## 2 Methods: Experiment and Numerical Simulation  
### The Model Tests Method  
According to the public data of diesel-electric submarine at home and abroad, a medium-sized diesel-electric submarine usually has a relatively high sail. This is hydrodynamically destabilizing because, as the submarine begins to roll, the rolling moment increases in the same direction, thereby rolling the submarine further. That is to say, submarines are prone to experience excessive roll, which greatly threatens the safety of submarine equipment and personnel. In order to investigate the emergency rising characteristics of these diesel-electric submarines, the Science and Technology on Autonomous Underwater Vehicle Laboratory of Harbin Engineering University has conducted early research in the area of model test of submarine emergency rising. Referring to the public data of some mother ships, researchers design a specific high-sail submarine model for test purposes, meanwhile, a series of model tests were organized in the comprehensive test water pool. Based on the previous model, tests without any tailplanes deflections, this laboratory further implemented the emergency rising test under the conditions of fixed stemplane angles. Please refer to the reference [27] for detailed information about the experiment, which is beyond the scope of this paper. Here is a brief introduction to these model tests.  
The model test is conducted in a \(50\times 30\times 10\) m water pool, and the layout of the experiment facilities is shown in Figure 1a, which mainly consists of a submarine model and its data acquisition system, a towing sled and its support bracket, and camera devices with lighting, etc. Before the start of a test, the submarine model was locked on the towing sled by an electromagnetic clamping mechanism and hoisted to the top of the support bracket in the pool. At the beginning of the tests, the variable-frequency motor is activated to accelerate the towing sled along the track. When the model speed is substantially stabilized at the target value, the electromagnetic release device is activated so that the submarine can be launched immediately and smoothly. During the rising process, the model posture is recorded by the embedded PC104 bus-based measurement system and then transmitted to the host computer via zero buoyancy cable. Meanwhile, a set of camera devices are employed to record snapshot videos for observing. As a result, an emergency rising model test is achieved by means of releasing the model with reserved buoyancy instantaneously.  
Figure 1: Layout schematic of the test facilities (**a**) and some video snapshots of the model test with excessive rolling before surfacing (**b–d**).  
Based on the above experimental principle, the researchers have carried out a large number of model tests for combinational conditions of various factors, including different blown position, speed, rudder angle, etc., and established a sufficient experimental database. In order to highlight the issues that this paper focuses on, 5 representative model tests as shown in Table 1, are selected to illustrate the irrelevant influence of moderate incidence angle and further verify the accuracy of the numerical results as well. Some video snapshots of the model test 1 from Table 1 are presented in Figure 1b-d, which occurs excessive roll before the model broaches the surface.