Dimensionless Dissipation Research Articles

Plastic dissipation in mixed-mode fatigue crack growth along plastically mismatched interfaces

A new theory of fatigue crack growth in ductile solids has recently been proposed based on the total plastic energy dissipation per cycle ahead of the crack. This and previous energy based approaches in the literature suggest that the total plastic dissipation per cycle can be closely correlated with fatigue crack growth rates under mode I loading. In a recent paper, the authors have extended the dissipated energy approach to the case of fatigue crack growth in a homogeneous material under sustained mixed-mode loading conditions. The goal of the current study is to further extend the approach to mixed-mode fatigue delamination of ductile interfaces in layered materials. Attention is restricted to material combinations with identical elastic properties, but with mismatches in plastic properties (both yield strength and hardening modulus) across the interface. Such systems can occur in brazing, soldering, welding, and a variety of layered manufacturing applications, where high-temperature material deposition can result in a mismatch in mechanical properties between the deposited material and the substrate. In this study, the total plastic dissipation per cycle is obtained through plane strain elastic–plastic finite element analysis of a stationary crack in a general layered specimen geometry under constant amplitude, mixed-mode loading. Numerical results for a dimensionless plastic dissipation per cycle are presented over the full range of relevant material combinations and mixed-mode loading conditions. Results suggest that while applied mode-mix ratio is the dominant parameter, mismatches in yield strength and hardening modulus can have a significant effect on the total plastic dissipation per cycle, which is dominated by the weaker/softer material.

About Magnetic Field Distribution in Granular Superconductors

Complicated Josephson structures consisting of several distributed junctions, containing one or more common points are considered. It is analytically shown that such structures must contain an integer number of magnetic flux quanta. It is also shown that in some structures multiquantum formations are preferable. Analytical conclusions are proved by numerical experiments. It is well known, that magnetic field penetrates in type II superconductors in the form of Abrikosov’s vortices, each containing a single quantum of magnetic flux Φ0 = hc/2e = 2, 07 · 10−7 gauss · cm. Similar phenomenon is observed in distributed Josephson junctions, where external magnetic field penetrates in it in the form of vortices called Josephson vortices. Though Josephson vortices differ from Abrikosov’s ones in the set of parameters (in particular, they have no nonsuperconducting core), they also carry single magnetic flux quantum. The research of high-temperature superconductors is usually based on a model of numerous stochastically positioned Josephson junctions with random parameters (plural Josephson medium). Assuming this medium as a bidimensional analogy of a distributed junction, the magnetic field also penetrates in it in the form of vortices called “hypervortices” and its structure has not been researched in details. Furthermore, the magnetic flux of the hypervortex is assumed now to be equal to Φ0. In this paper the distributed Josephson junction’s structure is being considered as a system, formed by several (N) half-infinite distibuted junctions with one common point ( the ”Star” topol-ogy), as shown on Figure 1. Figure 1: Several half-infinite junctions withone common point. Let common point has coordinate x = 0 for all junctions, the phase difference of the order parameter in each junction is counted clockwise, and the points of each junction have positive coordinates x ≥ 0. In each junction φ(x, t) is given by equation: ∂φ (x, t) ∂x2 − γ ∂φ (x, t) ∂t − ∂ φ (x, t) ∂t2 = sinφ (x, t) (1) where x and t are dimensionless (normalized) coordinate and time, γ – dimensionless dissipation parameter, due to junctions ohmic resistance. The normalized magnetic field in junction is determined by relation h (x, t) = ∂φ (x, t)/∂x. For infinite junction there are isolated solutions [2] φ0 (x) = 4 arctg e , the Josephson magnetic vortex given by h0 (x) = dφ0 (x)/dx = 4e x /( 1 + e ) and the value of it’s magnetic flux is Progress In Electromagnetics Research Symposium 2005, Hangzhou, China, August 22-26 409

Flow and energy dissipation in a magnetic fluid drop around a permanent magnet

This paper is devoted to the numerical modeling and simulation of hydrodynamic and dissipation processes in damper systems, where the working element is a magnetic fluid drop around a permanent magnet. Flow patterns and dimensionless dissipation coefficient depending on the Reynolds number and magnet position are established.

Delayed correlation between turbulent energy injection and dissipation

The dimensionless kinetic energy dissipation rate C(epsilon) is estimated from numerical simulations of statistically stationary isotropic box turbulence that is slightly compressible. The Taylor microscale Reynolds number (Re(lambda)) range is 20< or approximately equal to Re(lambda) < or approximately equal to 220 and the statistical stationarity is achieved with a random phase forcing method. The strong Re(lambda) dependence of C(epsilon) abates when Re(lambda) approximately 100 after which C(epsilon) slowly approaches approximately 0.5, a value slightly different from previously reported simulations but in good agreement with experimental results. If C(epsilon) is estimated at a specific time step from the time series of the quantities involved it is necessary to account for the time lag between energy injection and energy dissipation. Also, the resulting value can differ from the ensemble averaged value by up to +/-30%. This may explain the spread in results from previously published estimates of C(epsilon).

Baroclinic geostrophic adjustment in a rotating circular basin

Baroclinic geostrophic adjustment in a rotating circular basin is investigated in a laboratory study. The adjustment process consists of a linear phase before advective and dissipative effects dominate the response for longer time. This work describes in detail the hydrodynamics and energetics of the linear phase of the adjustment process of a two-layer fluid from an initial step height discontinuity in the density interface $\uDelta H$ to a final response consisting of both geostrophic and fluctuating components. For a forcing lengthscale $r_f$ equal to the basin radius $R_0$ , the geostrophic component takes the form of a basin-scale double gyre while the fluctuating component is composed of baroclinic Kelvin and Poincare waves. The Burger number $S\,{=}\,R/r_f$ ( $R$ is the baroclinic Rossby radius of deformation) and the dimensionless forcing amplitude $\epsilon\,{=}\,\uDelta H/H_1$ ( $H_1$ is the upper-layer depth) characterize the response of the adjustment process. In particular, comparisons between analytical solutions and laboratory measurements indicate that for time $\tau$ : $1 \,{ ( $\tau$ is time scaled by the inertial period $2 \pi/f$ ), the basin-scale double gyre is established, followed by a period where the double gyre is sustained, given by $S^{-1} \,{ for a moderate forcing and $S^{-1}\,{ for a weak forcing ( $\tau_D$ is the dimensionless dissipation timescale due to Ekman damping). The analytical solution is used to calculate the energetics of the baroclinic geostrophic adjustment. The results are found to compare well with previous studies with partitioning of energy between the geostrophic and fluctuating components exhibiting a strong dependence on $S$ . Finally, the outcomes of this study are considered in terms of their application to lakes influenced by the rotation of the Earth.

Plastic dissipation in fatigue crack growth under mixed-mode loading

A new theory of fatigue crack growth in ductile solids has recently been proposed based on the total plastic energy dissipation per cycle ahead of the crack. This and previous energy-based approaches in the literature suggest that the total plastic dissipation per cycle can be closely correlated with fatigue crack growth rates under mode I loading. The goal of the current study is to extend the dissipated energy approach to steady-state crack growth under mixed-mode I/II loading conditions, with ultimate application to cyclic delamination of ductile interfaces in layered materials. The total plastic dissipation per cycle is obtained herein by 2-D elastic–plastic finite element analysis of a stationary crack in a general mixed-mode specimen geometry under constant amplitude loading. Both elastic–perfectly plastic and bilinear kinematic hardening constitutive behaviors are considered, and numerical results for a dimensionless plastic dissipation per cycle are presented over the full range of relevant mechanical properties and mixed-mode loading conditions. Results provide substantial insight into the effects of crack-tip constraint, material hardening behavior and applied mode–mix ratio on the dissipated energy during fatigue crack growth.

Energy dissipation in body-forced plane shear flow

We study the problem of body-force driven shear flows in a plane channel of width l with free-slip boundaries. A mini-max variational problem for upper bounds on the bulk time averaged energy dissipation rate epsilon is derived from the incompressible Navier-Stokes equations with no secondary assumptions. This produces rigorous limits on the power consumption that are valid for laminar or turbulent solutions. The mini-max problem is solved exactly at high Reynolds numbers Re = U*l/nu, where U is the rms velocity and nu is the kinematic viscosity, yielding an explicit bound on the dimensionless asymptotic dissipation factor beta=epsilon*l/U^3 that depends only on the ``shape'' of the shearing body force. For a simple half-cosine force profile, for example, the high Reynolds number bound is beta <= pi^2/sqrt{216} = .6715... . We also report extensive direct numerical simulations for this particular force shape up to Re approximately 400; the observed dissipation rates are about a factor of three below the rigorous high-Re bound. Interestingly, the high-Re optimal solution of the variational problem bears some qualitative resemblence to the observed mean flow profiles in the simulations. These results extend and refine the recent analysis for body-forced turbulence in J. Fluid Mech. 467, 289-306 (2002).

A total dissipated energy theory of fatigue crack growth in ductile solids

This study proposes a new theory of fatigue crack growth in ductile solids based on the total plastic energy dissipation per cycle ahead of the crack. The fundamental hypothesis of the theory proposes a unified criterion for crack extension under monotonic and fatigue loading, so that the fatigue crack growth rate is given explicitly in terms of the total plastic dissipation per cycle and the monotonic plane stress or plane strain fracture toughness of the material. The total plastic dissipation per cycle is obtained herein by 2-D elastic–plastic finite element analysis of a stationary crack under constant amplitude, mode I loading (C(T) specimen geometry). Both elastic–perfectly plastic and bi-linear kinematic hardening constitutive behaviors are considered, and numerical results for a dimensionless plastic dissipation per cycle are presented over the full range of relevant mechanical properties and loading conditions. Finally, the results of the current theory are compared to measured Paris-regime crack growth data for a variety of ductile metals, as well as dissipated energy measurements previously reported in the literature.

Measurements of the turbulent energy dissipation rate

The one-dimensional surrogate for the dimensionless energy dissipation rate Cε is measured in shear flows over a range of the Taylor microscale Reynolds number Rλ, 70≲Rλ≲1217. We recommend that Cε should be defined with respect to an energy length scale derived from the turbulent energy spectrum. For Rλ≳300, a value of Cε≈0.5 appears to be a good universal approximation for flow regions free of strong mean shear. The present results for Cε support a key assumption of turbulence—the mean turbulent energy dissipation rate is finite in the limit of zero viscosity.

Noise-Induced Resonances in Superparamagnetic Particles

Noise-Induced Resonances in Superparamagnetic Particles

Multiple source modeling of low-reynolds-number dissipation rate equation with aids of DNS data

The paper reports a multiple source modeling of low-Reynolds-number dissipation rate equation with aids of DNS data. The key features of the model are to satisfy the wall limiting conditions of the individual source terms in the exact dissipation rate equation using the wall damping functions. The wall damping functions are formulated in term of dimensionless dissipation length scalel D + (≡l D (νe)1/4/ν) and the invariants of small and large scale turbulence anisotropy tensors,\(a_{ij} ( = \overline {u_i u_j } /k - 2\delta _{ij} /3)\) ande ij (=e ij /e-2δ ij /3). The model constants are optimized with aids of DNS data in a plane channel flow. Adopting the dissipation length scale as a parameter of damping function, the applicabilities ofk-e model are extended to the turbulent flow calculation of complex flow passages.

Charge transport measurement during turbulent electroconvection.

We report measurements of the energy dissipation during electroconvection of a nematic liquid crystal in the fully turbulent regime. The energy dissipation is quantified by measuring the electric current at constant potential difference. In certain cases, we observe the surprising result that the dimensionless energy dissipation ceases to increase with increasing potential difference. In some circumstances, a power-law scaling relationship between the dimensionless excess energy dissipation and the reduced voltage is observed, but the exponent in this relationship varies dramatically with both the time scale of the driving electric field and the separation between the electrodes.

Scaling of mean temperature dissipation rate

Expressions for Cε and Cεθ, the dimensionless mean energy and temperature dissipation rates, can be reasonably reconciled with measured and numerical data at small to moderate Rλ only if the Kolmogorov constant and more especially the Obukhov–Corrsin constant are assumed to depend on the flow and the Reynolds number.

Turbulence Characteristics In The Surface Boundary Layer Over The South American Pampa

This paper presents results of turbulence measurementsmade in the south of Brazil in the Pampa region.Data collected at 1Hz are used to calculatestandard deviations of temperature and velocities. Onthe other hand data collected at 10Hz areused to study the behaviour of spectra and cospectraof turbulence in the surface layer. Dimensionless dissipation rates of turbulent kinetic energy and temperature variance are also presented. The frameworkof Monin–Obukhov Similarity theory is used and allresults are compared with other experimentalstudies.

Towards lowering dissipation bounds for turbulent flows

We examine the background flow variational principle for calculating bounds on the energy dissipation rate in turbulent shear flow, and suggest to select this principle's test functions such that they comply with the small-scale smoothness of real turbulent velocity fields. A self-consistent algorithm implementing this requirement then yields an upper bound on the dimensionless dissipation coefficient which shows a weak power-law decrease at high Reynolds numbers, instead of approaching a nonzero constant, as it did in previous estimates.

Dissipation rates of turbulent kinetic energy and temperature and humidity variances over different surfaces

Dissipation rates of turbulent kinetic energy, and temperature and humidity variances have been analyzed using turbulent data collected from the Gobi desert, grassland, and suburban and urban sites that have different physical conditions. Instrumentation was installed at heights of 4.9 m, 3.45 m, 75 m and 47 m over the Gobi desert, grassland, and suburban and urban sites, respectively. The dimensionless dissipation rates of turbulent ϕ ε , kinetic energy, temperature variance ϕ N , and humidity variance ϕ γ are found to be more than 20% less than that required to balance the production of energy by wind shear and the variances by temperature and humidity gradients. The deficits appear to increase with the increase of absolute stability parameter. Combining the results from previous and present studies, the non-dimensional dissipation rates of turbulent kinetic energy, and temperature and humidity variances are modified by using the stability parameter.

The average dissipation rate of turbulent kinetic energy in the neutral and unstable atmospheric surface layer

The mean rate of dissipation of turbulent kinetic energy is related to the surface fluxes of momentum and heat through the turbulent kinetic energy budget equation. This relationship may be used to estimate surface fluxes from measurements of the dissipation rates. The success of recent applications of the approach has been limited by uncertainties surrounding the functional relationship between the dimensionless dissipation rates and the atmospheric stability parameter. A pair of field experiments was designed and carried out in the atmospheric surface layer to identify this functional relationship over a broad range of neutral and convective flows, covering greater than 3 orders of magnitude in the stability parameter. Mean dissipation rates were computed using Fourier power spectra, second‐order structure functions, and third‐order structure functions. Arguments are presented for the superiority of the third‐order approach. A three‐sublayer conceptual model is invoked to guide the dimensional analysis, and the resulting dissipation rates are shown to scale uniquely in the three sublayers. Near the wall, in the dynamic sublayer, dissipation is significantly less than production, as energy is transported up to the more convective regions, where an equality between dissipation and production is achieved.

Optimum Finned Tubular Space Radiator

A two-dimensional finite-difference method of analysis is employed to elicit information pertaining to the thermal performance characteristics of a tubular space radiator with attached fins. The potential importance of the base surface interaction is brought out. The analysis takes into account the variation of base temperature, which has not been considered so far. A wide range of thermal and geometric parameters that are normally employed in the design of a tubular radiator has been considered. The existence of an optimum fin height and its dependence on other parameters have been explored. A new dimensionless heat dissipation parameter has been defined, and correlations that would aid the designer are presented.

Surface layer turbulence spectra and dissipation rates during low winds in tropics

Spectral characteristics of surface layer turbulence in an urban atmosphere are investigated. The observations used for this purpose represent low wind conditions in the tropics. The normalized power spectral shapes exhibit the usual characteristics in the inertial subrange and obey Monin-Obukhov scaling. However, the low-frequency behaviours do not conform to the previous observed relations. For horizontal components, large energy is contained in the low frequencies in contrast to the vertical component where roll-off to zero frequency is faster. The turbulent kinetic energy dissipation rate estimated from the spectra using Kolmogorov's inertial subrange law is found to be isotropic unlike the velocity variances. The expressions for the dimensionless dissipation rate do not seem to work well in low winds in an urban atmosphere. For the data considered, the dissipation rate exhibits a power law relationship with the mean windspeed and the friction velocity.

Crossover from high to low Reynolds number turbulence.

The Taylor-Reynolds and Reynolds number (${\mathrm{Re}}_{\ensuremath{\lambda}}$ and Re) dependence of the dimensionless energy dissipation rate ${c}_{\ensuremath{\epsilon}}=\frac{\ensuremath{\epsilon}L}{{u}_{1,\mathrm{rms}}^{3}}$ is derived for statistically stationary isotropic turbulence, employing the results of a variable range mean field theory. Here $\ensuremath{\epsilon}$ is the energy dissipation rate, $L$ the (fixed) outer length scale, and ${u}_{1,\mathrm{rms}}$ a rms velocity component. Results for ${c}_{\ensuremath{\epsilon}}({\mathrm{Re}}_{\ensuremath{\lambda}})$ and also for ${\mathrm{Re}}_{\ensuremath{\lambda}}(\mathrm{Re})$ are in good agreement with experiment. Using the Re dependence of ${c}_{\ensuremath{\epsilon}}$ we account for the time dependence of the mean vorticity $\ensuremath{\omega}(t)$ for decaying isotropic turbulence. The lifetime of decaying turbulence, depending on the initial ${\mathrm{Re}}_{\ensuremath{\lambda},0}$ is predicted to saturate at $\frac{0.18{L}^{2}}{\ensuremath{\nu}}\ensuremath{\propto}{\mathrm{Re}}_{\ensuremath{\lambda},0}^{2}$ ($\ensuremath{\nu}$ the viscosity) for large ${\mathrm{Re}}_{\ensuremath{\lambda},0}$.