A. R. Wazzan

Lattice and Grain Boundary Self‐Diffusion in Nickel

Lattice and grain boundary self‐diffusion coefficients of radioactive nickel 63 into high purity nickel have been measured over the temperature range 650°–475°C. The lattice diffusion coefficients, measured by radioactive counting of the surface, are given by DL=1.9 exp(−66 800/RT) cm2sec−1 in agreement with previous measurements at higher temperatures. The grain boundary diffusion coefficients, determined from activity‐penetration data, are similarly given by DB=0.07 exp(−27 400/RT) cm2sec−1 and found to be independent of grain diameter in the range of about 0.03 to 0.07 mm.

Analysis of Enhanced Diffusivity in Nickel

The coefficient of self‐diffusion in annealed and prestrained nickel single crystals, Du, determined in the temperature range 948° to 1023°K by radioactive counting of the surface is Du=1.9 exp(−66 800/RT) cm2sec−1.The coefficient of self‐diffusion in annealed and prestrained fine‐grained nickel crystals, Du′, in the same temperature range is independent of the degree of prestrain: Du′=1.1×10−7 exp(−32 300/RT) cm2sec−1.The coefficient of self‐diffusion in nickel single crystals undergoing plastic deformation, Dd, was determined for strain rates ranging from 0.01 to 0.1035 h−1 in the same temperature range. Dd appears to vary with strain but eventually reaches an asymtotic value Dd. At a constant temperature, Dd/Du is almost linearly dependent on the strain rate e: Dd/Du=1+Ke, where K is 162, 225, and 470, (h−1) for temperatures 1023°, 973°, and 948°K, respectively.

Stability of Laminar Boundary Layers at Separation

The stability of laminar boundary layers at separation is considered. The velocity distribution is represented by (1) a Pohlhausen fourth‐degree polynomial P4, and (2) by a Falkner—Skan similarity profile at separation, Hartree β = − 0. 1988. The Orr—Sommerfeld equation is integrated using Runge—Kutta with Gram—Schmidt orthonormalization. Using single precision arithmetic, the method leads to satisfactory answers at Reynolds numbers R1 = 100 000 and larger. In either case the minimum critical Reynolds number is found to be of the order of 100. It is found that the neutral curves for the P4 profile obtained by solving the Orr—Sommerfeld equation, whether exactly (numerically) or within the framework of the asymptotic approximations, approach along the upper branch the same asymptotic value, namely α1 = 0.8028 (in the case of the β = − 0. 1988 profile, however, the corresponding values is α1 = 1.240). It is also found that the asymptotes to the lower branch in both cases vary with α1 according to R11/3∼α1 −...

Spatial Stability of Stagnation Water Boundary Layer with Heat Transfer

Neglecting temperature fluctuations, assuming viscosity is only temperature dependent, and assuming all other fluid properties are constant, the two‐dimensional linearized parallel flow stability problem is adequately treated by modifying the Orr‐Sommerfeld equation to include viscosity variations with temperature. The resulting equation is used to study the spatial stability of stagnation water boundary layer with heat transfer. The mean flow with free‐stream temperature T∞ = 60°F and wall temperature Tw ranging from 32 to 200°F is computed numerically, from the boundary layer equations with variable fluid properties. It is found that heating stabilizes the boundary layer and cooling destabilizes it. At Tw≅196°F the neutral curve degenerates to a singular point at frequency ω = 5×10−7 and Reynolds number Rδ* = 30.7×103. All disturbances become completely damped for Tw>196°F. It appears that the effect of viscosity μ is larger than the effect of its first derivative μ′ on stability, and that the effect of...

Tollmien-Schlichting waves and transition: Heated and Adiabatic Wedge Flows with Application to Bodies of Revolution

Abstract To date, no comprehensive method of predicting boundary layer transition is available in the literature. In a large class of boundary layers, where disturbances amplify slowly, there is a great separation between the onset of laminar instability and transition. In such flows, current theories on nonlinear instability, which describe the final stages of breakdown to turbulence, fail to predict transition. In these flows, a semi-empirical method based on linear instaibility theory, the so-called e9 method, currently appears to be the best method for computing transition; particularly for quiet boundary layer flows over smooth surfaces. The e9 method has some fundamental weaknesses. For example, why should the method, based on linear instability of small two-dimensional disturbances, be applicable to the transition process which in the final stages is three-dimensional in character? Further, disturbances encountered in practical flows and amplified by a factor of e9 clearly are no longer small disturbances, an assumption central to linear instability theory and the e9 method. In the face of these fundamental weaknesses the method has received some impressive experimental verification. The method requires detailed boundary layer and stability calculations. In this paper, the method is extended to water boundary layers with heat transfer. Computations of transition, based on the e9 method, for a family of heated wedge flows in water-boundary layers are used to formulate a short-cut method for predicting transition. The short-cut method is based on the observation that the interacting effects

Spatial stability of some Falkner—Skan profiles with reversed flow

The Orr‐Sommerfeld equation is solved numerically for the boundary layer profiles which are the solutions to Stewartsons branch of the Falkner‐Skan equation. These profiles are of significance in describing post‐separation flows with negative skin friction. The cases considered are for the Hartree pressure gradient parameter β = −0.18, −0.15, −0.10, and −0.05. The profiles become more stable as β decreases from ‐0.05 to ‐0.18 in contrast to the results of the Falkner‐Skan similarity profiles with positive skin friction.

Effect of boundary‐layer growth on stability of incompressible flat plate boundary layer with pressure gradient

The stability of an incompressible flat plate boundary layer with pressure gradient (Hartree pressure gradient parameter β = 1.0, 0.6, 0.4, 0.2, 0, −0.1, −0.14, and −0.1988) is computed from the linearized complete small disturbance equations. The analysis is nevertheless a quasiparallel treatment because although boundary layer growth is accounted for, the disturbance wave function is correct only in a strictly parallel flow. It is found that the nonparallel flow effect has a negligible influence on the critical Reynolds number Rδ*−c for 0.4 ≤ β ≤ 1.0, but leads to a decrease in Rδ*−c in the range −0.1988 ≤ β ≤ 0.4. The V terms lead to an increase in Rδ*−c in the range 0.4 ≤ β ≤ 1.0, and to a decrease in the range −0.1988 ≤ β ≤ 0.4. The stream tube stretching term led to a decrease in Rδ*−c in the range 0.4 ≤ β ≤ 1.0, and to an increase in the range 0.4 ≥ β ≥ −0.1988. The effect of the V terms and the stream tube stretching term ∂2U/∂x∂y appear to dominate all other boundary layer growth terms; near Rδ*−...

The effect of Mach number on the spatial stability of adiabatic flat plate flow to oblique disturbances

The linearized spatial stability of adiabatic flat plate flow to the first mode of oblique disturbances is computed numerically, using finite difference techniques, in the Mach number range M=1.6 to 6.0. The most unstable wave angle ψ is found in the range ψ=46° to 60°. Stability maps, in the form of curves of constant spatial amplification rate, are presented on the frequency‐Reynolds number diagram. The critical x‐Reynolds number is found to decrease monotonically with M, and is best fit with the expression R1/2x=579.34 M−1.18. This decrease is found to correspond with the outward displacement of the minimum critical layer and the ‘‘inflection’’ point, y at (U′/T)′=0, from y=0.248 and 0.231 at M=1.6 to 0.754 and 0.842 at M=6.0. No transition from viscous to inviscid instability is found with increasing Mach number, rather viscous instability persists to M=6.0. Some of the results agree with those obtained earlier by Mack, but others differ, particularly computations for M>3.0.

Temperature dependence of the single-crystal elastic constants of co-rich co-fe alloys

The single‐crystal elastic moduli, C11, C12, and C44 of three fcc cobalt‐iron alloys (Co–6 at.% Fe, Co–8 at.% Fe, Co–10 at.% Fe) were measured in the range 0–315°C. In addition C11 for the Co–6 at.% Fe alloy, and C′=(1/2)(C11+C12+2C44) for the three alloys are measured over the temperature range 0–1250°C. Plots of the elastic moduli vs temperature exhibit a change in slope and deviation from linearity in the neighborhood of the Curie temperature. The temperature variation of the shear anisotropy in the fcc phase Afcc (≡2C44/C11−C12) differs among the three alloys. Afcc exhibits a highly positive temperature dependence in the Co–10 at.% Fe alloy and a slight negative dependence in the Co–6 at.% Fe and Co–8 at.% Fe alloys. Previous statements in the literature that the hcp⇄fcc transformation in cobalt is preceded by a highly negative temperature dependence of the shear anisotropy ratio A (≡C44/C66) in the hcp phase between 523°K and the transition at about 743°K is not borne out by the present results. Rath...

Spatial stability of incompressible two‐dimensional Gaussian wake in steady viscous flow

Linear spatial stability characteristics of a Gaussian wake in two‐dimensional, steady viscous, incompressible flow are calculated. The results are in good agreement with the measurements of Sato and Kuriki in the linear region of a wake from a flat plate.