Steady Calculations Research Articles

A comparative study of the LBE and GKS methods for 2D near incompressible laminar flows

We compare the lattice Boltzmann equation (LBE) and the gas-kinetic scheme (GKS) applied to 2D incompressible laminar flows. Although both methods are derived from the Boltzmann equation thus share a common kinetic origin, numerically they are rather different. The LBE is a finite difference method, while the GKS is a finite-volume one. In addition, the LBE is valid for near incompressible flows with low-Mach number restriction Ma < 0.3, while the GKS is valid for fully compressible flows. In this study, we use the generalized lattice Boltzmann equation (GLBE) with multiple-relaxation-time (MRT) collision model, which overcomes all the apparent defects in the popular lattice BGK equation. We use both the LBE and GKS methods to simulate the flow past a square block symmetrically placed in a 2D channel with the Reynolds number Re between 10 and 300. The LBE and GKS results are validated against the well-resolved results obtained using finite-volume method. Our results show that both the LBE and GKS yield quantitatively similar results for laminar flow simulations, and agree well with existing ones, provided that sufficient grid resolution is given. For 2D problems, the LBE is about 10 and 3 times faster than the GKS for steady and unsteady flow calculations, respectively, while the GKS uses less memory. We also observe that the GKS method is much more robust and stable for under-resolved cases due to its upwinding nature and interpolations used in calculating fluxes.

Acceleration of Unsteady Incompressible Flow Calculation Using Extrapolation Methods

Extrapolation methods constitute a class of acceleration techniques in which the converged solution is predicted from a series of intermediate solutions generated by the iterative method. Advantages of the extrapolation methods are simplicity and ease of the implementation in existing CFD codes. In this study, the authors apply Minimal Polynomial Extrapolation (MPE) to 2-D laminar and 3-D turbulent problems to examine the performance of MPE in unsteady flow calculation. Also Initial Extrapolation (IE), which provides a good initial guess at the start of each timestep, is tested alongside MPE. Although only six intermediate solutions are used in MPE, it realizes reasonable speed-ups : 2.88 in the 2-D calculation and 1.89 in the 3-D LES. This computational cost is far lower than that in steady calculation reported in a literature. Furthermore, the combination of IE and MPE shows larger acceleration effects than in the case of single application of MPE because the speed-ups by the joint application of the two extrapolation methods reach 4.41 in the 2-D and 2.33 in the 3-D.

Studies on the Influence of Various Blade Outlet Angles in a Centrifugal Pump when Handling Viscous Fluids

In this study the centrifugal pump performances with different blade outlet angles are tested when handling water and viscous oils as Newtonian fluids. Also, this study shows a numerical simulation of the three-dimensional fluid flows inside the centrifugal pump with different blade outlet angles. For these numerical simulations the SIMPLEC algorithm is used for solving governing equations of incompressible viscous/turbulent flows through the pump at different operating conditions. The k-e turbulence model is adopted to describe the turbulent flow process. These simulations have been made with a steady calculation using the multiple reference frames (MRF) technique to take into account the impeller- volute interaction. Numerical results are compared with the experimental characteristic curve for each viscous fluid. The results show that when the outlet angle increases, the centrifugal pump performance handling viscous fluids improves. This improvement is due to decrease of wake at the exit of impeller. Also the results show that the well-known jet/wake flow model is not found in the impeller simulations.

Eulerian particle flamelet modeling of a bluff-body CH 4/H 2 flame

In this paper an axisymmetric RANS simulation of a bluff-body stabilized flame has been attempted using steady and unsteady flamelet models. The unsteady effects are considered in a postprocessing manner through the Eulerian particle flamelet model (EPFM). In this model the transient history of scalar dissipation rate, conditioned by stoichiometric mixture fraction, is required to generate unsteady flamelets and is obtained by tracing Eulerian particles. In this approach unsteady convective–diffusive transport equations are solved to consider the transport of Eulerian particles in the domain. Comparisons of the results of steady and unsteady calculations show that transient effects do not have much influence on major species, including OH, and the structure of the flame therefore can be successfully predicted by steady or unsteady approaches. However, it appears that slow processes such as NO formation can only be captured accurately if unsteady effects are taken into account, while steady simulations tend to overpredict NO. In this work turbulence has been modeled using the Reynolds stress model. Predictions of velocity, velocity rms, mean mixture fraction, and its rms show very good agreement with experiments. Performance of three detailed chemical mechanisms, the GRI Mech 2.11, the San Diego mechanism, and the GRI Mech 3.0, has also been evaluated in this study. All three mechanisms performed well with both steady and unsteady approaches and produced almost identical results for major species and OH. However, the difference between mechanisms and flamelet models becomes clearly apparent in the NO predictions. The unsteady model incorporating the GRI Mech 2.11 provided better predictions of NO than steady calculations and showed close agreement with experiments. The other two mechanisms showed overpredictions of NO with both unsteady and steady models. The level of overprediction is severe with the steady approach. GRI Mech 3.0 appears to overpredict NO by a factor of 2 compared to GRI Mech 2.11. The NO predictions by the San Diego mechanism fall between those of the two GRI mechanisms. The present study demonstrates the success of the EPFM model and when used with the GRI 2.11 mechanism predicts all flame properties and major and minor species very well, and most importantly the correct NO levels.

Hydrogeochemical and Flow Modeling of Aquitard Percolation in the Cariri Valley-Northeast Brazil

Flow modeling and hydrogeochemical inversion calculations were performed on the aquifer systems of the Crato-Juazeiro Graben in the Araripe Sedimentary Basin of the Cariri Valley, Northeast Brazil, in order to assess aquifer interconnections through an aquitard of the Araripe Plateau. Steady state hydraulic head numeric calculations with the finite difference method used Modflow software with hydrologically based boundary conditions and a piezometric surface as initial condition. Hydrogeochemical inversion with PHREEQC was performed for two water samples representing typical initial and final waters along the flow path. Flow simulation shows that approximately 20% of all recharge water from the superior aquifer system passes through the Santana aquitard reaching the middle aquifer system. Quantification of mineral dissolution/precipitation processes, ion exchange and microbiological redox reactions taking place in the aquifer systems also indicates hydraulic interconnection of the superior and middle aquifer systems through the Santana aquitard.

Calculations of Steady and Pulsating Impinging Jets—An Assessment of 13 Widely used Turbulence Models

Computational fluid dynamics (CFD) calculations of impinging jets have been performed with 13 widely spread Reynolds-averaged Navier-Stokes (RANS) turbulence models using commercial CFD software. It was the aim of these calculation to assess how heat transfer and flow structure can be predicted at different Reynolds numbers and different nozzle-to-plate distances. The only model able to predict correctly the laminar–turbulent transition occurring at small nozzle-to-plate distance was the SST k − ω model (“transitional flow option”). Most of the other models can only satisfactorily predict heat transfer in the turbulent wall jet region. When the SST k − ω model with transitional flow option is applied for calculation of pulsating jets, the tendencies are predicted correctly.

Behaviour of tip-leakage flow in an axial flow compressor rotor

The current paper reports on investigations with an aim to advance the understanding of the flowfield near the casing of a small-scale high-speed axial flow compressor rotor. Steady three-dimensional viscous flow calculations are applied to obtain flowfields at various operating conditions. To demonstrate the validity of the computation, the numerical results are first compared with available measured data. Then, the numerically obtained flowfields are analysed to identify the behaviour of tip-leakage flow, and the mechanism of blockage generation arising from flow interactions between the tip clearance flow, the blade/casing wall boundary layers, and non-uniform main flow. The current investigation indicates that the ‘breakdown’ of the tip-leakage vortex occurs inside the rotor passage at the near stall condition. The vortex ‘breakdown’ results in the low-energy fluid accumulating on the casing wall spreads out remarkably, which causes a sudden growth of the casing wall boundary layer having a large blockage effect. A low-velocity region develops along the tip clearance vortex at the near stall condition due to the vortex ‘breakdown’. As the mass flow rate is further decreased, this area builds up rapidly and moves upstream. This area prevents incoming flow from passing through the pressure side of the passage and forces the tip-leakage flow to spill into the adjacent blade passage from the pressure side at the leading edge. It is found that the tip-leakage flow exerts a little influence on the development of the blade suction surface boundary layer even at the near stall condition.

Plasma Spectroscopy in the Tandem Mirror GAMMA 10

Impurity ion radiation intensity has been studied in the GAMMA 10 plasma using both a collisional-radiative model (CR-model) and spectroscopic measurements. We have constructed absolutely calibrated soft X-ray, vacuum ultraviolet, ultraviolet and visible spectrographs for plasma diagnostics. Steady state CR-model calculation for carbon ions is used to obtain the carbon ion emissivities in the plasma. The CR-model calculation results of carbon ion radiation intensities are comparable to the results obtained by the impurity ion spectroscopy. Moreover, plasma rotation measurements are carried out in order to obtain radial electric potential profiles.

Methods and computer codes for nuclear systems calculations

Some numerical methods for reactor cell, sub-critical systems and 3D models of nuclear reactors are presented. The methods are developed for steady states and space-time calculations. Computer code TRIFON solves space-energy problem in (X, Y) systems of finite height and calculates heterogeneous few-group matrix parameters of reactor cells. These parameters are used as input data in the computer code SHERHAN solving the 3D heterogeneous reactor equation for steady states and 3D space-time neutron processes simulation. Modification of TRIFON was developed for the simulation of space-time processes in sub-critical systems with external sources. An option of SHERHAN code for the system with external sources is under development.

Numerical simulations of stall inside a centrifugal compressor

This paper presents a numerical simulation of stall flow phenomenon inside a turbocharger centrifugal compressor with vaneless diffuser. Three-dimensional Reynolds averaged compressible Navier-Stokes equations were solved with k-ɛ turbulence model using computational fluid dynamics software CFX. Entire geometry of the compressor, including the impeller, vaneless diffuser, and volute housing were included in the simulation. The stage performance curve was obtained using steady and unsteady calculations and compared with experimental results. The unsteady flow simulation was performed at reduced mass flowrates (compressor stall region) with a plenum chamber model added at the compressor housing outlet. The results show that there is a distinct stall frequency at the given compressor speed. The amplitude of the static pressure oscillation at this frequency in the diffuser is increased with reduction in compressor mass flow. The stall frequency is only marginally affected by the compressor mass flowrate. Time varying flow fields in the diffuser and in the volute indicate that there is a circumferential standing wave inside the volute. It is proposed that the volute behaves like a tuned pipe resonator and this dictates the stall frequency. The stall is also characterized by a periodically reversing flow at the centre of the volute discharge cross-section.

Power flow model/calculation for power systems with multiple FACTS controllers

This paper presents a new procedure for steady state power flow calculation of power systems with multiple flexible AC transmission system (FACTS) controllers. The focus of this paper is to show how the conventional power flow calculation method can systematically be modified to include multiple FACTS controllers. Newton–Raphson method of iterative solution is used for power flow equations in polar coordinate. The impacts of FACTS controllers on power flow is accommodated by adding new entries and modifying some existing entries in the linearized Jacobian equation of the same system with no FACTS controllers. Three major FACTS controllers (STATic synchronous COMpensator (STATCOM), static synchronous series compensator (SSSC), and unified power flow controller (UPFC)) are studied in this paper. STATCOM is modeled in voltage control mode. SSSC controls the active power of the link to which it is connected. The UPFC controls the active and the reactive power flow of the link while maintaining a constant voltage at one of the buses. The modeling approach presented in this paper is tested on the 9-bus western system coordinating council (WSCC) power system and implemented using MATLAB software package. The numerical results show the robust convergence of the presented procedure.

CFD를 이용한 부분흡입형 터빈 공력형상 설계

Aerodynamic shape design of a partial admission turbine using CFD has been performed. Two step approaches are adopted in this study. Firstly, two-dimensional blade shape is optimized using CFD and genetic algorithm. Initially, the turbine cascade shape is represented by four design parameters. By controlling the design parameters as variables, the non-gradient search is analyzed for obtaining the maximum efficiency. The final two-dimensional blade proved to have a more blade power than the initial blade. Secondly, the three-dimensional CFD analysis including the nozzle, rotor and stator has been conducted. To avoid a heavy computational load due to an unsteady calculation, the frozen rotor method is implemented in steady calculation. The frozen rotor method can detect a variation of the flow-field dependent upon the blade's circumferential position relative to the nozzle. It gives a better idea of wake loss mechanism starting from the lip of the nozzle than the mixing plane concept. Finally, the combination of two and three dimensional design method of the partial admission turbine in this study has proven to be a robust tool in development phase.

Numerical modeling of non-adiabatic heat-recirculating combustors

A two-dimensional numerical model of spiral counterflow heat recirculating combustors was developed including the effects of temperature-dependent gas and solid properties, viscous flow, surface-to-surface radiative heat transfer, heat conduction within the solid structure, one-step chemical reaction and heat loss from the combustor to its surroundings. A simplified model of heat loss in the 3rd dimension was implemented and found to provide satisfactory representation of such losses at greatly reduced computational cost compared to fully three-dimensional models. The model predicts broad reaction zones with structure decidedly different from conventional premixed flames. Extinction limits were determined over a wide range of Reynolds numbers (2 < Re < 5000) for propane–air mixtures. These limits showed reasonable quantitative agreement with experiments. Comparison of steady and unsteady calculations suggests there are no stability limits apart from these extinction limits. At Re > 500, modeling of turbulent flow and transport was required to obtain such agreement. Heat conduction along the heat exchanger wall has a major impact extinction limits; the wall thermal conductivity providing the broadest limits is actually less than that of air. Radiative heat transfer between walls was found to have an effect similar to that of heat conduction along the wall. In addition to weak-burning extinction limits, strong-burning limits in which the reaction zone moves out of the combustor center toward the inlet were also predicted by the numerical model, in agreement with experiments. It is concluded that several physical processes including radiative transfer, turbulence and wall heat conduction strongly affect the performance of heat-recirculating combustors, but the relative importance of such effects is strongly dependent on Re.

A steady state capturing and preserving method for computing hyperbolic systems with geometrical source terms having concentrations

We propose a simple well-balanced method named the slope selecting method which is efficient in both steady state capturing and preserving for hyperbolic system with geometrical source terms having concentrations. Physical problems under consideration include the shallow water equations with discontinuous topography, and the quasi-one-dimensional nozzle flows with discontinuous cross-sectional area. This method is an extension from the interface type method developed in [S. Jin, X. Wen, An efficient method for computing hyperbolic systems with geometrical source terms having concentrations, J. Comput. Math. 22 (2004) 230–249]. The slope selecting method keeps two merits of the previous method. It can be applied when the homogeneous system solver is available and has efficient steady state capturing property. Compared with the previous method, the slope selecting method has two improvements. One is this method also has satisfactory steady state preserving property. The other is this method can be applied to any conservative scheme for the homogeneous system. Numerical examples provide strong evidence on the effectiveness of this slope selecting method for various unsteady, steady and quasi-steady state solutions calculations as well as the flexibility of this method of being applicable to any conservative scheme for the homogeneous system.

The role of kink instability in Poynting-flux dominated jets

The role of kink instability in magnetically driven jets is explored through numerical one-dimensional steady relativistic MHD calculations. The instability is shown to have enough time to grow and influence the dynamics of Poynting-flux dominated jets. In the case of AGN jets, the flow becomes kinetic flux dominated at distances because of the rapid dissipation of Poynting flux. When applied to GRB outflows, the model predicts more gradual Poynting dissipation and moderately magnetized flow at distances of ~1016 cm where the deceleration of the ejecta due to interaction with the external medium is expected. The energy released by the instability can power the compact “blazar zone” emission and the prompt emission of GRB outflows with high radiative efficiencies.

Flow Analysis Inside a Pelton Turbine Bucket

The aim of this work is to provide a detailed experimental and numerical analysis of the flow in a fixed bucket of a Pelton turbine. The head, jet incidence, and flow rate have been varied to cover a wide range of the turbine functioning points. The experimental analysis provides measurements of pressure and torque as well as flow visualization. The numerical analysis is performed with the FLUENT code using the two-phase flow volume of fluid method. The results present a good consistency with experimental data. In particular, the pressure distribution is very well predicted for the whole range of the studied parameters. A detailed analysis of torque and thrust allows evaluating the losses due to the edge and the cutout of the bucket. These results give insight into the benefit we can expect of steady flow calculations through the optimization process of the design of Pelton turbines.

Building Pit Dewatering: Application of Transient Analytic Elements

Analytic elements are well suited for the design of building pit dewatering. Wells and drains can be modeled accurately by analytic elements, both nearby to determine the pumping level and at some distance to verify the targeted drawdown at the building site and to estimate the consequences in the vicinity. The ability to shift locations of wells or drains easily makes the design process very flexible. The temporary pumping has transient effects, for which transient analytic elements may be used. This is illustrated using the free, open-source, object-oriented analytic element simulator Tim(SL) for the design of a building pit dewatering near a canal. Steady calculations are complemented with transient calculations. Finally, the bandwidths of the results are estimated using linear variance analysis.

An algorithm for incorporation of frictional sliding conditions within a steady state rolling framework

AbstractA formulation for hyperelastic steady state rolling calculations is presented, focusing on the inclusion of frictional sliding conditions between a rolling tyre and a flat roadway. Algorithmically, it is seen that traditional return mapping algorithmic strategies for treatment of the friction are often ineffective for this problem even when well‐posed frictional solutions exist; accordingly, an algorithmic approach utilizing a global stick predictor is proposed to recover solutions to the sliding contact problem. Numerical examples for adherent and sliding contact cases are presented, to demonstrate the effectiveness of the approach advocated. Copyright © 2005 John Wiley &amp; Sons, Ltd.

The Importance of Shroud Leakage Modeling in Multistage Turbine Flow Calculations

Three-dimensional steady multistage calculations, using the mixing plane approach, are compared with experimental measurement in a low-speed three-stage model turbine. The comparisons are made with two levels of shroud seal clearance, one representative of a real turbine and one with minimal seal clearance and almost no shroud leakage. Three different calculations are compared. The first computes the main blade path with no modeling of shroud leakage. The second includes a simple model of shroud leakage using sources and sinks on the end-walls, and the third is a multiblock calculation with all leakage paths and cavities computed. It is found that neglect of shroud leakage makes the computed velocity profiles and loss distributions significantly different to those measured. Simple modeling of shroud leakage gives some improvement but full calculation of the leakage flows and cavities is necessary to obtain good agreement between calculation and measurement.

An artificial compressibility based characteristic based split (CBS) scheme for steady and unsteady turbulent incompressible flows

An artificial compressibility method is presented for the solution of incompressible turbulent flow problems at moderate Reynolds numbers. The presented approach has been used to solve both steady and unsteady state turbulent flow problems. Three different RANS models have been employed to investigate the application of present matrix solution free approach. They are one-equation model of Wolfstein, Spalart–Allmaras model and standard κ– ε model. In addition to the results of standard steady two-dimensional flow problems, solutions to transient two-dimensional flow past a circular cylinder and steady state three-dimensional turbulent flow in a model “upper human airway” are also presented. The results presented demonstrate that the artificial compressibility based CBS scheme is suitable for both steady and unsteady state incompressible turbulent flow calculations at moderate Reynolds numbers.