Analysis of the Factors Influencing the Trailing Infrared Characteristics of Underwater Vehicles under Surge Conditions Using the Orthogonal Method

Abstract

With its benefits of efficiency and speed, the orthogonal experimental design method is currently often employed in many domains for multi-factor experimental design. In this study, the wind–wave–flow multifunctional experimental flume was used to replicate surge circumstances using the orthogonal technique in order to investigate the contributing factors and their interactions on the sea surface IR characteristics of underwater vehicles’ wakes. According to the correlation analysis, the height of the swell and the surface temperature difference of the wake had only a weak negative correlation, while the dive depth of the underwater vehicle and the surface temperature difference of the wake had a significant negative correlation (p = −0.833). It was tentatively concluded that the surface temperature differential of the wake was found to be more sensitive to dive depth than to swell height. An investigation of the impact of trailing IR features can use this finding as a pertinent reference.

1. Introduction

Researchers found in the 1950s that the surface heat trails formed by the discharge of cooling water from surface and underwater vehicles had thermal infrared properties that are notably different from those of ordinary seawater and may be used as a key detection method. Therefore, the study of thermal trails left by submerged cars has steadily attracted the interest of scientists. Orthogonal experimental design (OED) is a design approach for studying various components and levels [1]; it is an efficient, quick, and advantageous experimental design method that selects representative points based on orthogonality. In this study, the orthogonal technique was utilized to analyze the experimental data further in order to determine the elements impacting the sea surface infrared features of an underwater vehicle’s wake and their interaction laws.

Researchers have conducted several theoretical evaluations, numerical simulations, and practical investigations of underwater vehicles’ wakes since 1960. Conclusions have been reached about the generating processes, disturbance causes, floating features, and other relevant parameters [2,3,4,5,6,7,8,9,10]. According to Yang et al., the key variable determining the detection distance is the temperature differential between the surrounding ocean and the underwater vehicle’s wake [11]. In order to detect vehicle wakes, Kou et al. developed a water-based infrared (WDPUV-IR) probability software and established models of detector detection probability and noise equivalent temperature difference, wake and sea surface temperature difference, and evaluation of the detection probability at various resolution levels [12]. A self-propulsion model was used by Stewart and Schooley [13] to investigate wakes in settings with different densities. Tsung-Lung Liu and Zong-Ming Gou examined the spectrum features of the surface disturbance while researching the influence of an undersea submerged body on a free surface. The submersible’s almost free surface navigation track may be acquired using this technique. According to the investigation, the navigation speed has the most impact on the free surface among the three influencing parameters of diving depth, body length, and navigation speed. The distinctive waveform of the submersible at a certain sailing speed may be seen at various depths. It is extremely doable to discover the characteristics of an unknown submersible by detecting the spectral features, which also make it possible to estimate the trip depth and the sailing speed of the submersible [14]. The evolution of a wake from towed and self-propelled submersibles was compared by K. Brucker et al., who found that the self-propelled submersible’s wake will fade more quickly on average. Additionally, buoyancy lengthens the duration of the disturbance’s wake. The wake width in the vertical direction is wider for self-propelled submersibles [15].

Previous wake trail thermal models were created under a variety of ideal conditions, such as calm water. The underwater vehicle’s hot wake’s heat exchange process will vary depending on the level of sea conditions, in contrast to the realistic marine environment where sea conditions of three or more levels are typical and where complex sea conditions produce swells that affect the underwater buoyancy pattern and surface distribution characteristics of the underwater vehicle’s wake. The examination of the affecting elements, such as speed, diving depth, hot wake spray speed, and hot wake temperature, also uses single-factor analysis. This work used the orthogonal method to preliminarily analyze the influencing factors of the surface infrared characteristics of the wake of underwater vehicles under surge conditions and their interaction; it increases the likelihood of detecting and precisely identifying the wake of large underwater vehicles by accurately modeling the radiation characteristics of the hot wake under surge conditions. Investigating the connection among dive depth, wave height, and wake temperature differential lays the groundwork for a later examination of the thermal properties of the wake under complicated sea circumstances.

2. Basic Theory

2.1. Numerical Calculation Theory of Fluid Heat Transfer

The influence of the underwater vehicle hull on the flow field, the strong disturbance of the flow field by the underwater vehicle propeller, the buoyancy effect of the cooling water jet into the seawater, and the configuration of the free surface of the sea are processes that need to be taken into account in the analysis of the formation mechanism of the underwater vehicle’s wake. For the numerical solution of the multiphase flow and heat transfer in this paper, the right turbulence equations and radiative transfer equations must be established in addition to meeting the mass, momentum, and energy conservation equations.

(1)

The mass conservation formula

Mass conservation between the calculation domain’s intake and outflow must be met while the flow condition is steady. The mass in and out of each unit control body when considering flow calculations fulfills the mass conservation equation, as indicated in Equation (1).

$$\frac{\partial \rho }{\partial t}+\nabla \cdot (\rho \overrightarrow{V})=S_m$$

(1)

where $t$ is time, $\rho$ is the density of the fluid, $\overrightarrow{V}$ is the velocity vector, and $S_m$ is the mass source term and represents the mass in the control body generated by the custom process.

(2)

Equation for momentum conservation [16]

All flow processes are also subject to the conservation of momentum, which is expressed in the equation for conservation of momentum, which is provided in Equation (2) as the conservation of kinetic energy in the form of

$$\frac{\partial \left(\rho \nabla \overrightarrow{V}\right)}{\partial t}+\nabla \cdot (\rho \overrightarrow{V}\overrightarrow{V})=-\nabla P+\nabla \cdot \stackrel{=}{\tau }+\rho \stackrel{-}{g}+\overrightarrow{F}$$

(2)

$$\stackrel{=}{\tau }=\mu \left[\left(\nabla \overrightarrow{V}+\nabla \overrightarrow{V}\right)-\frac{2}{3}\nabla \cdot \overrightarrow{V}I\right]$$

(3)

where $\stackrel{=}{\tau }$ represents the stress tensor, p represents the hydrostatic pressure of the fluid, as shown in Equation (3), $I$ represents the unit tensor, $\mu$ represents the dynamic viscosity coefficient of the fluid molecules, $\stackrel{-}{g}$ is the acceleration of gravity, taken as −9.81 m/s², $\rho \stackrel{-}{g}$ represents the volume force due to gravity, and $\overrightarrow{F}$ represents other external volume forces, also including source terms that are subordinate to other models.

(3)

Equation for energy conservation [16]

When a heat transfer process occurs simultaneously with a flow process, the process must also adhere to the law of conservation of energy and the law of conservation of energy’s equation in the form of Equation (4).

$$\frac{\partial (\rho E)}{\partial t}+\nabla \cdot \left[\overrightarrow{V}(\rho E+p)\right]=\nabla \cdot \left[k_{off}\nabla T-{\displaystyle \sum _j{h}_j{\overrightarrow{J}}_j+}\left(\stackrel{=}{{\tau }_{eff}}\cdot \overrightarrow{V}\right)\right]+S_h$$

(4)

In Equation (4), E is the total energy, which is the sum of internal and kinetic energy, $k_{off}$ is the effective thermal conductivity ($k_{off}=k+k_i$, where $k_i$ is the thermal conductivity of the turbulent process, as determined by the turbulence model), T is the temperature, and $h_j$ and ${\overrightarrow{J}}_j$ are the enthalpy and diffusion fluxes of the components $j$, respectively. The first three terms on the right-hand side of Equation (4) represent the energy transfer due to thermal conductivity, component diffusion, and viscous dissipation, respectively, and $S_h$ represents the energy source term, which can be either a heat generation or heat absorption process in various chemical processes, an energy conversion in a multiphase flow, or another defined type of heat source.

2.2. Theory of Sea Surface Infrared Calculations

(1)

Radiation from the sea surface target itself

The radiant energy of a surface target is based on the temperature field and emissivity of the target surface. Therefore, after calculating the temperature field of the target surface, the surface IR flux of the target can be calculated from Plante’s formula. The target surface can be assumed to be a diffuse gray body, and the spectral radiant flux of the target surface element i at a particular wavelength band is [17]

$$E_1={\displaystyle {\int }_{{\lambda }_1}^{{\lambda }_2}{\epsilon }_1\times }\frac{C_1}{{\lambda }^5\cdot \exp \left(\frac{C_2}{\lambda \cdot T_i}-1\right)}d\lambda$$

(5)

where $C_1$ is the first radiation constant, $C_1=3.742\times {10}^{-16}\mathrm{W}\cdot {\mathrm{m}}^2$, $C_2$ is the second radiation constant, $C_2=1.439\times {10}^{-2}\mathrm{m}\cdot \mathrm{K}$, $\lambda$ is the radiation wavelength, and $T$ is the thermodynamic temperature. The ${\epsilon }_1$ is the emissivity of the target surface. The optimal launch rate of the ship at different times and speeds is about 0.8 and is taken as ${\epsilon }_1$ = 0.8 for the surface of the underwater vehicle [18].

(2)

Reflection of sky radiation by sea surface targets

$$E_2={\rho }_t\left(\lambda \right)\cdot {\epsilon }_{sky}\sigma T_{\alpha }^4\cdot \frac{1+\cos \sum }{2}\cdot \frac{{\displaystyle {\int }_{{\lambda }_1}^{{\lambda }_2}{\epsilon }_1\times }\frac{C_1}{{\lambda }^5\cdot \exp \left(\frac{C_2}{\lambda \cdot T_{sky}}-1\right)}d\lambda }{\sigma T_{sky}^4}$$

(6)

where $\rho$ is the average reflectance of the sea surface to solar radiation, ${\epsilon }_{sky}$ is the sky target surface emissivity, $\sigma$ is the Stephen Boltzmann constant, $T_{sky}$ is the equivalent medium temperature, $T_{\alpha }$ is the air temperature, and $\sum$ is the inclination of the surface element of the target surface at sea. The horizontal surface $\sum$ = 0.

(3)

Reflection of solar radiation by sea surface targets [19,20]

$$E_3=(1-{\alpha }_{sum})\cdot \frac{solar-heat-flu{x}_i}{\alpha }\cdot \frac{{\displaystyle {\int }_{{\lambda }_1}^{{\lambda }_2}{\epsilon }_1\times }\frac{C_1}{{\lambda }^5\cdot \exp \left(\frac{C_2}{\lambda \cdot T_{sum}}-1\right)}d\lambda }{\sigma T_{sum}^4}$$

(7)

where $solar-heat-flu{x}_i$ is the density of solar heat flow received by the small surface element on the surface of the sea surface target, ${\alpha }_{sum}$ is the absorption rate on the surface of the sea surface target, and $T_{sum}$ is the solar temperature, taken as 5800 K. Again, as the calculation state in this paper is nighttime, this part does not need to be calculated.

(4)

Reflection of sea surface radiation by sea surface targets

$$E_4={\rho }_i\cdot {\epsilon }_{sea}\sigma T_{sea}^4\frac{1-\cos \sum }{2}\cdot \frac{{\displaystyle {\int }_{{\lambda }_1}^{{\lambda }_2}{\epsilon }_1\times }\frac{C_1}{{\lambda }^5\cdot \exp \left(\frac{C_2}{\lambda \cdot T_{sea}}-1\right)}d\lambda }{{\epsilon }_{sea}\sigma T_{sea}^4}{\cos }^{-1}\theta$$

(8)

where θ is the angle between the line connecting the detector and the center of the surface element and the normal of the surface element and $\sum$ is the target surface inclination of the sea surface. The horizontal surface $\sum =0$.

(5)

Infrared radiation characteristics model of a sea surface target

Similarly, as the distance between the sea surface target and the detector studied in this paper was less than 1 km and the calculated weather environment is a typical bright night without the direct influence of clouds, frost, rain, and fog, ignoring the effect of atmospheric path radiation and atmospheric transmission attenuation, through the above analysis, the total spectral radiation of the sea surface target is expressed as Equation (9)

$$E(\lambda )=E_1+E_2+E_3+E_4$$

(9)

3. Experimental Design

3.1. Theory of Sea Surface Infrared Calculations

(1)

Device for simulating underwater waves

Using the wind–wave–current multifunctional experimental tank of the State Oceanic Administration’s First Institute of Oceanography, Figure 1 shows the schematic diagram of the wind–wave–current multifunctional experimental flume. Figure 2 is a photograph of the experimental wind–wave–current water tank. The tank is 45 m long in total. A booster chamber is located at either end of the 32.4 m long, 1 m wide, and 1.8 m deep glass tank (5.2 m long and 3.0 m wide). The steel frame that surrounds the glass tank has laminated glass on both of its sides and at the bottom. The wavemaker is mounted at the top of the tank. Energy-dissipating rectification grilles are fitted at the wavemaker’s back and at the end of the tank. Installed in the gallery at the base of the tank, the pump and circulating flow pipe are connected to the booster chamber at both ends. The tank’s operating depth ranges from 0.2 to 1.2 m. The surge model may be used to train the wave-generation system to perform a variety of wave-generating tasks, including producing regular waves and irregular waves and breaking by superimposing various component waves.

(2)

Underwater vehicle

The experimental underwater vehicle was selected from the Tianjin Deep Blue “White Shark MAX” ROV, with dimensions of 590 mm × 510 mm × 330 mm, a weight of 15 kg, and a working depth up to 100 m, which can be remotely controlled by remote control. Figure 3 shows the tail flow experimental vessel.

(3)

Infrared camera parameters

A Xenics-Gobi 640-GigE long-wave infrared camera was used for this experiment, with specific camera parameters and images shown in

Table 1. The IR camera parameters.

Camera Models	Xenics-Gobi 640-GigE
Infrared Band	8 μm~14 μm
NETD	55 mk

and Figure 4 below.

3.2. Theory of Sea Surface Infrared Calculations

Based on the similarity principle in fluid dynamics, a geometric similarity ratio of 1:128 was used. The program that was written simulates an underwater surge at various heights. An underwater surge at different heights was achieved by a real-time capture of the infrared camera and the temperature correction by contact thermometry. The control of jet flow and flow velocity was achieved by tank pressurization injection and fixed bore. The following is a list of the experimental steps.

An upward image of the water’s surface from a 60-degree angle was captured using a long-wave infrared camera attached to the gantry. To simulate a submarine thermal jet, a jet pipe attached to the stern of the model submarine was used to inject hot water into the water under pressure through a 3 L container with a drain pipe diameter of 5 mm at an average discharge rate of 600 mL/min (the discharge temperature of the outlet was recorded in real time during the experiment as the drain pipe exchanged heat with the surrounding environment and there was attenuation during the discharge process).

An autonomous submersible that can be programmed to obtain precise depth and speed settings was used to replicate the undersea submarine. The submersible’s speed was adjusted to 2.4 m/min to be as near to the actual circumstance of a subsurface cooling water outflow as possible. The experiment measured the temperature of the thermal jet floating to the surface and the temperature differential between the surrounding water body using long-wave infrared non-contact temperature measurement and a contact thermometer for positive effects.

4. Experimental Results and Analysis

4.1. One-Factor Experimental Analysis

At various tailing test levels, good experimental findings were achieved for all components. Figure 5 shows the submersible temperature difference infrared image, where (a) was imaged at a temperature difference of 18 degrees and (b) was imaged at a temperature difference of 11 degrees.

Table 2. Statistics of IR wake rising in calm water.

Depth/cm	20	30	40	50	60	70
ΔT/°C	0.76	0.61	0.52	0.33	0.30	0.24

shows the statistics of an IR wake rising in calm water. Three sets of data were gathered for each set of experiments in order to decrease errors and mistakes; the arithmetic mean of the experimental data was used as the experimental findings. The arithmetic mean was determined from the findings.

In the single-factor wake experiments, under calm water conditions as the dive depth rose, the heat capacity of the cryogenic water above the submersible rose as well. This decreased the central high-temperature region where the heat wake spread up and significantly weakened the infrared radiation properties of the heat wake at the ocean surface, similarly to the results in the literature [19]. Due to the shortest route and shortest diffusion time, the wake came to the surface at a water depth of 20 cm with a significant temperature differential between the wake and the surrounding water column. The wake rose to the surface in a flocculent shape and developed into a long, continuous wake along the surface in the direction of motion as the submarine moved. The contour of the wake did not significantly alter as the depth rose.

In order to conduct infrared imaging tests of the wake thermal jet under simulated swell circumstances, the model was designed to establish various swell heights.

The swell height was set at 0.3 cm; the distance between the experimental test position and the wavemaker was 3.7 m. When the submersible was submerged to a depth of 30 cm, the infrared camera could clearly capture the abnormal area on the water surface. At that time, the wake thermometer’s temperature was 12.43 cm and the average water body temperature was 11.98 cm, with a temperature difference of 0.45 cm. At a depth of 40 cm, The temperature at the temperature measuring point of the wake is 12.46 °C, the average temperature of the surrounding water is 12.20 °C, and the temperature difference is 0.26 °C;. When diving to a depth of 50 cm, the phenomenon was still possible. The temperature of the tail track temperature measurement point was 12.40 °C, while the average water temperature in the area was 12.26 °C, resulting in a temperature differential of 0.14 °C.

When the submersible dove to a depth of 30 cm, the temperature of the wake temperature measurement point was 12.32 cm, the average temperature of the surrounding water body was 11.85 cm, and the temperature difference was 0.32 cm. When the dive depth was 40 cm, the temperature of the wake temperature measurement point was 12.12 cm, the average temperature of the surrounding water body was 11.85 cm, and the temperature difference was 0.32 cm. The infrared camera did not pick up any temperature anomalies in the surrounding water column as the submersible descended to a depth of 50 cm.

When the submersible descended to a depth of 20 cm, the thermal jet was able to float to the surface; the wake temperature measurement point was 12.51 cm, the average water body temperature was 11.82 cm, and the temperature difference was 0.69 cm. The set surge height was 1.2 cm, and the distance between the experimental position and the wavemaker was 3.7 m. The infrared camera did not pick up a temperature anomaly in the nearby water column when the submersible was lowered to a depth of 30 cm.

Through the aforementioned experimental results, it can be seen that, in the same dive depth when the height of the surge was increased, the seawater free surface layer in the wake area and the wake around the water’s temperature difference were both significantly reduced. The different heights of the underwater surge had a significant impact on the temperature change in the free surface layer. The water temperature management in the tank was, however, suboptimal due to the closeness of the experimental time period and some experimental errors occurred.

The wake was more strongly mixed with the surrounding water during the process of floating and spreading due to the effect of underwater surges, forming a fluid water mass mixed with hot and cold; so, the temperature fluctuations around the temperature measurement point were more violent, the temperature difference between the wake and the water surface was smaller, and the depth of the vehicle that created the wake was greater than in experiments on the infrared properties of the wake at calm water. The directional emissivity changed in response to transient changes in wake geometry at the water column’s surface, resulting in shadow obscuration and multiple reflections in the direction of the detector’s detection. This reduced the brightness of the thermal wake infrared radiation the detector could detect, making detection more challenging. The heat transfer between the wake and its surroundings as it rose to the surface may also have been accelerated by waves, another indirect contributor to the wake’s heat exchange at the sea–air interface. This suggests that one of the variables influencing the wake’s diffusion process was the surge.

4.2. Orthogonal Test Analysis

In order to discuss in more depth the primary and secondary relationships between the influence of the factors on the infrared characteristics of the underwater vehicle’s wake, the interaction between the factors was analyzed using orthogonal tests based on their single-factor analysis, the discussion of the influence, and the correlation relationships between the factors, as shown in

Table 3. The form of orthogonal table.

Test Serial Number	Column Number
	1	2	3	4	5
1	1	1	1	1	1

.

The orthogonal table is denoted by L for the code of the orthogonal table, n is the number of trials, t is the number of levels, and c is the number of columns, i.e., the maximum number of factors that can possibly be arranged. For example, L₈ (2⁵) means that eight trials were required and up to five factors could be arranged, with each factor taking two levels, as shown in

Table 4. The factor-level orthogonal testing design of thermal characteristics of surface under swell conditions.

Level	Depth (A)	Surge Height (B)
1	30 cm	0 cm
2	40 cm	0.3 cm
3	50 cm	0.5 cm

.

In the experiment, the interaction between the factors should be fully considered. In order to reflect the relationship between the factors scientifically, the interaction analysis of the orthogonal test between the two factors shown above was carried out according to the requirements of the experiment. Six tests needed to be conducted. Three factors could be arranged at most, and three levels were taken for each factor. The table header design scheme of the experiment was obtained from the orthogonal table L₆ (3³) as

Table 5. The orthogonal testing header design of thermal characteristics of surface under swell conditions.

Column Number	1	2	3
Factors	A	B	AB

Note: AB indicates the interaction of factor A with factor B.

.

In accordance with the designed scheme to carry out experiments, we obtained the factors. Each factor in different combinations of levels of surge conditions, wake water surface thermal characteristics data, and orthogonal results are shown in the

Table 6. Data on the thermal characteristics of the wake surface for each factor and each factor at different combinations of levels of surge conditions.

2	1	1	1	2	2
3	1	2	2	1	2
4	1	2	2	2	1
5	2	1	2	1	2
6	2	1	2	2	1
7	2	2	1	1	1
8	2	2	1	2	2
8	2	2	1	2	2

.

The orthogonal test of the thermal characteristics of the water surface of the tail race was set up with two factors, depth (A) and surge height (B), with three levels taken for each factor. The three levels of factor A were A₁ = 30 cm, A₂ = 40 cm, and A₃ = 50 cm, respectively. The three levels of factor B were B₁ = 0 cm, B₂ = 0.3 cm, and B₃ = 0.5 cm, respectively. Thee orthogonal test design scheme is shown in the

Table 7. The orthogonal testing results of thermal characteristics of surface under swell conditions.

	A	B	AB	Temperature Difference (°C)
1	1	1	1	0.61
2	1	3	3	0.47
3	2	3	2	0.38
4	2	2	2	0.26
5	3	2	3	0.14
6	3	1	1	0.33
K1	0.54	0.47	0.47
K2	0.32	0.2	0.32
K3	0.235	0.425	0.31
R	0.305	0.225	0.16

Where K₁, K₂, and K₃ are the mean values of the different levels of the trailing temperature difference for each factor and R is the extreme difference of the trailing temperature difference. “1”, “2”, and “3” represent the levels of the factors, respectively. Although “1”, “2”, and “3” in AB have no practical significance, their calculated extreme differences, R, are statistically significant.

.

According to the orthogonal table, the influence of this component on the wake temperature difference increased as the polar difference increased. By the magnitude of the polar difference R in Table 4, the following two variables and their interaction had an effect on the main and secondary relationships: A > B > AB; therefore, it was evident that the influence of the dive depth on the wake buoyancy diffusion to the water surface thermal characteristics was higher than the impact of the underwater surge on it.

By correlation (

Table 8. Correlation analysis.

	Depth	Surge Height	Trailing Temperature Difference
Depth	1	−0.250 0.633	−0.833 * 0.040
Surge Height		1	−0.123 0.817
Trailing Temperature Difference			1

Note: * significantly correlated at the 0.05 level (two-sided).

) analysis, it was seen that the depth of the underwater vehicle dive and the wake buoyancy spread to the surface of the temperature difference had a significant correlation, with an absolute value greater than 0.8, indicating a negative correlation; the surge conditions and wake temperature difference correlation coefficient absolute value were less than 0.3, indicating a weak negative correlation. This further demonstrated that the influence of the dive depth of this underwater vehicle on the temperature difference between the buoyancy of the wake and the spread to the surface was larger than the effect of the seawater surge factor.

5. Conclusions

This article is based on research on the tail track floating diffusion process and a preliminary examination of the influence of waves on that process. At the same experimental location, due to the influence of swell, the heat exchange between the wake and the surrounding environment is strengthened, and the wake appears discontinuous on the water surface; Through correlation analysis, it was discovered that the depth of the underwater vehicle and the surface temperature difference of the wake had a significantly negative correlation (p = −0.833), with the depth of the underwater vehicle having a greater impact on the temperature difference of the wake than the height of the swell. The experimental results also require further analysis because the temperature, humidity, and detector condition are not thought to have significantly affected how easily the infrared wake could be seen and the stratification of the temperature and the speed of the surface wind are not thought to have been more representative of the complexity of the real ocean.