先进铸造技术英文文献翻译

先进铸造技术英文文献翻译沈阳理工大学 材料科学与工程 学院学生姓名 王鹏飞 班级 09050101 学号 17 课程题目 先进铸造技术 指导教师 杜晓明 文献题目:Modelling the dynamics of the tilt-casting process and the effect of the mould design on the casting qualityH. Wanga,G. Djambazova, K.A. Pericleousa, R.A. Hardingb, M. WickinsbCentre for Numerical Modelling and Process Analysis, University of Greenwich, London SE10 9LS, UK b IRC in Materials Processing, University of Birmingham, Birmingham, B15 2TT, UReceived 29 June 2010 Revised 9 November 2010 Accepted 12 November 2010 Available online 21 November 2010AbstractAll titanium alloys are highly reactive in the molten condition and so are usually melted in a water-cooled copper crucible to avoid contamination using processes such as Induction Skull Melting (ISM). These provide only limited superheat which, coupled with the surface turbulence inherent in most conventional mould filling processes, results in entrainment defects such as bubbles in the castings. To overcome these problems, a novel tilt-casting process has been developed in which the mould is attached directly to the ISM crucible holding the melt and the two are then rotated together to achieve a tranquil transfer of the metal into the mould. From the modelling point of view, this process involves complex three-phase flow, heat transfer and solidification. In this paper, the development of a numerical model of the tilt-casting process is presented featuring several novel algorithm developments introduced into a general CFD package (PHYSICA) to model the complex dynamic interaction of the liquid metal and melting atmosphere. These developments relate to the front tracking and heat transfer representations and to a casting-specific adaptation of the turbulence model to account for an advancing solid front. Calculations have been performed for a 0.4m long turbine blade cast in a titanium aluminide alloy using different mould designs. It is shown that the feeder/basin configuration has a crucial influence on the casting quality. The computational results are validated against actual castings and are used to support an experimental programme. Although fluid flow and heat transfer are inseparable in a casting, the emphasis in this paper will be on the fluid dynamics of mould filling and its influence on cast quality rather than heat transfer and solidification which has been reported elsewhere.Keywords Tilt-casting; Mould design; 3-D computational model; Casting process；1. IntroductionThe casting process is already many centuries old, yet many researchers are still devoted to its study. Net shape casting is very attractive from the cost point of view compared to alternative component manufacturing methods such as forging or machining. However, reproducible quality is still an issue; the elimination of defects and control of microstructure drive research. Casting involves first the filling of the mould and subsequently the solidification of the melt. From the numerical modelling point of view, this simple sequence results in a very complex three-phase problem to simulate. A range of interactions of physical phenomena are involved including free surface fluid flow as the mould fills, heterogeneous heat transfer from the metal to the mould, solidification of the molten metal as it cools, and the development of residual stresses and deformation of the solidified component.In industry there are many variants of the casting process such as sand casting, investment casting, gravity, and low and high pressure die casting. In this study, the investment casting process, also called lost-wax casting, has been investigated. One of the advantages of this process is that it is capable of producing (near) net shape parts, which is particularly important for geometrically complex and difficult-to-machine components. This process starts with making a ceramic mould which involves three main steps: injecting wax into a die to make a replica of the component and attaching this to a pouring basin and running system; building a ceramic shell by the application of several layers of a ceramic slurry and ceramic stucco to the wax assembly; de-waxing and mould firing. The pouring of the casting is performed either simply under gravity (no control), or using a rapid centrifugal action 1 (danger of macro-segregation plus highly turbulent filling), or by suction as in counter-gravity casting (e.g. the Hitchiner process2), or by tilt-casting. In this study, tilt-casting was chosen in an attempt to achieve tranquil mould filling. Tilt-casting was patented in 1919 by Durville 3 and has been successfully used with sand castings4 and aluminium die castings5. In the IMPRESS project 6, a novel process has been proposed and successfully developed to combine Induction Skull Melting (ISM) of reactive alloys with tilt-casting7, 8, 9and10, with a particular application to the production of turbine blades in titanium aluminide alloys. As shown in Fig. 1, this is carried out inside a vacuum chamber and the mould is pre-heated in situ to avoid misruns (incomplete mould filling due to premature solidification) and mould cracking due to thermal shock.Tilt-casting process: (a) experimental equipment; (b) schematic view of the ISM crucible and mould, showing the domed shape acquired by the molten metal; (c) different stages of mould filling showing the progressive replacement of gas by the metal.The component(s) to be cast are attached to a pouring basin which also doubles as a source of metal to feed the solidification shrinkage. The components are angled on the basin to promote the progressive uni-directional flow of metal into the mould. As the metal enters the mould it displaces the gas and an escape route has to be included in the design so that the two counter-flowing streams are not mixed leading to bubbles trapped in the metal. Vents are also used to enable any trapped gas to escape. The feeder used to connect the mould to the crucible is normally in any casting the last portion of metal to solidify, so supplying metal to the mould to counter the effects of solidification shrinkage. In tilt-casting, the feeder is also the conduit for the tranquil flow of metal into the mould and also for the unhindered escape of gas. For this reason, the fluid dynamics of the mould feeder interface merit detailed study.As well as the mould/feeder design, the production of castings involves several other key parameters, such as the metal pouring temperature, initial mould temperature, selective mould insulation and the tilt cycle timing. All these parameters have an influence on the eventual quality of the casting leading to a very large matrix of experiments. Modelling (once validated) is crucial in reducing the amount of physical experiments required. As mentioned above, the mathematical models are complex due to the fact that this is a three-phase problem with two rapidly developing phase fronts (liquid/gas and solid/liquid). In this paper, a 3-D computational model is used to simulate the tilt-casting process and to investigate the effect of the design of the basin/feeder on the flow dynamics during mould filling and eventually on casting quality.2. Experimental descriptionDetails of the experimental setup have been published elsewhere 11, but for completeness a summary description is given here. Fig. 1a shows an overall view of the equipment used to perform the casting. The Induction Skull Melting (ISM) copper crucible is installed inside a vacuum chamber. To enable rotation, it is attached to a co-axial power feed, which also allows cooling water containing ethylene glycol to be supplied to the ISM crucible and the induction coil. The coil supplies a maximum of 8kA at a frequency of 6kHz. The crucible wall is segmented, so that the induction field penetrates through the slots (by inducing eddy currents into each finger segment) to melt the charge and at the same time repel the liquid metal away from the side wall to minimise the loss of superheat. A billet of TiAl alloy is loaded into the crucible before clamping on the ceramic shell mould. The mould is surrounded by a low thermal mass split-mould heater. After evacuating the vacuum chamber, the mould is heated to the required temperature (1200C maximum) and the vessel back-filled with argon to a partial pressure of 20kPa prior to melting. This pressure significantly reduces the evaporative loss of the volatile aluminium contained in the alloy. The power applied to the induction coil is increased according to a pre-determined power vs. time schedule so that a reproducible final metal temperature is achieved. At the end of melting (78min), the mould heater is opened and moved away. The induction melting power is ramped down and, simultaneously, the ISM crucible and mould are rotated by 180 using a programmable controller to transfer the metal into the mould. The mould containing the casting is held vertically as the metal solidifies and cools down.3. Mathematical model3.1. Fluid flow equationsThe modelling of the castingprocess has involved a number of complex computational techniques since there are a range of physical interactions to account for: free surface fluid flow, turbulence, heat transfer and solidification, and so on. The fluid flow dynamics of the molten metal and the gas filling the rest of the space are governed by the NavierStokes equations, and a 3D model is used to solve the incompressible time-dependent flow: (1)(2)where u is the fluid velocity vector; is the density; is the fluid viscosity; Su is a source term which contains body forces (such as gravitational force, a resistive force (Darcy term) 12) and the influence of boundaries. There is a sharp, rapidly evolving, property interface separating metal and gas regions in these equations as explained below. 3.2. Free surface: counter diffusion method (CDM)One of the difficulties of the simulation arises from the fact that two fluid media are present during filling: liquid metal and resident gas and their density ratio is as high as 10,000:1. Not only does the fluid flow problem need to be solved over the domain, but the model also has to track the evolution of the interface of the two media with time. A scalar fluid marker was introduced to represent the metal volume fraction in a control volume and used to track the interface of the two fluids, called the Scalar Equation Algorithm (SEA) by Pericleous et al. 14. In a gas cell, =0; in a metal cell, =1; for a partially filled cell takes on an intermediate value which the interface of the two media crosses through. The dynamics of the interface are governed by the advection equation: (3)The interface then represents a moving property discontinuity in the domain, which has to be handled carefully to avoid numerical smearing. As in 14, an accurate explicit time stepping scheme such as that by Van Leer 15 may be used to prevent smearing. However, the scheme is then limited to extremely small time steps for stability, leading to very lengthy computations. To overcome this problem, a new tracking method, the counter diffusion method (CDM) 11and16, was developed as a corrective mechanism to counter this numerical diffusion. This discretizes the free surface equation in a stable, fully implicit scheme which makes the computations an order of magnitude faster. The implementation assumes that an interface-normal counter diffusion flux can be defined for each internal face of the computational mesh and applied with opposite signs to elements straddling the interface as source terms for the marker variable. The equation for the flux per unit area F can be written as: (4)where C is a scaling factor, a free parameter in CDM allowing the strength of the counter diffusion action to be adjusted, and n is the unit normal vector to the face in the mesh. Of the two cells either side of the face, the one with the lower value of the marker D becomes the donor cell while the richer cell A is the acceptor (in order to achieve the counter diffusion action). The proposed formula makes the counter diffusion action self-limiting as it is reduced to zero where the donor approaches zero (gas) and where the acceptor reaches unity (liquid). In this form, the adjustment remains conservative. Quantitative validation of CDM against other VOF type techniques is given in a later section of the paper for accuracy and efficiency. 3.3. Heat transfer and solidificationHeat transfer takes place between the metal, mould and gas, and between cold and hot metal regions as the mould filling is carried out. The heat flow is computed by a transient energy conservation equation: (5)where T is the temperature; k is the thermal conductivity; cp is the specific heat (properties can be functions of the local temperature or other variables); ST is the source term which represents viscous dissipation, boundary heat transfer and latent heat contributions when a phase change occurs. For the latter, a new marker variable fL is used to represent the liquid fraction of the metal with (1fL) being the volume fraction of solidified metal. Voller et al. 13 used a non-linear temperature function to calculate the liquid fraction. In this study, the liquid fraction is assumed to be a linear function of the metal temperature: (6)TL is the liquidus temperature and TS is the solidus temperature. 3.4. LVEL turbulence model (applied to solid moving boundaries)Even at low filling speeds, the Reynolds number is such that the flow is turbulent. The LVEL method of Spalding 17 is chosen to compute the turbulence because of its mixing-length simplicity and robustness. LVEL is an abbreviation of a distance from the nearest wall (L) and the local velocity (VEL). The approximate wall distance is solved by the Eqs. (7)and(8): (7)(W)=-1where W is an auxiliary variable in the regions occupied by the moving fluid with boundary conditions W=0 on all solid walls. (8)This distance and the local velocity are used in the calculation of the local Reynolds number from which the local value of the turbulent viscosity t is obtained using a universal non-dimensional velocity profile away from the wall. The effective turbulent viscosity is then computed from the following equation: (9)where =0.417 is the von Karman constant, E=8.6 is the logarithmic law constant 17 and u+ is determined implicitly from the local Reynolds number Reloc=uL/ with the magnitude of the local velocity u and the laminar kinematic viscosity 17. The LVEL method was extended to moving solid boundaries and in particular to solidifying regions by setting W=0 in every region that is no longer fluid and then solving Eqs. (7)and(8) at each time step. In simulating the tilt-casting process, the geometry is kept stationary and the gravitational force vector is rotated to numerically model the tilt instead of varying the coordinates of the geometry. The rotating gravitational force vector appears in the source term of Eq. (1) for the tilt-casting process. A mathematical expression relating the tilting speed to the tilting angle has been used. Since is a function of time, the variable rotation speed is adjustable to achieve tranquil filling. This technique neglects rotational forces within the fluid (centrifugal, Coriolis) since they are negligible at the slow rotation rates encountered in tilt-casting. Finally, the numerical model of the tilt-casting process and the new algorithm developments were implemented in the general CFD package (PHYSICA).4. Description of simulations4.1. Geometry, mould design and computational meshThe casting is a generic 0.4m-long turbine blade typical of that used in an Industrial Gas Turbine. Fig. 2 shows three mould designs which comprise the blade, a feeder/basin and a cylindrical crucible. Fig. 2a incorporates a separate cube-shaped feeder that partially links the root of the blade and the basin. Fig. 2b is a variant in which the plane of the blade is rotated through 90. In both cases, the computational mesh contains 31,535 elements and 38,718 points. Six vents are located on the platform and the shroud of the blade, as seen in Fig. 2a and b. Fig. 2c is an optimised design where the feeder and basin are combined to provide a smooth connection between the blade and the crucible. Two vents are located in the last areas to be filled to help entrapped gas to escape from the mould.Mesh of the crucible-mould assembly for the three cases investigated.The mesh for the last case contains 30,185 elements and 37,680 vertices. As in all the cases presented, numerical accuracy depends on mesh fineness and also the degree of orthogonality. To ensure a mostly orthogonal mesh the various components of the assembly were created separately using a structured body-fitted mesh generator and then joined using a mixture of hexahedral and tetrahedral cells. The mesh was refined as necessary in thin sections (such as the blade itself or the shroud and base plates), but not necessarily to be fine enough to resolve boundary layer details. For this reason the LVEL turbulence model was used rather than a more usual two-equation model of turbulence that relies on accurate wall function representation. The practical necessity to run in parallel with the experimental programme also limited the size of the mesh used. As with all free surface tracking algorithms, the minimum cell size determines the time step size for the stable simulations. Although the CDM method is implicit, allowing the time step to exceed the cell CFL limit, accuracy is then affected. With these restrictions, turnaround time for a complete tilt-casting cycle was possible within 24h.As stated earlier, the feeder is necessary to minimise the solidification shrinkage porosity in the blade root. Two alternative designs have been considered: a cubic feeder with a volume to cooling surface area ratio of 14.5mm, and a cylindrical feeder designed with better consideration of fluid dynamics during mould filling and which had a slightly lower volume to area ratio of 13.8mm.4.2. Initial and boundary conditionsThe choice of parameters for the calculations was based on the experiments 16. The properties of the materials used in the calculations are listed in Table 1. The initial conditions (the same as in the trials) and boundary conditions of the calculations are shown in Table 2.Table 1.Properties of the materials in this study.Ti46Al8Ta alloyMouldDensity (kg/m3)50002200Thermal conductivity (W/(mK)21.61.6Specific heat (J/(kgK)10001000Viscosity (kg/(ms)0.51060.1Liquidus temperature (C)1612Solidus temperature (C)1537Latent heat (J/kg)355,000100,0004.3. Tilt cycleThe molten metal in the ISM crucible is poured via the basin/feeder into the mould by rotating the assembly. A parabolic programmed cycle 16 is employed to complete the castingprocess with a total filling time of 6s. The carefully designed cycle includes a fast rotation speed at the early stage of the mould filling to transfer the molten metal into the basin/feeder, a subsequent deceleration to a nearly zero velocity to allow most of the metal to fill the mould horizontally and to avoid forming a back wave and surface turbulence, and then the rapid completion of the filling to reduce the heat loss to the mould wall.5. Computing requirementsThe results presented here have been obtained using an Inter (R) Xeon (R) CPU E5520 2.27GHz, 23.9GB of RAM. For a typical mesh of 30,000 finite volume cells, each full tilt-casting simulation (real time 6s) took approximately 15h and 1200time steps to complete. The CDM algorithm uses a fixed time step of 0.005s which is a