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Extended range munitions (ERM) are systems whose performance is subject to aerodynamic, internal ballistics and trajectory effects. There are models in the literature for each of these aspects; thus, a holistic approach that unifies them would—theoretically—be able to predict the performance of an ERM from bench tests. In this work, we propose such approach. From the integration of chemical composition data, bench tests, combustion simulations, aerodynamic simulations and trajectory dynamics simulations, the behavior of a Base Bleed (BB) unit could be satisfactorily estimated. The results obtained suggest that the composition of combustion products plays a key role in the performance of BB systems.

The present work aims at developing a new flexible computational framework to simulate macro and microscale two-phase flows with dynamic boundaries. Such a technique is extremely useful for periodic and very large domains which requires exhaustive computational resources, consequently reducing the required numerical domain . In this article an interface tracking Finite Element (FE) method is used to solve the equations governing the motion of two immiscible incompressible fluids in the Arbitrary Lagrangian–Eulerian framework (ALE). The equations are written in axisymmetric coordinates, however the proposed moving boundary technique can be easily extended to 3-dimensional flows and other methods using the ALE framework such as the finite volume method . The two-phase interface separating the fluids is a subset of the domain mesh, therefore a layer of zero thickness is achieved assuring sharp transition of properties among phases. At the scale of interest, surface tension plays an important role and is thus considered in the flow equations. Several validations and results are presented for gravity dominated problem, including the sessile drop test and rising of spherical and Taylor bubbles, as well as the divergent and sinusoidal channels, showing accuracy for modeling two-phase flows in large and periodic domains.

Nonlinear models for pattern evolution by ion beam sputtering on a material surface present an ongoing opportunity for new numerical simulations. A numerical analysis of the evolution of preexisting patterns is proposed to investigate surface dynamics, based on a 2D anisotropic damped Kuramoto-Sivashinsky equation, with periodic boundary conditions. A finite-difference semi-implicit time splitting scheme is employed on the discretization of the governing equation. Simulations were conducted with realistic coefficients related to physical parameters (anisotropies, beam orientation, diffusion). The stability of the numerical scheme is analyzed with time step and grid spacing tests for the pattern evolution, and the Method of Manufactured Solutions has been used to verify the proposed scheme. Ripples and hexagonal patterns were obtained from a monomodal initial condition for certain values of the damping coefficient, while spatiotemporal chaos appeared for lower values. The anisotropy effects on pattern formation were studied, varying the angle of incidence of the ion beam with respect to the irradiated surface. Analytical discussions are based on linear and weakly nonlinear analysis.

Spatio-temporal pattern formation in complex systems presents rich nonlinear dynamics which leads to the emergence of periodic nonequilibrium structures. One of the most prominent equations for the theoretical and numerical study of the evolution of these textures is the Swift–Hohenberg (SH) equation, which presents a bifurcation parameter (forcing) that controls the dynamics by changing the energy landscape of the system, and has been largely employed in phase-field models. Though a large part of the literature on pattern formation addresses uniformly forced systems, nonuniform forcings are also observed in several natural systems, for instance, in developmental biology and in soft matter applications. In these cases, an orientation effect due to forcing gradients is a new factor playing a role in the development of patterns, particularly in the class of stripe patterns, which we investigate through the nonuniformly forced SH dynamics. The present work addresses amplitude instability of stripe textures induced by forcing gradients, and the competition between the orientation effect of the gradient and other bulk, boundary, and geometric effects taking part in the selection of the emerging patterns. A weakly nonlinear analysis suggests that stripes are stable with respect to small amplitude perturbations when aligned with the gradient, and become unstable to such perturbations when when aligned perpendicularly to the gradient. This analysis is vastly complemented by a numerical work that accounts for other effects, confirming that forcing gradients drive stripe alignment, or even reorient them from preexisting conditions. However, we observe that the orientation effect does not always prevail in the face of competing effects, whose hierarchy is suggested to depend on the magnitude of the forcing gradient. Other than the cubic SH equation (SH3), the quadratic–cubic (SH23) and cubic–quintic (SH35) equations are also studied. In the SH23 case, not only do forcing gradients lead to stripe orientation, but also interfere in the transition from hexagonal patterns to stripes.

The determination of species concentration profiles in reactive flows with variable inlets is a problem of practical interest to many fields such as in flow reactor transient operation and in cyclic degradable pollutants disposals in watercourses. In these cases, the inflow condition often consists of a time-dependent function, which may imply unsteady outflows, not always well represented by the usual boundary conditions (BC) used so far. A new approach, using an outlet condition in the form of a material derivative, termed Material Derivative Boundary Condition (MDBC), is introduced and a numerical model to solve convection-diffusion-reaction equations in two-dimensional (2-D) incompressible flows is developed. Upon reviewing the literature, it is noted that the Finite Element Method (FEM) is rarely used in the simulation of reactive flows, in spite of its ability of consistently coping with variable BCs. The above facts are reasons to explore its use along with a semi-discrete formulation with the Galerkin Method in our simulations. Results are obtained for various conditions, in order to show features of the code, and are compared to existing solutions. Use of the MDBC is shown to provide a better approximation of the exit concentrations and use of FEM in reactive flows is further enhanced.

This chapter deals with quasi one-dimensional flows, including isentropic flows, normal shock waves, including the thickness of the waves, and flow in ducts with constant cross section with heat transfer and friction (Rayleigh and Fanno lines). The chapter also addresses the effects of friction and heat transfer in variable transversal section ducts, where the critical Mach number M = 1 is not attained at ducts throat. In sequence, the chapter discusses the flow of gases in isothermal ducts, followed by pointing the analogy with open channel hydraulics.

This chapter presents the time-dependent three-dimensional equation governing the evolution and the steady state compressible potential associated with the irrotational flow of compressible fluids. Some particular cases of the complete equations are presented, followed by a classification of Partial Differential Equations. In sequence, the chapter addresses sound propagation questions, including the numerical solution of the wave equation in one and two dimensions, in the frequency domains, using Finite Differences and Finite Elements methods.

This chapter summarizes the basic equations of compressible fluid flow. The complete time-dependent three-dimensional continuity and momentum equations are presented, including the constitutive equation of Newtonian fluids. The time-dependent Bernoulli equation for both compressible rotational and irrotational flows are discussed. The chapter presents the evolution equation of the circulation, where conditions for generation of vorticity and the necessary conditions for an irrotational flow to stay irrotational are discussed. One-dimensional mass, momentum, and energy equation are then presented.

This chapter addresses the principles of small perturbation theory, where a high speed incoming flow is perturbed by slender bodies aligned or quasi aligned to the flow. Steady state is assumed. The equation of the potential ϕ associated with irrotational compressed flow is simplified for subsonic and supersonic regimes, where the problem is linear. The nonlinear equation governing the behavior of steady three-dimensional transonic flow is presented. A derivation is given for the pressure coefficient. The chapter discusses the problem of two-dimensional steady flow over a periodic-shaped wall both in the linear subsonic and supersonic regimes.

The formation of reservoirs usually incorporates the inundation of terrestrial vegetation in the basin. The decomposition of organic matter from the flooded vegetation may have several implications for reservoir functioning, including eutrophication and dissolved oxygen depletion. The hydrostatic pressure increases with depth in a reservoir, and its influence on the decomposition process has not previously been evaluated. This study was undertaken to evaluate the decomposition of terrestrial plant detritus of different qualities (leaves and branches) under different hydrostatic pressure conditions. Detritus were placed separately in glass bottles in the laboratory and incubated in tight stainless steel pressure vessels, simulating three different depths (surface, 30 and 100 m). The masses (mg) of particulate organic carbon (POC), dissolved organic carbon (DOC) and inorganic carbon (IC) were determined for the 4 months of the detritus decomposition simulated in this study. The mass values were transformed in percentages of the initial detritus carbon. The results of temporal variations of the compounds studied were fitted to a first-order biphasic decay model. The hydrostatic pressure exhibited no significant effects on litter decomposition. On the other hand, the detritus chemical composition (i.e. the presence of labile and refractory compounds) was the determining factor for the decomposition curve shape and for the differences observed between the leaves and branches. The greatest POC loss from leaves, and resulting larger DOC mass, indicated the leaves were more labile than the branches. The results also indicated the branches are the main detritus remaining in a reservoir over time.

Passive cooling systems (PCSs) are engineering solutions to perform the function of heat transfer using the temperature difference between hot and cold sources to generate the driving force. These systems have increasing importance to nuclear power industry and are object of many studies since 1960s. One of the main concerns in PCSs is thermal-hydraulic stability. This work presents the results of a linear and a non-linear stability analysis of a single-phase natural circulation loop coupled to a nuclear spent fuel pool. The effect of the pool on the stability of the system is studied by linear and non-linear models. Results show that stability natural cooling loops are modified by the coupling with the pool. Moreover, the amount of water in the pool is non-monotonically related to the stability of the system.

The safety and efficacy of drug-eluting stents are strongly influenced by the transport of the antiproliferative/anti-inflammatory drugs in the arterial wall. Dissolution in the polymer coating and specific binding in the artery wall play an important role in the process. We consider the model of dissolution, transport and binding of sirolimus on an axisymmetric domain representing the polymer coating layer and the porous artery wall in the vicinity of a stent strut. We employ the FEM on an unstructured mesh to discretize the governing equations. We employ a nonlinear dissolution model for the dynamics in the coating, and a nonlinear saturable binding model that includes both specific and non-specific binding in the arterial wall as separate phases, as proposed by McGinty and Pontrelli (J Math Chem 54:967–976, 2016). The arterial wall is considered an anisotropic porous media, and the flow is considered to be governed by Darcy flow. The permeability in the polymer coating is considered to be very small, but finite. The endothelium lamina, where present, is modelled as a no-flow boundary. The effect of slow and fast release polymers is considered, showing that the time evolution of the process can be efficiently controlled by the polymer diffusion coefficient. In fact, an order of magnitude decrease in the polymer diffusion coefficient results in an order of magnitude increase in the time of drug delivery. It is estimated that 52–54% of the sirolimus mass actually diffuses into the arterial wall. However, the spatial distribution of the sirolimus is greatly influenced by the flow and the arterial wall properties, being therefore susceptible to patient health conditions.