Nonlinear Temperature Gradient Research Articles

Transport Bifurcation in a Rotating Tokamak Plasma

The effect of flow shear on turbulent transport in tokamaks is studied numerically in the experimentally relevant limit of zero magnetic shear. It is found that the plasma is linearly stable for all nonzero flow shear values, but that subcritical turbulence can be sustained nonlinearly at a wide range of temperature gradients. Flow shear increases the nonlinear temperature gradient threshold for turbulence but also increases the sensitivity of the heat flux to changes in the temperature gradient, except over a small range near the threshold where the sensitivity is decreased. A bifurcation in the equilibrium gradients is found: for a given input of heat, it is possible, by varying the applied torque, to trigger a transition to significantly higher temperature and flow gradients.

Microwave-induced adjustable nonlinear temperature gradients in microfluidic devices

We describe on-chip microwave generation of spatial temperature gradients in a polymeric microfluidic device that includes an integrated microstrip transmission line. The transmission line was fabricated photolithographically on commercially available adhesive copper tape. The fluid temperature during microwave heating was measured by observing the temperature-dependent fluorescence intensity of a dye solution in the microchannel. Large interference effects, which were produced by superposition of a sinusoidal and two exponential temperature distributions, were measured at 12 GHz and 19 GHz. Temperature extremes of 31 °C and 53 °C at the minimum and maximum of the sinusoid were established within 1 s. The sinusoid also produced a quasilinear temperature gradient along a 2 mm distance with a slope of 7.3 °C mm−1. This technique has the potential to benefit many biological, chemical and physical applications requiring rapid temperature gradients.

Microfluidic gradient PCR (MG-PCR): a new method for microfluidic DNA amplification

This study develops a new microfluidic DNA amplification strategy for executing parallel DNA amplification in the microfluidic gradient polymerase chain reaction (MG-PCR) device. The developed temperature gradient microfluidic system is generated by using an innovative fin design. The device mainly consists of modular thermally conductive copper flake which is attached onto a finned aluminum heat sink with a small fan. In our microfluidic temperature gradient prototype, a non-linear temperature gradient is produced along the gradient direction. On the copper flake of length 45 mm, width 40 mm and thickness 4 mm, the temperature gradient easily spans the range from 97 to 52 degrees Celsius. By making full use of the hot (90-97 degrees Celsius) and cold (60-70 degrees Celsius) regions on the temperature gradient device, the parallel, two-temperature MG-PCR amplification is feasible. As a demonstration, the MG-PCR from three parallel reactions of 112-bp Escherichia coli DNA fragment is performed in a continuous-flow format, in which the flow of the PCR reagent in the closed loop is induced by the buoyancy-driven nature convection. Although the prototype is not optimized, the MG-PCR amplification can be completed in less than 45 min. However, the MG-PCR thermocycler presented herein can be further scaled-down, and thus the amplification times and reagent consumption can be further reduced. In addition, the currently developed temperature gradient technology can be applied onto other continuous-flow MG-PCR systems or used for other analytical purposes such as parallel and combination measurements, and fluorescent melting curve analysis.

Thermal stresses in radiant tubes: A comparison between recuperative and regenerative systems

A comparison was made between thermal stresses occurring in radiant tubes used in regenerative and recuperative systems. It was found that higher temperatures close to the annealing temperatures lead to stress relieving. The only stresses occurring were due to the non-linear axial temperature gradients along the length of the radiant tube in a recuperative system, whereas the radiant tube in a regenerative system remained essentially stress free due to a comparatively linear axial temperature gradient.

Effect of skewed joints on the performance of jointed concrete pavement through 3D dynamic finite element analysis

The effect of skewing the transverse joints in concrete rigid pavements is studied through 3D finite element modelling. Models of multi-layered systems consisting of Portland cement concrete slabs, base and subgrade were developed. These consisted of slabs having straight as well as skewed joints. In order to study the state of stresses and strains in both straight and skewed slabs, the models were subjected to moving axle loads as well as non-linear temperature gradients. More refined models were developed and subjected to falling weight deflectometer dynamic loads to study the state of stresses at the dowels–concrete interfaces. The study, shows that skewing the joints did not reduce the level of stresses and strains in critical locations in the concrete slab. Also a close study of the induced stresses and strains showed that fatigue relations adapted for concrete pavements needed to be refined. The distribution of stresses around the dowel sockets indicates the formation of a tensile stress component, which initiates a tensile crack before any failure of concrete material in compression.

Numerical Modelling of the Influence of Joint Typologies on the 3D Behaviour of a Steel Sub-Frame Under a Natural Fire

In order to address the complex loading condition of steel joints in fire, and based on the experimental fire tests on steel frames with different joint typologies, performed at the University of Coimbra (Santiago et al. 2008), a detailed three-dimensional model was developed and calibrated to simulate the behaviour of welded and bolted end plate beam-to-column joints. The structural frame is modeled combining 3D shell, solid and joint elements, thereby taking into account the effect of the local failure modes, and the realistic behaviour of the frame exposed to a natural fire. The numerical model accounts for the initial geometrical imperfections, non-linear temperature gradient, geometrical and material nonlinearity and temperature dependent material properties. The results show the performance of each individual structural joint component under heating and cooling conditions and identify the main dependencies of the geometrical and mechanical variables of the components on the joint behaviour. The global behaviour of the frame and the joint failure modes are compared and discussed with the experimental observations.

Clarifications to the limitations of the s-α equilibrium model for gyrokinetic computations of turbulence

In the context of gyrokinetic flux-tube simulations of microturbulence in magnetized toroidal plasmas, different treatments of the magnetic equilibrium are examined. Considering the Cyclone DIII-D base case parameter set [Dimits et al., Phys. Plasmas 7, 969 (2000)], significant differences in the linear growth rates, the linear and nonlinear critical temperature gradients, and the nonlinear ion heat diffusivities are observed between results obtained using either an s-α or a magnetohydrodynamic (MHD) equilibrium. Similar disagreements have been reported previously [Redd et al., Phys. Plasmas 6, 1162 (1999)]. In this paper it is shown that these differences result primarily from the approximation made in the standard implementation of the s-α model, in which the straight field line angle is identified to the poloidal angle, leading to inconsistencies of order ε (ε=a/R is the inverse aspect ratio, a the minor radius and R the major radius). An equilibrium model with concentric, circular flux surfaces and a correct treatment of the straight field line angle gives results very close to those using a finite ε, low β MHD equilibrium. Such detailed investigation of the equilibrium implementation is of particular interest when comparing flux tube and global codes. It is indeed shown here that previously reported agreements between local and global simulations in fact result from the order ε inconsistencies in the s-α model, coincidentally compensating finite ρ∗ effects in the global calculations, where ρ∗=ρs/a with ρs the ion sound Larmor radius. True convergence between local and global simulations is finally obtained by correct treatment of the geometry in both cases, and considering the appropriate ρ∗→0 limit in the latter case.

Finite element cohesive fracture modeling of airport pavements at low temperatures

Low temperature cracking induced by seasonal and daily thermal cyclic loads is one of the main critical distresses in asphalt pavements. The safety of aircraft departure and landing becomes a crucial issue in runways when thermal cracks occur in airport pavements. The low-temperature fracture behavior of airport pavements was investigated using a bilinear cohesive zone model (CZM) implemented in the finite element method (FEM). Nonlinear temperature gradients of pavement structures were estimated based on national weather data and an integrated climate prediction model. Experimental tests were conducted to obtain the numerical model inputs such as viscoelastic and fracture properties of asphalt concrete using creep compliance tests, indirect tensile strength tests (IDT), and disk-shaped compact tension (DC(T)) tests. The finite element pavement fracture models could successfully predict the progressive crack behavior of asphalt pavements under the critical temperature and heavy aircraft gear loading conditions.

Effects of Temperature Gradients in Batch Kraft Cooking of Wood Species Mixtures

A batch kraft cooking non-isothermal digester was modelled based on chemical kinetics and mass transfer equations for softwood. Kraft pulping modelling had been designed for non-isothermal batch cooks of chip mixtures: either mixed-size chips, according to a thickness distribution law, or mixtures of different wood species. The case of existing linear or non-linear radial temperature gradients in a digester was examined. Several chip populations with different thickness distribution were used: normal (major abundance of 3-5 mm chips); uniform (equal abundance of chips in the range 3-12 mm); Gaussian-type (centred on 7 mm chips); Poisson-type (major abundance of 3 mm chips). The effect on cooking results due to temperature gradients in digester was predicted along with the existing non-uniformity arising from the effect of chip size distribution, density, and wood mixtures of different composition and chemical properties (rate constants, activation energies). Results are presented as a kappa number, yield and rejects distributions and mean values. The rather sharp kappa number distributions obtained for isothermal cooks were found to be severely spread in the linear temperature gradient case. The above effects were attenuated when a central core in the digester was kept isothermal. The stratification of chips resulted in significantly reduced width in kappa number distributions. Highest density chips cooked lower; however, since diffusion effects were more prominent in them, their apparent activation energy was also less. So they were slightly less affected by temperature gradients in the digester. Cooking different wood species together also affected the spread of the kappa number distribution. This cumulated more or less to temperature gradients effects, depending on chemical activation energy data and possible differences between species.

Effects of plasma shaping on nonlinear gyrokinetic turbulence

The effects of flux surface shape on the gyrokinetic stability and transport of tokamak plasmas are studied using the GS2 code [M. Kotschenreuther, G. Rewoldt, and W. M. Tang, Comput. Phys. Commun. 88, 128 (1995); W. Dorland, F. Jenko, M. Kotschenreuther, and B. N. Rogers, Phys. Rev. Lett. 85, 5579 (2000)]. Studies of the scaling of nonlinear turbulence with shaping parameters are performed using analytic equilibria based on interpolations of representative shapes of the Joint European Torus [P. H. Rebut and B. E. Keen, Fusion Technol. 11, 13 (1987)]. High shaping is found to be a stabilizing influence on both the linear ion-temperature-gradient (ITG) instability and the nonlinear ITG turbulence. For the parameter regime studied here, a scaling of the heat flux with elongation of χ∼κ−1.5 or κ−2.0, depending on the triangularity, is observed at fixed average temperature gradient. While this is not as strong as empirical elongation scalings, it is also found that high shaping results in a larger Dimits upshift of the nonlinear critical temperature gradient due to an enhancement of the Rosenbluth-Hinton residual zonal flows.

Numerical simulations of rotating axisymmetric sunspots

A numerical model of axisymmetric convection in the presence of a vertical magnetic flux bundle and rotation about the axis is presented. The model contains a compressible plasma described by the non-linear MHD equations, with density and temperature gradients simulating the upper layer of the Sun's convection zone. The solutions exhibit a central magnetic flux tube in a cylindrical numerical domain, with convection cells forming collar flows around the tube. When the numerical domain is rotated with a constant angular velocity, the plasma forms a Rankine vortex, with the plasma rotating as a rigid body where the magnetic field is strong, as in the flux tube, while experiencing sheared azimuthal flow in the surrounding convection cells, forming a free vortex. As a result, the azimuthal velocity component has its maximum value close to the outer edge of the flux tube. The azimuthal flow inside the magnetic flux tube and the vortex flow is prograde relative to the rotating cylindrical reference frame. A retrograde flow appears at the outer wall. The most significant convection cell outside the flux tube is the location for the maximum value of the azimuthal magnetic field component. The azimuthal flow and magnetic structure are not generated spontaneously, but decay exponentially in the absence of any imposed rotation of the cylindrical domain.

Numerical study of a steel sub-frame in fire

Steel-framed buildings are generally designed with “simple” shear-resisting connections, and lateral forces are resisted by vertical bracing and shear walls. When a beam is considered then the effects of the longitudinal restraints by the adjacent structure and the rotational restraint by the connections has to be taken into account. Because of structural interaction, the beam behaviour at elevated temperature is rather complex. This paper presents a numerical parametric study of a structural system consisting of an exposed steel beam restrained between a pair of fire protected steel columns. The structural sub-frame is modelled using 3D shell elements, thereby taking into account the effect of the local failure modes, and the realistic behaviour of the sub-frame exposed to natural fire. The numerical model accounts for the initial geometrical imperfections, nonlinear temperature gradient over the cross-section, geometrical and material nonlinearity and temperature dependent material properties. Results obtained using a general Finite Element software – LUSAS and a fire dedicated software – SAFIR, are compared. The influence of following variables: beam span/depth ratio, lateral restraint, gradient temperature within the cross-section and mechanical load level is presented in the paper. The failure modes, the development of the internal forces and displacements throughout the analysis are considered to exemplify the effects of the variables considered.

Analysis of dynamic deformation processes with adaptive KALMAN-filtering

The analysis of dynamic deformation processes is an important task in civil and in mechanical engineering. One main emphasis is set on the derivation of the objects transmission function, represented by systems of ordinary or partial differential equations (“white box”-models). The parametric identification of the initial and boundary conditions and relevant material parameters is one of the new challenges in the application of least-square algorithms. Embedding the investigation of the deformation process in a combination of a theoretical and an experimental system analysis suitable methods are provided with adaptive KALMAN-filtering as central identification tool. In this paper the approach of a full system analysis is shown quantifying a dynamic “white-box”-model for the calculation of thermal deformations of bar-shaped machine elements. The task was motivied from mechanical engineering searching new methods for the precise prediction and computational compensation of thermal influences in the heating and cooling phases of machine tools (i.e. robot arms, etc.). The quantification of thermal deformations under variable dynamic loads requires the modelling of the non-stationary spatial temperature distribution inside the object. Based upon FOURIERS law of heat flow the high-grade non-linear temperature gradient is represented by a system of partial differential equations within the framework of a dynamic Finite Element topology. It is shown that adaptive KALMAN-filtering is suitable to quantify relevant disturbance influences and to identify thermal parameters (i.e. thermal diffusivity) with a deviation of only 0,2%. As result an identified (and verified) parametric model for the realistic prediction respectively simu-lation of dynamic temperature processes is presented. Classifying the thermal bend as the main deformation quantity of bar-shaped machine tools, the temperature model is extended to a temperature deformation model. In lab tests with an aluminium column control measurements show that the identified model can be used to predict the columns bend with a mean deviation smaller than 10 mgon. Consequently the deformation model is a precise predictor and suitable for realistic simulations of thermal deformations under variable dynamic loads. In future our activities will be primarily focussed on applications in industrial manufacturing. 1. Parametric identification of dynamic deformation processes The creation of a realistic parametric dynamic deformation model is directly associated with the task to combine systems of differential equations (theoretical physical model) with empirical measurements. Consequently basic principles of system theory can be adapted to the geodetic deformation analysis. The parametric identification of a dynamic “white box”-model 3rd IAG / 12th FIG Symposium, Baden, May 22-24, 2006

Validation of 3DFE Analysis of Rigid Pavement Dynamic Response to Moving Traffic and Nonlinear Temperature Gradient Effects

The response of dowel jointed concrete pavements to the combined effect of nonlinear thermal gradient and moving axle load is examined using three-dimensional finite-element (3DFE) modeling. The 3DFE-computed response to moving axle load was field validated versus measured concrete slab response to a fully loaded moving dump truck. The 3DFE-predicted slab curling due to nonlinear thermal gradient through the slab thickness was validated versus: (1) corner-dowel bar bending as measured using instrumented dowel embedded in an instrumented rigid pavement section in West Virginia; and (2) Westergaard’s closed-form solution. The effects of slab thickness, slab length, axle loading position, and axle type on slab stresses are examined. It is shown that while a negative temperature gradient reduces the intensity of traffic-induced stresses, positive temperature gradient increases it several fold. Formulas are developed for the computation of the peak principal stresses due to the combined effect of tandem axle l...

Thermomechanical Stability of Imperfect Functionally Graded Plates Based on the Third Order Theory

Mechanical and thermal buckling analysis of rectangular functionally graded plates with initial geometric imperfections is presented in this paper. It is assumed that the nonhomogeneous mechanical properties vary linearly through the thickness of the plate. The plate is assumed to be under three types of mechanical loadings, namely, uniaxial compression, biaxial compression, and biaxial compression and tension; and two types of thermal loadings, namely, the uniform temperature rise and nonlinear temperature gradient through the thickness. The equilibrium, stability, and compatibility equations are derived using the third-order shear deformation plate theory. Resulting equations are employed to obtain the closed-form solution for the critical buckling load for each loading case. The results are compared with the known data in the literature.

Failure prediction of skewed jointed plain concrete pavements using 3D FE analysis

A section of skewed jointed plain concrete pavements (JPCPs) that was constructed in the northern part of Indiana failed with premature transverse cracks. The cracks were observed within 3–4 years of construction. This research was performed to determine if the failure of the skewed JPCPs could have been predicted using a 3D finite element (FE) analysis. A representative 3D FE model was developed and analyzed using three different subgrade materials under traffic and nonlinear thermal loads. The dowel bars and aggregate interlock action were modelled at the skewed joints between adjacent concrete slabs. The effects of linear and nonlinear temperature gradients were compared with regard to the predicted failure of the pavements. The finite element analysis predicted not only the failure of the pavement, but also the correct orientation of the cracks.

The Crucial Role of Trehalose and Structurally Related Oligosaccharides in the Biosynthesis and Transfer of Mycolic Acids in Corynebacterineae

Trehalose (alpha-D-glucopyranosyl-alpha'-D-glucopyranoside) is essential for the growth of the human pathogen Mycobacterium tuberculosis but not for the viability of the phylogenetically related corynebacteria. To determine the role of trehalose in the physiology of these bacteria, the so-called Corynebacterineae, mutant strains of Corynebacterium glutamicum unable to synthesize trehalose due to the knock-out of the genes of the three pathways of trehalose biosynthesis, were biochemically analyzed. We demonstrated that the synthesis of trehalose under standard conditions is a prerequisite for the production of mycolates, major and structurally important constituents of the cell envelope of Corynebacterineae. Consistently, the trehalose-less cells also lack the cell wall fracture plane that typifies mycolate-containing bacteria. Importantly, however, the mutants were able to synthesize mycolates when grown on glucose, maltose, and maltotriose but not on other carbon sources known to be used for the production of internal glucose phosphate such as fructose, acetate, and pyruvate. The mycoloyl residues synthesized by the mutants grown on alpha-D-glucopyranosyl-containing oligosaccharides were transferred both onto the cell wall and free sugar acceptors. A combination of chemical analytical approaches showed that the newly synthesized glycolipids consisted of 1 mol of mycolate located on carbon 6 of the non reducing glucopyranosyl unit. Additionally, experiments with radioactively labeled trehalose showed that the transfer of mycoloyl residues onto sugars occurs outside the plasma membrane. Finally, and in contradiction to published data, we demonstrated that trehalose 6-phosphate has no impact on mycolate synthesis in vivo.

A novel tunable dispersion slope compensator based on nonlinearly thermally chirped fiber Bragg grating

We propose a novel method for introducing a chirp on a fiber Bragg grating. Applying a controllable nonlinear temperature gradient across a uniformly written Bragg grating chirps it nonlinearly to realize a tunable dispersion slope compensator for waveform distortion compensation. This scheme allows an adjustable, repeatable, stable, and precise nonlinear chirp onto the grating. The dispersion slope of the device was tuned from −37.06 to −199.45 ps/nm 2, with observed GDR as low as ±5 ps.

Nonlinear Temperature Gradient Effects in Dowel Jointed Concrete Slabs

The effect of nonlinearity in Temperature Gradient Profile (TGP) on dowel jointed concrete slabs is examined using nonlinear Three-Dimensional Finite Element (3DFE) modeling. The model's thermal response is validated versus field-measured data collected from a heavily instrumented section on the Robert Byrd Highway (Route 33) near Elkins, West Virginia, USA. Results indicate that TGP nonlinearity has its maximum effect on the longitudinal stress 0.28 m away from the transverse joint, i.e. near the end of the embedded dowel bars. A TGP that includes a uniform temperature drop is shown to induce a large magnitude of tensile thermal stress at mid slab. This stress is unaffected by the extent of nonlinearity in TGP and depends on the magnitude of temperature drop and the difference between slab top and bottom temperatures. It is shown that dowel bar bending, due to slab curling, introduces a significant edge restraint to slab contraction and expansion due to ambient temperature changes. Mid-slab longitudinal stress is shown to be minimal for a 4.6 m long slab.

大水深セメンチング技術

More and more drilling occurs in frontier areas and particularly in deep water. In this environment, where the water depth often ranges between 1000 and 3000 m, the temperature at the seabed is extremely low, reaching 1 degC. In addition, a nonlinear temperature gradient in this water column and the sea currents further participate in and accelerate the cooling of the fluids in the wells. These low temperatures considerably slow cement hydration, which adversely affects the compressive strength development of the cement slurries.The young, soft formations encountered in the first few thousand meters below the seafloor preclude the use of normal-density cement slurries. However, conventional low density cements take a long time to set and develop significant strength at these very low temperatures. The daily rate of the rigs able to drill these deepwater wells is fairly high. In addition, the latest generation of offshore deepwater rigs is designed to work faster and deliver wells drilled more efficiently. It is therefore important to have lightweight cement systems that set quickly and develop high strength in the short period of time compatible with the operation of these new rigs.Often, the permeable layers below the seabed contain either free gas, when the water depth (and pressure) is reasonable, or gas hydrates at greater water depth. The lightweight cement system used in deepwater wells must therefore also control gas during its setting process at these low prevailing temperatures.This paper will address the selection of proper deepwater cement slurry. Several case histories are also presented, where lightweight cements capable of setting quickly and managing gas flow in low temperatures have been required to economically drill and case formations with low fracture gradient in deepwater wells.