Simulation of jet-flow solid fraction during spray forming

Transcription

1 International Journal of Minerals, Metallurgy an Materials Volume 24, Number 6, June 2017, Page 657 DOI: /s Simulation of jet-flow soli fraction uring spray forming Zi-qiang Pi 1), Xin Lu 1), Yuan Wu 2), Lu-ning Wang 1), Cheng-chang Jia 1), Xuan-hui Qu 1), Wei Zheng 3), Li-zhi Wu 3), an Qing-li Shao 3) 1) Institute for Avance Materials an Technology, University of Science an Technology Beijing, Beijing , China 2) State Key Laboratory for Avance Metals an Materials, University of Science an Technology Beijing, Beijing , China 3) Heye Special Steel Co., Lt., Shijiazhuang , China (Receive: 1 November 2016; revise: 20 January 2017; accepte: 15 February 2017) Abstract: A numerical moel was evelope to simulate the jet-flow soli fraction of W18Cr4V high-spee steel uring spray forming. The whole moel comprises two submoels: one is an iniviual roplet moel, which escribes the motion an thermal behaviors of iniviual roplets on the basis of Newton s laws of motion an the convection heat transfer mechanism; the other is a roplet istribution moel, which is use to calculate the roplet size istribution. After being verifie, the moel was use to analyze the effects of parameters, incluing the initial gas velocity, eposition istance, superheat egree, an the ratio of gas-to-metal mass flow rates, on the jet-flow soli fraction. Finally, an equation to preict the jet-flow soli fraction irectly an conveniently accoring to the parameters was presente. The values preicte by the equation show goo agreement with those calculate by the numerical moel. Keywors: moeling; steel; spray forming; soli fraction 1. Introuction As a novel rapi soliification an near-net-shape technique, spray forming has various avantages, such as elimination of macrosegregation compare to casting technology an fewer process steps compare to conventional power metallurgy. As a result, spray forming has receive tremenous attention in the materials manufacturing fiel. Mesquita an Barbosa [1] reporte that spray-forme AISI M3:2 high-spee steel has a finer an more uniform microstructure an greater isotropy than conventionally cast steel. Schulz et al. [2] reporte that laboratory-scale spray-forme high-alloy steels were competitive with conventional proucts in terms of toughness an strength. Zhang et al. [3] observe that, in the case of spray-forme T15 high-spee steel, M 6 C an MC carbies were spherically refine an uniformly istribute after thermomechanical processing. In recent years, spray forming has been wiely use to esign an prepare various high-performance alloys. For instance, FGH95 superalloy [4], AA7050 alloy [5], Al 50Si (wt%) alloy [6], an Cu 11.85Al 3.2Ni 3Mn (wt%) shape memory alloy [7] exhibit fine an uniform microstructures as well as goo mechanical properties when prepare by spray forming. During the spray-forming process, the surface soli fraction of the eposite preform is a key factor etermining the properties an qualities of the proucts. In the case of an excessively high soli fraction, high ensity of the eposite preform can harly be achieve; by contrast, the spray yiel will be reuce in the case of a low soli fraction. However, the surface soli faction of the eposit is very ifficult to measure irectly. Given that the surface soli fraction is etermine by the roplets cooling process, an iniviual roplet s soli fraction an the istribution of the roplet size are usually combine an simulate to reflect the surface fraction. Thus far, research on the simulation technology of spray forming has le to substantial avancements. Grant et al. [8] establishe an iniviual roplet moel to investigate the motion an thermal history of a roplet. Using this moel, the influential parameters for spray forming, incluing the roplet size istribution, initial axial gas velocity, melt mass flow rate, melt superheat, an the alloy Corresponing author: Xin Lu, luxin@ustb.eu.cn; Xuan-hui Qu, quxh@ustb.eu.cn. The Author(s) This article is publishe with open access at link.springer.com

2 658 Int. J. Miner. Metall. Mater., Vol. 24, No. 6, Jun composition, were investigate [9]. On the basis of the results of these investigations, Grant an Cantor [10] analyze complex equations to give an approximate expression for the spray soli fraction as a function of process parameters. Mi an Grant [11 12] later moifie the moel an presente a companion moel to simulate the heat flow an soliification of Ni superalloy rings uring spray forming. Cai an Lavernia [13 14] evelope a porosity moel base on roplet thermal history, particle-packing theory, an flow mechanics to estimate the porosity in a eposite IN718 alloy billet. Kang an Chang [15] establishe a theoretical moel to preict the shape of the billet an the effects of the most ominant processing conitions. In aition, Hattel et al. [16] evelope an integrate moel to preict the shape of a Gaussian or a billet eposit. Cui an Schulz [17] evelope a shape moel for cla eposits. Mi et al. [18] evelope an integrate, multiphysics numerical moel that consiste of an atomization moel, a roplet spray moel, a roplet eposition moel, an a porosity moel. Jiang et al. [19] reviewe the physical moels an avance methos use in simulations of gas liqui two-phase jet flows uring atomization an spray processes. A gas jet superposition moel, couple with a series of newly evelope numerical-parameter-inepenent submoels, incluing the raius-of-influence collision moel, mean collision time moel, an the polar interpolation moel, was propose by Gao et al. [20] for computing group-hole nozzle sprays. In another work, Du an Wei [21] establishe a 3D numerical moel of flow an heat-transfer to analyze the appropriate forming conitions. However, few simulation stuies concerning spray-forme high-spee steel have been reporte. Therefore, the previous simulation results cannot be irectly applie to the spray forming of high-spee steels. Aitionally, few of the previously reporte simulation results have been verifie in an inustrial prouction process. In this paper, the motion an heat-transfer mechanisms of W18Cr4V high-spee steel roplets uring spray forming were investigate an the optimal prouction parameters were iscusse. 2. Moel establishment 2.1. Gas motion an cooling behaviors The scheme of the spray-forming process is shown in Fig. 1. The axial gas velocity shows an exponential ecay with increasing istance an can be escribe as g gi exp Z v = v (1) λv where v g is the gas velocity, v gi is the gas velocity at the exit from the atomizer or the initial gas velocity, Z is the eposition istance, an v n 0 gi λ = av is the exponential ecay coefficient, where a 0 = m 0.24 s 1.24 an n=1.24 [8]. Fig. 1. Live-action (a) an schematic (b) of the spray-forming process. The gas temperature T g increases exponentially from an initial temperature T gi = 25 C at the atomizer exit to a final temperature T gf = 75 C on the surface of the eposite preform [8]: Z Tg = Tgf ( Tgf Tgi) exp λt where λ T is a constant an equals 0.1 m. (2) 2.2. Droplet motion an cooling behaviors Droplet motion behaviors Droplets were consiere to be essentially stationary. A rag force, which results from the ifference in velocity between the roplets an the atomizing gas, can cause the roplets to accelerate or ecelerate. The acceleration of the roplets is expresse on the basis of Newton s secon law [22]:

3 Z.Q. Pi et al., Simulation of jet-flow soli fraction uring spray forming 659 ( ) v ρ 3 g ρ C v v v v = 1 g+ t ρ 4ρ g D g g where ρ an v are the roplet ensity an roplet velocity, respectively, ρ g an v g are the gas ensity an velocity, respectively, t is roplet flight time, g is the acceleration of gravity, is the roplet iameter, an C D is the rag coefficient, which can be obtaine by 6 21 CD = Re + Re (4) where Re = (ρ g v v g )/μ g is the Reynols number (0.1 Re 4000) an μ g is the gas viscosity Droplet cooling behaviors The typical W18Cr4V roplet cooling process comprises four stages. First, the molten roplets cool. Because of a lack of heterogeneous nucleation sites, roplets cool rapily below the alloy liquius temperature T 1 from the initial roplet temperature T i = T 1 + ΔT until reaching the nucleation temperature T n, where ΔT is the superheat egree. Thus, the supercoole roplets gain sufficient energy for nucleation. In this stage, the roplet temperature is calculate by ( Tg) T 6hT = (5) t C ρ l where T an C are the temperature an specific heat of iniviual roplets, respectively, ρ 1 is the ensity of the melt metal, T g is the temperature of gas, an h is the heat-transfer coefficient, which is given by ( ) kg Re Pr h = (6) where k g is the thermal conuctivity of gas, Pr = C g μ g /k g is the Prantl number of gas, an C g is the specific heat of gas. Secon, nucleation an recoalescence occur. At the beginning of nucleation, the high unercooling egree, which provies a strong riving force, leas to rapi nucleation. During the nucleation, the latent heat is release within an extremely short perio. As a consequence, the roplet temperature rapily increases to the liquius temperature. The frequency of heterogeneous nucleation is escribe as Eq. (7) [23]: ( θ) 40 16π I = 10 exp 3kT H T 3 2 σsltl F B ρδ f Δ where σ SL is the interfacial energy between the soli an the liqui interface, θ is the wetting angle of a nucleus on the wheel surface, ΔT is the unercooling egree, k B is the Boltzmann constant, an ΔH f is the latent heat per unit mass. The catalytic efficiency of heterogeneous nucleation F(θ) is (3) (7) given by [8] 1 3 a2 F( θ) = ( 2 3cos θ + cos θ) = a1 + (8) 4 where a 1 = an a 2 = μm [24 25]. The roplet soli fraction f = ΔT C 1 /ΔH f, where C 1 is specific heat of the melt metal. Thir, the phase transition occurs. After recoalescence, the unercooling egree of roplets ecreases; hence, the soliification rate slows. When the latent heat cannot affor the heat loss through convection, the roplet temperature ecreases again. Until the melting point T m is reache, the equivalent specific heat C equ = C + ΔH f /(T 1 T m ) is use to replace the latent heat; thus, the roplet temperature can be escribe as ( Tg) T 6hT = (9) t ρcequ The change of the roplet soli fraction in phase transition can be calculate by the Scheil equation: f Tm T = 1 Tm Tl 1 k 1 0 (10) where k 0 is the equilibrium partition coefficient. Fourth, the soli roplets cool. Soliification is complete when the melting temperature T m is reache, then the full soli-state roplets continue cooling. The temperature can be escribe by T t ( Tg) 6hT = (11) ρ C 2.3. Jet-flow soli fraction The jet-flow soli fraction f s is calculate by combining the iniviual roplets soli fraction an the roplet size istribution. s 0 ( ) f = P f( )ln (12) i i where P( i ) is the roplet probability ensity with iameter i an is given by Eq. (13) [26]: 1 ( ln ) 2 i ln 50 P( i ) = exp (13) 2 2π lnσ 2ln σ where σ = ( 50 /13) 1/3 is the geometric stanar eviation an 50 is the average iameter, which can be calculate by Eq. (14), as propose by Lubanska [27]. κ σ 1 = D β 1+ κ R m m 50 2 gvd g (14) where D is the iameter of the molten metal nozzle, β is a

4 660 Int. J. Miner. Metall. Mater., Vol. 24, No. 6, Jun constant an equals 40, κ m is the kinematic viscosity of the molten metal, κ g is the kinematic viscosity of the gas, R is the ratio of gas-to-metal mass flow rates, an σ m is the surface tension of the molten metal. 3. Results an iscussion 3.1. Motion an thermal behaviors of iniviual roplets The values of thermophysical properties of N 2 atomizing gas an W18Cr4V high-spee steel use in the calculation are liste in Table 1. The velocities, heat-transfer coefficients, temperatures, an soli fractions of iniviual roplets are calculate from the moel escribe in the paper; the results are shown in Figs. 2 5 for roplet sizes of 20 to 200 μm, an initial gas velocity of 300 m/s, a eposition istance of 0.5 m, a superheat egree of 100 K, an a ratio of gas-to-metal mass flow rates of As shown in Fig. 2, the roplet velocity with ifferent iameters increases rapily to a maximum value an then ecreases graually. The roplet velocity is strongly affecte by the roplet iameter. The smaller roplets show sharp acceleration or eceleration; however, the larger ones graually accelerate an ecelerate slowly ue to their larger inertia. For instance, roplets with a iameter of 20 μm reach the maximum velocity of 205 m/s at a istance of 0.13 m, whereas the 130-μm ones reach the maximum velocity of 110 m/s at a istance of 0.34 m. Table 1. Thermophysical properties of N 2 atomizing gas an W18Cr4V high-spee steel Nitrogen gas [23] ρ g = kg m 3 μ g = Pa s k g = W m 1 K 1 C g = J kg 1 K 1 W18Cr4V ρ = 8700 kg m 3 ρ 1 = 8100 kg m 3 C = J kg 1 K 1 C 1 = J kg 1 K 1 T m = K T 1 = K ΔH f = 242 J kg 1 σ SL = 1.5 J m 2 Fig. 2. Single roplet motion behavior (v gi = 300 m/s, ΔT = 100 K, R = 0.55): (a) change of a single roplet velocity vs. eposition istance; (b) velocity istribution of a single roplet in the jet flow. Fig. 3 shows the heat-transfer coefficient as a function of eposition istance. The initial heat-transfer coefficients of all the roplets are extremely high because of the large relative velocity between the roplets an the

5 Z.Q. Pi et al., Simulation of jet-flow soli fraction uring spray forming 661 gas. The gas then accelerates the roplets sharply, which reuces the relative velocity; as a consequence, the heat-transfer coefficients ecrease rapily. When the roplet velocity is equal to the gas velocity, the heat-transfer coefficients momentarily ecrease to a minimum value. Subsequently, the heat-transfer coefficients again increase because the ecay of the gas velocity increases the relative velocity between the roplets an the gas molecules. Fig. 4 shows roplet temperature as a function of eposition istance. Four ifferent cooling stages are observe, incluing rapi cooling of the melt roplets, nucleation an recoalescence, phase transition, an cooling of the soli roplets. The 20-μm roplets are clearly observe to unergo four cooling stages. Because smaller roplets favor higher cooling rates, the smaller roplets nucleate at a shorter istance an have a lower temperature when they reach the eposition surface. Fig. 3. Heat-transfer coefficient of a single roplet varying with eposition istance (v gi = 300 m/s, ΔT = 100 K, R = 0.55). Fig. 4. Single roplet thermal behavior (v gi = 300 m/s, ΔT = 100 K, R = 0.55): (a) temperature of a single roplet varying with eposition istance; (b) temperature istributions of a single roplet in the jet flow. Fig. 5 shows the soli fraction of iniviual roplets as a function of eposition istance. This figure shows that the roplet soli fraction ecreases with increasing roplet iameter. At a certain eposition istance of 0.5 m, roplets with a iameter of 20 μm are fully soliifie, whereas roplets with a iameter of 50 μm or greater are semisoli. Aitionally, with ecreasing roplet iameter, the cooling rate increases; as a result, the istance require for nucleation an recoalescence ecreases an the soli fraction achieve uring nucleation an recoalescence increases.

6 662 Int. J. Miner. Metall. Mater., Vol. 24, No. 6, Jun Motion an thermal behaviors of jet flow Fig. 5. Variation of the soli fraction of a single roplet as a function of eposition istance (v gi = 300 m/s, ΔT =100 K, R = 0.55). The jet-flow soli fraction was calculate by combining the soli fraction of iniviual roplets an the roplet size istribution. The effects of initial gas velocity, eposition istance, superheat, an the ratio of gas-to-metal mass flow rates were investigate. Fig. 6 shows the heat transfer coefficient, velocity, flight time, temperature, an soli fraction of 80-μm roplets as a function of the eposition istance, with the same superheat egree of 100 K an the same ratio of gas-to-metal mass flow rate of 0.55, but with an initial gas velocity increasing from 250 to 350 m/s. Fig. 6. Variations of the parameters of roplets with ifferent initial velocities of gas: (a) heat transfer coefficient; (b) velocity; (c) time; () temperature; (e) size istribution of roplets; (f) soli fraction.

7 Z.Q. Pi et al., Simulation of jet-flow soli fraction uring spray forming 663 As epicte in Fig. 6(a), the heat transfer coefficient increases with increasing initial gas velocity. Moreover, for roplets with a larger initial gas velocity, the point where the heat transfer coefficient ecreases to the minimum value is farther from the nozzle than the corresponing point for roplets with a smaller initial gas velocity; the mean heat transfer coefficient is also eviently larger. The acceleration of roplets epens on the gas; therefore, a larger initial gas velocity results in a larger roplet velocity, as shown in Fig. 6(b). Aitionally, we observe that the relative velocity between roplets an gas ecreases to 0 m/s at a point an then increases. For roplets with a larger initial gas velocity, the 0 m/s point is farther from the nozzle than the corresponing points for roplets with a smaller initial gas velocity. Compare with Fig. 6(a), the relative velocity an the heat transfer coefficient have a similar variation tren because the latter has a positive relationship with the former, as shown in Eq. (5). Fig. 6(c) shows the flight time as a function of eposition istance. This figure clearly shows that the increase in initial gas velocity will shorten the roplet flight time. For example, the flight time over a 0.5-m eposition istance ecreases from to s when the initial gas velocity increases from 250 to 350 m/s. The roplet temperature is etermine by its cooling rate an time. We conclue that the mean heat transfer coefficient increases with increasing gas velocity, as shown in Fig. 6(a). Consequently, the cooling rate also increases. However, roplets will require less time to reach the surface of the eposit, as shown in Fig. 6(c). The result of these two antagonistic factors is that the roplet temperature with a larger initial gas velocity is slightly higher compare to that with a lower initial gas velocity; consequently, the soli fraction of roplets is smaller, as shown in Figs. 6() an 6(f), respectively. Fig. 6(e) shows that the increase in gas velocity causes an increase in the percentage of smaller roplets because the gas has more energy to atomize the molten metal better. On the basis of the analysis for the parameters how to affect the soli fraction of iniviual roplets, the variations in jet-flow soli fraction as functions of the parameters were investigate. Fig. 7(a) shows the variation of jet-flow soli fraction with the eposition istances of 0.4, 0.5, an 0.6 m in the range of initial gas velocities from 200 to 400 m/s at 50 m/s intervals, a gas-to-metal mass flow rate ratio of 0.55, an a superheat egree of 100 K. The jet-flow soli fraction increases linearly with increasing initial gas velocity. This behavior is attributable to two aspects: (1) a ecrease in soli Fig. 7. Variations of the jet-flow soli fraction with ifferent parameters: (a) initial gas velocity; (b) ratio of gas-to-metal mass flow rates; (c) superheat egree.

8 664 Int. J. Miner. Metall. Mater., Vol. 24, No. 6, Jun fraction of iniviual roplets, as shown in Fig. 3(f), which ecreases the jet-flow soli fraction, an (2) a narrower particle size istribution, which has the opposite effect of the first aspect. However, the secon aspect has a greater influence; therefore, when the initial gas velocity increases, the jet-flow soli fraction also increases. Fig. 7(b) shows a soli fraction of jet flow as a function of the ratio of the gas-to-metal mass flow rate from 0.35 to 0.75, with eposition istances of 0.4, 0.5, an 0.6 m, with an initial gas velocity of 300 m/s, an with a superheat egree of 100 K. When the ratio increases, the roplet size istribution becomes narrower because of the gas having more power to atomize the liqui metal to smaller roplets. Accoringly, the soli fraction of jet flow increases. Fig. 7(c) shows the jet-flow soli fraction as a function of superheat egree from 50 to 250 K, with eposition istances of 0.4, 0.5, an 0.6 m, an initial gas velocity of 300 m/s, an a gas-to-metal mass flow rate ratio of We conclue that the jet-flow soli fraction ecreases with increasing superheat egree because each iniviual roplet contains more heat compare to those with a lower superheat egree at the same eposition istance. To verify the moel, an infrare thermometer was use to measure the surface temperature of the preform uring spray forming, with an initial gas velocity of 300 m/s, a gas-to-metal mass flow rate ratio of 0.55, eposition istances of 0.4, 0.5, an 0.6 m, an a superheat egree of 100 K. As exhibite in Figs. 8(a) 8(c), the values calculate by the numerical moel are certainly consistent with the measure values; thus, the correctness of the numerical moel has been emonstrate. Fig. 8. Comparison between the calculate an the measure values of the preform surface temperature: (a) Z = 0.4 m; (b) Z = 0.5 m; (c) Z = 0.6 m Preiction of the jet-flow soli fraction During a sufficiently short perio of time Δt, the spray process can be ivie into three steps, as shown in Fig. 9. First, the alloy is melte. Secon, the molten alloy is atomize into tiny roplets. Thir, the roplets crash into the substrate an the billet are forme. In the entire process, the molten alloy has the same weight m = MΔt but ifferent temperatures as the newly forme billet, where m is the weight of the alloy epositing on the substrate uring the perio of time Δt an M is the mass flow rate of the molten alloy. Thus, as shown by steps 1 to 3 in Fig. 9, the change in heat of the newly eposite alloy Q 1 can be calculate on the basis of the thermal physical properties of the metals as Q = MΔtCΔ T + MΔtΔ H f + MΔtC ( T T ) (15) 1 l f s l surface where T surface an f s are the average temperature an the soli fraction of the jet flow on the surface of the billet, respectively.

9 Z.Q. Pi et al., Simulation of jet-flow soli fraction uring spray forming 665 Fig. 9. Sketch of the three steps of the spray forming process uring a very short time. Further analysis reveals that the ifferent temperatures of molten metals an the newly forme billet are mainly cause by Q 2, which is the heat issipation of roplets. Therefore, Q 2 can be calculate by accumulating the heat issipation of each single roplet as ( Tg) 6mh i T Q2 = ρ + Δt 6hT ( Tg) = M Δ t P( ) ln 0 i t = MΔtQ 0 ρ m (16) where Q m is the heat release by the jet flow per unit mass an m ( T) + Δt 6hT 0 i 0 ρ g = ( ) ln (17) Q P t Apparently, Q 1 = Q 2 ; thus, Qm = ClΔ T +Δ Hf fs + C ( Tl Tsurface) (18) Q m is calculate accoring to the numerical moel in this paper with a wie range of parameters; etails of the analysis are shown in Figs Specifically, Fig. 10 shows the variation in Q m as a function of v 0.22 gi over the range 200 v gi 400 m/s at 50-m/s intervals, with ifferent eposition istances Z, an with gas-to-metal mass flow rate ratios R. The best-fit line is 0.22 Q = kv (19) m gi where k is the slope of the best-fit line. The values of k an R-square were calculate; the results are liste in Table 2. The minimum R-square value of means that the points agree well with the best-fit lines. Fig. 11 shows the variation in Q m as a function of R 19 over the range of 0.35 R 0.75 at 0.1 intervals, with v gi = 250, 300, an 350 m/s an Z = 0.4, 0.5, an 0.6 m. Also, the best-fit lines were calculate an plotte. Qm 0.19 = kr (20) where the value of k an R-square are liste in Table 3. The points show reasonable agreement with the best-fit lines. Fig. 10. Variations in Q m as a function of v 0.22 gi. Table 2. Slopes an R-square values of the best-fit lines for the variation of jet-flow heat per unit mass Q m with the initial gas velocity v gi Z / m R k R-square

10 666 Int. J. Miner. Metall. Mater., Vol. 24, No. 6, Jun Table 4. Slopes an R-square values for the best-fit lines for the variation of jet-flow heat per unit mass Q m with the eposition istance Z Fig. 11. Variations in Q m as a function of R Table 3. Slopes an R-square values of the best-fit lines for the variation of jet-flow heat per unit mass Q m with the gas-to-metal mass flow rate ratio R v gi / (m s 1 ) Z / m k R-square v gi / (m s 1 ) R k R-square As a consequence, a relatively simple equation can be obtaine from Eqs. (19), (20), an (21): Q = Av R Z (22) m gi where A is a constant. Substituting all the points in Figs. 5(a) 5(c) into Eq. (22) gives the best-fit value A = m 0.62 s 0.22, with an R-square value of an a stanar error of kj/kg, showing goo agreement between the preicte an calculate variations in Q m, as shown in Fig. 13. Fig. 12 shows the variation in Q m as a function of Z 0.40 over the range of 0.3 Z 0.7 m at 0.1-m intervals, with v gi = 250, 300, an 350 m/s an R = 0.45, 0.55, an In aition, the best-fit lines were also calculate an plotte in Fig. 12. Qm 0.40 = kz (21) where the value of k an R-square are liste in Table 3. The points show goo agreement with the best-fit lines. Fig. 13. Comparison between the preicte an calculate Q m values. Fig. 12. Variations in Q m as a function of Z Substituting Eq. (22) into Eq. (18) gives C Δ T +Δ H f + C ( T T ) = Av R Z (23) 1 f s 1 surface gi Accoring to the equivalent specific heat metho an heat balance, C ( T T ) +Δ H f = C ( T T ) (24) l surface f s equ l surface Substituting C equ = C + ΔH f /(T 1 T m ) into Eq. (24) gives ( Tl Tsurface) = ( Tl Tm ) fs (25) Substituting Eq. (25) into Eq. (23) gives

11 Z.Q. Pi et al., Simulation of jet-flow soli fraction uring spray forming 667 A Cl fs = vgi R Z ΔT Δ Hf + ( Tl Tm) C Δ Hf + ( Tl Tm) C (26) Assuming that A = A/[ Δ H + T T C ] (27) 1 f l ( m) ( ) A2 = Cl /[ Δ Hf + Tl Tm C] (28) then, f = Av R Z A Δ T (29) s 1 gi 2 It can be calculate by substituting the values of A, ΔH f, T 1, T m, an C into Eqs. (27) an (28) that A 1 = m 0.62 s 0.22 an A 2 = K 1. Substituting all of the points plotte in Fig. 4 into Eq. (29) gives the maximum ifference of between the f s value preicte by Eq. (29) an the f s value calculate using the moel. The main sources of the error are the assumption that the physical properties of the alloy o not change with temperature an the use of the equivalent specific heat metho. Also, the best-fit values of A 1 an A 2, m 0.62 s 0.22 an K 1, respectively, were calculate on the basis of the points in Fig. 4, with an R-square of an a stanar error of The maximum ifference between the f s value preicte by Eq. (29) an the f s value calculate by the numerical moel was reuce to , which means the preicte f s shows a goo agreement with the values calculate using the establishe numerical moel. On the basis of the heat balance in Eqs. (16) an (18), Eq. (29) buils a irect relationship between the variations of the jet-flow soli fraction an the process parameters v gi, R, Z, an ΔT, which can be use to conveniently an rapily preict the jet-flow soli fraction accoring to the process parameters. Eq. (29) can contribute to the optimization of prouction parameters. Fig. 14(a) shows the spray-forme billet with a ripple surface. Accoring to Eq. (29), the surface soli fraction was 65.83%, which is a bit lower than the optimal soli fraction of 70%. Therefore, the parameters shoul be optimize to increase the soli fraction. When the superheat egree was lowere from 150 to 100 K, the soli fraction became 71.16% accoring to Eq. (29), which is similar to the optimal value. The spray-forme billets prepare uner the optimize parameters exhibite goo shapes, as shown in Fig. 14(b). Fig. 14. Spray-forme high-spee steel billets with ifferent superheat egrees (R = 0.55, v gi = 300 m/s, an Z = 0.5 m): (a) ΔT = 150 K; (b) ΔT = 100 K. As shown in Fig. 15(a), the soli fraction was 76.51% accoring to Eq. (29), which is higher than the optimal soli fraction of 70%, which means a lack of liqui alloy for carbie precipitation. However, when the initial gas velocity Fig. 15. Microstructures of the high-spee steel billets spray-forme with ifferent initial gas velocities (R = 0.55, ΔT = 100 K, an Z = 0.5 m): (a) v gi = 400 m/s; (b) v gi = 300 m/s; (c) v gi = 200 m/s.

12 668 Int. J. Miner. Metall. Mater., Vol. 24, No. 6, Jun was change to 200 m/s, the soli fraction became 64.18% accoring to Eq. (29), which means that excessive liqui alloy not only leas to the growth of carbies, but also may result in a ripple surface, as shown in Fig. 15(c). When the initial gas velocity was change to 300 m/s, the soli fraction was 71.16% accoring to Eq. (29), which is close to the optimal value. The carbies present a thin network istribution in the billet, as shown in Fig. 15(b). In conclusion, Eq. (29) is useful in optimizing the prouction parameters by comparing the calculate soli fraction to the optimal value. When the calculate value is close to the optimal value, the billet may have goo shape an fine microstructure. 4. Conclusions The motion an cooling processes of iniviual roplets an the jet-flow soli fraction of spray-forme W18Cr4V high-spee steel were investigate using the establishe numerical moel. The following conclusions were rawn from the iscussion: (1) A numerical moel has been establishe to escribe the motion an thermal behaviors of roplets an to calculate the jet-flow soli fraction. (2) An equation to preict the jet-flow soli fraction f s accoring to process parameters, incluing the gas initial velocity v gi, gas-to-metal mass flow rate ratio R, eposition istance Z, an superheat egree ΔT, has been establishe on the basis of heat balance: f = Av R Z A Δ T s 1 gi 2, where the best-fit values are A 1 = m 0.62 s 0.22 an A 2 = K 1, with an R-square of The f s values preicte by Eq. (29) show a reasonably goo agreement with the calculate values. (3) Eq. (29) can be use to preict the jet-flow soli fraction irectly an conveniently accoring to the process parameters, which saves time an costs an will be a great ai in the manufacturing process. Acknowlegements This work was financially supporte by the National High-Tech Research an Development Program of China (No. 2012AA03A509) an the National Natural Science Founation of China (No ). Open Access This article is istribute uner the terms of the Creative Commons Attribution 4.0 International License ( which permits unrestricte use, istribution, an reprouction in any meium, provie you give appropriate creit to the original author(s) an the source, provie a link to the Creative Commons license, an inicate if changes were mae. References [1] R.A. Mesquita an C.A. Barbosa, Spray forming high spee steel properties an processing, Mater. Sci. Eng. A, 383(2004), No. 1, p. 87. [2] A. Schulz, V. Uhlenwinkel, C. Escher, R. Kohlmannc, A. Kulmburg, M.C. Monteroe, R. Rabitschf, W. Schützenhöferf, D. Stocchig, an D. Vialeh, Opportunities an challenges of spray forming high-alloye steels, Mater. Sci. Eng. A, 477(2008), No. 1-2, p. 69. [3] G.Q. Zhang, H. Yuan, D.L. Jiao, Z. Li, Y. Zhang, an Z.W. Liu, Microstructure evolution an mechanical properties of T15 high spee steel prepare by twin-atomiser spray forming an thermo-mechanical processing, Mater. Sci. Eng. A, 558(2012), p [4] Y. Xu, C.C. Ge, an Q. Shu, Microstructure, tensile properties an heat treatment process of spray forme FGH95 superalloy, J. Iron Steel Res. Int., 20(2013), No. 4, p. 59. [5] H.A. Goinho, A.L.R. Beletati, E.J. Giorano, an C. Bolfarini, Microstructure an mechanical properties of a spray forme an extrue AA7050 recycle alloy, J. Alloys Comp., 586(2014), Suppl.1, p [6] Y.D. Jia, F.Y. Cao, S. Scuino, P. Ma, H.C. Li, L. Yu, J. Eckert, an J.F. Sun, Microstructure an thermal expansion behavior of spray-eposite Al 50Si, Mater. Des., 57(2014), p [7] R.D. Cava, C. Bolfarini, C.S. Kiminami, E.M. Mazzer, W.J.B. Filho, P. Gargarella, an J. Eckert, Spray forming of Cu 11.85Al 3.2Ni 3Mn (wt%) shape memory alloy, J. Alloys Comp., 615(2014), suppl.1, p [8] P.S. Grant, B. Cantor, an L. Katgerman, Moelling of roplet ynamic an thermal histories uring spray forming: I. Iniviual roplet behaviour, Acta Metall. Mater., 41(1993), No. 11, p [9] P.S. Grant, B. Cantor, an L. Katgerman, Moelling of roplet ynamic an thermal histories uring spray forming: II. Effect of process parameters, Acta Metall. Mater., 41(1993), No. 11, p [10] P.S. Grant an B. Cantor, Moelling of roplet ynamic an thermal histories uring spray forming: III. Analysis of spray soli fraction, Acta Metall. Mater., 43(1995), No. 3, p [11] J. Mi an P.S. Grant, Moelling the shape an thermal ynamics of Ni superalloy rings uring spray forming: Part 1. Shape moeling Droplet eposition, splashing an reeposition, Acta Mater., 56(2008), No. 7, p [12] J. Mi an P.S. Grant, Moelling the shape an thermal ynamics of Ni superalloy rings uring spray forming: Part 2. Thermal moelling Heat flow an soliification, Acta Mater., 56(2008), No. 7, p [13] W.D. Cai an E.J. Lavernia, Moeling of porosity uring

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