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When submerged under a liquid, the microstructure of a SuperHydrophobic Surface (SHS) traps a lubricating layer of gas pockets, which has been seen to reduce the skin friction of the overlying liquid flow in both laminar and turbulent regimes. More recently, spatially homogeneous SHS have also been shown to delay laminar–turbulent transition in channel flows, where transition is triggered by modal mechanisms. In this study, we investigate, by means of topology optimization, whether a spatially inhomogeneous SHS can be designed to further delay transition in channel flows. Unsteady direct numerical simulations are conducted using the spectral element method in a 3D periodic wall-bounded channel. The effect of the SHS is modelled using a partial slip length on the walls, forming a 2D periodic optimization domain. Following a density-based approach, the optimization procedure uses the adjoint-variable method to compute gradients and a checkpointing strategy to reduce storage requirements. This methodology is adapted to optimizing over an ensemble of initial perturbations. This study presents the first application of topology optimization to laminar–turbulent transition. We show that this method can design surfaces that delay transition significantly compared to a homogeneous counterpart, by inhibiting the growth of secondary instability modes. By optimizing over an ensemble of streamwise phase-shifted perturbations, designs have been found with comparable mean transition time and lower variance.

Post fuel injection in the expansion stroke is used for diesel particulate filter regeneration; however, fuel spray impinges on the cylinder liner due to the low temperature and pressure conditions. Fuel adhesion and fuel flowing down across the cylinder liner, the so-called "wall-flow," was observed by high-speed video images, and this adhesion is a cause of diesel engine lubricant oil dilution and the deterioration of fuel consumption in diesel engines. In this article, the fuel adhesion and the wall-flow of post diesel fuel injections were investigated with a high pressure-temperature constant volume optical chamber. The in-cylinder temperatures and pressures at 30, 60, and 90 degrees CA ATDCs, conditions commonly employed in post fuel injection timings, were measured by an actual engine, and similar conditions were created in the constant volume chamber by the combustion of a pre-mixed gas of ethylene, oxygen, and nitrogen. Fuel masses of 0.6, 1.1, and 1.7 mg per hole were injected at each ATDC setting. The weight of the adhered fuel on the wall and the fuel in the piston-cylinder crevice were measured by precision balance, and the liquid-vapor phases in the spray were observed by Mie scattering and shadowgraph methods. To measure the thickness of the adhered fuel on the cylinder wall, the laser-induced fluorescence method was employed. The results show that the fuel spray penetration and adhesion on the cylinder wall were different in the test conditions investigated here. With the early post injection, most of the injected fuel vaporizes without penetrating to the cylinder liner and gaseous diesel fuel is condensed on the cylinder wall. A thin and widely spread out fuel film is formed on the cylinder wall; however, no wall-flow could be confirmed by the high-speed video images. With late post fuel injections, the strong penetration of liquid fuel reaches the cylinder wall, and a thick and widely spread out fuel film was formed on the cylinder wall and the wall-flow phenomenon was observed here. However, the quantity of fuel involved in the wall-flow was smaller than that of the fuel adhering to the cylinder wall. The effects of in-cylinder pressure and temperature on the fuel adhesion on the cylinder wall were investigated. With the increase in pressure and temperature, the quantity of adhering fuel was reduced, suggesting that the boost pressure increase by turbo charging and a higher engine load is effective to reduce fuel adhesion. Furthermore, the effects of multiple post fuel injections on fuel adhesion to the cylinder wall were investigated, maintaining the total fuel injection amounts. With increases in the number of fuel injections, the total percentage of adhering post fuel on the cylinder wall was reduced. In the multiple fuel injections, it was observed that fuel motion takes place during the spray pass after the first and second fuel injections and that the penetration length of the second and third fuel sprays increases.

A Brinkman extended Darcy model has been used to study the effect of spatial nonuniformity of wall temperatures on the multiplicity of steady convective flows within a square porous enclosure saturated with low Prandtl fluid (Pr = 0.026). The convection is assumed to be driven by the hotter bottom wall in conjunction with colder side walls, where bottom-side wall junctions maintain continuity of temperature to represent a more realistic situation. This configuration enforces nonuniformity on either bottom wall or side walls or both bottom and side wall temperatures. The degree of nonuniformity of wall temperatures are varied parametrically in terms of thermal aspect ratio (?) to simulate various possible scenarios of nonuniform bottom/side wall temperatures and steady solution branches are traced in the parameter space of ? to investigate the variation of multiplicity of the flows. A perturbation technique has been used to initiate the steady solution branches, which are then traced by numerical continuation scheme. A penalty finite element approximation in conjunction with Newton-Raphson method and parameter continuation scheme has been used to construct the bifurcation diagrams of various steady branches. This work reveals three steady symmetric branches and four steady asymmetric branches with exhibition of symmetry breaking bifurcation. This work also shows that the nonuniformity of wall temperatures play a crucial role for the existence of multiple solutions as well as the multiplicity of convective flows. � 2012 Elsevier Ltd. All rights reserved.

Heat transfer in wall-flow monoliths has gained in interest because of the widespread adoption of these systems by automotive industry to fulfil soot emission regulations and the importance of heat exchange on the regeneration process control to avoid damaging the monolith. This paper presents a heat transfer model for wall-flow diesel particulate filters coupled with an unsteady compressible flow solver. The heat exchange between the gas and the solid phase is based on a bi-dimensional discretisation of the porous medium both in axial and tangential directions. The monolith can be discretised in the radial direction to account for the heat fluxes towards the environment through the monolith and the canister, which is also coupled with the inlet and outlet ducts of the filter. The model is validated against experimental data obtained in a flow test rig. A test campaign under non-reacting conditions has been conducted to show the capability for thermal response prediction. Tests cover clean and soot loaded monolith, continuous flow under steady and transient thermal conditions, and pulsating flow. In this case, the characteristics of the pressure waves in amplitude and frequency are similar to those that the monolith can undergo depending on its location along the exhaust line. © 2012 Elsevier Ltd., This work has been partially supported by the Spanish Ministerio de Ciencia e Innovacion through grant number DPI2010-20891-C02-02.

This paper describes in detail a novel formulation of the method of characteristics for its application to solve one-dimensional compressible unsteady non-homentropic flow advected along porous wall channels. In particular, the method is implemented into a wall-flow monolith Diesel particulate filter model whose purpose is the pressure drop prediction. The flow inside the monolith channels is considered to be one-dimensional and the flow through the porous wall treated as a source term agree with the Darcy's law. The flow dynamic behaviour at internal nodes of the channels is solved by means of shock capturing methods, whereas the end nodes, or boundary conditions, are solved applying the method of characteristics. The derived solution in this study of the Riemann variables and the entropy level includes the variation along the space-time plane due to cross-section area changes, friction and heat transfer as traditionally stated, but also takes into account the key influence on every line of the flow leaving or entering to the channels through the porous walls. © 2011 Elsevier Inc.

The present numerical study deals with natural convection flow in closed trapezoidal enclosures. The detailed analysis is carried out in two cases: (1) linearly heated side walls; (2) linearly heated left wall and cold right wall. In both the cases bottom wall is uniformly heated and top wall is well insulated. A penalty finite element method with bi-quadratic elements is used to obtain the results in the form of isotherms, streamlines and heatlines and local and average Nusselt numbers. Numerical results are obtained for various values of Rayleigh number Ra ( 10 3 ≤ R a ≤ 10 5 ), Prandtl number Pr ( 0.015 ≤ Pr ≤ 1000 ) and inclination angles (φ = 45°, 60° and 90°). Results signify that, at low Ra ( R a = 10 3 ) heat transfer is conduction dominant. At R a = 10 5 , multiple circulations of streamlines and heatlines results in enhanced convection. For linearly heated side walls (case 1), symmetric pattern in fluid flow and heat flow is observed. Enhanced thermal transport is observed from bottom wall to top portion of side walls via dense heatlines along the vertical center line. It is found that, less intense circulations occurs in square cavity (φ = 90°) compared to other cavities φ = 45°, 60°. In case 2, the cold right wall receives larger amount of heat from bottom wall compared to that of linearly heated left wall. The formation of boundary layer on the walls is explained based on heatlines. The local and average Nusselt numbers are also illustrated using heatlines. It is found that, Nub distribution exhibits sinusoidal variation at P r = 1000 in case 1. It is also found that, Nul and Nur display wavy pattern at higher Ra for all Pr in case 2. Finally, it is concluded that, overall heat transfer rates are larger for square cavity (φ = 90°) compared to other angles (φ = 45°, φ = 60°) irrespective of heating patterns for side walls.

Applications involving porous media occur widely in chemical engineering processes, e.g., oil and gas production, groundwater pollution, food processing, nuclear waste repository etc. The present study focuses on enhancing thermal processing of materials via distributed heating. Thermal mixing during laminar natural convection is analyzed in four different discretely heated porous square cavities. Heatline approach of visualizing heat flow is implemented to gain in-depth understanding of complex heat flow patterns for wide range of parameters ( Pr = 0.015 – 1000 , Da = 10 − 6 – 10 − 3 , Ra = 10 3 – 10 6 ). Results indicate that at lower Da ( = 10 − 6 ) heat flow is weak and transport is conduction dominant. At Da = 10 − 3 , the smaller hydraulic resistance of porous medium results in enhanced convection. The role of hot regime at bottom wall or hot regime at side walls to efficiently heat the cavity has been depicted via heatlines. It is illustrated by heatlines that when the heat sources are centrally located on the wall of the cavity, thermal mixing is significantly increased with subsequent rise in maximum temperature in the cavity. Effect of Da on local and average Nusselt numbers in different cases of porous cavities are adequately explained based on heatlines for the first time in this work. Average Nusselt number distributions show that hot regime of bottom wall transfers larger amount of heat whereas cold regimes of side wall receive larger amount of heat, especially at higher Da for all cases (cases 1–4). Further, cup-mixing temperature is evaluated for various cases to establish optimal thermal mixing by distributed heating in comparison to conventional bottom wall heating.

Natural convection in trapezoidal enclosures for uniformly heated bottom wall, linearly heated vertical wall(s) in presence of insulated top wall have been investigated numerically with penalty finite element method. Parametric studies for the wide range of Rayleigh numbers ( Ra = 10 3 - 10 5 ) and Prandtl numbers ( Pr = 0.7 - 1000 ) with various tilt angles of side walls ( φ ) have been performed. For linearly heated side walls, symmetry in flow pattern is observed. In addition, secondary circulations are observed near the bottom wall for φ = 0 ° especially for larger Pr ( Pr ⩾ 0.7 ) . In contrast, for linearly heated left wall and cooled right wall, the secondary circulations are stronger near the top portion of the left wall especially for larger Pr. Streamlines show that the strength of convection is larger for φ = 45 ° and flow intensities are found to be larger for higher Prandtl numbers. Local heat transfer rates are found to be relatively larger for φ = 0 ° . Average Nusselt number plots show higher heat transfer rates for φ = 0 ° and the overall heat transfer rates at the bottom wall is larger for the linearly heated left wall and cooled right wall. A non-monotonic trend in average Nusselt number vs Rayleigh number due to presence of multiple circulations is observed for φ = 0 ° .

The phenomena of natural convection within a trapezoidal enclosure filled with porous matrix for linearly heated vertical wall(s) with various inclination angles φ has been studied numerically. A penalty finite element analysis with bi-quadratic elements is used for solving the Navier–Stokes and energy balance equations. Wide range of parameters such as Rayleigh number, Ra ( 10 3 ⩽ Ra ⩽ 10 6 ) , Prandtl number, Pr ( 0.026 ⩽ Pr ⩽ 1000 ) and Darcy number, Da ( 10 - 5 ⩽ Da ⩽ 10 - 3 ) have been used. Numerical results are presented in terms of streamlines, isotherms and Nusselt numbers. It has been found that secondary and tertiary circulations appear at the bottom half of the cavity for φ = 30° and φ = 0° with Pr = 0.026 and 0.7 , Da = 10 - 3 and Ra = 10 6 for linearly heated side walls. On the other hand, for linearly heated left wall and cold right wall, multiple circulations occur near the top portion of the cavity. For linearly heated side wall, the local Nusselt number ( Nu b ) shows sinusoidal behavior with distance at high Darcy number for all tilt angles whereas increasing trend in Nu s is observed in the upper half of the side wall for all tilt angles. For linearly heated left wall with cold right wall, increasing trend in Nub is observed irrespective to Da and Pr and Nub is even larger for higher Da. Increasing trend is also observed in Nul for all tilt angles for linearly heated left wall. Due to discontinuity in right corner, Nur first decreases and thereafter that increases for Y ⩾ 0.2 . The average Nusselt number remains constant up to Ra = 10 6 at low Da for Pr = 0.026 whereas for Pr = 1000 and high Ra, that starts to decrease for bottom wall whereas that starts to increase for side walls due to convection dominant effect at high Da. In general, the average Nusselt number increases with the increase of Da and Ra for higher Da.

Natural convection and flow circulation within a cavity has received significant attention in recent times. The wide range of applicability of flow inside a cavity (food processing industries, molten metal industries, etc.) requires thorough understanding for cost efficient processes. This paper is based on comprehensive analysis of heat flow pattern using Bejan's heatline concept. The key parameters for our study are the Prandtl number, Rayleigh number and Nusselt number. The values of Prandtl number (0.015, 0.026, 0.7 and 1000) have been chosen based on wide range of applicability. The Rayleigh number has been varied from 102 to 105. Interesting results were obtained. For low Rayleigh number, it is found that the heatlines are smooth and perfectly normal to the isotherms indicating the dominance of conduction. But as Ra increases, flow slowly becomes convection dominant. It is also observed that multiple secondary circulations are formed for fluids with low Pr whereas these features are absent in higher Pr fluids. Multiple circulation cells for smaller Pr also correspond multiple cells of heatlines which illustrate less thermal transport from hot wall. On the other hand, the dense heatlines at bottom wall display enhanced heat transport for larger Pr. Further, local heat transfer (Nul, Nut) are explained based on heatlines. The comprehensive analysis is concluded with the average Nusselt number plots. A correlation for average heat transfer rate and Ra has been developed and the range of Rayleigh number is also found, to depict the conduction dominant heat transfer. � 2009 Elsevier Ltd. All rights reserved.

The sloshing pressures on the side wall and on the top cover plate of a tank partially filled with liquid and rigidly mounted on a barge in irregular waves are investigated through physical model tests. The barge was allowed to oscillate freely in the combined degrees of excitation, i.e. sway, heave, and roll. Four liquid fill levels with aspect ratios hs/ l (where hs is the static liquid depth and l is the tank length) of 0.163, 0.325, 0.488, and 0.585 are considered for the present study. The effect of peak wave excitation frequencies on the pressure variation is studied in detail, the results of which are herein reported. It is observed that the impact pressure on the top panel of the tank is about 1.6 times the pressure observed on the side wall.

The axisymmetric and plane extrusion flows of a liquid foam are simulated assuming that the foam is a homogeneous compressible Newtonian fluid that slips along the walls. Compressibility effects are investigated using both a linear and an exponential equation of state. The numerical results confirm previous reports that the swelling of the extrudate decreases initially as the compressibility of the fluid is increased and then increases considerably. The latter increase is sharper in the case of the exponential equation of state. In the case of non-zero inertia, high compressibility was found to lead to a contraction of the extrudate after the initial expansion, similar to that observed experimentally with liquid foams and to decaying oscillations of the extrudate surface. The time-dependent calculations show that the oscillatory steady-state solutions are stable. These steady-state oscillatory solutions are not affected by the length of the extrudate region nor by the boundary condition along the wall. © Springer-Verlag 2007. 47 1 49 62 Cited By :26

Structure-based turbulence models (SBM) carry information about the turbulence structure that is needed for the prediction of complex non-equilibrium flows. SBM have been successfully used to predict a number of canonical flows, yet their adoption rate in engineering practice has been relatively low, mainly because of their departure from standard closure formulations, which hinders easy implementation in existing codes. Here, we demonstrate the coupling between the Algebraic Structure-Based Model (ASBM) and the one-equation Spalart-Allmaras (SA) model, which provides an easy route to bringing structure information in engineering turbulence closures. As the ASBM requires correct predictions of two turbulence scales, which are not taken into account in the SA model, Bradshaw relations and numerical optimizations are used to provide the turbulent kinetic energy and dissipation rate. Attention is paid to the robustness and accuracy of the hybrid model, showing encouraging results for a number of simple test cases. An ASBM module in Fortran-90 is provided along with the present paper in order to facilitate the testing of the model by interested readers. © 2014 Elsevier Inc. 52 111 128 111-128

Two linear eddy-viscosity models, the v2-f and k-ω models, have been combined with an algebraic structure-based algorithm for the evaluation of the Reynolds stresses. This closure was originally designed as an integral part of the algebraic structure-based model (ASBM) to capture the turbulent anisotropy occurring in rotating wall bounded flows. It is shown that the algebraic structure-based evaluation of the Reynolds stresses can be used directly with conventional turbulence models sensitizing them to rotation. Significant improvement in the prediction of anisotropic turbulent flow can be achieved without an additional tuning of the closure coefficients. The models are evaluated in spanwise rotating channel flow and in flat plate boundary layers. The sensitivity to the Reynolds and rotation numbers is investigated. The results are compared with DNS data. © 2006 Elsevier Inc. All rights reserved. 27 653 660 653-660

Detailed quantitative maps of the heat transfer distribution near a 180° sharp turn of a square channel with rib turbulators are measured by means of infrared thermography associated with the heated-thin-foil technique. Air flows into the channel where ribs are mounted on two opposite walls and placed at 60° with respect to its axis. Two rib pitches, two different rib arrangements and two heating conditions are investigated. Results are presented in terms of local and averaged Nusselt numbers which are normalized with the classical Dittus and Boelter correlation for three different Reynolds numbers.

Numerical simulation for natural convection flow in fluid filled enclosures with curved side walls is carried out for various fluids with several Prandtl numbers ( Pr = 0.015, 0.7 and 1000) in the range of Rayleigh numbers ( Ra = 10 3 –10 6 ) for various cases based on convexity/concavity of the curved side walls using the Galerkin finite element method. Results show that patterns of streamlines and heatlines are largely influenced by wall curvature in concave cases. At low Ra , the enclosure with highest wall concavity offers largest heat transfer rate. On the other hand, at high Ra , heatline cells are segregated and thus heat transfer rate was observed to be least for highest concavity case. In convex cases, no significant variations in heat and flow distributions are observed with increase in convexity of side walls. At high Ra and Pr , heat transfer rate is observed to be enhanced greatly with increase in wall convexity. Results indicate that enhanced thermal mixing is observed in convex cases compared to concave cases. Comparative study of average Nusselt number of a standard square enclosure with concave and convex cases is also carried out. In conduction dominant regime (low Ra ), concave cases exhibit higher heat transfer rates compared to square enclosure. At high Ra , low Pr , concave cases with P 1 P 1 ′ = 0.4 is advantageous based on flow separation and enhanced local heat transfer rates.

An analysis is performed to obtain the non-similar solution of a steady compressible laminar boundary layer flow over a yawed infinite circular cylinder with non-uniform slot injection (or suction) and non-uniform wall enthalpy. The difficulties arising at the starting point of the streamwise coordinate, at the edges of the slot and at the point of separation are overcome by applying the method of quasilinear implicit finite-difference scheme. It is observed that the separation can be delayed by non-uniform slot suction and also by moving the slot downstream but the effect of non-uniform slot injection is just the reverse. An increase in March number and total enthalpy at wall causes the separation to occur earlier while cooling delays it. The non-uniform total enthalpy at the wall (i.e., the cooling or heating of the wall in a slot) has very little effect on the skin friction and hence on the point of separation. ? 2001 Elsevier Science Ltd. All rights reserved.

The performance of Reynolds stress transport (RST) models in non-equilibrium flows is limited by the lack of information about two dynamically important effects: The role of energy-containing turbulence structure (dimensionality) and the breaking of reflectional symmetry due to strong mean or frame rotation. Both effects are fundamentally non-local in nature and this explains why it has been difficult to include them in one-point closures like RST models. Information about the energy-containing structure is necessary if turbulence models are to reflect differences in dynamic behavior associated with structures of different dimensionality (nearly isotropic turbulence vs turbulence with strongly organized two-dimensional structures). Information about the breaking of reflectional symmetry is important whenever mean rotation is dynamically important (flow through axisymmetric diffuser or nozzle with swirl, flow through turbomachinery, etc.). Here we present a new one-point model that incorporates the needed structure information, and show a selection of results for homogeneous and inhomogeneous flows. © 2000 Begell House Inc. Published by Elsevier Science Inc. All rights reserved. 21 599 605 599-605

SUMMARY A numerical procedure is developed for the analysis of flow in a channel whose walls describe a travelling wave motion. Following a perturbation method, the primitive variables are expanded in a series with the wall amplitude as the perturbation parameter. The boundary conditions are applied at the mean surface of the channel and the first-order perturbation quantities are calculated using the pseudospectral collocation method. Although limited by the linear analysis, the present approach is not restricted by the Reynolds number of the flow and the wave number and frequency of the wavy-walled channel. Using the computed wall shear stresses, the positions of flow separation and reattachment are determined. The variations in velocity and pressure with frequency of excitation are also presented. © 1998 John Wiley & Sons, Ltd.

The response of turbulent flow to abrupt changes in pipe wall roughness is studied here. It is shown that a circumferential flow will not develop near the wall in a pipe with a short patch of circumferentially varying roughness. It is therefore concluded that the secondary flow mechanism would play no part in the liquid film distribution in horizontal annular flow.