Three-dimensional Laminar Flow Research Articles

Three-dimensional laminar flow using physics informed deep neural networks

Physics informed neural networks (PINNs) have demonstrated their effectiveness in solving partial differential equations (PDEs). By incorporating the governing equations and boundary conditions directly into the neural network architecture with the help of automatic differentiation, PINNs can approximate the solution of a system of PDEs with good accuracy. Here, an application of PINNs in solving three-dimensional (3D) Navier–Stokes equations for laminar, steady, and incompressible flow is presented. Notably, our approach involves deploying PINNs using feed-forward deep neural networks (DNNs) without depending on any simulation or experimental data. This investigation focuses on 3D square channel flow and 3D lid-driven cavity flow. For each case, one deep neural network was trained using only the governing equations and boundary conditions. Finally, the PINNs' results were compared with the computational fluid dynamics results. The goal was to assess the ability of PINNs (with DNN architectures) to predict the solution of Navier–Stokes equations in the 3D domain without any simulation or experimental data (unsupervised learning).

Simulations of Flows via CFD in Microchannels for Characterizing Entrance Region and Developing New Correlations for Hydrodynamic Entrance Length.

Devices with microchannels are relatively new, and many correlations are not yet developed to design them efficiently. In microchannels, the flow regime is primarily laminar, where entrance length may occupy a significant section of the flow channel. Therefore, several computational fluid dynamic simulations were performed in this research to characterize the developing flow regime. The new correlations of entrance length were developed from a vast number of numerical results obtained from these simulations. A three-dimensional laminar flow for 37 Reynolds numbers (0.1, 0.2, …, 1, 2, …, 10, 20, …, 100, 200, …, 1000), primarily in low regime with water flow through six rectangular microchannels (aspect ratio: 1, 0.75, 0.5, 0.25, 0.2, 0.125), has been modeled, conducting 222 simulations to characterize flow developments and ascertain progressive velocity profile shapes. Examination of the fully developed flow condition was considered using traditional criteria such as velocity and incremental pressure drop number. Additionally, a new criterion was presented based on fRe. Numerical results from the present simulations were validated by comparing the fully developed velocity profile, friction factor, and hydrodynamic entrance length for Re > 100 in rectangular channels, for which accurate data are available in the literature. There is a need for hydrodynamic entrance length correlations in a low Reynolds number regime (Re < 100). So, the model was run numerous times to generate a vast amount of numerical data that yielded two new correlations based on the velocity and fRe criteria.

Laminar drag reduction in surfactant-contaminated superhydrophobic channels

Although superhydrophobic surfaces (SHSs) show promise for drag reduction applications, their performance can be compromised by traces of surfactant, which generate Marangoni stresses that increase drag. This question is addressed for soluble surfactant in a three-dimensional laminar channel flow, with periodic SHSs made of long finite-length longitudinal grooves located on both walls. We assume that bulk diffusion is sufficiently strong for cross-channel concentration gradients to be small. Exploiting long-wave theory and accounting for the difference between the rapid transverse and slower longitudinal Marangoni flows, we derive a one-dimensional model for surfactant transport from the full three-dimensional transport equations. Our one-dimensional model allows us to predict the drag reduction and surfactant distribution across the parameter space. The system exhibits multiple regimes, involving competition between Marangoni effects, bulk and interfacial diffusion, bulk and interfacial advection, shear dispersion and surfactant exchange between the bulk and the interface. We map out asymptotic regions in the high-dimensional parameter space, and derive explicit closed-form approximations of the drag reduction, without any fitting or empirical parameters. The physics underpinning the drag reduction effect and the negative effect of surfactant is discussed through analysis of the velocity field and surfactant concentrations, which show both uniform and non-uniform stress distributions. Our theoretical predictions of the drag reduction compare well with results from the literature solving numerically the full three-dimensional transport problem. Our atlas of maps provides a comprehensive analytical guide for designing surfactant-contaminated channels with SHSs, to maximise the drag reduction in applications.

Modal Instabilities over Blunted Cones at Angle of Attack in Hypersonic Flow

The effects of nose radius and angle of attack on the linear modal amplification over blunt circular cones at hypersonic speeds are computationally investigated. The three-dimensional laminar flow solutions over a 1.5-m-long, 7°-half-angle cone with 5.080, 9.525, and 25.40 mm nosetip radii are computed for selected angle-of-attack values and freestream conditions that match the Mach 10 experiments at a freestream unit Reynolds number of 17.1 million per meter conducted within the Hypervelocity Wind Tunnel 9 at the Air Force Arnold Engineering Development Complex (AEDC). Results indicate that the linear amplification of stationary and traveling crossflow waves along inflection lines increases with the angle of attack and decreases with the nosetip radius. The trend in transition front with respect to increasing angle of attack and bluntness is found to be consistent with the predicted increase in the amplification factors for Mack’s second mode (MM) disturbances along the streamline trajectories for the small and medium bluntness cases. The increase in the MM amplification along the windward ray for higher angles of attack is shown to be the result of a progressively earlier entropy-layer swallowing. Computations also indicate that the transition amplification factor along the windward ray increases with the angle of attack and decreases with the nosetip radius. Furthermore, the transition -factors along the leeward ray are below 2 and, therefore, rather small to lead to transition.

Calculation of the development length of spanwise rotating three-dimensional laminar channel flow

Calculation of the development length of spanwise rotating three-dimensional laminar channel flow

Three-dimensional coupled flow and heat transfer in non-newtonian magnetic nanofluid: An application of Cattaneo-Christov heat flux model

This article has been fine-tuned with studying the three-dimensional laminar flow of a magnetic liquid over a stretching sheet with the influence of thermal radiation and Cattaneo-Christov heat flux. Moreover, this article mainly focuses on moderate saturation magnetization and low Curie temperature. The dynamics of propylene glycol –paraffin wax nanofluid + water mixture and zinc oxide (ZnO)-SAE50 Nano-lubricant fluid flow is examined. The modeling equations are converted into non-linear ordinary differential equations (ODEs) using the required similarity transformations. The Runge-Kutta-Fehlberg fourth-to-fifth order (RKF-45) technique is used to solve the resultant non-linear ODEs numerically. Numerous regulating factors that affect the velocity and temperature profiles are examined via graphs. Research of the present study has shown that Deborah number accounts for the decelerating radial and tangential flow of both nanolubricant and nanofluids. The ZnO-SAE50 Nano-lubricant flow shows high heat transfer and increases faster followed by propylene glycol – water mixture + paraffin wax nanofluid flow for the increase in values of radiation parameter. The ZnO-SAE50 Nano-lubricant flow shows high heat transfer rate than propylene glycol–water mixture-based nanoliquid for rising values of radiation parameter.

A computational study of three-dimensional laminar boundary layer flow and forced convective heat transfer in a porous medium

A computational study of three-dimensional laminar boundary layer flow and forced convective heat transfer in a porous medium

Direct numerical simulation of interaction between a stationary crossflow instability and forward-facing steps

The interaction between forward-facing steps of several heights and a pre-existing critical stationary crossflow instability of a swept-wing boundary layer is analysed. Direct numerical simulations (DNS) are performed of the incompressible three-dimensional laminar base flow and the stationary distorted flow that arise from the interaction between an imposed primary stationary crossflow perturbation and the steps. These DNS are complemented with solutions of the linear and the nonlinear parabolised stability equations, used towards identifying the influence of linearity and non-parallelism near the step. A fully stationary solution of the Navier–Stokes equations is enforced numerically, in order to isolate the mechanisms pertaining to the interaction of the stationary disturbance with the step. Results provide insight into the salient modifications of the base laminar boundary layer due to the step, and the response of the incoming crossflow instability to these changes. The fundamental spanwise Fourier mode of the disturbance field gradually lifts up as it approaches the step and passes over it. The flow environment around the step is characterised by a sudden spanwise modulation of the base-flow streamlines. Additional stationary perturbation structures are induced at the step, which manifest in the form of spanwise-aligned velocity streaks near the wall. Shortly downstream of the step, the fundamental component of the crossflow perturbation maintains a rather constant amplification for the smallest steps studied. For the largest step, however, the fundamental crossflow perturbation is stabilised significantly shortly downstream of the largest step. This surprising result is ascribed to a modulation of the kinetic energy transfer between the base flow and the fundamental perturbation field, which is brought forward as a new step interaction mechanism. Possible non-modal growth effects at the step are discussed. Furthermore, the results from DNS indicate significant amplification of the high-order harmonic crossflow components downstream of the step.

Influence of Thermophoretic Particle Deposition on the 3D Flow of Sodium Alginate-Based Casson Nanofluid over a Stretching Sheet.

The wide range of industrial applications of flow across moving or static solid surfaces has aroused the curiosity of researchers. In order to generate a more exact estimate of flow and heat transfer properties, three-dimensional modelling must be addressed. This plays a vital role in metalworking operations, producing plastic and rubber films, and the continuous cooling of fibre. In view of the above scope, an incompressible, laminar three-dimensional flow of a Casson nanoliquid in the occurrence of thermophoretic particle deposition over a non-linearly extending sheet is examined. To convert the collection of partial differential equations into ordinary differential equations, the governing equations are framed with sufficient assumptions, and appropriate similarity transformations are employed. The reduced equations are solved by implementing Runge Kutta Fehlberg 4th 5th order technique with the aid of a shooting scheme. The numerical results are obtained for linear and non-linear cases, and graphs are drawn for various dimensionless constraints. The present study shows that improvement in the Casson parameter values will diminish the axial velocities, but improvement is seen in thermal distribution. The escalation in the thermophoretic parameter will decline the concentration profiles. The rate of mass transfer, surface drag force will reduce with the improved values of the power law index. The non-linear stretching case shows greater impact in all of the profiles compared to the linear stretching case.

Effect of Nanoparticle Shape and Volume Fraction on Nanofluid Flow in Serpentine Microtube

The nanofluid flow in serpentine microtube was numerically investigated in this study. The study has been carried out in three-dimensional laminar flow (750≤Re≤2000) condition. Al2O3 – water nanofluid with different nanoparticle volume fractions (1.0%, 2.0%, 3.0%) have been used as the working fluid in the numerical analyzes. In addition, studies were carried out for blade, platelet and cylindrical nanoparticle shapes. The average Nusselt numbers and the average Darcy friction factors have been used to estimate the flow and heat transfer performance of nanofluid flow in serpentine microtubes. Velocity and temperature distributions inside the microtube were also examined for different cases. Numerical results of the study have been presented as the variation of average Nusselt number and average Darcy friction factor with Reynolds number, nanoparticle shape and nanoparticle volume fraction. As a result, the highest convective heat transfer performance has been obtained for platelet nanoparticle shape of the Al2O3-water nanofluid with 3.0% nanoparticle volume fraction.

On the Use of Probability-Based Methods for Estimating the Aerodynamic Boundary-Layer Thickness

In this paper, known probabilistic methods for estimating the thickness of the boundary layer of a two-dimensional laminar flow of viscous incompressible fluid are extended to three-dimensional laminar flows of a viscous compressible medium. Their applicability to the problems of boundary-layer stability is studied with the LOTRAN3 software package, which allows us to compute the position of laminar-turbulent transition in three-dimensional aerodynamic configurations.

CFD study of Convective Heat Transfer of Water Flow Through Micro-Pipe with Mixed Constant Wall Temperature and Heat Flux Wall Boundary Conditions

The dissipation of heat in tiny engineering systems can be achieved with fluid flow through micro pipes. They have the advantage of less volume to large surface ratio convective heat transfer. There are deep-rooted analytical relations for convective heat transfer available for fluid flow through macro size pipes. But differences exist between the convective heat transfer for fluid flow through macro and micro pipes. Therefore, there is a good scope of work in micro convection heat transfer to study the mechanism of fundamental flow physics. There have been studies with either constant heat flux wall boundary conditions or constant wall temperature boundary conditions with constant and variable property flows. In this article, first, the numerical simulations are validated with the experimental data for 2D axisymmetric conventional pipe with pipe diameter of 8 mm is taken with laminar, steady, and single-phase water flows with constant wall heat flux boundary condition of 1 W/cm2. The computed Nusselt number is compared to the experimental results at different Reynolds numbers of 1350, 1600 and 1700. In the next study, three-dimensional micropipe laminar flow is studied numerically using water with an inlet velocity of 3 m/s and pipe diameter of 100 µm. The mixed wall boundary conditions with upper half pipe surface subjecting to constant wall temperature of 313 K and lower half surface subjecting to 100 W/cm2 are used in the simulations. The focus of research would be to consider the effect of temperature-dependent properties like thermal conductivity, viscosity, specific heat, and density (a combined effect we call it as variable properties) on micro-pipe flow characteristics like Nusselt number at mixed wall boundary conditions and compare it with the constant property flows. The conventional pipe showed no significant difference with variable and constant property flows with different Reynolds numbers. On contrary the flow through 3D micropipe shows that the Nusselt number with variable property flows is less as compared to the constant property flows.

Lagrangian Transport and Chaotic Advection in Three-Dimensional Laminar Flows

AbstractTransport and mixing of scalar quantities in fluid flows is ubiquitous in industry and Nature. While the more familiar turbulent flows promote efficient transport and mixing by their inherent spatio-temporal disorder, laminar flows lack such a natural mixing mechanism and efficient transport is far more challenging. However, laminar flow is essential to many problems, and insight into its transport characteristics of great importance. Laminar transport, arguably, is best described by the Lagrangian fluid motion (“advection”) and the geometry, topology, and coherence of fluid trajectories. Efficient laminar transport being equivalent to “chaotic advection” is a key finding of this approach. The Lagrangian framework enables systematic analysis and design of laminar flows. However, the gap between scientific insights into Lagrangian transport and technological applications is formidable primarily for two reasons. First, many studies concern two-dimensional (2D) flows, yet the real world is three-dimensional (3D). Second, Lagrangian transport is typically investigated for idealized flows, yet practical relevance requires studies on realistic 3D flows. The present review aims to stimulate further development and utilization of know-how on 3D Lagrangian transport and its dissemination to practice. To this end, 3D practical flows are categorized into canonical problems. First, to expose the diversity of Lagrangian transport and create awareness of its broad relevance. Second, to enable knowledge transfer both within and between scientific disciplines. Third, to reconcile practical flows with fundamentals on Lagrangian transport and chaotic advection. This may be a first incentive to structurally integrate the “Lagrangian mindset” into the analysis and design of 3D practical flows.

Stability analysis and modeling for the three-dimensional Darcy-Forchheimer stagnation point nanofluid flow towards a moving surface

In this research, the three-dimensional (3D) steady and incompressible laminar Homann stagnation point nanofluid flow over a porous moving surface is addressed. The disturbance in the porous medium has been characterized by the Darcy-Forchheimer relation. The slip for viscous fluid is considered. The energy equation is organized in view of radiative heat flux which plays an important role in the heat transfer rate. The governing flow expressions are first altered into first-order ordinary ones and then solved numerically by the shooting method. Dual solutions are obtained for the velocity, skin friction coefficient, temperature, and Nusselt number subject to sundry flow parameters, magnetic parameter, Darcy-Forchheimer number, thermal radiation parameter, suction parameter, and dimensionless slip parameter. In this research, the main consideration is given to the engineering interest like skin friction coefficient (velocity gradient or surface drag force) and Nusselt number (temperature gradient or heat transfer rate) and discussed numerically through tables. In conclusion, it is noticed from the stability results that the upper branch solution (UBS) is more reliable and physically stable than the lower branch solution (LBS).

Unsteady three-dimensional laminar flow over a submerged plate in electrically conducting fluid with applied magnetic field

In this work, the three-dimensional unsteady flow was scrutinized adjacent to a flat plate immersed inside a fluid with electric conductivity in the presence of constant magnetic field. An extended model of group transformation method was exploited, comprising three parameters, to transform the mathematical model into a new system of ordinary differential equations (ODEs). The proposed method is rarely and seldom used in handling higher dimensions coupled equations. Two cases were studied, the stretching and shrinking plate. In the first case, the results showed that both of magnetic parameter, M, and Prandtl number, Pr, affected inversely the fluid velocity, the shear stress and the temperature distribution. On the contrary, the heat flux increased when both M and Pr increase. That could be interpreted by the effect of larger magnetic force and fluid viscosity, respectively. In case of shrinking plate, the attained results were opposite to those of stretching case specially for the effect of magnetic parameter.

Mixing and combustion in a laminar shear layer with imposed counterflow

Abstract

Thermal characterization and stability analysis of aqueous ZnO-based nanofluids numerically implemented in microchannel heat sinks

Water-based nanofluids prepared with ZnO nanoparticles (⩽17 nm) were characterized. The thermal conductivity and viscosity were measured as a function of temperature (278–303 K), for two ZnO concentration (1wt% and 3wt%) establishing that, whereas the nanofluid prepared with a concentration of 1wt% registered an average improvement of the thermal conductivity of 10.31% at a concentration of 3wt%, the viscosity decreased an average of 5.03% respect to the base fluid. An analysis of the stability of these nanofluids was carried out via UV–vis, finding that for a concentration of 3wt% the stability is better, since it requires 168 h to decrease its absorbance in the same amount as the sample of 1wt%. Additionally, the laminar three-dimensional flow of these nanofluids has been numerically studied considering symmetric microchannels (200 ⩽Re⩽ 1200) of fixed-width rectangular cross-section (283 μm) and three different heights (200 μm, 600 μm, and 400 μm), subjected to a constant heat flux in the lower wall (50 W/cm2). The microchannels have been simulated considering the properties of the nanofluid variable with respect to temperature through experimentally determined models (for 1wt% and 3wt%), finding that thermal conductivity improves mostly for a concentration of 1wt%, registering an increase in average 10.31% in the studied temperature range.The numerical results showed that the use of nanofluids favors heat transfer at low Reynolds numbers with the maximum improvement in the coefficient of heat transfer by convection (42.33%). A decrease in temperature of the base of the microchannel is also observed, which is more significant at low Reynolds numbers for a concentration of 1wt%. In the case of MCH-1 with Re=200, the decrease in the mean temperature of the lower wall is 5.65% (20.45 K), a value that decreases to 0.90% (2.94 K) for Re=1200. This configuration also offers the highest net heat gain, considering the increase in the coefficient of friction produced by the incorporation of ZnO nanoparticles. Finally considering the experimental studies of the thermal properties and stability of nanofluids, and the numerical results associated with the thermal and fluid-dynamic performance of the microchannels, a methodology is proposed to carry out a comprehensive approach to the application of nanofluids in microchannels.

Simulation of heat transfer characteristics of phase change material dispersed with Titanium oxide nanoparticles in horizontal channel

Phase Changing Materials (PCM) is proving to be one of the major breakthroughs in industries as it has various applications in sustainable and renewable energy. The present study investigates the melting and solidification of phase change material (ice) in the presence of titanium oxide nanoparticles in a horizontal channel with internal heat source. The parametric study is carried out by varying the inlet velocity, heat source strength and nanoparticle volume fractions. The problem is modeled as three-dimensional laminar steady flow considering the effects of melting and solidification using Ansys Fluent. The heat sources mounted at the lower wall of the channel are specified with constant wall temperature boundary condition and the remaining walls are considered as adiabatic. The forced velocity inlet boundary condition is specified for the longitudinal velocity at the inlet and pressure outlet boundary condition is considered at the outlet of the channel. The results are analyzed by plotting the pathlines, longitudinal velocity contours, pressure and temperature contours. The results indicate that the longitudinal inlet velocity significantly affects the flow and heat transfer characteristics inside the horizontal channel. The increase in inlet velocity strengthens the melting rate and increases the heat transfer rate inside the channel. It is also found that the melting rate increases linearly with increase in the heat source intensity and nanoparticle volume fraction.

Numerical Investigation on the Optimum Thermal Design of the Shape and Geometric Parameters of Microchannel Heat Exchangers with Cavities.

Due to the large surface-area-to-volume ratio, microchannel heat exchangers have a higher heat transfer rate compared with traditional scale heat exchangers. In this study, the optimum microchannel cavity with high heat transfer and low flow resistance is designed to further improve microchannel exchangers’ thermal performance. A three-dimensional laminar flow model, consisting of Navier–Stokes equations and an energy conservation equation is solved and the conjugate heat transfer between the silicon basement and deionized water is taken into consideration. The impact of the shape, aspect ratio, size and spacing of the cavity on the thermal performance of microchannel exchangers are numerically investigated, respectively. The results indicated that the cavity on the sidewall can enhance heat transfer and reduce flow resistance simultaneously, and cavities with a relatively small expansion angle and streamlined edge could enhance thermal performance the most. Based on the conclusions, a new cavity shape is proposed, and the simulation results verify its excellent thermal performance as expected. Furthermore, investigation is performed to figure out the optimum design of the new cavity and the optimal geometric parameters of the cavity under different flow conditions have been obtained in principle for microchannel exchangers’ design.

Numerical Investigation to Derive Correlations for Hydrodynamic Entrance Length in Very Low Reynolds Number Regime in Rectangular Microchannels

Abstract A three-dimensional laminar flow model was used for 37 Reynolds numbers (0.1, 0.2…1, 2…10, 20…100, and 200…1000) through six rectangular microchannels (aspect ratios: 1, 0.75, 0.5, 0.25, 0.2, and 0.125) to develop correlations for hydrodynamic entrance length. The majority of the Reynolds numbers are in the low regime (Re &amp;lt; 100) to fulfill the need to determine the hydrodynamic entrance length for microchannels. Examination of the fully developed flow condition was considered using the velocity or fRe criteria. Numerical results from the present simulations were validated by comparing the fRe results. Two new correlations were developed from a vast amount of numerical data (222 simulations). The velocity criterion correlations predict entrance length with a mean error of 4.67% and maximum error of 10.28%. The fRe criterion generated better correlations and were developed as a function of aspect ratio to predict entrance length with a mean error less than 2% and maximum error of 5.75% for 0.1 ≤ Re ≤ 1000 and 0 ≤ α ≤ ∞.