Turbulent wall pressure fluctuation is an important hydrodynamic noise source, and it is necessary to carry out the corresponding calculation and experimental research. In addition, the sonar is installed on the bow of the submarine, and it is easily affected by self-noise. Therefore, it is important to understand the change in the flow field on the bow at different velocities to improve the performance of the submarine itself.
Benefiting from the development of computer technology, computational fluid dynamics (CFD) is increasingly applied to submarine hydrodynamic research. Huang et al. [
1] analyzed the wake of the SUBOFF model with various appendages through experiments and provided the velocity information, which was used to develop the CFD capability for the prediction of flow fields around underwater bodies. Abedi et al. [
2] used the Reynolds-averaged Navier–Stokes (RANS) to calculate the three-dimensional axisymmetric flow of the SUBOFF without any appendages and carried out numerical simulation and comparison of the cross-flow vortex structure of the submarine with the SUBOFF and DRDC STR precursors. The calculated data agreed with the experimental. Manoha et al. [
3] used the large eddy simulation (LES) to calculate the pressure fluctuation of the unsteady flow field at the blunt trailing edge of the thick plate, then analyzed the pressure fluctuation on the wall of the trailing edge, and the evolution of its amplitude, frequency, and flow direction. Both were in good agreement with the measurements of blunt trailing-edge airfoils. Posa et al. [
4] simulated the submarine wake flow field based on LES and it was shown that the wake of the body was affected mainly by the shear layer from the trailing edge of the fins and the turbulent boundary layer growing along the stern, while the influence of the wake of the sail was minimal. Broglia et al. [
5] analyzed both the global loads and the vortices originating from the sail of submarine, but focused on the coherent structures shed from the tip and the root of the appendages, where the results showed that the pattern of the coherent structures produced by the stern appendages was substantially dependent on the maneuvering conditions. Ashok et al. [
6] used PIV to investigate the turbulent wake of the submarine, that in yaw was expected to generate wakes that were inherently more persistent than one in pitch, and the strong asymmetries in yaw were expected to produce a net rolling moment on the body. In recent years, hybrid formulations such as the detached eddy simulation (DES) [
7] and stress-blended eddy simulation (SBES) have been widely used. The starting point for the hybrid formulation was designed to cover all attached boundary layers in the RANS model and to only switch to the LES model in detached zones. Alin et al. [
8,
9] used LES, DES, and RANS models to investigate the effect of the different simulation methods and to demonstrate the feasibility of using DES and LES on the relatively coarse grids for submarine flows. Liu et al. [
10] adopted the DES model to investigate the horseshoe vortex generated around the appendage-body junction of submarines and analyzed the flow characteristics around the appended submarine body, where a new method on the vortex control baffle was presented. Wang et al. [
11] studied the effect of the enclosure shape on the hydrodynamic noise of the submarine by the SST-SBES turbulence model and analyzed the influence of the leading and trailing edges with different shapes on the flow field and noise of the underwater vehicle, where the results demonstrated that the front edge of the enclosure could effectively suppress the noise. Magionesi et al. [
12] investigated the physical properties of the pressure fluctuation under the turbulent boundary layer on the ship wall through a self-power spectrum and cross-spectrum to reduce the vibration source that may cause noise. Bhushan et al. [
13] applied the SST-URANS, SA-DDES, k-ω-DDES, and RANS/LES hybrid methods to simulate the flow field and vortex structure around the SUBOFF enclosure and wake, respectively. Magionesi et al. [
14] used Farabee’s semi-empirical formula to compare with measurements of the mean square value of the pressure fluctuation in the turbulent boundary layer of the bow sonobuoy, and found that the experimental values of the zero pressure gradient test section agreed better with the empirical values, and the experimental values of the inverse pressure gradient test section were significantly higher than the empirical values. Li et al. [
15] used the IDDES model to capture the variation characteristic of the eddy and showed that the pump-jet propulsor had significant force fluctuation and more complex vortices evolution in drifts. Dietiker et al. [
16] used the DES method to calculate the pressure fluctuation of the backstage flow, and the calculated main frequency was in good agreement with the test, and the power spectrum was consistent with the empirical model. Meng et al. [
17,
18] applied the LES method to calculate the pressure fluctuation in the low-speed case of a thin-plate wing with arching and combined it with the FW–H equation for radiated noise. The calculated frequency spectrum and spreading correlation of the pressure field in the edge region of the wing surface were in good agreement with the experiment.
At present, there are few researchers exploring the analysis of pressure fluctuation from the perspective of energy. Based on the analysis of the law of axial pressure change, this paper analyzed the variation of pressure fluctuation at the bow of the submarine from the perspective of energy change under different velocities by calculating the self-power spectrum and wave-number frequency spectrum.