Problems with the T-Method

This article shows that the T-Method, a new numerical method for optimizing duct networks, fails under certain conditions. The authors discovered this phenomenon while they were developing software that implements the T-Method. The method worked fine until they used C-coefficients that are referenced to the dynamic pressures of duct sections other than the duct sections to which the C-coefficients are actually assigned. (Such C-coefficients are important because duct designers use them to account for the dynamic pressure losses at junctions and crosses.) The T-Method became unstable and it produced grossly oversized ducts. To prove that certain C-coefficients cause problems for the T-Method the authors devised two realistic one-dimensional problems which differ only in one aspect: problem number one contains a C-coefficient that is referenced to an adjacent duct section while the C-coefficient of problem number two is referenced to the section it belongs to. For problem one the T-Method produced a duct diameter that deviated significantly from the true optimum, but it gave accurate results for problem two. The authors studied the theory of the T-Method to find an explanation for the above-mentioned findings. The only part of the theory that seemed suspicious was the assumption that a certain derivative is negligible. The assumption seems necessary for the T-Method scheme but the creators of the T-Method do not prove its validity. The authors show that the T-Method gives the correct answers when this assumption is avoided. Unfortunately this can only be done for one-dimensional problems. In conclusion: the results presented in this article show that the T-Method is unable to optimize duct systems that contain C-coefficients referenced to duct sections other than the section to which the coefficient is assigned. This article does not propose a solution to this problem. However, it does prove that the T-Method cannot be used in certain circumstances, which casts doubts on its overall practicality.