1. In the non-continuum flow regime, we utilize a DSMC code, named Modeling Of Transitional-Ionized Flows (MOTIF),12-14which has been developed at JAXA. In the MOTIF code, the computational time step is chosen with the one associated with molecular collisions. The no time counter (NTC) scheme1is employed for modeling the molecular collision frequency, and the variable hard sphere (VHS)1model is used for modeling the collision cross section between particles. For modeling rotation-translation (R-T) and vibration-translation (V-T) energy transfers, the Borgnakke-Larsen (BL)15model with temperaturedependent rotational and vibrational relaxation numbers is used. For the gas-surface interaction modeling, both the Maxwell and Cercignani-Lampis-Lord (CLL)16reflection models are employed. In the Maxwell model, the Maxwell accommodation factor of the surface, α, determines the ratio of a diffuse reflection to a specular reflection. The CLL model supposes no coupling between the normal and tangential components of the velocity during the reflection process. Therefore, three accommodation parameters for normal and tangential velocities and energy fraction are required in this model. Further details of the MOTIF code can be found in Ref. 13. In this work, three-dimensional (3D) DSMC calculations are carried out for 100 % N2nozzle flows. Although the nozzle flow is assumed to be chemically frozen, R-T and V-T energy transfers are considered. In low temperature range, the reference diameter of 5.1 Ä at 120 K, the viscosity index of 0.8617are used in the VHS model. The gas-surface interaction is modeled using the Maxwell model, and a diffuse condition with total energy and momentum accommodation at the measured surface temperature is used for the nozzle surface. Macroparameter sampling is started after a time period that is sufficient to reach the steady state and the total number of time steps used in the sampling is approximately 25,000. For the outer boundary condition, an equilibrium condition at the measured ambient pressure is assumed. The time step, cell size, computational domain, the total number of simulated molecules, and the inflow boundary condition have been investigated to obtain results that are independent of these DSMC numerical parameters. B. Test Model Integration in DSMC
2. First, the dependence of the pitot tube length, Lpt, ontheimpactpressurehasbeenstudied. TheHRWT flow condition in the test section on the symmetric axis at T0=280Kand750Kwasusedasthefreestream condition for the pitot tube DSMC calculations. In Fig. 10, pressure contour plots around a 2.5mm-pitot tube for the non-heated condition are compared with increasing Lptfrom0to10mm(Lpt/D =0-4). Also, the dependence of the pitot tube length on the impact pressure is summarized for three different tubes in Fig. 11. It can be seen in the figures that the impact pressure rarely increases along with the tube length for 2.5-mm and 1.6-mm tubes. In contrast, for the 0.8-mm tube, the impact pressure increases along with the Lptincrease if Lpt/D <2. This trend is similar to Ref. 20 in that a ratio of the measured to the theoretical impact pressure, P0m/P02, increases along with increasing Lpt/dinfor Lpt/din< 2 with KnD> 0.4. In Table 3, the corresponding Knudsen numbers for each pitot tube are listed. Since the KnDis higher than 0.4 only for tube (3), the sensitivity of the impact pressure to the tube length can be found for this case. This is due to collisions between free stream and probe molecules within the aperture section. The converged impact pressure ratio (P0m/P02) at T0=280 K is also compared between the measured and computed results in Table 3. As shown in Fig. 11, good agreement in the impact pressure ratio between HRWT and DSMC was found for tubes (2) and (3). Meanwhile, the DSMC predicts higher impact pressure than the measured one for tube (1). We consider that this originates from probe cooling effects. Wainwright et al. investigated the probe cooling effect for hypersonic flows (M ≈ 10), and it is shown in Fig. 4d of Ref. 21 that the impact pressure ratio becomes lower than unity due to the probe cooling effect for KnDbetween 0.1 and 10 while this result was obtained for the orifice-type probe. According to this analysis, we infer that the decrease in the impact pressure for tube (1) is attributed to the cooling effect. Another possible reason is that the aperture section of tube (1) may have a slight orifice-type configuration. Unfortunately, the pitot tube probe temperature was not measured in this work, and thus, further investigation will be performed for tube (1).