factor were estimated as 22.148 KJ/mol and A = 2.710 min -1 respectively.

Crustal thickness and Poisson's ratio were estimated at 11 broadband seismic stations established in a profile along the Lohit river valley of Arunachal Himalaya passing across the Tuting-Tidding Suture Zone (TTSZ). The average crustal thickness (H) and Poisson's ratio were estimated with the help of H-k stacking analysis of receiver functions at each station. The study reveals a thickening of crust from ~46 km beneath the Brahmaputra valley in the west to ~55 km in the western part of the Lohit Plutonic Complex (LPC). Marginal uplifts of Moho depths (~50–52 km) are observed at some stations to the eastern part of the profile (LTL, HWI and SDL stations). The estimated Poisson’s ratio in the Brahmaputra valley is low (0.23), suggesting the felsic composition of the crust. The Poisson’s ratio is intermediate in the Mishmi Thrust zone (0.249–0.261) and in some parts of the LPC. High Poisson’s ratio (0.277–0.293) is observed beneath the TTSZ and western part of the LPC, indicating the effect of aqueous fluid/partial melt present in the crust. The seismicity in the study area has been investigated based on data recorded by our network and data obtained from the reviewed catalogue of the International Seismological Center (ISC) bulletin. Seismicity is observed to be distributed mainly at a shallow depth range ~1–15 km. However, earthquakes of M > 4.0 are primarily concentrated at ~25–35 km depths. This bimodal distribution of seismicity has a significant role in understanding subsurface configuration beneath the profile.

We solve the Euler equations to simulate a cylindrical blast wave in an enclosure. The blast is initiated close to the bottom wall of a square enclosure. An initial Mach 10 shock wave moves into ambient air, causing a mushroom structure behind the shock. We relate the development of this structure to the passage of the reflected shock from the bottom wall through the core of low-density air, which appears to trigger the Richtmyer–Meshkov instability. Use of a ninth-order derivative formula with a four-stage third-order Runge–Kutta time stepping scheme allows us to visualize the vortical motion at the core of the blast in great detail, including the spikes of ambient air penetrating the blast core and two symmetric trails of small-scale vortices behind the primary vortices.

Computational results are presented for an evolving Refrigerant-22 bubble after its interaction with a Mach 1.22 shock wave. Initially, the bubble is kept stationary in surrounding air, presenting a fast/slow interface to the approaching shock wave. We solve the Euler equations in two dimensions using the low dissipation AUSMD algorithm coupled with a ninth-order upwind scheme for the convective terms and a four-stage third-order Runge–Kutta time integration scheme. The high resolution solver reveals intricate details of vorticity generation during and after the interaction. In the early phase, the detected wave structure matches with available experimental and computational results. Going beyond what is available in literature, we show how the central jet that has drawn attention of researchers could be explained by observing the Richtmyer–Meshkov instability driven mushroom structure that appears behind a cylindrical blast wave set off near the ground. Initial growth of vorticity generated by the baroclinic torque, appearance of opposite signed vorticity during emergence of the transmitted wave, interaction of vortices of various sizes and their accumulation in regions of intense mixing are all captured well. Tracking the area within the bubble where mole fraction of Refrigerant-22 is between 0.05 to 0.8, we show that mixing of air and Refrigerant-22 is increases with a period of time. Fourier spectra of streamwise kinetic energy is indicative of redistribution of energy to lower Fourier modes during long time bubble growth. This redistribution of energy occurs through merger of vortices during their interaction.

A model order reduction scheme of the transient response of large-scale randomly parametrized linear finite element system in state space form has been proposed. The reduced order model realization is aimed at preserving the invariant properties of the dynamic system model based on the dominant coupling characteristics of the specified system inputs and outputs. An a-priori model reduction strategy based on the balanced truncation method has been proposed in conjunction with the stochastic spectral Galerkin finite element method. Approximation of the dominant modes of the controllability Gramian has been performed with iterative Arnoldi scheme applied to Lyapunov equations. The reduced order representation of the randomly parametrized dynamical system has been obtained with Arnoldi–Lyapunov vector basis using an implicit time stepping algorithm. The performance and the computational efficacy of the proposed scheme has been illustrated with examples of randomly parametrized advection–diffusion–reaction problem under the action of transient external forcing functions. The convergence of the proposed reduced order scheme has been shown with a-posteriori error estimates.

Uncertainty analysis of corrugated skins has been performed for random perturbations in geometric and elastic parameters of a chosen baseline model. The corrugated skins are particularly suitable for morphing applications in aerospace structures and their sensitivity to the various input uncertainties is a major concern in their design. The various sources of uncertainty include random perturbations of the geometrical parameters of the corrugation units, surface roughness and parametric uncertainty of the elastic parameters. These uncertainties are described here within the probabilistic framework and have been incorporated into the discretized stochastic finite element model used for their analysis. The propagation of these uncertainties to the dynamic response of the structure is a computationally intensive exercise especially for high dimensional stochastic models. Such high dimensional models have been resolved with statistical methods such as Gaussian Process Emulation and polynomial interpolation based sparse grid collocation techniques. The brute force Monte Carlo simulation technique results have been used as benchmark solutions. A global sensitivity analysis has been performed to identify the key uncertainty sources which affect the system response and the equivalent models using Sobol’s importance measure.