Essential computation of the structure is the basis of the preliminary design of the wind tunnel, which will not be discussed in this paper. We focus on the nozzle parameters and the contraction curve, which are important in improving the flow field quality of the test section.
3.1. Nozzle Parameters
The choice of the nozzle is directly related to the effect of injection and the quality of the flow field.
Many relevant studies were carried out in the China Aerodynamics Research and Development Centre [
43,
44,
45]. In this paper, three different nozzles are selected to make a comparison of their ejection effects. These three alternative nozzles are provided considering the simulated environment and the wind tunnel structure. The parameters of the three nozzles are shown in
Table 2.
To select the nozzle with the best ejection effect for this wind tunnel, a series of computational fluid dynamics (CFD) calculations are conducted. A group of nozzle inlet pressure is selected, and the static pressure at the outlet of the nozzle is set as 900 Pa.
It should be mentioned that although the nozzles are used to spray the two-phase flows composed of particles and compressed gases, only the single-phase flow simulations are carried out to evaluate the nozzles. The first reason for this is that particle concentration is a variable that varies with working conditions. The other reason is that the mass flow of the particles is relatively small compared with the mass flow of the compressed gas. Therefore, the single-phase flow comparison is an unavoidable trade-off but provides valuable guidance.
The area enclosing the nozzle and its external cylinder is set as the flow field. The 3D structured grid is generated. The grid near the nozzle wall is processed to increase the density. The grid-independence analysis is carried out, and the total numbers of grid cells reach to 3,710,000, 4,990,000, and 5,410,000 for the 1#, 2#, and 3# nozzle, respectively. The realizable k-epsilon viscous model is employed. The inlet of the nozzle is set as the pressure-inlet, and the pressures are set to 0.01 MPa, 0.05 MPa, and 0.1 MPa. The bottom surface of the cylinder, except the nozzle, is set as the pressure-inlet with the pressure of 900 Pa, and the other bottom surface is set as the pressure-outlet with the pressure of 900 Pa. The solver is set as the pressure-based Navier-Stokes solution algorithm. The solver is selected as the pressure-based coupled-implicit Solver.
The velocity distributions of the three different nozzles are shown in
Figure 2,
Figure 3 and
Figure 4. As can be observed from the figures, the gas flows are under supercritical conditions. After exiting the nozzle, the supersonic gas continues to expand and eventually becomes a subsonic gas flow after acceleration and deceleration. Comparing the two convergent nozzles as shown in
Figure 2 and
Figure 3, the increase of the outlet aperture increases the mass flow of the ejected air and the expansion area. This results in more adequate mixing of the gas. Moreover, the axial attenuation of the gas flow is faster for the nozzle with a larger outlet aperture. In contrast, as shown in
Figure 4, the gas flow from the Laval nozzle is more stable, and the axial velocity gradient of gas flow is relatively small. Thus, it implies a longer settling chamber.
Next, we compare the ejection characteristics of the three different ejector nozzles. The detailed data are shown in
Table 3.
Compared with the other two nozzles, the Laval nozzle has the largest ejection coefficient under supercritical conditions. Since the gas has accelerated to the sound velocity before reaching the outlet of the nozzle, the mass flow rate of the nozzle is directly limited by the size of the cross-sectional area of the outlet. For the convergent nozzle, the increase of the throat area is helpful for increasing the ejected gas flow rate but reduces the ejection coefficient.
To demonstrate the stability of the gas flow ejected by the three nozzles, (1) the static pressure distribution and (2) the Mach numbers along the nozzle outlet axis are plotted as shown in
Figure 5 and
Figure 6.
For the convergent nozzles, the static pressure changes are similar, and both reach a relatively stable value at
x = 0.05 m. Due to the high upstream pressure, the gas flow reaches the sound speed at the throat of the nozzles, and then forms the supersonic flow. Combined with the velocity distribution shown in
Figure 2,
Figure 3 and
Figure 4, it can be found that the supersonic flow is decelerated by the shock waves at the outlet of the nozzle. For the Laval nozzle, the change of the ejected gas flow is the most stable compared to the other two nozzles, but the gas flow requires a longer distance to stabilize.
At the same upstream pressure, the outlet gas velocity changes of the three nozzles are not the same. There are two main reasons for this: (1) the difference in the mass flow rate of the mixed flow, and (2) the difference in the radial flow distribution. The 2# nozzle has the largest mixed gas mass flow rate with a relatively small axial velocity. This means that the mixed gas flow of the 2# nozzle has the best diffusion effect in the radial direction and its gas flow mixing is the most uniform.
After a comprehensive comparison, the 2# nozzle is considered to be the most suitable for this Mars wind tunnel.
3.2. Contraction Curve
Generally, there are three alternative curves that are available for the contraction section: the Witozinsky curve, the bicubic curve, and the quintic curve [
46].
Figure 7 shows the profiles of the three contraction curves. Considering the application of the Mars wind tunnel, the inlet and the outlet of the contraction should be relatively stable with a small gradient to stabilize the gas flow. From
Figure 7 we can find that the gradient of the inlet of the Witozinsky curve is large and the outlet is small, and it is just the opposite for the bicubic curve and the quintic curve. However, the question of which of these curves is most suitable for the Mars wind tunnel presented in this paper needs further discussion. Thus, we carried out a series of CFD simulations to compare these curves.
Figure 8 is a symmetrical diagram from the ejector assembly to the test section. The inlet of the contraction is 0.8 m × 0.8 m squared. The distance from the ejector assembly to the contractions is 0.9 m, the contraction is 0.6 m long, and the test section is 0.6 m long.
The mesh model of the above sections is shown in
Figure 9. Since the structure is axisymmetric, only a 1/4-size model is built.
Figure 10 shows the inlet nozzles of the Mars wind tunnel. Based on the previous discussion, we utilize the 2# nozzle here. Comparing the flow field of the 2# nozzle and the size of the contraction, we distribute the 64 nozzles (8 × 8) evenly at the inlet of the tunnel, and the spacing between each nozzle is 0.1 m. As the mesh model in
Figure 9. is 1/4 of the actual size, only 16 nozzles are shown in
Figure 10.
Hexahedral structured mesh is used in the fluid domain, and the mesh at the wall is refined. The grid-independence analysis is carried out, and the total number of grid cells is 1,210,000. The realizable k-epsilon viscous model is employed. The inlets of the nozzles are set as the pressure-inlet. The inlet of the wind tunnel, except the nozzles, is set as the pressure-inlet with a pressure of 900 Pa; the outlet of the test section is set as the pressure-outlet with a pressure of 900 Pa. The solver is selected as the pressure-based coupled-implicit solver.
We calculate the velocity distribution of the three wind tunnels with different contractions, then analyze the velocity uniformity and velocity stability of the test sections to find the optimal contraction curve.
Figure 11 shows the velocity distribution on the symmetry plane of the three wind tunnels. The velocity distribution in the test section seems uniform and can be maintained at about 120 m/s, while the velocity in the contraction with the Witozinsky curve changes more slowly than the others. This helps to uniform the velocity distribution in the radial direction of the test section. Comparatively, the gas velocities in the bicubic curve contraction and the quintic curve contraction change mildly, resulting in poor velocity uniformity in the test section.
To quantify the flow uniformities and flow stabilities of the test sections of the three different wind tunnels, we select nine points in a test section and measure some key parameters. The nine measuring points, named ‘A~H’ and ‘O’, are shown in
Figure 12. The test section (0.6 m long) is divided into three cross sections:
x = 0.1 m,
x = 0.3 m, and
x = 0.5 m.
We introduce the velocity inhomogeneity (VI) and the dynamic pressure inhomogeneity (DPI) to describe the flow uniformity—velocity uniformity of the test section. The velocity inhomogeneity (VI) is defined as:
where
i represents the nine measuring points A, B, C…,
is the velocity at each measuring point, and
is the average velocity of the nine points.
The dynamic pressure inhomogeneity (DPI) is defined as:
where
is the dynamic pressure at each measuring point, and
is the average dynamic pressure of the nine points.
The maximum
and
of the three wind tunnels with different contraction curves are shown in
Table 4. It is evident that the trends of VI and DPI for the three test sections are the same. The flow uniformity in the test section with the Witozinsky curve contraction is the worst. This reflects the poor rectification effect of the Witozinsky curve on low-density flow. By contrast, the rectification effect of the bicubic curve and the quintic curve is relatively satisfactory.
As for the flow stability, the axial static pressure gradient (ASPG) is introduced to describe the velocity stability of each test section. The test section is divided into
n equal parts along the axis direction. The axial static pressure of the
j = 1, …,
n part is defined as:
where the Δ
P is the static pressure difference of the part,
ρ is the average density, and
u is the axial gas velocity. The axial static pressure gradient is defined as:
where
L is the length of the test section. The ASPGs of three different test sections are illustrated in
Table 5. Under the test condition of 0.05 MPa inlet pressure, the ASPGs of the test section with the Witozinsky curve and the bicubic curve are relatively close, while the quintic curve has poor flow stability.
After comprehensively comparing the flow uniformity and the flow stability of the three different test sections, the bicubic curve is considered the best choice for the contraction.
To investigate the rectification effect of the bicubic curve at different flow velocities, CFD studies are carried out under the inlet pressures of 0.01 MPa, 0.05 MPa, and 0.1 MPa. The calculated index parameters for the test section are shown in
Table 6.
As shown in
Table 6, changes in VI and DPI are positively correlated with the changes in gas velocity in the test section. Furthermore, the increase in gas velocity reduces the flow uniformity. ASPG is more stable compared with flow uniformity. Overall, the flow uniformity in the test section is acceptable under different working conditions when using the bicubic curve as the contraction curve.