The control force application procedure also posed a challenging problem initially. As mentioned earlier, there are two methods of bubble control. The “whole domain” control method utilized manipulation of gravity throughout the domain to achieve buoyancy forces which balanced the lift and drag forces. For low complexity flows (low shear, low relative velocity, laminarflows) the “whole domain” method proved to be more robust and allowed for quick control convergence. However, as the shear rates and relative velocities increased, this method proved to be futile due to the need for large changes in gravity to balance the larger lift and drag forces. The large changes in gravity resulted in numerical divergence of the pressure Poisson equation solve at the prescribed velocity outflow boundaries due to mass conservation. The “bubble” control method was therefore used for higher complexity flows (large shear rate, large relative velocities, turbulence, etc.), where the control forces were applied only to the inside of the bubble and its interface region, thus eliminating the numerical divergence induced at the prescribed velocity outflow boundaries that arose from steeply altering the domain gravity.
and Al 2 O 3 -water based nanofluids. Two volume fractions ϕ = 0.006 and 0.016 have been considered. Simulation 1 combines Eqs (7) and (10), whereas simulation 2 uses Eqs (8) and (9). It is clear that the two sets of correlations provide rather the same results in terms of the average value of the heat transfer coefficient with differences of about 17% and 33% for ϕ = 0.006 and 0.016, respectively, compared to the experiments. It shows in particular that for these sets of parameters, the correlations do not considerably influence the accuracy of the single-phase model. As shown previously, the results are not influenced by the particle volume fraction. Though the effect of Brownian motion is accounted for in Equation (10), it has no noticeable influence in laminarflows. This confirms the previous work of Keblinski et al. , who suggested that the motion of nanoparticles due to the Brownian motion is too slow to transport a significant amount of heat through a nanofluid. They ignored the effect of Brownian motion in the enhancement of thermal conductivity of nanofluids.
The objective of this work is the thermal study of incompressible laminarflows in a tank mechanically agitated by an anchor agitator and the fluids used are viscoplastic with Bingham model. The modeling difficulties of the problem lie in the viscoplastic nature of the fluid. We perform a numerical simulation of hydrodynamics and heat transfer using the industrial code (Fluent ®). The results obtained give us the possibility to make a comparative study between our results and previous work from the point of view of energy consumption (Power Number), and heat transfer (Nusselt number).
In this research, a cell-by-cell artificial neural network approach is used to predict the velocity vectors of steady- state, viscous, incompressible, laminarflows in a two-dimensional computational domain. The flow behaviour is characterized by the initial flow velocity, and the geometry of the wall boundaries. A feedforward neural network architecture is applied in this research. The model is trained using Levenberg-Marquardt and Bayesian regularization backpropagation algorithms. The training data for the model are obtained by solving the Navier-Stokes equations for two- dimensional, steady-state, viscous, incompressible, laminar flow using commercial ANSYS Fluent software. The results show that the predicted values produced by the model is in good agreement with the simulation data. Even though the introduction of artificial neural networks at the cell level increases the complexity of the training process, this drawback is compensated by the increase in flexibility (generality) of the model. More importantly, the results show that the cell-by-cell artificial neural network approach is capable of providing an accurate prediction of the fluid velocity field for the flow investigated in this research. The outcomes designate that the new ANN approach is capable of getting an accurate velocity vector prediction as several statistical parameters confirmed. Since all the computation cost took place in the training phase, the new approach calculated the result faster than the traditional numerical methods. Such simulation provides a reliable perception about the fluid behaviour with respect to momentum and equations. In addition to the preceding recorded data, the proposed method considers the geometrical boundaries profile as a major contribution for ANN training phase.
numbers, closed to 1. The Mach numbers interval 1.1≤M ≤1.7 of unsteady regimes is established here. Significant changeability of computational results is a feature of this family of unsteady flows due to strong influence of the numerical method dissipation on dis- turbances generation resulted from a Kelvin-Helmholtz instability of three contact discontinuities available in these flows. It may be supposed, that laminarflows may be close to second order method solutions, highly turbulent flows are influenced by turbulent dissipation and oscillations may be partly or fully damped similarly to damping in present numerical first order method simulations, but this question require next investiga- tions.
The nonlinear, time-series solutions for the spectral velocity wave compo- nents are obtained from a modified Lorenz-type set of equations that is sensitive to the initial conditions applied to the integration of the equations. The control parameters for these equations are the steady state boundary layer velocity gra- dients that are determined by the particular value of the kinematic viscosity for the system. Experimental measurements of the unsteady fluctuation levels in la- minar boundary layers when subjected to free stream turbulence have been pre- sented by Walsh and Hernon . These results indicate that the free stream turbulence level has a significant effect on the resulting entropy generation rates in laminar boundary layers. The initial conditions for the integration of the Lo- renz-type equations are heuristically assumed to be attenuated levels of the tur- bulence imposed on the system from the free stream.
The transition to turbulence of wall-bounded shear flows remains a fundamental problem in fluid mechanics because of the complexity of the flows observed, the depth of the mathematical issues involved, and the numerous practical implications. The central issue is that shear flows are usually linearly stable (e.g., pipe flow and plane Couette flow) yet nonlinearly unstable to small but finite-amplitude disturb- ances that typically trigger transition in practical situations. This transition is abrupt, immediately leading to complicated spatiotemporal flows [1–3]. There has, however, been con- siderable recent success in viewing such transitional fluid flows as large dynamical systems where transition amounts to the flow being disturbed out of the basin of attraction of the laminar shear flow [4–6]. Key to making progress with this picture has been the discovery of simple exact unstable solutions (equilibria, traveling waves, periodic orbits) to the Navier-Stokes equations [7–11], which are born in saddle- node bifurcations. These solutions are either embedded in the basin boundary (between the laminar and turbulent states) or sit in the basin of attraction of the turbulent state, possibly even being buried in the turbulent attractor itself. If the turbulent state is not an attractor, the more general concept of an “ edge ” (a codimension one hypersurface dividing initial conditions that enjoy a turbulent episode from those that immediately relaminarize) is needed. Mapping out the stable and unstable manifolds of some of these solutions embedded in the basin boundary (or edge) has revealed much about what particular disturbances are most efficient in triggering transition [12–14] and the transition process itself [15,16]. Doing the same for solutions embedded in the turbulent attractor generates a skeleton in phase space over which the turbulent dynamics is draped [17,18].
The numerical approach based on finite volume method was applied to solve the steady laminar magnetohydrodynamics pipe flows in the entrance region. A two-dimensional liquid metal developing flow through a pipe subjected to an external magnetic field was studied for different values of the Reynolds and Hartmann numbers. Afterward, the artificial neural network was trained to develop the output datasets obtained from the numerical solution. Eventually, by using the curve fitting on the developed datasets, the correlation for predicting development length was proposed for different ranges of Re and Ha. In addition, the effect of Re and Ha on the MHD development length, MHD fully developed centerline velocity, pressure losses and the Lorentz force were discussed. It was concluded that with increasing of the Reynolds number, the MHD development length and the MHD fully developed centerline velocity augment; in contrast, the MHD development length and the MHD fully developed centerline velocity reduce when the Hartmann number increases. Furthermore, the results show that with the increase of the Hartmann number the pressure losses rise up.
Simulations of short laminar separation bubbles have been carried out in two and three dimensions. The three-dimensional simulations show full transition to turbu- lence, the process being characterized by breakdown of Λ-vortices. Budgets of turbu- lence kinetic energy and Reynolds stresses show that the flow just after reattachment consists of an upper region, corresponding quite closely to the upper half of a turbulent mixing layer and a near-wall portion with a redeveloping turbulent boundary layer. The relaxation towards equilibrium is slow. At least seven bubble lengths are required to reach the usual log law. Stability analysis showed that profiles with more than 15% reverse flow were required for absolute instability, whereas the bubbles simulated had lower levels of reverse flow. Two-dimensional simulations do not appear to represent adequately the characteristics of the short separation bubbles. Further simulations should address the issue of bursting of short separation bubbles to form long bubbles. The authors would like to thank British Aerospace, Sowerby Research Centre for their financial support of this work and Dr H. P. Horton and Professor M. Gaster for helpful suggestions during the research. National supercomputer time was provided by EPSRC under grants GR/K43957 and GR/M08424.
 M. Abarham, P. Zamankhan, J.W. Hoard, D. St yles, C.S. Sluder, J.M. St orey, M.J. Lance, D. Assanis, CFD analysis of particle transport in axi-symmetric tube flows under the influence of thermophoretic force, International Journal of Heat and Mass Transfer, 61 (2013) 94-105.  J.-Z. Lin, Z.-Q. Yin, P.-F. Lin, M.-Z. Yu, X.-K. Ku,
The recirculating ﬂow in a 3D lid-driven cavity presents the occurrence of some consid- erable 3D features, even at relatively low Reynolds numbers. One of the most remark- able is the formation of Taylor–Görtler-like (TGL) vortices at the corners of the bot- tom of the cavity. Small counter-rotating vortices are formed as a result of the curva- ture of the streamlines due to the main vortex in the middle of the cavity. Following the work of Gravemeier et al. , we simulate the 3D cavity ﬂow at Reynolds numbers Re = 3200, 7500, 10,000, to cover respectively the laminar, transient and turbulent regimes. Also for this test, we ﬁrst aim to obtain a good accuracy with a relatively coarse spatial resolution. The computational grid consists of a 32 3 partition of the unit cube, uniform in
Alhamdulillah, all praise belongs to Allah for His guidance and for giving me the strength to finish this arduous study. The journey to complete the study is not always smooth as laminar flow. Unpredictable things occur just like a turbulence flow and making life extra complicated to handle. But I believe, the more turbulent your journey, the sweeter your reward. Therefore, I am grateful to Him for all tests and trials befall upon me, and I am sure that without His help, this thesis would not have been possible.
Fluid is transported in several ways in the microchannels used in microfluidic devices. Two important methods of transport are flows driven by pressure differential and electro-osmotic flows. In the former case, flow is transported by means of applied pressure differences. In the latter case, flow transport is initiated by application of a high electric field. This type of flow is broadly classified as electrokinetic’s flow. Capillary driving forces owing to surface tension, ‘‘wetting’’ of surfaces by the fluid, can also lead to pressure gradients in liquids. This pressure gradient causes flow transport, so it is similar in many ways to pressure driven flows. However, the shape of the interface is an important factor in this type of flow. Free surface flows are caused by gradients in interfacial tension (Marangoni flows). These can be manipulated using the dependence of surface tension on temperature or chemical concentration (Tuba Bayraktar, Srikanth B. Pidugu, 2006).
Effects of Unsteady MHD flow problems have become more important industrially. Indeed, MHD laminar boundary layer behavior over a stretching surface is a significant type of flow having considerable practical applications in chemical engineering, electrochemistry and polymer processing. The study of boundary layer flow over a stretching plate has generated much interest in recent years in view of its significant applications in industrial manufacturing processes such as glass-fiber and paper production, hot rolling, wire drawing, drawing of plastic films, metal and polymer extrusion and metal spinning. Both the kinematics of stretching and the simultaneous heating or cooling during such processes has a decisive influence on the quality of the final products. In his pioneering work, Sakiadis  developed the flow field due to a flat surface, which is moving with a constant velocity in a quiescent fluid. Crane  extended the work of Sakiadis  for the two-dimensional problem where the surface velocity is proportional to the distance from the flat surface. As many natural phenomena and engineering problems are worth being subjected to MHD analysis, the effect of transverse magnetic field on the laminar flow over a stretching surface was studied by a number of researchers .
investigation presents new data describing the transition to turbulence, under sinusoidal and asymmetric oscillatory flows, over flat featureless beds of immobile uniform sediments (ranging from fine to coarse sands). These data were collected using an oscillating trolley system in a fluid medium (fresh water), using a variety of visual and numerical interpretative methods. New empirical relationships for sinusoidal and asymmetric flows are derived from these data in conjunction with the large (sinusoidal) data sets of Li (1954) and Manohar (1955). These latter data sets provide observations made using similar equipment and methodology, over relatively large ranges of grain size and wave period. By using laboratory observations, no numerical assumptions are necessary regarding the mechanisms by which turbulence is initiated, under such a variety of conditions. Accepting the relatively small degree of scatter caused potentially by experimental noise and differences in methodology, the absolute and relative effect of the flow and bed parameters are studied. The relationships between several aspects of the boundary layer, considered to be important in regulating the transition to turbulence, are then discussed.
We use B = 5.5 and κ = 0.4 because of the following reason: In our anal- ysis, it is convenient that the entire flow from the bottom to the surface is one inertial boundary layer. Using B = 5.5 and κ = 0.4 provides an agreement between the inner and outer regions of the developed boundary flow and en- sures that the layer has universal velocity structure [20, 21]. Nikuradse  first found the constants B = 5.5 and κ = 0.4 for hydraulically smooth pipe flow. In , Keulegan assumed that the same values for these constants can be adopted for smooth open channels. In the literature, these empirical con- stants can have different values. An extensive survey of mean velocity profile measurements in various 2-D turbulent boundary layer flows by Coles  showed that the law of the wall is well represented by equation (4.2) when using κ = 0.4 and B = 5.1. Huffman and Bradshaw  used the values B = 5.0 and κ = 0.41. More recently, Steffler et al.  adopted the val- ues B = 5.5 and κ = 0.4 and presented some turbulence measurements for uniform flow in a smooth rectangular channel. They found that the velocity measurements in the viscous sublayer agree well with the linear form of the law of the wall.
HE development of gas-kinetic schemes for solving compressible flows in recent time has received a lot of attention and progress, especially in the last two decades. Among those notably promising ones are the Equilibrium Flux Method (EFM) , the Kinetic Flux Vector Splitting (KFVS) scheme  and the BGK scheme . The KFVS scheme is very diffusive and less accurate in comparison with the gas-kinetic BGK scheme. The diffusivity of the KFVS scheme is mainly due to the particle or wave-free transport mechanism, which sets the CFL (Courant–
In contrast, the mean visibility scores for both the anterior and the posterior laminar borders were better with the EDI OCT. The signal strengths of the deep ONH structures in the HP-OCT images were comparable with or even stronger than those in the EDI OCT images. In the HP-OCT images, however, low image contrast between the lamina cribrosa and the prelaminar or retrolaminar tissue sometimes complicated the identification of the laminar borders. Both OCT systems incorporate an image averaging algorithm to improve image contrast. Image averaging can improve image quality by reducing speckle noise, which is the cause of a grainy or textured appearance of the structures that complicates the delineation of tissue surfaces. On the other hand, image averaging can also be disadvantageous, by increasing motion artifacts, because it takes longer time to acquire more images. In our study eyes, image averaging substantially improved the image contrast, and thus, the advantageous effect of image averaging exceeded the disadvantage of causing possible motion artifacts. Our prototype HP-OCT provided averaging of up to 32 B-scans, whereas the EDI OCT allowed up to 100 B-scans. The higher image contrast of the EDI OCT may be, at least in part, attributable to the image averaging.