Three-Dimensional Parallel Twin-Jets

3.2.1 Flow and Simulation Conditions

Fig. 3.13 schematically shows two parallel near-continuum thin orifice free jets (nitrogen gas, orifice diameter=3mm, distance of two orifice centers=9mm) issuing into a near-vacuum environment. This flow has been experimentally measured by Soga et al. [1984]

with background pressure ~3.7Pa. Since only limited computational domain is utilized, vacuum boundary conditions are employed at all outer boundaries for simplicity. In addition, only 1/4 of the whole physical domain is simulated due to the geometrical symmetry. Inflow conditions at the thin orifices, as summarized in Table 3.4, are assumed to be sonic with flow data obtained from 1-D inviscid flow analysis. Indeed, this restriction can be relieved if a pressure-based NS solver, unlike the current HYB3D code, is selected that can be used to simulate starting from the stagnation reservoir. Clearly, this flow is too dense for a meaningful DSMC simulation based on the flow conditions at the orifices (Knthroat=0.00385), while it is

too rarefied for a correct NS simulation due to the near-vacuum ambient environment.

Fig. 3.14 shows the global surface mesh distribution, which is used for the coupled method, along with an exploded view of the surface mesh distribution near the orifice. Note only tetrahedral mesh is used in this simulation. Computational domain extends up to 20D, 10D and 10D, respectively, in the direction of x- (streamwise), y- (crosstreamwise) and z-coordinate (crosstreamwise). Mesh near the orifice lip is intentionally refined considering the large gradient of flow properties in this region. Resulting number of cells is approximately

0.52 million, while other simulation conditions are summarized in Table 3.5. Among these,

. Thr

Knmax and P_Tne^Thr.are chosen as 0.05 and 0.1, respectively. One cell layer is used for Ω^B, and none for Ω^C. In addition, at all outer boundaries supersonic flow boundary conditions and vacuum boundary conditions are assumed, respectively, in the NS and DSMC solver. Fig. 3.15 illustrates the exploded view of the surface mesh distribution of DSMC domain (breakdown region) in the coupled method after 2^nd iteration. Related timing data are also shown in Table 3.6 for reference.

3.2.2 Distributions of Flow Properties

Fig. 3.16 illustrates the density contour distribution at the symmetric and orifice planes.

In each orifice jet, the flow expands very quickly into the near-vacuum environment, while at the symmetric line between two orifice jets a secondary jet is clearly formed due to the

expanding molecules from both jets. Fig. 3.17a illustrates the contour distribution of thermal non-equilibrium (P ) at the symmetric and orifice planes, while Fig. 3.17b shows the contour _Tne^. distribution of thermal non-equilibrium near the orifice with the surface of the breakdown domain in the enlarged view. It clearly shows that except near the entrance of the orifice jet most regions are highly non-equilibrium, which necessitates the use of DSMC solver. The region simulated by the NS solver is considerably small; however, it becomes a formidable task using the DSMC solver alone at this low Knudsen number (0.00385).

3.2.3 Profile along Center Line between Parallel Twin-Jets

Fig. 3.18 and Fig. 3.19, respectively, illustrate the simulated profile of density and rotational temperature along the symmetric line between the two jets, along with pure NS data and experimental data [Soga et al., 1984]. Note both the predicted normalized densities (hybrid and pure NS), with respect to their peak value, are shown along with the normalized measured density data in Fig. 3.18a since only relative experimental density data were provided [Soga et al., 1984], while only absolute predicted ones are illustrated in Fig. 3.18b for comparison. Thus, Fig. 3.18a only serves to demonstrate the general trend of both predictions (hybrid and pure NS) coincide with the measurements, except in the near-wall region. However, Fig. 3.18b clearly shows large discrepancy between the results obtained by the coupled and NS methods, since the values of continuum breakdown parameters are large (>0.05) along this symmetric line due to large gradients of flow properties in the near field and

strong rarefaction in the far field. Results show that density first increases very rapidly with increasing x/D, then reaches a maximal value near x/D=2 due to the collisions of gas molecules from both jets and finally decreases rapidly towards ambient value. In contrast, temperature decreases continuously from ~200K at x/D=0 with increasing x/D. Note only the total temperature obtained in the pure NS method is presented due to the assumption of thermal-equilibrium in the NS solver (HYB3D). In this highly rarefied region, the simulated temperature data using coupled method agree reasonably well with experimental data within experimental uncertainties, while the temperature data by NS solver deviate greatly from experimental data as expected. In addition, the simulation data of the coupled method deviate relatively large from the experimental data near the wall region (x/D≤1), which requires further investigation. There are two possible reasons of this large deviation. One is that it might originate from the errors introduced by reflection of light from the wall in Soga’s study using fluorescence technique [Soga et al., 1984]. Another possible reason is the inlet flow data assuming 1-D inviscid flow conditions.

3.2.4 Convergence History of Parallel Twin-Jets

Fig. 3.20 and Fig. 3.21 show the convergence history of the L2-norm deviation of density and temperature, respectively. The density deviation decreases from 1.1E-4 kg/m³ down to 1.3E-5 kg/m³ and levels off quickly after two coupling iterations, while the temperature deviation shows similar trend decreasing from 30K down to ~1.5K. This fast

convergence of the deviation as compared to the case of quasi-2-D wedge flow can be clearly explained by Fig. 3.22, which shows the Mach number contour distribution near the breakdown interface for both cases of quasi-2-D wedge flow and of two parallel jets. In Fig.

3.22a subsonic flow dominates in the regions near the breakdown interface above the boundary layer along the wedge wall that necessitates more number of couplings to exchange the information between two solvers, although supersonic flow dominates in the regions near the breakdown interface around the oblique shock. However, in Fig. 3.22b, supersonic flow dominates near the breakdown interface around entrance regime of orifice jets, which greatly reduces the number of couplings required for convergence as seen from the simulation. The above observation is very important from the viewpoints of practical implementation. For example, in the early stage of simulation we can determine the number of couplings required for convergence by simply monitoring to which the flow regime near the breakdown interface belongs. If most flows near the breakdown interface are supersonic, then two coupling iterations should be enough for convergence. If not, more coupling iterations are required to have a converged solution. Further investigation in determining the optimum number of coupling iterations is required in practical applications of the current coupled method.