Flowfield initialization and approach to stationary conditions in unsteady combustion simulations

The initial transient leading to stationary conditions in unsteady combustion simulations is investigated by considering flow establishment in model combustors. Quiescent initial conditions with the chamber initially filled with an inert, hot gas are used to provide physically realistic starting conditions and robust, reliable combustion initiation. Transient processes are visualized by using a distinct initial fluid in the combustor whose concentration is tracked as it is expelled. The duration of the transient is shown to be dependent on the characteristic turn-over time for recirculation zones and the time for the chamber pressure to reach steady conditions. Substantial changes in the initial condition did not materially affect the length of the transient. Different combustor geometries changed the ratio of pressure equilibration time and species replenishment time, but did not have a major effect on the overall duration of the transient. Representative comparisons of the time-averaged, stationary results with experiment are presented to document the computations.     

Broadband slat noise prediction based on CAA and stochastic sound sources from a fast random particle-mesh (RPM) method

The application of a low-cost computational aeroacoustics (CAA) approach to a slat noise problem is studied. A fast and efficient stochastic method is introduced to model the unsteady turbulent sound sources in the slat-cove of a high-lift airfoil. It is based on the spatial convolution of spatiotemporal white-noise and can reproduce target distributions of turbulence kinetic energy and length scales, such as that provided by a RANS computation of the time-averaged turbulent flow problem. The computational method yields a perfectly solenoidal velocity field. For homogeneous isotropic turbulence, the complete second-order two-point velocity correlation tensor is realized exactly. Two RANS turbulence models are applied to the slat noise problem to study how sensitive the aeroacoustics predictions depend on turbulence kinetic energy predictions. Results for the sound generation at the slat are given for a Menter SST turbulence model with and without Kato-Launder modification. The aeroacoustic simulations yield a characteristic narrow band spectrum that compares very well with the experimental data. The directivities found point toward an edge noise mechanism at the slat as the main cause for slat noise sound generation.     

Space-time adaptive simulations for unsteady Navier-Stokes problems

In this paper we apply to the unsteady Navier-Stokes problems some results concerning a posteriori error estimates and adaptive algorithms known for steady Navier-Stokes, unsteady heat and reaction-convection-diffusion equations and unsteady Stokes problems. Our target is to investigate the real viability of a fully combined space and time adaptivity for engineering problems. The comparison between our numerical simulations and the literature results demonstrates the accuracy and efficiency of this adaptive strategy.     

Incompressible flow calculations with a consistent physical interpolation finite volume approach

The computation of incompressible three-dimensional viscous flow is discussed. A new physically consistent method is presented for the reconstruction for velocity fluxes which arise from the mass and momentum balance discrete equations. This closure method for fluxes allows the use of a cell-centered grid in which velocity and pressure unknowns share the same location, while circumventing the occurrence of spurious pressure modes. The method is validated on several benchmark problems which include steady laminar flow predictions on a two-dimensional cartesian (lid driven 2D cavity) or curvilinear grid (circular cylinder problem at Re = 40), unsteady three-dimensional laminar flow predictions on a cartesian grid (parallelopipedic lid driven cavity) and unsteady two-dimensional turbulent flow predictions on a curvilinear grid (vortex shedding past a square cylinder at Re = 22,000).     

Numerical computation of transient coaxial entry tube flows

A numerical program was developed to compute transient laminar flows in two dimensions including multicomponent mixing and chemical reaction. The program can compute both incompressible flows and compressible flows at all speeds, and it is applied to describe transient and steady state solutions for low subsonic, coaxial entry, tube flows. Single component, non-reacting flows comprise most of the solutions, but one steady state solution is presented for trace concentration constituents engaging in a second order reaction. Numerical stability was obtained by adding at each calculation point a correction for numerical diffusion errors caused by truncation of the Taylor series used to finite difference the conservation equations. Transient computations were made for fluids initially at rest, then subjected to step velocity inputs that were uniform across each region of the entry plane and were held constant throughout the computation period. For center tube to annulus velocity ratios of 0.5 and 2.0, the bulk fluid in the tube initially moved in plug flow, but strong radial flows developed near the injection plane which moved the fluid into the high shear region between the jets and away from the tube wall. The entrance flows penetrated the bulk flow until steady state was attained. A computation with only the center jet flowing developed a recirculation vortex in the annulus that propagated downstream. The calculation of steady state reacting flows showed formation of a third specie in the mixing zone. Both short and long tube solutions are presented.     

Dynamic hybridization of MILES and RANS for predicting airfoil stall

Hybridization comprised of an algebraic turbulence model based on the Reynolds average Navier-Stokes (RANS) equations with a monotonically integrated large eddy simulation (MILES) is proposed to simulate transient fluid motion during separation and vortex shedding at high Reynolds numbers. The proposed hybridization utilizes the Baldwin-Lomax model with the Degani-Schiff modification as the RANS model in the near-wall region and a MILES far from the wall. Although the hybridization is assumed to be a MILES with wall modeling, the transition line between the RANS and the MILES modes is determined by the turbulent intensity that is dominated by the large eddies in the grid-scale. This hybrid model is applied to the flows past three different types of airfoils (NACA63₃-018, NACA63₁-012 and NACA64A-006) near stall, at a chord Reynolds number of Re = 5.8 × 10⁶. These airfoils are classified as trailing-edge-stall, leading-edge-stall and thin-airfoil-stall airfoils, respectively. The computed results are compared with wind tunnel experiments. The hybrid model successfully demonstrates accurate stall angle and surface pressure distribution predictions near the stall for each type of airfoil. The airfoil simulation results confirmed that the hybrid model provides a better prediction than the RANS model for unsteady turbulent flows with separation and vortex shedding simulations.     

MATLAB在稳态与动态导热过程分析中的应用

在传热过程分析研究中需要求解微分方程,而这些描述传热过程的微分方程在多数情况下无法获得解析解,只能利用数值方法求解。通过MatLab在若干导热过程实例中的应用,探讨稳态与动态传热过程中温度分布、传热量、热通量等参数的求解与分析方法。结果表明MatLab工具能够十分有效、快速、准确地求解稳态与动态传热微分方程,为传热过程的数值分析研究提供了一个强有力的工具。     

Steady and unsteady flow past a rotating circular cylinder at low Reynolds numbers

Results of calculations of the steady and unsteady flows past a circular cylinder which is rotating with constant angular velocity and translating with constant linear velocity are presented. The motion is assumed to be two-dimensional and to be governed by the Navier-Stokes equations for incompressible fluids. For the unsteady flow, the cylinder is started impulsively from rest and it is found that for low Reynolds numbers the flow approaches a steady state after a large enough time. Detailed results are given for the development of the flow with time for Reynolds numbers 5 and 20 based on the diameter of the cylinder. For comparison purposes the corresponding steady flow problem has been solved. The calculated values of the steady-state lift, drag and moment coefficients from the two methods are found to be in good agreement. Notable, however, are the discrepancies between these results and other recent numerical solutions to the steady-state Navier-Stokes equations. Some unsteady results are also given for the higher Reynolds numbers of 60, 100 and 200. In these cases the flow does not tend to be a steady state but develops a periodic pattern of vortex shedding.     

Numerical simulation of flow-induced cavity noise in self-sustained oscillations

The generation and near-field radiation of aerodynamic sound from a low-speed unsteady flow over a two-dimensional automobile door cavity is simulated by using a source-extraction-based coupling method. In the coupling procedure, the unsteady cavity flow field is first computed solving the Reynolds- averaged Navier–Stokes (RANS) equations. The radiated sound is then calculated by using a set of acoustic perturbation equations with acoustic source terms which are extracted from the time-dependent solutions of the unsteady flow. The aerodynamic and its resulting acoustic field are computed for the Reynolds number of 53,266 based on the base length of the cavity. The free stream flow velocity is taken to be 50.9 m/s. As first stage of the numerical investigation of flow-induced cavity noise, laminar flow is assumed. The CFD solver is based on a cell-centered finite volume method. A dispersion-relation-preserving (DRP), optimized, fourth-order finite difference scheme with fully staggered-grid implementation is used in the acoustic solver.     

Laminar free-surface flow into a vertical cylinder

This study concerns the unsteady free-surface flow of a Newtonian fluid issuing vertically upwards from a tube in the base of a vertical cylindrical cavity. Experimental and numerical results are presented and discussed.The experiments involve a photographic procedure for measuring point velocities and surface profiles in an unsteady velocity field. Numerically, a marker-and-cell technique is used in conjunction with a Dufort-Frankel finite-difference approximation for solving the Navier-Stokes equation in two-dimensional cylindrical coordinates. It is found that the numerical solutions are generally stable for large values of the time step in spite of high fluid viscosities. Good agreement is obtained between the numerical and experimental results.     

Simulation of a simple reacting gas flow with an upwind scheme

Good results have been obtained using the Random Choice Method (RCM) in the computation of reacting gas flow problems. The RCM is an unfamiliar method and difficult to program. The question arises as to whether a simpler difference approximation can obtain as effective results with less computational difficulty. Among all difference schemes upwind methods have been proven to have excellent properties. Thus, such methods serve as models for the effectiveness of all difference schemes.A standard upwind scheme modified to include a fractional heat conduction step is used to compute solutions of one dimensional compressible fluid flow equations with a finite heat conduction coefficient. The gas is assumed to be chemically reacting and thus to deposit energy in the field. Comparison is made to the known qualitative behavior of the solutions for different ratios of the reaction rate and the heat conduction coefficient. This difference scheme is seen to compare unfavorably with the RCM.     

Blunted cone-flare in hypersonic flow

Computational fluid-dynamics results are presented to show the flowfield around a blunted cone-flare in hypersonic flow. This problem is of particular interest since it features most of the aspects of the hypersonic flow around planetary entry vehicles. The region between the cone and the flare is particularly critical with respect to the evaluation of the surface heat flux. Indeed, flow separation is induced by the shock wave-boundary layer interaction, with subsequent flow reattachment, that can dramatically enhance the surface heat transfer. The exact determination of the extension of the recirculation zone is a particularly delicate task for numerical codes.Laminar flow computations have been carried out using a full Navier-Stokes solver, with freestream conditions provided by the experimental data obtained in the Von Karman Institue (VKI) H3 Mach 6 wind tunnel.A grid sensitivity analysis has been performed until grid-solution independence is achieved.The numerical results are compared with the measured pressure and surface heat flux distributions in the H3 wind tunnel and a good agreement is found, although some discrepancies are present, especially on the length of the recirculation region. A sensitivity analysis has been performed to investigate the influence of the wall temperature, that has shown an influence of the wall temperature on both surface heat flux and surface pressure. A numerical model has been developed to take into account the heating of the test model, and a closer agreement with the experimental data is found.     

Experimental and numerical modeling of the effect of solid surface on NOx emission in the combustion chamber of a water heater

A combined experimental and CFD modeling study of the turbulent non-premixed natural gas on a laboratory scale has been performed. Effect of solid surface enhancement in combustion chamber on the flame temperature and NO emission was investigated. The solid surface called as filling material (FM) was cylindrical and was placed coaxially in the center of combustion chamber. The temperature and NO distribution in the combustion chamber were compared for different geometries of the filling material. The diameters of the filling materials were 25 and 30 cm with two lengths of 20 and 40 cm. Experimental study has been carried out on a fire tube water heater. The flame temperature on the center line of the combustion chamber, gas temperature and NO emission in the combustion chamber were measured. The actual geometry of the fire tube water heater and the burner were modeled and then analyzed by the FLUENT code. Turbulent diffusion flames were investigated numerically using a finite volume method for the solution of the conservation and reaction equations governing the problem. The measured values were specified as the boundary conditions. The elemental analysis of the natural gas was taken as a mixture of hydrocarbon and air was the oxidizer. The standard k-ε model was used for the modeling of the turbulence phenomena in the combustor. The non-premixed combustion model was chosen. In the conserved scalar approach, turbulence effects were accounted for with the help of an assumed shape probability density function or PDF. The discrete ordinates (DO) radiation model was used for modeling of the radiative heat transfer in the combustion room. The model results were compared with the experimental results. The model results were in good agreement with the measurements. The filling material provided the recirculation of the cooler gases into the flame. The recirculation reduced the oxygen concentration in the flame and controlled the flame temperature. It was found that the filling material with the diameter bigger than the flame diameter increased the heat transfer rate in the back flow around the flame.     

MEMS-based combustor with hairpin-shape design of gas recirculation channel

This paper describes the design, fabrication and test of a silicon-based micro combustor, which is a part of a micro power generation system under development. Based on the three-dimensional computational fluid dynamics (CFD) simulation and analysis of different micro combustor design, a hairpin-shape design for air/fuel recirculation channel is adopted. The combustor is fabricated from seven single crystal silicon wafers using deep reactive ion etching (DRIE) process. It has been assembled successfully with gas tubing and thermal couplers for monitoring the exit gas temperature. The effect of mass flow rate on the combustion characteristics is studied experimentally and numerically under several operating conditions. The exhaust gas temperature can reach the range from 870 to 1,100 K. The results indicate that with the increases of the mass flow rate, the combustor exhaust gas temperature increase as well in both experimental and the simulated results. This is due to the heat released in the combustor increases with the fuel/air mass flow rate.     

MEMS-based combustor with hairpin-shape design of gas recirculation channel

This paper describes the design, fabrication and test of a silicon-based micro combustor, which is a part of a micro power generation system under development. Based on the three-dimensional computational fluid dynamics (CFD) simulation and analysis of different micro combustor design, a hairpin-shape design for air/fuel recirculation channel is adopted. The combustor is fabricated from seven single crystal silicon wafers using deep reactive ion etching (DRIE) process. It has been assembled successfully with gas tubing and thermal couplers for monitoring the exit gas temperature. The effect of mass flow rate on the combustion characteristics is studied experimentally and numerically under several operating conditions. The exhaust gas temperature can reach the range from 870 to 1,100 K. The results indicate that with the increases of the mass flow rate, the combustor exhaust gas temperature increase as well in both experimental and the simulated results. This is due to the heat released in the combustor increases with the fuel/air mass flow rate.

     

Two- and three-dimensional transient melt-flow simulation in vapour-pressure-controlled Czochralski crystal growth

Flow and thermal properties associated with semiconductor melt flow in an axisymmetric crucible container are studied numerically. Axisymmetric and three-dimensional computational solutions are obtained using a standard-Galerkin, finite-element solver. The crucible and crystal are optionally rotated, and the influence of gravity (through buoyancy) is accounted for via a Boussinesq approximation in the controlling Navier–Stokes equations. The results indicate a strong dependence of the flow on both rotation and buoyancy. Results for axisymmetric flows, computed with both flat and curved geometries, are presented first, and strongly suggest that rotation of crystal and crucible in the same direction (iso-rotation) is most favourable for producing a desired convexity for the crystal/melt interface. Three-dimensional results are then presented for higher Reynolds numbers, and, in particular, reveal that for iso-rotation under moderate buoyancy, the flow undergoes a switch from a steady 2D state to an unsteady 3D state, and that the temperature becomes non-trivially advected by the flow beneath the crystal. Further evidence reveals however, that on a time scale more appropriate to the crystal growth process, the (time-averaged) flow has a weaker three-dimensionality, in relation to the mean axisymmetric part, and there is only slight distortion to the temperature field beneath the crystal. A detailed examination of the instability properties is also made, revealing the underlying nonlinear mode interaction and associated frequency responses around the bifurcation point.     

Verification of RANS solvers with manufactured solutions

This paper discusses code verification of Reynolds-Averaged Navier Stokes (RANS) solvers with the method of manufactured solutions (MMS). Examples of manufactured solutions (MSs) for a two-dimensional, steady, wall-bounded, incompressible, turbulent flow are presented including the specification of the turbulence quantities incorporated in several popular eddy-viscosity turbulence models. A wall-function approach for the MMS is also described. The flexiblity and usefulness of the MS is illustrated with calculations performed in three different exercises: the calculation of the flow field using the manufactured eddy-viscosity; the calculation of the eddy-viscosity using the manufactured velocity field; the calculation of the complete flow field coupling flow and turbulence variables. The results show that the numerical performance of the flow solvers is model dependent and that the solution of the complete problem may exhibit different orders of accuracy than in the exercises with no coupling between the flow and turbulence variables.     

Inertial thin film flow on planar surfaces featuring topography

A range of problems is investigated, involving the gravity-driven inertial flow of a thin viscous liquid film over an inclined planar surface containing topographical features, modelled via a depth-averaged form of the governing unsteady Navier-Stokes equations. The discrete analogue of the resulting coupled equation set, employing a staggered mesh arrangement for the dependent variables, is solved accurately using an efficient full approximation storage (FAS) algorithm and a full multigrid (FMG) technique; together with error-controlled automatic adaptive time-stepping and proper treatment of the associated nonlinear convective terms. An extensive set of results is presented for flow over both one- and two-dimensional topographical features, and errors quantified via detailed comparisons drawn with complementary experimental data and predictions from finite element analyses where they exist. In the case of one-dimensional (spanwise) topography, moderate Reynolds numbers and shallow/short topographical features, the results obtained are in close agreement with corresponding finite element solutions of the full free-surface problem. For the case of flow over two-dimensional (localised) topography, it is shown that the free-surface disturbance is influenced significantly by the presence of inertia leading, as in the case of spanwise topography, to an increase in the magnitude and severity of the resulting capillary ridge and trough formations: the effect of inclination angle and topography aspect ratio are similarly explored.     

Heat and mass transfer computations for laminar flow in an axisymmetric sudden expansion

Detailed heat or mass transfer rate predictions are made using a finite difference computer model for laminar flow in an axisymmetric sudden expansion. The structure of the recirculation zone and the distribution of mass transfer rate downstream of the expansion are calculated as functions of Reynolds number, inlet velocity profile, geometry and Schmidt number. It is shown that a Couette flow analysis of the appropriate scaled equations gives the essential details of the mass transfer behaviour.     

Numerical investigation of the structure of a silicon six-wafer micro-combustor under the effect of hydrogen/air ratio

Research reports indicate that sufficiently high equivalence ratio of the hydrogen/air mixture leads to the upstream burning in the recirculation jacket, possibly damaging the micro- combustor due to the high wall temperature. This work investigates the influences of the equivalence ratio of the mixture on the structure of a micro-combustor device. Numerical simulation approaches focused on the structural design of the micro-combustor with the flame burning in the recirculation jacket. Combustion characteristics of the combustor were first analyzed based on 2D computational Fluid Dynamics (CFD), and then thermo-mechanical analysis on the combustor was carried out by means of 3D Finite Element Analysis (FEA) method. The results showed that the most dangerous locations where the critical failure could possibly occur lay at the burning areas in the recirculation jacket due to the poor bonding, the high temperature and the residual stress. The results of this study can be used for the design and improvement of the micro-combustors.