Results: Transition Onset
5.2 Boundary Layer Transition Correlations
5.2.2 Reynolds Numbers
5.2.2.1 Unit Reynolds Number Effect
Past investigators have identified a so-called “unit Reynolds number effect”, which is the name given to variations in the nondimensional parameter ReTrobserved in ground testing facilities. This effect makes it difficult to compare between results acquired in different facilities as well as to extrapolate to atmospheric flight conditions. Morkovin (1988) points out that this “pernicious nonconstancy of ReTr” is not in general the result of any single phenomenon, but rather the cumulative effect of the nonideal aspects of wind-tunnel experiments, with contributors including sound radiated from supersonic nozzles and sidewalls, freestream disturbances, roughness, and leading- edge geometry. Schneider (2001) reviews the disparate unit Reynolds number effects found in the literature from a number of supersonic and hypersonic experiments, and hypothesizes that the major contributor to the effect in this flow regime is radiated noise from turbulent boundary layers on the nozzle wall. Schneider (2008a) proposed that tunnels specially designed to eliminate this radiated noise might mitigate the unit Reynolds number effect.
Like most hypersonic ground-test transition data, the present results reveal a strong unit Reynolds number effect on the transition Reynolds number (see Pate (1971), Schneider (2001), and more recently Wagner et al. (2011) and Wagner et al.
(2013)). These results are presented in Figure 5.8(a). This effect is also present for other relevant transition parameters, including (x/δ99)Tr (Figure 5.9(a)) and NTr (Figure 5.10(a)), and is also observed if the data are plotted in terms of unit Re∗ (Figures 5.8(b), 5.9(b), and 5.10(b)). There is a small variation of xTr observed in the present study (0.389 to 0.758 m), limited by the geometry of the cone, the test conditions, and the selection of conditions with clear transition onset. The cone was instrumented only between 0.221 and 0.942 m (see Table 3.1). The maximum and min- imum observable values of ReTr based upon these limits are included in Figure 5.8(a).
A linear fit indicates that the the transition Reynolds number is proportional to the
unit Reynolds number with a constant of proportionality of 0.57 (95% confidence interval: 0.50 to 0.63).
Schneider (2001) observed that quiet tunnel results should show less dependence on unit Re through reduction of the noise radiated from the nozzle wall. However, whether this effect holds for high enthalpy flows with vibrationally relaxing CO2
is unknown. No comparable results for CO2 were found in the literature, and the freestream noise measurements of Parziale et al. (2014), discussed above with respect to air, did not include any CO2 or 50% CO2 cases.
0 2 4 6 8 10 12
x 106 0
2 4 6 8 10 12x 106
unit Re [1/m]
ReTr
100% CO2
50% CO2
Air N2
(a) ReTr vs. unit Re
0 0.5 1 1.5 2
x 107 0
2 4 6 8 10x 106
unit Re* [1/m]
Re* Tr
100% CO2
50% CO2
Air N2
(b) Re∗Tr vs. unit Re∗
Figure 5.8: The unit Reynolds number effect on transition onset Reynolds number is identified in the present study both when physical properties are evaluated at (a) the boundary layer edge; and (b) Dorrance reference conditions.
It is widely thought (Pate and Schueler, 1969, Schneider, 2001) that an impor- tant driver of the unit Reynolds number effect is noise radiated from the boundary layer which forms on the wall of a supersonic nozzle, and the present data are consis- tent with this conclusion. Figure 5.11(a) presents the most amplified frequency (ΩTr) computed by STABL at the observed point of transition in terms of the boundary thickness δ99 at the same location. Thicker boundary layers result in a lower most amplified second mode frequency, as predicted by Equation (1.1). Figure 5.11(b) shows the relationship between ΩTr and nondimensionalized transition onset length,
0 2 4 6 8 10 12 x 106 200
300 400 500 600 700 800 900
unit Re [1/m]
(x/δ99)Tr
100% CO2
50% CO2
Air N2
(a) (x/δ99)Tr vs. unit Re
0 0.5 1 1.5 2
x 107 200
300 400 500 600 700 800 900
unit Re* [1/m]
(x/δ99)Tr 100% CO2
50% CO2 Air N2
(b) (x/δ99)Tr vs. unit Re∗
Figure 5.9: The unit Reynolds number effect on nondimensionalized transition onset length (x/δ99)Tr is identified in the present study both when physical properties are evaluated at (a) the boundary layer edge; and (b) Dorrance reference conditions.
0 2 4 6 8 10 12
x 106 2
4 6 8 10 12 14
unit Re [1/m]
NTr onset
100% CO2
50% CO2
Air N2
(a) NTr vs. unit Re
0 0.5 1 1.5 2
x 107 2
4 6 8 10 12 14
unit Re* [1/m]
NTr onset
100% CO2
50% CO2
Air N2
(b) NTr vs. unit Re∗
Figure 5.10: The unit Reynolds number effect on disturbance amplification rate at transition onset, NTr, as computed by PSE-Chem, is identified in the present study both when physical properties are evaluated at (a) the boundary layer edge; and (b) Dorrance reference conditions.
(x/δ99)Tr. With similar ΩTr, the normalized transition onset position is further down- stream for CO2 cases than it is for air or N2 experiments. Parziale et al. (2014) showed that most of the noise in the T5 freestream is at relatively low frequencies (<500 kHz), and observed a decrease in RMS density fluctuations with increasing fre-
quency. This observation is consistent with the present results, which show a shorter
nondimensional transition onset length for lower computed most amplified frequencies at transition, ΩTr.
0.5 1 1.5 2 2.5 3
0 500 1000 1500 2000 2500
δ99Tr [mm]
ΩTr onset [kHz]
100% CO2
50% CO2
Air N2
(a) ΩTr vs. δ99Tr
0 500 1000 1500 2000 2500
200 300 400 500 600 700 800 900
ΩTr onset [kHz]
(x/δ 99) Tr
100% CO2
50% CO2
Air N2
(b) (x/δ99)Tr vs. ΩTr
Figure 5.11: (a) Most amplified frequency (ΩTr) computed by STABL at the observed point of transition in terms of the boundary layer thickness at transition; and (b) the relationship between normalized transition onset length, (x/δ99)Tr, and most ampli- fied frequency (ΩTr). Most amplified frequency varies inversely with boundary layer thickness as predicted by Equation (1.1). For equivalent values of ΩTr, experiments in both 100% and 50% CO2 tend to transition later than air or N2 experiments in terms of nondimensionalized transition onset distance (x/δ99)Tr.