Thermochemical nonequilibrium flow analysis in low enthalpy shock-tunnel facility

A thermochemical nonequilibrium analysis was performed under the low enthalpy shock-tunnel flows. A quasi-one-dimensional flow calculation was employed by dividing the flow calculations into two parts, for the shock-tube and the Mach 6 nozzle. To describe the thermochemical nonequilibrium of the low enthalpy shock-tunnel flows, a three-temperature model is proposed. The three-temperature model treats the vibrational nonequilibrium of O2 and NO separately from the single nonequilibrium energy mode of the previous two-temperature model. In the three-temperature model, electron-electronic energies and vibrational energy of N2 are grouped as one energy mode, and vibrational energies of O2, O2+, and NO are grouped as another energy mode. The results for the shock-tunnel flows calculated using the three-temperature model were then compared with existing experimental data and the results obtained from one- and two-temperature models, for various operating conditions of the K1 shock-tunnel facility. The results of the thermochemical nonequilibrium analysis of the low enthalpy shock-tunnel flows suggest that the nonequilibrium characteristics of N2 and O2 need to be treated separately. The vibrational relaxation of O2 is much faster than that of N2 in low enthalpy condition, and the dissociation rate of O2 is manly influenced by the species vibrational temperature of O2. The proposed three-temperature model is able to describe the thermochemical nonequilibrium characteristics of N2 and O2 behind the incident and reflected shock waves, and the rapid vibrational freezing of N2 in nozzle expanding flows.


Comment 1:
The flow which is treated as quasi-one-dimensional flow is right or not?

Response:
The three-dimensional flow calculations have an advantage of the performance analysis of the shocktunnel facility 1 .However, the computational costs of the three-dimensional calculations are enormous to analyze the thermochemical nonequilibrium phenomena of the shock-tunnel flows.In the work by Nomelis et al. 2 , the two-dimensional axi-symmetric calculations of the shock-tunnel flow were preformed, and it was compared with the results by the quasi-one-dimensional calculations and the measured data of the shock-tunnel facility.The comparisons confirmed that the quasi-one-dimensional calculations are acceptable to analyze the thermochemical nonequilibrium of the shock-tunnel flows.
Hence, the thermochemical nonequilibrium analysis of the shock-tunnel flows has been widely performed by using the quasi-one-dimensional calculations 3 .
In the revised manuscript, the explanation of the quasi-one-dimensional calculations are added in

Comment 2:
The three-temperature model is proposed by author or referenced other authors?

Response:
The three-temperature model is proposed by authors.There have been several attempts to model the thermochemical nonequilibrium phenomena using a multi-temperature model.In the present threetemperature model, unlike the previous thermochemical nonequilibrium models, the electronelectronic-N2 vibrational temperature and species vibrational temperature of O2 and NO are treated as the separated nonequilibrium modes.

Comment 3:
Treating the vibrational nonequilibrium of O2 and NO separately is not suitable

Response:
As a reviewer commented, in the previous two-temperature model, the vibrational nonequilibrium modes of O2 and NO do not be treated as separately.The objective of the previous two-temperature model is to describe the nonequilibrium phenomena at the high-enthalpy flows above 8 /.In the high enthalpy environments, the dissociation of O2 occurs rapidly, and the influence of the species vibrational nonequilibrium of O2 and NO is not significant.However, in low-enthalpy shock tunnel flows below 8 /, where the stagnation temperature is less than 6,000 , the dissociation rate of O2 is mild, and it couples with the species vibrational nonequilibrium of O2.Therefore, a more sophisticated consideration of species vibrational nonequilibrium is required.
In the low-enthalpy shock tunnel flows, the species vibrational relaxation time of O2 differs from that of N2, and the species vibrational nonequilibrium of NO is not significant because the amount of NO produced from the exchange reaction is relatively small.Hence, in the present work, the species vibrational nonequilibrium of O2 and NO are treated as one species vibrational nonequilibrium mode, and treated separately from the electron-electronic-N2 vibrational nonequilibrium mode.

Comment 4:
The conclusions should include more information, data is better.

Response:
As the reviewer suggested.We add more information which can be inferred from the present work in 'Discussion and conclusions' on the lines 565-581 in pages 25-26.

Reviewer #2
Overall comments: This is a good paper for this journal and should be accepted with some revisions.A very detailed analysis, but in real shock tube flows, the three-dimensional effects are going to swamp the thermochemical issues associated with the two-temperature model.

Response:
As a reviewer commented, there are three-dimensional effects in real shock-tube which significantly affect the flow, especially in terms of performance and measurement aspects.In the present work, we limited our scope to quasi-one-dimensional flow for the detailed analysis of shock-tunnel flows in thermochemical nonequilibrium aspects.
In the revised manuscript, the more explanation of the quasi-one-dimensional calculations are added in 'Introduction' on the lines 28-41 in page 3.

Comment 1 (Abstract):
'The proposed three-temperature model was able to describe the different thermochemical nonequilibrium characteristics of N2 and O2 behind the incident and reflected shock waves and at the nozzle exit'.I'm not sure what is meant by different.Please clarify specific fluid mechanic of thermochemical phenomena.

Response:
As the reviewer suggested, we added the physical explanation of the present results in 'Abstract'.

Comment 2 (Introduction):
'Unfortunately, it is difficult to measure all flow properties, because the flow duration is typically only a few hundreds of milliseconds.You mean s few milliseconds.A few hundred would be terrific.

Response:
It is our mistake to express as "a few hundreds of milliseconds".As the reviewer suggested, we corrected the sentence on the lines 24-25 in page 3.

Comment 3 (Thermochemical nonequilibrium model):
Darcy-Weisbach friction factor .This assumes laminar flow, correct?This may not be the case.

Response:
We believe that Darcy-Weisbach friction factor  can be used in the shock-tube flow where the Reynolds number is up to 10 5 .Though the turbulent flow cannot be directly considered in quasi-onedimensional calculation, the viscous effects can be considered.This can be achieved by calculating the wall shear stress in the viscous source term using Darcy-Weisbach friction factor  , which can be explicitly determined from Reynolds number.The correlation of Reynolds number and Darcy-Weisbach friction factor  has been extensively investigated in the Reynolds number range of 3000 to 10 8 .This method has been generally adopted for quasi-one-dimensional calculation of shock-tunnel flows, for example, L1D code in the university of Queensland.We reflected this comment in the revised manuscript including the equation on the lines 258-263 in pages 13-14.
Comment 4 (Thermochemical nonequilibrium analysis in the K1 shock-tunnel facility): 'Na was employed to measure the electron-electronic-vibrational temperature   .The electronic temperature was modeled on the emissions spectra of Na, and the concentration of Na was varied between 10 and 100 ppm by volume'.Seeding sodium in the shock tunnel is going to change the reaction rates.Why is this a valid comparison?

Response:
We agree with the reviewer's comment.In line-reversal methods, the metallic seeding species are used to approximately measure the vibrational temperature of diatomic molecules.However, it is found that the concentration of seeding species could enhance the vibrational relaxation process.In the Park's work, which this study benchmarked, the vibrational relaxation time between Na and N2 was set to physically-fastest time to reflect this matter, and the calculation for the nozzle flow was performed under varying concentration of Na up to 100 ppm.The present study followed this approach, and it can be seen in

Response:
As a reviewer suggested, we corrected the Table 5 in page 25.
Fig 3 (b) that the N2 vibrational temperature changes with the concentration of Na.For conciseness, we have only mentioned about the method used in Park's work, but have not included the results of the Park's work.We reflected this matter by modifying the Fig 3 (b) which now includes the calculation results from Park's work, for the code-to-code validation as well as the comparison with experimental measurements on the lines 302-313 in page 16.Comment 5 (Thermochemical nonequilibrium analysis in the K1 shock-tunnel facility): 'Reservoir and nozzle exit conditions of K1 shock-tunnel flows'.Why are only some conditions completely listed.Please list all conditions.