Results: Turbulent Spots
6.5 Conclusions
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.04
0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12
Tw/T
e
T w/T aw
100% CO2 50% CO2 Air N2
Figure 6.18: Tw/Taw and Tw/Te for the present study. These cold wall properties are far removed from the near-adiabatic conditions available in cold flow experimental hypersonic facilities and most commonly computed in the literature.
Z&H Fiala Mee Clark K&S J&K J&K S&F
1996 2006 2002 1994 2006 2008 2008 2010
Type Exp. Exp. Exp. Exp. Comp. Comp. Comp. Comp.
Me 8.02 b 3.5 6.1 1.86 6 5 5 5.35
Ue [m/s] a 1300b 3370 580b a a a 875b
unit Re [/m] a 2.9×106 4.9×106 16.0×106 a a a 14.3×106 Tw/Te 4.38 b 0.97b 0.37b 1.23 b 7 5.19 1 5.7 Tw/Taw 0.37 b 0.32b 0.065b 0.77 b 0.98b 1 0.19b 1
Cle 0.98 0.81 0.90±0.10 0.83±0.04 0.89 0.96 0.89 0.91
Cm – 0.60–0.69 – 0.64±0.02 0.76 c – – –
Cte 0.68 0.40 0.50±0.10 0.53±0.02 0.53 0.54 0.23 0.79
a Value not reported.
bCalculated from other reported values.
c Spot “wing tip” convection velocity.
Table 6.3: Results from past spot propagation studies, based on supersonic and hy- personic experiments (Zanchetta and Hillier (1996), Fiala et al. (2006), Mee (2002), and Clark et al. (1994)) and computations (Krishnan and Sandham (2006), two re- sults from Jocksch and Kleiser (2008), Jocksch (2009) and Sivasubramanian and Fasel (2010)) reported for a range of conditions and presented together in this table.
observed propagating in both heat transfer traces and heat flux “movies” of the devel- oped cone surface. These observations are used to calculate turbulent spot convection rates, which are compared with previous experimental and computational results. Al- though the present results were obtained at different conditions from past experiments, the normalized spot propagation results for the present Mach ∼5 conditions appear to be generally consistent with past supersonic and hypersonic experiments, as well as with the computational results.
However, the flow conditions in all of the reviewed simulations are essentially nonreactive (cold flow with frozen composition), and the ratios of freestream to wall temperature, as well as adiabatic to nonadiabatic wall temperature, in the simulations are far from our experimental conditions. The flow conditions in these T5 tests are de- signed to simulate hypervelocity atmospheric flight and the flow over the model is hot, partially dissociated gas with some amount of chemical and vibrational nonequilib- rium due to the rapid expansion process in the nozzle. The available computational results of spot propagation in hypersonic flow in the present literature survey sim- ulated much higher wall temperature ratios Tw/Te and adiabatic wall temperature ratios Tw/Taw than actually occur in either reflected shock tunnel experiments or flight (see Table 6.3 and Figure 6.18).
At present, there are no high Mach number computational turbulent spot prop- agation studies in the literature which fully match the low wall-temperature ratios which are characteristic of high-enthalpy shock tunnels like T5 and T4. At lower Mach numbers, such as the results of Clark et al. (1994), the subsonic (first) mode is the dominant linear boundary layer instability mechanism. At hypersonic Mach num- bers (>4), instabilities in the second (Mack) acoustic mode dominate the boundary layer transition mechanism. For cold-wall hypervelocity flow with a hot freestream, the first mode is expected to be damped and the higher inviscid modes are amplified, so that the second mode would be expected to be the only mechanism of linear in-
stability. The present results are thus most directly comparable, in terms of Mach number and wall temperature ratio, to the flat plate T4 results of Mee (2002), and indeed are largely within the uncertainty range of Mee’s measurements. Computa- tions with realistic wall-temperature ratios would be quite valuable for comparison with the present experiments.
While the design of the experiment precludes precise measurement of spot spread- ing angleα, approximate bounding values for this parameter have been obtained. For example, for shot 2654, we estimate 2◦ < α <13◦. This result brackets the reported value of 3.5◦±0.5◦ of Mee (2002) for similar Mach numbers, as well as the reported value of 6.75◦±1.0◦ of Fiala et al. (2006) for lower Mach numbers. These are the two nearest experimental studies to the present work in terms of conditions. Both of these values are also consistent with the Mach number–spreading angle relationship, Equation (6.1), reported in Doorley and Smith (1992). More precise measurements of spreading angle would be possible with the addition of thermocouples in a more circumferentially dense pattern. The relatively small uncertainty on the spreading angle measurements in Mee (2002) and Fiala et al. (2006) is due to the use of densely packed thin film arrays extending on the test article surface in the direction orthog- onal to the flow field. Mee (2002) used seven sensors at 5 mm pitch and Fiala et al.
(2006) used 18 sensors at 4 mm pitch. By contrast, the present work uses rows of four sensors at pitches ranging from 19.2 mm for the first row to 82.1 mm for the last row.
With the measured parameters, a simple geometric model for the propagation of turbulent spots has been adapted from Jewell (2008) and used, following Mee and Tan- guy (2013), to infer turbulent spot generation rates nfrom a set of 17 experimentally measured transition onset and completion distances in three different gas mixtures.
The results indicate that n is significantly higher in air and N2 boundary layers than for experiments with 50% CO2. While spot generation rates were higher than those found by Mee and Tanguy (2013), most of the difference is accounted for by differing
model inputs for Cte, and the Mee results were acquired on a flat plate in a different facility.
The present results represent the first attempt to infer turbulent spot generation rate in T5, as well as the best available data on the effect of CO2 on spot forma- tion in a hypervelocity boundary layer. Turbulent spot generation is the outcome of the boundary layer receptivity process (Fedorov, 2003) and its characterization is therefore important for understanding both receptivity and the region of intermittent turbulence which occurs between transition onset and completion. In particular, pre- dicting the time-resolved heat flux in this region, both for flight and for ground tests, depends upon a model for turbulent spot generation and propagation. As different tunnels have disparate acoustic spectra, particulate contamination properties, and other noise and disturbance sources, information about the spot generation rate in each facility is also important for comparing transition measurements to each other, especially the onset to completion distance.