Steady-state Incompressible Flow Research Articles

The jet-stream channels of gas and plasma in atmospheric-pressure plasma jets

A solution to the fluid momentum equation for incompressible steady-state flow is obtained for the streams of gas and plasma inside a jet nozzle and in the open-air space. Three pressure forces are considered in the equation. The first is the pressure force of the shear stress resulting from the flow viscosity and is balanced against the second pressure force of the gas stream that is ejected into the air. The third pressure force is due to the radial expansion of the fluid channel, reducing the velocity of the fluid to zero so that we obtain the reaching distance of the fluid after ejection from the nozzle. From the solution for the fluid channel, the regional profile and the density profile of the plasma flow are also determined. The maximum distance of the gas flow with a critical Reynolds number of Rnc ≈ 2000 is calculated to be 100 times that of the nozzle diameter for Ar, Ne, and He. Because the radial expansion of the plasma is ten times larger than that of neutral gases, the length of the plasma flume is a few tens of the nozzle diameter, which is significantly shorter than the gas flow distance. In the experiments, the maximum length of the plasma plume increases and then saturates as the operation voltage increases.

Mathematical model of neutral line on the contact zone in alloyed bar rolling by the round-oval-round pass sequence

For determining the neutral line on the contact zone to determine the relative slip condition between the contact surface of rolling pieces and the roll, the contact boundary curve was proposed by obtaining the radius of flow line and the bite angle of points on the contact boundary based on the flow line method, and then the contact surface was discretized as flow line elements to build a novel analytic model to reconstruct the geometry of contact surface. Moreover, the velocity of flow lines on the contact surface along the direction of X-axis was derived by the condition of steady-state incompressible flow, and the function of neutral line was obtained by determining the neutral radius and the neutral angle of the points on the neutral line. In addition, the three-dimensional rectangular coordinates of points on the neutral line were derived.Based on these mathematical models, the three dimensional geometry of contact surface and neutral line were drawn up by mathematical software. The validity of the theoretical model was verified by rolling experiments of alloyed bar and the numerical simulation by rigid-plastic FEM software. Compared with the experimental data and simulation results, the prediction error is acceptable and the results of the mathematical model is satisfying.

Research on the characteristics of forward slip and backward slip in alloyed bar rolling by the round-oval-round pass sequence

For determining the neutral line on the contact zone to distinguish the forward slip zone and backward slip zone on the contact surface between the deformed pieces and the roll, the contact surface was discretized as finite flow line elements to build a novel analytic model to reconstruct the geometry of contact surface. Moreover, the velocity of flow lines on the contact surface along the direction of x-axis was derived by the condition of steady-state incompressible flow, and the function of neutral line was obtained by determining the neutral radius and the neutral angle of the points on the neutral line. In addition, the forward slip coefficient and backward slip coefficient was derived and the relative slip condition of contact surface between the roll and the rolled pieces was determined. Based on these mathematical models the geometry of contact surface and neutral line were drawn up by mathematical software. The validity of the theoretical model was verified by rolling experiments of alloyed bar and the numerical simulation by rigid-plastic FEM software. Compared with the experimental data and simulation results, the prediction error of the mathematical model is acceptable and results from the mathematical model are satisfying.

Gauge condition for studying intrinsic magnetospheres

We propose an analytical model based on the solution of the magnetohydrodynamics (MHD) equations for studying intrinsic magnetospheres. For this purpose, we introduce a new gauge condition for the electromagnetic vector potential, which simplifies the solution of this complex system of nonlinear equations. Using this model, we analyse the deformation of the terrestrial magnetic field due to the presence of the solar wind. By comparing the results with experimental observations, we find that our model reproduces with good agreement the geometrical configuration of the magnetosphere, and that the solar wind should have a finite conductivity. This model could also be used to perform linear stability analysis of fluid and magnetic instabilities. Finally, our solution is not limited to magnetospheric configurations but also applies to a steady-state incompressible and irrotational flow with large plasma parameter and small velocity fluctuations.

Effects of urban configuration on the wind energy distribution over a building

A numerical study to investigate the wind energy potential for various building configurations is presented. Steady-state incompressible flow simulations were performed using the finite volume method of ANSYS Fluent with the k-ε turbulence model. A simplified city model was used to study the flow behavior over a building rooftop for various configurations of the upwind structure. Results show an increase of up to 29% in the available energy compared to the free stream due to variations in the dimensions of the separation bubble over the rooftop. This study shows the influence of building configuration on the wind resource near buildings and how it can affect the feasibility of a small-scale wind turbine project.

An Efficient Scheme of Differential Quadrature Based on Upwind Difference for Solving Two-dimensional Heat Transfer Problems

In this paper, a new technique of differential quadature method called the upwind difference - differential quadature method (UDDQM) for solving two-dimensional heat transfer (convection-diffusion) problems is proposed. Also, investigated the effects of physical quantities on behavior of flow problems, and combined effects of upwind difference mechanism together with differential quadrature method to modified the numerical solutions of heat transfer problems are presented. To validate our proposed UDDQM, two convection-diffusion problems ((i) Steady-state incompressible flow problem has exact solution and (ii) Natural convection motion of the incompressible fluid flow problem hasn't exact solution) are solving numerically. Graphical results on the effects of parameter variation on velocity, temperature, Peclet number, Grashof number, and Prandtl number are presented and discussed. Numerical experiments are conducted to test its accuracy and convergence and compare it with the standard DQM and other numerical methods that are available in literature. The numerical results show the efficiency of the proposed method to handle the problems, and it is more accurate and convergent than other methods.

Development of a Novel Fully Coupled Solver in OpenFOAM: Steady-State Incompressible Turbulent Flows in Rotational Reference Frames

In this article, the fully coupled block algorithm for the solution of three-dimensional incompressible turbulent flows presented in a companion article [1] is extended for use with multiple reference frames and multiple mesh blocks. The implicit block coupling is applied to the extra rotational terms, and to the multiblock interfaces. Furthermore, implementation details on the linearization of cyclic and other boundary conditions are detailed. These modifications allow the coupled solver to retain its improved performance and robustness in addition to mesh size scalability while solving turbomachinery-type applications. The performance and mesh size scalability of the coupled solver is compared to that of a segregated pressure based solver [2] using three industrial-size test cases.

Radial Flow of Non-Newtonian Power-Law Fluid in a Rough-Walled Fracture: Effect of Fluid Rheology

Fluid flow in a single rough-walled rock fracture has been extensively studied over the last three decades. All but few of these studies, however, have been done with Newtonian fluids and unidirectional flow in rectangular fractures. Notwithstanding the importance of such setups for theoretical understanding of fundamental issues in fracture flow, practical applications in drilling and petroleum engineering often involve radial flow of a non-Newtonian fluid. An example is a borehole intersecting a natural fracture during drilling in a fractured rock. In this study, steady-state incompressible radial flow from a circular well into a self-affine rough-walled fracture was simulated numerically using the lubrication theory approximation. The fluid rheology was power law. The flow behavior index was equal to 0.6, 0.8, 1.0 (Newtonian), 1.2, or 1.4. Asperities diverted the flow from an axisymmetric radial pattern that would be observed in a smooth-walled fracture. The extent of the deviation from radial flow was found to increase as the fluid became more shear-thickening. To reveal finer details of the flow, a tracer was introduced at the borehole wall and was transported by the flow. The front of the tracer propagating into the fracture was found to become slightly smoother with a more shear-thickening fluid. In the vicinity of contacts between fracture faces a more shear-thickening fluid could deliver the tracer closer to the contact spots.

Numerical Investigation of the Effect of Wire Screen Mesh Specification and Evaporator Length on Thermal Performance of Cylindrical Heat Pipe

A numerical model has been developed to determine the effect of the wire screen mesh (wick) type on the heat transfer performance of copper–water wicked heat pipe. This model represented as steady-state incompressible flow. The governing equations in cylindrical coordinates have been solved in vapor region, wick structure and wall region, using finite difference with forward-backward upwind scheme. The results show that increasing the mesh number led to decreasing the maximum heat transfer limit and increasing the capillary pressure. While, for the same heat input the operating temperature of the heat pipe increase when the mesh number increase. Also, it was found that increasing the evaporation length, with constant condensation length, decrease the operating temperature and increase the maximum heat transfer limit. For verification of the current model, the results of liquid pressure drop for a heat pipe have been compared with the previous study for the same problem and a good agreement has been achieved.

Development of a Novel Fully Coupled Solver in OpenFOAM: Steady-State Incompressible Turbulent Flows

In this work a block coupled algorithm for the solution of three-dimensional incompressible turbulent flows is presented. A cell-centered finite-volume method for unstructured grids is employed. The interequation coupling of the incompressible Navier-Stokes equations is obtained using a SIMPLE-type algorithm with a Rhie-Chow interpolation technique. Due to the simultaneous solution of momentum and continuity equations, implicit block coupling of pressure and velocity variables leads to faster convergence compared to classical, loosely coupled, segregated algorithms of the SIMPLE family of algorithms. This gain in convergence speed is accompanied by an improvement in numerical robustness. Additionally, a two-equation eddy viscosity turbulence model is solved in a segregated fashion. The substnatially improved performance of the block coupled approach compared to the segregated approach is demonstrated in a set of test cases. It is shown that the scalability of the coupled solution algorithm with increasing numbers of cells is nearly linear. To achieve this scalability, an algebraic multigrid solver for block coupled systems of equations has been implemented and used as linear solver for the system of block equations. The presented algorithm has been entirely embedded into the leading open-source computational fluid dynamics (CFD) library OpenFOAM.

Aerodynamic study of aerofoil and wing in simulated rain environment via a two-way coupled Eulerian-Lagrangian approach

AbstractAerodynamic performance degradation has been considered a critical hazard to aircraft due to flying in heavy rain. In this work, a two-way momentum coupled Eulerian-Lagrangian approach is developed to study the aerodynamic performance of a two-dimensional (2D) transport-type NACA 64-210 cruise and landing configuration aerofoil as well as a three-dimensional (3D) NACA 64-210 cruise configuration rectangular wing in heavy rain environment. Raindrop impacts, splashback and formed water film are modeled. The steady-state incompressible air flow field and the raindrop trajectory are calculated alternately by incorporating an interphase momentum coupling term through a curvilinear body-fitted grid surrounding the aerofoil/wing. Our simulation results agree well with the experimental results and show significant aerodynamic penalties for all the test cases in heavy rain. Rain-induced premature boundary-layer transition and separation are observed and details of the raindrop splashback effect on the boundary layer are examined. A 1° rain-induced decrease in stall angle-of-attack is predicted. An uneven water film upon the wing surface is observed and its effect on the wing surface roughness is also examined.

Experimental study of mixing layer in a closed compound channel

This paper presents an experimental study performed in a given compound channel under steady-state incompressible air flow. Hot wire probes and Pitot tube were employed to measure mean velocity and velocity fluctuations characteristics in a turbulent flow between parallel plates. Test sections were formed by two parallel plates attached on a side wall of a wind channel, forming a slot with width d and depth p. Results showed that this sort of channel produces unstable velocity profiles and periodical traces of velocity as well, quite similar to a mixing layer. Using local scales of velocity and length both, velocity profiles and Strouhal number could be described, regardless of the channel’s dimension or its depth. Despite a certain scattering of the dimensionless frequency, the Strouhal numbers remained almost constant for any p/d-ratio. In this paper ten test sections were studied covering p/d-ratio from 5.00 up to 12.50. The Reynolds number was defined using a velocity reference, Uref; the hydraulic-diameter of the test section, Dh and the kinematic viscosity, ν.

Twist parameter Influence on Heat Transfer Coefficient Augmentation for a square Twisted Tube

Heat transfer augmentation due to twisting parameter was investigated in atwisted tube of square cross sectional area. Twisting parameter is defined as the ratio of the length of the tube where it completed twisting of360 degrees to its hydraulic diameter. Four twist parameters were chosen;5, 10, 25 and 50, and a comparison is made with a straight untwisted duct. Two sets of Reynolds numbers were considered for laminar and transient flow. The laminar flow is performed at Re=500,1000,1500 and 2000. While for transient flow the range of Reynolds number are Re=5000,6000,7000,8000 and 9000.Theinfluence of twist parameter on convective heat transfer coefficient in laminar and transient flow was investigated. Numerical simulations were performed for three-dimensional, steady state incompressible flow in body-fitted coordinate using finite volume method and standard k-ε turbulence model. For the heat transfer problem the uniform wall temperature (UWT) boundary condition at tube wall is considered. It was observed that the heat transfer coefficient increases with decreasing twist parameter. This is interpreted to the nature of span wise swirling flow generated. The swirling increases cross flow velocity vectors as it becomes far from tube center towards walls. At tube wall the thickness of boundary layer becomes thinner as near wall velocity become larger which leads to a boundary layer of good thermal characteristics. Also swirling increases internal mixing process which enhances internal thermal equilibrium. The heat transfer coefficient also increases as Reynolds number increased as velocity components are increased

A Class of Physically Stable Non-linear Models of Flow Through Anisotropic Porous Media

A linear stability analysis of the single-phase conservation equation in multidimensional porous media is performed, for both weakly compressible and compressible fluids. Non-Newtonian and non-Darcy effects are accounted for using a non-linear Darcy-like form for the superficial velocity, where the mobility tensor is velocity-dependent and proportional to the permeability. It is found that under this hypothesis, flows at an angle with respect to the principal axes of the permeability tensor can be unstable, unless the mobility is a function of the velocity magnitude in terms of the inverse permeability norm. As shown by previous authors, for steady-state incompressible flows this is also the condition ensuring that the governing equation derives from the minimization of a dissipation potential.

Free Convective Heat Transfer in an Enclosure Filled with Porous Media with and without Insulated Moving Wall

The present work is concerned with the free convective two dimensional flow and heat transfer, in isotropic fluid filled porous rectangular enclosure with differentially heated walls for steady state incompressible flow have been investigated for non-Darcy flow model. Effects of Darcy number (0.0001  Da  10), Rayleigh number (10  Ra  5000), and aspect ratio (0.25  AR  4), for a range of porosity (0.4    0.9) with and without moving lower wall have been studied. The cavity was insulated at the lower and upper surfaces. The right and left heated surfaces allows convective transport through the porous medium, generating a thermal stratification and flow circulations. It was found that the Darcy number, Rayleigh number, aspect ratio, and porosity considerably influenced characteristics of flow and heat transfer mechanisms. The results obtained are discussed in terms of the Nusselt number, vectors, contours, and isotherms.

OpenFOAM을 이용한 액체 로켓 연소기의 산화제 매니폴드 내 유동 해석

Flow in the oxidizer manifold of a liquid rocket combustor has been analysed using an open source CFD toolbox, OpenFOAM. The applicability of OpenFOAM to the problems with complex geometries involving porous media zones for simulating the pressure drop induced by the injectors has been evaluated by performing turbulent, incompressible steady-state flow analysis. The usefulness and applicable area of the OpenFOAM as a design evaluation and analysis tool will be confirmed and enlarged by further evaluation with various computational cases representing major physical phenomena in rocket combustion devices.

A high-order compact local integrated-RBF scheme for steady-state incompressible viscous flows in the primitive variables

This study is concerned with the development of integrated radialbasis- function (IRBF) method for the simulation of two-dimensional steady-state incompressible viscous flows governed by the pressure-velocity formulation on Cartesian grids. Instead of using low-order polynomial interpolants, a high-order compact local IRBF scheme is employed to represent the convection and diffusion terms. Furthermore, an effective boundary treatment for the pressure variable, where Neumann boundary conditions are transformed into Dirichlet ones, is proposed. This transformation is based on global 1D-IRBF approximators using values of the pressure at interior nodes along a grid line and first-order derivative values of the pressure at the two extreme nodes of that grid line. The performance of the proposed scheme is investigated numerically through the solution of several linear (analytic tests including Stokes flows) and non-linear (recirculating cavity flow driven by combined shear & body forces and lid-driven cavity flow) problems. Unlike the global 1D-IRBF scheme, the proposed method leads to a sparse system matrix. Numerical results indicate that (i) the present solutions are more accurate and converge faster with grid refinement in comparison with standard finite-difference results; and (ii) the proposed boundary treatment for the pressure is more effective than conventional direct application of the Neumann boundary condition.

A steady-state lattice Boltzmann model for incompressible flows

In this paper, we propose a steady-state lattice Boltzmann equation which is independent of time for steady incompressible flows. On the basis of the steady-state lattice Boltzmann equation, we find a way of modeling some steady-state problems using the lattice Boltzmann model. In further study, we investigate steady-state incompressible flows with the method of the higher-order moment of equilibrium distribution functions and a series of partial differential equations for different space scales. By assuming ρ = constant , we obtain the momentum equation for incompressible steady-state flow. The numerical results show that the new method is effective.

On the application of the minimum polynomial extrapolation method to incompressible flows with heat transfer

In this paper, the Minimum Polynomial Extrapolation method (MPE) is used to accelerate the convergence of the Characteristic---Based---Split (CBS) scheme for the numerical solution of steady state incompressible flows with heat transfer. The CBS scheme is a fractional step method for the solution of the Navier---Stokes equations while the MPE method is a vector extrapolation method which transforms the original sequence into another sequence converging to the same limit faster then the original one without the explicit knowledge of the sequence generator. The developed algorithm is tested on a two-dimensional benchmark problem (buoyancy---driven convection problem) where the Navier---Stokes equations are coupled with the temperature equation. The obtained results show the feature of the extrapolation procedure to the CBS scheme and the reduction of the computational time of the simulation.

스마트 원자로냉각재펌프의 축소모형에 대한 수력성능 예측

An analysis was conducted to predict the hydraulic performance of a reactor coolant pump (RCP) of SMART at the off-design as well as design points. In order to reduce the analysis time efficiently, a single passage containing an impeller and a diffuser was considered as the computational domain. A stage scheme was used to perform a circumferential averaging of the flux on the impeller-diffuser interface. The pressure difference between the inlet and outlet of the pump was determined and was used to compute the head, efficiency, and break horse power (BHP) of a scaled-down model under conditions of steady-state incompressible flow. The predicted curves of the hydraulic performance of an RCP were similar to the typical characteristic curves of a conventional mixed-flow pump. The complex internal fluid flow of a pump, including the internal recirculation loss due to reverse flow, was observed at a low flow rate.