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Analysis of the influence of deflector shape on heat transfer rate in glass tempering process

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The thickness of tempered glass is usually more than 3 mm. To achieve thinner tempered glass, it is necessary to clarify the stress change during its quenching process. Glass toughening involves high temperatures, which made the real-time measurement of the temperature distribution, stress distribution, and phase changes occurring difficult. However, these parameters directly affect the strength of the tempered glass. In this paper, for the purpose of evaluating and optimizing the tempering process, nonlinear finite element analysis method has been used to simulate the distribution of the temperature gradient, and the final residual stress of the glass samples with different thickness. The geometry and mathematical model to be used were established, and the boundary conditions for the simulations were set on the basis of the actual toughening conditions. It is found that the thickness has a great influence on the quenching period, temperature gradient and stress fields distribution.
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A numerical investigation was carried out on circular jet impingement heat transfer from a constant temperature circular cylinder to understand the major parameters which influence the fluid flow and heat transfer characteristics. In this study, air was considered as the working fluid. The flow was considered to be three-dimensional, incompressible, and turbulent. To select a suitable turbulence model for the parametric study, numerical simulations were carried out with standard k-, standard k-ω, RNG k-, Realizable k-, and SST k-ω turbulence models for modeling Reynolds stress terms. Simulations were also carried out using four low Reynolds number models. The results obtained using these models were compared with the available experimental results of jet impingement heat transfer from circular cylinder. It was identified that the RNG k- model predicts heat transfer characteristics better compared to all other turbulence models considered in this study. Using this turbulence model, a parametric study was carried out for the Reynolds number (Red ), defined based on the diameter of the nozzle ranging from 10,000 to 50,000. The ratio of distance between the nozzle exit and the cylinder surface to the diameter of the jet (h/d) was varied from 4 to 16 and the ratio of nozzle diameter to cylinder diameter (d/d) varied from 0.11 to 0.25. For a fixed Red and d/d, the stagnation point Nusselt number increases as h/d decreases. The stagnation point Nusselt number decreases as d/d increases for a fixed value of Red and h/d. The effects of change in h/d and d/D are significant only near the stagnation region.
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The performance of several turbulence models in the prediction of convective heat transfer due to slot jet impingement onto flat and concave cylindrical surfaces is evaluated against available experimental data. The candidate models for evaluation are (1) the standard k – ϵ model, (2) the RNG k – ϵ model, (3) the realizable k – ϵ model, (4) the SST k – ω model, and (5) the LRR Reynolds stress transport model. Various near-wall treatments such as equilibrium wall function and two-layer enhanced wall treatment are used in combination with these turbulence models. The computations are performed using the commercial computational fluid dynamics (CFD) code Fluent. From the validation exercises, it is found that when the impingement surface is outside the potential core of the jet, most of the turbulence models predict reasonably accurate thermal data (local Nusselt number variation along the impingement surface). When the impingement surface is within the potential core of the jet, the turbulence models grossly overpredict the Nusselt number in the impingement region, but in the wall jet region the Nusselt number prediction is fairly accurate. Overall, the RNG k – ϵ model with the enhanced wall treatment and the SST k – ω model predict the Nusselt number distribution better than the other models for the flat plate as well as for the concave surface impingement cases. However, the hydrodynamic data such as the mean velocity profiles are not accurately predicted by the SST k – ω model for the concave surface impingement case, whereas the RNG k – ϵ model predictions of the velocity profiles agree very well with the experiment. The Reynolds stress model does not show any distinctive advantage over the other eddy viscosity models.
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A modified SIMPLEC scheme for flow computations on collocated grids has been developed. It is demonstrated that the standard SIMPLEC scheme [1] is inconsistent when applied on collocated grids. Hence, for steady computations the computed solution depends on the velocity underrelaxation parameter f u , whereas the solutions of unsteady computations for small time steps are polluted by unphysical wiggles. A revised scheme is proposed that extends the capability of the SIMPLEC method to cope with collocated grids in a general and consistent way. The efficiency of the new scheme is demonstrated by computing flows past a circular cylinder and an airfoil.
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The thermal tempering of flat glass in a laboratory facility and an industrial unit with single-jet and multi-jet coolings have been modelled. Firstly the influence of radiation on the transient and residual stresses through the glass thickness was considered. 3D computational fluid dynamic (CFD) models were then developed to analyse the air flow and determine the convective heat transfer at the glass surface during tempering. By coupling these models with 3D finite element models taking both structural and stress relaxation into account, the residual tempering stresses were computed. Photoelastic measurements of the stresses on the surface and through the thickness of the tempered glass plates were used to validate the numerical approach. The homogeneity of the temperature distribution and the residual stresses in the multi-jet configuration were analysed. Finally, a new ultrasonic method to control the residual tempering stresses is proposed. The measurements made on glass plates tempered using a single-jet configuration were in agreement with the numerical predictions.
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The present paper develops and validates a 3D model for the simulation of glass tempering. It is assembled from well-known models of temperature dependent viscoelasticity and structural relaxation and predicts both transient and steady-state stresses in complex 3D glass geometries. The theory and implementation of the model is comprehensively given and the model is carefully checked and validated. It is demonstrated that by adjusting a single parameter in the model, experimental results can be replicated accurately even for cooling rates far from normal.
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Study of the time dependence of physical properties in the transformation range of glass is complicated by the “memory effect” and the inherent nonlinearity which are characteristic of structural relaxation. A multiparameter model of structural relaxation is presented that differs from earlier models in that it takes account of both these effects. This model fits available experimental data well; these data were obtained for the most part by observing the evolution of properties (such as density or refractive index) following a step change in temperature. The present model also permits prediction of the physical properties of glass subjected to arbitrary and more complex temperature-time histories. It should, therefore, also be useful in the rational design of heat treating processes such as annealing.
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This paper deals with impinging air jets cooling applied to thermal glass tempering. The static tempering of a square flat glass sample in an industrial unit is modelled to assess the convective heat transfer from the glass surface to the cooling jets. The flow in the air supply nozzles is first investigated to verify the uniformity of the flow conditions at the jet outlets. The numerical simulation of the static tempering of a flat glass sample is validated by comparison with measurements of the residual stresses by photoelasticity and with surface temperature measurements by pyrometry. Heat transfer coefficients are calculated for four different jets Reynolds numbers. It is found that the relative deviation of the local heat transfer from the average heat transfer is independent of the Reynolds number and that the average Nusselt number correlates to the Reynolds number by a power law in good agreement with those commonly found in the literature. The heat transfer is low compared to other correlations, because of the relatively large H/D ratio and of the strong cross flow induced by the large amount of spent air.
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