Numerical modeling of subsonic axisymmetric reacting gas flows

A numerical algorithm is developed and implemented for modelling axisymmetric subsonic reacting gas flows based on a previously created program for plane flows. The system of Navier-Stokes equations in the low Mach number limit is used as a mathematical model. Calculations of ethane pyrolysis for axisymmetric and plane flow of mixture at heat supply from the reactor’s walls are carried out. Through the interplay of the developed code and the code for plane flows it becomes possible to identify the geometric factor role at the presence of a large number of nonlinear physicochemical processes. We found that diffusion of synthesized molecular hydrogen mainly influences heat supply from the reactor’s walls to gas and pyrolysis products distribution along its length.

Phragm\’{e}n-Lindel\”{o}f alternative results in time-dependent double-diffusive Darcy plane flow

This paper investigates the spatial behavior of the solutions of the double-diffusive Darcy plane flow in a semi-infinite channel. Using the energy estimate method and the differential inequality technology, a differential inequality about the solutions is derived. By solving this differential inequality, it is proved that the solutions grow polynomially or decay exponentially with spatial variable. In the case of decay, we obtain the upper bound for the total energy. We also give some remarks to generalize the results of this paper.

A Generalized Reduced Fluid Dynamic Model for Flow Fields and Electrodes in Redox Flow Batteries

High dimensional models typically require a large computational overhead for multiphysics applications, which hamper their use for broad-sweeping domain interrogation. Herein, we develop a modeling framework to capture the through-plane fluid dynamic response of electrodes and flow fields in a redox flow cell, generating a computationally inexpensive two-dimensional (2D) model. We leverage a depth averaging approach that also accounts for variations in out-of-plane fluid motion and departures from Darcy’s law that arise from averaging across three-dimensions (3D). Our Resulting depth-averaged 2D model successfully predict the fluid dynamic response of arbitrary in-plane flow field geometries, with discrepancies of < 5% for both maximum velocity and pressure drop. This corresponds to reduced computational expense, as compared to 3D representations (< 1% of duration and 10% of RAM usage), providing a platform to screen and optimize a diverse set of cell geometries.

Edge Race-Tracking during Film-Sealed Compression Resin Transfer Molding

Edge race-tracking is a frequently reported issue during resin transfer molding. It is caused by highly permeable channels and areas between the preform edge and cavity, which can significantly change the preform impregnation pattern. To date, information is scarce on the effect of edge race-tracking in compression resin transfer molding (CRTM). To close this gap, laboratory equipment was developed to study the CRTM preform impregnation via flow visualization experiments. The preform was thereby encapsulated in thin thermoplastic films sealing its impregnation. Film-sealed compression resin transfer molding (FS-CRTM) experiments of preforms with a small geometrical aspect ratio showed fast filling of the injection gap and a subsequent through-thickness preform impregnation. Creating an edge race-tracking channel, an additional lateral in-plane flow from the channel towards the preform center was observed, initiating soon after the injection started and caused by the spatial connection between the injection gap and the race-tracking channel. To diminish edge race-tracking, a passive flow control strategy was implemented via a split design of the upper tool to spatially isolate the injection gap from the channel and to pre-compact the preform edge. A delayed and reduced lateral race-tracking flow was observed, showing that the passive flow control strategy increases the process robustness of FS-CRTM regarding edge race-tracking effects.

Comparison of Crushed-Zone Skin Factor for Cased and Perforated Wells Calculated with and without including a Tip-Crushed Zone Effect

A number of different factors can affect flow performance in perforated completions, such as perforation density, perforation damage, and tunnel geometry. In perforation damage, any compaction at the perforation tunnels will lead to reduced permeability, more significant pressure drop, and lower productivity of the reservoir. The reduced permeability of the crushed zone around the perforation can be formulated as a crushed-zone skin factor. For reservoir flow, earlier research studies show how crushed (compacted) zones cause heightened resistance in radially converging vertical and horizontal flow entering perforations. However, the effects related to crushed zones on the total skin factor are still a moot point, especially for horizontal flows in perforations. Therefore, the present study will look into the varied effects occurring in the crushed zone in relation to the vertical and horizontal flows. The experimental test was carried out using a geotechnical radial flow set-up to measure the differential pressure in the perforation tunnel with a crushed zone. Computational fluid dynamics (CFD) software was used for simulating pressure gradient in a cylindrical perforation tunnel. The single-phase water was radially injected into the core sample with the same flow boundary conditions in the experimental and numerical procedures. In this work, two crushed zone configuration scenarios were applied in conjunction with different perforation parameters, perforation length, crushed zone radius, and crushed zone permeability. In the initial scenario, the crushed zone is assumed to be located at the perforation tunnel’s side only, while in the second scenario, the crushed zone is assumed to be located at a side and the tip of perforation (a tip-crushed zone). The simulated results indicate a good comparison with regard to the two scenarios’ pressure gradients. Furthermore, the simulations’ comparison reveals another pressure drop caused by the tip crushed zone related to the horizontal or plane flow in the perforations. The differences between the two simulations’ results show that currently available models for estimating the skin factor for vertical perforated completions need to be improved based on which of the two cases is closer to reality. This study has presented a better understanding of crushed zone characteristics by employing a different approach to the composition and shape of the crushed zone and permeability reduction levels for the crushed zone in the axial direction of the perforation.

Solvability of an Optimization Problem for the Unsteady Plane Flow of a Non-Newtonian Fluid with Memory

This paper deals with an optimization problem for a nonlinear integro-differential system that describes the unsteady plane motion of an incompressible viscoelastic fluid of Jeffreys–Oldroyd type within a fixed bounded region subject to the no-slip boundary condition. Control parameters are included in the initial condition. The objective of control is to match the velocity field at the final time with a prescribed target field. The control model under consideration is interpreted as a continuous evolution system in an infinite-dimensional Hilbert space. The existence of at least one optimal control is proved under inclusion-type constraints for admissible controls.

The Interaction of Purge Flows With Secondary Flow Features in Turbine Center Frames

The turbine center frame (TCF) is an inherent component of modern turbofan aircraft engines, used for facilitating the large radius change between the high-pressure (HPT) and low-pressure (LPT) turbines. Secondary flow features that develop in the TCF result in total pressure loss of the mainstream flow and a subsequent performance reduction for the whole of the engine. Purge flows from the HPT interact with these flow features affecting their development and strength. Understanding the details of this interaction is therefore of paramount importance for the design of more efficient engines of the future. This paper presents a detailed investigation of the interaction of purge flows from the hub and shroud cavities upstream and downstream of the HPT rotor with the secondary flow features in a TCF. The investigation was conducted using aerodynamic and seed gas concentration measurements in an engine-representative HPT-TCF setup and under engine-realistic operating conditions. The upstream purge flows interact with the flow-field of the rotor, and especially with the upper and lower passage vortices where they are mainly entrained, forming “zones-of-influence” that occupy the upper and lower 35% of the span at the TCF inlet. Dilution of these purge flows occurs through vortex-to-vortex interactions and in-plane flow migrations driven by the vortices. At the outlet of the TCF, the upstream purge flows form effectiveness bands that encapsulate the various counter-rotating vortices near the hub and shroud. This indicates that these counter-rotating vortices were formed at the inlet of the TCF, in a flow that already includes the upstream purge flows. The downstream purge flows exit the hub and shroud cavities forming effectiveness boundary layers at the inlet of the TCF of thickness equal to around 15% of the span. The circumferential distribution of these purge flows is however asymmetric, owing to the also asymmetric static pressure distribution at the inlet of the TCF, as a result of the effect of the propagated flow-field of the stator vanes. At the outlet of the TCF, the distribution of the downstream hub purge appears as distinct effectiveness lobes with the same periodicity as the HPT vanes. The formation of the lobes is as a result of intense interaction between the counter-rotating vortex pairs and the downstream hub purge flow. The viscous shear mixing due to this interaction is also the cause for the low total pressure in the regions influenced by the lobes. The distribution of the downstream shroud purge appears as alternating regions of high and low effectiveness as a result of radially inwards and outwards flow migrations caused by the shearing actions of the counter rotating vortices near the shroud. These migrations are the cause of regions with the lowest total pressure at the outlet of the TCF.

Curvature-driven feedback on aggregation-diffusion of proteins in lipid bilayers

Membrane bending is an extensively studied problem from both modeling and experimental perspectives because of the wide implications of curvature generation in cell biology. Many of the curvature generating aspects in membranes can be attributed to interactions between proteins and membranes. These interactions include protein diffusion and formation of aggregates due to protein-protein interactions in the plane of the membrane. Recently, we developed a model that couples the in-plane flow of lipids and diffusion of proteins with the out-of-plane bending of the membrane. Building on this work, here, we focus on the role of explicit aggregation of proteins on the surface of the membrane in the presence of membrane bending and diffusion. We develop a comprehensive framework that includes lipid flow, membrane bending energy, the entropy of protein distribution, and an explicit aggregation potential and derive the governing equations. We compare this framework to the Cahn-Hillard formalism to predict the regimes in which the proteins form patterns on the membrane. We demonstrate the utility of this model using numerical simulations to predict how aggregation and diffusion, coupled with curvature generation, can alter the landscape of membrane-protein interactions.

Numerical simulation of plane flow field and the force on the inner rod induced by planetary motion of the rod string

In order to a the flow of the plane flow field induced by the inner rod rotates and revolves in the cylinder, the Fluent software is used to numerically simulate the plane flow field of the eccentric annulus generated by the planetary motion of the rod string and based on the superposition principle. The velocity distribution and secondary flow of the two flow fields, as well as the fluid force on the inner rod are analyzed. The calculation results show that the flow field induced by the eccentric rotation of the inner rod and the self-rotation of the outer cylinder is quite different from the planetary motion of the inner rod. When rotation of the inner rod has the same direction with the revolution direction, the fluid velocity distribution near the wall of the inner rod is that the velocity on the narrow space side of the annulus is large, and on the wide space side is small. There is a critical value of eccentricity for secondary flow appears when the eccentricity is greater than this value. When rotation of the inner rod is contrary to the revolution, the fluid velocity distribution near the wall of the inner rod is that the velocity on the wide space side of the annulus is large, on the narrow space side is small. Different eccentricity has obvious secondary flow phenomenon where appears in a wide gap and close to the inner rod. When the inner rod revolves, there is a critical value of eccentricity, the inner rod is pushed outward by the fluid force when the eccentricity is less than this critical value. On the contrary, the inner rod is pushed inward. When rotation and revolution are reversed, the critical value of eccentricity increases, when the rotation and revolution are in the same direction, the critical value of eccentricity decreases.