A three-dimensional transient thermomechanical analysis has been performed for the Gas Metal Arc Welding process using the finite element method. Because the heat generated due to elasto-visco-plastic straining in welding is negligible in comparison to the arc heat input, the thermomechanical analysis is uncoupled into two parts. The first part performs a three-dimensional transient heat transfer analysis and computes entire thermal history of the weldment. The second part then uses results of the first part and performs a three-dimensional transient thermo-elastoplastic analysis to compute transient and residual distortions, strains and stresses in the weld. The thermomechanical model incorporates all the thermophysical and mechanical properties of the material as functions of temperature. Boundary conditions used in the numerical simulation are quite general and are matched with the experiment carried out to measure transient strains in the mild steel (0.22 percent carbon steel) weld. Good qualitative agreement was achieved between calculated and measured transient strains.

Standard and extended k–ε turbulence closure models have been employed for three-dimensional heat transfer calculations for radially outward flow in rectangular and square cooling passages rotating in orthogonal mode. The objective of this modeling effort is to validate the numerical model in an attempt to fill the gap between model predictions and the experimental data for heat transfer in rotating systems. While the trend of heat transfer predictions by the standard k–ε turbulence model is satisfactory, the differences between the data and the predictions are approximately 30 percent or so in the case of high rotation number flow. The extended k–ε turbulence model takes an approach where an extra “source” term based on a second time scale of the turbulent kinetic energy production rate is added to the equation for the dissipation rate of turbulent kinetic energy. This yields a more effective calculation of turbulent kinetic energy as compared to the standard k–ε turbulence model in the case of high rotation number and high density ratio flow. As a result, comparison with the experimental data available in the literature shows that an improvement of up to a significant 15 percent (with respect to data) in the heat transfer coefficient predictions is achieved over the standard k–ε model in the case of high rotation number flow. Comparisons between the results of the standard k–ε model and the extended formulation are made at different rotation numbers, different Reynolds numbers, and varying temperature ratio. The results of the extended k–ε turbulence model are either as good or better than those of the standard k–ε model in all these cases of parametric study. Thus, the extended k–ε turbulence model proves to be more general and reduces the discrepancy between the model predictions and the experimental data for heat transfer in rotating systems.

Cooling of Gas turbine buckets to ensure adequate life margin with coolants at advanced engine conditions of pressure and temperature requires that the internal heat transfer as influenced by rotation be known with sufficient accuracy. The existing data base, comprised of information readily available in the open literature has limited advanced design applicability considering the range of geometric and fluid-thermal dimensionless parameters of interest. Further, studies conducted with the aid of computational fluid dynamics (CFD) have demonstrated that, as the range of such parameters is extended, the characteristics of the predicted heat transfer capability change significantly, to the extent that bucket coolant passage designs that are fully acceptable at state-of-the-art conditions are marginal or unacceptable at advanced conditions. The purpose of this paper is threefold, to: a) demonstrate the need for extending the current internal heat transfer data base, accounting for the effects of rotation, b) provide a physical understanding of the expected heat transfer characteristics at advanced conditions, and c) describe a test rig and test program focused on obtaining the data of interest.

The objective of the current modeling effort is to validate the numerical model and improve upon the prediction of heat transfer in rotating systems. Low-Reynolds number turbulence model (without the wall function) has been employed for three-dimensional heat transfer predictions for radially outward flow in a square cooling duct rotating about an axis perpendicular to its length. Computations are also made using the standard and extended high-Reynolds number kturbulence models (in conjunction with the wall function) for the same flow configuration. The results from all these models are compared with experimental data for flows at different rotation numbers and Reynolds number equal to 25,000. The results show that the low-Reynolds number model predictions are not as good as the high-Re model predictions with the wall function. The wall function formulation predicts the right trend of heat transfer profile and the agreement with the data is within 30% or so for flows at high rotation number. Since the Navier-Stokes equations are integrated all the way to wall in the case of low-Re model, the computation time is relatively high and the convergence is rather slow, thus rendering the low-Re model as an unattractive choice for rotating flows at high Reynolds number.The extended k-ε turbulence model is also employed to compute heat transfer for rotating flows with uneven wall temperatures and uniform wall heat flux conditions. The comparison with the experimental data available in literature shows that the predictions on both the leading wall and the trailing wall are satisfactory and within 5-25% agreement.

The two-equation models (k -E) have been employed to predict turbulent flow and heat transfer for radially outward flow in a cooling duct rotating in orthogonal mode. The low-Reynoldsnumber model, which permits integration of the Navier-Stokes equations to the wall, has been used. The results from the low-Re model and the high-Re model with "Wall Function" are compared with the experimental data available in literature. Computations have been made for a range of Reynolds numbers (2500 to 25000) and a range of rotation numbers (0.088 to 0.24). Different conditions such as uniform wall temperature, uniform wall heat flux and uneven wall temperatures have been used as boundary conditions for heat transfer. The low-Re model does not perform as well as the Wall Function model in predicting heat transfer for flows at high Reynolds number. However, the low-Re model predictions are better than those from the high-Re Wall Function model for flows at low Reynolds number. In fact, for the geometry considered (1.27 cm x 1.27 cm duct) it becomes necessary to use the low-Re model for flows at low Reynolds number because of the limitation of the Wall Function. Heat transfer predictions from the low-Re model are within 10-40% for flows at low Reynolds number. The disadvantage of the low-Re model, in addition to the large number of cells requirement, is the slow convergence rate.