Incompressible Laminar Flow Research Articles

A three-dimensional high-order flux reconstruction lattice boltzmann flux solver for incompressible laminar and turbulent flows

A three-dimensional (3D) high-order flux reconstruction lattice Boltzmann flux solver (FR-LBFS) is developed in this paper for accurate and efficient simulations of incompressible laminar and turbulent flows. The original lattice Boltzmann flux solver (LBFS) is a second-order finite volume method (FVM) which combines the advantages of conventional Navier-Stokes (N-S) solvers and lattice Boltzmann equation (LBE) solvers. But it is not convenient to construct high-order FVM, and the compactness is always a bottleneck. The present work separates LBFS from FVM and combines LBFS with high-order FR scheme. Thus, the FR-LBFS inherits the superiority of LBFS and FR and shares the following attractive features: (i) a fully-explicit arbitrary order compact method, (ii) weakly compressible (WC) model for unsteady incompressible flows and (iii) evaluating inviscid and viscous fluxes simultaneously and no particular technique requirement, such as local discontinuous Galerkin method (LDG), for viscous term discretization. To validate the current method, various 3D incompressible laminar isothermal and thermal numerical experiments are presented first. Good agreements are achieved between the current results and the previous experimental and numerical data whilst the present high-order solver adopt coarse meshes. Furthermore, the ability of the proposed method to perform accurate and stable computations of incompressible decaying homogeneous isotropic turbulent flows and turbulent channel flows with different mesh resolutions and accuracy orders are investigated. The results show that the present 3D FR-LBFS is a promising tool for under-resolved or implicit large eddy simulation (ILES) of incompressible turbulent flows.

Effects of MWCNT nanoparticles injection points on incompressible laminar hydrogen flow through discrete phase modeling by CFD approach

Discrete phase model used in the aerospace industry to stimulate the behavior of particles inside the aircraft engines. The application of the discrete phase modeling (DPM) is extensive in solving the real-time engineering problems in optimization of numerous systems. In the current study, the DPM model has been simulated to examine the effect of injection point on the hydrogen flow field. A domain has been proposed and the injection point has been positioned in the four different places at the regular intervals. The location of the injection points was 0.2 m, 0.3 m, 0.4 m and 0.6 m. Dense discrete Eulerian lagrangian numerical simulation has been employed to analyze the effect of the multi-walled carbon nanotubes (MWCNT) nanoparticles. The hydrogen has been supplied at the injection velocity of 2 m/s. ANSYS implicit simulation setup has been tested across various injection points. The research found that the location of injection points plays a significant role in DPM concentration, with the highest concentration at 0.2 m and the lowest at 0.6 m, but has no significant impact on dynamic pressure. MWCNT nanoparticles had a negligible effect on skin friction coefficient, but shifting the injection point could reduce skin friction rates. The inclusion of MWCNT nanoparticles increased hydrogen flow velocity through downstream effects, vortices, and the nano-enhancement effect. The study suggests that MWCNT can significantly enhance hydrogen flow velocity in various applications, and DPM concentration data can provide valuable insights for optimizing injection locations to prevent unwanted nanoparticle effects.

The effect of central gap and wind screens on the aeroelastic stability of long-span bridge decks: Comparison of numerical analyses and experimental results

As long-span bridges are usually built at exposed locations and high winds can cause disruptions to traffic, relatively tall wind screens are often used to protect vehicles which are prone to suffer from wind induced accidents. This paper presents the results of a series of two-dimensional discrete vortex method simulations of laminar incompressible flow past standard aerofoil mono-boxes and twin-boxes, conducted to investigate the aerodynamic impact of wind screens on bridge decks in relation to steady-state and divergent instability (classical flutter) behaviour. A comparison against the outcome of a series of parametric wind tunnel tests is also presented. The quality of the agreement between the numerical simulations and the observed experimental behaviour is such that designers, under certain conditions, could rely on computational bridge aerodynamics at feasibility or early design stages to identify potential instabilities and introduce mitigation measures aimed at optimizing the aerodynamic performance of the deck.

Numerical Investigation of the Three-Dimensional Flow around a Surface-Mounted Rib and the Onset of Unsteadiness

The incompressible laminar isothermal flow of a Newtonian fluid at steady state around a surface-mounted rib is studied in a three-dimensional (3D) numerical experiment. The dimensionless Navier–Stokes equations are solved numerically using the Galerkin finite element method for Reynolds numbers 1 to 800. The expansion ratio of the problem is 1:9.6, while the aspect ratio is 1:20. The transition from the steady to the unsteady state and the identification of the critical Reynolds number are investigated in this paper. Numerical results of the skin-friction lines at the bottom and streamlines throughout the computational field are presented. A comparison between the 2D and 3D flow is made to show the effect of the walls on the flow, which reaches the plane of symmetry and affects the flow there; hence, also affecting the stability of the flow. It is concluded that the flow is three-dimensional even for a Reynolds number equal to 10. The critical Reynolds number is 600, and the steady-state equations can be used for any calculations up to this value.

Unsteady Carbon Nanotubes Nanofluid Flow due to a Moving Cylinder with Thermal Radiation and Temperature Oscillation Effects

This paper discusses transient two-dimensional boundary layer laminar viscous incompressible free convective flow of nanofluids containing carbon nanotubes (SWCNTs and MWCNTs) over a moving vertical cylinder in the presence of thermal radiation and temperature oscillation. The governing boundary layer equations are converted to a dimensionless form and then solved using the Crank Nicolson type’s unconditionally stable and convergent implicit finite difference method. With diverse parameters such as Grashof number (Gr), volume fraction (Φ), phase angle (ωt), and thermal radiation parameter (N), numerical results are achieved for velocity and temperature profiles along with Nusselt number and skin friction coefficients. The numerical results are analysed in detail using graphs for both water-based nanofluid and kerosene-based nanofluids with single and multi-wall carbon nanotubes as the nanomaterials. It has been found that CNTs Water-based nanofluid has higher temperatures, velocities, skin friction coefficient values for all Gr, N, Φ, and ωt when compared to kerosene-based nanofluid with CNTs. But, Kerosene-based CNTs nanofluid has a higher Nusselt number coefficient values concerning all Gr, N, Φ, and ωt than water-based CNTs nanofluid.

Improvement of Plate-Fin Heat Exchanger Performance with Assistance of Various Types of Vortex Generator

A 3-dimensional incompressible laminar flow and heat-transfer in a plate-fin heat exchanger (PFHE) where investigated numerically in this article. The influence of mounting a longitudinal vortex generator (LVG) on the offset rectangular-triangular fin (ORT) in the PFHE, on thermal and hydro-dynamic fields are presented. The novelty of this study is by attaching a LVG to an offset strip fin (OSF) surface. The cases of study for the PFHE are established, by using a built-in rectangular winglet pair type RWP longitudinal vortex generator carried out and fitted on this fin to improve the convective heat transfer of the (ORT) fin while minimizing pressure loss. The upper and lower plates are exposed to constant heat flux and the working fluid is air where chosen under a laminar range of RE (600 to 1400). The laminar flow and heat-transfer are governed by continuity, momentum and energy equations. ANSYS FLUENT (2021 R1) is used to get the numerical results, based on the finite volume method. The performance of the VG is assessed for an optimum winglet attack angle (45°), as well as by modifying the geometrical size parameters, namely the height and placement (L) of the RWP LVG. The result shows that the Nusselt number reaches its optimum enhancement values by using a common flow up CFU built-in rectangular winglet pair type RWP VG with a height and entrance length of (h=1.25mm, L=0.5mm), by 22.23% as compared with base case configuration (ORT). Finally, a two more LVG are tested with the optimum conditions of the RWP, which they are a delta winglet pair (DWP) and trapezoidal winglet pair (TWP). In addition, the temperature fields for the primary and secondary flows were shown in contour and streamline diagrams

The heat transfer effects of MHD slip flow with suction and injection and radiation over a shrinking sheet by optimal homotopy analysis method

The current study investigates the laminar flow of boundary layer using a porous surface shrinking exponentially under varying magnetic field, suction/injection, radiation on velocity and thermal slips. The dimensionless nonlinear differential equations were also defined in terms of governing partial differential equations and applying similarity transformations. The equations were analytically solved following the homotopy analysis method (HAM). An excellent agreement is observed in comparison with theavailable literature in special case (Skin friction coefficient). In the current study, an analytic solution is obtained for the laminar incompressible MHD boundary layer viscous fluid flow problem on the exponentially electrically conducting porous shrinking surface. The impact of different parameters like injection/suction, Prandtl number, radiation, velocity slip, thermal slip, as well as the magnetic field on different velocity and temperature values have been presented graphically, and have been discussed in detail. The f″(0) skin friction rises with higher suction parameter s(>0) values, magnetic parameter M but it decreases when the slip parameter value is increased. Whereas heat transfer rate −θ′(0) rises with an increasing M, s and λ..

Hybrid nanofluid flow within cooling tube of photovoltaic-thermoelectric solar unit

In this work, the thermoelectric generator (TEG) layer has been combined with conventional layers of photovoltaic-thermal (PVT) modules to use the waste heat and increase the efficiency. To reduce the cell temperature, there exists a cooling duct in the bottom of the PVT-TEG unit. Type of fluid within the duct and structure of duct can change the performance of the system. So, hybrid nanofluid (mixture of Fe3O4 and MWCNT with water) has been replaced instead of pure water and three various configurations of cross section [STR1 (circular), STR2 (rhombus), STR3 (elliptic)] have been implemented. Through the tube incompressible laminar flow of hybrid nanofluid has been solved while in solid layers of panel, pure conduction equation has been simulated involving heat sources resulting from optical analysis. According to simulations, the third structure (elliptic) has the best performance and rise of inlet velocity causes overall performance to enhance about 6.29%. The values of thermal and electrical performances for elliptic design with equal fractions of nanoparticles are 14.56% and 55.42%, respectively. With the best design, electrical efficiency improves about 16.2% in comparison with an uncooled system.

MHD flow and heat transfer of micropolar nanofluid on a linearly stretching/shrinking porous surface

In this paper, there is considered incompressible steady two-dimensional laminar MHD boundary layer flow, heat and mass transfer characteristics of micropolar nanofluid across a linearly stretching/shrinking porous surface. The effects of the magnetic, thermal slip, mass slip and heat source sink parameters are also considered. By applyingn appropriate similarity variables, the system of governing partial differential equations associated to micropolar nanofluid flow is transformed into a system of non - linear ordinary differential equations. The resulting equations are numerically solved in the Maple software by using shooting technique. The impact of the different applied parameters on skin friction, couple stress, Nusselt and the Sherwood numbers along the related profiles are determined for both stretching and shrinking cases of the surfaces. It was observed that with an increase in suction and magnetic parameters, the fluid velocity decreased. An increment in the thermal slip, the fluid temperature decreased and nanoparticles concentration decreases as the mass slip parameter is enhanced. An increase in concentration decreases but temperature increases. While, concentration and temperature both increase due to increase in thermophoresis parameter, and concentration also increases by increase in rate of chemical reaction. Thus, suction at the boundary and magnetic parameter acted as flow controlling parameter. It is believed that this type of investigation is very much helpful for the manufacturing of complex fluids and also for cleaning oil from surfaces.

Meshless simulation of a macrosegregation benchmark considering the solid motion

We have extended the existing two-dimensional rigid solid phase benchmark for binary substance with the solid phase motion in the present paper. Incompressible laminar Newtonian flow is assumed, and a standard mixture formulation is used for the mass, momentum, energy, and solute transport. A coherency solid motion model accounts for the free-floating grains, assuming that the solid velocity is proportional to the mixture velocity and the liquid fraction. The lever rule is used to describe the mass fractions of the phases. A two-dimensional benchmark is solved using the semi-implicit meshless diffuse approximate method with an adaptive subdomain upwinding strategy. The results of the meshless method are compared to the finite volume method results with a reasonable agreement. The new benchmark results show that the solid motion has an essential effect on the macrosegregation pattern.

Steady solver for incompressible Navier-Stokes equation with automated adaptive mesh refinement using FEniCS

This study demonstrates steady incompressible flow over a cylinder section using the finite element method. An open-source framework was used to increase the accuracy of the results of the analysis. The Python-based open-source computing platform FEniCS was used for the problem formulation. The mesh generator used is Gmsh. FEniCS offers automated adaptive mesh refinement and higher-order elements of order three and higher, which produce more accurate results. These features are not available in most FEM software. The problem DFG benchmark 2D-1 in Featflow was analyzed using the open-source framework. The drag and lift coefficients and the pressure difference between the front and back of the cylinder were found and compared with the benchmark values. The results obtained prove that the proposed open-source framework is incredibly effective in solving fluid flow problems. The FEniCS code to perform this DFG 2D-1 benchmark analysis is given in this work. It shows the problem formulation, setting of boundary conditions, and the adaptive solver. Thus, the same open-source framework can be used to analyze any laminar incompressible flow by simply creating a different geometry and varying the flow characteristics and boundary conditions.

Generalized UNIFAES derivatives applied to the correlations of the transport equations for fluctuating kinetic energy, helicity and enstrophy in an oscillated laminar flow

The original UNIFAES, as any exponential-type scheme, applies to the combined advective and diffusive terms of the viscous fluid transport equations. This work generalizes the scheme by making explicit the first and second derivatives of its interpolating curve, so that it can be applied, alongside classic central differencing schemes, to the statistical correlations of the transport equations of fluctuating kinetic energy, helicity and enstrophy. Tests are performed in a perturbed laminar incompressible Couette flow, obtained with a three-dimensional primitive variables solver using the original UNIFAES, the semi-staggered mesh, the Poisson equation for pressure and the forth order Runge-Kutta time-wise integration. Both the asymptotic tendencies of the correlations at low Reynolds number and the numerical stability of the solver for any Reynolds number are demonstrated with modest meshes.

Loss Analysis of a Transonic Rotor with a Differential Approach to Entropy Generation

The loss mechanism of transonic axial compressors is a long-standing problem that involves almost all types of entropy generation in fluid flows, such as skin friction, shock waves, shear flows, corner separation, and tip vortices. Primarily, sources need to be identified and quantitative comparisons of their contributions need to be made. For such determination, we propose herein a differential approach to entropy generation, called the “differential approach”. Two case studies are analyzed to determine the applicability of this approach: (1) laminar and turbulent incompressible flows in straight circular ducts and (2) turbulent compressible flows in convergent-and-divergent nozzles with shock waves. The results lead to the following conclusions: (a) Qualitatively, the differential approach works well, and the quantified measure is reliable if it is calculated with quality meshes and a suitable turbulence model. This means that the differential approach can be a good tool for predesign optimization. (b) When shocks occur within flow fields, the shock-induced boundary-layer separation can generate more loss than the shock loss alone. Subsequently, the differential approach is applied to complex flows in the NASA Rotor 67, which is a well-known bench-test transonic rotor. The results show that the differential approach not only determines the local losses and associates the source of losses with the flow structures but also qualitatively compares and identifies the largest contributors. These results provide a theoretical foundation for optimizing rotor design and enhancing stability.

Unsteady Magnetohydrodynamic (MHD) Cu–Al2O3/Water Hybrid Nanofluid Flow and Heat Transfer from an Exponentially Accelerated Plate

The present study intends to explore heat transfer characteristics of the unsteady natural convective flow of Cu–Al2O3/water hybrid nanofluid due to exponentially accelerated vertical plate. 2D Laminar viscous incompressible boundary layer fluid flow is considered in the presence of MHD and accelerating parameter. The governing partial differential equations with appropriate boundary conditions are solved using the Crank-Nicolson numerical technique. Plots for skin friction coefficient, velocity, temperature, Nusselt number concerning Magnetic parameter (M), Accelerating parameter (a), Grashof number (Gr), Volume fraction (Φ2), and time are disclosed. The study imparted that Cu–Al2O3 hybrid nanoparticles with water as base fluid facilitate a higher heat transfer rate and soaring Nusselt number compared to nanofluid Cu/water. Furthermore, we found an elevated skin friction coefficient in nanofluid Cu/water than in hybrid nanofluid Cu–Al2O3/water in all non-dimensional parameters.

Airfoil inverse design based on laminar compressible adjoint lattice Boltzmann method

AbstractA new optimization techniques based on the adjoint lattice Boltzmann method is derived for airfoil inverse design in laminar compressible flows. In this study, the developed adjoint lattice Boltzmann scheme based on the circular function (CF) is extended for airfoil inverse design problems in laminar incompressible and compressible flows. New mathematical derivation based on compressible lattice Boltzmann equations (LBE) is developed which can find target shape of an airfoil with available desired pressure distribution. The adjoint lattice Boltzmann method is extended for both the incompressible and compressible flows by selecting the circular function idea for calculating the equilibrium distribution functions. So, the adjoint equation is also expanded based on CF idea for calculation of objective function gradient vector. The steepest decent technique is utilized as gradient optimizer. Also, a novel solution is presented to remove singularity problem of the adjoint boundary condition. In order to validate the developed optimization algorithm, results are presented for both incompressible and compressible inverse problem in steady and unsteady flow and accurate results are obtained.

Correlations Describing Laminar Hydrodynamic Development in a Circular Pipe

AbstractComputational fluid dynamics (CFD) is employed to study incompressible and steady laminar flow in the hydrodynamic entrance region of circular pipes for a wide range of Reynolds numbers. Dimensionless analytic expressions for streamwise variations of the centerline velocity, skin friction coefficient, and pressure drop are derived by applying a two-stage nonlinear regression analysis to computational solutions of the Navier–Stokes equations for various Reynolds numbers between 1 and 2000. Similar expressions are also presented for the correction factors for the momentum and kinetic energy fluxes. First, the correlation parameters for a flow variable are obtained for each Reynolds number considered. Subsequently, a second nonlinear regression analysis is conducted to obtain another set of equations for the variation of fitting parameters with the Reynolds number. Constant parameter correlations are also given for the Reynolds number range between 200 and 2000, which are less accurate than the expressions containing Reynolds number-dependent terms. The correlations presented here are also valid for flows with heat transfer, under the assumptions of constant property and zero buoyancy.

Neural-network-based fluid–structure interaction applied to vortex-induced vibration

In this paper, a fluid–structure interaction (FSI) solver with neural-network-based fluid-flow prediction is proposed. This concept is applied to the problem of vortex-induced vibration of a cylinder. The majority of studies that are concerned with fluid-flow prediction using neural networks solve problems with fixed boundary. In this paper, a convolutional neural network (CNN) is used to predict unsteady incompressible laminar flow with moving boundary. A deformable non-Cartesian grid, which traces the boundary of the fluid domain, is used in this paper. The CNN is trained for oscillating cylinder with various frequencies and amplitudes. The dynamics of the elastically-mounted cylinder is modelled using a linear spring–mass–damper model and solved by an implicit differential scheme. The results show that the CNN-based FSI solver is capable of capturing the so-called lock-in phenomenon for the problem of vortex-induced vibration of a cylinder and the quantitative behaviour is similar to the results of the CFD-based FSI solver. Moreover, the CNN-based FSI solver is two orders of magnitude faster than the CFD-based FSI solver and the speedup is expected to be even greater on larger problems.

Lagrangian transport in the time-periodic two-dimensional lid-driven square cavity

The Lagrangian transport in the laminar incompressible flow in a two-dimensional square cavity driven by a harmonic tangential oscillation of the lid is investigated numerically for a wide range of Reynolds and Strouhal numbers. The topology of fluid trajectories is analyzed by stroboscopic projections revealing the co-existence of chaotic trajectories and regular Kolmogorov–Arnold–Moser (KAM) tori. The pathline structure strongly depends on the Reynolds number and the oscillation frequency of the lid. Typically, most pathlines are chaotic when the oscillation frequency is small, with few KAM tori being strongly stretched along instantaneous streamlines of the flow. As the frequency is increased, the fluid motion becomes more regular and the size of the KAM tori grows until, at high frequencies, they resemble streamlines of a mean flow.

Effect of the lid-driven on mixed convection in an open flexible wall cavity with a partially heated bottom wall

The FSI-mixed convection heat transfer in a lid–driven vented cavity is studied in the present work. The heat source is set partially on the base of the cavity; the left flexible wall is cold, while the remaining walls are adiabatic. The top wall of the cavity moves in different cases depending on its movement; stationary wall (case 0), moving to the left (case I) and moving to the right (case II). The arbitrary Lagrangian-Eulerian formulation and finite element method are utilized to solve the governing equations. A two-dimensional incompressible laminar flow with an unsteady-state condition is used in the present model. The effects of relevant factors like the Richardson number 0.01≤ Ri ≤ 100 and the ratio of the velocities of moving top wall to that of the air entering the cavity, which is governed by Reynolds numbers ratio 1 ≤ Rer ≤ 4 have been studied. The outcomes demonstrate the feasibility of using a flexible wall and a special movement of the top wall. The percentage increase of the Nusselt number due to the flexible wall alone is about 4.5% while when the top wall moving to the left (case I), the augmentation rises to 28%.

Visualization of thermo-magnetic natural convective heat flow in a square enclosure partially filled with a porous medium using bejan heatlines and Hooman energy flux vectors: Hybrid fuel cell simulation

The aim of the article is to study the magneto-convective laminar incompressible flow within a differentially heated square enclosure partly filled with porous medium saturated with ionized helium gas in the presence of a transverse magnetic flux, as a model for emerging fuel cell designs. A Darcy model is utilized for porous medium bulk drag effects. Visualization of heat line and energy flux vectors is computed via Bejan's heat line approach and the Hooman energy flux vector method. The horizontal (i.e., bottom and top) wall boundaries are considered adiabatic and impermeable, while the side walls (cold and hot walls) are maintained at different but constant temperatures. The nonlinear coupled conservation equations under prescribed boundary conditions are solved with a finite difference-based vorticity-stream function approach. Appropriate convergence criteria factors are deployed. Furthermore, validation with earlier studies for the purely fluid, non-magnetic case i. e. in the absence of porous medium (Da) and Hartmann number (Ha) effects, is included. A parametric examination of the impact of Rayleigh number (Ra), Darcy number (Da) and Hartmann number (Ha) on temperature contours, heat lines, energy flux vectors and streamline patterns for ionized helium gas (Prandtl number, Pr = 0.71) is conducted. An increment in Hartmann magnetic number decreases the magnitudes of heat lines, suppresses heat transmission in the enclosure and curtails flow circulation. Enhancing the magnetic parameter and Rayleigh number however boosts the average heat transfer rate. Average Nusselt number at the left hot wall is elevated with increasing permeability of the porous medium and Rayleigh number. Mid-section velocities are enhanced in the porous layer but depleted in the non-porous layer of the enclosure with greater Rayleigh number. The simulations find provide some insight into applications in emerging hybrid electromagnetic fuel cells enabling better visualization of the thermal/fluid characteristics via the novel heat flow visualization heat-function and energy flux vectors analogy.