Semi-implicit Method For Pressure-linked Equations Research Articles

Numerical Analysis of Airflow in Trachea Affected by Thyroid Cancer Using Finite Volume Method

The study aims to analyze the airflow in the trachea due to thyroid cancer. Thyroid cancer is a cancer that attacks the thyroid gland. The thyroid gland is located in the neck below the Adam's apple. In general, thyroid cancer causes stenosis of the trachea due to cancer compression of the tracheal wall. This problem is solved using the finite volume method with SIMPLE (Semi Implicit Method for Pressure Linked Equation) discretization. This method is well suited for the discretization of irregularly shaped fluid flows. The software used is Matlab and Ansys Fluent. Matlab is used to compute numerical solutions and display graphs, while Fluent is used to visualize the air flow. The result of this study is that the greater the percentage of stenosis, the velocity of the airflow is faster and the pressure of the airflow is lower. The most critical condition for respiratory power loss is when the airflow velocity exceeds the normal limit, i.e. when the narrowing is more than 50%, the initial velocity is more than 0,1 m/s.

Numerical Modeling of Non-Isothermal Laminar Flow and Heat Transfer of Paraffinic Oil with Yield Stress in a Pipe

This paper presents the results of a study on the non-isothermal laminar flow and heat transfer of oil with Newtonian and viscoplastic rheologies. Heat exchange with the surrounding environment leads to the formation of a near-wall zone of viscoplastic fluid. As the flow proceeds, the transformation of a Newtonian fluid to a viscoplastic state occurs. The rheology of the Shvedoff–Bingham fluid as a function of temperature is represented by the effective molecular viscosity apparatus. A numerical solution to the system of equations of motion and heat transfer was obtained using the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm. The calculated data are obtained at Reynolds number Re from 523 to 1046, Bingham number Bn from 8.51 to 411.16, and Prandl number Pr = 45. The calculations’ novelty lies in the appearance of a “stagnation zone” in the near-wall zone and the pipe cross-section narrowing. The near-wall “stagnation zone” is along the pipe’s radius from r/R = 0.475 to r/R = 1 at Re = 523, Bn = 411.16, Pr = 45, u1 = 0.10 m/s, t1 = 25 °C, and tw = 0 °C. The influence of the heat of phase transition of paraffinic oil on the development of flow and heat transfer characteristics along the pipe length is demonstrated.

Thermal-hydraulic performance of turbulent flows across a heated round tube installed through several perforated twisted tapes

PurposeThe purpose of this study is to advance turbulent thermal convection inside the constant heat-flux round tube inserted by multiple perforated twisted tapes.Design/methodology/approachThe novel design of this study is accomplished by inserting several twisted tapes and drilling some circular perforations near the tape edge (C1, C3, C5: solid tapes; C2, C4, C6: perforated tapes). The turbulence flow appearances and thermal convective features are examined for various Reynolds numbers (8,000–14,000) using the renormalization group (RNG) κ−ε turbulent model and Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm.FindingsThe simulated outcomes reveal that inserting more perforated-twisted tapes into the heated round tube promotes turbulent thermal convection effectively. A swirling flow caused by the twisted tapes to produce the secondary flow jets between two reverse-spin tapes can combine with the main flow passing through the perforations at the outer edge to enhance the vortex flow. The primary factors are the quantity of twisted tapes and with/without perforations, as the perforation ratio remains at 2.5 in this numerical work. Weighing friction along the tube, C6 (four reverse-spin perforated-twisted tapes) brings the uppermost thermal-hydraulic performance of 1.23 under Re = 8,000.Research limitations/implicationsThe constant thermo-hydraulic attributes of liquid water and the steady Newtonian fluid are research limitations for this simulated work.Practical implicationsThe simulated outcomes will avail the inner-pipe design of a heat exchanger inserted by multiple perforated twisted tapes to enhance superior heat transfer.Originality/valueThese twisted tapes form tiny circular perforations along the tape edge to introduce the fluid flow through these bores and combine with the secondary flow induced between two reverse-spin tapes. This scheme enhances the swirling flow, turbulence intensity and fluid mixing to advance thermal convection since larger perforations cannot produce large jet velocity or the position of perforations is too far from the tape edge to generate a separated flow. Consequently, this work contributes a valuable cooling mechanism toward thermal engineering.

Numerical Analysis of Three Vertical Axis Turbine Designs for Improved Water Energy Efficiency

A hydrokinetic turbine with a vertical axis is specifically designed to harvest the kinetic energy from moving water. In this study, three vertical axis water turbines, namely Gorlov, Darrieus, and Savonius turbines, were compared for their efficiency via numerical modeling for steady-state conditions via the ANSYS 2022 R2 Fluent model. The Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) was implemented with an SST k-ω turbulence model. The dynamic mesh technique, which allows modeling according to changes in angular velocity at each time step, was used to simulate flow around the turbines for six different velocities (from 0.5 to 3 m/s). The efficiency of the turbines was compared and the results were analyzed. The pressure, velocity, and turbulence kinetic energy distributions around the rotor were measured at different rotational angles and results indicated a wider operating range for the Darrieus and Gorlov turbines compared to the Savonius turbine. The highest power coefficient of 0.293 was achieved in the model featuring a Darrieus turbine, corresponding to a TSR value of 1.34, compared to 0.208 for the Gorlov and 0.257 for the Savonius turbine, at TSR values of 1.3 and 1.06, respectively. Numerical modeling results pointed to a significantly higher self-starting capacity for the Savonius turbine compared to the others.

Development of transient thermal-hydraulic analysis model for the two-phase loop thermosyphon

To comprehensively and accurately simulate and predict the flow and heat transfer characteristics of the two-phase loop thermosyphon (TPLT), a two-fluid two-phase model was developed. A six-equation set was formulated to account for two-phase flow, encompassing mass equations, momentum equations, and energy equations. The interactions between the fluids in terms of mass, momentum, and energy were also taken into account. To obtain numerical solutions for the partial differential equations within a staggered mesh framework, we employed the 2nd-order Lax-Wendroff scheme to obtain the discrete linear system, complemented by the inclusion of a flux limiter. The Semi-Implicit Method for Pressure-Linked Equation (SIMPLE) algorithm was employed to address the solution of the linear equation system. Data from a small-scale TPLT test was used to assess the accuracy and reliability of both the physical models and the numerical method proposed in this study. Simulations were performed under two working conditions of the thermosyphon with filling ratio of 45 % and 64 %. The simulation results exhibited good agreement with the experimental data, demonstrating the accuracy of the model. Furthermore, the model is capable of providing information on the complex two-phase flow inside the TPLT that cannot be measured experimentally.

A duality-preserving adjoint method for segregated Navier–Stokes solvers

Adjoint methods efficiently compute gradients for systems with many inputs and have been widely used for large-scale gradient-based optimization in fluid mechanics. To ensure optimization's numerical robustness, we need to develop an adjoint solution algorithm that has a similar, if not the same, convergence rate as the primal flow solver at each optimization iteration. This consistent primal-adjoint convergence behavior is also called duality-preserving (DP). Existing DP adjoint methods are mostly for fully coupled Navier–Stokes (NS) solvers with compressible flows. However, few DP adjoints have been proposed for segregated NS solvers, e.g., the semi-implicit method for pressure-linked equations (SIMPLE) algorithm solvers widely used for incompressible flow simulations. This study will fill this gap by deriving a fixed-point segregated adjoint formulation that fully preserves the convergence behavior of primal solvers. We first rewrite the steady-state segregated NS primal solution process into a fully coupled left-preconditioned Richardson format. Then, we transpose the preconditioner matrix to obtain a DP iterative adjoint formulation. In addition to algebraic derivation, we create a new graph representation that significantly streamlines the DP adjoint development for new segregated solvers. We prove that the proposed graph representation is equivalent to the above preconditioner transpose approach and guarantees duality. We evaluate our proposed algorithm using three cases with increasing complexity: a miniature-sized problem, an airfoil, and a wing. To quantify duality, we compare the eigenvalues between the primal and adjoint solvers and observe excellent agreements. We also evaluate to what extent various numerical settings (e.g., inner iteration tolerances and non-dual preconditioner) impact the eigenvalue distributions. Our proposed adjoint achieves machine-precision accurate gradient computation with competitive speed. Finally, we incorporate our adjoint solver into a large-scale gradient-based optimization framework and demonstrate its capability for wing aerodynamic shape optimization. The proposed fixed-point adjoint approach has the potential to make the adjoint solution more robust and efficient for any segregated NS solvers.

Thermal performance of Al2O3-TiO2/water hybrid nanofluids for cooling system using a helically coiled tube in a brushless direct current motor

Thermal performance of Al2O3-TiO2/water hybrid nanofluids for cooling system using a helically coiled tube in a brushless direct current motor has been investigated numerically. The numbers of helical coils number were varied by 4, 6, 8, and 10 in coils and represented by Helical numbers 362, 355, 352, and 350, respectively. To solve the velocity and pressure discretization, the SIMPLE (Semi Implicit Method for Pressure Linked Equations) method was applied whereas to solve the energy and momentum equations, second order upwind was used. The result revealed that Nusselt number of Al2O3-TiO2/water hybrid nanofluids is greater than water, with an increased Nusselt number of 3.7% and 10.42% for 1 vol.% and 2 vol.%, respectively. The added nanoparticles concentration of Al2O3-TiO2/water hybrid nanofluids could not reduce significantly the stator temperature. Al2O3-TiO2/water hybrid nanofluids can reduce the stator temperature by 0.92% and 1.82% for 1 vol.% and vol.2%, respectively compared to water. However, the increased Reynolds number can reduce the stator temperature for all the observed working fluids. Helical number can affect the Nusselt number due to the influence of the helical geometry on the fluid’s flow behavior, heat transfer properties, and turbulence levels. Nusselt number of Al2O3-TiO2/water hybrid nanofluids at 1 vol.% has a higher value than water in each variation with an average increase in Nusselt number of 4.12% for all helical numbers.

A New Calculation Model for Equivalent Circulating Density Considering Interface Effect between Various Fluids during Cementing Process

Summary Equivalent circulating density (ECD) is an essential parameter in the construction of oil and gas wells, which can be used to control the downhole pressure and prevent serious incidents such as well leakage or blowouts. Different engineering tasks will lead to changes in the ECD calculation model; the classical pipe flow theory can be used to calculate the ECD of circulating drilling fluid, but it is not suitable for the cementing displacement because it does not consider the interface effect between various fluids. In this paper, a new ECD calculation model has been developed that accounts for the changes in fluid interface morphology between displacing fluid and displaced fluid during the cementing process. Moreover, a simulation of the effects of borehole radius, casing eccentricity, displaced fluid density, and flow rate on the ECD were analyzed and quantified by a numerical approach to solve the fluid dynamics equilibrium equations that describe the flow in the eccentric annuli based on the semi-implicit method for pressure-linked equations (SIMPLE) algorithm. The results show that the calculated ECD predicted by the proposed model is larger than the traditional model with the reduction in the borehole radius, and the maximum deviation at the inlet position can reach 0.03 g·cm−3. Variation in the length of the interface transition zone is the main reason for the deviation in ECD prediction accuracy. In the case of constant casing outer diameter, fluid rheology, and displaced fluid density, the ECD decreases with increasing borehole radius. Meanwhile, it increases with higher displaced fluid density, eccentricity, and annular velocity. It is also shown that the length of the mixing zone can reach up to 40% of the pipe length under the conditions of eccentricity and displacement described in the paper. The proposed model predicts the ECD in the annulus by considering the influence of different engineering parameters on the movement of displacement interface, which can effectively ensure the safety of the cementing operation.

Physically Realistic Inlet-Velocity Profiles in Duct Flows

A uniform inlet velocity profile is widely used in the numerical simulations of fluid flow and heat transfer in ducts for both incompressible and compressible flows. In incompressible flows, the calculated fluid pressure at the inlet edge is extremely high and affects the calculation of the average pressure. In compressible flows, the fluctuation of pressure in the flow direction results in the fluctuation in the velocity. This has motivated this study to numerically investigate a physically realistic velocity profile at the inlet of a pipe rather than using a uniform velocity profile. The numerical simulations were based on the control volume-based power law scheme and the semi-implicit method for pressure-linked equations (SIMPLE) algorithm. The continuity and momentum equations for a flow in a pipe with the rounded inlet corner were solved to obtain a physically realistic inlet velocity profile. The obtained inlet velocity profile was expressed by a simple expression in the range of Reynolds number from 100 to 2000. Using this velocity profile, both the incompressible and compressible flows in a pipe were numerically investigated. The results resolved the previously observed inconsistencies in the pressure that were previously observed in the numerical simulations with uniform inlet velocity profiles.

Free convection of thermodependent non-Newtonian fluids in a square enclosure partially heated at one side

This article exhibits a numerical analysis on free convection cooling of a heater located on the left side of a square enclosure using thermodependent power-law fluids. The temperature of the right sidewall is maintained relatively cold, while the unheated portions of the left wall and the horizontal ones are thermally insulated. The governing differential equations are numerically solved using a finite volume technique based on the iterative Semi-Implicit Method for Pressure Linked Equation (SIMPLE) algorithm. The objective of this article is to analyze the impacts of the Rayleigh number, the Pearson number, the power-law index, and the location and length of the heat source on the fluid structure and temperature patterns, and to subtract the impact of these control parameters on the cooling efficiency of the cavity. The results reveal that rising the heater size and the Rayleigh number improves free convection inside the cavity. Moreover, using shear-thinning fluids (i.e. n < 1) with high value of the Pearson number enhances the thermal performance of the enclosure. The findings also point to the existence of a peak in the average Nusselt number variation, corresponding to an optimal heater location.

Effect of surface radiation on double diffusion convection in a low Mach number compressible gaseous mixture (H2–air)

This study aims to numerically investigate the effect of surface radiation on double diffusion convection in a low Mach number compressible gaseous mixture, specifically focusing on the H2–air system in a square cavity. The cavity is subjected to low horizontal temperature and concentration gradients and isolated from its flat walls. The mathematical model's equations were discretized using the finite volume method based on the semi-implicit method for pressure-linked equations revised algorithm for the pressure–velocity coupling. The radiosity method is employed to calculate the radiative heat exchange between the internal walls of the cavity. This work addresses a significant research gap by exploring the interplay between surface radiation, compressibility effects, and double diffusion convection. It makes a novel contribution to the field and has implications for combustion, astrophysics, and industrial heat exchange processes. Comparing the results with those obtained for a light gaseous mixture, the findings demonstrate that the presence of radiation considerably modifies the thermal, dynamic, and mass fields, as well as the thermophysical properties of the gaseous mixture in the case of heavy gaseous mixtures. These modifications can reach up to 20%.The outcomes of this study provide a foundation for further research and experimentation, with applications ranging from engineering to astrophysics.

Instabilities in tidal turbine wakes

We report on the observation of vortex instabilities in the wake of a tidal turbine undergoing harmonic unsteady axial inflow (e.g. due to surface waves). The work was carried out using unsteady RANS (URANS) modelling using the open-source CFD software OpenFOAM, using the `pimpleDyMFoam' solver. The PIMPLE algorithm used in the URANS solver is a combination of the PISO (Pressure Implicit with Splitting of Operator) and SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithms. URANS simulations usually have a limitation on the time step set by the Courant number (C = u (delta t)/(delta x), where delta x is the minimum cell length and u the local velocity. In the PISO algorithm, C&lt;1 is usually required. However, the PIMPLE algorithm allows stable transient simulations at C&gt;&gt;1 by applying under-relaxation to each time-step until a convergence criterion is met, before allowing the time-step to complete with no applied relaxation factors. The turbulence model used was komega-SST, which has been used extensively in tidal turbine modelling.&#x0D; As with a wind turbine, the response of a tidal turbine to unsteady flow is heavily influenced by the behaviour of the helical wake that returns in close proximity to the turbine blades times per revolution ( – number of blades). Unsteady inflow causes the blades to shed vorticity into the wake, which in turn leads to a spatial variation in wake vortex strength, such that the vorticity of adjacent returning wake segments can differ, and thus there is a spatially varying velocity deficit in the wake. This spatial variation in velocity deficit triggers instability in the blade tip vortices, the emergence of which we demonstrate is governed by the non-dimensional group relating the blade passing frequency to the gust frequency. If the ratio between these two frequencies is an integer, the wake is stable. If not, the tip vortices exhibit various forms of instability. If the wake is unstable, adjacent wake segments will eventually coalesce as they move downstream, such that the wake consists of larger regions of vorticity with lower spatial frequency, compared to the wake immediately behind the turbine. There is also some indication that these unstable, coalesced wakes persist further downstream, compared with stable wakes. This has implications for wind and tidal farm design, where interaction of a row of turbines with the wakes of upstream turbines is an important consideration.

Improving performance of H-Type NACA 0021 Darrieus rotor using leading-edge stationary/rotating microcylinders: Numerical studies

In the current paper, a computational study has been performed to simulate a novel concept in which a fixed/rotating microcylinder is installed upstream of the leading edge of the NACA 0021 airfoil, aiming to enhance the performance of the H-type Darrieus rotor. The idea behind implementing a fixed/rotating microcylinder is to enhance the lift to drag ratio due to increasing near-wall momentum through generated vortices transferring the momentum from the outer flow to the near-wall flow region of the airfoil. Parametric analyses for the microcylinder including its location, size, shape (circular, square and rhombus), and rotation were performed. The commercial Computational Fluid Dynamics (CFD) package ANSYS Fluent was used for solving the Unsteady Reynolds Averaged Navier-Stokes (URANS), and turbulence equations. The code has been based on Finite Volume Method (FVM) with the pressure-based solver developed for low-speed incompressible flows. The semi-implicit method for pressure-linked equation (SIMPLE) was used to solve the discretized equations. The URANS was used with adopting the SST k-ω turbulence model to find out the optimum rotor by utilizing the microcylinder model. An optimization methodology using Response Surface Optimization (RSM) based on Kriging method has been first performed to find the optimum size and location of a circular microcylinder. The optimization study indicated an optimum microcylinder diameter (d/C = 0.0085313), at an upstream chordwise distance and normal to it 0.070275 and 0.02303 of the chord length (C), respectively. The results showed also that a small static circular microcylinder of d/C = 0.009 and installed at 0.075C from the leading edge (MC5) is an efficient geometry at high regime of tip-speed ratios (TSR≥2.2) rather than lower regime of TSRs. When these superior set of rotating (5 rad/s) microcylinder (MC5) parameters were adopted, significant enhancement of power coefficient (Cp) could be achieved and a considerable improvement of the maximum power coefficient (Cpmax) up to 120 % at TSR = 3 appeared. A physical analysis of the flow fields using the contours of vorticity, pressure and turbulence energy has been performed to illustrate the effect of rotating microcylinder for improving rotor performance. The vorticity contours showed the ability of rotating microcylinder for generating a strong vortex structure in its wake for enhancing turbulence production around the blades, which delayed the known strong stall of the blades by diminishing the separation bubble size. This generally improved the blades aerodynamic performance and enhancing the lift-to-drag ratio.

Numerical Investigation by Cut-Cell Approach for Turbulent Flow through an Expanded Wall Channel

The expanded wall channel backward-facing step (BFS) and axisymmetric diffuser plays an important role in the society of fluid dynamics. Using a cut-cell technique is an established new method to treat the inclined wall of an axisymmetric diffuser. Cut-cell handle to reach the shape of the inclined wall, an axisymmetric diffuser and complex geometry. It helps treat the boundary condition at the wall in an accurate physical way. The turbulent flow through the geometries is solved by using Reynolds averaged Navier-Stokes equations (RANS) with the standard k-ε model. A self-built FOTRAN code based on the finite volume method with the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm for pressure velocity coupling is established and examined with published experimental data for two different geometries backward-facing step (BFS) and axisymmetric diffuser. The results of the new technique reflect good agreement between the numerical results and the experimental data. A parametric study of the impact of area ratios (2, 2.5, 3, 3.5) in a backward-facing step on pressure, velocity, and turbulent kinetic energy. The angles (7°, 10°, 14°) and area ratios (2, 2.5, 3, 3.5) effect of an axisymmetric diffuser on the streamlines, local skin friction, pressure, velocity, turbulent kinetic energy, and separation zone.

Effect of natural convection hybrid nanofluid flow on the migration and deposition of MWCNT-Fe[formula omitted]O[formula omitted] in a square enclosure

In the present study, the migration and deposition of multi-walled carbon nanotube (MWCNT)-Fe3O4 nanocomposite particles in a square enclosure for natural convection hybrid nanofluid flow are analysed numerically using the Eulerian–Lagrangian model with one-way coupling. The governing equations are solved by the finite volume method and Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm. The location and velocity of 3000 selected composite particles in the host nanofluid are obtained by employing the Lagrangian approach. The influences of Rayleigh number and nanoparticle volume fraction on the thermal and flow behaviours of the system are presented. It is observed that the increasing volume fraction leads to a rise in the average Nusselt number at low Rayleigh numbers, while the case of ϕ=0.1% is the optimum volume fraction of nanoparticle in terms of heat transfer enhancement and strength of flow structure at Ra≥104. The simulations of Lagrangian particle tracking demonstrate that the minimum deposition rate of composite particles with dp=0.5 μm is obtained for a given Rayleigh number. The number of deposited large composite particles for the case of ϕ=0.1% is slightly more than for ϕ=0.3%, while the deposition rate of ultra-fine composite particles gets a higher value in the case of ϕ=0.3%. Moreover, the thermophoresis force plays a more significant role in small particle deposition than the Brownian random force.

A modified dual time integration technique for aerodynamic quasi-static and dynamic stall hysteresis

Simulation of the aerodynamic stall phenomenon in both quasi-static and dynamic conditions requires expensive computational resources. The computations become even more costly for static stall hysteresis using an unsteady solver with very slow variation of angle of attack at low reduced frequencies. In an explicit time-marching solver that satisfies the low Courant number condition, that is, [Formula: see text], the computational cost for such simulations becomes prohibitive, especially at higher Reynolds numbers due to the presence of thin-stretched cells with large aspect ratio in the boundary layer. In this paper, a segregated solver method such as the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) is modified as a dual pseudo-time marching method so that the unsteady problem at each time step is reformulated as a steady state problem. The resulting system of equations in the discretized finite volume formulation is then reduced to zero or near-zero residuals using available convergence acceleration methods such as local time stepping, multi-grid acceleration and residual smoothing. The performance and accuracy of the implemented algorithm was tested for three different airfoils at low to moderate Reynolds numbers in both incompressible and compressible flow conditions covering both attached and separated flow regimes. The results obtained are in close agreement with the published experimental and computational results for both quasi-static and dynamic stall and have demonstrated significant savings in computational time.

An Aerodynamic Property Investigation of an Unmanned Aerial Vehicle (UAV) in case of Forward Flight by Numerical Approach

In the golden era of digitalization, flow calculation research based on a numerical approach has become increasingly popular in the scientific world and has played a vital role in revealing the aerodynamic characteristics of various aircraft models. This paper, belonging to computational fluid dynamics, describes the process and results of a numerical simulation approach using the software OpenFOAM for an unmanned aerial vehicle (UAV) in the case of forwarding flight with a low Reynolds number. With regard to the numerical approach, the aerodynamic properties are investigated through the turbulence model k-ω-SST (shear stress transport), which is a part of the turbulence calculation approach Reynolds average Navier–Stokes (RANS). Furthermore, the entire process of mesh generation and the numerical calculation process by simpleFoam in OpenFOAM, which is the solver using the semi-implicit method for pressure-linked equations (SIMPLE) algorithm for steady, incompressible flow, are also depicted in this paper. In addition, the characteristics of the flow field surrounding the model and the characteristic aerodynamic coefficients (drag coefficient, lift coefficient, lift-to-drag ratio versus angle of attack and pressure coefficients, and skin-friction coefficients for special positions on the wing) of the model are also clearly illustrated. Finally, the simulation illustrations in ParaView, including the velocity field, pressure field and vortices in the stagnation region, are shown. The process description and results contribute a clear picture of the numerical execution steps in OpenFOAM and aerodynamic knowledge for a particular unmanned aerial vehicle model to the computational fluid dynamics field in the aerospace industry.

Numerical analysis of air entrapment during water droplet impact on a substrate

As a liquid droplet impact on a substrate, it spreads flattens, and air may become trapped between the droplet and the substrate. This trapped air first evolves into an air film, which passes through many stages before eventually becoming an air bubble through retraction, contraction, toroid creation, pinching off, and so forth. The droplet cools while spreading across the substrate and finally freezes to create a splat. In most thermal spray coating applications, this phenomena is seen in the individual droplet solidification. The major purpose of this research is to develop an OpenFOAM solution that can model the effect of molten droplets on solid surfaces using free surface evolution. The PIMPLE algorithm, which is used in this solution, combines the PISO (Pressure Implicit with Splitting of Operators) and SIMPLE (Semi Implicit Method for Pressure-Linked Equations) approaches. In this approach, pressure–velocity equations are resolved, and the continuous surface flow model is used to simulate the surface tension force. Furthermore, the solution incorporates the dynamic contact angle. An enthalpy-based formulation that takes solidification into account is used to simulate the energy equation. The solver is validated with the aid of the available experimental results. Hydrodynamics can be used to properly simulate the various stages of air entrapment.

A comparative numerical analysis and environment assessment to examine hydrothermal behavior of two serpentine heatsink with water/silver Nano fluid applying two-phase mixture model

In the present study, the hydrothermal characteristics of two different a) serpentine (Conf. A), and b) double serpentine (Conf. B) heatsinks with water/silver Nano Fluid (NF) were studied. To this end, the Finite volume method was performed, and the governing equations were discretized based on the second upwind approach and solved numerically applying the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) scheme. The results demonstrated that the thermal resistance (R) of Conf. A is lower than that of Conf. B at low Re numbers, and these two configurations have an identical R as Re increases to 2000. Also, the convective heat transfer in Conf. A is slightly higher than that in Conf. B and for Re=2000 both configurations have a same h value. Moreover, the increasing of nanoparticle concentration from 0% to 1% increases h by 12.55% and decreases the pressure drop (ΔP) by 4.25%. In addition, the CPU mean temperature of Conf. A is 0.8% and 0.1% lower than that of Conf. B for Res of 500 and 2000, respectively. On the other hand, ΔP in Conf. A is 74% higher than that in Conf. B. Besides, Conf. B exhibits a better temperature uniformity as compared to other configuration. The parameter of figure of merit was obtained as 1.47 to 1.52 at Res of 500 and 2000, respectively, which showed that Conf. B provides a higher hydrothermal performance over the other configuration.The environmental impact of the designed heat sink is equal to 0.5388.

Experimental methods in chemical engineering: Computational fluid dynamics/finite volume method—CFD/FVM

AbstractComputational fluid dynamics (CFD) applies numerical methods to solve transport phenomena problems. These include, for example, problems related to fluid flow comprising the Navier–Stokes transport equations for either compressible or incompressible fluids, together with turbulence models and continuity equations for single and multi‐component (reacting and inert) systems. The design space is first segmented into discrete volume elements (meshing). The finite volume method, the subject of this article, discretizes the equations in time and space to produce a set of non‐linear algebraic expressions that are assigned to each volume element—cell. The system of equations is solved iteratively with algorithms like the semi‐implicit method for pressure‐linked equations (SIMPLE) and the pressure implicit splitting of operators (PISO). CFD is especially useful for testing multiple design elements because it is often faster and cheaper than experiments. The downside is that this numerical method is based on models that require validation to check their accuracy. According to a bibliometric analysis, the broad research domains in chemical engineering include: (1) dynamics and CFD‐DEM, (2) fluid flow, heat transfer, and turbulence, (3) mass transfer and combustion, (4) ventilation and the environment, and (5) design and optimization. Here, we review the basic theoretical concepts of CFD and illustrate how to set up a problem in the open‐source software OpenFOAM to isomerize n‐butane to i‐butane in a notched reactor under turbulent conditions. We simulated the problem with 1000, 4000, and 16 000 cells. According to the Richardson extrapolation, the simulation underestimates the adiabatic temperature rise by 7% with 16 000 cells.