Effect of crucible wall roughness on the laminar/turbulent flow transition of the Ga75In25 alloy stirred by a rotating magnetic field

Abstract

The critical magnetic induction (Bcr) values of a melt flow produced by a rotating magnetic field (RMF), remaining laminar or turbulent, are essential in different solidification processes. In an earlier paper (Metall Res Technol 100: 1043–1061, 2003), we showed that Bcr depends on the crucible radius (R) and frequency of the magnetic field (f). The effect of wall roughness (WR) on Bcr was investigated in this study. Using ten different wall materials, we determined the angular frequency (ω) and Reynolds number (Re) as a function of the magnetic induction (B) and f using two different measuring methods (pressure compensation method, PCM; height measuring method, HMM). The experiments were performed at room temperature; therefore, the Ga75wt%In25wt% alloy was chosen for the experiments. Based on the measured and calculated results, a simple relationship was determined between Bcr and Re*, f, R, and WR, where the constants K1, K2, K3, and K4 depended on the physical properties of the melt and wall material:$$Bcr\left({Re}^{*},f,R,WR\right)=\frac{{Re}^{*}}{{R}^{2}}({K}_{1} {f}^{-K2}+{K}_{3} {f}^{-K4} WR)$$ B c r Re ∗ , f , R , W R = Re ∗ R 2 ( K 1 f - K 2 + K 3 f - K 4 W R )

The Angular Velocity as a Function of the Radius in Molten Ga75In25 Alloy Stirred Using a Rotation Magnetic Field

“…Earlier [32,33], the pressure at the wall was measured across a hole in the cover of the crucible near the wall (Figure 12a). Because it revealed the suspicion that, precisely at the wall, the angular velocity (and, thus, the measurable pressure) differs from the actual value, in this work, the hole was made on the crucible wall (Figure 12b), which was also carried out in [6].…”

“…The viscosity of the molten alloys and the wall roughness of the crucible could not be negligible, so the angular velocity changes in the rotated melt along the radius. In two earlier papers, we showed the effect of magnetic induction on the angular velocity of the melt in the case of a crucible with smooth [32] and rough [33] walls (wall friction) on the angular velocity. The angular velocity was determined using the Pressure Compensation Method (PCM) near the wall of the crucible (r ≈ R, where R is the radius of the crucible).…”

“…Metals 2024, 14, 368 7 of 20 The Δp = ρgΔh differential pressure is compensated by an external pcomp = ρgΔh pressure produced by a compressor at measurement gauge "b"; the "0" level is restored at both gauges "a" and "b" (Figure 9) [31][32][33]. Advantages:…”

“…Consequently, the angular velocity measured in [32,33] close to the crucible wall has only given information about the minimum angular velocity as a function of magnetic induction B and the crucible's radius, R. The ω(st) will be the maximum (stationer) angular velocity at the radius, r. It can be seen from Figure 17 that at a higher radius (r 2 ), this maximum ω(st) is lower than at the smaller one (r 1 ). By using Equations ( 9) and ( 10), we can obtain the following:…”

“…It is known that obtaining information about the melt flow from industrial casting is impossible, so we must conduct some cold experiments with well-monitored parameters (like Hg, Ga, GaIn, and GaInSn alloys) [19][20][21][22][23][24][25][26][27]. Because only very little correctly measured data for the ω(B, r) function can be found in the literature [21][22][23]25,[28][29][30][31][32][33][34][35], any previous simulations of the melt flow induced by an RMF ignored the function to solve the problem mentioned above [6][7][8][9][10][11]. After analysing the known methods used to determine the ω(B, r) function, the most suitable method, namely the Press Compensation Method (PCM), was chosen.…”