## 2 Materials and Methods
### System Design and Test
#### 2.2.2 Test Workflow  
Design workflows determine parameter values of principle solutions for defined design scenarios. With this determined parameter value set, a technical variant is created. In contrast to design workflows, test workflows check whether the developed technical variant meets all requirements. This is necessary because not all boundary conditions and requirements are generally considered in the design. For example, hydrodynamic pumps are designed for the best efficiency point consisting of rotational speed, flow rate, and head (pressure difference between pump intake and output). During operation, however, the speed is varied to adapt the flow rate to the heat dissipation requirements in the cooling circuit. The pump is then operated off the best efficiency point. The resulting energy consumption in operation is, therefore, a quantity that is not captured by the design workflow but calculated in the test workflow. Identifying the most suitable design point considering the later operation is an engineering challenge. In this paper, the exemplary requirements for the electric coolant pump, as shown in Figure 6 will be considered for the test workflow. Figure 5: Design workflow for the design of a pump impeller. From the higher-level requirements for high efficiency, low installation space, and stable operation, a range of values are derived for the head coefficient. The head coefficient is a characteristic value calculated from the physical quantities of a pump and characterizes its operating behavior [36]. The head coefficient should be as high as possible for compact and efficient pumps [37]. A lower bound of \(\psi_{Th,min}=1.0\) is therefore selected. However, a head coefficient that is too high can lead to unstable flow rate behavior and vibration excitations in the cooling circuit [38]. The value of the head coefficient is therefore limited to \(\psi_{Th,max}=1.3\) using a practical value according to [39]. The installation space requirement is further refined in maximum impeller diameter and width. These limits depend on the application and are here set to \(D_{2,max}=150\) mm and \(b_{2,max}=30\) mm. Additionally, the pump shall be operated at a maximum speed of \(n_{max}=2500\frac{1}{min}\) for noise and material strength reasons. Further requirements weigh the importance of installation space and efficiency of the pump. The so defined weights can be used to compare different technical variants. The WLTC is used as the design cycle. The pump must provide enough flow rate to dissipate the heat generated by the engine in the cycle. The requirements are checked utilizing constraint elements in the MBSE system model. For brevity, only one such element is shown in Figure 6 for the upper limit of the head coefficient. These constraints are later reused identically in MDAO. A test workflow is modeled similarly to the design workflow in an activity diagram (Figure 7). It consists of the sections _get_, _calculate_, and _set_. In the present example, two successive tests in the form of simulations are performed: A mechanical (_calculateMechPower_) and an electrical (_calculateE1 Energy_) performance test. The implementations of  
Figure 6: Requirements of the electric coolant pump. calculateMechPower_ and _calculateEEnergy_ are described in detail in Section 3.4. For the mechanical performance test, the previously determined pump impeller design variable values and the flow rate cycle are loaded using get actions. The mechanical performance test determines the time histories of the mechanical pump torque and rotational speed, as well as the maximum required pump speed \(n_{cycle,max}\) in the flow rate cycle. For the electrical performance test, parameter values of the electric motor are loaded by means of get actions. This test receives the additional time histories of torque and speed and calculates the consumed electrical energy \(E_{EI}\) in the flow rate cycle. The design of the electric motor is not considered in this paper. Therefore, the parameter values of the electric motor remain constant.