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The flow and heat transfer characteristics are investigated in micro and mini communicating channel pressure driven flows by 2D numerical simulations using a computational method. The continuum based Navier–Stokes and continuity equations are solved by the Spectral Element Method (SEM). Flow and heat transfer characteristics are determined for 10 2 L ˆ and an aspect ratio of r = a ˆ / ( 2 L ˆ ) is used, where a ˆ is the height of block within the channel and L ˆ is the periodic length. For low Reynolds number, viscous forces dominate and two stationary symmetric vortices are generated between blocks with very laminar parallel viscous flow in the upper and lower communicating channel. For moderate Reynolds numbers, numerical results show a transition scenario with two Hopf flow bifurcations, as the flow evolves from a laminar to a time-dependent flow regime. The first Hopf bifurcation B1 occurs at a critical Reynolds number (Rec1) leading to a periodic flow characterized by a frequency ω1. A quasi periodic flow sets in for higher Reynolds numbers through a second Hopf flow bifurcation B2 occurring at a critical Reynolds number (Rec2

The enhancement characteristics of heat transfer, through a transition scenario of flow bifurcations, in asymmetric wavy wall channels, are investigated by direct numerical simulations of the mass, momentum and energy equations, using the spectral element method. The heat transfer characteristics, flow bifurcation and transition scenarios are determined by increasing the Reynolds numbers for three geometrical aspect ratios r = 0.25, 0.375, and 0.5, and Prandtl numbers 1.0 and 9.4. The transition scenarios to transitional flow regimes depend on the aspect ratio. For the aspect ratios r = 0.25 and 0.5, the transition scenario is characterized by one Hopf flow bifurcation. For the aspect ratio r = 0.375, the transition scenario is characterized by a first Hopf flow bifurcation from a laminar to a periodic flow, and a second Hopf flow bifurcation from a periodic to quasi-periodic flow. The periodic and quasi-periodic flows are characterized by fundamental frequencies ω 1 , and ω 1 and ω 2 , respectively. For all the aspect ratios and Prandtl numbers, the time-average mean Nusselt number and heat transfer enhancement increases with the Reynolds number as the flow evolves from a laminar to a transitional regime. For both Prandtl numbers, the highest increase in the Nusselt number occurs for the aspect ratio r = 0.5; whereas, the lowest increases happen to r = 0.25. The increase of the Nusselt number occurs at the expense of a higher pumping power, which, for both Prandtl numbers, grows as the aspect ratio increases from r = 0.25 to r = 0.5 for reaching a specific Nusselt number. This enhancement is obtained without the necessity of high volumetric flow rates associated with turbulent flow regimes, which demand much higher pumping powers. Significant heat transfer enhancements are obtained when the asymmetric wavy channel is operated in the appropriate transitional Reynolds number range.

During the last years the aerodynamics characteristics of airfoils have been studied solving numerically the Navier-Stokes (NS) equations. These calculations require a significant computational cost due to both the second order and the nonlinear characteristics of the NS partial differential equations. Therefore, efforts have been devoted to reduce this cost and increase the accuracy of the numerical methods. The Lattice-Boltzmann Method (LBM) has become a great alternative to simulate this problem and a variety of fluid flows. In this method, the convective operator is linear and the pressure is calculated directly by the equation of state without implementing iterative methods. This work represents a preliminary investigation of a laminar flow over airfoils under low Reynolds number conditions (Re = 500). Solutions are obtained using a Multi-Block mesh refinement method. In order to validate the computational code, calculations are performed on a SD7003 airfoil at an angle of attack of 4° and 30°, which corresponds to the available numerical and experimental results. The results of this study agree well with previous experimental and numerical studies demonstrating the capabilities of the LBM to simulate accurately laminar flows over airfoils as well as capturing and predicting the laminar separation bubbles.Copyright © 2013 by ASME

Numerical investigation of laminar, transitional and chaotic flows in converging–diverging channels are performed by direct numerical simulations in the Reynolds number range 10 < Re < 850. The temporal flow evolution and the onset of turbulence are investigated by combining classical fluid dynamics representations with dynamical system flow characterizations. Modern dynamical system techniques such as timedelay reconstructions of pseudophase spaces, autocorrelation functions, fractal dimensions and Eulerian Lyapunov exponents are used for the dynamical flow characterization of laminar, transitional and chaotic flow regimes. As a consequence of these flow characterizations, it is verified that the transitional flow evolves through intermediate states of periodicity, two-frequency quasi-periodicity, frequency-locking periodicity, and multiple-frequency quasi-periodicity before reaching a non-periodic unpredictable behaviour corresponding to low-dimensional deterministic chaos.Qualitative and quantitative differences in Eulerian dynamical flow parameters are identified to determine the predictability of transitional flows and to characterize chaotic, weak turbulent flows in converging–diverging channels. Autocorrelation functions, pseudophase space representations and Poincaré maps are used for the qualitative identification of chaotic flows, assertion of their unpredictable nature, and recognition of the topological structure of the attractors for different flow regimes. The predictability of transitional flows is determined by analysing the autocorrelation functions and by representing their attractors in the reconstructed pseudophase spaces. The transitional flow behaviour is examined by the geometric visualization of the evolution of the attractors and Poincaré maps until the appearance of a strange attractor at the onset of chaos. Eulerian Lyapunov exponents and fractal dimensions are quantitative parameters to establish the onset of chaos, the persistence of chaotic flow behaviour, and the long-term persistent unpredictability of chaotic Eulerian flow regimes. Lastly, three-dimensional simulations for converging–diverging channel flow are performed to determine the effect of the spanwise direction on the route of transition to chaos.

A study of Lagrangian chaos, Eulerian chaos, and mixing enhancement in converging–diverging channel flows, using spectral element direct numerical simulations, is presented. The time‐dependent, incompressible Navier–Stokes and continuity equations are solved for laminar, transitional, and chaotic flow regimes for 100≤Re≤850. Classical fluid dynamics representations and dynamical system techniques characterize Eulerian flows, whereas Lagrangian trajectories and finite‐time Lagrangian Lyapunov exponents identify Lagrangian chaotic flow regimes and quantify mixing enhancement. Classical representations demonstrate that the flow evolution to an aperiodic chaotic regime occurs through a sequence of instabilities, leading to three successive supercritical Hopf bifurcations. Poincare sections and Eulerian Lyapunov exponent evaluations verify the first Hopf bifurcation at 125

Direct numerical simulations of the transition process from laminar to chaotic flow in converging–diverging channels are presented. The chaotic flow regime is reached after a sequence of successive supercritical Hopf bifurcations to periodic, quasiperiodic, and chaotic self‐sustained flow regimes. The numerical experiments reveal three distinct bifurcations as the Reynolds number is increased, each adding a new fundamental frequency to the velocity spectrum. In addition, frequency‐locked periodic solutions with independent but synchronized periodic functions are obtained. A scenario similar to the Ruelle–Takens–Newhouse scenario of the onset of chaos is verified in this forced convective open system flow. The results are illustrated for different Reynolds numbers using time‐velocity histories, Fourier power spectra, and phase space trajectories. The global structure of the self‐sustained oscillatory flow for a periodic regime is also discussed.

The flow and heat transfer characteristics of an impinging jet on a perpendicular flat surface are obtained by two dimensional numerical simulations of laminar and transitional flow regimes for the Reynolds number of Re = 300, 350, and 400 for a Prandtl number of Pr = 0.7. A fixed jet to plate spacing of H/W = 5 and a given heat flux on the plate surface are considered. Temporal evolution of velocity and temperature fields, Fourier spectra of the velocity temporal evolution and time average local and global Nusselt numbers are obtained for increasing Reynolds numbers for determining the time depending behavior and its effect on the heat transfer characteristics. Numerical simulation results demonstrate that self-sustained transitional periodic flow regimes arise from a laminar regime, when the Reynolds number is further increased to Re = 400 and that these regimes spread out to the whole domain with similar time dependent characteristics due to the flow incompressibility. Evaluations of time average local and global Nusselt numbers demonstrate the asymmetric Gaussian-type spatial distribution and the increase of both parameters when the flow evolves through the transitional periodic regime, with reasonable increases on the pumping power requirements.Copyright © 2010 by ASME

Heat transfer enhancement characteristics, through a transition scenario of flow bifurcations in symmetric wavy wall channels, are investigated by direct numerical simulations of the mass, momentum, and energy equations using spectral element methods. Flow bifurcations, transition scenarios, and heat transfer characteristics are determined by increasing the Reynolds numbers from a laminar to a transitional flow for the geometrical aspect ratios r =0.125 and r = 0.375. The numerical results demonstrate that the transition scenario to transitional flow regimes depends on the aspect ratio. For r =0.375, the transition scenario is characterized by one Hopf flow bifurcation in a frequency-doubling transition scenario, where further increases in the Reynolds number always lead to periodic flows; whereas, for r = 0.125, the transition scenario is characterized by a first Hopf flow bifurcation from a laminar to a time-dependent periodic flow and a second Hopf flow bifurcation from a periodic to a quasiperiodic flow. For r =0.125, the flow bifurcation scenario is similar to the Ruelle―Takens―Newhouse (RTN) transition scenario to Eulerian chaos observed in asymmetric wavy and grooved channels. The periodic and quasiperiodic flows are characterized by fundamental frequencies ω 1 , and ω 1 and ω 2 , respectively. For the aspect ratio r = 0.375, the Nusselt number increases slightly as the Reynolds number increases in the laminar regime until it reaches a critical Reynolds number of Re c ≈ 126. As the flow becomes periodic, and then quasiperiodic, the Nusselt number continuously increases with respect to the laminar regime, up to a factor of 4, which represents a significant heat transfer enhancement due to a better flow mixing.

The stretching and flow mixing enhancement characteristics in mini and micro wavy channels have been investigated by solving the Boltzmann Transport Equation (BTE) with the Lattice-Boltzmann method (LBM). The Eulerian and Lagrangian flow characteristics are obtained for a 2D symmetric wavy channel with the geometrical aspect ratios r = 0.375 and 0.1875, by performing numerical simulations of a Newtonian incompressible flow and a Newtonian compressible flow. Extended and reduced domain are used for determining the existence of spatial periodicity the Eulerian and Lagrangian characteristics for increasing Reynolds numbers. The Eulerian flow characteristics for micro channels configuration are determined for different Knudsen numbers, pressure ratio and accommodation coefficients with the objective of obtaining reliable velocity and flow patterns. The Lagrangian characteristics are obtained by integrating the Eulerian velocity field. Thousands of massless fluid particles are used to determine fluid particle Lagrangian trajectories, future and past stretching fields, and Lagrangian Lyapunov exponents, which are used for determining the channel regions with high stretching and flow mixing enhancement. The numerical results demonstrate that mini and micro wavy channels flows develop different Lagrangian characteristics. In mini wavy channels, flow mixing enhancement develops for time dependent 2D flows; whereas, in micro wavy channels, future and past stretching fields describe existence of flow mixing enhancement for very low, stable and time independent Reynolds number flow regime.Copyright © 2008 by ASME

Numerical investigations of transition scenarios due to flow bifurcations from laminar to time-dependent transitional flows in asymmetric wavy channels with different spatial periodicity on the sinusoidal wall are performed by direct numerical simulations of the mass and momentum conservation equations using a spectral element method computational program. Three aspect ratios r = a/(2L) are considered in this study: 0.125, 0.25, y 0.375. Computational meshes for both extended and periodic computational domains are used to determine first, the existence of spatial periodicity and second, the transitional flow behavior for increasing Reynolds numbers. Numerical results shows that the transition scenarios are highly dependent on the aspect ratio, r. The following scenarios develop: a) a first transition scenario with one flow bifurcation to a relatively low Reynolds numbers, Rec ; b) a second scenario, with also one flow bifurcation, to a relatively high Reynolds numbers, Rec* ; and, c) a third flow transition scenario with two Hopf bifurcations B1 and B2 , occurring at critical Reynolds numbers Rec1 y Rec2 , respectively. In this third scenario, fundamental frequencies ω1 and ω2 , and sub and super harmonic combinations of the fundamental frequencies develop as the Reynolds number increases from a laminar to higher transitional flow regime. This transition scenario from a laminar flow to high transitional flow regimes is very similar to the Ruelle-Takens-Newhouse (RTN) found in another confined flow channels such as symmetric wavy, grooved and communicating channels.Copyright © 2008 by ASME

The Eulerian and Lagrangian characteristics of a rarified gas flow have been investigated and related to flow mixing enhancement in micro grooved channels. The governing Boltzmann Transport Equation (BTE) is solved by the Lattice-Boltzmann method (LBM) for the Knudsen number range of 0.01−0.1. First, the Eulerian flow characteristics are determined by performing numerical simulations for different Knudsen numbers, pressure ratio and accommodation coefficients with the objective of obtaining reliable velocity characteristics and flow patterns, and determining the transition characteristics from the macro to microscale. The numerical predictions are compared to existing analytical and numerical results. Then, the Lagrangian characteristics are obtained by integrating the Eulerian velocity field by a 4t order Runge-Kutta scheme. Ten thousands (10,000) pairs of fluid particles are used to determine fluid particle Lagrangian trajectories, future stretching fields, and Lagrangian Lyapunov exponents, which are used for determining the grooved channel regions with high and low flow mixing enhancement. Our results demonstrate that rarified gas flows develop a future stretching field leading to the existence of Lagrangian chaos and flow mixing enhancement for very low, stable and time independent Reynolds number flow regime. This flow behavior departure from the well accepted concept that Lagrangian chaos and flow mixing enhancement need a time dependent 2D flow.Copyright © 2008 by ASME

Numerical simulations of time-dependent thermal energy transport in semiconductor thin films are performed using the Lattice Boltzmann Method applied to phonon transport. The discrete Lattice Boltzmann Method is derived from the continuous Boltzmann transport equation assuming nonlinear, frequency-dependent phonon dispersion for acoustic and optical phonons. Results indicate that the heat conduction in silicon thin films displays a transition from diffusive to ballistic energy transport as the characteristic length of the system becomes comparable to the phonon mean free path, and that the thermal energy transport process is characterized by the propagation of multiple, superimposed phonon waves. The methodology is used to characterize the time-dependent temperature profiles inside films of decreasing thickness. Thickness-dependent thermal conductivity values are computed based on steady-state temperature distributions obtained from the numerical models. It is found that reducing feature size into the subcontinuum regime decreases the thermal conductivity when compared to bulk values, at a higher rate than what was displayed by the Debye-based gray Lattice Boltzmann Method.Copyright © 2007 by ASME

We investigate the heat transfer enhancement due to flow mixing enhancement in a frequency-doubling transition scenario in symmetric wavy channels by direct numerical simulations of the mass, momentum and energy equations. The governing equations are solved for laminar and transitional flow regimes by the spectral element method, using a periodic computational domain, and with a high aspect ratio of r = a /(2L) = 0.375, where L is the periodic length, and a , the wavy wall amplitude. The frequency-doubling transition scenario is characterized by one flow bifurcation that develops to a critical Reynolds numbers Rec , leading to a periodic flow. Further increases in the Reynolds number leads to successive periodic flows where the fundamental frequency ω1 , increases continuously. This scenario is different to the Ruelle-Takens-Newhouse transition scenario obtained for a symmetric wavy channel with an aspect ratio of 0.125, where periodic and quasi periodic flow regimes develop as the Reynolds number increases. Heat Transfer simulations are carried out assuming a constant heat flux on one wall and an adiabatic condition on the other wall. Numerical results demonstrate that the time-average mean Nusselt number increases significantly as the flow passes from a laminar to a periodic flow regime. As the flow becomes periodic and for increasing Reynolds numbers, the Nusselt number increases with respect to the laminar flow Nusselt number, up to a factor of 4, depending on the Reynolds number, which represents a significant heat transfer enhancement due to a better flow mixing. This increase is accompanied by a reasonable increase in both the friction factor and the pumping power. The obtained qualitative and quantitative features are compared to other channel geometries, such as grooved and asymmetric wavy channels, which also develop different transition scenarios.Copyright © 2007 by ASME

The flow transition scenario in symmetric communicating channels has been investigated using direct numerical simulations of the mass and momentum conservation equations in the Reynolds numbers range of Re = [170–227]. The governing equations are solved for laminar and time-dependent transitional flow regimes by the spectral element method, using a periodic computational domain, for a periodic length of nL and an aspect ratio of r = aˆ / (2Lˆ) = 0.0405, where aˆ = 2a is the height of block within the channel, n an integer and Lˆ = L + 1 is the periodic length. Periodic computational domains with n = 1 and 2 are used in this investigation to determine the periodic length effect on the flow pattern characteristics. Numerical investigations with different domain meshes are carried out for determining the appropriate discretization for capturing transitional time-dependent flows. The numerical results show a transition scenario with two-flow Hopf bifurcations which develop as the pressure gradient is increased from a laminar to a time-dependent flow regime. The first Hopf bifurcation occurs to a critical Reynolds number of Rec1 and leads to a time-dependent periodic flow characterized by a fundamental frequency ω1. Further increases in the pressure gradient lead to successive quasi periodic flows after a second Hopf bifurcation B2 occurring to a critical Reynolds number Rec2 < Rec1, with two fundamental frequencies ω1 and ω2, and linear combinations of both frequencies—where the fundamental frequency ω1 increases continuously—and ω2 > ω1. This transition scenario is somewhat different from the Ruelle-Takens-Newhouse transition scenario obtained for symmetric wavy channels; in symmetric wavy channels, periodic and quasi periodic flow regimes develop as the Reynolds number increases. The friction factor for the symmetric communicating channel in the transitional regime is higher than the friction factor for the Poiseuille plane channel. The qualitative and quantitative behavior is compared to other channel geometries that also develop other transition scenarios.

The flow bifurcation scenario and heat transfer characteristics in grooved channels, are investigated by direct numerical simulations of the mass, momentum and energy equations, using the spectral element methods for increasing Reynolds numbers in the laminar and transitional regimes. The Eulerian flow characteristics show a transition scenario of two Hopf bifurcations when the flow evolves from a laminar to a time-dependent periodic and then to a quasi-periodic flow. The first Hopf bifurcation occurs to a critical Reynolds number Rec1 that is significantly lower than the critical Reynolds number for a plane-channel flow. The periodic and quasi-periodic flows are characterized by fundamental frequencies ω1 and m· ω1+n·ω2, respectively, with m and n integers. Friction factor and pumping power evaluations demonstrate that these parameters are much higher than the plane channel values. The time-average mean Nusselt number remains mostly constant in the laminar regime and continuously increases in the transitional regime. The rate of increase of this Nusselt number is higher for a quasi-periodic than for a periodic flow regime. This higher rate originates because better flow mixing develops in quasi-periodic flow regimes. The flow bifurcation scenario occurring in grooved channels is similar to the Ruelle-Takens-Newhouse transition scenario of Eulerian chaos, observed in symmetric and asymmetric wavy channels.

Computational investigations of flow mixing and oxygen transfer characteristics in an intravenous membrane oxygenator (IMO) are performed by direct numerical simulations of the conservation of mass, momentum, and species equations. Three-dimensional computational models are developed to investigate flow-mixing and oxygen-transfer characteristics for stationary and pulsating balloons, using the spectral element method. For a stationary balloon, the effect of the fiber placement within the fiber bundle and the number of fiber rings is investigated. In a pulsating balloon, the flow mixing characteristics are determined and the oxygen transfer rate is evaluated. For a stationary balloon, numerical simulations show two well-defined flow patterns that depend on the region of the IMO device. Successive increases of the Reynolds number raise the longitudinal velocity without creating secondary flow. This characteristic is not affected by staggered or non-staggered fiber placement within the fiber bundle. For a pulsating balloon, the flow mixing is enhanced by generating a three-dimensional time-dependent flow characterized by oscillatory radial, pulsatile longitudinal, and both oscillatory and random tangential velocities. This three-dimensional flow increases the flow mixing due to an active time-dependent secondary flow, particularly around the fibers. Analytical models show the fiber bundle placement effect on the pressure gradient and flow pattern. The oxygen transport from the fiber surface to the mean flow is due to a dominant radial diffusion mechanism, for the stationary balloon. The oxygen transfer rate reaches an asymptotic behavior at relatively low Reynolds numbers. For a pulsating balloon, the time-dependent oxygen-concentration field resembles the oscillatory and wavy nature of the time-dependent flow. Sherwood number evaluations demonstrate that balloon pulsations enhance the oxygen transfer rate, even for smaller flow rates.

This work investigates the transition scenario and heat transfer characteristics in a channel with a block tandem, as the flow evolves from a laminar to a transitional regime, by two-dimensional direct numerical simulations (DNS) of the time dependent, incompressible continuity, Navier-Stokes and energy equations. This investigation uses an extended computational domain with 10 blocks to determine the existence of a fully developed flow and self-similar temperature profiles, and a reduced computational domain to investigate the heat transfer enhancement for laminar and transitional flow regimes. This investigation demonstrates that significant heat transfer enhancements can be obtained at supercritical transitional flow Reynolds numbers with a minimum of dissipation due to viscous stresses. This enhancement is obtained without the necessity of operating this channel to high volumetric flow rates associated to turbulent flow regimes, which demand high pumping powers. In this channel, the transitional flow regime is more efficient than a laminar flow regime as a method of cooling electronics.

Spectral element computational simulations of the conservation of mass, momentum and species equations are performed to investigate the flow and oxygen transfer characteristics of an Intravenous Membrane Oxygenator (IMO). The simulations consider a three-dimensional IMO computational model consisting of equally-spaced fibers, an elastic balloon with non-permeable walls positioned longitudinally within the vena cava, and a Newtonian and time-dependent incompressible flow. Flow characteristics and oxygen transfer parameters are determined for operating conditions of a stationary and a pulsating balloon. For the stationary balloon configuration the flow is two-dimensional, parallel, laminar and without secondary flows for the Reynolds number range of 5.7-455.2. Evaluations of the oxygen transfer characteristics for the stationary balloon indicate that the main transport mechanisms are diffusion and convection in the crosswise and streamwise directions, respectively. Additionally, evaluations of oxygen transfer rates and Sherwood numbers in this Reynolds number range indicate that the oxygen transfer rate reaches an asymptotic limit at relatively moderate Reynolds numbers. For the pulsating balloon, flow characteristic results demonstrate the existence of a strong secondary flow around the fiber, and between the balloon and the fiber. This secondary flow induces oscillatory crosswise and streamwise velocities and a seemingly random spanwise flow which enhances the flow mixing as well as the transport of oxygen from the fiber surface to the bulk flow.