Numerical computation and experimental assessment of a pressure-retaining

Seawater pressure

The pressure of seawater is not only directly related to the depth of the seawater, but also to its temperature, density, and salinity³². However, depth is the most critical factor affecting the pressure of seawater. Various methods exist to calculate seawater pressure, including the formula method, measurement method, empirical method, among others. For the convenience of calculation and analysis, the empirical formula proposed by McAllister and Myers³³ is used here to calculate the pressure at the working depth of seawater:

where: h is the depth of seawater, m; P(h) is the ambient pressure under the water depth(h), which takes into account the influence of the change in the elastic modulus on the density of seawater.

The velocity (V_sam) of the submersible during descent and recovery in the vertical direction typically ranges from 20 to 60 m/min. Combined with the seawater pressure-depth curve, the expression for the ambient seawater pressure P(τ) as a function of timeτ(min) is derived:

where V_sam is the submersible’s descent velocity, m/min; P(τ) is the seawater pressure at given moment τ, MPa; τ is the time, min.

Distribution law of seawater temperature

The sampler is mounted on a submersible for both descent and recovery. During the descent, sampling, and recovery processes, the temperature of the external seawater at various depths dictates the temperature of the nitrogen within the pressure-compensation device. Thus, understanding the vertical temperature profile of seawater is essential for addressing the temperature changes within the nitrogen. The surface water temperature of the ocean typically ranges from − 2 to 30 °C, with an annual mean of about 17 °C. The Pacific Ocean is the warmest, with an average temperature of about 19 °C, whereas the Atlantic Ocean averages 16.9 °C. From the sea surface down to the main oceanic thermocline, the water temperature decreases markedly. The depth of the main thermocline varies by latitude, ranging from approximately 300 m to 800 m. An assumed depth of 400 m is used in this analysis. Below the main oceanic thermocline, the water temperature decreases gradually with increasing depth, albeit with a very weak gradient. Below 1,000 m, the water temperature changes minimally with depth, and below 3,000 m, it essentially remains constant at approximately 1.5 °C. Based on the measured temperature data from the research vessel “TANSUO-1” during its third expedition to the Mariana Trench in March 2017, with the sea surface temperature at approximately 30 °C, the vertical distribution of seawater temperature was approximated by a simplified function (3). The temperature distribution profile is depicted in Fig. 2.

where h is the seawater depth, m; T_w(h) is the seawater temperature corresponding to that depth, °C.

Temperature distribution curve of seawater.

When the water depth was less than 100 m, the seawater temperature remained above 30 °C, however, upon reaching 150 m, the temperature of the seawater began to drop rapidly. At a water depth of approximately 300 m, the seawater temperature had decreased to about 10 °C. The seawater temperature dropped to approximately 5 °C at a depth of about 1000 m. Below water depths of 3300 m, the seawater temperature was essentially constant at around 1.5 °C. Based on the distribution of seawater temperature, the variation of ambient seawater temperature Tw(h) over time τ(min) during the descent process can be expressed as: