研究
学位論文
博士論文（近日公開予定）
Analysis of Vortex Structures Induced by the Synthetic Jet for the Control of Separated Flows
剥離流れ制御にむけたシンセティックジェットが生み出す渦構造の解析
Abstract
In this thesis a control mechanism of separated flow using a small devise called“synthetic jet”are studied by detailed computational fluid dynamics. The thesis describes the feature
of flow-field generated by synthetic jet without outer flow (in a static air), the effects of the flow-field changed by the control parameter and the mechanism of control of separated
flow using a synthetic jet with applying a backward-facing step flow. Recently, a synthetic jet which has capability and possibility of dynamic flow-control
for various flow conditions has been researched. The synthetic jet, which consists of one orifice connected to a cavity, the bottom which oscillates with a small amplitude by piezoelectric
device, piston and speaker and produces weak and periodic flow from the orifice. The weight of the devise is lighter than conventional devises. The devise has dynamic
flow-control capability and possibility depending on flow conditions or application because the induced flow can be controlled electrically by changing voltage and amplitude.
Many previous experimental studies on the synthetic jet have been focused on demonstrating effects of the synthetic jet for flow control, or finding optimal conditions from the
viewpoints of parameter study. For example, some researches focus on optimal condition, e.g. the location, momentum coefficient and frequency of synthetic jet over an airfoil,
backward facing step and circular cylinder. However, the physical evidence of the control mechanism has not been shown and these optimal values are inconsistency because the
control mechanism of separated flow has not been clarified. Furthermore, the technology of separated flow control using the synthetic jet of actual aircraft level (high Reynolds
number, high dynamics pressure, large scale) has not been developed, yet. Therefore, in order to make synthetic jets applicable for practical flight level, the objectives of the thesis
are to understand control mechanism of separated flow instead of current trial-and-error experimental studies and adding index of parameter setting of the flow control. Since a
computation of fluctuation components of physical value is important for clarification of control mechanism of separated flow from the previous studies, LES study using compact
difference scheme is conducted.
Firstly, the computation of synthetic jet including three-dimensional flow inside the synthetic jet cavity, orifice and the flow outside the cavity and blowing to static air was
conducted. The LES results with flow inside the cavity resolved and with the boundary condition given are compared with previous experimental results. Comparison of the
present LES result with experimental data has shown that the time averaged vertical velocities of the cavity model agree quantitatively with the experimental data and time averaged
vertical velocity fluctuation agree qualitatively with the experimental data. It reveals that the longitudinal vortices induced from the orifice significantly affect two-dimensional
y-direction vortices when considering three-dimensional modeling of the flow inside the cavity. The vortex structure induced by synthetic jet is understood as above. Then, the
effects of nondimensional parameters of the synthetic jet on the inducement flow field were investigated. The flow-fields turn to turbulent (three-dimensional) flow as Reynolds
number (the reference velocity is the time maximum value of the spatially averaged vertical velocity at the orifice exit, which is analytically obtained, when incompressible flow
is assumed.) increase. The flow-fields maintain laminar flow and turn to two-dimensional vortices as Reynolds number decrease. On the other hand, the induced vortices strongly
interact and decay because the cycle of vortices induced is short as Strouhal number (the reference velocity is the time maximum value of the spatially averaged vertical velocity
at the orifice exit, which is analytically obtained, when incompressible flow is assumed) increases. The induced vortices do not interact and decay because the cycle of vortices
induced is large as Strouhal number decrease. It summarizes that the difference of the Reynolds number changes three-dimensional vortices structure and the difference of the
Strouhal number changes intensity of vortices. Moreover, the effects of design parameters of synthetic jet were also investigated. As the frequency increases, the Reynolds number
increases. Thus, the flow-fields turn to turbulent flow. As the amplitude increases, the Reynolds number increases and the Strouhal number decreases. Thus, the flow-fields
turn to turbulent flow and the induced vortices do not decay. These results show that large amplitudes and high frequencies are effective in order to generate a strong three dimensional
vortex. Larger amplitudes and low frequencies are effective for generation of a strong two-dimensional vortex. These results reveal that not only frequency but also
amplitude are important for separated flow control.
Secondly, an analysis with an outer flow is conducted to understand control mechanism of separated flow. Not an airfoil but an backward-facing step is chosen as analysis objects
because parameters (i. e. Angle of attack, airfoil configuration and separation type) are few, separation point is fixed and flow field is easily comprehensible. Three-dimensional
Navier-Stokes equations are solved. Implicit large-eddy simulation (LES) using the high order compact difference scheme is conducted. The 3D-LES analysis is conducted including
cavity configuration and the effect of non-dimensional frequency, which is shown to be important parameter of separated flow control by previous researches, is studied. Two
cases are selected; the case computing flow with synthetic jet control at F+h =0.2, and the case computing flow with synthetic jet control at F+h =2.0, where non-dimensional frequency
F+h is normalized with the height of backward-facing step and the freestream velocity. These values consulted F+h =1.0 and 10, where non-dimensional frequency F+h is normalized with
the length of separation region and the freestream velocity because previous studies showed that both these values are important for control, respectively. From time-averaged analysis,
size of the separation length in the case of the flow controlled at F+ h =2.0 is almost the same as the case without control. On the other hand, the present computation shows that separation
length in the case of the flow controlled at F+h =0.2 is 20 percent shorter than the case without control, because strong Reynolds shear stress enhance mixing in the shear layer and the
recirculation region. Frequency analysis clarified the reason for suppression of separation, because non-dimensional frequency normalized with the momentum thickness of separated shear
layer and the freestream velocity is close to unstable frequency of separated shear layer. This result means frequency should not be normalized by the height of backward-facing step but be normalized by the momentum
thickness of separated shear layer (boundary layer). Phase averaged analysis shows that the short period vortices generated from the synthetic jet decay in the shear layer and
Reynolds shear stress generated is that turbulent component is totally dominant in F+h =2.0. The pairing of the vortex generated from synthetic jet and vortices induced from
the edge of backward-facing step induce strong two-dimensional vortices (roller structure). The pairing also induce longitudinal vortices (rib structure) in the region (braid region)
between two-dimensional vortices and two-dimensional vortices in F+h =0.2. Moreover, the strong two-dimensional vortices generate the periodic component of Reynolds shear
stress, while the region between vortices and vortices generate the turbulent components Reynolds shear stress. Especially, the turbulent component is totally dominant. The
each periodic and turbulent components of Reynolds shear stress enhance mixing in the separated shear layer and recirculation region, respectively.
From the above discussions, it is important to induce two-dimensional vortices by pairing and longitudinal vortices by two-dimensional vortices for separated flow control.
These obtained knowledge can be applied for separated flow control over not only the airfoils but also the general separated flows using other active flow control devises (e.g. DBD plasma actuator).
Abstract(in Japanese)
本論文はシンセティックジェットと呼ばれる小型デバイスの剥離制御メカニズムを詳細な流体解析を行って調べたものである．主流がない場合のシンセティックジェットがつくる
流れ場の特性，およびこれに制御パラメータが与える影響，バックステップ流れに剥離制御を適用した場合にどのようなメカニズムで剥離を制御できるかをそれぞれ詳細に論じて
いる．近年気流条件に応じて動的制御が可能な，微小デバイスであるシンセティックジェットが盛んに研究されている．これはキャビティ下面の壁面が上下に振動することで，オリ
フィス出口で渦を発生させる装置であり，壁面の駆動装置としては圧電素子やピストン，スピーカーなどが用いられる．本装置は従来型の制御デバイスに比べ軽量小型であり，交
流電源を用いた駆動であるため，電圧や周波数を変えることによって流れの変化や用途に合わせたより動的な制御も可能である．これまでに，このシンセティックジェットに対し
多くの研究が実験を中心にパラメータスタディの観点からなされている．例えば翼型や円柱，バックステップの剥離制御に関してはジェットの設置位置，ジェットの無次元周波数，
ジェットの運動量の最適値に関する研究報告がある．しかし剥離制御メカニズムがはっきりと分かっていないため，ジェットの設置位置や無次元周波数の最適値に関しては，物理
的な根拠が示されておらず，研究によって値の不一致やずれがある．また実機を想定した高レイノルズ数，高動圧，高マッハ数流れの剥離制御の実証例はまだない．そこで，本研
究ではシンセティックジェットの実用化に向けて，試行錯誤的ではなく，実験では困難な剥離流れ制御のメカニズムを物理現象ベースで理解し，さらにパラメータ設定の指針を得
ることを目的としている．剥離制御メカニズムの解明には，過去の研究からシンセティックジェットが誘起する小さい変動成分の解析が重要であると考え，コンパクト差分法を用
いたLES(Lage Eddy Simulation) 解析を行った．
まず，外部流れのない静止気体中に対する解析を行った．シンセティックジェットのモデル化の影響を調べるために， 3 次元解析を行い境界条件で近似したモデルとキャビ
ティ内部流れを解いたモデルを過去の実験と比較した．時間平均速度は実験と良い一致を示し，変動値に関しては定性的な一致が得られた．また3 次元性とキャビティ内部流れを
共に考慮した場合は，オリフィス出口から生成されるスパン方向に軸を持つ渦に対して，オリフィス出口の垂直な渦（縦渦）が大きな影響を与えることを明らかにした．この様に
シンセティックジェットが誘起する渦構造の理解をした．また以上のことからキャビティ内部外部共に3 次元で且つLES で解く必要があることを示した．次に無次元パラメータ
の渦構造に対する影響を調べた．レイノルズ数（非圧縮流れを仮定した場合のキャビティ下壁面の変形速度が最大時のオリフィス出口平均速度とオリフィス幅で無次元化）を上げ
ると流れが乱流に遷移し3 次元的な渦構造となるが，レイノルズ数を下げると，層流を保ち続け2 次元的な渦構造となる．一方ストロハル数（非圧縮流れを仮定した場合のキャビ
ティ下壁面の変形速度が最大時のオリフィス出口平均速度とオリフィス幅で無次元化）を上げると誘起される渦の放出間隔が短くなり，渦同士が干渉し減衰するが，ストロハル数
を下げると渦放出の間隔が広くなるので渦同士が干渉せず渦が減衰しにくい．これら無次元パラメータの影響をまとめると，レイノルズ数を変えると渦構造の3 次元性が変わり，
ストロハル数を変えると渦の強さが変わるということになる．さらに設計パラメータである周波数と振幅の影響も調べた．周波数を上げるとレイノルズ数が高くなり，3 次元的な
渦構造になることが分かった．また，振幅を上げると，レイノルズ数が高くなり渦が3 次元的になると共に，ストロハル数が下がるので渦が減衰しにくくなる．以上のことから3
次元的な強い渦を生成したい場合は，周波数よりも振幅を大きくすることが有効であり，2 次元的な強い渦を生成したい場合は周波数を下げて振幅を大きくすることが有効である
ことがわかった．本論文から剥離制御においては，周波数だけではなく振幅も重要なパラメータであることが明らかになった．
シンセティックジェットによる剥離流れ制御メカニズムを理解するために次の段階として，外部流れのある場合の解析を行った．解析対象には翼型よりもパラメータが少なく，
剥離点が固定されて流れ現象を理解しやすいバックステップ形状を選んだ．キャビティ内部流れも考慮した3 次元LES 解析を行い，過去の研究で示されている重要な流れ制御パ
ラメータである無次元周波数の効果について調べた．無次元周波数は，翼型の剥離制御でそれぞれ有効であると示されている無次元周波数F+（翼弦長および剥離領域の長さと一
様流流速で無次元化）=1 程度と10 程度の値を参考にF+h （バックステップ高さh と一様流流速で無次元化）=0.2 と2.0 とした．時間平均流れ場の解析よりF+h =2.0 で制御した場
合は剥離領域の大きさは剥離制御をしなかった場合とほぼ変わらなかったが，一方，F+h=0.2 で制御した場合は剥離制御していない場合と比較して剥離領域が20 パーセント小さ
くなった．これは剥離剪断層と再循環領域で，強いレイノルズ剪断応力による混合が促進されたためである．次に周波数解析を行いF+h =0.2 で制御した際に，剥離を大幅に抑える
ことができたのは，運動量厚さと一様流流速で定義した剥離剪断層の無次元周波数が，剥離剪断層自身の不安定周波数に近かったためである事を明らかにした．このことから周波
数の無次元化の代表長は，バックステップ高さではなく，剪断層厚さ（境界層厚さ）でするべきであると考えられる．さらに位相平均解析を行うことにより，F+h=2.0 で制御し
た場合は，シンセティックジェットから発生する弱く周期の短い渦が，剥離剪断層で消えて無くなっていることが分かった．また，発生するレイノルズ剪断応力は非周期的な成分
が支配的であることも分かった．F+h =0.2 で制御した場合は，シンセティックジェットによって発生する2 次元的な強い渦と，剥離剪断層から発生する渦が合体することにより，
より強い2 次元的な渦（ローラー構造）が生まれ，2 次元的な渦の間の領域（ブレイド領域）に縦渦（リブ構造）が発生することが分かった．さらに，強い2 次元的な渦がレイノ
ルズ剪断応力の周期的な成分を，2 次元的な渦の間に発生する領域で，縦渦が非周期的なレイノルズ剪断応力を生じ，特にこの非周期成分が支配的であることが分かった．また，
それぞれのレイノルズ剪断応力の成分が，剥離剪断層および再循環領域の混合を促進して剥離を制御でしていることも分かった．
以上のことから，渦の合体によって2 次元的な強い渦を早く作り，さらにその渦同士の間に縦渦を作ることが剥離制御に重要であることが分かった．よって剥離制御に有効な
2 次元的な強い渦構造作るためには，無次元周波数を剥離剪断層の周波数に合わせた上でシンセティックジェットから発生する渦が2 次元的な渦構造になるように振幅を変えるこ
とが有効であると言える．この知見は，翼型等の剥離制御にも有効であると考えられる．
修士論文
領域並列化分割手法を用いた非構造格子の並列化/高速化に関する研究
学士論文
超音速旅客機の空力解析
発表論文
査読付き論文
(1) International Journal of Aerospace and Engineering
Computational Study on Effect of Synthetic Jet Design Parameters, Koichi Okada, Akira Oyama, Kozo Fujii, and Koji Miyaji
Volume 2010 (2010), Article ID 364859, 11 pages
Abstract
Effects of amplitude and frequency of synthetic jet on the characteristics of induced jet are investigated. To estimate effects of the parameters, flow inside the synthetic jet cavity and orifice and the outer flow is simultaneously simulated using large-eddy
simulation (LES). Comparison of the present LES result with the experimental data shows that three-dimensional LES of the flow inside the cavity is essential for accurate estimation of the velocity and velocity fluctuation of the synthetic jet. Comparison of the
present results under various flow conditions shows that amplitude and frequency can control profiles of time-averaged vertical velocity and fluctuation of the vertical velocity as well as damping rate of the induced velocity and fluctuation.
(2) Transaction of JSASS
Vol. 55 (2012) , No. 1 p.1-11
http://www.jstage.jst.go.jp/browse/tjsass/55/1/_contents/-char/ja/
Computational Study of Effects of Nondimensional Parameters on Synthetic Jets, Koichi Okada, Akira Oyama, Kozo Fujii, and Koji Miyaji
国内学会
(1) 岡田, 藤井, 宮路, "シンセティックジェット詳細形状による流れ場への影響に関する研究", 計算工学講演会論文集, (2007) Vol.12
Abstract
Computational results of synthetic jet considering internal flow in the cavity are compared with those with boundary condition approximation in two-dimensional and three-dimensional cases. In the
two-dimensional cases, though computed time-mean velocity agrees with that of the experiment in both cases, time-mean velocity fluctuation does not due to two-dimensional effect. In the three-dimensional
cases, time-mean velocity fluctuation of computed synthetic jet considering internal flow in the cavity qualitatively agrees with the experiment while computation with synthetic jet boundary condition model
does not.
(2) 岡田, 藤井, 宮路, "シンセティックジェットのキャビティ内部流れに関する研究", 第21回数値流体力学シンポジウム講演集, (2007)
Abstract
Three-dimensional computations on the synthetic jet with internal flow in the cavity are carried and compared with the experimental data. Through this simulation, The three-dimensional spanwise
instability by longitudinal vortices is captured, which is found to be important in quantitatively agrees with the experiment. The effects of Reynolds number and Strouhal number are analyzed to understand the
effects of longitudinal vortices. Transition from laminar to turbulent flow by the longitudinal vortices is observed due to Reynolds number effect. While, Strouhal number effect change the intensity of induced
vortices.
(3) 岡田, 藤井, 宮路, "シンセティックジェットを用いたバックステップ流れの能動制御に関する研究 -周波数効果- ''第22 回数値流体力学シンポジウム論文集' , (2008).
(4) 岡田, 藤井, 宮路, "シンセティックジェットを用いたバックステップ剥離流れ制御の数値解析''流体力学講演会／航空宇宙数値シミュレーション技術シンポジウム講演集',(2009).
Abstract
In order to clarify the effect of the synthetic jet on the massively separated flow appearing at the backward-facing step, CFD simulation were carried out using implicit large eddy simulation and compact difference scheme.
The characteristics of the synthetic jet frequency are focused on in the present analysis. At non-dimensional frequency F+h=0.2, separation region is shorter than the case of synthetic jet because the vortices induced by
the jet interacts with the shear layer, which results in the increase in the Reynolds stress in the shear layer. However, at F+h=2.0, separation region is almost same as no synthetic jet because the weak and short periodic
vortices induced from the jet do not interact with the shear layer so as to increase the Reynolds stress in the shear layer.
(5) 岡田, 藤井, 宮路, 浅田, "シンセティックジェットが生み出すバックステップ剥離制御の渦構造 ''第24 回数値流体力学シンポジウム論文集' , (2010).
Abstract
Vortex structure of separated flow over a backward-facing step controlled with a synthetic jet is investigated with implicit large-eddy simulation using high-order compact difference scheme.
The present computation shows that separation length in the case of the flow controlled at F+h =0.2 is 20 percent shorter than the case without control. Strong two-dimensional vortices generated from
the synthetic jet interact with the shear layer, which results in the increase of the periodic component of Reynolds shear stress in the shear layer region. These vortices are deformed into three-dimensional
structures, which make the unperiodic component of Reynolds shear stress stronger in the recirculation region. Size of the separation length in the case of the flow controlled at F+h =2.0 is almost the same as
the case without control because the mixing between the synthetic jet and the shear layer is not enhanced. Weak and short periodic vortices induced from the synthetic jet do not interacts with the shear layer very
much and diffuse in the recirculation region.
国際学会
(1) Okada, K.; Fujii, K. and Miyaji, K., "Effect of Internal Flows in Synthetic Jet Cavity", Proceedings of the ICCFD 5 - International Conference on Computational Fluid Dynamics, Seoul, (2008).
Abstract
Three-dimensional computations of internal flow in synthetic jet cavity are carried out to
understand the effect of cavity flow and compared with the experimental data. High-order compact difference
scheme is used to resolve weak induced flow of the synthetic jet. Though this simulation, the three-dimensional
longitudinal vortices due to the flow in the cavity is captured, which may be important for flow control using
synthetic jet.
(2) Okada, K.; Fujii, K. and Miyaji, K., "COMPUTATIONAL STUDY OF THE SEPARATED FLOW STRUCTURE INDUCED BY THE SYNTHETIC JET ON A BACKWARD-FACING STEP'', The 10th International Conference on Fluid Control, Measurements, and Visualization', (2009).
Abstract
In order to clarify the mechanis m of the synthetic jet on the massively separated flow appearing at the backward-facing step, flow-fields with/without the synthetic jet are numerically simulated. Implicit large eddy
simulation using high-order and high-resolution compact difference scheme is applied. A flow field without a synthetic jet, flow fields with the synthetic jet at non-dimensional frequencies of the wall oscillation, F+h =0.2 and
F+h =2.0, are computed, where no-dimensional frequency of F+h is normalized with the height of backward-facing step and free stream velocity. Although previous studies show that each F+h is good conditions, the present
computation shows that length of the separation region only at F+h =0.2 become 25 percent shorter than that without synthetic jet. It seems that F+h =0.2 is near shear layer instability frequency without the synthetic jet. Strong
two-dimensional vortices induced fro m the synthetic jet interact with the shear layer, which results in the increase of the Reynolds stress. At F+h =2.0, length of the separation region is almost same as that without synthetic jet. Mixing
is not enhanced in the shear layer because Reynolds stress does not increase. Weak and short periodic vortices induced fro m the synthetic jet do not interacts with the shear layer very much.
(3) Okada, K.; Fujii, K. and Miyaji, K., "Computational Study of Frequency and Amplitude Effects on Separation Flow Control With the Synthetic Jet", 'ASME 2009 International Mechanical Engineering Congress & Exposition', (2009).
Abstract
In order to investigate the frequency and amplitude effects of the synthetic jet on the flow field, numerical simulation is carried out. Even though the final objective of this study is to understand mechanism of separation control for various
objects, streamline and bluff bodies, the configuration of backward-facing step is chosen as the first step because of the simplicity. Three-dimensional Navier-Stokes equations are solved. Implicit large eddy simulation using high-order
compact difference scheme is applied. The present analysis is addressed on the frequency characteristics of the synthetic jet for understanding frequency characteristics and flow-filed. Three cases are selected, No-control, F+h =0.2 and F+h =2.0,
where non-dimensional frequency F+h is normalized with the height of backward-facing step and the free stream velocity. The present computation shows that at F+h =0.2, separation length is 20 percent shorter than the No-control case. Strong
two-dimensional vortices generated from the synthetic jet interact with the shear layer, which results in the increase of the Reynolds stress in the shear layer region. These vortices are deformed into three-dimensional structures, which make
Reynolds stress stronger in the recirculation region. At F+h =2.0, size of the separation length is almost same as the No-control case because the mixing between the synthetic jet and the shear layer is not enhanced. Weak and short periodic
vortices induced from the synthetic jet do not interacts with the shear layer very much and diffuse in the recirculation region.
(4) Okada, K.; Fujii, K., Oyama, A., Nonomura, T., Asada, K. and Miyaji, K., "Computational Study of the Synthetic Jet on Separated Flow over a Backward-Facing Step", 'ASME 2010 International Mechanical Engineering Congress & Exposition', (2010).
Abstract
Frequency effects of the synthetic jet on the flow field over a backward facing step are investigated using numerical analysis. Three-dimensional Navier-Stokes equations are solved. Implicit large-eddy simulation using high-order compact
difference scheme is conducted. The present analysis is addressed on the frequency characteristics of the synthetic jet for understanding frequency characteristics and flow filed. Three cases are analyzed; the case computing flow over
backward facing step without control, the case computing flow with synthetic jet control at F+h =0.2, and the case computing flow with synthetic jet control at F+h =2.0, where non-dimensional frequency F+h is normalized with the height of
backward-facing step and the freestream velocity. The present computation shows that separation length in the case of the flow controlled at F+h =0.2 is 20 percent shorter than the case without control. Strong two-dimensional vortices generated
from the synthetic jet interact with the shear layer, which results in the increase of the Reynolds stress in the shear layer region. These vortices are deformed into three-dimensional structures, which make Reynolds stress stronger in the recirculation region.
Size of the separation length in the case of the flow controlled at F+h =2.0 is almost the same as the case without control because the mixing between the synthetic jet and the shear layer is not enhanced. Weak and short periodic vortices induced from
the synthetic jet do not interacts with the shear layer very much and diffuse in the recirculation region.
専門
乱流力学、渦力学、剥離制御、数値流体力学
一応CFDは構造格子と非構造格子両方やっていました。今も色々とやっています。
シンセティックジェット
藤井研では近年様々なデバイスを用いた剥離制御（DBDプラズマアクチュエーターやシンセティックジェット）の研究をおこなっています。
私は長年シンセティックジェットというデバイスを用いた剥離制御の研究をしています。詳細は論文を見てください。
国内では、防衛大学、秋田大学、東京理科大学でも研究がされているようです。
元々は航空宇宙分野で開発されてきたものですが、最近では自動車にも適用されているようです。
ルノー
http://www.greencarcongress.com/2006/02/renault_altica_.html
フェラーリ
http://loveferrari.blog119.fc2.com/blog-entry-571.html
DBDプラズマアクチュエーターについては・・・
http://www.jsme-fed.org/newsletters/2007_12/no2.html
のDBDプラズマアクチュエータ -バリア放電を利用した新しい流体制御技術
または
ながれ 第29巻（２０１０）第4号の特集
http://www.nagare.or.jp/publication/nagare/archive/2010/4.html
を参考にしてください。
NASA/CTRでも翼型にシンセティックジェットをつけたのLES解析している人もいるようです。
http://ctr.stanford.edu/ResBriefs07/27_you2_pp311_322.pdf
以下自分が知っている限りのシンセティックジェットの論文リスト
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Rumsey, C. L. (2006), Reynolds-Averaged Navier-Stokes Analysis of Zero Efflux Flow Control over a Hump Model, in 'AIAA-2006-1114'.
Sahu, J. (2004), UNSTEADY CFD MODELING OF AERODYNAMIC FLOW CONTROL OVER A SPINNING BODY, in 'AIAA-2004-747'.
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