Results: Transition Onset
5.3 Analysis for Comparison with Past Studies 9
5.3.2 Statistical Comparison with Past Work
Datasets in air (n = 22), CO2 (n = 15), and N2 (n = 11) from shots referenced by Adam (1997) and Adam and Hornung (1997) are presented in Tables 5.7, 5.8, and 5.9, respectively. Some of these experiments were performed by, and first referenced in, Germain (1993) and Germain and Hornung (1997). Observed transition onset locationxTr is reproduced here as reported in Adam (1997), but the other parameters have been recalculated by the present methods, described in Chapters 2 and 3, for consistency. In the case of Re∗/m for Dorrance reference conditions, δ99Tr, and fTr, the parameters have been calculated here for the first time.
2 4 6 8 10 12 14 16
10 20 30 40 50 60 70 80 90
Reservoir Pressure [MPa]
Reservoir Enthalpy [MJ/kg]
Air (Adam 1997) Air (injection series) Air
N2 (Adam 1997) N2
Figure 5.12: Tunnel operating parameters hres and Pres for the present studies in air and N2, compared with past conditions from Adam and Hornung (1997) and the injection experiments described in Chapter 7 and Jewell et al. (2011).
The tunnel parameters for which transition onset was observed during the present studies in air and nitrogen are compared with those of two past data sets in air and nitrogen in Figure 5.12. The present work both overlaps and extends the parameters of the past studies, including those performed for the injection work described in Chapter 7, especially for low pressure and enthalpy. As described in Section 3.2,
there is a significant correlation between the reservoir enthalpy and pressure for the T5 operating envelope. The R2 values for the correlation between the two parameters are, respectively, 0.52 and 0.64 for conditions represented in the present N2 and Air data sets, and 0.10, 0.82, and 0.59, respectively, for the Adam and Hornung (1997) air and N2, and Jewell et al. (2011)/Chapter 7 data sets. This correlation is important to recognize because it necessitates careful statistical analysis before any trend may be attributed to hres orPres separately.
4 5 6 7 8 9 10
20 30 40 50 60 70 80 90 100
Reservoir Pressure [MPa]
Reservoir Enthalpy [MJ/kg]
CO2 (Adam 1997) CO2
CO2 (50%)
Figure 5.13: Tunnel operating parametershres andPres for the present studies in CO2 and 50% CO2, compared with past CO2 conditions from Adam and Hornung (1997).
The tunnel parameters for which transition onset was observed during the present studies in CO2 and 50% air/CO2 mixtures are compared with those of past data sets in CO2 in Figure 5.13. The present work overlaps the past studies with the exception of the upper range of reservoir pressure and enthalpy, and extends the parameters of the past studies in the lower range of reservoir pressure. It should be noted that equivalent higher-enthalpy CO2 tests were undertaken for the present work, as well (see Appendix A for the full list of run conditions), but no transition was observed by the end of the cone for those cases, even though transition was observed on the cone
for the equivalent historical cases. This is believed to be due to the more intensive tunnel cleaning procedure described in Section 2.1.3. The R2 values for the correlation between the two parameters are, respectively, 0.24 and 0.77 for conditions represented in the present CO2 and 50% air/CO2 data sets, and 0.02 for the Adam and Hornung (1997) CO2 data set.
For consistency with previously reported results, in these comparisons freestream conditions are taken as the conditions at the nozzle exit. The 100:1 area ratio con- toured nozzle is designed to operate at Mach 6. Because the shape is optimized for a single condition, there is significant variation of the exit Mach number over the range of possible tunnel operating parameters, presented in Figure 5.14 for air over the conditions of both past and present work. The range of Reynolds numbers evalu- ated at the boundary layer edge and Dorrance (1962) reference temperature, which is used as representative of conditions within the boundary layer, over the same range is presented for air in Figure 5.15. The historical results from Tables 5.7, 5.8, and 5.9 are also analyzed as described above.
20 40 60
7 5 11 9 3000 3500 4000
Pr [MPa]
hr [MJ/kg]
Uexit [m/s]
20 40 60
7 5 11 9 550 600 650 700 750 800
Pr [MPa]
hr [MJ/kg]
aexit [m/s]
20 40 60
7 5 11 9 5.4 5.6 5.8
Pr [MPa]
hr [MJ/kg]
Mexit
Figure 5.14: Calculated nozzle exit velocity, sound speed, and Mach number in air over a range of tunnel operating parameters hres and Pres.
Both the present N2 and air xTr results have a positive dependence onhres (linear model coefficient 0.56 for N2, 0.54 for air) and a negative dependence on Pres (−0.45 for N2, −0.14 for air; however, the air result, with p-value = 0.102, is only marginally significant). The historical air data of Adam and Hornung (1997) are analyzed in the
20 40
60 6
8 10 12
5 10 15
x 106
Pr [MPa]
hr [MJ/kg]
Unit Re [1/m]
20 40
60 6
8 10 12
2 4 6 8
x 106
Pr [MPa]
hr [MJ/kg]
Unit Re* [1/m]
Figure 5.15: Reynolds number evaluated at the boundary layer edge in air (left) and at Dorrance reference conditions in air (right) over a range of tunnel operating parameters hres and Pres.
same way, and likewise show a significant positive dependence of xTr on hres (0.72) and negative dependence on Pres (−0.28). No statistically significant dependence for xTr was found in the historical N2 data.
Both the present N2 and air results have a positive dependence on Pres (linear model coefficient 0.31 for N2, 0.59 for air) for the transition Reynolds number eval- uated at Dorrance reference conditions, Re∗tr, but neither have a dependence on hres that is statistically significant. The historical air and N2 data of Adam and Hor- nung (1997) and Germain and Hornung (1997) likewise show a significant positive dependence of Re∗Tr on Pres (0.34 for air, 0.48 for N2), but no statistically significant dependence onhres.
No statistically significant correlation of Re∗Tr with reservoir enthalpy hres is ob- served for any data set, either in the present data or in a statistical re-examination of Germain and Hornung (1997) and Adam and Hornung (1997), except for historical CO2 and the present 50% CO2 results10. Adam and Hornung (1997) and Germain and Hornung (1997) reported an increase in Re∗Tr with increasing hres, but did not control for Pres, which varied from 10 to 85 MPa in their air experiments. In both
10The present 100% CO2 results also show a positive correlation (linear model coefficient 0.36) of Re∗Tr with reservoir enthalpyhres, but the overallF-statisticp-value for the Re∗Tr model was 0.088, so this result is only marginally significant.
hres Pres unit Re unit Re∗ xTr δ99Tr ∼fTr
MJ/kg MPa 1/m 1/m m mm kHz
675 10.20 58.5 5.60×106 4.23×106 0.54 1.13 1074 683 10.43 65.5 5.94×106 4.51×106 0.41 0.96 1280 684 11.10 60.9 5.25×106 4.09×106 0.46 1.07 1180 685 10.32 56.9 5.37×106 4.06×106 0.43 1.04 1178 686 12.95 55.4 4.02×106 3.20×106 0.59 1.38 974 687 13.06 57.3 4.14×106 3.33×106 0.59 1.35 1001 688 13.27 62.3 4.38×106 3.55×106 0.62 1.33 1018 689 10.65 59.0 5.34×106 4.09×106 0.54 1.15 1070 879 11.65 79.1 6.26×106 5.00×106 0.49 1.00 1289 888 11.55 79.1 6.28×106 4.97×106 0.63 1.14 1124 1113 11.37 77.2 6.34×106 5.04×106 0.48 0.98 1293 1115 7.38 68.7 9.66×106 6.20×106 0.43 0.83 1275 1151 10.03 45.0 4.46×106 3.29×106 0.57 1.32 907 1152 8.88 43.3 4.97×106 3.50×106 0.40 1.06 1076 1153 12.19 40.7 3.30×106 2.53×106 0.72 1.70 769 1155 8.08 44.3 5.66×106 3.80×106 0.45 1.09 1007 1156 7.80 48.0 6.34×106 4.18×106 0.39 0.96 1124 1157 5.83 47.2 8.94×106 4.90×106 0.23 0.67 1421 1159 11.41 42.5 3.67×106 2.80×106 0.72 1.61 788 1160 10.41 41.9 4.00×106 2.98×106 0.66 1.49 819 1162 9.04 34.4 3.91×106 2.74×106 0.60 1.48 773 1163 11.17 68.1 5.73×106 4.47×106 0.59 1.15 1094
Table 5.7: Experiments performed in air referenced in Germain and Hornung (1997) and Adam and Hornung (1997), with unit Reynolds numbers evaluated at the bound- ary layer edge and Dorrance reference conditions, observed transition onset location, and δ99 and ∼ f calculated at the transition onset location. Observed transition on- set location xTr is as reported in Adam (1997), but the other parameters have been recalculated by the present methods for consistency, and in the case of Re∗/m, δ99, and f, calculated here for the first time.
present and past data, Re∗Trappears to correlate most strongly with Pres. The bound- ary layer edge pressure, and therefore the reservoir pressure, is important both in the mean flow and vibrational-translational damping processes. While the reservoir enthalpy, statistically, has been shown to be secondary to pressure, it is important to vibrational-translational relaxation due to its effect on vibrational populations, es- pecially for CO2. As noted above, at a given temperature, air and N2 have much lower vibrational populations than CO2 due to the higher characteristic vibrational temperatures of air and N2 in comparison to CO2.
hres Pres unit Re unit Re∗ xTr δ99Tr ∼fTr
MJ/kg MPa 1/m 1/m m mm kHz
353 10.50 62 6.05×106 4.07×106 0.45 1.03 1229 361 5.64 19 3.94×106 1.93×106 0.64 1.75 548 532 10.00 53 5.49×106 3.60×106 0.45 1.10 1130 536 13.54 60 4.30×106 3.29×106 0.57 1.32 1071 540 7.31 57 8.57×106 4.81×106 0.38 0.87 1242 542 3.25 11 4.56×106 1.64×106 0.48 1.62 460 546 5.54 16 3.41×106 1.65×106 0.53 1.73 549 548 9.33 55 6.18×106 3.91×106 0.45 1.05 1148 561 12.18 85 6.84×106 4.95×106 0.57 1.07 1265 563 12.84 85 6.47×106 4.83×106 0.57 1.09 1277 565 14.47 80 5.22×106 4.15×106 0.57 1.18 1237
Table 5.8: Experiments performed in N2 referenced in Germain and Hornung (1997) and Adam and Hornung (1997), with unit Reynolds numbers evaluated at the bound- ary layer edge and Dorrance reference conditions, observed transition onset location, and δ99 and ∼ f calculated at the transition onset location. Observed transition on- set location xTr is as reported in Adam (1997), but the other parameters have been recalculated by the present methods for consistency, and in the case of Re∗/m, δ99, and f, calculated here for the first time.
hres Pres unit Re unit Re∗ xTr δ99Tr ∼fTr
MJ/kg MPa 1/m 1/m m mm kHz
690 7.09 52.0 7.79×106 9.95×106 0.49 0.76 1138 1117 7.57 92.9 12.2×106 16.2×106 0.45 0.58 1537 1119 9.35 71.6 7.91×106 10.6×106 0.46 0.72 1352 1121 9.93 40.8 4.50×106 5.83×106 0.63 1.13 877 1123 6.50 55.2 8.87×106 11.2×106 0.46 0.69 1206 1124 6.06 59.9 10.1×106 12.7×106 0.39 0.60 1363 1125 4.65 61.2 13.5×106 16.1×106 0.36 0.51 1448 1126 4.56 62.2 13.8×106 16.4×106 0.37 0.51 1433 1130 5.30 49.1 9.53×106 11.6×106 0.42 0.66 1178 1131 6.36 49.9 8.21×106 10.3×106 0.43 0.70 1183 1132 7.76 52.3 7.11×106 9.18×106 0.42 0.73 1224 1133 5.26 48.2 9.49×106 10.5×106 0.37 0.61 1256 1136 5.87 60.4 10.9×106 13.6×106 0.42 0.61 1332 1148 5.89 44.2 8.07×106 9.95×106 0.45 0.73 1105 1149 5.08 44.5 9.28×106 11.1×106 0.47 0.70 1083
Table 5.9: Experiments performed in CO2 referenced in Germain and Hornung (1997) and Adam and Hornung (1997), with unit Reynolds numbers evaluated at the bound- ary layer edge and Dorrance reference conditions, observed transition onset location, and δ99 and ∼ f calculated at the transition onset location. Observed transition on- set location xTr is as reported in Adam (1997), but the other parameters have been recalculated by the present methods for consistency, and in the case of Re∗/m, δ99, and f, calculated here for the first time.
xTr Re¯ ∗Tr Re¯ Tr P¯res coefficient -0.28405 0.33725 0.27436
p-value 0.01308 3.07×10−4 3.24×10−4
¯hres coefficient 0.72414 0.10048 -0.043046 p-value 1.23×10−5 0.28530 0.57148
Table 5.10: Multivariable linear regression analysis for historical air results (n = 22) referenced in Germain and Hornung (1997) and Adam and Hornung (1997). Pres and hres are normalized by their respective maximum values. The coefficients found to be statistically significant (p <0.05) are in bold print.
xTr Re¯ ∗Tr Re¯ Tr P¯res coefficient -0.25907 0.47606 0.41048
p-value 0.18609 5.48×10−4 3.75×10−4 h¯res coefficient 0.36978 -0.08002 0.30036
p-value 0.13572 0.47584 8.69×10−3
Table 5.11: Multivariable linear regression analysis for historical N2 results (n = 11) referenced in Germain and Hornung (1997) and Adam and Hornung (1997). Pres and hres are normalized by their respective maximum values. The coefficients found to be statistically significant (p <0.05) are in bold print.
xTr Re¯ ∗Tr Re¯ Tr P¯res coefficient -0.16878 0.35199 0.44392
p-value 0.04956 9.45×10−6 4.45×10−5
¯hres coefficient 0.32474 -.15363 -0.30262 p-value 4.06×10−4 3.20×10−3 3.77×10−4
Table 5.12: Multivariable linear regression analysis for historical CO2 results (n= 15) referenced in Germain and Hornung (1997) and Adam and Hornung (1997). Pres and hres are normalized by their respective maximum values. The coefficients found to be statistically significant (p <0.05) are in bold print.