###### Abstract  
The meridional distribution of the flow parameters inside the centrifugal compressor is of great importance to its overall performance, as well as its matching performance under a thermal cycle. A time-marching throughput method for the off-design performance analysis of the centrifugal compressor is described. The method is based on the strictly conservative throughput-governing equations, and an improved method of boundary-condition enforcement is developed based on [PERSON]'s method to achieve a robust and fast throughflow simulation. An inviscid blade force model was adopted to obtain the flow deflection inside the blade passage. Empirical loss models were integrated into the throughflow model to simulate the viscous force effects in the real three-dimensional flow. Two test cases are presented to validate the throughflow method by comparisons with the experimental data or CFD results, including the NASA low-speed centrifugal compressor (LSCC) and the Allison high-performance centrifugal compressor (HPCC). The simulation indicated that the developed enforcement method for the inlet and outlet boundary conditions significantly improves the computational robustness. For both the LSCC and HPCC cases, reasonable flow-parameter distribution was obtained and accurate overall characteristics were also predicted under the off-design conditions. The results indicated that the developed time-marching throughflow method is effective and efficient for the performance analysis of centrifugal compressors. t +
Footnote †: journal: _Sci. low-order models and high-fidelity models, such as the one-dimensional (1D) mean-line method, the two-dimensional (2D) throughflow method, and the three-dimensional (3D) method. Among them, the throughflow method has become the backbone of turbomachinery design. Benefitting from its good balance between computation efficiency and accuracy, the throughflow method has been commonly adopted in the preliminary design and optimization stage both for axial [1; 2; 3; 4; 5; 6] and radial turbomachinery [7; 8; 9; 10]. As has been reported, up to 80% or more of the design parameters may be fixed during the throughflow modeling phase [11]. Apparently, an improved throughflow method is still of great interest to the industrial community. Since the concept of the S2 stream surface was introduced by [PERSON] in the 1950s [12], several kinds of throughflow methods have been developed based on different mathematic approaches. These approaches can be mainly categorized into three kinds: the stream function method (SFM) first introduced by [PERSON] [13], the streamline curvilinear method (SCM) introduced by [PERSON] and [PERSON] [14; 15] and the time-marching-based method pioneered by [PERSON] [16]. In the first two methods, usually called the classical throughflow flow methods, the original set of governing equations are reduced to a single differential equation: the stream function equation for the SFM and the radial equilibrium equation for the SCM. Though they are different numerical approaches in principle, it has been concluded by [PERSON] that there is little to choose between them [17]. As the common drawbacks, the simplifications make these approaches conceptually unable to predict choking conditions or capture shock waves [18; 19]. This causes striking difficulties in the throughflow analysis of the turbomachinery, especially when the flow inside the blade passage becomes transonic. Although several strategies were implemented [6; 8; 20] to enhance their performances in transonic flow analysis, the classical throughflow approaches are inherently weak in these situations. To overcome the major drawbacks of the two classical throughflow approaches mentioned above, the time-marching throughflow method has been proposed, in which the complete set of Euler/Navier-Stokes equations are discretized and solved by advancing in pseudo time on the S2 surface.