1. Introduction
On April 19, 1971, the world’s first space station, Salyut 1, was successfully launched into orbit, marking the arrival of space age. In the following decades, the U.S. Skylab, the Mir Space Station, and the International Space Station (ISS) were successively built and continuously developed, becoming the base of deep space exploration. However, continuously growing space debris increases collision probability among space debris and spacecrafts, which has caused widespread international concerns [
1]. It was reported that many leak accidents occurred on the ISS [
2], leading to an urgent demand of on-orbit leak detection. The differential pressure method [
3] has been widely used on the pressure vessels of spacecrafts to detect the occurrence of leak. However, it cannot give the leak location. In order to locate the leak-induced noise source, on-orbit sensing technology based on acoustic emission has drawn widespread attention due to its low resource occupancy, little structural constraints and real-time monitoring [
4]. In order to verify the effectiveness of the acoustic emission technology, the European Space Agency (ESA) conducted verification tests on the experimental cabin of the ISS [
5]. Furthermore, a handheld ultrasonic leak detector developed by National Aeronautics and Space Administration (NASA) has been successfully applied to leak detection in orbit [
6].
The current acoustic emission leak detection method is to detect and analyze the 40 KHz ultrasonic signals generated by the vortex structures downstream the leak-induced jet [
7]. However, because the leak jet enters the vacuum directly, the acoustic emission signal propagating backwards into the pressure vessels is very weak. Therefore, the focus of the acoustic emission research is mainly concentrated on the characteristics of the structure-borne ultrasonic signals in the pressure vessel skin and the improvement of signal manipulations. Schafer and Janovsky [
8] reported propagation characteristics of stress waves in a thin aluminum plate and honeycomb sandwich panel, and then used a sensor network with positioning algorithm to locate high-speed impact sources. Reusser et al. [
9] studied propagation and reflection mechanisms of low-order Lamb waves in stiffener components and constructed a generalized impedance model, which had good agreement with numerical simulation results.
The above researches focused on the propagation mechanism of the leak noise in the cabin skin to provide theoretical supports for leak location. However, neglecting generation mechanisms of the leak noise makes it unable to evaluate and classify the leak source. Physically speaking, the spacecraft’s leak noise is a flow-induced noise excited by jet’s instability waves. In the research of vacuum jet, Draper and Hill [
10] proposed an approximate analytical method to predict the external jet density field in vacuum, with the results agreeing well with the traditional characteristic method. Shuvalov et al. [
11] imposed two approximate models to improve the accuracy of solving the parameter distribution, such as density, Mach number. Kannenberg and Boyd [
12] applied direct simulation of Monte Carlo (DSMC) method for plume impingement and obtained good agreements with experimental data. There are few studies on jet noise in vacuum environment, but the research on jet noise in conventional environment on the ground is more mature. For subsonic jet noise, Lighthill [
13] is a pioneer of aeroacoustic who proposed the theory of acoustic analogy and V
8 law to predict jet noise, which inspires many improved models [
14,
15,
16,
17]. Tam and Golebiowski [
18] proposed a similarity spectra method. Furthermore, Tam and Chen [
19] reported two components of the similarity spectra, one from fine-scale turbulence and the other from large-scale turbulence. For supersonic jet noise, Tam [
20] summarized three noise generation mechanisms, namely turbulent mixing noise caused by unstable turbulence, broadband shock noise associated with the quasi-periodic shock cell structure, and screech tones excited by the feedback loop.
Although there are many theories on jet in a vacuum environment, they mainly focus on the effects of plumes generated by thrusters on spacecrafts, such as force, torque, heat, etc. However, leak jet dynamics is rarely studied. Secondly, there are many studies on the conventional jet noise on the ground, and various forecasting models are also mature. But due to significant changes of density, pressure, and temperature in vacuum environment, the terrestrial jet noise model cannot accurately predict the characteristics of the leak jet noise in vacuum environment. Abedi’s group [
21,
22] conducted a leak detection test on the ISS and the measured spectrum showed obvious harmonic wave series, which cannot be explained by screen tone theory in supersonic jet noise. Furthermore, the turbulence mixing noise in vacuum environment has not yet been fully understood. Therefore, this paper concentrates on the numerical simulation of a specific leak condition, preliminarily revealing the aerodynamic properties and mechanism of the noise propagation in vacuum environment. Specifically,
Section 2 introduces the setup configurations of numerical simulation meanwhile
Section 3 presents corresponding analysis of the simulation results. Finally,
Section 4 draws the conclusion of the whole paper.
2. Numerical Simulation Setup
The main pressure vessel of the space station cabin is a cylindrical shell structure with a thickness of 2.5 mm. As leak holes formed by the impact of tiny space debris are generally at the millimeter level, the computation model is simplified to an axisymmetric model with a leak hole of 2.5 mm in length and 2 mm, 1 mm, 0.5 mm in diameter, respectively. The pressure inlet, defined as the 1 atm atmospheric environment is in front of the leak hole, while the pressure outlet, defined as vacuum environment, is after the leak hole. The specific numerical region is depicted in
Figure 1 and the commercial CFD software Fluent 19 Ansys Inc., which is located at Southpointe 2600 Ansys Drive Canonsburg, PA 15317, USA, is used in this paper for calculation.
As the ambient pressure on the orbit of the space station is in the order of 10−7~10−4 Pa, the pressure outlet should be set very low to mimic the actual working conditions. However, extremely low setting of outlet pressure imposes high requirements on computational convergence. Besides, the Navier–Stokes (N–S) equations are restricted to describe continuous flow, with limited descriptions of rarefied flow. To fully describe the vacuum jet flow, CFD-DSMC (Computational Fluid Dynamic-Direct Simulation of Monte Carlo) method is widely used. Roughly speaking, the CFD calculation is firstly proceeded to calculate the continuous region and capture the boundary surface between continuous and rarefied region through Knudsen number, denoted by . Then, the captured boundary surface is used to initiate the plume field calculation based on DSMC method.
In the numerical calculation, this paper concentrates on the CFD calculation as the acoustic pressure perturbation is mostly related to the continuous fields. To get the convergence, two different configurations of output pressure with 1 Pa and 10 Pa are conducted, where the convergence of steady velocity, pressure, density and temperature is depicted in
Figure 2. The results show the difference of aerodynamic properties in continuous region between the two configurations are so minor that they are almost negligible. In other words, under the condition that the back pressure is sufficiently small, the specific value of the back pressure has little effect on the computation accuracy in continuous region. As such, the pressure outlet is set to 10 Pa to improve the computational convergence while the pressure inlet is set to 1 atm to simulate actual pressure condition in the space station cabin.
The temperature in the area in front of the leak hole is uniformly set to 300 K to simulate real thermal condition inside the spacecraft cabin. However, the temperature in orbit is greatly affected by solar radiation so that the temperature range outside the cabin is exceptionally large. In low earth orbit where most spacecrafts work, the temperature in the sun light area can reach above 120 degrees Celsius, while the temperature in the shadow area will quickly drop to below minus 100 degrees Celsius [
23]. Therefore, the effect of temperature cannot be neglected. As such, the temperature in the area behind the leak hole is set to 173 K, 300 K and 393 K respectively. In order to explain the dynamic properties and aeroacoustic characteristics, jet in atmospheric environment under the same computational model and pressure difference is also provided, where the pressure inlet and outlet is set to 2 atm and 1 atm respectively, meanwhile other setups remain unchanged.
It is obvious in
Figure 2 that the vacuum leak jet is a supersonic flow with a strong density gradient, thus the gas compressibility cannot be neglected. As such, the ideal gas state equation is used in this paper to model the density characteristic of compressible gas, satisfying:
where
is the density,
p is the absolute pressure,
T is the static temperature, M is the average molecular weight of air, and
is the universal gas constant (taken as 8.31
).
As the temperature changes are obvious in the vacuum leak, the fluid viscosity change should be considered. In numerical calculation, the Sutherland equation is introduced to model the viscosity:
where
is the viscosity coefficient,
is the reference viscosity (taken as 1.716 × 10
−5 ),
T is the static temperature,
is the reference temperature (taken as 273.11 K), and S is the Sutherland constant (taken as 110.56 K).
In terms of numerical calculation, the turbulent characteristics of the jet must be taken into consideration to fully simulate the acoustic characteristics. There are usually three method to calculate a turbulence: Direct Numerical Simulation (DNS), Large Eddy Simulation (LES), and Reynolds Averaged Navier–Stokes (RANS). DNS can obtain the vortex structure on almost every scale by directly solving the N-S equations. But it requires grid number reach Re
9/4, which greatly increases the amount of computation. LES uses the N-S equations to directly solve large-scale eddies and imposes the effect of fine-scale vortices on instantaneous motion through various theoretical models. RANS has a weaker resolution of fluctuation terms than DNS and LES, but it has been widely used in the engineering community because of its reliable calculation accuracy, low computation resource requirement, and widely applicable Reynolds number. Therefore, after comprehensive consideration of computation resource and computation precision, a RANS method is used in this paper. Many scholars have proposed a large number of turbulence models to enclose the equations, among which k-ε model has been widely used. Khavaran [
24] applied a k-ε model to the computation of supersonic jet mixing noise and successfully predicted the noise source strength. Li X. D. [
25] used a modified two-equation standard k-ε model to study a circular jet and not only the predicted shock cell structure and radial density profiles, but also the amplitudes of the flapping and helical modes coincide with the experiments very well. Compared with the standard k-ε model [
26], the Realizable k-ε model [
27] has higher computation accuracy on jet simulation. As such, the Realizable k-ε model is adopted in this paper with the transport equation being:
It is shown by Thies [
28] that the realizable k-ε model has higher prediction accuracy in solving supersonic turbulent jets where the Mach number is not very large if
,
,
,
,
,
and
.
In terms of non-reflecting boundary conditions in aeroacoustic numerical simulation, the common method is to apply appropriate mathematical processing on the boundary conditions to eliminate the reflection on the boundary [
29,
30]. However, it requires a lot of theoretical derivation and programming. A mixed structed–unstructed grid is created in this paper, as shown in
Figure 3, where the grid size in the structed area should be small enough to adequately resolve the jet structure and pressure fluctuation meanwhile the grid size in the unstructed area should grow uniformly along the radial direction and be large enough near the inlet and outlet areas. The reason of the grid setup in this paper is to use the numerical viscosity brought about by the change of grid size to dissipate the pressure fluctuation completely before reaching the boundary to avoid the effect of boundary reflection.
4. Conclusions
The realizable k-ε model is adopted in this paper to numerically simulate the aerodynamic properties and aeroacoustic characteristics of a leak-induced jet with different external environment, different leak hole diameter and different external thermal condition. Numerical results show that:
(1) On the space station, the leak gas will expand into outer vacuum space rapidly and form a supersonic jet with a Mach number of 2 to 3, the diameter of the jet potential core being about 25 times the diameter of the leak hole. Although there are large velocity, density, pressure, and temperature gradients, no typical shock cell structure is observed. In contract, conventional terrestrial leak jet under the same pressure difference of 1 atm is still subsonic and no obvious expansion can be seen.
(2) The jet noise in vacuum environment shows a phenomenon of acoustic cavity reflection. Compared with widely used criterion in vacuum plume dynamics, the criterion seems more appropriate to define the acoustic cavity wall. Within the acoustic cavity which is judged by , the reflected waves reflect upstream along the acoustic cavity wall, exciting multiple resonance harmonic modes. Interestingly, the criterion is universally suitable for different leak hole diameter and external temperature, which may confront in the on-orbit applications. In addition, it is not difficult to find that the source of vacuum leak jet noise is mainly composed of turbulent mixing broadband noise and resonance harmonic noise.
(3) Although the RANS method’s weaker resolution of the fluctuation terms makes it unable to accurately describe the turbulent mixing broadband noise, it still has a high resolution of the jet dynamic properties and the time-averaged characteristics of pressure disturbance propagation. Furthermore, the computation resource requirement is relatively small. Therefore, RANS method can effectively analyze the characteristics of harmonic noise caused by resonance.