Crack growth by grain boundary cavitation in the transient and extensive creep regimes

Crack growth due to cavity growth and coalescence along grain boundaries is analyzed under transient and extensive creep conditions in a compact tension specimen. Account is taken of the finite geometry changes accompanying crack tip blunting. The material is characterized as an elastic-power law creeping solid with an additional contribution to the creep rate arising from a given density of cavitating grain boundary facets. All voids are assumed present from the outset and distributed on a given density of cavitating grain boundary facets. The evolution of the stress fields with crack growth under three load histories is described in some detail for a relatively ductile material. The full-field plane strain finite element calculations show the competing effects of stress relaxation due to constrained creep, diffusion and crack tip blunting. and of stress increase due to the instantaneous elastic response to crack growth. At very high crack growth rates the Hui-Riedel fields dominate the crack tip region. However. the high growth rates are not sustained for any length of time in the compact tension geometry analyzed. The region of dominance of the Hui-Riedel field shrinks rapidly so that the near-tip fields are controlled by the HRR-type field shortly after the onset of crack growth. Crack growth rates under various conditions of loading and spanning the range of times from small scale creep to extensive creep are obtained. We show that there is a strong similarity between crack growth history and the behaviour of the C(t) and C(t) parameters. so that crack growth rates correlate rather well with C(t) and C(t). A relatively brittle material is also considered that has a very different near-tip stress field and crack growth history.

Compressible laminar boundary-layer flows of a dusty gas over a semi-infinite flat-plate

The compressible laminar boundary-layer flows of a dilute gas-particle mixture over a semi-infinite flat plate are investigated analytically. The governing equations are presented in a general form where more reasonable relations for the two-phase interaction and the gas viscosity are included. The detailed flow structures of the gas and particle phases are given in three distinct regions : the large-slip region near the leading edge, the moderate-slip region and the small-slip region far downstream. The asymptotic solutions for the two limiting regions are obtained by using a seriesexpansion method. The finite-difference solutions along the whole length of the plate are obtained by using implicit four-point and six-point schemes. The results from these two methods are compared and very good agreement is achieved. The characteristic quantities of the boundary layer are calculated and the effects on the flow produced by the particles are discussed. It is found that in the case of laminar boundary-layer flows, the skin friction and wall heat-transfer are higher and the displacement thickness is lower than in the pure-gas case alone. The results indicate that the Stokes-interaction relation is reasonable qualitatively but not correct quantitatively and a relevant non-Stokes relation of the interaction between the two phases should be specified when the particle Reynolds number is higher than unity.

Statistics of Turbulence in Benthal Boundary Layers

This paper deals with turbulence behavior inbenthalboundarylayers by means of large eddy simulation (LES). The flow is modeled by moving an infinite plate in an otherwise quiescent water with an oscillatory and a steady velocity components. The oscillatory one aims to simulate wave effect on the flow. A number of large-scale turbulence databases have been established, based on which we have obtained turbulencestatisticsof the boundarylayers, such as Reynolds stress, turbulence intensity, skewness and flatness ofturbulence, and temporal and spatial scales of turbulent bursts, etc. Particular attention is paid to the dependences of those statistics on two nondimensional parameters, namely the Reynolds number and the current-wave velocity ratio defined as the steady current velocity over the oscillatory velocity amplitude. It is found that the Reynolds stress and turbulence intensity profile differently from phase to phase, and exhibit two types of distributions in an oscillatory cycle. One is monotonic occurring during the time when current and wave-induced components are in the same direction, and the other inflectional occurring during the time when current and wave-induced components are in opposite directions. Current component makes an asymmetrical time series of Reynolds stress, as well as turbulence intensity, although the mean velocity series is symmetrical as a sine/cosine function. The skewness and flatness variations suggest that the turbulence distribution is not a normal function but approaches to a normal one with the increasing of Reynolds number and the current-wave velocity ratio as well. As for turbulent bursting, the dimensionless period and the mean area of all bursts per unit bed area tend to increase with Reynolds number and current-wave velocity ratio, rather than being constant as in steady channel flows.

Receptivity to free-stream disturbance waves for blunt cone axial symmetry hypersonic boundary layer

Based on high-order compact upwind scheme, a high-order shock-fitting finite difference scheme is studied to simulate the generation of boundary layer disturbance waves due to free-stream waves. Both steady and unsteady flow solutions of the receptivity problem are obtained by resolving the full Navier-Stokes equations. The interactions of bow-shock and free-stream disturbance are researched. Direct numerical simulation (DNS) of receptivity to free-stream disturbances for blunt cone hypersonic boundary layers is performed.

A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations.

The effects of complex boundary conditions on flows are represented by a volume force in the immersed boundary methods. The problem with this representation is that the volume force exhibits non-physical oscillations in moving boundary simulations. A smoothing technique for discrete delta functions has been developed in this paper to suppress the non-physical oscillations in the volume forces. We have found that the non-physical oscillations are mainly due to the fact that the derivatives of the regular discrete delta functions do not satisfy certain moment conditions. It has been shown that the smoothed discrete delta functions constructed in this paper have one-order higher derivative than the regular ones. Moreover, not only the smoothed discrete delta functions satisfy the first two discrete moment conditions, but also their derivatives satisfy one-order higher moment condition than the regular ones. The smoothed discrete delta functions are tested by three test cases: a one-dimensional heat equation with a moving singular force, a two-dimensional flow past an oscillating cylinder, and the vortex-induced vibration of a cylinder. The numerical examples in these cases demonstrate that the smoothed discrete delta functions can effectively suppress the non-physical oscillations in the volume forces and improve the accuracy of the immersed boundary method with direct forcing in moving boundary simulations.

Twinning partial multiplication at grain boundary in nanocrystalline fcc metals

Most deformation twins in nanocrystalline face-centered cubic fcc metals have been observed to form from grain boundaries. The growth of such twins requires the emission of Shockley partials from the grain boundary on successive slip planes. However, it is statistically improbable for a partial to exist on every slip plane. Here we propose a dislocation reaction and cross-slip mechanism on the grain boundary that would supply a partial on every successive slip plane for twin growth.This mechanism can also produce a twin with macrostrain smaller than that caused by a conventional twin.

Effects of wall temperature on boundary layer stability over a blunt cone at Mach 7.99

Effects of wall temperature on stabilities of hypersonic boundary layer over a 7-degree half-cone-angle blunt cone are studied by using both direct numerical simulation (DNS) and linear stability theory (LST) analysis. Four isothermal wall cases with Tw/T0= 0.5, 0.7, 0.8 and 0.9, as well as an adiabatic wall case are considered. Results of both DNS and LST indicate that wall temperature has significant effects on the growth of disturbance waves. Cooling the surface accelerates unstable Mack II mode waves and decelerates the first mode (Tollmien–Schlichting mode) waves. LST results show that growth rate of the most unstable Mack II mode waves for the cases of cold wall Tw/T0=0.5 and 0.7 are about 45% and 25% larger than that for the adiabatic wall, respectively. Numerical results show that surface cooling modifies the profiles of rdut/dyn and temperature in the boundary layers, and thus changes the stability haracteristic of the boundary layers, and then effects on the growth of unstable waves. The results of DNS indicate that the disturbances with the frequency range from about 119.4 to 179.1 kHz, including the most unstable Mack modes, produce strong mode competition in the downstream region from about 11 to 100 nose radii. And adiabatic wall enhances the amplitudes of disturbance according to the results of DNS, although the LST indicates that the growth rate of the disturbance of cold wall is larger. That because the growth of the disturbance does not only depend on the development of the second unstable mode.

Large-eddy simulation of flows past a flapping airfoil using immersed boundary method

The numerical simulation of flows past flapping foils at moderate Reynolds numbers presents two challenges to computational fluid dynamics: turbulent flows and moving boundaries. The direct forcing immersed boundary (IB) method has been devel- oped to simulate laminar flows. However, its performance in simulating turbulent flows and transitional flows with moving boundaries has not been fully evaluated. In the present work, we use the IB method to simulate fully developed turbulent channel flows and transitional flows past a stationary/plunging SD7003 airfoil. To suppress the non-physical force oscillations in the plunging case, we use the smoothed discrete delta function for interpolation in the IB method. The results of the present work demonstrate that the IB method can be used to simulate turbulent flows and transitional flows with moving boundaries.

Euler Solution Using Adaptive Cartesian Grid With A Gridless Boundary Treatment

A quadtree-based adaptive Cartesian grid generator and flow solver were developed. The grid adaptation based on pressure or density gradient was performed and a gridless method based on the least-square fashion was used to treat the wall surface boundary condition, which is generally difficult to be handled for the common Cartesian grid. First, to validate the technique of grid adaptation, the benchmarks over a forward-facing step and double Mach reflection were computed. Second, the flows over the NACA 0012 airfoil and a two-element airfoil were calculated to validate the developed gridless method. The computational results indicate the developed method is reasonable for complex flows.

Acoustic Calculation for Supersonic Turbulent Boundary Layer Flow

An approach which combines direct numerical simulation (DNS) with the Lighthill acoustic analogy theory is used to study the potential noise sources during the transition process of a Mach 2.25 flat plate boundary layer. The quadrupole sound sources due to the flow fluctuations and the dipole sound sources due to the fluctuating surface stress are obtained. Numerical results suggest that formation of the high shear layers leads to a dramatic amplification of amplitude of the fluctuating quadrupole sound sources. Compared with the quadrupole sound source, the energy of dipole sound source is concentrated in the relatively low frequency range.

Direct numerical simulation of hypersonic boundary layer transition over a blunt cone with a small angle of attack

The direct numerical simulation of boundary layer transition over a 5° half-cone-angle blunt cone is performed. The free-stream Mach number is 6 and the angle of attack is 1°. Random wall blow-and-suction perturbations are used to trigger the transition. Different from the authors’ previous work [Li et al., AIAA J. 46, 2899(2008)], the whole boundary layer flow over the cone is simulated (while in the author’s previous work, only two 45° regions around the leeward and the windward sections are simulated). The transition location on the cone surface is determined through the rapid increase in skin fraction coefficient (Cf). The transition line on the cone surface shows a nonmonotonic curve and the transition is delayed in the range of 0° ≤ θ ≤ 30° (θ = 0° is the leeward section). The mechanism of the delayed transition is studied by using joint frequency spectrum analysis and linear stability theory (LST). It is shown that the growth rates of unstable waves of the second mode are suppressed in the range of 20° ≤ θ ≤ 30°, which leads to the delayed transition location. Very low frequency waves VLFWs� are found in the time series recorded just before the transition location, and the periodic times of VLFWs are about one order larger than those of ordinary Mack second mode waves. Band-pass filter is used to analyze the low frequency waves, and they are deemed as the effect of large scale nonlinear perturbations triggered by LST waves when they are strong enough.The direct numerical simulation of boundary layer transition over a 5° half-cone-angle blunt cone is performed. The free-stream Mach number is 6 and the angle of attack is 1°. Random wall blow-and-suction perturbations are used to trigger the transition. Different from the authors’ previous work [ Li et al., AIAA J. 46, 2899 (2008) ], the whole boundary layer flow over the cone is simulated (while in the author’s previous work, only two 45° regions around the leeward and the windward sections are simulated). The transition location on the cone surface is determined through the rapid increase in skin fraction coefficient (Cf). The transition line on the cone surface shows a nonmonotonic curve and the transition is delayed in the range of 20° ≤ θ ≤ 30° (θ = 0° is the leeward section). The mechanism of the delayed transition is studied by using joint frequency spectrum analysis and linear stability theory (LST). It is shown that the growth rates of unstable waves of the second mode are suppressed in the range of 20° ≤ θ ≤ 30°, which leads to the delayed transition location. Very low frequency waves (VLFWs) are found in the time series recorded just before the transition location, and the periodic times of VLFWs are about one order larger than those of ordinary Mack second mode waves. Band-pass filter is used to analyze the low frequency waves, and they are deemed as the effect of large scale nonlinear perturbations triggered by LST waves when they are strong enough.

Experimental Study Of Vortex-Induced Vibrations Of A Cylinder Near A Rigid Plane Boundary In Steady Flow

In this study, the vortex-induced vibrations of a cylinder near a rigid plane boundary in a steady flow are studied experimentally. The phenomenon of vortex-induced vibrations of the cylinder near the rigid plane boundary is reproduced in the flume. The vortex shedding frequency and mode are also measured by the methods of hot film velocimeter and hydrogen bubbles. A parametric study is carried out to investigate the influences of reduced velocity, gap-to-diameter ratio, stability parameter and mass ratio on the amplitude and frequency responses of the cylinder. Experimental results indicate: (1) the Strouhal number (St) is around 0.2 for the stationary cylinder near a plane boundary in the sub-critical flow regime; (2) with increasing gap-to-diameter ratio (e (0)/D), the amplitude ratio (A/D) gets larger but frequency ratio (f/f (n) ) has a slight variation for the case of larger values of e (0)/D (e (0)/D > 0.66 in this study); (3) there is a clear difference of amplitude and frequency responses of the cylinder between the larger gap-to-diameter ratios (e (0)/D > 0.66) and the smaller ones (e (0)/D < 0.3); (4) the vibration of the cylinder is easier to occur and the range of vibration in terms of V (r) number becomes more extensive with decrease of the stability parameter, but the frequency response is affected slightly by the stability parameter; (5) with decreasing mass ratio, the width of the lock-in ranges in terms of V (r) and the frequency ratio (f/f (n) ) become larger.