Turbulent Navier-Stokes Equations Research Articles

Numerical Investigation of Diffusion Flame in Transonic Flow with Large Pressure Gradient

A finite-volume method for the steady, compressible, reacting, turbulent Navier–Stokes equations is developed by using a steady-state-preserving splitting scheme for the stiff source terms in chemical reactions. Laminar and turbulent reacting flows in a mixing layer with a large streamwise pressure gradient and acceleration are studied and compared to boundary-layer solutions. It reveals that chemical reactions strongly enhance turbulent transport due to the intensive production of turbulence by the increased velocity gradients and thus produce large turbulent viscosities in the reaction region. The influence of vitiated air on the combustion process and aerodynamic performance is also investigated in the cases of turbulent mixing layers and highly loaded transonic turbine cascades. Both cases indicate the viability of the turbine-burner concept.

Numerical Modeling of Supersonic Combustion of Hydrogen in the Wake Region of a Strut

Numerical modeling of combustion of a sonic hydrogen stream injected into a supersonic stream of air using a strut is presented. Results are obtained by numerically solving unsteady, compressible, turbulent Navier-Stokes equations, using Unstructured Finite Volume Method (UFVM) incorporating RNG based κ−ε two equation model and time integration using three stage Runge Kutta method. Reaction is modeled using an eight step H2-air chemistry. The developed numerical procedure is based on the implicit treatment of chemical source terms by preconditioning and solved along with unsteady turbulent Navier Stokes equations explicitly. Code is validated against a standard wall jet experimental data and is successfully used to model the reacting flow field resulting due to combustion of hydrogen in the wake region of strut placed in heated supersonic air stream.

A three-dimensional coupled well-reservoir flow model for determination of horizontal well characteristics

Horizontal wells have gained considerable interest among petroleum engineers and hydrologists in the last decades. Many attempts were made to reach a better understanding of fluid flow behaviour inside the reservoir/aquifer, especially in the near-wellbore regions. In most of the previous studies on horizontal wells, each well is treated as a volumetric source term in governing equations describing the fluid flow in the main reservoir/aquifer. Many important features affecting the fluid flow, such as the realistic wellbore geometry, have been ignored for mathematical convenience. In the present study, the three-dimensional single-phase fluid flow through a large size reservoir block is coupled to wellbore flow through imposing the pressure and flux continuity at the reservoir-well interface. As the momentum equations, the Darcy and turbulent Navier–Stokes equations are used in the reservoir block and wellbore, respectively. The governing equations are discretized on unstructured grids and solved by using the finite volume method. Using the computed pressure and velocity distributions, the horizontal well characteristics are numerically estimated and compared with available analytic data for various cases. It is shown that the calculated well index, a coefficient in reflecting the geometric features of the well-reservoir system, deviates from its analytic value, as a result of reservoir block boundary condition, the pattern of the wellbore open intervals, the horizontal well drilling path, and its vertical eccentricity. In addition, the proposed approach is used to improve Economides model, an analytical model for horizontal well index, by estimating its pseudo-skin factor in various cases of the well vertical eccentricity, horizontal orientation, and reservoir block conditions.

A Numerical Investigation of Synthetic Jet Effect on Dynamic Stall Control of Oscillating Airfoil

At high angles of attack, the dynamic stall phenomenon could be appearing owing to the vortex shedding particularly in an oscillating airfoil. The consequences of this event are a considerable decrease in the lift and an increase in the drag as well as the pitching moment coefficients. The flow was assumed to be unsteady and turbulent at a Mach number 0.2 and for Reynolds number 1million. This research was done for a range of angle of attack 15o±10o. In order to carry out the numerical analysis of the problem, the 2-D compressible turbulent Navier-Stokes equations based on “Roe” scheme with second-order accuracy were solved. Turbulence modeling was carried out using the three-equation k-kL-ω model. Regarding the obtained results, it was observed that this flow control method had a significant ability in eliminating the dynamic stall. It was also revealed that the phase difference between the jet and airfoil oscillations is more affected by the dynamic stall decrement. In these changes, use of the SJ with 0.1 momentum coefficient, led to the highest amplitude of lift at φ=-30°, and the multiplication of drag amplitude and amplitude of moment coefficient at φ=-10° offered the best performance in addition to the considerable decrease.

Application of the Harmonic Balance method for regime change prediction using Francis-99 test case

An efficient method for predicting the turbine start-up and shut-down flow parameters is presented in this paper. Due to start-up or shut-down usually lasting a large number of periods, simulations of such processes are highly demanding and long lasting. To alleviate this, a modified Harmonic Balance method is used, thus casting a problem into spectral space and solving start-up and shut-down simultaneously, as a complete period. By doing this, the results are obtained in a fraction of time required by time-accurate simulation. Furthermore, the same approach could be used for any change of regime from operating point OP1 to operating point OP2 and back to OP1. The method is implemented in foam-extend and suitable for solving incompressible turbulent Navier–Stokes equations. Validation is performed on two test cases: a simple 2D pump case for initial validation, followed by a Francis turbine. Francis turbine test case and experimental data are provided by the Francis-99 Workshop. For Francis turbine the power curve is assembled and compared with experiment.

Numerical analysis of multiphase flow through axial vortex tube cyclone separators

Axial cyclone separators are used as primary filtration components in many internal combustion engine applications. A numerical study of gas-solid flow through an axial cyclone separator is carried out by Eulerian-Lagrangian CFD approach, which uses discrete phase modelling (DPM) of particles and solution of incompressible turbulent Navier-Stokes equations with RNG k—ɛ closure model. The effective filtration of inlet air from dust particles is an important requirement for prolonged engine life cycle. In axial cyclone separators, a helical swirl generator is used for imparting swirling motion to theparticle laden flow and particles are filtered by centrifugal separation and then scavenged using a vortex tube. In the present work, the modelling done in OpenFOAM successfully captures the features of the swirling flow, along with particle–gas and particle–wall interactions for a varying size distribution at the inlet. Studies were aimed at analysing the effect of particles and its effect on improving the performance of the filter.

Trajectory modification of a transonic spherical projectile under Hop-up mechanism

Improvement of shooting accuracy of air gun pellets is important in sport competitions which is questioned by shooting enthusiasts. Hence, the performance of a transonic spherical projectile as an air gun pellet with 4.5 mm-caliber under a mechanism known as Hop-up is numerically examined in the present study. Hop-up mechanism is resulted in a rotational motion of spherical projectile, so a Magnus Force is generated which prevents the altitude loss of the projectile caused by its weight. The motion of the projectile is assumed in four degrees of freedom including three translational motions and one transverse rotational motion. The projectile confronts the continuous variations of velocity due to the influence of the aerodynamic forces so experiences an unsteady flow. In order to numerical analysis of the problem, the 3-D compressible turbulent Navier-Stokes equations based on “Roe” scheme and dynamic equations of the projectile motion are solved in a coupled form as a fluid-structure interaction and in a moving computational grid. The results obtained from these studies show that the proper rotation of the projectile for a certain distance, can neutralize the altitude loss. It is also demonstrated that the momentum of the projectile is decreased by increasing its angular velocity.

Investigation and comparison of performance of some air gun projectiles with nose shape modifications

Shooting accuracy of air gun projectiles is very important in sport tournaments and has always been questioned by enthusiasts. For this purpose, the performance of four samples of air gun projectiles (pellets) with various shapes and calibers of 4.5, 5.5 and 6.35 mm was studied in this article. The projectiles were four basic shapes: flat nose, sharp nose, round nose and spherical. After these projectiles were modeled geometrically, the three-dimensional compressible turbulent Navier–Stokes equations and dynamic equations of the projectiles’ motion were solved in a coupled form and in a moving computational grid. The computed results describe the trajectory, velocity variations and the altitude loss of the projectiles with time and location. Comparisons indicate that the round nose projectile had the best performance at long distances compared to the other samples. The flat nose projectile exhibited great performance at short distances, but behaved weakly at long distances. In addition, the effect of nose shape on the performance of the sharp and round nose projectiles was studied and the optimum nose shapes were identified.

Parametric study on the heat transfer of a blunt body with counterflowing jets in hypersonic flows

A quantified parametric study for the heat transfer acting on a hypersonic blunt body with counterflowing jets is presented. Three-dimensional turbulent Navier-Stokes equations are solved to simulate freestream-jet interactive flowfields. The freestream and jet controlling parameters are treated as input sources of variation, and a point-collocation non-intrusive polynomial chaos (NIPC) method is utilized to quantify the variations in the output surface heat flux and total surface heat load acting on the blunt body by identifying the maximum and minimum of surrogate response values predicted by the NIPC. All of the sample cases are confirmed to form steady jet structures. Furthermore, through a global sensitivity analysis, Sobol indices evaluated by the NIPC, are used to rank the contributions of each input parameter to the variation in output quantities of interest. It is found that the designed upstream injection of baseline case effectively reduces the heat transfer to body surface compared with the no-jet case. The variations of input parameters induce remarkable variations of output heat flux and total heat load. The sensitivity analysis indicates that the jet-to-freestream total-pressure ratio is the top contributor to variations in heat flux, followed by the freestream Mach number. The jet total temperature is mainly important on the front part of forebody, while the contributions of jet Mach number and freestream temperature slightly increase downstream. The freestream density has the smallest effect. The sensitivity of total heat load to input parameters coincides with that of heat flux. This parametric study is expected to illustrate the significance of flow-controlling parameters to the heat transfer over blunt body and provide insight for aerothermal management by using counterflowing jets in hypersonic flows.

Simulation of In-Flight Reduction of the Fine Iron Ore Concentrate by Hydrogen

Abstract A mathematical model has been proposed to simulate a novel method for direct reduction of iron concentrate by hydrogen. Flight of fine particles in a vertical reactor containing a gaseous mixture of H2-N2-H2O has been studied. Effect of generating gaseous jet on the residence time of the particles has been also investigated. Coupled turbulent Navier-Stokes equations with eddy kinetic energy equation have been solved using a developed homemade code. Kinetics of this reaction has been studied using the unreacted core model. Accuracy of the model predictions has been approved by the experimental data. Finally, effects of vital variables (i. e. temperature, particle size, hydrogen concentration and particle feed rate) on the particle residence time and also fractional conversion have been studied.

Using the VBARMS method in parallel computing

We introduce a new graph compression algorithm for block construction, which extends the method by Ashcraft and requires one simple to use parameter.We describe an improved block factorization computation in the VBARMS method.We conduct a parallel performance study of the VBARMS method using parallel graph partitioning.We solve turbulent three-dimensional Navier-Stokes equations on large realistic unstructured meshes. The paper describes an improved parallel MPI-based implementation of VBARMS, a variable block variant of the pARMS preconditioner proposed by Li etźal. 200314 for solving general nonsymmetric linear systems. The parallel VBARMS solver can detect automatically exact or approximate dense structures in the linear system, and exploits this information to achieve improved reliability and increased throughput during the factorization. A novel graph compression algorithm is discussed that finds these approximate dense blocks structures and requires only one simple to use parameter. A complete study of the numerical and parallel performance of parallel VBARMS is presented for the analysis of large turbulent Navier-Stokes equations on a suite of three-dimensional test cases.

Numerical Investigation of Inclusion Behaviour in a Multi-Strand Tundish During Strand Blockages

Inclusion removal in the continuous casting tundish is an essential technology for production of high-grade steels. In the present study, a three dimensional numerical investigation has been carried out on six strand delta shape tundish. The aim of the work is to investigate the inclusion entrapment and removal phenomenon in a tundish. A parametric study has been carried out to study the behavior of the inclusions in a steelmaking tundish and the results have been compared on the basis of densities and diameters of inclusions. Bare tundish as well as a tundish occupied with Advance Pouring Box (APB) have been studied to predict the transport behavior of inclusion particles. Further, effect of strand blockages has been considered. The turbulent Navier–Stokes equations have been solved to predict the flow velocity distributions and inclusion trajectories were calculated using a Lagrangian particle tracking method. The numerical results were validated using available experimental results and found to be in good agreement. The results indicate that the use of APB has changed the fluid flow pattern and consequently the inclusion particles movement. The density of inclusion particles plays an important role. It has been seen that low dense particles have higher chances to get trapped or removed from tundish. It was also found that larger diameter of inclusion particles have more chances of floatation.

Modeling Coal/coke Combustion Behavior in Tuyere-raceway-dripping Zone in Blast Furnace

Based on the operation conditions of the iron making blast furnace of 580 m3 in the industrial base of MCC Company, a three-dimensional mathematical model for analyzing combustion behavior of gas, pulverized coal and coke bed in the tuyere-raceway-dripping zone of blast furnace has been developed in the present research. The gas was modeled with steady-state turbulent Navier-Stokes equations; the pulverized coal particles were modeled by using a DPM (discrete particle model) approach and coke bed was treated simply as porous media. Two cases, the normal PCI case and the intensified PCI case, were then analyzed and compared. The simulation results indicate that, compared to the normal PCI case, the intensified PCI case has the advantage of an increase of 0.1 volume fraction of CO in the gas and moreover some 60 kg-coke/tHM could be saved. The negative effects of the proposed intensified PCI mode mainly include the drop of combustion temperature and the shrinkage of raceway.

Mathematical modeling of the fluid flow in a mixing device for melting/dissolving solid particles in a liquid alloy

ABSTRACTA study of the fluid flow in a mixing device proposed to dissolve alloying elements in iron baths is performed through a mathematical model in order to predict the best operating conditions for a proper melting/dissolution of solid alloying particles. The mathematical model consists in the mass and momentum conservation equations (continuity and Turbulent Navier-Stokes equations), and the standard two k-epsilon turbulence model. The model is numerically solved in transient regime with the Volume of Fluid algorithm (VOF) to calculate the vortex shape. VOF is built-in the CFD (Computational Fluid Dynamics) software ANSYS FLUENT 14. A flow of metal enters tangentially in the mixing chamber of the proposed mixing device (taken from an open patent) to generate a vortex. The shape and height of the vortex reached in this chamber depends on several design variables, but in this work only the presence or absence of a barrier in the device is analyzed. Results are obtained on the vortex sizes and shapes, liquid flow patterns, turbulent structure, residence times of the particles of alloying elements added to the melt and mixing times (Residence time distribution curves) of two devices: one with a barrier and the other without this barrier. It is found that the presence of the barrier in the device increases turbulence, destroys the vortex, decreases the residence time of the particles, and decreases the volume of fluid in the device. Most of the features of the barrier are detrimental for mixing and inhibits melting/dissolution of the alloying elements. Then, it is suggested a device without the presence of barrier for better performance.

Development and Assessment of a Backward Facing Steps Planar Rocket Nozzle

Large Rocket engine nozzles performance deteriorate because of asymmetric flow separation that lead to side loads. The dual-bell nozzle is a promising two operating modes nozzle which consists of a base nozzle with low area ratio and a nozzle extension with high area ratio. Although the dual-bell nozzle improves the performance of large rocket engines, it suffers from side loads that occur during the transition between the two operating modes. This paper presents and assess a new nozzle that consist of backward facing steps to minimize/eliminate side loads. The backward facing steps geometry guarantees fixed stable local separation at the steps edges at all altitudes, thus eliminates the possibility of side loads as the rocket ascends. The assessment of the nozzle performance is carried out using CFD simulation of turbulent Navier-Stokes equations solver (fluent 14.5). The computed results for both dual-bell and backward facing steps nozzles are compared with the dual-bell nozzle experimental data.

Quasi-Steady Modeling of Ice Accretion on a Helicopter Fuselage in Forward Flight

Computational modeling of ice accretion on a rotorcraft is an alternative and/or a complement for flight test in icing certification and ice protection system design. Although computational fluid dynamics solutions of helicopter flow have advanced in the last few years, icing simulations are rare and, to the best of the authors’ knowledge, none has modeled helicopter icing completely. In this work, a three-dimensional simulation of long-term in-flight ice accretion, accounting for rotor-fuselage quasi-steady interaction, is performed. For flow solution, the three-dimensional compressible turbulent Navier–Stokes equations are solved, with the rotor modeled as an actuator disk that imparts radial and azimuthal distributions of pressure rise and swirl to the flow field. The authors’ code FENSAP-ICE is used to solve the three-dimensional flow, impingement, and ice accretion. The flow solutions for a test case, at two forward speeds, are obtained and validated against published experimental results and then used to illustrate icing on the helicopter’s fuselage. Also, in this work, the effects of different parameters (such as forward speed, ambient temperature, droplet diameter, and liquid water content) on droplet impact, ice accretion, and the aerodynamic degradation of helicopter fuselage, were studied.

A Computational Analysis of Flow Field in Twin-Track Subway Tunnel to Improve Air Quality

A computational model of existing Seoul subway tunnelwas analyzed in this research. The computational model was comprised of one natural ventilationshaft, two mechanical ventilationshafts, one mechanical airsupply, a twin-track tunnel, and a train. Understanding the flow pattern of the train-induced airflow in the tunnel was necessary to improve ventilation performance. The research objective wasto improve the air quality in the tunnel by investigating train-induced airflow in the twin-track subway tunnel numerically. The numerical analysis characterized the aerodynamic behavior and performance of the ventilation system by solving three-dimensional turbulent Reynolds-averaged Navier-Stokes equations. ANSYS CFX software was used for the computations. The ventilation and aerodynamic characteristics in the tunnel were investigated by analyzing the mass flowrateat the exits of the ventilation mechanicalshafts. As the train passed the mechanical ventilation shafts, the amount of discharged-air in the ventilationshafts decreased rapidly. The air at the exits of the ventilation shafts was gradually recovered with time, after the train passed the ventilation shafts. The developed mechanical air-supply for discharging dusty air and supplying clean airwas investigated.The computational results showed that the developed mechanical air-supplycould improve the air quality in the tunnel.

Influence of Geometrical Parameters of Heat Shield on Flow Characteristics at Transonic Mach

The numerical simulation over the bulbous heat shield is carried out by solving time-dependent compressible axisymmetric turbulent Reynolds-averaged Navier-Stokes equations. The solution of these equations is obtained employing the Baldwin-Lomax turbulence model. A three-stage Runge-Kutta time-stepping scheme has been used in conjunction with finite-volume discretization of the computational domain. The flowfield features over the bulbous payload shroud have been analyzed using the density contour plots and surface pressure distributions. Flow separation on the payload shroud due to the terminal shock wave is observed at transonic Mach numbers range. The normal shock movement on the heat shield is simulated for various transonic Mach numbers. The maximum diameter of the various heat shields is kept constant in order to evaluate the movement of terminal shock. A recirculation zone of the flowfield is formed in the boat-tail region of the payload shroud. The density increases ahead of the stagnation region of the heat shield moves close to the heat shield with the increasing transonic Mach number. It also depends on the cone angle of the heat shield as observed in the density contours plots of the flowfield.

Numerical Simulation of Electromagnetic Stirring Effect on Flow Pattern of Metal Melt

In this study, a mathematical model was developed to simulate 2-D axisymmetric melt flow under magnetic field in a cylindrical container. The modeling of this process required the simultaneous solution of the turbulent Navier-Stokes equations together with Maxwell equations. The flow pattern in liquid bath was obtained using a two-equation κ-є turbulent flow model, which was further used to obtain the solute distribution. The governing differential equations were solved numerically using finite volume based finite difference method. The computed results, were found to be in good agreement with the measurements reported in the literature. The effect of stirring parameters on temperature homogeneity of the melt have been discussed and presented.

Numerical Simulation of Tower Rotor Interaction for Downwind Wind Turbine

Downwind wind turbines have lower upwind rotor misalignment, and thus lower turning moment and self-steered advantage over the upwind configuration. In this paper, numerical simulation to the downwind turbine is conducted to investigate the interaction between the tower and the blade during the intrinsic passage of the rotor in the wake of the tower. The moving rotor has been accounted for via ALE formulation of the incompressible, unsteady, turbulent Navier-Stokes equations. The localizedCP,CL, andCDare computed and compared to undisturbed flow evaluated by Panel method. The time history of theCP, aerodynamic forces (CLandCD), as well as moments were evaluated for three cross-sectional tower; asymmetrical airfoil (NACA0012) having four times the rotor's chord length, and two circular cross-sections having four and two chords lengths of the rotor's chord. 5%, 17%, and 57% reductions of the aerodynamic lift forces during the blade passage in the wake of the symmetrical airfoil tower, small circular cross-section tower and large circular cross-section tower were observed, respectively. The pronounced reduction, however, is confined to a short time/distance of three rotor chords. A net forward impulsive force is also observed on the tower due to the high speed rotor motion.