With a fixed pyrolysis rate, a lighter gas, or equivalently gas with a larger gas constant, Rg
, gives rise to a larger volume
and larger flow velocities. The chocking cross-section of the core, φAp
is scaled by the core porosity φ. , typically at core prints, determines peak flow ve-
locity which can then be related to peak core gas pressure. Only a fraction of the geometric area is open to gas flow, hence Ap
permeability, K, such as obtained in finer grade/larger AFS number sand cores. Finally, the peak gas pressure will in- crease as the maximum distance from core surface to the print, L, is increased.
Further, higher pressure losses are expected for gas mixtures of higher viscosity, µg
The described relationships can be summarized in an ap- proximate equation for peak gas pressure in a given core:
Equation 1
The first bracket gives the inverse density of the transported gas. The second gives the binder loss rate and the third the pressure drop per unit volumetric flow rate. The essential difference between Equation (1) and its variant appearing in Reference 6 is the explicit form of the binder mass loss rate (2nd
to give ranges 36.1-38.6 g/mol, and 215-230 J/kg/K for mo- lar mass and the gas constant respectively. The higher value of the gas constant corresponds to the species still volatile at room temperature.
bracket). A pyrolysis model for PUCB binder derived
from the thermo-gravimetric analysis by McKinley et al.3 will be used to compute the pyrolysis speed for a specific core in a specific casting. Further difference is the emphasis on the role of the mixture gas constant for pressure predic- tions. This constant will be computed in section two from the composition analysis of the outgassing species reported in Reference 1.
The actual gas pressure developing in a core will be limited by the combined confining metal flow pressure at the core wall, Pm
, and a typically smaller surface tension pressure: Equation 2
where γ is the surface tension of the metal, including possible effects of the oxide film and solidified skin, and R is the size of the gas bubble generated when core gas is blown into the casting. In general one cannot deduce gas pressures from the right hand side of Equation (2), for it only provides an upper bound. In the special case of a mechanical balance, or right after the gas is sealed in the core, the gas pressure is known.
Physical Description of the PUCB Binder Gas
The essential properties of the binder gas for core pressure prediction are the mixture gas constant (Rg
) and the mixture gas viscosity (µg 58 ). These can be calculated from detailed
In aluminum castings the highest-achieved sand core tem- perature will be lower than 900C (1652F). Additional com- position data is available from a parallel study by McKin- ley3
on the PUCB binder at a lower pyrolysis temperature
of 700C (1292F). The main volatile products are the same, though relative amounts differ. Most importantly for this study, the gas constant remains essentially the same, now 228 J/kg/C for gases volatile at room temperature (about 91 % by mole faction).
The mole-fraction-weighted estimate of gas viscosity at room temperature from Table 1 is 1.1X10-5
Pa s, consider-
ably lower than the viscosity of air. At an elevated tempera- ture of 230C (446F), consistent with mean temperature con- ditions in casting sand cores, the viscosity is estimated to be as high as 1.6X10-5
Pa s.
Pyrolysis Rate of Resin Binder in Aluminum Castings
The measurements of Lytle et al.1 and McKinley3 also produced in Table 2.
provide data needed for computation of the rate of binder pyrolysis. Specifically, these authors performed thermo- gravimetric analysis (TGA) at a fixed heating rate of 150C/ min (302F/min). The mass loss rate curve peaked roughly at 230C (446F) and no more mass change was observed above 680C (1256F). The residue fraction was 30%. The ac- tual rate of mass loss curve had multiple peaks. McKinley3 identifies nine, each one parametrized by the weight fraction attributed to the peak, ∆ωi reaction parameters, Ei
and Ci
, and by two first-order Arrhenius . This parameterization is re-
International Journal of Metalcasting/Summer 2011 , and for cores with smaller intrinsic
composition data obtained in laboratory isothermal pyrolysis studies of Lytle et al.1
The light volatile compounds and their
to Equation (3) to obtain the mean molar mass of the gas, M, and its gas constant;
Equation 3
relative quantities produced in a 900C (1652F) pyrolysis ex- periment are listed in Table 1. These were found to account for 99.9% of all volatiles detected at the temperature of the experiment. Further, 80.8% of these by weight and 92.3% by molar content remain volatile down to room temperature. Of the three compounds that are semi-volatile -(1-pentene, 1,3-pentadiene and 2-propenenitrile)—the highest normal boiling point is 77C (171F), which suggests that these com- pounds, at least partially will be volatilized during transport through the heated cores. The molar fractions, χi masses, Mi
, and molar , of species in Table 1 can be combined according
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56 |
Page 57 |
Page 58 |
Page 59 |
Page 60 |
Page 61 |
Page 62 |
Page 63 |
Page 64 |
Page 65 |
Page 66 |
Page 67 |
Page 68 |
Page 69 |
Page 70 |
Page 71 |
Page 72 |
Page 73 |
Page 74 |
Page 75