5.3 Validation of CFD-FD2TD Combined Method with Experimental Re-
5.3.3 Uncertainty in chemical reaction rate model
(a) Short grid (b) Long grid
Fig. 5.33: Computational grid systems of ARD for parametric study
ionization of air due to strong shock wave around the ARD. In particular, the electron number density is high because of the high-temperature region in the front and lateral regions. On the other hand, in the wake region, the electron number density is low enough to allow electromagnetic waves propagate into the TDRS for all cases. Although all cases have the regions not exceeding the critical electron number density in the wake region, it can be seen that the electron number density in the wake region changes according to respective chemical reaction rates in associative ionizations. The cases 2 and 5 having a high reaction rate show the low electron number density compared with other cases. Meanwhile, the results of cases 3 and 4 are similar to that of case 1 though they are the cases having a high reaction rate. In cases 6 and 9, the most highest electron number density at this altitude forms. On the other hand, in cases 7 and 8, the similar results are acheived with case 1 even though they have a low reaction rate.
From these results, it is confirmed that the generation of electrons around the ARD vehicle is mainly determined by the associative ionizations. In addition, it is confirmed that the reaction 5.4 has the greatest effect in terms of the generation of electrons, the reaction 5.6 is second and the reaction 5.5 has the least effect. The reason why the reaction 5.4 has the greatest effect is that the nitrogen atoms are a larger percentage of the plasma flows around the reentry vehicle. In addition, when having a high reaction rate, the flowfield is close to chemical equilibrium, and the electron number density rapidly decreases because the temperature rapidly decreases in the wake region. When having a low reaction rate, the flow is close to chemically frozen. From these reasons, it can be seen that uncertainty in the chemical reaction rate model strongly affects the formation of electrons around the reentry vehicle, especially in the wake region.
Figure 5.35 shows the distributions of electron number density in the x–y plane (z = 0 mm) around the ARD obtained by the numerical simulation of flowfield in cases 1–9 at an altitude of 77 km. At this altitude, the effect of uncertainty in the chemical reaction rate model can be seen more clearly. First, highly dense plasma for all cases forms around the ARD vehicle compared with the case of an altitude of 85 km because the density of inflow gas increases. The cases 1, 3, 4, 7, and 8 show similar results which have a large region exceeding the critical electron number density. In cases 2 and 5, a relatively small region exceeding the critical electron number density is distributed.
On the other hand, in cases 6 and 9, the ARD vehicle is completely blocked by the
(a) Case 1 (b) Case 2 (c) Case 3
(d) Case 4 (e) Case 5 (f) Case 6
(g) Case 7 (h) Case 8 (i) Case 9
Fig. 5.34: Distributions of electron number density in case 1-9 at an altitude of 85 km around the ARD vehicle
region exceeding the critical value.
Figure 5.36 shows the distributions of electron number density in the x–y plane (z = 0 mm) around the ARD obtained by the numerical simulations of flowfield in cases 1–9 at an altitude of 70 km. At this altitude, more highly dense plasma for all cases are generated around the ARD. Whereas the ARD, in cases 1, 3, 4, and 6–9, is totally blocked by the region where exceed the critical electron number density, only cases 2 and 5 show the results having possibility which the electromagnetic wave may tranmit into the TDRS, by passing through the plasma layer. As such, uncertainty in the reaction rate model strongly affects the generation of electrons and the evaluation of RF blackout.
Next, the behavior of electromagnetic waves are numerically investigated by the FD2TD method using the plasma properties obtained by the flowfield simulations
(a) Case 1 (b) Case 2 (c) Case 3
(d) Case 4 (e) Case 5 (f) Case 6
(g) Case 7 (h) Case 8 (i) Case 9
Fig. 5.35: Distributions of electron number density in case 1-9 at an altitude of 77 km around the ARD vehicle
described in above. The computational domain for these calculations is set to be a cuboid with a length of 10.0 m in thex direction, a height of 7.0 m in the y direction, and a width of 6.0 m in the z direction for all cases. The computational grid is set as 800 (x) × 560 (y) × 480 (z) nodes. The behaviors of electromagnetic waves in the x–y plane (z = 0 mm) for cases 1–9 at an altitude of 85 km around the ARD vehicle are shown in Fig. 5.37. In all cases, the electromagnetic waves emitted from the antenna propagate into the rear region of the ARD vehicle where the electron number density is low, whereas the electromagnetic waves are completely reflected by the region exceeding the critical electron number density in front of the ARD. In particular, the electromagnetic waves propagate with less attenuation in cases 2 and 5.
The behaviors of electromagnetic waves in the x–y plane (z = 0 mm) for cases 1–9 at an altitude of 77 km around the ARD vehicle are shown in Fig. 5.38. In case 1, the
(a) Case 1 (b) Case 2 (c) Case 3
(d) Case 4 (e) Case 5 (f) Case 6
(g) Case 7 (h) Case 8 (i) Case 9
Fig. 5.36: Distributions of electron number density in case 1-9 at an altitude of 70 km around the ARD vehicle
electromagnetic waves are observed to propagate through the thick plasma region into the leeward side of the vehicle although they have strong attenuation. In addition, in the cases 3, 4, 7, and 8, the similar results with that of case 1 are acheived. The cases 2 and 5 show the results that the electromagnetic waves propagate into the leeward side with less attenuation comparing with case 1. On the other hand, in cases 6 and 9, the electromagnetic waves cannot propagate through the plasma region because the ARD vehicle is almost totally blocked by highly dense plasma and most of the electromagnetic waves are reflected with strong attenuation. From these results, RF blackout may be observed at an altitude of 77 km in cases 6 and 9. In addition, the results of all cases, except cases 6 and 9, show that if the antenna is mounted on the leeward side and the signal receiver is located at the leeward side, less attenuation of the electromagnetic waves will be observed.
(a) Case 1 (b) Case 2 (c) Case 3
(d) Case 4 (e) Case 5 (f) Case 6
(g) Case 7 (h) Case 8 (i) Case 9
Fig. 5.37: Behavior of electromagnetic waves in case 1-9 at an altitude of 85 km around the ARD vehicle
The signal losses calculated by the FD2TD simulation are validated by the compar-ison with the experimental results [26]. Figure 5.39 shows the comparcompar-ison of signal loss profile for the TDRS between the measured results and computational results of cases 1–9. In the actual flight data, no RF blackout is observed although strong attenuation is appeared. The case 1 predicts the RF blackout at altitudes between 77 and 65 km, and more strong attenuation is observed than that measured. In cases 2 and 5 having high reaction rates, the computational results show good agreement with the experi-mental results. These cases predict no RF blackout though the plasma attenuation is stronger than the measured data. Meanwhile, the cases 3 and 4 show the signal loss profiles which are similar to those of case 1 although these cases used the high reaction rates. This is because the reaction 5.4 has the greatest effect in terms of the generation of electrons as mentioned previously. On the other hand, the cases 6 and 9 predict the
(a) Case 1 (b) Case 2 (c) Case 3
(d) Case 4 (e) Case 5 (f) Case 6
(g) Case 7 (h) Case 8 (i) Case 9
Fig. 5.38: Behavior of electromagnetic waves in case 1-9 at an altitude of 77 km around the ARD vehicle
RF blackout at altitudes between 80 and 60 km. In addition, the signal losses in these cases are stronger than other cases. This is because the flow is close to being chemi-cally frozen due to using the low reaction rates. Whereas, in cases 7 and 8 having low reaction rates, RF blackout occurs at altitudes from 77 to 60 km, and the signal losses are similar to those in case 1. This is because the reactions 5.5 and 5.6 do not affect the formation of electrons around the reentry vehicle as much as the reaction 5.4 does, as mentioned previously. These results show that the computed signal losses in all cases qualitatively are in agreement with the trends of the actual flight data at all altitudes.
In particular, the results of cases 2 and 5 are in great agreement with the measured data. It is confirmed that the present CFD-FD2TD simulation model for evaluating RF blackout reproduces the signal loss profile well. In addition, the discrepancies in computed signal losses are caused by uncertainty in the chemical reaction rate model.
Therefore, it is reasonable to say that uncertainty in the reaction rate model should be considered to evaluate the RF blackout simulation properly.
Fig. 5.39: Comparison of signal losses with parametric study
Conclusion
Numerical simulations of the plasma flows and the behavior of electromagnetic waves around the reentry vehicles were performed to evaluate the radio frequency blackout and signal losses during atmospheric reentry. The flowfields around the reen-try vehicles were assumed to be in thermochemical nonequilibrium. A four-temperature model was adopted in the present simulation model to express thermal nonequilibrium flow accurately, and the temperature was separated into translational, rotational, vi-brational, and electron temperatures. In addition, detailed internal energy-exchange and complex chemical reactions were considered. The axisymmetric and the three-dimensional models were both used in the present study. In both axisymmetric and three-dimensional models, mathematical formulations of complicated flowfields in the shock layer were established to reproduce the reentry conditions accurately. Addition-ally, its implementations through the effective numerical methods were achieved. In particular, the overset grid system was used to avoid the presence of a singular line along the axis of symmetry for the three-dimensional model. The behavior of electromag-netic waves around the reentry vehicle was investigated using the frequency-dependent finite-difference time-domain method with the plasma properties obtained in plasma flow simulations.
To validate the present simulation model, numerical simulations were performed around the OREX and the ARD, and the results were compared with their experimental results. Through the present study, the following conclusions were made:
(1) The plasma flow simulations were performed around the OREX to validate the both axisymmetric and three-dimensional flowfield simulation model. The numerical results were compared with corresponding experimental data of the saturation ion current. The numerical results were in generally good agreement with the experimental data. Although some errors, possibly resulting from the recombination reaction, were observed near the wall surface, it was confirmed that both models reproduce the plasma flows around the reentry vehicle, appropriately.
(2) In the present study, the numerical simulations of the axisymmetric model and three-dimensional model with an angle of attack of -20 degrees were performed around the ARD at altitudes of 92 - 40 km according to reentry orbit data to investigate the effect of angle of attack on reproducing the distribution of the electron number density around the reentry vehicle and on evaluating the radio frequency blackout.
The results of the three-dimensional model differ markedly from the results of the axisymmetric model in the wake region, even if the results in the front region where
96
the shock layer formed were approximately the same. The distributions of electron number density in the wake region decreased by considering an angle of attack because there are fewer ionization reactions in the wake region owing to the lower density of gas when a non-zero angle of attack is considered. The signal losses of the electromagnetic waves were compared between the actual flight data and the results obtained by the FD2TD method. The computed signal losses in both cases were in qualitatively good agreement with the trends of the experimental results. However, in both cases, the radio frequency blackout were observed at several altitudes, whereas no radio frequency blackout was observed in the actual flight test. In addition, the computed signal losses of the axisymmetric model case show better agreement with the experimental results although more electrons are generated around the ARD in case of the axisymmetric model than the three-dimensional model, because of the formation of a region where the electron number density exceeds the critical value near the antenna in case of three-dimensional model. From these results, we concluded that the angle of attack strongly affects the formation of the electron number density around a reentry vehicle, and it has to be considered in evaluating the possibility of radio frequency blackout during atmospheric reentry.
(3) Next, numerical simulations of plasma flows and electromagnetic waves around the ARD were performed to evaluate the effect of the surface catalysis on the predic-tion accuracy of the radio frequency blackout during atmospheric reentry. The three-dimensional model with the non-catalytic wall condition and the finite-catalytic wall condition were adopted for plasma flow simulations. In case of finite-catalytic wall con-dition, the electron number density was reduced around the ARD compared with the case of non-catalytic wall condition because the electrons are generated less at the wall surface due to the finite catalytic recombination reactions, and the number of electrons flowing into the wake region decrease. In addition, the computed signal losses were compared with the experimental results. The predicted signal losses in case of finite-catalytic wall condition showed better agreement with the actual flight data. From these results, we concluded that the surface catalysis strongly affects the formation of the electron number density in the wake region, and this effect has to be considered in investigating the possibility of radio frequency blackout during atmospheric reentry.
(4) Finally, a parametric study was performed by multiplying the forward reac-tion rates of associative ionizareac-tions by uncertainty factors, to investigate the effect of uncertainty in chemical reaction rate models on the evaluation of radio frequency blackout. The numerical simulations around the ARD were implemented for nine cases considering uncertainty in chemical reaction rate models, and each case was performed at altitudes between 92 and 40 km. From the results of the plasma flow simulations, it was confirmed that uncertainty in the associative ionization reaction rate model strongly affects the generation of electrons around a reentry vehicle, and high reaction rates, especially in an associative ionization reaction of nitrogen, reduce the electron number density in the wake region. In addition, the computed signal lossess generally showed good agreement with the measured results for all cases. In particular, the cases 2 and 5 having high reaction rates were in great agreement with the actual flight data.
From these results, we concluded that the associative ionization reaction of nitrogen has the greatest effect in terms of the formation of electrons around a reentry vehicle and the evaluation of radio frequency blackout, and the uncertainty in the reaction rate model should be considered in investigating the possibility of radio frequency blackout
during atmospheric reentry.
From the present study, it was confirmed that the present simulation model can be effectively used to evaluate radio frequency blackout and signal loss in the design and development of reentry vehicles. However, some discrepancies between the computed and measured signal losses were seen at few altitudes. The uncertainty in physical models including the chemical reactions and internal energy exchange might cause these discrepancies as the uncertainty in chemical reaction rate models strongly effects the formation of electrons around a reentry vehicle and the evaluation of radio frequency blackout. In addition, theses discrepancies might also be come from the effect of ablation and the flight conditions including the vibration and rotation of a reentry vehicle which were not considered in this study. It is necessary to do further study about these issues.
Acknowledgments
The computations were mainly carried out using the computer facilities at Research Institute for Information Technology, Kyushu University.
First and formost, I would like to express my sincere gratitude to my supervisor Professor Ken-ichi Abe for his brilliant advice and guidance on this research throughout the course of this study. He also has been my excellent and honorable advisor in my personal life.
I would like to appreciate Professor Nobuhiko Yamasaki (Kyushu University) and Professor Naoji Yamamoto (Kyushu University) for taking time out of their busy sched-ule to read this thesis as the second readers.
My sincere appreciation also goes to Assistant Professor Hisashi Kihara (Kyushu University) for his excellent advice and helpful discussions made during this study. I am also grateful for his encouragement and support in my daily life.
And also, my special appreciation goes to Assistant Professor Yusuke Takahashi (Hokkaido University) for supplying his computational code for electromagnetic waves.
His invaluable advice and insightful discussions made during this research were thank-fully very constructive.
I sincerely appreciate all the members of the Fluid Mechanics Laboratory at Kyushu University. Their familiar learning environment and exciting activities were quite en-joyable and memorable.
My genuine gratitude also goes to Dr. Jonghyeok Park, Dr. Kihun Jeong, Mr.
Chunghyeon Choi, Mr. Juncheol Seo, Mr. Haewon Seo and all the members of Korea-Japan Joint Government Scholarship Program in Kyushu University. They shared a hard time and cared for each other like a real family.
I would like to thank all my friends in Korea, especially Wonhyun Jeong, Hyunwoo Kim and Joohyung Pahk, who always encouraged me even though I was far apart.
There are no words to express my deepest gratitude to my beloved, Gayoung Kim who has always been supportive of me for everything. Without her encouragement, my efforts would have surely been in vain.
Finally, I would like to express my heartfelt appreciation and dedicate this work to my beloved family members including my late grandmother who have made the numerous sacrifices and countless support for me.
A.1 Jacobian Matrices of Inviscid Term
The inviscid Jacobian matrices A, B, and C are evaluated as follows:
Q=
ρ
l m
n E ρ1 ... ρns Erot Evib Ee
, E =
ρu ρu2+p
ρuv ρuw (E+p)u
ρ1u ... ρnsu Erotu Evibu Eeu
, F =
ρv ρuv ρv2+p
ρvw (E+p)v
ρ1v ... ρnsv Erotv Evibv Eev
, G=
ρw ρuw ρvw ρw2+p (E+p)w
ρ1w ... ρnsw Erotw Evibw Eew
(A.1)
where l = ρu, m = ρv, and n = ρw. The Jacobian matrices can be obtained by differentiating partially the flux vectors by the conservative vector:
A= ∂E
∂Q, (A.2)
B= ∂F
∂Q, (A.3)
C = ∂G
∂Q. (A.4)
Considering the fifth column and the first row of A, the following expression yields
∂(E+p)u
∂ρ = ∂
∂ρ
[(E+p)l ρ
]
=u(pρ−h). (A.5)
100
Hence, A,B and C can be given by
A=
0 1 0 0 0 0 · · · 0 0 0 0
−u2+pρ 2u+pl pm pn pE pρ1 · · · ρns pErot pEvib pEe
−uv v u 0 0 0 · · · 0 0 0 0
−uw w 0 u 0 0 · · · 0 0 0 0
u(pρ−h) h+upl upm upn u(1 +pE) upρ1 · · · upρns upErot upEvib upEe
−uρ1/ρ ρ1/ρ 0 0 0 u · · · 0 0 0 0
... ... ... ... ... ... . .. ... ... ... ...
−uρns/ρ ρns/ρ 0 0 0 0 · · · u 0 0 0
−uErot/ρ Erot/ρ 0 0 0 0 · · · 0 u 0 0
−uEvib/ρ Evib/ρ 0 0 0 0 · · · 0 0 u 0
−uEe/ρ Ee/ρ 0 0 0 0 · · · 0 0 0 u
(A.6)
B=
0 0 1 0 0 0 · · · 0 0 0 0
−uv v u 0 0 0 · · · 0 0 0 0
−v2+pρ pl 2v+pm pn pE pρ1 · · · pρns pErot pEvib pEe
−vw 0 w v 0 0 · · · 0 0 0 0
v(pρ−h) vpl h+vpm vpn v(1 +pE) vpρ1 · · · vpρns vpErot vpEvib vpEe
−vρ1/ρ 0 ρ1/ρ 0 0 v · · · 0 0 0 0
... ... ... ... ... ... . .. ... ... ... ...
−vρns/ρ 0 ρns/ρ 0 0 0 · · · v 0 0 0
−vErot/ρ 0 Erot/ρ 0 0 0 · · · 0 v 0 0
−vEvib/ρ 0 Evib/ρ 0 0 0 · · · 0 0 v 0
−vEe/ρ 0 Ee/ρ 0 0 0 · · · 0 0 0 v
(A.7)
C =
0 0 0 1 0 0 · · · 0 0 0 0
−uw w 0 u 0 0 · · · 0 0 0 0
−vw 0 w v 0 0 · · · 0 0 0 0
−w2+pρ pl pm 2w+pn pE pρ1 · · · pρns pErot pEvib pEe w(pρ−h) wpl wpm h+wpn w(1 +pE) wpρ1 · · · wpρns wpErot wpEvib wpEe
−wρ1/ρ 0 0 ρ1/ρ 0 w · · · 0 0 0 0
... ... ... ... ... ... . .. ... ... ... ...
−wρns/ρ 0 0 ρns/ρ 0 0 · · · w 0 0 0
−wErot/ρ 0 0 Erot/ρ 0 0 · · · 0 w 0 0
−wEvib/ρ 0 0 Evib/ρ 0 0 · · · 0 0 w 0
−wEe/ρ 0 0 Ee/ρ 0 0 · · · 0 0 0 w
(A.8)
Partial derivatives of pressure can be obtained by differentiating Eq. (2.89) with respect to the corresponding variables:
pρ= (ˆγ−1)q2
2, (A.9)
pl =−(ˆγ−1)u, (A.10)
pm =−(ˆγ−1)v, (A.11)
pn=−(ˆγ−1)w, (A.12)
pE = ˆγ−1, (A.13)
pρs =
−(ˆγ−1)∆h0s+ p−pe
γ−1, s̸= e
0, s= e
(A.14)
pErot =−(ˆγ−1), (A.15)
pEvib =−(ˆγ−1), (A.16)
pEe =−(ˆγ−1). (A.17)
From Eqs. (A.6), (A.7) and (A.8), the Jacobian matrix Pe =
(Ae or Be orCe )
can be expressed by
Pe=
0 kx ky kz 0 0 · · · 0 0 0 0
kxpρ−uU U−kxu(pE−1) kyu−kxvpE kzu−kxwpE kxpE kxpρ1 · · · kxρns kxpErot kxpEvib kxpEe
kypρ−vU kxv−kyupE U−kyv(pE−1) kzv−kywpE kypE kypρ1 · · · kyρns kypErot kypEvib kypEe
kzpρ−wU kxw−kzupE kyw−kzvpE U−kzw(pE−1) kzpE kzpρ1 · · · kzρns kzpErot kzpEvib kzpEe
(pρ−h)U kxh−uU pE kyh−vU pE kzh−wU pE (1 +pE)U U pρ1 · · · U pρns U pErot U pEvib U pEe
−U ρ1/ρ kxρ1/ρ kyρ1/ρ kzρ1/ρ 0 U · · · 0 0 0 0 ..
.
.. .
.. .
.. .
.. .
..
. . .. ...
.. .
.. .
.. .
−U ρns/ρ kxρns/ρ kyρns/ρ kzρns/ρ 0 0 · · · U 0 0 0
−U Erot/ρ kxErot/ρ kyErot/ρ kzErot/ρ 0 0 · · · 0 U 0 0
−U Evib/ρ kxEvib/ρ kyEvib/ρ kzEvib/ρ 0 0 · · · 0 0 U 0
−U Ee/ρ kxEe/ρ kyEe/ρ kzEe/ρ 0 0 · · · 0 0 0 U
(A.18)
where U = kxu+kyv +kzw and Pe = kxA+kyB+kzC. Moreover, (kx, ky, ky) = (ξx, ξy, ξz) for A, (ke x, ky, kz) = (ηx, ηy, ηz) for B, and (ke x, ky, kz) = (ζx, ζy, ζz) for C,e respectively. The eigenvectorΛ of this matrix is expressed as following:
Λ= diag[U, U, U+c
√
k2x+ky2+k2z, U−c
√
k2x+ky2+k2z, U, · · · , U]t (A.19)