A neural network has been used to predict stagnation region heat transfer in the presence of freestream turbulence. The neural network was trained using data from an experimental study to investigate the influence of freestream turbulence on stagnation region heat transfer. The integral length scale, Reynolds number, all three components of velocity fluctuations and the vorticity field were used to characterize the freestream turbulence. The neural network is able to predict 50% of the test data within ±1%, while the maximum error of any data point is under 3%. A sensitivity analysis of the freestream turbulence parameters on stagnation region heat transfer was performed using the trained neural network. The integral length scale is found to have the least influence on the stagnation line heat transfer, while the normal and spanwise turbulence intensities have the highest influence.
Stagnation region heat transfer is important in many engineering applications. For example, heat transfer from the combustion gases to the turbine blades in a gas turbine is highest in the stagnation region. Accurate predictions of heat transfer in this region are essential to improve the design of blade cooling systems. However, accurate estimation of the stagnation region heat transfer on turbine blades is difficult due to the complexity of the flow field (Maciejewski and Moffat, 1962, Larsson, 1997 and Guo et al., 1998). There have been several experimental studies on the effect of freestream turbulence on stagnation region heat transfer, and correlations between the stagnation region heat transfer and the characteristics of freestream turbulence such as turbulent intensity (u′), integral length scale (λx) and Reynolds number (ReD) have been developed ( Lowery and Vachon, 1975, Mehendale et al., 1991 and VanFossen et al., 1995). In most cases, however, the correlations are experiment specific since the heat transfer is not only dependent on the turbulence parameters u′, λx and ReD, but also on the distinct nature of the turbulence. For example, the combustion gases exiting the combustor tend to be highly anisotropic and well laced with distinct coherent vortical structures. Hence, for more accurate predictions, the correlation models must take into account the distinct nature of the turbulence. This can be achieved by incorporating the rms of all three components of velocity fluctuations (u′, v′, w′) and vorticity (ωy, ωz) in addition to λx ( Oo and Ching, 2001 and Oo and Ching, 2002). The increased number of variables, however, makes it more difficult to obtain accurate correlations and to determine the relative importance of the different parameters on the heat transfer. In this instance, it is difficult to perform a parametric study due to the difficulty of changing a single turbulence parameter while keeping the others fixed. For example, changing the turbulence grid size to increase the turbulence intensity also increases the integral length scale.
An alternative to developing a correlation using standard regression analysis is to train a neural network (NN) to predict the stagnation region heat transfer. The advantage of this is that the trained neural network can then be used to perform a sensitivity analysis of the turbulence parameters on stagnation region heat transfer. This is particularly useful as it allows some insight into the physics of the problem, especially when the underlying physical–mathematical model is complicated. Neural networks have been used successfully in many engineering applications and are capable of representing the physical knowledge of complex systems. A neural network extracts knowledge from the data presented to it, where the physical knowledge of the system is contained within the rules of the network.
The objective of this paper is to present a neural network technique to predict stagnation region heat transfer in the presence of freestream turbulence. The neural network was trained using experimental data, and ReD, λx, u′, v′, w′, ωy and ωz were used to characterize the freestream turbulence. The trained neural network was then used to perform a sensitivity analysis of the freestream turbulence parameters on the stagnation region heat transfer.
A neural network has been developed to predict stagnation region heat transfer in the presence of freestream turbulence. The network was trained using experimental data, and the integral length scale, Reynolds number, all three components of velocity fluctuations and the vorticity field was used to characterize the freestream turbulence. The experiments were performed using a heat transfer model with a cylindrical leading edge in a low speed wind tunnel. The freestream turbulence was generated using a grid of parallel rods, with the rods oriented parallel and normal to the stagnation line. The network consists of one input layer, one hidden layer and one output layer. There are 7 input neurons, 12 hidden neurons and 1 output neuron in the respective layers. The number of hidden neurons and the learning rate of the neural network were optimized to obtain the smallest root mean square error. An error analysis of the validation of the neural network indicate that the error for about 80% of the validation data is below 2%, while the largest error of any point is below 3%. The present work has demonstrated that a neural network can be trained effectively to predict heat transfer using a large number of input variables. A sensitivity analysis has been performed to determine the relative importance of the freestream turbulence characteristics on the stagnation region heat transfer. The results indicate that the normal turbulence intensity has the highest influence, while the integral length scale has the least influence on stagnation region heat transfer. These results are in agreement with the hypothesis that the heat transfer enhancement in the presence of freestream turbulence is due to vortex stretching of the primary vortices aligned normal to the stagnation line and freestream directions.
