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

卡诺电池的逆设计需要对所有组件采用连续逆方法，包括考虑当地市场情况。这既包括支出方面的投资成本(资本支出)和业务成本(经营成本)，也包括收入方面的潜力。因此，对于逆方法，不同设计层次(市场、热力循环、组件)之间的传递函数是必要的。利用传递函数进行建模，可以采用逆方法，得到带有市场参数的帕累托前沿。市场条件或市场需求是决定帕累托前沿的制约因素。热力学循环可以理解为从这些市场需求到部件需求的传递函数。建立了特定压头与几何变量之间的传递函数，这里将其定义为几何传递函数。直径和体积流量(即通流面积)由与效率有关的表面积比确定。在第二步中，将由热力学循环和流体确定的质量流量包含在质量的传递函数中。该函数以质量流量和压力水平影响机器的效率和数量(可能是多流)的形式来描述质量。几何传递函数中定义的能量转换决定了级数和机械强度要求，也影响了质量和数量。考虑到“最佳”机器的函数关系，可以使用比扬程和周向马赫数来确定其他变量。但是，这仅限于设计点，不提供有关机器灵活性的任何信息，因此也不提供有关部分负载行为的信息。在“最佳”流量和比扬程之间的函数关系在这里没有定义。根据热力循环传递函数定义的灵活性描述了机器设计的极限。所需的柔度影响几何和质量传递函数，并代表了柔度传递函数的进一步发展。利用该传递函数，在叶轮机械设计中考虑了部分负荷的要求，极大地扩展了关于逆设计方法的知识。传递函数的连续描述以及设计方法的抽象允许逆系统设计。这一抽象支持优先计划的以下目标：a.尺寸依赖、部分负载行为和波动；b.灵活的流体能源机器及其作为流体、负载范围和压力比的函数的行为。

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.