Magnetic Field Effects On Backward-facing Step Flow of Ferrofluids

Backward-facing step (BFS) flow is a benchmark case study in fluid mechanics. Its control by means of electromagnetic actuation has attracted great interest in recent years. This paper focuses on the effects of a uniform stationary magnetic field on the laminar ferrofluid BFS flows for the Reynolds number range 0.1=Re=400 and different expansion ratios. The coupled ferrohydrodynamic equations, including the microscopically derived magnetization equation, for a two-dimensional domain are solved numerically by an Open FOAM solver after validation and a test of accuracy. The application of a magnetic field causes the corner vortices in the concave corner behind the step to be retracted compared with their positions in the absence of a magnetic field. The maximum percentage of the normalized decrease in length of these eddies reaches 41.23% in our simulations. For small Reynolds numbers (<10), the flow separation points on the convex corner are lowered in the presence of a magnetic field. Furthermore, the dimensionless total pressure drop between the channel inlet and outlet decreases almost linearly with Reynolds number Re, but the drop is greater when a magnetic field is applied. On the whole, the normalized recirculation length of the corner vortex increases nonlinearly with increasing magnetic Reynolds number Rem and Brownian Péclet number Pe, but it tends to constant values in the limits Re ≪ 1 and Re ≫ 1.

Breakdown of similarity solutions: a perturbation approach for front propagation during foam-improved oil recovery

The pressure-driven growth model has been employed to study a propagating foam front in the foam-improved oil recovery process. A first-order solution of the model proves the existence of a concave corner on the front, which initially migrates downwards at a well defined speed that differs from the speed of front material points. At later times, however, it remains unclear how the concave corner moves and interacts with points on the front either side of it, specifically whether material points are extracted from the corner or consumed by it. To address these questions, a second-order solution is proposed, perturbing the aforementioned first-order solution. However, the perturbation is challenging to develop, owing to the nature of the first-order solution, which is a similarity solution that exhibits strong spatio-temporal non-uniformities. The second-order solution indicates that the corner’s vertical velocity component decreases as the front migrates and that points initially extracted from the front are subsequently consumed by it. Overall, the perturbation approach developed herein demonstrates how early-time similarity solutions exhibiting strong spatio-temporal non-uniformities break down as time proceeds.

Effects of Processing Parameters for Vacuum-Bagging-Only Method on Shape Conformation of Laminated Composites

Complex composite structures manufactured using a low-pressure vacuum bag-only (VBO) method are more susceptible to defects than flat laminates because of the presence of complex compaction conditions at corners. This study investigates the contribution of multivariate processing parameters such as bagging techniques, curing profiles, and laminate structures on laminates’ shape conformation. Nine sets of laminates were produced with a concave corner and another nine sets with a convex corner, both with a 45° inclined structure. Three-way analysis of variance (ANOVA) was performed to quantify thickness variation and spring effect of laminated composites. The analysis for concave and convex corners showed that the bagging techniques is the main factor in controlling the laminate thickness for complex shape applications. The modified (single) vacuum-bag-only (MSVB) technique appeared to be superior when compared to other bagging techniques, exhibiting the least coefficients of variation of 0.015 and 0.016 in composites with concave and convex corners, respectively. Curing profiles and their interaction with bagging techniques showed no statistical significance in the contribution toward laminate thickness variation. The spring effect of laminated composites was investigated by calculating the coefficient of determination (R2) relative to that of the mold. The specimens exhibited a good agreement with R2 values ranging from 0.9824 to 0.9946, with no major data offset. This study provides guidelines to reduce thickness variations and spring effect in laminated composites with complex shapes by the optimum selection of processing parameters for prepreg processing.

Incipient Separation Near Corners

Chapter 4 analyses the transition from an attached flow to a flow with local recirculation region near a corner point of a body contour. It considers both subsonic and supersonic flow regimes, and shows that the flow near a corner can be studied in the framework of the triple-deck theory. It assumes that the body surface deflection angle is small, and formulates the linearized viscous-inviscid interaction problem. Its solution is found in an analytic form. It also presents the results of the numerical solution of the full nonlinear problem. It shows how, and when, the separation region forms in the boundary layer. In conclusion, it suggests that in the subsonic flow past a concave corner, the solution is not unique.

Oblique shockwaves and expansion fans

External supersonic gas flow in which changes in the fluid and flow properties are brought about by direction change is analysed in this chapter. In addition, it is shown that flow over a corner between two flat surfaces resulted in an oblique shockwave if the angle between the two surfaces is less than 180° (a concave corner). The analysis of flow through an oblique shockwave is based upon the superposition of the flowfield for a normal shock onto a uniform flow parallel to the shock. It is also shown that both weak and strong oblique shocks can occur. For an angle in excess of 180° (a convex corner), the flow is turned through an isentropic Prandtl-Meyer expansion fan. Analysis of a Prandtl-Meyer expansion fan starts from consideration of an infinitesimal flow deflection through a Mach wave.

Foam front advance during improved oil recovery: similarity solutions at early times near the top of the front

The pressure-driven growth model is used to determine the shape of a foam front propagating into an oil reservoir. It is shown that the front, idealised as a curve separating surfactant solution downstream from gas upstream, can be subdivided into two regions: a lower region (approximately parabolic in shape and consisting primarily of material points which have been on the foam front continuously since time zero) and an upper region (consisting of material points which have been newly injected onto the foam front from the top boundary). Various conjectures are presented for the shape of the upper region. A formulation which assumes that the bottom of the upper region is oriented in the same direction as the top of the lower region is shown to fail, as (despite the orientations being aligned) there is a mismatch in location: the upper and lower regions fail to intersect. Alternative formulations are developed which allow the upper region to curve sufficiently so as to intersect the lower region. These formulations imply that the lower and upper regions (whilst individually being of a convex shape as seen from downstream) actually meet in a concave corner, contradicting the conventional hypothesis in the literature that the front is wholly convex. The shape of the upper region as predicted here and the presence of the concave corner are independently verified via numerical simulation data.

Free boundary problems in shock reflection/diffraction and related transonic flow problems

Shock waves are steep wavefronts that are fundamental in nature, especially in high-speed fluid flows. When a shock hits an obstacle, or a flying body meets a shock, shock reflection/diffraction phenomena occur. In this paper, we show how several long-standing shock reflection/diffraction problems can be formulated as free boundary problems, discuss some recent progress in developing mathematical ideas, approaches and techniques for solving these problems, and present some further open problems in this direction. In particular, these shock problems include von Neumann's problem for shock reflection–diffraction by two-dimensional wedges with concave corner, Lighthill's problem for shock diffraction by two-dimensional wedges with convex corner, and Prandtl-Meyer's problem for supersonic flow impinging onto solid wedges, which are also fundamental in the mathematical theory of multidimensional conservation laws.