Kenneth J. De Witt

Three-dimensional simulation of electrothermal deicing systems

This paper examines three-dimensional transient heat transfer in a multilayered body that is ice covered. The physical application studied is the process of melting and removal of ice from aircraft components by use of electrothermal heaters. To model the ice-phase change, a predictor-corrector technique is used which assumes a phase for each ice gridpoint. This allows the use of the method-of-Douglas three-dimensio nal alternating direction numerical solver to iteratively converge on the correct phase of each ice node for each time step. Three-dimensional results are presented and the usefulness of the code as a design tool is illustrated. Comparisons between experimental deicer test results and numerical simulations are discussed. Nomenclature Cp = specific heat capacity, Btu/lb-°F H = enthalpy, Btu/lb h = heat transfer coefficient, Btu/h-ft2-°F k = thermal conductivity, Btu/h-ft-°F L = latent heat of fusion of ice, Btu/lb Q = rate of heat generation per unit volume, Btu/h-ft3 Rx — jc-direction Fourier number, dimensionless Ry = y-direction Fourier number, dimensionless Rz = z-direction Fourier number, dimensionless T = temperature, °F

Experimental Heat Transfer Coefficients from Ice-Roughened Surfaces for Aircraft Deicing Design

Experimental Stanton numbers are presented for seven aluminum model castings of ice-roughened surfaces in parallel air e ow for Rex ranging from 5 :3 £ 10 4 to 1:3 £ 10 6 . The Stanton numbers were generally higher than those for previous studies with hemispherical and truncated cone roughness elements, and the majority of the data were in the fully turbulent regime. In general, the rime feather ice roughness produced the highest rate of heat transfer, followed by the rough glaze roughness, the smooth rime roughness, and the smooth glaze roughness, respectively.In thefully developed turbulentregimethelocalStantonnumbercould bedescribed by apowerlawof theformStx = aRem Pr i 0:4 where a andm correlated well with the newly dee ned Index of Random Roughness and the roughness height, respectively. This work provides a set of measured values of the Stanton number, specie c to thecaseofstochasticallyaccretediceonaircraftsurfaces,neededfortheeffectivedesignofin-e ightdeicingsystems.

Simulation of overexpanded low-density nozzle plume flow

The direct simulation Monte Carlo method was applied to the analysis of low-density nitrogen plumes exhausting from a small converging-diverging nozzle into finite ambient pressures. Two cases were considered that simulated actual test conditions in a vacuum facility. The numerical simulations readily captured the complicated flow structure of the overexpanded plumes adjusting to the finite ambient pressures, including Mach disks and barrel-shaped shocks. The numerical simulations compared well to experimental data of Rothe.

Icing Calculations on a Typical Commercial Jet Engine Inlet Nacelle

A procedure is presented to analyze a commercial jet engine inlet during icing. The essential steps in the numerical simulation are discussed: e owe eld calculations, determination of droplet trajectories hitting the surface, and computation of the heat transfer phenomena. A three-dimensional e owe eld solver utilizing the panel method was found to be adequate for modeling noncomplicated engine inlet nacelles at subsonic speeds. Droplet trajectories were produced using a three-dimensional grid-based code. Predicted collection efe ciencies were in good agreement with experimental results. Heat transfer calculations are performed with the NASA Lewis ANTICE code. Two example cases are presented.

Measurement of local convective heat transfer coefficients from a smooth and roughened NACA-0012 airfoil - Flight test data

Wind tunnels typically have higher free stream turbulence levels than are found in flight. Turbulence intensity was measured to be 0.5 percent in the NASA Lewis Icing Research Tunnel (IRT) with the cloud making sprays off and around 2 percent with cloud making equipment on. Turbulence intensity for flight conditions was found to be too low to make meaningful measurements for smooth air. This difference between free stream and wing tunnel conditions has raised questions as to the validity of results obtained in the IRT. One objective of these tests was to determine the effect of free stream turbulence on convective heat transfer for the NASA Lewis LEWICE ice growth prediction code. These tests provide in-flight heat transfer data for a NASA-0012 airfoil with a 533 cm chord. Future tests will measure heat transfer data from the same airfoil in the Lewis Icing Research Tunnel. Roughness was obtained by the attachment of small, 2 mm diameter hemispheres of uniform size to the airfoil in three different patterns. Heat transfer measurements were recorded in flight on the NASA Lewis Twin Otter Icing Research Aircraft. Measurements were taken for the smooth and roughened surfaces at various aircraft speeds and angles of attack up to four degrees. Results are presented as Frossling number versus position on the airfoil for various roughnesses and angles of attack.

DSMC and continuum analyses of low-density nozzle flow

Two different approaches, the direct-simulation Monte Carlo (DSMC) method based on molecular gas dynamics and a finite-volume approximation of the Navier-Stokes equations, which are based on continuum gas dynamics, are employed in the analysis of a low-density gas flow in a small converging-diverging nozzle. The fluid experiences various kinds of flow regimes including continuum, slip, transition, and free-molecular. Results from the two numerical methods are compared with Rothes experimental dam, in which density and rotational temperature variations along the centerline and at various locations inside a low density nozzle were measured by the electron-beam fluorescence technique. The continuum approach showed good agreement with the experimental data as far as density is concerned. The results from the DSMC method showed good agreement with the experimental data both in the density and the rotational temperature. It is also shown that the simulation parameters, such as the gas/surface interaction model, the energy exchange model between rotational and translational modes, and the viscosity temperature exponent, have substantial effects on the results of the DSMC method.

A numerical study of parameters affecting gas bubble dissolution

Abstract The mass transfer driven dissolution of a gas bubble containing either a single component or a multicomponent mixture, and which can include the presence of a nonsoluble gas, is analyzed by a finite difference procedure. Various effects including surface tension, gas expansion, and the presence of solvent vapor are examined. The predicted results with inclusion of these effects compare favorably with available experimental data and are compared with the results obtained using approximate solutions. For multicomponent gas bubble dissolution, it is found that the conventional assumption that neglects the gas expansion effect inside the bubble may lead to an erroneous prediction of the time-dependent bubble radius and concentration. The dissolution process is initially governed by solubility. However, at large times, the diffusivity and the concentration difference in the liquid are important. For a bubble containing a nonsoluble gas, the results show that even a small amount of this species will alter the behavior of bubble shrinkage. The final radius is dependent upon the content of the nonsoluble gas and the saturation condition of the liquid.

Three‐dimensional pulsatile flow through a bifurcation

Pulsatile flow of an incompressible, Newtonian fluid through a symmetric bifurcated rigid channel was numerically analysed by solving the three‐dimensional Navier‐Stokes equations. The upstream flow conditions were taken from an experimentally measured human arterial pulse cycle. The bifurcation was symmetrical with a branch angle of 60° and a daughter to mother area ratio of 2.0. The predicted velocity patterns were in qualitative agreement with experimental measurements available in the literature. The effect of unsteadiness on the various flow characteristics was studied. The most drastic effect observed was on the flow reversal regions. There was no flow reversal at the highest inlet Reynolds number in the pulse cycle, whereas in the case of steady flow at the same Reynolds number, the flow reversal region was the largest. The presence of secondary flow was observed at all times during the pulse cycle. Shear stress was calculated along the outer and inner walls and the low and high time averaged shear stress regions correspond to the clinically observed sites of formation of atherosclerotic plaque and lesions.

Analysis of plume backflow around a nozzle lip in a nuclear rocket

The structure of the flow around a nuclear thermal rocket nozzle lip has been investigated using the direct simulation Monte Carlo method. Special attention has been paid to the behavior of a small amount of harmful particles that may be present in the rocket exhaust gas. The harmful fission product particles are modeled by four inert gases whose molecular weights are in a range of 4 131. Atomic hydrogen, which exists in the flow due to the extremely high nuclear fuel temperature in the reactor, is also included. It is shown that the plume backflow is primarily determined by the thin subsonic fluid layer adjacent to the surface of the nozzle lip, and that the inflow boundary in the plume region has negligible effect on the backflow. It is also shown that a relatively large amount of the lighter species is scattered into the backflow region while the amount of the heavier species becomes negligible in this region due to extreme separation between the species. Results indicate that the backscattered molecules are very energetic and are fast-moving along the surface in the backflow region near the nozzle lip. 22 refs.

Rarefied gas flow through two-dimensional nozzles

A kinetic theory analysis is made of the flow of a rarefied gas from one reservoir to another through two-dimensional nozzles with arbitrary curvature. The Boltzmann equation simplified by a model collision integral is solved by means of finite-difference approximations with the discrete ordinate method. The physical space is transformed by a general grid generation technique and the velocity space is transformed to a polar coordinate system. A numerical code is developed which can be applied to any two-dimensional passage of complicated geometry for the flow regimes from free-molecular to slip. Numerical values of flow quantities can be calculated for the entire physical space including both inside the nozzle and in the outside plume. Predictions are made for the case of parallel slots and compared with existing literature data. Also, results for the cases of convergent or divergent slots and two-dimensional nozzles with arbitrary curvature at arbitrary knudsen number are presented.