Numerical simulation on directional solidification and heat treatment processes of turbine blades

Study on turbine blades is crucial due to their critical role in ensuring the efficient and reliable operation of aircraft engines.Nickel-based single crystal superalloys are extensively used in the hot manufacturing of turbine blades due to their exceptional high-temperature mechanical properties.The hot manufacturing of single crystal blades involves directional solidification and heat treatment.Experimental manufacturing of these blades is time-consuming,capital-intensive,and often insufficient to meet industrial demands.Numerical simulation techniques have gained widespread acceptance in blade manufacturing research due to their low energy consumption,high efficiency,and rapid turnaround time.This article introduces the modeling and simulation of hot manufacturing in single crystal blades.The discussion outlines the prevalent mathematical models employed in numerical simulations related to blade hot manufacturing.It encapsulates the advancements in research concerning macro to micro-level numerical simulation techniques for directional solidification and heat treatment processes.Furthermore,potential future trajectories for the numerical simulation of single crystal blade hot manufacturing are also discussed.

NUMERICAL SIMULATIONS OF TEMPERATURE FIELD IN DIRECT METAL LASER SINTERING PROCESS

A mathematical model is developed for simulating the heat transferring behavior in a direct metal laser sintering process. The model considers the thermal phenomena involved in the process, including conduction, radiation, and convection. A formula for the calculation of the heat conductivity of a sintering system containing solid phase, liquid phase, and gas phase is given. Due to the continuous movement of the laser beam, a local coordinate system centered on the laser beam is used to simplify the analytical calculation. Assuming that it is approximately a Gaussian laser beam, the heat conduction equation is resolved based on the assumption of the thermal insulating boundary conditions and the fixed thermal physical parameters. The FORTRAN language is employed to compile the program to simulate the temperature field in the direct copper powder sintering process. It shows a good agreement with the preliminary experimental results.[KH3/4D]

Phase-field simulation of forced flow effect on random preferred growth direction of multiple grains

The random distribution problem of dendrite preferred growth direction was settled by random grid method.This method was used to study the influence of forced laminar flow effect on multiple grains during solidification.Taking high pure succinonitrile （SCN） undercooled melt as an example,the forced laminar flow effect on multiple grains was studied by phase-field model of single grain which coupled with flow equations at non-isothermal condition.The simulation results show that the random grid method can reasonably settle the problem of random distribution and is more effective.When the solid fraction is relatively low,melt particles flow around the downstream side of dendrite,and the flow velocity between two dendrite arms becomes high.At the stage of solidification time less than 1800Δt,every dendrite grows freely;the upstream dendrites are stronger than the downstream ones.The higher the melt flow rate,the higher the solid fraction.However,when the solid fraction is relatively high,the dendrite arm intertwins and only a little residual melt which is not encapsulated can flow;the solid fraction will gradually tend to equal to solid fraction of melt without flow.

DIRECT NUMERICAL SIMULATION OF VIBRATIONINDUCED T-S WAVE ON BOUNDARY LAYER WALL

The spatial growth of the disturbance in the boundary layer is directly numerically simulated, and the receptivity of the Blasius basic flow to the local two-dimensional （2-D） sustainable micro-vibration is investigated. Results show that the disturbance velocity presents the sine vibration features with the change of time, and the vibration period is identical to the vibration of the local wall. The disturbance velocity presents the fluctuation feature downstream, and the streamwise wave length approximates to the results from the Orr-Sommerfeld equation （OSE）. The growth rate from direct numerical simulation（DNS） is a little greater than that from OSE, and their trends are almost consistent. Under the condition of Re= 2 800, the disturbance amplitude gradually grows in the given computational region with the period T=30. However, it firstly increases and then decreases with the period T= 20. The disturbance harmonic of the former is obviously larger than that of the latter. The maximum streamwise and vertical disturbance velocities from DNS do not fully coincide with those from OSE at the vicinity of the local vibration wall, but coincide well with the former when they travel downstream. The 2-D disturbance induced by the local micro-vibration represents the form of Tollmien-Schlichting （T-S） wave on the boundary layer.

Numerical simulation on sand sedimentation and erosion characteristics around HDPE sheet sand barrier under different wind angles

For the safety of railroad operations,sand barriers are utilized to mitigate wind-sand disaster effects.These disasters,characterized by multi-directional wind patterns,result in diverse angles among the barriers.In this study,using numerical simulations,we examined the behavior of High Density Polyethylene(HDPE)sheet sand barriers under different wind angles,focusing on flow field distribution,windproof efficiency,and sedimentation erosion dynamics.This study discovered that at a steady wind speed,airflow velocity varies as the angle between the airflow and the HDPE barrier changes.Specifically,a 90°angle results in the widest low-speed airflow area on the barrier’s downwind side.If the airflow is not perpendicular to the barrier,it prompts a lateral airflow movement which decreases as the angle expands.The windproof efficiency correlates directly with this angle but inversely with the wind’s speed.Notably,with a wind angle of 90°,wind speed drops by 81%.The minimum wind speed is found at 5.1H(the sand barrier height)on the barrier’s downwind side.As the angle grows,the barrier’s windproof efficiency improves,extending its protective reach.Sedimentation is most prominent on the barrier’s downwind side,as the wind angle shifts from 30°to 90°,the sand sedimentation area on the barrier’s downwind side enlarges by 14.8H.As the angle grows,sedimentation intensifies,eventually overtakes the forward erosion and enlarges the sedimentation area.

Direct numerical simulation of compressible turbulent flows

This paper reviews the authors＇ recent studies on compressible turbulence by using direct numerical simulation （DNS）,including DNS of isotropic（decaying） turbulence, turbulent mixing-layer,turbulent boundary-layer and shock/boundary-layer interaction.Turbulence statistics, compressibility effects,turbulent kinetic energy budget and coherent structures are studied based on the DNS data.The mechanism of sound source in turbulent flows is also analyzed. It shows that DNS is a powerful tool for the mechanistic study of compressible turbulence.

Numerical Simulation of Multi-track and Multi-layer Temperature Field on Laser Direct Metal Shaping

To improve the mechanical properties of the parts fabricated by Laser Direct Metal Shaping(LDMS),it is of great significance to understand the distribution regularities of transient temperature field during LDMS process.Based on the“el- ement birth and death”technique of finite element method,a three-dimensional multi-track and multi-layer model for the transient temperature field analysis of LDMS is developed by ANSYS Parametric Design Language(APDL)for the first time.In the fab- ricated modal,X-direction parallel reciprocating scanning paths is introduced.Using the same process parameters,the simulation results show good agreement with the microstructure features of samples which fabricated by LDMS.

An enhanced image binarization method incorporating with Monte-Carlo simulation

We proposed an enhanced image binarization method.The proposed solution incorporates Monte-Carlo simulation into the local thresholding method to address the essential issues with respect to complex background,spatially-changed illumination,and uncertainties of block size in traditional method.The proposed method first partitions the image into square blocks that reflect local characteristics of the image.After image partitioning,each block is binarized using Otsu’s thresholding method.To minimize the influence of the block size and the boundary effect,we incorporate Monte-Carlo simulation into the binarization algorithm.Iterative calculation with varying block sizes during Monte-Carlo simulation generates a probability map,which illustrates the probability of each pixel classified as foreground.By setting a probability threshold,and separating foreground and background of the source image,the final binary image can be obtained.The described method has been tested by benchmark tests.Results demonstrate that the proposed method performs well in dealing with the complex background and illumination condition.

Experimental Study and Numerical Simulation of Directionally Solidified Turbine Blade Casting

The directional solidification process of turbine blade sample castings was investigated in the work. Variable withdrawal rates were used in one withdrawal process and compared with the other using uniform rate. A mathematical model for heat radiation transfer and microstructure simulation of directional solidification process was developed based on CA-FD method. The temperature distribution and microstructure w.ere simulated and compared with the experimental results. The stray grains were predicted and compared with the experimental results. The uneven temperature distribution of platform was the main reason of the formation of stray grains.

Numerical simulation of dendrite growth in Ni-based superalloy casting during directional solidification process

An understanding of dendrite growth is required in order to improve the properties of castings. For this reason, cellular automaton-finite difference(CA-FD) method was used to investigate the dendrite growth during directional solidification(DS)process. The solute diffusion model combined with macro temperature field model was established for predicting the dendrite growth behavior. Model validation was performed by the DS experiment, and the cooling curves and grain structures obtained by the experiment presented a reasonable agreement with the simulation results. The competitive growth of dendrites was also simulated by the proposed model, and the competitive behavior of dendrites with different misalignment angles was also discussed in detail.Subsequently, 3D dendrites growth was also investigated by experiment and simulation, and both were in good accordance. The influence on dendrites growth of initial nucleus was investigated by three simulation cases, and the results showed that the initial nuclei just had an effect on the initial growth stage of columnar dendrites, but had little influence on the final dendritic morphology and the primary dendrite arm spacing.

Direct numerical simulation of turbulent boundary layer over an anisotropic compliant wall

Direct numerical simulation of a spatially developing turbulent boundary layer over a compliant wall with anisotropic wall material properties is performed. The Reynolds number varies from 300 to approximately 860 along the streamwise direction, based on the external flow velocity and the momentum thickness. Eight typical cases are selected for numerical investigation under the guidance of the monoharmonic analysis. The instantaneous flow fields exhibit the traveling wavy motion of the compliant wall, and the frequency-wavenumber power spectrum of wall pressure fluctuation is computed to quantify the mutual influence of the wall compliance and the turbulent flow at different wave numbers. It is shown that the Reynolds shear stress and the pressure fluctuation are generally enhanced by the wall compliance with the parameters considered in the present study. A dynamical decomposition of the skin-friction coefficient is derived, and a new term (CW) appears due to the wall-induced Reynolds shear stress. The influence of the anisotropic compliant wall motion on the turbulent boundary layer through the wall-induced negative Reynolds shear stress is discussed. To elucidate the underlying mechanism, the budget analysis of the Reynolds stresses transportation is further carried out. The impact of the wall compliance on the turbulent flow is disclosed by examining the variations of the diffusion and velocity-pressure correlation terms. It is shown that increase of the Reynolds stresses inside the flow domain is caused by enhancement of the velocity-pressure correlation term, possibly through the long-range influence of the wall compliance on the pressure field, rather than diffusion of the wall-induced Reynolds shear stress into the fluid flow.

AN ANALYSIS OF SUBGRID-RESOLVED SCALE INTERACTIONS WITH USE OF RESULTS FROM DIRECT NUMERICAL SIMULATIONS

Subgrid nonlinear interaction and energy transfer are analyzed using direct numerical simulations of isotropic turbulence. Influences of cutoff wave number at different ranges of scale on the energetics and dynamics have been investigated. It is observed that subgrid-subgrid interaction dominates the turbulent dynamics when cut-off wave number locates in the energy-containing range while resolved-subgrid interaction dominates if it is in the dissipation range. By decomposing the subgrid energy transfer and nonlinear interaction into ‘forward’ and ‘backward’ groups according to the sign of triadic interaction, we find that individually each group has very large contribution, but the net of them is much smaller, implying that tremendous cancellation happens between these two groups.

Satellite-based RAR performance simulation for measuring directional ocean wave spectrum based on SAR inversion spectrum

Some missions have been carried out to measure wave directional spectrum by synthetic aperture radar （SAR） and airborne real aperture radar （RAR） at a low incidence.Both them have their own advantages and limitations.Scientists hope that SAR and satellite-based RAR can complement each other for the research on wave properties in the future.For this study,the authors aim to simulate the satellite-based RAR system to validate performance for measuring the directional wave spectrum.The principal measurements are introduced and the simulation methods based on the one developed by Hauser are adopted and slightly modified.To enhance the authenticity of input spectrum and the wave spectrum measuring consistency for SAR and satellite-based RAR,the wave height spectrum inversed from Envisat ASAR data by cross spectrum technology is used as the input spectrum of the simulation system.In the process of simulation,the sea surface,backscattering signal,modulation spectrum and the estimated wave height spectrum are simulated in each look direction.Directional wave spectrum are measured based on the simulated observations from 0 ？ to 360 ？ .From the estimated wave spectrum,it has an 180 ？ ambiguity like SAR,but it has no special high wave number cut off in all the direction.Finally,the estimated spectrum is compared with the input one in terms of the dominant wave wavelength,direction and SWH and the results are promising.The simulation shows that satellite-based RAR should be capable of measuring the directional wave properties.Moreover,it indicates satellite-based RAR basically can measure waves that SAR can measure.

Direct Numerical Simulation of Particle Dispersion in Gas-Solid Compressible Turbulent Jets

A numerical method was developed to directly simulate the compressible, particle-laden turbulent jets.The fourth order compact finite difference schemes were used to discretize the space derivatives. The Lagrangian method was adopted to simulate the particle motion based on one-way coupling. It is found that the turbulent intensity profiles attain self-similar status in the jet downstream regions. At the Stokes number of 1, particles are concentrated largely in the outer boundaries of the large-scale vortex structures with the most uneven distribution and the widest dispersion in the lateral direction. Particles at the much smaller Stokes numbers are distributed evenly in the flow field, and the lateral dispersion is also considerable. Distribution of particles at much larger Stokes numbers is more uniform and the lateral dispersion becomes small. In addition, the inflow conditions have different effects on the particle dispersion. The direct numerical simulation (DNS) results accord with the previous experiments and numerical studies.

Multiscale modelling and simulation of single crystal superalloy turbine blade casting during directional solidification process

As the key parts of an aero-engine,single crystal(SX)superalloy turbine blades have been the focus of much attention.However,casting defects often occur during the manufacturing process of the SX turbine blades.Modeling and simulation technology can help to optimize the manufacturing process of SX blades.Multiscale coupled models were proposed and used to simulate the physical phenomena occurring during the directional solidification(DS)process.Coupled with heat transfer(macroscale)and grain growth(meso-scale),3D dendritic grain growth was calculated to show the competitive grain growth at micro-scale.SX grain selection behavior was studied by the simulation and experiments.The results show that the geometrical structure and technical parameters had strong influences on the grain selection effectiveness.Based on the coupled models,heat transfer,grain growth and microstructure evolution of a complex hollow SX blade were simulated.Both the simulated and experimental results show that the stray grain occurred at the platform of the SX blade when a constant withdrawal rate was used in manufacturing process.In order to avoid the formation of the stray crystal,the multi-scale coupled models and the withdrawal rate optimized technique were applied to the same SX turbine blade.The modeling results indicated that the optimized variable withdrawal rate can achieve SX blade castings with no stray grains,which was also proved by the experiments.

Analysis of typhoon wind hazard in Shenzhen City by Monte-Carlo Simulation

As one of the most serious natural disasters,many typhoons affect southeastern China every year.Taking Shenzhen,a coastal city in southeast China as an example,we employed a Monte-Carlo simulation to generate a large number of virtual typhoons for wind hazard analysis.By analyzing 67-year historical typhoons data from 1949 to 2015 using the Best Track Dataset for Tropical Cyclones over the Western North Pacific recorded by the Shanghai Typhoon Institute,China Meteorological Administration(CMASTI),typhoon characteristic parameters were extracted and optimal statistical distributions established for the parameters in relation to Shenzhen.We employed the Monte-Carlo method to sample each distribution to generate the characteristic parameters of virtual typhoons.In addition,the Yah Meng(YM)wind field model was introduced,and the sensitivity of the YM model to several parameters discussed.Using the YM wind field model,extreme wind speeds were extracted from the virtual typhoons.The extreme wind speeds for different return periods were predicted and compared with the current structural code to provide improved wind load information for wind-resistant structural design.

Direct numerical simulation of viscoelastic-fluid-based nanofluid turbulent channel flow with heat transfer

Our previous experimental studies have confirmed that viscoelastic-fluid-based nanofluid(VFBN) prepared by suspending nanoparticles in a viscoelastic base fluid(VBF, behaves drag reduction at turbulent flow state) can reduce turbulent flow resistance as compared with water and enhance heat transfer as compared with VBF. Direct numerical simulation(DNS) is performed in this study to explore the mechanisms of heat transfer enhancement(HTE) and flow drag reduction(DR) for the VFBN turbulent flow. The Giesekus model is used as the constitutive equation for VFBN. Our previously proposed thermal dispersion model is adopted to take into account the thermal dispersion effects of nanoparticles in the VFBN turbulent flow. The DNS results show similar behaviors for flow resistance and heat transfer to those obtained in our previous experiments. Detailed analyses are conducted for the turbulent velocity, temperature, and conformation fields obtained by DNSs for different fluid cases, and for the friction factor with viscous, turbulent, and elastic contributions and heat transfer rate with conductive, turbulent and thermal dispersion contributions of nanoparticles, respectively. The mechanisms of HTE and DR of VFBN turbulent flows are then discussed. Based on analogy theory, the ratios of Chilton–Colburn factor to friction factor for different fluid flow cases are investigated, which from another aspect show the significant enhancement in heat transfer performance for some cases of water-based nanofluid and VFBN turbulent flows.

Numerical simulation on the influence of plant root morphology on shear strength in the sandy soil,Northwest China

Serious riverbank erosion,caused by scouring and soil siltation on the bank slope in the lower reaches of the Tarim River,Northwest China urgently requires a solution.Plant roots play an important role in enhancing soil shear strength on the slopes to maintain slope soils,but the extent of enhancement of soil shear strength by different root distribution patterns is unclear.The study used a combination of indoor experiments and numerical simulation to investigate the effects of varying plant root morphologies on the shear strength of the sandy soil in the Tarim River.The results showed that:(1)by counting the root morphology of dominant vegetation on the bank slope,we summarized the root morphology of dominant vegetation along the coast as vertical,horizontal,and claw type;(2)the shear strength of root-soil composites(RSCs)was significantly higher than that of remolded soil,and the presence of root system made the strain-softening of soil body significantly weakened so that RSCs had better mechanical properties;and(3)compared with the lateral roots,the average particle contact degree of vertical root system was higher,and the transition zone of shear strength was more prominent.Hence,vegetation with vertical root system had the best effect on soil protection and slope fixation.The results of this study have important guiding significance for prevention and control of soil erosion in the Tarim River basin,the restoration of riparian ecosystems,and the planning of water conservancy projects.

Application and development of numerical simulation for under- ground horizontal directional drilling

In coalmines of China, horizontal directional drilling （HDD） is an increasingly popular method for underground in-seam gas drainage. Numerical simulation, especially finite element analysis, is often used as an effective method to improve HDD operation. These improvements focus on rock-breaking efficiency, directional precision, stability of the borehole wall, and reliability of the drill equipment. On the basis of underground drilling characteristics, typical numerical simulation exam- ples in drilling techniques and equipment are summarized and analyzed. In the end, the future development trends of numerical simulation in underground in-seam drilling are proposed.

Prediction of hot tearing susceptibility of direct chill casting of AA6111 alloys via finite element simulations

To predict hot tearing susceptibility(HTS)during solidification and improve the quality of Al alloy castings,constitutive equations for AA6111 alloys were developed using a direct finite element(FE)method.A hot tearing model was established for direct chill(DC)casting of industrial AA6111 alloys via coupling FE model and hot tearing criterion.By applying this model to real manufacture processes,the effects of casting speed,bottom cooling,secondary cooling,and geometric variations on the HTS were revealed.The results show that the HTS of the billet increases as the speed and billet radius increase,while it reduces as the interfacial heat transfer coefficient at the bottom or secondary water-cooling rate increases.This model shows the capabilities of incorporating maximum pore fraction in simulating hot tearing initiation,which will have a significant impact on optimizing casting conditions and chemistry for minimizing HTS and thus controlling the casting quality.