NUMERICAL SIMULATION OF CELLULAR/DENDRITIC PRIMARY SPACING

A numerical model has been established to calculate the primary spacing of cellular or dendritic structure with fluid flow considered. The computing results show that the primary spacing depends on the growing velocity, the temperature gradient on the interface and fluid flow. There is a critical growing velocity for the cell-dendrite transition, which has a relationship with the temperature gradient: Rcr = (3-4)×10-9GT. Fluid flow leads to an increase of the primary spacing for dendritic growth but a decrease for cellular growth, resulting in an instability on the interface.

Evaluation of Well Spacing for Primary Development of Fractured Horizontal Wells in Tight Sandstone Gas Reservoirs

Methods for horizontal well spacing calculation in tight gas reservoirs are still adversely affected by the complexity of related control factors,such as strong reservoir heterogeneity and seepage mechanisms.In this study,the stress sensitivity and threshold pressure gradient of various types of reservoirs are quantitatively evaluated through reservoir seepage experiments.On the basis of these experiments,a numerical simulation model(based on the special seepage mechanism)and an inverse dynamic reserve algorithm(with different equivalent drainage areas)were developed.The well spacing ranges of Classes I,II,and III wells in the Q gas field are determined to be 802–1,000,600–662,and 285–400 m,respectively,with their average ranges as 901,631,and 342.5 m,respectively.By considering both the pairs of parallel well groups and series well groups as examples,the reliability of the calculation results is verified.It is shown that the combination of the two models can reduce errors and provide accurate results.

Effect of melt convection on primary dendrite arm spacing in directionally solidified Pb-26%Bi hypo-peritectic alloys

Primary dendrite arm spacing（PDAS） of α phase in directionally solidified Pb-26%Bi（mass fraction） hypo-peritectic alloys was measured by considering the effect of melt convection in cylindrical samples with different diameters.The experimental results show the measured PDAS increases with increasing diameter of the sample.At the growth velocity of 5 μm/s,its value changes from 161.5 μm for the sample with 1.8 mm in diameter to 240.4 μm for the sample with 7 mm in diameter.The strong melt convection in large diameter samples causes a high bulk alloy composition and a high concentration gradient in peritectic β phase,resulting in a larger PDAS.Simultaneously,the high concentration gradient could effectively promote the peritectic transformation,enhancing the dissolution of the thin α dendrite.

Influence of directional solidification variables on primary dendrite arm spacing of Ni-based superalloy DZ125

The primary dendrite morphology and spacing of DZ125 superalloy have been observed during directional solidification under high thermal gradient about 500 K/cm. The results reveal that the primary dendrite arm spacing decreases from 94 μm to 35.8 μm with the increase of directional solidification cooling rate from 2.525 K/s to 36.4 K/s. The regression equation of the primary dendrite arm spacings A, versus cooling rate is λ1=0.013（GV）-0.32. The predictions of Kurz/Fisher model and Hunt/Lu model accord reasonably well with the experimental data. The influence of directional solidification rate under variable thermal gradient on the primary dendrite arm spacing has also been investigated.

History-dependent Selection of Primary Dendritic Spacing in Directionally Solidified Alloy

Directional solidification experiments were carried out for succinonitrile-1.0 wt pct acetone alloy with the orientation of dendritic arrays being not parallel to the direction of the temperature gradient. Experimental results show that there exists an allowable range of primary dendritic spacing under a given growth condition.The average primary spacing depends not only on the current growth conditions but also on the way by which the conditions were achieved. The upper limit of the allowable range becomes smaller in comparison with that with 〈001〉 direction of dendrite arrays parallel to the direction of the temperature gradient, which means that the history-dependence of dendritic growth is weaker under this condition. The lower limit obtained is compared with a self-consistent model, which shows a good agreement with experimental results.

Correlation Between Process Parameter and Primary Dendrite Arm Spacing in Laser Welding of Cu and Al

A combined numerical model of thermal field and the primary dendrite arm spacing （PDAS） was proposed to correlate the process parameters and PDAS in laser welding of Cu and A1. The solidification parameters simulated by the finite volume method with commercial software ANASYS FLUENT were applied in the PDAS model to predict the dendrite arm spacing of fusion zone. Dendrite was also examined by the metallographic method to validate the model. Results indicate that the calculated PDAS agrees with metallographic measurements reasonably, especially the Hunt model. PDAS increases apparently with increasing laser power while decreases slightly with increasing welding speed. Increasing laser power increases the secondary dendrite and increasing welding speed increases the microporosity in dendrite.

The Worlds on the Other Side of the Big Bang

Taking the Big Bang as an established fact, the question inevitably arises about what exactly caused it, in what environment could it have happened and what happened before it. The developed approach allows us to shed light on many raised questions and to establish what universal laws and structures formed what happened before the Big Bang, to understand its cause and the dynamic processes that led to it. This required a radical revision of many views, giving them a new meaning and content. This approach has led to a consistent and conceptually new understanding of these phenomena, which allowed correctly formulate questions to which there are still no clear answers. Based on this formulation of the problem, we came to new ideas about the nature of Dark energy, Dark matter and the region of their birth, formulated and described the mechanism of the formation of worlds and their hierarchy on the other side of the Big Bang and the mechanism of this explosion itself. The Primary Parent Particle was introduced into the concept, which was the basis of everything and is the carrier of the fundamental Primary space introduced by us, which had at least two phase states. This particle consists of Beginnings united in the form of Borromeo rings. This made it possible to calculate the structure and primary spectrum of elementary particles that arose on the other side of the Big Bang, the mechanisms of their formation and the resulting fundamental interactions that lead to the existence of vortices before the Big Bang;the mechanisms of the birth of multiple universes and much more are also considered. The concept of the “cosmic genetic code" is introduced, the characteristics and mechanism of its formation before the Big Bang are presented.

INTERFACE MORPHOLOGIES AND MICROSTRUCTURES DURING DENDRITE-TO-CELL TRANSITION AT HIGH GROWTH RATE

The interface morphologies and microstruetures of the directionally solidified Ni-5wt-% Cu alloy during dendrite-to-cell transition at high growth rates have been investigated with a newly developed apparatus for unidirectional solidification with the temperature gradient at the solid/liquid interface higher than 1000 K/cm.The results show that in the vicinity of dendrite-to-cell transition point,the well developed sidebranches become shrivelled with the increase of growth rate and disappear at the dendrite-to-cell transition,and the primary spacing decreases simultaneously.Moreover,the length of mushy zone decreases greatly dur- ing the dendrite-to-cell transition.Cells obtained at high growth rates have very similar morphologies to those at low growth rates,but with much smaller cell spacings and unsmoothed cell walls which may be attributed to the different stability conditions of the cell walls at low and high growth rates respectively.

Directional Solidification of Cu-Cr Alloy

The directional solidification of Cu0.8 wt%Cr alloy was investigated. An nonequilibrium microstructure with the primary α(Cu) dendrites and the [α(Cu)+β(Cr)] eutectics is formed during the directionally solidifying process, when the temperature gradient ahead of the S/L interface is 30℃/cm, and the growth velocities are 3 μm/s and 30 μm/s respectively. The arm spacing of the primary αcrystals is increased with the increase of the growth rate, which is not consistent with the KurzFisher model but with the Hunt model at low velocity. The growth conditions of a fibrelike chromium phase are also discussed.

Prediction of Primary Dendrite Arm Spacing in Pulsed Laser Surface Melted Single Crystal Superalloy

Primary dendritic arm spacing(PDAS)is an important microstructure feature of the nickel-base single crystal superalloys.In this paper,a numerical model predicting the PDAS evolution with additive manufacturing parameters using pulsed laser is established,which combines the theoretical PDAS models with the temperature field calculation model during pulsed laser process.Based on this model,processing maps that related process parameters to the evolution of PDAS are generated.To obtain more accurate prediction model,the parameters of different solidification conditions,G^(-0.5)V^(-0.25) and G^(-0.5)V^(-0.25),are selected to calculate PDAS.The simulation results show that the PDAS increases as the arise of P and t.The processmgPDAS map can accurately predict the evolution of PDAS with pulsed laser process parameters,which is well in accordance with the experimental results.Additionally,the PDAS values calculated by the G^(-0.5)V^(-0.25) are more in line with the experimental results than those calculated by the G^(-0.5)V^(-0.25).

Effect of abruptly changing withdrawal rate on solidification microstructure in directionally solidified Al-4.5wt%Cu alloy

Al-4.5wt.%Cu alloy has been directionally solidified at constant and abruptly changing withdrawal rates, respectively. The effects of the withdrawal rate on solidification microstructure, primary dendrite arm spacing(PDAS) and liquid solute distribution in front of the solid-liquid interface were investigated. The experimental results for the PDAS at a constant withdrawal rate agree well with the values calculated by the Hunt, Trivedi and Hunt-Lu models. At an abrupt change in the withdrawal rate, the maximum to minimum ratio of the PDAS at a given solidification parameter, i.e. λ1max/λ1min, is more than 2, and the PDAS values are remarkably history-dependent. Further, the liquid-solute distribution curve based on theoretical calculation shows that the larger the initial withdrawal rate is, the smaller the minimum of liquid solute concentration in front of the solid-liquid interface is after the abrupt change in withdrawal rate.

Effect of Process Parameters on Defects,Melt Pool Shape,Microstructure,and Tensile Behavior of 316L Stainless Steel Produced by Selective Laser Melting

Previous studies have revealed that laser power and energy density are significant factors affecting the quality of parts manufactured by selective laser melting(SLM).The normalized equivalent density E_(0)^(*) and dimensionless laser power q^(*),which can be regarded as a progress on the understanding of the corresponding dimensional quantities,are adopted in this study to examine the defects,melt pool shape,and primary dendrite spacing of the SLM-manufactured 316 L stainless steel,because it reflects the combined effect of process parameters and material features.It is found that the number of large defects decreases with increasing E_(0)^(*) due to enough heat input during the SLM process,but it will show an increasing trend when excessive heat input(i.e.,utilizing a high E_(0)^(*))is imported into the powder bed.The q^(*) plays an important role in controlling maximum temperature rising in the SLM process,and in turn,it affects the number of large defects.A large q^(*) value results in a low value of absolute frequency of large defects,whereas a maximum value of absolute frequency of large defects is achieved at a low q^(*) even if E_(0)^(*) is very high.The density of the built parts is greater at a higher q^(*) when E_(0)^(*)remains constant.Increasing the melt pool depth at relatively low value of E_(0)^(*) enhances the relative density of the parts.A narrow,deep melt pool can be easily generated at a high q^(*) when E_(0)^(*) is sumciently high,but it may increase melt pool instability and cause keyhole defects.It is revealed that a low E_(0)^(*) can lead to a high cooling rate,which results in a refined primary dendrite spacing.Relatively low E_(0)^(*) is emphasized in selecting the process parameters for the tensile test sample fabrication.It shows that excellent tensile properties,namely ultimate tensile strength,yield strength,and elongation to failure of 773 MPa,584 MPa,and 46%,respectively,can be achieved at a relatively low E_(0)^(*) without heat treatment.

Microstructure Evolution and Growth Orientation of Directionally Solidified Mg–4 wt% Zn Alloy with Different Growth Rates

The microstructure evolution and growth orientation of directionally solidified Mg-4 wt% Zn alloy in the growth rate range from 20 to 200μm/s were investigated. A typical cellular structure was observed with a growth rate of 20 μm/s, and the cellular spacing was 115 μm. When the growth rate increased to 60 μm/s, cellular structure with some developed perturbations was obtained and the cellular spacing was 145 μm, suggesting that the cell-to-dendrite transition happened at the growth rate lower than 60 μm/s. As the growth rate further increased, the microstructure was dendritic and the primary dendritic arm spacing decreased. The relationship between the primary dendritic arm spacings and the growth rates was in good agreement with Trivedi model during dendritic growth. Besides, X-ray diffraction and transmission electron microscopy analyses showed that the growth direction of directionally solidified Mg-4 wt% Zn alloy was （1120） lay in {0002} crystal plane, and the preferred orientation was explained with the lattice vibration model for one-dimensional monatomic chain.

Microstructure and Stress-Rupture Property of Large-Scale Complex Nickel-Based Single Crystal Casting

The microstructure and stress-rupture property of the large-scale complex single crystal（SX） casting DD10 were investigated in high-rate solidification process. It is found that the primary dendrite arm spacing（PDAS） does not increase monotonically with the height increase. When across the platform, the temperature gradient increases due to the effect of platform, and the corresponding PDAS decreases. The distribution of eutectic volume fraction in large-scale complex SX casting is affected by PDAS, solid back diffusion, and the development of high order dendrites. The eutectic volume fraction contained in the sample taken below the platform decreases with the height increase. While the eutectic volume fraction contained in the sample taken upper the platform increases gradually with the height increase. After heat treatment,most of the γ/γ＇ eutectics are eliminated and the components are distributed uniformly. The similar stress rupture properties of the samples at different heights in the same direction are obtained.