Ghulam Arshed

THERMAL ANALYSIS OF A COLD ROLLING PROCESS — A NUMERICAL APPROACH

The deformation of material and friction between the roll and deforming material contact region produce a large amount of heat. This heat energy is conducted toward the roll and the workpiece (strip). A well-designed cooling system is needed to control the material properties and grain structure of the rolled product. Therefore, complete knowledge of the temperature distribution in both the roll and strip is necessary to design an efficient cooling system to control the material properties. In this work, both the roll and strip have been modeled as a coupled heat transfer problem to predict the temperature distribution. Using a finite-volume approach, the governing differential equations as well as the boundary conditions are discretized, which are then solved numerically to predict the temperature distributions. The stability of the solution was examined by changing the grid sizes in the bite region; in addition, the numerical results are validated against published work in the literature for certain special operating conditions. The impact of roll speed and heat transfer coefficient on the distribution of heat flow in both the roll and workpiece are demonstrated through the temperature contour plots.

Minimizing errors from linear and nonlinear weights of WENO scheme for broadband applications with shock waves

Abstract Improvements in the numerical algorithm for the dynamics of flows that involve discontinuities and broadband fluctuations simultaneously are proposed. These two flow features suggest numerical strategies of a paradoxical nature because the discontinuities demand dissipation, and the small-scale smooth features require the opposite. There may be several ways to approach such a complicated issue, but the natural choice is a numerical technique that can adjust adaptively with flow regimes. The weighted essentially non-oscillatory (WENO) scheme may be this choice. However, there are two sources of dissipation associated with the WENO procedure: the upwind optimal stencil and the nonlinear adaption mechanism. The current work suggests a robust and comprehensive treatment for the minimization of dissipation error from these two sources. The optimization technique, which is guided by restriction on the linear optimal weights derived from stability and consistency requirement, is used to delay the dissipation of the upwind optimal stencil to those wavenumbers for which the dispersion error is large. The parallel advantage of this technique is the improvement of the dispersion property. Nevertheless, optimization decreases the formal order of accuracy of the optimal stencil from fifth order to third order. This loss of accuracy is derived by Taylor series expansion. Using Taylor-series expansion and WENO procedure, the third-order accuracy is verified in the smooth region, except at the critical point of order two, where the order of accuracy reduces to at least second order. This possible loss of accuracy at the second-order critical point is restored in an attempt to reduce the dissipation induced by the nonlinear adaptive weights. Modification of the nonlinear weights to reduce the dissipation is introduced by redefining them with an additional smoothness indicator. Other suggestions to minimize the dissipation of the nonlinear weights are also reviewed. The numerical approximation of the spatial derivative is performed by means of a conservative and consistent finite difference method based on monotone local Lax–Friedrichs Riemann solver. The resulting scheme is then integrated by the optimal third-order TVD Runge–Kutta method to ensure the nonlinear stability of the overall numerical method. A variety of benchmark problems, ranging from non-broadband to broadband, are solved using the proposed schemes and compared with the existing ones. Most test problems are validated against exact or reference data. The numerical results with bandwidth optimization and modification of the nonlinear weights are consistently superior.

Implementation of Improved WENO Scheme to Higher Dimensions in Relation to Shock-Turbulence Interaction

In the previous efforts, the capability of the WENO scheme of Jiang and Shu was increased by decreasing its numerical diffusion so that it performs better for shockturbulence applications. The WENO scheme after modifications was applied to scalar and vector equations in one dimension and found the results quite promising. In the present effort, continuing in the same spirit, the scheme is extended to two dimensions. The WENO scheme due to Jiang and Shu and its modified version are investigated and implemented to the system of Euler equations in two dimensions. Both versions of order five with consistent and conservative non-monotone or monotone flux method are used to discretize the spatial derivatives in both directions. The numerical flux at the cell interface in each direction is achieved by the one dimensional WENO reconstruction by keeping the variation in the other direction fixed. The system of equations is solved by characteristic field decomposition. The time integration is performed by the optimal third-order TVD Runge-Kutta scheme. The results of several crucial bench-mark problems in relation to applications which require low dissipation of the numerical schemes are produced and discussed.

In Preparation of a High-Resolution Scheme for a Shock-Turbulence Interaction

Various aspects of higher-order numerical schemes are investigated as a logical first step in preparation of a DNS code for a shock-turbulence interaction governed by a three dimensional compressible Navier-Stokes equations. In order to achieve this goal, a numerical scheme is planned to adopt in such a way that it is both shock-capturing and capable of resolving high-frequency turbulent fluctuations. As an initial step a shock-capturing scheme i.e., the well-known WENO scheme of Jiang and Shu, is investigated and implemented to the scalar conservation law and the system of Euler equations in one-dimensional space. However, the WENO scheme loses optimal accuracy near critical points. A slight modification to the scheme introduced by Henrick et al. preserves the optimal accuracy near critical points. Moreover, the slope modification method of Yang is also implemented to decrease the smearing around a contact discontinuity. The WENO scheme of order five with consistent and conservative non-monotone or monotone flux method is used to discretize the spatial derivative. The time integration is performed by the optimal third-order TVD Runge-Kutta scheme. The system of equations is solved by characteristic field decomposition. The results of several but crucial bench-mark problems are compared and are found in good agreement with the exact or reference solutions.

Investigation into Flow Field in Relation to Laser Gas Assisted Processing: Influence of Assisting Gas Velocity on the Flow Field

A transiently developing jet finds application in metal processing, such as a vapor jet produced during laser ablation of solid surfaces. In the present study, laser gas-assisted processing is considered and vapor ejection from the solid surface during the ablation process is modeled. In this case, a transiently developing jet emerging from the solid wall and steady jet opposing (impinging onto) the transiently developing jet situation is studied. Since the thermal properties of vapor ejecting from the wall is not known, transiently developing helium jet is considered to resemble the vapor emanating from the wall. An air jet is employed to impinge onto the developing jet. The transient flow properties of the developing jet are obtained from the previous study. The flow and temperature fields are predicted numerically using a control volume approach. A low Reynolds number k–ϵ turbulence model is used to account for the turbulence. In order to investigate the influence of mean velocity of the steady jet on the flow field near the transiently developing jet, four mean velocities are considered. It is found that mean velocity of the steady jet has significant effect on the flow field in the region close to the transiently developing jet. In this case, a circulation cell is developed next to the steady jet boundary and the orientation of cell is influenced by the steady jet flow conditions.

Opposing steady and transiently developing jets in relation to laser machining

The opposing jet situation in relation to laser gas assisted drilling process is considered. In this case, impinging steady jet resembling the assisting gas jet and transiently developing jet resembling the vapour jet emanating from the solid surface due to laser ablation are employed in the analysis. A numerical method using a control volume approach is introduced for simulating the flow and temperature fields. Since the thermophysical properties of the transiently developing vapour jet are not known, helium jet at 1500 K is accommodated in the simulations. Helium is a chemically stable inert gas, which does not ionize at 1500 K. The inlet conditions of transiently developing jet are taken from the previous study. It is found that the enhancement of the radial flow, due to opposing situation, generates a circulation cell next to the steady jet boundary. The orientation and size of the circulation cell changes with time thereby modifying the streamline curvature of the steady jet. The transiently developing jet does not behave like a transiently self-developing one. Moreover, the radial jet resulted from the opposing jets behaves almost like a free jet.

Transient Helium Jet Expansion Into Stagnant Air in Relation to Laser Drilling

Abstract Transient helium jet expansion into a stagnant air environment is modelled to resemble the laser vapour ejection from the cavity during the drilling process. As the metal vapour properties are not known, helium is employed while the previously measured jet inlet velocity profiles are introduced in the simulations. A numerical scheme employing a control volume approach is used to discretize the governing equations of flow. The predictions are validated through a case study associated with an incompressible transient jet flow. It is found that the jet inlet profile influences considerably the self-similar behaviour of the jet. Moreover, the jet expands radially in the early period while as time progresses, the axial penetration of the jet becomes high.