A numerical code based on a finite volume technique was developed to simulate laminar flow over a three-dimensional horizontal forward-facing step. Pressure and velocity fields were linked by the SIMPLE algorithm. A rectangular channel encloses the forward-facing step such that the expansion ratio (ER) and the aspect ratio (AR) are equal to two and four, respectively. The channel total length in the stream-wise direction is equal to sixty times the step height and the step edge is located at a distance equal to twenty times the step height downstream of the channel inlet. At the channel inlet flow is considered to be fully developed and three-dimensional. Effect of variation of Reynolds number (Re = 100, 200, 400, and 800) on locations of the reattachment line, the separation line, velocity profiles at different planes, and spanwise averaged Nusselt numbers are discussed.

The main goal of this manuscript is to generalize Darcy’s law from conventional calculus to fractal calculus in order to quantify the fluid flow in subterranean heterogeneous reservoirs. For this purpose, the inherent features of fractal sets are scrutinized. A set of fractal dimensions is incorporated to describe the geometry, morphology, and fractal topology of the domain under study. These characteristics are known through their Hausdorff, chemical, shortest path, and elastic backbone dimensions. Afterward, fractal continuum Darcy’s law is suggested based on the mapping of the fractal reservoir domain given in Cartesian coordinates $x_i$ into the corresponding fractal continuum domain expressed in fractal coordinates ${\xi }_i$ by applying the relationship ${\xi }_i={ϵ}_0{(x_i/{ϵ}_0)}^{{\alpha }_i-1}$, which possesses local fractional differential operators used in the fractal continuum calculus framework. This generalized version of Darcy’s law describes the relationship between the hydraulic gradient and flow velocity in fractal porous media at any scale including their geometry and fractal topology using the ${\alpha }_i$-parameter as the Hausdorff dimension in the fractal directions ${\xi }_i$, so the model captures the fractal heterogeneity and anisotropy. The equation can easily collapse to the classical Darcy’s law once we select the value of 1 for the alpha parameter. Several flow velocities are plotted to show the nonlinearity of the flow when the generalized Darcy’s law is used. These results are compared with the experimental data documented in the literature that show a good agreement in both high-velocity and low-velocity fractal Darcian flow with values of alpha equal to $0<{\alpha }_1<1$ and $1<{\alpha }_1<2$, respectively, whereas ${\alpha }_1=1$ represents the standard Darcy’s law. In that way, the alpha parameter describes the expected flow behavior which depends on two fractal dimensions: the Hausdorff dimension of a porous matrix and the fractal dimension of a cross-section area given by the intersection between the fractal matrix and a two-dimensional Cartesian plane. Also, some physical implications are discussed.

Designing a combustion chamber for gas turbines is considered both a science and an art. This study presents a comprehensive methodology for designing an annular combustion chamber tailored to the operating conditions of a CFM-56 engine, a widely used high bypass ratio turbofan engine. The design process involved calculating the basic criteria and dimensions for the casing, liner, diffuser, and swirl, followed by an analysis of the cooling sections of the liner. Numerical simulations using NUMECA software and the HEXPRESS meshing tool were conducted to predict the combustion chamber’s behavior and performance, employing the κ-ε turbulence model and the Flamelet combustion model. Methane was used as the fuel, and simulations were performed for three fuel injection angles: axial, 45°, and 60°. Results demonstrate that the combustion chamber is properly dimensioned and achieves complete combustion for all configurations. The pressure ratio is 0.96, exceeding the minimum design criteria. Additionally, the emissions of unburned hydrocarbons are zero, while nitrogen oxides and carbon monoxide levels are below regulatory limits. These findings validate the proposed design methodology, ensuring efficient and environmentally compliant combustion chamber performance.

This research focuses on analyzing the aerodynamic characteristics of residual air currents generated by vehicle movement and evaluating their feasibility for energy generation, then designing a vertical axis wind turbine. The parameters assessed include the characteristic velocity profile, the average and maximum velocities, disturbance lifetimes, as well as the frequency and probability of recurrence of these disturbances. Using the data, projections are made on the electrical energy amount that can be produced by a wind turbine operating under such wind conditions. Measurements were taken at four locations: three within Mexico City (CDMX) and one on the outskirts. The measurement station, consisting of a 2.35 m vertical tower equipped with eight vertically aligned thermos-resistive anemometers, is installed on medians less than 0.50 m from moving vehicles. The data from within CDMX show maximum wind velocities ranging from 6 to 8 m/s at ground level, while measurements on the outskirts record velocities of up to 19.5 m/s. A probabilistic analysis reveals that usable air currents could be present 58% of the time. Based on electrical production calculations, it is estimated that harnessing this residual energy could power approximately 4500 homes, considering the national cost per kWh and the average electricity consumption of a four-person household.

Power generation using renewable technologies has become a primordial option to satisfy the energy demand all over the world, with solar concentrating technologies widely applied for this purpose. A combination of a parabolic trough collector with direct steam generation has been considered an excellent option for power generation as the economic cost and complexity in the plant are reduced. The thermal evaluation of a solar power plant as well as the PTC in the DSG process is very important in viability and economic analyses. In this sense, as the main objective of this work, a numerical tool for evaluating DSG with PTC technology was developed. The SOLEEC software is a versatile, reliable, accurate, and user-friendly option to thermally evaluate a DSG with PTC technology. The user has the possibility of comparing the thermal behavior of different geometrical dimensions for a PTC and even consider different materials to satisfy the demand of superheated steam by a DSG process. The software has an error of less than 5% when compared with the literature results and was used in this paper to evaluate a power plant in Mexico, showing that the change to DSG proposing different PTC could reduce the solar field by about 35%.

In this paper a new generalized fractal equation for studying the behaviour of self-similar beams using the Timoshenko beam theory is introduced. This equation is established in fractal dimensions by applying the concept of fractal continuum calculus $F^{\alpha }$-CC introduced recently by Balankin and Elizarraraz in order to study engineering phenomena in complex bodies. Ultimately, the achieved formulation is a fourth-order fractal single equation generated by superposing a shear deformation on an Euler–Bernoulli beam. A mapping of the Timoshenko principle onto self-similar beams in the integer space into a corresponding principle for fractal continuum space is formulated employing local fractional differential operators. Consequently, the single equation that describes the stress/strain of a fractal Timoshenko beam is solved, which is simple, exact, and algorithmic as an alternative description of the fractal bending of beams. Therefore, the elastic curve function and rotation function can be described. Illustrative examples of classical beams are presented and show both the benefits and the efficiency of the suggested model.