## 1 Introduction  
In the past few years, the navigational safety of submersibles has garnered increasing and widespread attention. High-pressure blowing is a critical method for ensuring submersible surfacing. Among these applications, the two most prevalent scenarios are rudder jamming during high-speed navigation and emergency procedures in response to flooding compartments [1]. Short-circuit blowing specifically refers to an effective technique for expelling ballast water directly from tanks using compressed gas sourced from a cylinder group, bypassing the gas distribution mechanism. Its efficiency is influenced by various operational factors, including gas pressure and other relevant parameters [2]. Currently, primary methods for studying short-circuit blowing encompass mathematical modeling, numerical calculations, and experiments conducted on actual vessels or dedicated test benches. In the domain of mathematical modeling and numerical simulations, Computational Fluid Dynamics (CFD) techniques are employed to investigate the formation and evolution of the gas-liquid two-phase interface within ballast tanks during short-circuit blowing, providing a comprehensive analysis of discharge rate variations [1]. Several studies in this area have examined individual operational factors, including the flow area of the sea valve [3], outboard back pressure, high-pressure cylinder group gas pressure, cylinder volume [4], and supply pipelines for both gas and water [5]. Utilizing the Laval nozzle theory, an emergency surfacing motion model for submersibles that incorporates short-circuitblowing was developed. Additionally, a water ingress restriction line within the safety boundary diagram for underwater maneuverability was derived [6]. While these studies offer valuable insights, they lack specific experimental validations and generalizability; due to their omission of comprehensive operational factors, they did not fully encapsulate the physics principles underlying short-circuit blowing. In the realm of real-ship or bench experiments, an emergency short-circuit blowing test was conducted on a Spanish S-80 submarine, achieving an instantaneous blowing gas pressure of up to 25 (MPa), equivalent to an outboard back pressure at a depth of 2500 m, which poses significant safety risks [7]. Additionally, small-scale emergency gas jet blowing-off bench experiments were performed to simulate the blowing and drainage performance at a depth of 100 m, yielding relative errors in the drainage percentages of 5% and 10%, respectively [8; 9]. Experiments utilized a small-scale short-circuit blowing test bench to evaluate the physics principles underlying the Laval nozzle theory and resulted in a relative error of 8% concerning the flow rate from the high-pressure gas cylinder group, an outcome closely linked to the ballast tank drainage percentage [10; 11; 12]. While data from the real-ship experiments were highly credible, they entailed considerable risk. Conversely, although the small-scale bench experiments can validate theoretical models, their results were constrained by the scale effect and thus lacked substantial guidance for actual ship manipulation or engineering designs. Nevertheless, proportional short-circuit blowing model experiments serve as a method for investigating the performance characteristics of short-circuit blowing in real ships. These test benches simulated gas cylinder deflation and various ballast tank drainage processes to analyze how factors, such as gas cylinder group volume and pressure, and sea valve flow area, influence blowing efficiency. The resulting relative error for peak gas pressure within the ballast tank remained below 15% when the high-pressure conditions did not exceed 15 (MPa) [2; 13; 14]. However, compared with actual ship short-circuit blowing, this approach does not encompass the full range of operational conditions and overlooks several critical manipulation factors, including outboard back pressure, along with pipeline length and inner diameter, as well as blowing duration.