Inverse design of turbomachines using transfer functionsSub-project related to the priority program "Carnot Batteries: Inverse Design from Market to Molecules"

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The inverse design of a Carnot Battery requires a continuous inverse method for all components, including the consideration of local market conditions. This includes both the investment costs (capex) and the operating costs (opex) on the expenditure side, as well as the potentials on the revenue side. Therefore, transfer functions between different levels of the design (market, thermodynamic cycle, components) are necessary for the inverse method. Modelling with the transfer functions makes it possible to follow an inverse approach and obtain a Pareto front with the parameters of the market as the result. The market conditions or market requirements are the constraints for determining the Pareto front. The thermodynamic cycle can be understood as a transfer function from these market requirements to the requirements of the components. The transfer function between the specific head and the geometric variables is to be formulated, which is defined here as the transfer function of geometry. The diameter and the volumetric flow rate, respectively the throughflow area, are determined by a surface-to-volume ratio which is related to the efficiency. The mass flow determined from the thermodynamic cycle and the fluid is included in the transfer function of the quality in the second step. This function describes the quality in a form that the mass flow and the pressure level influence the efficiency and the "quantity" of the machines (possibly multi-flow). The energy conversion defined in the transfer function of the geometry determines the number of stages and the mechanical strength requirements and impacts quality and quantity as well. Considering the functional relationship for an "optimal" machine, the specific head and the circumferential Mach number can be used to determine the other variables. However, this is limited to the design point and does not provide any information about the flexibility of the machine and, thus, no information about the part-load behavior. The functional relationship outside the "optimum" between the volume flow and the specific head is not defined here. The flexibility defined from the transfer function of the thermodynamic cycle describes the limits for the machine design. The required flexibility influences the geometry and quality transfer functions and represents a further development named the transfer function of flexibility. With this transfer function, a significant expansion of knowledge regarding inverse design methods is achieved, in which the requirements for part-load are included in the turbomachine design. A continuous description of the transfer function and, thus, abstraction of the design methodology allows an inverse system design. This abstraction supports the following objectives of the priority program: a. Size dependence, part-load behavior and fluctuations; b. Flexible fluid energy machines and their behavior as a function of fluid, load range and pressure ratio.