Reduced-Order Models of Zero-Net Mass-Flux Jets for Large-Scale Flow Control Simulations

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1 Reuce-Orer Moels of Zero-Net Mass-Flux ets for Large-Scale Flow Control Simulations Reni Raju, Ehsan Aram an Rajat Mittal Department of Mechanical an Aerospace Engineering, The George Washington University, Washington, DC an Louis Cattafesta, Interisciplinary Microsystems Group Department of Mechanical an Aerospace Engineering, University of Floria, Gainesville, FL - Although computational tools are well suite for moeling the ynamics of zero-net mass-flux actuators, the computational costs involve in large-scale flow control simulations necessitate the use of reuce-orer moels for these evices. A new reuce-orer moel base on moeling only the slot of ZNMF jets in grazing flows is propose. A parametric stuy of imensionless parameters governing the characteristics of a ZNMF jet in grazing flow was conucte for the reuce-orer moel along with the commonly use sinusoial plug flow bounary conition an full cavity simulations. Comparisons of the current moel are presente in terms of the vortex ynamics an mean integral quantities, an the performance of the new reuce-orer moel is encouraging. In aition, the fielity of the moel has also been explore for a canonical separate flow. On the global scale of the flow, the reuce-orer moel is able to provie a more accurate representation of the full cavity simulation as compare to the conventional bounary conition. Nomenclature C () t = n moment of the jet, (m /s ) C () t = r moment of the jet, (m /s ) δ = Bounary layer thickness, (m) = Slot with/orifice iameter, (m) f = Separation bubble frequency, (Hz) f SL = Shear layer frequency, (Hz) h = Slot/Orifice height, (m) H = Cavity height, (m) L = Length of the prescribe velocity profile, (m) Ω () t = Instantaneous vorticity flux, (m /s ) = Phase angle, ( ) p = pressure, (N) Re δ = Bounary layer Reynols number, = U δ υ Re = et Reynols number, = V υ S = Stokes number, = πf υ Grauate Stuent, Department of Mechanical & Aerospace Engineering, Stuent Member AIAA. Grauate Stuent, Department of Mechanical & Aerospace Engineering, Stuent Member AIAA. Professor, Department of Mechanical & Aerospace Engineering, Associate Fellow AIAA, mittal@gwu.eu Professor, Department of Mechanical & Aerospace Engineering, Associate Fellow AIAA, cattafes@ufl.eu. American Institute of Aeronautics an Astronautics

2 St = Strouhal number, = π f u = Streamwise velocity (in x-irection), (m/s) U V U v V, top = Velocity amplitues, (m/s) = Freestream velocity, (m/s) = Cross-stream velocity (in y-irection), (m/s) = Spatially an temporally average jet velocity, (m/s) V = Prescribe velocity amplitue, (m/s) W x c z = With of the cavity, (m) = Center of the prescribe velocity profile, (m) ξ = Spanwise vorticity, (s - ) I. Introuction ERO-net mass-flux (ZNMF) actuators or synthetic jets have potential applications in the area of mixing Z enhancement, heat transfer,, mass transfer, jet vectoring, an active flow control of separation -8 an turbulence. 9 The ynamics an performance of these evices epen on several geometrical, structural an flow parameters. - When compare to the global omain, such as an airfoil, in which the actuator is imbee, the scales of the actuator are typically - - times smaller in size. Due to the range of scales involve, inclusion of a high-fielity moel of a ZNMF actuator within a macro-scale computational flow moel turns out to be an expensive, if not prohibitive, proposition. The esire to compute the flow physics associate with the ZNMF jet control makes reuce-orer moeling of these evices a practical necessity in these simulations. In the past these actuators have been represente as a reuce-orer moel in simulations in one form or another. Kral et al. moele the actuator via simplifie surface bounary conitions for velocity an pressure without the slot an cavity. For variations of the spatial istribution of the velocity profile, it was foun that the top-hat function provie the closest match to the experiments. Rizzetta et al. have use the recore flow fiel from a simulation of the isolate jet at the exit of a D perioic jet as a bounary conition to an external flow fiel. On the other han, Lockerby et al. have use a theoretical approach base on classic thin plate theory to moel the iaphragm eflection, while the slot is moele base on unsteay pipe-flow theory. A reuce-orer moel approximating D or D synthetic jets via quasi-d Euler equations was presente by Yamaleev & Carpenter. Filz et al. have moele D irecte synthetic jets using lumpe eterministic source terms (LDST) traine by a neural network. Rathnasingham & Breuer 8 have presente a semi-empirical analytical moel of ZNMF actuators using a system of couple nonlinear state equations escribing the structural an flui characteristics of the evice. An analytical lumpe element moel (LEM) of a piezoelectric-riven synthetic jet has been presente by Gallas et al. The moel represente the iniviual components of the synthetic jet as elements of an equivalent electric circuit using conjugate power variables. Sharma 9 has also use an alternate moel for LEM. More recently Tang et al. have compare the performance of the Dynamic Incompressible Flow moel (DI moel), Static Compressible Flow Moel (SC moel) an LEM in preicting the instantaneous space-average velocity at the orifice exit. Loworer moeling of two-imensional synthetic jets via Proper Orthogonal Decomposition (POD) was carrie out by Reiniotis et al. The ynamical moel base on Galerkin projection was erive from the flow for specific Reynols an Stokes numbers. Kihwan et al. have evelope a ynamical moel base on system ientification to ientify the interaction of synthetic jets with a laminar bounary layer with potential application to feeback control. The top-hat profile use by Kral et al. is the simplest moel of the jet an is referre to as the zeroth-orer moel in the current stuy. Such a representation eliminates the nee of simulating the cavity an the slot. A similar approach has also been aopte in some previous stuies., However, it is not clear to what extent such a bounary conition accurately moels the key features of the jet. Since the control mechanism of the actuator epens on transfer of the momentum or vorticity flux to the external bounary layer, it is essential that any such moel shoul be able to represent these quantities accurately. The purpose of the current stuy is to explore the issues of actuator moeling via numerical simulations. Base on these simulations we propose a new moel for ZNMF jets in grazing flows. The moel is compare with the ful cavity simulations an the zeroth-orer moel in attache flows. In aition, the effectiveness of the propose moel with the moifie bounary conition representation versus full cavity simulations has also been stuie for a separate bounary layer in a canonical flow configuration. American Institute of Aeronautics an Astronautics

3 II. Slot-Only ZNMF Actuator Moel The major reason for the shortcoming of the moifie bounary conition moels is the neglect of the flow physics associate with the slot. Our previous stuies show that flow in the slot tens to separate at the top an bottom lips, an the formation of seconary vortices near the exit tens to significantly alter the flow fiel. Thus the working hypothesis for the current reuce-orer moel is that the inclusion of just the slot with appropriate bounary conitions shoul significantly improve the fielity of the actuator moel. This hypothesis is supporte by past stuies, that have shown that the shape of the cavity has very little effect on the flow emanating from the jet provie that the incompressible flow assumption insie the actuator cavity is vali. The approach use for the current stuy explores the significance of the slot via simplifie bounary conitions an hence effectively reuces the computational complexity. An attempt is thus mae to replicate the flow physics insie the slot to further improve the fielity of the moel. Consier the flow insie the D slot of a typical ZNMF actuator as seen in Figure (a). The area change from the cavity to the slot causes the flow to turn near the bottom lip of the slot, an the flow pattern uring expulsion is similar to the one cause by a sink present somewhere along the slot center uring the expulsion phase. Hence the flow enters the slot raially at any given time uring expulsion an, in terms of its Cartesian components, will have two components of velocity, u an v. As seen in Figure (a), at the entrance to the slot the u -velocity will be significant, while near the slot center the v -velocity will ominate. Thus an approximation of this flow pattern prescribes a corresponing bounary conition profile for the u - velocity which varies linearly in the x-irection from a maximum positive value near the left wall to a minimum negative value near the right wall (see Table ). (a) (b) (c) Figure : Schematic showing (a) the typical flow pattern seen in a ZNMF jet slot for a full cavity () configuration an (b) moifie bounary conition (MBC) an (c) Propose slot-only (SO) moel. A. Moel Comparison Base on the above arguments, three separate flow configurations have been chosen for comparison. These inclue the full-cavity (), the slot-only (SO) an moifie bounary conition (MBC) configurations. As the name suggests, the moel consists of full-cavity simulations an is a complete representation of a D ZNMF jet, as seen in Figure (a). The river isplacement is represente as an oscillatory bounary conition at the bottom of the cavity an has been foun to be a fairly accurate representation when compare with experimental results. On American Institute of Aeronautics an Astronautics

4 the other han Figure (b) shows the MBC configuration, which consists of prescribing only the vertical component of the velocity over the exit plane of the jet, as mentione earlier. The propose SO moel is base on the configuration shown in Figure (c). For this configuration the slot is moele by consiering the full length of the slot, i.e., h=%, which is necessary for the replicating the sink type behavior of a configuration. Two variants of the slot-only moels are consiere. For the first, calle the SO- moel, only the sinusoial v-velocity is prescribe at the bottom while for the secon, the SO- moel, bounary conitions for both the u- & v-velocities uring expulsion have been use. Here the u-velocity is prescribe as a linearly varying sinusoial profile that satisfies no-slip conition at the bounary. Table lists the bounary conitions use for the ifferent configurations uring both expulsion an ingestion phases with the corresponing location. Table : Bounary conitions use for the ifferent configurations consiere for current work. y Expulsion Ingestion Moel location u vxt (, ) uxt (, ) vxt (, ) ( xt, ) w.r.t to y V sin( ωt) V sin( ω t) - MBC h+ H V sin( ωt) V sin( ω t) SO- H V sin( ωt) V sin( ω t) SO- H V sin( ωt) x U sin( ) ω t, for < x < V sin(, at x = & Care has been taken to ensure that the mass flow rate at the exit of the slot for the configuration an reuceorer moels are the same. The imensionless parameters of significance for a ZNMF jet uner quiescent conition are the Strouhal number, St, jet Reynols number, Re, velocity ratio, U an bounary-layer thickness to jet with ratio, δ. Table lists the cases along with the corresponing parameters use for the current stuy. It is known that the jet characteristics are etermine by functional epenence on the parameters as U δ fn St,,, Re j Vj. Hence for the current stuy three ifferent simulation sets were consiere for each of these parameters while keeping the rest constant. The velocity amplitue ratio U V = was maintaine for all the cases. Table : Parameters use for reuce-orer moeling simulations Case Re S U V δ Re δ St American Institute of Aeronautics an Astronautics

5 All the computations use a single gri of imensions 8 8 for the simulations an a omain size of 9. For the remaining configurations the gri resolution in the slot an external flow fiel is hel constant at all times. The irect numerical simulations are use to moel synthetic jets issuing from a cavity. Incompressible Navier-Stokes equations are solve in time using a secon-orer accurate fractional step metho. In a Cartesian framework, a secon-orer Aams-Bashforth scheme is employe for the convective terms, while the iffusion terms are iscretize using an implicit Crank-Nicolson scheme that eliminates the viscous stability constraint. The solver has been rigorously valiate by comparisons of several test cases against establishe experimental an computational ata incluing synthetic jets.,8 B. Canonical Separate Flow Configuration Whereas the above stuy examines the performance of the ifferent moes for an attache grazing flow, a relevant issue to be examine is to what extent the etails of the actuator moel moify the effect of the jet on a separation bubble. In orer to aress this issue we have also examine a case where a separation bubble is create ownstream of the jet by prescribing a blowing-suction bounary conition on the top bounary of the omain. A zero-vorticity conition, along the lines of Na & Moin 9 is applie on this bounary as follows: u G vxl (, y ) = Gx ( ), = () y x where Gx ( ) ( xl, y ) is the prescribe blowing an suction velocity profile efine in the form of: π( x xc ) Gx ( ) = Vtop sin e L β ( x x c ) α L where L is the length an xc is the center of the velocity profile. The parameters Vtop, α an β are set to U, an, respectively. Figure shows the configuration use to generate the separate flow. The, SO- an MBC moel configurations were teste uner these conitions. The simulations have been carrie out on the omain with size using a gri of imensions for case an same resolution for two other configurations. () Figure : Flow configuration use for simulating a canonical separate flow. III. Results A. Moel Performance in Attache Grazing Flow Holman et al. have shown that the jet formation criterion is etermine by the relation, Re S = St>K an is proportional to the non-imensional vorticity flux. Here, K is a constant foun to be O() for D jets an ~. for axisymmetric jets. Thus for the given set of conitions of St =.8, a jet is forme an is able to impart a significant amount of vorticity flux to external flow. Figure shows the comparison of the spanwise vorticity at the peak expulsion ( =9 ) an peak ingestion ( = ) for all moels at Re =, S =, U =. an δ =.. The flow tens to separate near the bottom lip of the slot for the full cavity simulations. The separating shear layers ten to roll up on either wall uring expulsion at the exit plane of the slot an a strong clockwise vortex American Institute of Aeronautics an Astronautics

6 is forme that is swept away by the incoming bounary layer. The MBC moel, seen in Figure (b), forms a smaller clockwise vortex near the lip of the slot in comparison to the moel. The SO moels are able to reprouce the flow physics of the baseline flow in the proximity of the slot exit, as seen in Figure (c) & (). Unlike the moel, insie the slot the bounary layer remains attache to the walls for SO- moel. On the other han the SO- oes show flow separation on the slot walls but is unable to capture roll up of the bounary layer on the walls. This ifference can be attribute to larger incoming angle of the flow from the cavity for the moel. The ingestion phase for the SO moels shows a near perfect match with the moel within the slot, proving the valiity of using a simple Neumann bounary conition for the u-velocity. The SO moels are able to capture even the seconary vortex prouce uring expulsion, although for the SO- moel the vortex loses its strength ownstream. ~9 ~ (a) (b) (c) () Figure : Instantaneous spanwise vorticity uring peak expulsion an peak ingestion for (a), (b) MBC moel (c) SO- moel an () SO- moel for Re =, S =, U =. an δ =.. Dashe lines compare the locations of vortex structures for the three moels with respect to configuration. American Institute of Aeronautics an Astronautics

7 The characteristics of the jet can be therefore efine on the basis of the integral quantities such as vorticity flux, momentum flux an kinetic energy flux. The unsteay variations of these quantities are compare for the representative cases in Figure. Note the efinitions for momentum flux an kinetic energy flux are ρ C () t v( x,) t x = ρ [ ] an ρ () ρ [ (,)] C t = v x t x an have been normalize by a suitable quantity. On the other han the vorticity flux is efine as () t ξ ( x,) t v( x, t) Ω = x. Figure shows that the accumulation of z vorticity from shear layer separation causes peaks in the integral quantities for the moel uring expulsion. Similar features are seen for the SO- moel an, although they are lower in magnitue, they appear to give a closer match to the moel than the SO- moel uring expulsion. On the other han the MBC moel is unable to preict the flow behavior in the slot uring most of the cycle. Hence although the flow fiel is significantly altere by seconary vortices, the integral measures can be reasonably approximate by using the SO- moel; although for a better match the incoming flow angle, i.e. U V ratio, might nee to be moifie further. SO- Moel SO- Moel SO- Moel - ρc /ρv ρc /ρv Figure : Comparison of the vorticity flux (left), momentum flux (mile) an kinetic energy flux (right) for all moels as a function of phase for Re =, S =, U =., δ =., St =.8. Simulations at higher Strouhal number ( St =.) are presente in Figure where Re =, S =, U V =. an δ =.. This correspons to the no-jet formation case ue to the high St, an uring peak expulsion the bounary layers near the bottom lips thicken to form a vena-contracta. At the exit, the shear layer rolls up to form a relatively small clockwise vortex which oes not travel far from the slot uring the suction stroke. Note that the expulsion stroke is efine as o < 8 o o an suction stroke as 8 < o. Interestingly it is foun that all the moels give a reasonable approximation to the moel at the slot exit uring the expulsion phase of the cycle. However, the MBC moel oes not prouce coherent vortex structures as seen for the rest of the configurations near the right exit lip which is apparent uring the suction stroke, as seen in Figure (b). The SO- moel captures the vena-contracta of the flow near the slot inlet which, although not seen for the SO- moel, oes not seem to significantly affect the external flowfiel. Both moels replicate the flow behavior of moel uring the suction stroke. American Institute of Aeronautics an Astronautics

8 ~9 ~ (a) (b) (c) () Figure : Instantaneous spanwise vorticity uring peak expulsion an peak ingestion for (a), (b) MBC moel (c) SO- moel an () SO- moel at Re =, S =, U =., δ =.. Dashe lines compare the locations of vortex structures for the three moels with respect to configuration. At higher Strouhal numbers, as is the case for Re =, S =, U V =. an δ =., seen in Figure, the integral measures o not show peaks uring the expulsion cycle. An increase in St tens to ecrease the contribution of vorticity flux of the jet to the external bounary layer. This also remains true for the momentum an kinetic energy fluxes. Both the SO moels compare reasonably well with the moel uring the whole cycle. On the other han, the MBC moel shows a slight phase shift uring the expulsion phase for the vorticity flux, while it prouces slightly larger eviations for the momentum an kinetic energy fluxes. 8 American Institute of Aeronautics an Astronautics

9 SO- Moel SO- Moel SO- Moel - ρc /ρv ρc /ρv Figure : Comparison of the vorticity flux (left), momentum flux (mile) an kinetic energy flux (right) for all moels as a function of phase for Re =, S =, U =., δ =., St =.. Similar analyses have been conucte for the other cases. Figure (a) an (b) compare the integral quantities for Re =, S =, U V =., δ =. an Re =8., S =, U =., δ =., respectively, where St =.8 for both the cases. When compare with Re =, S =, U =., δ =. shown in Figure, it can be seen that, although the Strouhal number remains the same, as Re increases the vorticity flux uring the expulsion phase also tens to increase an istort the sinusoial profile. These peaks correspon to the expulsion of vortices from the exit plane of the jet. On the other han the suction phase behavior remains the same for these cases. In terms of moel performance for Re =, S =, U =. an δ =. the SO- moel tens to slightly overpreict the integral measures versus the moel uring the expulsion phase, while the SO- moel slightly unerpreicts these values. Surprisingly the MBC moel also shows a reasonable match for the vorticity flux uring the expulsion phase but not for the other quantities. During ingestion the SO moels match the quantities at all times. However, this is not the case for the MBC moel. For Re =8., S =, U =. an δ =., similar behavior is observe with the SO- moel proviing the best approximation. At higher Strouhal numbers, as is the case for Re =, S =, U =. an δ =., seen in Figure (c) where St =., the integral measures show slightly lower values. Note that for this case the vorticity flux again shows several peaks uring the expulsion phase inicating that the jet is forme uner these conitions. The integral quantities of both SO moels compare reasonably well with the moel uring the whole cycle an are able to capture the small peaks in the vorticity flux. Note that for this case, the behavior of both moel is similar, inicating that uner these conitions the shear layer separation at the bottom lip is not as important as the cases with St =.8 where the SO- moel oes not perform as well as the SO- moel. This is apparent from Figure where both these moels show similar representation of the flow physics. In aition to the significance of Re an St, the effects of freestream to jet velocity ratio, U V an the bounary layer thickness to jet iameter ratio, δ are presente in Figure 8. The variation in the velocity ratio is presente in the Figure 8(a) an (b) for Re =, S =, U =., δ =. an Re =, S =, U V =., δ =. respectively. Due to the lower freestream velocity, the magnitues of the peaks are reuce. It can be observe that increasing the velocity ratio leas to an increase in the momentum an kinetic energy fluxes. For these cases the SO- moel is able to yiel a better approximation to the configuration, while both the SO- an MBC moels significantly unerpreict the moments uring the expulsion phase. On the other han, ecreasing the bounary layer thickness significantly alters the integral quantities an leas to an increase in the integral measures over a cycle with sharper peaks as seen in Figure 8(c) an () for two ifferent ratios δ =. an δ =., respectively. The preictive capabilities of the moels eteriorate as the bounary layer thickness is reuce, although the SO- moel consistently gives better performance over other moels. Overall the ingestion phase of both SO moels compares well with the moel. This implies that the inclusion of the slot is a significant factor for improvement of the moel, while accounting for the separation at the bottom lip of the slot increases the fielity of the moel still further. 9 American Institute of Aeronautics an Astronautics

10 SO- Moel SO- Moel SO- Moel - ρc /ρv ρc /ρv (a) (b) SO- Moel SO- Moel ρc /ρv ρc /ρv SO- Moel SO- Moel ρc /ρv ρc /ρv SO- Moel SO- Moel (c) Figure : Comparison of the vorticity flux (left), momentum flux (mile) an kinetic energy flux (right) for all moels as function of phase for (a) Re =, S =, U =., δ =., St =.8, (b) Re =8., S =, =., =., St =.8, an (c) Re =, S =, =., δ =., St =.. U δ U American Institute of Aeronautics an Astronautics

11 SO- Moel SO- Moel SO- Moel - ρc /ρv ρc /ρv (a) SO- Moel SO- Moel SO- Moel - ρc /ρv ρc /ρv (b) SO- Moel ρc /ρv SO- Moel ρc /ρv SO- Moel (c) SO- Moel SO- Moel 8 SO- Moel ρc /ρv ρc /ρv () Figure 8: Comparison of the vorticity flux (left), momentum flux (mile) an kinetic energy flux (right) for all moels as function of phase for (a) Re =, S =, U =., δ =., St =.8, (b) Re = S =, U δ U =., =., St =.8, (c) Re =, S =, =., δ =., St =.8 an () Re =, S =, U V =., δ =., St =.8. American Institute of Aeronautics an Astronautics

12 Figure 9: Spanwise vorticity an mean streamlines for the unforce separate flow. B. Moel Performance for a Canonical Separate Flow As seen in Figure 9, a separation bubble was create by imposing the bounary conition escribe in Eq. ()- () with length, L sep =. The effect of forcing of the ZNMF jet, place approximately. upstream of the point of separation, on the separation bubble has been examine for ifferent moel configurations. As seen in the previous section, since the SO- moel performs superior to other moels, it was teste along with an MBC configurations for six ifferent forcing frequencies base on shear layer frequency, such that f = ε f SL. The six values of ε were chosen as.,.,.,,. an.. For all the cases examine for the separate flow, the rest of the flow characteristics were hel fixe at Re =, U V = an δ =. Figure shows contours of instantaneous spanwise vorticity at peak expulsion an mean streamlines for these three cases at one particular forcing frequency ( f =. fsl ). By comparing the mean streamlines it can be seen that an SO- configuration yiel a very similar effect on the separation bubble. For both these cases the size of the separation bubble is reuce by a factor of.. On the other han the MBC moel, as expecte, is unable to match the moel, where the separation bubble size is reuce by a factor of. It is clear that the SO- moel is able to able to provie a better representation of the ZNMF actuator on a global scale. (a) (b) (c) Figure : Instantaneous spanwise vorticity an mean streamlines for the a), b) SO-, an c) MBC moels for f =. f. SL American Institute of Aeronautics an Astronautics

13 Figure compares the performance of three moels for ifferent forcing frequencies. The separation bubble frequency in this figure is efine, base on the separation bubble size, as f = U / L. It is foun that the SO- moel gives a goo approximation to the moel for separation bubble control at all forcing frequencies, especially for ε.. The maximum percentage ifference of separation bubble size seen between SO- an moel is approximately 8%. On the other han the MBC moel unerestimates the performance of on separation control for low frequencies ( f < fsl ) where control is most effective. Overall the percentage ifference of separation bubble size for the MBC moel varies from %. It is also clear that the separation bubble size is reuce by ecreasing the jet frequency, an maximum reuction in this particular problem an this frequency range is approximately %. sep sep Figure : Effect of forcing frequency on the separation bubble size for three moels. IV. Conclusions A simple reuce-orer moel is presente for the representation of ZNMF jets in large-scale flow control simulations. The moel inclues the slot of the actuator ue to its importance in governing the ynamics of the interaction process with a grazing flow. Two variants of the slot-only moel were consiere, an a parametric numerical stuy was carrie out to etermine the performance of each moel compare to a conventional moifie bounary conition. It was foun that, unlike the conventional MBC moel, the slot-only moels were able to capture more of the flow physics associate with full cavity simulations. A comparison of the integral measures of vorticity, momentum, an kinetic energy fluxes for these moels showe that the slot-only moel that assumes a sink-like flow at the slot inlet (i.e., the SO- moel) provies the best moeling approximation. The performance of the moel was also compare with full cavity simulations an the simple MBC moel for a canonical separate flow at ifferent forcing frequencies. It was foun that at lower forcing frequencies, the flow separation extent was reuce significantly, an the SO- moel was able to preict the separation bubble size reuction with improve accuracy. Future work in this irection will focus on etermining the appropriate value of U V, use in SO-, as a function of the imensionless flow parameters to stuy the effect of incoming flow angle at the bottom lip of the slot. Acknowlegments This work is supporte by grants from AFOSR an a NASA Cooperative Agreement NNXAD9A monitore by Dr. Brian Allan. American Institute of Aeronautics an Astronautics

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