David E. Glass

HYPERBOLIC STEFAN PROBLEM WITH APPLIED SURFACE HEAT FLUX AND TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY

Abstract The hyperbolic Stefan problem with an applied surface heat flux and temperature-dependent thermal conductivity is solved numerically for a semi-infinite slab using Mac-Cormacks predictor-corrector method. Solutions are presented for cases where the melt temperature is both below and above the instantaneous jump in surface temperature at time t = O+. The interface condition, surface temperature, and internal temperatures are presented for different Stefan numbers and melt temperatures, as well as thermal conductivity both increasing and decreasing with temperature. The results obtained from the hyperbolic solution are compared with those obtained from the parabolic solution.

Formulation and solution of hyperbolic Stefan problem

The interface condition for hyperbolic phase change problems, which includes sensible heat at the interface, is derived as an extension of the interface condition for standard parabolic phase change problems. The enthalpy formulation of the hyperbolic Stefan problem is presented and is used to numerically solve for the temperature distributions and the interface position. MacCormack’s predictor–corrector method is applied to solve the hyperbolic phase change problem and is validated by comparing the limiting case where the thermal relaxation parameter approaches zero to the parabolic phase change problem, in which the relaxation parameter is zero. Solutions with an applied surface temperature greater than the melt temperature are presented for two different Stefan numbers. It is noted that a discontinuity occurs at the phase change interface as well as at the thermal front.

Variable Specific Heat and Thermal Relaxation Parameter in Hyperbolic Heat Conduction

Figure 2 shows that the refractive index at which the maximum emittance occurs increases with the increase in albedo. This complicated behavior is because of the combined influence of scattering and boundary reflection. This is consistent with the results for planar and cylindrical geometries. Besides, the directional emittance decreases with the increase in the albedo and the optical radius. Such behaviors are also consistent with those for planar and cylindrical geometries. Since the planar medium is infinite in all directions parallel to the boundaries, the cylindrical medium is infinite only in the axial direction, and the spherical medium is finite in all directions, we can expect that the directional emittance of a sphere is smaller than that of a slab or that of a cylinder with the same physical parameters. The normal emittance of a sphere with n = 1.6 is about two-thirds as large as that of a slab with the same refractive index, and the difference between the normal emittance of a slab and that of a sphere increases with the decrease in refractive index, as shown in Fig. 3. This is because the influence of geometry decreases with the increase in surface reflectivity.

Hyperbolic heat conduction with convection boundary conditions and pulse heating effects

This paper describes the numerical simulation of hyperbolic heat conduction with convection boundary conditions. The effect of a step heat loading, a sudden pulse heat loading, and a pulse internal heat source are considered in conjunction with convection boundary conditions. Two methods of solution are presented for predicting the transient behavior of the propagating thermal disturbances. In the first method, MacCormacks predictor-corrector method is employed for integrating the hyperbolic system of equations. Next the transfinite element method, which employs specially tailored elements, is used for accurately representing the transient response of the propagating thermal wavefronts. The agreement between the results of various numerical test cases not only validates the representative behavior of the thermal wave fronts but also provides an understanding of the representative behavior due to convection boundary conditions and varied heating effects.

Platinum substitutes and two-phase-glass overlayers as a low cost alternatives to platinum aluminide coatings

The feasibility of processing less-expensive alternative coatings to platinum aluminide was examined. Three approaches were followed: (1) enhancement of nickel-aluminide coatings by application of sol-gel derived two-phase-glass (TPG) overlayers, (2) evaluation of TPG coatings on bare IN 738LC, and (3) substitution of Pt with a less expensive platinum group metal (palladium). Accordingly, IN 738LC coupons were tested with several coatings including TPG, aluminide coatings (platinum aluminide, palladium aluminide, and conventional nickel aluminide), and TPG overlayers on the aluminide coatings. Isothermal-oxidation, cyclic-oxidation, and hot-corrosion tests were conducted at 900°C for 500 h to evaluate the coatings. The results showed that the TPG by itself provided superior protection compared to the platinum-aluminide coatings under both oxidation and hot-corrosion conditions. The TPG coating also showed promise as an overcoat on aluminide coatings.

Fabrication and testing of heat pipes for a heat-pipe-cooled leading edge

Refractory-composite/heat-pipe-cooled wing and tail leading edges are being considered for use on hypersonic vehicles to limit maximum temperatures to values below material reuse limits and to eliminate the need to actively cool the leading edges. The development of a refractorycomposite/heat-pipe-cooled leading edge has evolved from the design stage to the fabrication of full-size, leading-edge-shaped heat pipes. A three-foot-long, D-shaped, molybdenum-rhenium heat pipe with a lithium working fluid was fabricated and tested at an operating temperature of 2460°F (~1350°C) to verify the individual heat-pipe design. Following the fabrication of this heat pipe, three additional straight heat pipes were fabricated and embedded in carbon/carbon with a 0.005-in-thick layer of Grafoil® placed between the curved portion of the heat pipe and the carbon/carbon. Finally, a single leading-edge-shaped (J-tube) heat pipe was fabricated. The wick for the J-tube heat pipe, made of 400x400 Mo-Re screen, was fabricated with wedges cut out on the inside surface to conform to the 0.5-inleading-edge radius. Due to lack of funding, testing on the heat pipes embedded in carbon/carbon and the J-tube heat pipe has not been completed.

Cryogenic mechanical properties of Gore-Tex® fabric

Mechanical properties of a Gore-Tex® woven fabric were determined at ambient, elevated, liquid nitrogen, and liquid helium temperatures. Data is presented for both creep and static strength testing at temperatures from 20 K to 450 K, and showed an increasing strength with decreasing temperature. The material appears well suited for applications where a strong and flexible material is required at cryogenic temperatures.

Numerical simulation of hyperbolic heat conduction with convection boundary conditions and pulse heating effects

The paper describes the numerical simulation of hyperbolic heat conduction with convection boundary conditions. The effects of a step heat loading, a sudden pulse heat loading, and an internal heat source are considered in conjunction with convection boundary conditions. Two methods of solution are presened for predicting the transient behavior of the propagating thermal disturbances. In the first method, MacCormacks predictor-corrector method is employed for integrating the hyperbolic system of equations. Next, the transfinite element method, which employs specially tailored elements, is used for accurately representing the transient response of the propagating thermal wave fronts. The agreement between the results of various numerical test cases validate the representative behavior of the thermal wave fronts. Both methods represent hyperbolic heat conduction behavior by effectively modeling the sharp discontinuities of the propagating thermal disturbances.

Improved Test Planning and Analysis Through the Use of Advanced Statistical Methods

The goal of this work is, through computational simulations, to provide statistically-based evidence to convince the testing community that a distributed testing approach is superior to a clustered testing approach for most situations. For clustered testing, numerous, repeated test points are acquired at a limited number of test conditions. For distributed testing, only one or a few test points are requested at many different conditions. The statistical techniques of Analysis of Variance (ANOVA), Design of Experiments (DOE) and Response Surface Methods (RSM) are applied to enable distributed test planning, data analysis and test augmentation. The D-Optimal class of DOE is used to plan an optimally efficient single- and multi-factor test. The resulting simulated test data are analyzed via ANOVA and a parametric model is constructed using RSM. Finally, ANOVA can be used to plan a second round of testing to augment the existing data set with new data points. The use of these techniques is demonstrated through several illustrative examples. To date, many thousands of comparisons have been performed and the results strongly support the conclusion that the distributed testing approach outperforms the clustered testing approach.

Platinum Substitutes and Two-Phase-Glass Overlayers as Low Cost Alternatives to Platinum Aluminide Coatings

The feasibility of processing less-expensive alternative coatings to platinum aluminide was examined. Three approaches were followed: 1) enhancement of nickel-aluminide coatings by application of sol-gel derived two-phase-glass (TPG) overlayers, 2) evaluation of TPG coatings on bare IN 738LC, and 3) substitution of Pt with a less expensive platinum group metal (palladium). Accordingly, IN 738LC coupons were tested with several coatings including TPG, aluminide coatings (platinum aluminide, palladium aluminide, and conventional nickel aluminide), and TPG overlayers on the aluminide coatings. Isothermal-oxidation, cyclic-oxidation, and hot-corrosion tests were conducted at 900°C for 500 hours to evaluate the coatings. The results showed that the TPG by itself provided superior protection compared to the platinum-aluminide coatings under both oxidation and hot-corrosion conditions. The TPG coating also showed promise as an overcoat on aluminide coatings.Copyright