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.

Investigations on High-Speed Flash Boiling Atomization of Fuel Based on Numerical Simulations

Flash boiling atomization(FBA)is a promising approach for enhancing spray atomization,which can generate a fine and more evenly distributed spray by increasing the fuel injection temperature or reducing the ambient pressure.However,when the outlet speed of the nozzle exceeds 400 m/s,investigating high-speed flash boiling atomization(HFBA)becomes quite challenging.This difficulty arises fromthe involvement ofmany complex physical processes and the requirement for a very fine mesh in numerical simulations.In this study,an HFBA model for gasoline direct injection(GDI)is established.This model incorporates primary and secondary atomization,as well as vaporization and boilingmodels,to describe the development process of the flash boiling spray.Compared to lowspeed FBA,these physical processes significantly impact HFBA.In this model,the Eulerian description is utilized for modeling the gas,and the Lagrangian description is applied to model the droplets,which effectively captures the movement of the droplets and avoids excessive mesh in the Eulerian coordinates.Under various conditions,numerical solutions of the Sauter mean diameter(SMD)for GDI show good agreement with experimental data,validating the proposed model’s performance.Simulations based on this HFBA model investigate the influences of fuel injection temperature and ambient pressure on the atomization process.Numerical analyses of the velocity field,temperature field,vapor mass fraction distribution,particle size distribution,and spray penetration length under different superheat degrees reveal that high injection temperature or low ambient pressure significantly affects the formation of small and dispersed droplet distribution.This effect is conducive to the refinement of spray particles and enhances atomization.

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]

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.

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.

Three-Dimensional Direct Numerical Simulation of Flow past A Near-Wall Circular Cylinder:Combined Effects of Gap Ratio and Boundary Layer Thickness on Flow Profiles and Pressure Distribution

Three-dimensional direct numerical simulations of the wake flow downstream of a near-wall circular cylinder at different gap ratios and boundary layer thicknesses are carried out by using the iterative immersed boundary method.The non-dimensional gap between the cylinder and the wall,G/D=0.2,0.6 and 1.0,the non-dimensional boundary layer thickness,δ/D=0.0,0.7 and 1.6,the Reynolds number,Re=350,and the aspect ratio of the cylinder,L/D=25are adopted.High-resolution visualizations of the complex vortex structures at differentδ/D and G/D are presented.The transition of the streamwise vortex mode,the combined effects ofδ/D and G/D on the flow statistics,the pressure and shear stress distribution and the hydrodynamic forces are analyzed.Results show that with decreasing G/D and increasingδ/D,the gap flow and its vortex-shedding are significantly weakened,together with an elongated wake and an enlarged low-velocity area near the wall,leading to the wake mode transition from the two-sided to one-sided vortex-shedding.Different relative positions of the cylinder regarding the boundary layer alter the flow features of the shear layers.With an increase inδ/D,the front stagnation point shifts to the upper surface,and the distance between the flow divergence point and the maximum pressure position increases.The mean drag coefficient and r.m.s.values of drag and lift coefficients decrease with a decrease in G/D and an increase inδ/D,while the mean lift coefficient increases with decreasing G/D but decreases with increasingδ/D.

Parallelization strategies for resolved simulations of fluid-structure-particle interactions

Fluid-structure-particle interactions in three spatial dimensions happen in many environmental and engineering flows.This paper presents the parallel algorithms for the hybrid diffuse and sharp interface immersed boundary(IB)method developed in our previous work.For the moving structure modeled using the sharp interface IB method,a recursive box method is developed for efficiently classifying the background grid nodes.For the particles modeled using the diffuse interface IB method,a‘master-slave’approach is adopted.For the particle-particle interaction(PPI)and particle-structure interaction(PSI),a fast algorithm for classifying the active and inactive Lagrangian points,which discretize the particle surface,is developed for the‘dry’contact approach.The results show that the proposed recursive box method can reduce the classifying time from 52seconds to 0.3 seconds.Acceptable parallel efficiency is obtained for cases with different particle concentrations.Furthermore,the lubrication model is utilized when a particle approaches a wall,enabling an accurate simulation of the rebounding phenomena in the benchmark particle-wall collision problem.At last,the capability of the proposed computational framework is demonstrated by simulating particle-laden turbulent channel flows with rough walls.

Numerical Modeling of Mass Transfer in the Interaction between River Biofilm and a Turbulent Boundary Layer

In this article dedicated to the modeling of vertical mass transfers between the biofilm and the bulk flow, we have, in the first instance, presented the methodology used, followed by the presentation of various results obtained through analyses conducted on velocity fields, different fluxes, and overall transfer coefficients. Due to numerical constraints (resolution of relevant spatial scales), we have restricted the analysis to low Schmidt numbers (Sc=0.1, Sc=1, and Sc=10) and a single roughness Reynolds number (Re*=150). The analysis of instantaneous concentration fields from various simulations revealed logarithmic concentration profiles above the canopy. In this zone, the concentration is relatively homogeneous for longer times. The analysis of results also showed that the contribution of molecular diffusion to the total flux depends on the Schmidt number. This contribution is negligible for Schmidt numbers Sc≥0.1, but nearly balances the turbulent flux for Sc=0.1. In the canopy, the local Sherwood number, given by the ratio of the total flux (within or above the canopy) to the molecular diffusion flux at the wall, also depends on the Schmidt number and varies significantly between the canopy and the region above. The exchange velocity, a purely hydrodynamic parameter, is independent of the Schmidt number and is on the order of 10% of in the present case. This study also reveals that nutrient absorption by organisms near the wall depends on the Schmidt number. Such absorption is facilitated by lower Schmidt numbers.

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.

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.

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.

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.

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.

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.

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.

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.

Direct numerical simulation study of the interaction between the polymer effect and velocity gradient tensor in decaying homogeneous isotropic turbulence

Direct numerical simulation of decaying homogeneous isotropic turbulence （DHIT） of a polymer solution is performed. In order to understand the polymer effect on turbulence or additive-turbulence interaction, we directly investigate the influence of polymers on velocity gradient tensor including vorticity and strain. By visualizing vortex tubes and sheets, we observe a remarkable inhibition of vortex structures in an intermediate-scale field and a small-scale field but not for a large scale field in DHIT with polymers. The geometric study indicates a strong relevance among the vorticity vector, rate-of-strain tensor, and polymer conformation tensor. Joint probability density functions show that the polymer effect can increase ＂strain generation resistance＂ and ＂vorticity generation resistance＂, i.e., inhibit the generation of vortex sheets and tubes, ultimately leading to turbulence inhibition effects.

Rotational dynamics of bottom-heavy rods in turbulence from experiments and numerical simulations

We successfully perform the three-dimensional tracking in a turbulent fluid flow of small axisymmetrical particles that are neutrally-buoyant and bottom-heavy,i.e.,they have a non-homogeneous mass distribu-tion along their symmetry axis.We experimentally show how a tiny mass inhomogeneity can affect the particle orientation along the preferred vertical direction and modify its tumbling rate.The experiment is complemented by a series of simulations based on realistic Navier-Stokes turbulence and on a point-like particle model that is capable to explore the full range of parameter space characterized by the gravi-tational torque stability number and by the particle aspect ratio.We propose a theoretical perturbative prediction valid in the high bottom-heaviness regime that agrees well with the observed preferential ori-entation and tumbling rate of the particles.We also show that the heavy-tail shape of the probability distribution function of the tumbling rate is weakly affected by the bottom-heaviness of the particles.

Validation of the RANS-SOM Combustion Model Using Direct Numerical Simulation of Incompressible Turbulent Reacting Flows

The second-order moment combustion model, proposed by the authors is validated using the direct numerical simulation （DNS） of incompressible turbulent reacting channel flows. The instantaneous DNS results show the near-wall strip structures of concentration and temperature fluctuations. The DNS statistical results give the budget of the terms in the correlation equations, showing that the production and dissipation terms are most important. The DNS statistical data are used to validate the closure model in RANS second-order moment （SOM） combustion model. It is found that the simulated diffusion and production terms are in agreement with the DNS data in most flow regions, except in the near-wall region, where the near-wall modification should be made, and the closure model for the dissipation term needs further improvement. The algebraic second-order moment （ASOM） combustion model is well validated by DNS.