Order Upwind Research Articles

Numerical Analysis of Fluid Flow on Wall Cylinder Circular with K-ε Modeling for a High Reynolds Rate

This study discusses the numerical study of two-dimensional analysis of flow through circular cylinders. The original physical information entered in the equation governing most of the modeling is transferred into a numerical solution. Fluid flow on two-dimensional circular cylinder wall using high Reynolds k-ε modeling (Re = 106), Here we will do 3 modeling first oder upwind, second order upwind and third order MUSCL by using k-ε standard. The general procedure for this research is formulated in detail for allocations in the dynamic analysis of fluid computing. The results of this study suggest that MUSCL's third order modeling gives more accurate results better than other models.

Some Results from the Upwinding Compact Scheme on Continuous and Non-continuous Functions

In this paper, an 8th order Upwinding Compact Scheme is derived by using the idea of the nth order polynomial. Also, the dissipation and dispersion analysis of the scheme is obtained by Fourier analysis after getting the wave number of the scheme. When applying the proposed scheme on continuous functions, high order of accuracy is achieved with high resolution due to the properties of compact schemes. The idea of WENO smoothness indicator is used to detect discontinuity locations. To overcome the global dependency issue, which causes problems near discontinuities in compact schemes, the technic of the decoupling system is used to switch into a local dependency in non-smooth regions. In this work, the promise and success of the proposed scheme is verified by gaining high order, high resolution, and non-oscillation from various numerical examples. Additionally, there is a plan to confirm the achievement of the present scheme when applying it to multidimensional flows with shock-turbulence interaction problems from Computational Fluid Dynamics (CFD).

Comparison of varieties of numerical methods applied to lid-driven cavity flow: coupling algorithms, staggered grid vs. collocated grid, and FUDS vs. SUDS

The effectiveness of different methods, schemes, algorithms, and approaches is of substantial challenging problems in numerical modeling of transport phenomena. In the present paper, a lid-driven cavity problem is modeled via two basically different approaches of spatial discretization: collocated and staggered. The non-dimensionalized governing equations are semi-discretized by using a finite volume approach. Then, the full discretization is performed in each of collocated and staggered grids, separately. Upwind and central difference schemes are implemented in order to discretize the convective and diffusion terms of equations, respectively. After mesh independency study, the performances of collocated and staggered grids in comparison with the reference benchmark are presented. Next, the effectiveness of the first and the second order upwind schemes are presented, as well as different coupling algorithms of SIMPLE, SIMPLEC, and SIMPLER. Finally, an overall comparison of the methods is provided and acceptable agreements with benchmark are attained.

Generalized Sensitivity Parameter Free Fifth Order WENO Finite Difference Scheme with Z-Type Weights

A modified fifth order Z-type (nonlinear) weights, which consist of a linear term and a nonlinear term, in the weighted essentially non-oscillatory (WENO) polynomial reconstruction procedure for the WENO-Z finite difference scheme in solving hyperbolic conservation laws is proposed. The nonlinear term is modified by a modifier function that is based on the linear combination of the local smoothness indicators. The WENO scheme with the modified Z-type weights (WENO-D) scheme and its improved version (WENO-A) scheme are proposed. They are analyzed for the maximum error and the order of accuracy for approximating the derivative of a smooth function with high order critical points, where the first few consecutive derivatives vanish. The analysis and numerical experiments show that, they achieve the optimal (fifth) order of accuracy regardless of the order of critical point with an arbitrary small sensitivity parameter, aka, satisfy the Cp-property. Furthermore, with an optimal variable sensitivity parameter, they have a quicker convergence and a significant error reduction over the WENO-Z scheme. They also achieve an improved balance between the linear term, which resolves a smooth function with the fifth order upwind central scheme, and the modified nonlinear term, which detects potential high gradients and discontinuities in a non-smooth function. The performance of the WENO schemes, in terms of resolution, essentially non-oscillatory shock capturing and efficiency, are compared by solving several one- and two-dimensional benchmark shocked flows. The results show that they perform overall as well as, if not slightly better than, the WENO-Z scheme.

Reaction kinetic parameters for a distributed model of transport and reaction in Pd/Rh/CeZrO three-way catalytic converters

This paper presents a two-dimensional distributed model for the transport and reaction of combustion gases in channels of three-way catalytic converters, considering a detailed reaction kinetics with 16 chemical reactions in palladium and rhodium catalysts, and taking into account diffusive effects within the coating, to obtain a new set of reaction kinetic parameters that do not depend on the thickness of the coating. The model was solved using a finite volume method with a first order upwind scheme and simulations were conducted using computational fluid dynamics. The model with the new distributed reaction kinetic parameters, produced an excellent agreement with the experimental data of concentration at the end of the channels. Also, the model reproduced the most important concentration changes for the gas components in the specified temperature range and allowed simulations with excess oxygen and different thicknesses.

Modeling and simulation of the drying process of natural gas pipeline using vacuum drying method

Vacuum drying is one of the most effective methods to protect submarine natural gas pipes from blockage caused by hydrate and internal corrosion. This article presents a model for analyzing the mass, momentum, and energy transfer processes in pipeline drying with vacuum drying method. Model of the evaporation rate of liquid water is derived from Hertz–Knudsen–Schrage equation. Finite volume method is employed to discretize the governing equations with an upwind implicit scheme in present work, and 2nd order upwind scheme for energy equation is adopted to weaken numerical dissipation. Non-linear algebraic equations after discretization are solved by Newton-Raphson method. Reliability and accuracy of this model are validated via three experimental cases. Numerical results coincide well with the experimental data, and the relative errors of the calculated drying time are 1.7% in Case 1, 1.2% in Case 2, and 5.5% in Case 3. Finally, the dynamic characteristics of the vacuum drying process are analyzed such as dynamic distributions of pressure, temperature, mass flow rate, and liquid holdup. Mathematical model and algorithm developed in present work provide understanding and insights of the vacuum drying process, which aids in determining cost-effective pipeline drying scheme.

CFD modelling of pump-around jet mixing tanks: a reliable model for overall mixing time prediction

ABSTRACT Over the past two decades or so, computational fluid dynamics (CFD) has been employed to predict overall mixing times inside jet mixing tanks instead of non-universal mixing time correlations obtained by experiments. However, the numerical methods for jet mixing tank simulations were not clearly tested and the discretization errors of the previous CFD models were not assessed. So, in this paper, the suitable turbulence model and numerical methods for pump-around jet mixing tank simulations were investigated. Further, the discretization errors of the present CFD models were estimated with the help of grid convergence index (GCI). The results revealed that the realizable k-epsilon model, SIMPLE, second order upwind, and first order implicit were proper turbulence model and numerical methods for pump-around jet mixing tank simulations. From GCI analyses, the maximum discretization uncertainty in overall mixing time of the present CFD models was about ±0.08 s.

HEAT TRANSFER AND FRICTION CHARACTERISTICS OF AN ARRAY OF PERFORATED FINS UNDER LAMINAR FORCED CONVECTION

Three-dimensional incompressible laminar fluid flow and heat transfer of a heated array of circular perforated fins are examined numerically. The Navier–Stokes and energy equations are solved by a finite volume method using the SIMPLE algorithm. The second order upwind technique is employed to discretize the momentum and energy equations. Computations were performed for a range of Reynolds numbers 100 ≤Re ≤ 350. Thermal performance and effectiveness as well as friction coefficient of perforated and solid fins are determined for the optimum porosity. The results show that the average coefficient of friction reduces with increasing the Reynolds number and the number of perforations. The heat transfer rate increases with the porosity and the Reynolds number. It is found that perforated fin effectiveness decreases with the number of peroration at constant Reynolds numbers.

Generation of Water Waves Using Momentum Source Wave‐Maker Applied to a RANS Solver

Nowadays, as the development of Computational Fluid Dynamics (CFD) and the numerical wave tank (NWT) has advanced, numerical analysis has become increasingly useful and powerful for the ship designing and ship hydrodynamics. In this study, a momentum source wave‐maker and an analytical relaxation wave absorber were embedded into 2D RANS equation model with RSM turbulence closure scheme to establish the NWT for ship designing and hydrodynamics. The VOF (volume‐of‐fluid) method was applied to accurately capture the water free surface. The body force‐weighted scheme is chosen for pressure interpolation and the second order upwind scheme for discretization of the momentum equation. In order to calculate convection and diffusion fluxes through the control volume faces, PISO algorithm is adopted for pressure‐velocity coupling. The momentum source function for wave generation and the analytical relaxation function for wave absorption were deduced for constructing the NWT (numerical wave tank). The proposed NWT was then validated by the laboratory measurements of Umeyama and the analytical solution, indicating that the constructed NWT is effective and accurate.

A numerical model based on the curvilinear coordinate system for the MAC method simplified

In this paper we developed a numerical methodology to study some incompressible fluid flows without free surface, using the curvilinear coordinate system and whose edge geometry is constructed via parametrized spline. First, we discussed the representation of the Navier-Stokes and continuity equations on the curvilinear coordinate system, along with the auxiliary conditions. Then, we presented the numerical method – a simplified version of MAC (Marker and Cell) method – along with the discretization of the governing equations, which is carried out using the finite differences method and the implementation of the FOU (First Order Upwind) scheme. Finally, we applied the numerical methodology to the parallel plates problem, lid-driven cavity problem and atherosclerosis problem, and then we compare the results obtained with those presented in the literature.

Effect of Length Ratio on Heat Exchange Rate by a Triangular Heat Generating Conductive Body Inside an Enclosure

This paper presents a numerical analysis of the conjugate heat exchange inside a square enclosure full of a copper-water nanofluid. The enclosure also contains a heat-generating solid triangular block (a source of heat) at the center. While the horizontal walls of the enclosure are viewed as adiabatic, its perpendicular walls are operated at a consistently low temperature. The second order upwind scheme is used for the convective term and SIMPLE algorithm, to lead the numerical analysis and solve the discrete equations using the commercial software FLUENT 15.0. The consequences of the numerical investigations are then used to clear up the effect of length-ratio and transfer of heat. As per observations, the expansion in the length-ratio influences the rate of heat transfer.

A high-resolution Navier–Stokes solver for direct numerical simulation of free shear flow

A high-resolution, Navier–Stokes solver is developed for direct numerical simulation (DNS) of free shear flow. All terms in Navier–Stokes equations are discretized using higher order methods. Diffusion term is discretized using fourth order central difference scheme while second order Adams–Bashforth is used for time derivative. Advecting velocity is approximated using fourth order Lagrangian interpolation. For the approximation of advected velocity, a blended fifth order-upwind scheme is proposed. Developed high resolution solver is used for DNS of round jet in transitional and turbulent regimes. A novel open outlet boundary condition (OOBC) is proposed which has the ability to dynamically adjust according to prevailing local condition at the outlet thereby minimizing reflections from outlet. Ability of blended fifth order upwind scheme and fifth order WENO is assessed in terms of algorithmic efficiency as well as fidelity of simulations. It is demonstrated that the proposed blended fifth order upwind scheme outperforms the WENO scheme in terms of algorithmic efficiency. Assessment of fidelity of simulations reveals that WENO displays a tendency to over-predict momentum advection in transitional as well as fully turbulent regime of the round jet. In contrast, the proposed advection scheme is not faced with such limitation.

Determination of Heat Exchange Rate by A Triangular Heat Generating Conductive Body in an Enclosure Using CFD

This paper performs a numerical analysis of the conjugate heat exchange inside a square enclosure full of a copper-water nanofluid. The enclosure also contains a heat-generating solid triangular block (a source of heat) at the center. While the horizontal walls of the enclosure are viewed as adiabatic, its perpendicular walls are Kept up at a consistently low temperature. The second order upwind scheme is used for convective term and SIMPLE algorithm, to lead the numerical analysis and solve the discrete equations using the commercial software FLUENT15.0. The consequences of the numerical investigations are then used to clear up the effect of relevant factors, e.g. Rayleigh number, solid-volume proportion, thermal conductivity of the source of heat and transfer of heat. The result is accounted in terms of streamlines, isotherms, velocity and temperature profiles over the enclosure, and local and average Nu numbers. As per my findings, the growth of Rayleigh number and the solid volume fraction enhance the thermal performance of the enclosure. At last, the higher thermal conductivity of the source of heat is related to increases in the temperature of the nanofluid in the enclosure, the temperature of the source of heat, and the average Nu.

Mixed convection heat transfer from a triangular cylinder subjected to upward cross flow

Unsteady laminar mixed (forced and free) convection heat transfer and fluid flow over long horizontal equilateral triangular cylinder subjected to upward cross flow are investigated numerically. The computation model is a two-dimensional unconfined rectangular domain with an aspect ratio of 1.4. A second order upwind scheme was used for differencing of the convection terms, and SIMPLE algorithm was adopted. The working fluids are air (Pr = 0.7) and water (Pr = 7). The equilateral isothermal triangular cylinder is placed in a uniform stream. The effect of buoyancy is incorporated into the Navier-Stokes (NS) equations using the Boussinesq approximation. This study is a case of “assisting flow” where the buoyancy-induced flow and fluid motions have the same upward direction. The basic dimensionless simulation variables, Reynolds and Richardson numbers, are varied in the range 10 ≤ Re ≤ 200 and 0 ≤ Ri ≤ 10. The flow characteristics such as the mean drag, mean rms lift coefficients and the Strouhal number are computed for each simulation. The flow patterns and isotherms are generated to interpret and understand the underlying physical mechanism. The cylinder surface mean Nusselt number was computed for mixed as well as for forced and free convection conditions. The computational data were used to develop the several Nusselt number correlations for forced, free and mixed convection flow.

Bi-directional integral pumping devices for dual mechanical seals: Influence of mesh type on accuracy of numerical simulations

A numerical study is conducted to simulate the performance of barrier fluid flow through a bi-directional dual mechanical seal with an integral radial pumping ring. Standard K-ε model is implemented as a turbulence model. Multiple Reference Frame approach is implemented to model the rotation of the pumping ring. The present study is a sequel to a previous companion work done in the area of visualization of barrier fluid flow. Improvements to the previous work depended on two aspects. First, a multi-block hybrid (tetra, prism and hexa) mesh is used where it is aimed to reduce numerical false diffusion by orienting the cells to be aligned with flow direction as much as possible. Second, expanding model’s boundaries to include inboard sealing faces. The numerical results are validated against Q-ΔP curves produced from experimental tests where an experimental setup is constructed, and appropriate instrumentation is employed to measure the pressure, temperature, and flow rate of the barrier fluid.Moreover, implementation of two spatial discretization schemes is illustrated to verify the numerical performance of each method. Second order Upwind and QUICK (Quadratic Upstream Interpolation for Convective Kinematics) schemes are used for the discretization of convective terms. The validity of implementation of each method is investigated since higher-order methods are known to be more computationally expensive but their accuracy are higher. The results by the hybrid mesh indicate that the use of the Second-order scheme provides more accurate prediction of Q-ΔP curves than the previous companion work. Moreover, the impact of using the QUICK scheme is the increased computational time while providing slightly more accurate Q-H curve relative to the second-order scheme.Finally, expanding model’s boundaries to include inboard sealing faces revealed that closed barrier fluid circulation takes place in the vicinity of the inboard sealing faces indicating poor renewal of the barrier fluid contained within this zone compared to the outboard sealing faces.

Transient sub-channel code development for lead-cooled fast reactor using the second-order upwind scheme

For its unique safety and economic advantages, the lead cooled fast reactor has become one of the most interesting candidate reactors for the Generation IV nuclear system. To study the thermal-hydraulics of the core under transient conditions, KMC-SUBtra--a sub-channel code for transient thermal-hydraulic analysis of lead cooled fast reactor has been developed. The code uses a modified pressure gradient method to solve the simultaneous equations of the fluid mass, momentum and energy containing cross flow and turbulent mixing, in which the axial pressure gradients are solved as pending variables of the simultaneous equations. A staggered mesh scheme is used for scalar and vector quantities and the second-order upwind scheme is adopted in the discretization of the convection term. The code was validated and verified by the experimental data and CFD simulation results on the steady and transient conditions so its capability for lead cooled reactors was confirmed. The transient flow and heat transfer in the fuel assembly with time-varying boundary conditions were studied, which revealed different transient thermal characteristics of the coolant and fuel rods. In addition, the results calculated using different order upwind schemes were compared and showed the second-order derivative of the axial flow is small.

Numerical analysis of flow parameters on solar updraft tower (SUT) with and without thermal energy storage (TES) system

Effect of thermal energy storage (TES) system of solar updraft tower (SUT) is studied in this work. A 3D numerical model was developed to analyze the same and estimate the performance parameters. Two models were developed: case-I and case-II. Case-I is without TES system and the case-II with TES system. The collector diameter 3.5 m, chimney height 6 m, chimney diameter 0.6 m, inlet gap 0.15 m, slope of the collector 30° were the dimensions considered for the model of case-I. Case-II consisted of same dimensions of case-I with additional storage material of thickness 0.15 m and diameter of 3.5 m. Steady-state pressure-based solver with realizable k–ɛ turbulent model and solar ray-tracing algorithm were employed. SIMPLE scheme was used for pressure–velocity coupling and in spatial discretization; first order upwind for momentum and second-order upwind for energy were used. Flow parameters such as velocity, pressure, density, and temperature were estimated for both the cases. Results from the numerical simulations showed that adding TES to the SUT plant decreases the pressure, velocity, and temperature of air because certain amount of heat energy was stored in case-II setup.

A simple embedded discrete fracture–matrix model for a coupled flow and transport problem in porous media

Accurate simulation of fluid flow and transport in fractured porous media is a key challenge in subsurface reservoir engineering. Due to the high ratio between its length and width, fractures can be modeled as lower dimensional interfaces embedded in the porous rock. We apply a recently developed embedded finite element method (EFEM) for the Darcy problem. This method allows for general fracture geometry, and the fractures may cut the finite element mesh arbitrarily. We present here a velocity model for EFEM and couple the Darcy problem to a transport problem for a passive solute. The main novelties of this work are a locally conservative velocity approximation derived from the EFEM solution, and the development of a lowest order upwind finite volume method for the transport problem. This numerical model is compatible with EFEM in the sense that the same computational mesh may be applied, so that we retain the same flexibility with respect to fracture geometry and meshing. Hence, our coupled solution strategy represents a simple approach in terms of formulation, implementation and meshing. We demonstrate our model by some numerical examples on both synthetic and realistic problems, including a benchmark study for single-phase flow. Despite the simplicity of the method, the results are promising.

Study on Influence factors of Purification efficiency of wall absorbing haze automatically

A new type of wall absorbing haze automatically was presented based on industrial architecture. The purification efficiency of wall absorbing haze automatically was simulated and analyzed by Fluent. A particle trajectory analysis model based on Lagrange method was established. RNG k-ε turbulence eddy viscosity model was used to analyzing air flow. The momentum and turbulence equations were dispersed by the two order upwind scheme. SIMPLE algorithm was used to calculate the coupling solution of pressure and velocity. The variation of particle concentration and air pressure in wall absorbing haze automatically were simulated. The results show that the concentration change of particles in wall absorbing haze automatically is mainly affected by the adsorption of the adsorbents. The resistance that wall absorbing haze automatically acts on the air is affected by the change of air pressure. And then it affects the volume of induced ventilation of the wall. So, it has an important effect on the effect of air purification of wall absorbing haze automatically.

High-order upwind and non-oscillatory approach for steady state diffusion, advection–diffusion and application to magnetized electrons

Steady state simulations of magnetized electron fluid equations with strong anisotropic diffusion based on the first-order hyperbolic approach is carried out using cell-centered higher order upwind schemes, linear and weighted essentially non-oscillatory (WENO). Along with the magnetized electrons, the diffusion equation is also simulated to demonstrate the implementation and design order of the accuracy of the approach due to their similar upwind structure. We show the adequacy of linear upwind schemes for diffusion equation and the use of shock-capturing scheme like WENO does not have any adverse effect on the solution, unlike the total-variation diminishing (TVD) methods. We further extended the approach to advection–diffusion equation, and appropriate boundary conditions have obtained a consistent design accuracy of the third and fifth order. We implemented the WENO approach to advection–diffusion equation by using the split hyperbolic method to demonstrate the advantage of non-oscillatory schemes to capture sharp gradients in boundary layer type problems without spurious oscillations. Finally, numerical results for magnetized electrons simulations indicate that with increasing strength of magnetic confinement it is possible to capture sharp gradients without oscillations by WENO scheme.