Numerical simulation of a powered-lift landing, tracking flow features using overset grids, and simulation of high lift devices on a fighter-lift-and-control wing

NASA-CR194260 MCAT Institute Final Report 93-18

Numerical Simulation of a Powered-Lift

Landing, Tracking Flow Features Using

Overset Grids, and Simulation of High Lift

Devices on a Ficihter-Lift-And-Control Wing

( NA SA-CR-194260) NUMERICAL N94-14322 SIMULATION OF A POWERED-LIFT LANDING, TRACKING FLOW FEATURES USING OVERSET GRIDS, AND SIMULATION Unci as Kalpana Chawla OF HIGH LIFT DEVICES ON A F IGHTER-LIFT-AND-CONTROL WING Final

0184995

August 1993

'. NCC2-563

MCAT Institute

3933 Blue (,u.ii Drive

San Jose, CA 95127

4MfA WTA1$S Final Report Numerical Simulation of a Powered-Lift Landing, Tracking Flow Features Using Overset Grids, and Simulation of High Lift Devices on a Fighter- Lift-And-Control Wing Kalparia Chawla The work performed under grant NCC2-563 in the time period September 1992 to August 1993 included finishing the simulation of a landing powered-lift delta wing; tracking flow features using overset grids; and simulating flaps on the FLAC wing.

Within the first project, flow simulation was performed for a landing delta wing with thrust reverser jets starting from a height of one wing span above the ground and ending at a one-quarter of a wing span above the ground. The simulation captures the initial increased lift due to conventional ground cushion effect as the delta wing approaches the ground. The computed lift coefficients are over-predicted; however, the simulation can capture at least the qualitative trends in lift-loss encountered by thrust-vectoring aircraft operating in ground effect. Power spectra of temporal variations of pressure indicate that computed vortex shedding frequencies close to the jet exit are in the experimentally observed frequency range. Additionally, power spectra of temporal variations of pressure have provided insights into the mechanisms of lift oscillations. The detailed results of this work are included in Appendix I.

The second project dealt with tracking of dynamic flow features. Features of interest such as moving shock waves and vortices are overset with relatively fine tracker grids.

Solutions are computed on the various grids and information is exchanged at intergrid boundaries. A grid track-sensor variable such as pressure is used to track the position of the flow feature to be resolved. The tracker grid is moved to the position where the track-sensor variable has the desired value (generally a maximum or a minimum) and new interpolation coefficients are computed for information exchange across grid boundaries.

Solutions are computed at the current location and time-step, and grid motion is brought into the solution via time metrics. The method is demonstrated by tracking a moving shock and vortices shed behind a circular cylinder. It is conjectured that the method would show significant benefits in resolving features such as wakes behind oscillating airfoils and trajectories of jets issuing from rotating nozzles as encountered during thrust-vectoring.

The results of this work are included in Appendix II.

Finally, under the same grant, Chimera gridding strategies were devised to resolve narrow gaps between the control surfaces and the adjacent surfaces for Wright Patterson Lab's FLAC wing. Flow field simulations are in progress for various leading and trailing edge flap deflection angles. Appendix III shows surface grids for the FLAC wing and pressure coefficient contours for a Mach no. of 0.18 and Reynolds no. of 2.5 million.

Appendix

72nd Fluid Dynamics Panel Meeting

and

Symposium

on

Computational and Experimental Assessment of

Jets in Cross Flow

Winchester, United Kingdom, April 19-23, 1993

Numerical Simulation of

a Powered-Lift Landing

by Kalpana Chawla MCAT Institute, M.S. 258-1 NASA Ames Research Center and William R. Van Dalsem M.S. T045-2 NASA Ames Research Center Moffett Field, CA 94035

32-1 PRECEDING PAGE BLANK NOT FILMED

Numerical Simulation of a Powered-Lift Landing

Kalpana Chawla MCAT Institute M.S. 258-1, NASA Ames Research Center and William R. Van Dasem M.S. T045-2, NASA Ames Research Center Moffett Field, California 94035-1000 U.S.A descent cases.

1. SUMMARY To understand the jet related flow physics of the The flow field about a delta wing equipped with suck-down phenomenon, Van Dalsem 2 '3 conducted a thrust reverser jets in slow speed flight near the numerical study of the impingement of an unsteady ground has been computed. Results include the pre- three-dimensional jet on a ground plane, in cross-flow, diction of the flow about the delta wing at four fixed by solution of the Reynolds-averaged Navier-Stokes heights above the ground, and a simulated landing, equations. This work simulated the experimental in which the delta wing descends towards the ground.

work of Stewart, Kuhn and Walters.' Insights into Comparison of computed and experimental lift coef- the impinging jet flow physics, for example, the sen- ficients indicates that the simulations can capture at sitivity of ground vortex location to the level of mix- least the qualitiative trends in lift-loss encountered by ing in the wall jet were obtained in this work. 3 Also thrust-vectoring aircraft operating in ground effect.

the computed ground vortex locations and the pres- sure coefficient distribution compared well with the experimental data. This effort quantified the ability of Computational Fluid Dynamics (CFD) to predict 2. INTRODUCTION the strength and location of the primary features of the impinging jet flow-field.

Thrust vectoring can be used to improve short field, up-and-away, and post-stall maneuvering per- To understand the suck-down effect, it was re- formance of high-performance aircraft. When vec- quired to introduce an airframe in the above study, so that the interaction of the jets with the ground tored thrust is used to meet short runway require- ments, as in the case of the Harrier AV-811, a complex and the airframe could be studied. To concentrate resources on resolving the complex flow physics, flow fluid dynamics interaction between the vectored jets, was computed about a simple configuration consist- the ground, and the airframe is encountered. This ing of a delta planform with two jets in ground effect flow field can put the aircraft at risk due to lift loss and hot-gas/debris ingestion. As a result of these (Refs. 5-7). The experimental work of Paulson and Kemmerly 1 had indicated that the flow about this risks, operational flexibility and performance may be configuration produces much the same flow physics reduced. Experiments performed by Paulson and as the flow about even a very complex and realistic Kemmerly1 at NASA Langley's Vortex Research Fa- configuration, such as an F-18 in ground effect. The cility (VRF) indicate that for a STOVL (Short Take- Off and Vertical Landing) configuration the magni- non-time-accurate simulations of flow past the delta wing showed the capability to capture jet impinge- tude of the loss in wing-borne lift is a strong function ment/entrainment, ground vortex formation, and the of its rate of descent. Although this phenomenon is ability to predict lift loss in ground proximity.7 not fully understood, it is known that during a land- ing with a rapid rate of descent, the lift loss is much In the present paper, time-accurate simulations of less than in the case of a low (or zero) rate of de- both straight-and-level and descending flight profiles scent. It is conjectured that at rapid rates of descent, are presented. Both the mean and unsteady char- insufficient time exists for the complete ground vor- acteristics of these flows are analyzed. Of particular tex structure to form under the aircraft. A computa- interest is the flow unsteadiness due to apparent in- tional study has been carried out to predict the lift- stabilities in the jet and ground vortex structures.

loss experienced by aircraft using thrust-vectoring in Analysis of lift coefficient and pressure histories and ground effect, and to understand the differences in extensive flow visualization are used to develop an un- flow physics in the straight-and-level flight and the derstanding of the relationship between the observed

32-2 forces on the delta wing and the flow dynamics.

descent is simulated by moving the ground upwards.

The ground grid is moved up at the effective experi- mental descent rate of Mach no. 0.004475 (4.9 ft/sec).

3. COMPUTATIONAL MODEL For the descent simulations, the descent is started at h/b = 1.0 as opposed to the experimental starting The computational model consists of a 600 delta height of h/b = 2.0 (where h is the height of the delta wing in a free-stream Mach number of 0.064 (70 wing measured at two-thirds of the chord above the ft/sec), and chord length (31 in.) based Reynolds ground, and b is the wing span) to lower computa- number of 1.2 million, in ground effect. The wing tional expense. The experimental data shows small is equipped with two choked thrust reverser jets (di- differences between descending and straight-and-level ameter 0.6 in.) exiting from jet pipes at an angle lift coefficients at h/b = 1.0, indicating that there of to the delta wing and at NPR (nozzle pres- should be little difference between the static and dy- sure ratio) of 1.8. These geometrical and flow condi- namic flow structures at this height. Therefore, the tions correspond to the conditions in the wind-tunnel descending case can be initialized using the flow field and VRF experiments used for the validation of this for straight-and-level flight at h/b = 1.0 without in- study. The computational model duplicates the wind- troducing significant errors.

tunnel conditions for straight-and-level flight (Fig. 1).

In the wind-tunnel simulations of the straight-and- 3.1 Grids The accuracy of the simulation of a complex flow problem, such as under study here, depends strongly upon the choice of grids. The straight-and-level flight simulations were performed using grids that would be extendible to the descent case. Body-conforming grids were generated about the delta wing, the jet pipe, and the ground to resolve the boundary-layers, and an overset "jet" grid was used to resolve the jet (Figs. 3, 4, 5). The mated delta-wing, jet, and Fig. 1: The Wind-Tunnel setup.

pipe grids overset a ground grid. The overset topol- level flight cases, the floor of the wind-tunnel is re- placed by a moving belt to remove the boundary layer absent in flight tests. Identical procedure is followed in the computational model.

For the descent simulation there are some differ- ences in the conditions between the computational model and the VRF experiment. In the VRF exper- iments, the delta wing is suspended from a cart that moves horizontally on rails, while the descent is sim- ulated by the horizontal motion of the wing above a slanted ground board (Fig. 2). The VRF test sec- Support Strut, sting, high pressure airline and instrurnentation Test section ceiling Fig. 3: The ground-plane grid.

ye0 ogy allows relative motion of component grids and ArZZ thus efficiently manages grid points for moving-body Ground board simulations. It has been used in the past to sim- Test section floor ulate store separation 8 and the separation of the Solid Rocket Boosters from the Shuttle/Main Tank assembly.' Here, the descent is simulated by moving Fig. 2: The Vortex Research Facility setup the ground grid in the upward direction. The data tion is 150 ft. long. The ground board for the first transfer between the grids is achieved using a new 100 ft. of the test section is slanted upwards and implementation of a grid communication scheme the last 50 ft. is horizontal thus allowing simulation referred to as the Chimera scheme. 11 Using this of descent followed by straight-and-level flight. In scheme, solutions are computed independently on all the computational model, the delta wing remains sta- the grids. Overset/overlapping grids feel the influence tionary and the free-stream moves over it, while the of other grids via hole and outer boundaries. Hole

32-3 boundaries are artificial boundaries in grids. The so- is possible by using subiterations. The code is used lution is ignored on all points within a hole bound- to solve the conventional dependent variable vector ary as this area/volume is either overset by a solid [p,pu,pv,pw,e] T where p is density, u,v, and w are body (hole made by delta wing in the ground and Cartesian velocity components, and e is the total en- the jet grids), or it is resolved by a finer grid (hole ergy per unit volume. Speed of sound, delta wing made by the jet grid in the ground grid). In the centerline chord, free-stream density, and y x pressure straight-and-level flight computations, the interpola- (y is specific heat ratio for air) are used as reference tion coefficients required for grid communication at quantities.

the outer and the hole boundaries are computed just once. However, for the descent simulation they have 3.3 Boundary Conditions - Straight-and-level to be recomputed periodically due to the relative mo- flight cases tion of grids.

Ground grid inflow and jet exit values are specified to match the wind-tunnel conditions. The ground plane moves at the same velocity as the free stream to remove the boundary layer effects. A no slip con- dition is used at the delta wing and pipe surfaces.

On solid surfaces, density is extrapolated from one grid point away and pressure is computed by solving the normal momentum equation. All variables are

'9

extrapolated at the ground grid outflow plane.

3.4 Boundary Conditions - Descent cases In the VRF experiments, the delta wing moved relative to the ground, however in these simulations the delta wing remains stationary and the free-stream moves over it. The inflow boundary conditions on the ground grid are specified to match the delta wing velocity (70 ft/sec), and sea-level density and pres- sure. Additionally, the co-ordinate transformation Fig. 4: The delta wing grid.

between the VRF setup and the computational model requires that the floor of the computational ground grid move at the same speed as the free-stream. All other boundary conditions are specified in a similar manner as for the straight-and-level flight cases.

4. RESULTS 4.1 Parametric Studies Parametric computational studies were performed utilizing the straight-and-level flight setup to evaluate the effect of grid density. It was determined that the computed lift is a strong function of the jet trajectory.

In turn, it was found that the jet trajectory can be heavily influenced by the level of grid refinement. It Fig. 5: The pipe and the jet grids.

was found that no practical Cartesian ground plane grid could support the experimentally observed jet trajectory. Rather, the total jet momentum would 3.2 Numerical Algorithm decay rapidly with distance from the nozzle exit, and Time-accurate computations were carried out on a the jet would finally become so weak that it would be Cray-YMP by solving the three-dimensional Navier- deflected downstream by the oncoming flow. This was Stokes equations, using the OVERFLOW" code, in distinct disagreement with the experimental flow on overset grids. Flow was computed on one half of visualizations of Paulson.' It is for this reason that the configuration with the assumption of symmetry the jet grid was added to the computational model.

about the x-z plane. The equations are discretized With the jet grid, and low levels of spatial numerical by using a diagonalized three-factor scheme, which dissipation, the jet penetrates far upstream, impacts is second-order accurate in space, and at most first- the ground plane, and spreads to form a thin wall order accurate in time. Higher-order time accuracy jet. The high speed and large surface area of the wall

32-4 jet result in significant flow entrainment. Because the following the procedure outlined in Fig. 7. The com- entrained flow accelerates, a low static pressure region puted data presented in Fig. 6 for the descent case forms under the delta wing, and lift loss occurs. The has been filtered so as to match the sampling rate of results of these parametric studies were used to select the experimental data. However, no smoothing pro- the grid topology and density for all work presented cedure similar to the experimental procedure (Fig. 7) here.

has been carried out.

For the descent simulations, additional two- dimensional parametric studies were carried out to determine the effect of time step At on simula- tions involving moving grids by descending a two- Cl 0.5 Balance output dimensional center section of the delta wing in ground effect. It was shown that for a high value of At (1.0), the ground cushion effect may not be captured. For 0.5 smaller time steps (At=0.5), the solution indicates increased lift with ground proximity based on con- ^btractIng inertias

ventional ground effect. Further reductions in time tnk

0 0 step indicate convergence of lift histories and do not show any new flow physics. In these simulations, a

• 1AA

• Hand fairing At = 0.002 is used due to stability considerations.

0.0 L

• The above study shows that the chosen time step is -100 0 100 200 small enough to accurately capture the flow features X, ft 0.2 in the descent simulation.

Replotas 0.0 CI f(h/b) ACI 4.2 Test Case Studies x=0-lOOft: h/b=2.5-0.25 Visualizations of the flow about the delta wing at -od .

1.0 x = 100-150 ft: h/b = 0.25 h/b = 0.25 and 1.0 for straight-and-level flight are h/b presented in Plate 1. The instantaneous streamlines Fig. 7: VRF raw data processing.14 passing through the nozzle exit plane indicate that at h/b = 1.0 the jet does not have sufficient momen- At, higher heights above the ground, insignificant tum to impact the ground. As a result, the level of differences are observed between the straight-and- flow entrainment is low and little lift loss is encoun- level flight and the descent cases. The gross flow fea- tered. However, at h/b = 0.25 the jet does impact the tures and mechanism of lift loss are same for both the ground and, as described above, significant flow en- cases. The descent lift curve indicates increased lift trainment occurs, a low pressure pocket forms under between h/b = 0.5 and 0.4 due to the conventional the delta wing, and significant lift loss is encountered.

ground cushion effect. However as the delta wing Because of the care taken in minimizing computa- approaches the ground, differences become apparent tional errors due to numerical dissipation and grid as indicated by higher value of C, at h/b = 0.35 for resolution, the predicted lift coefficients are in rea- the descent case as compared to the straight-and-level sonable agreement with experimental data (Fig. 6).

flight case.

The computed time histories of the lift-coefficient 0.6 for both the straight-and-level flight at various heights above the ground (Fig. 8) and the descent 0.4 case (Fig. 9) show large temporal variations and in- creased amplitude in lift oscillation with ground prox- 0.2 imity. Preferred frequencies of these oscillations are Ci 0.0 0CFD-no j.4 • W/T -no 1.4 A CM-static -0.2 £ WIT -.4.410 - CFD-d..c.nt • VRF-d..c.nt ci 'VRF-st.4Ic -0.4 -h/b=1.0 V 0.0 0.5 1.0 1.5 2.0 2.5 1.0 --- h/b=0.5 -- h/b = 0.25 -1 5 1000 4000 2000 3000 Fig. 6: Comparison between the experimental and com- Iteration (t .002) putational C, values.

Fig. 8: The lift history of the straight-and-level flight cases.

The experimental values obtained from the VRF were smoothed by Paulson and Kemmerly (Ref. 14)

32-5 (3 C/) C/) - CL C C]) a)> N (D I II E -o D o cj c - -0 ci) -o cj - 0 C/) 'I- Cl) -0 Ca) :J 0 c3

o

(I)

-

-I- C,) C) a) C 0 C) cz -C > C -C ci) Cl) -o •;: CZ C CL II C/) o a) :2 cz-.

#1 C]) L1 .4j CZ CL cz

32-6 jet configuration. Finally, the ground vortex height

*4#0

oscillates.

P rM

CI 0.O To determine if the ring vortex dynamics causes the observed variation in lift, temporal variations in pres- sure at the jet lip and four diameters downstream are Wb analyzed (Fig. 12, 13). Power spectra of these pres- Fig. 9: Lift history of the descent case.

identified by computing power spectra of the time- varying lift histories (Fig. 10, 11). Power of all spec- tra presented in this work has been normalized using maximum power. For the descent case, the spectra are obtained over segments of descent (Fig. 11).

Powi Fig. 12: Vortex shedding at the jet lip: Probe locations.

0.00 0.05 0.10 Strouhej Number Fig. Power spectra of lift history for the 10: straight-and-level flight cases.

Pressu 2.0 2.25 2.50 2.75 3.00 to .936 0.75 L .... h/bo.936 to .872 Time 1 1 !;,j to .809 Power ..e..P,/b..809 to .745 1in a 0.0 ....h/bO. 715 to .681 : Fig. 13: Pressure samples at the jet probe locations.

U !

t _..—h/bO,681 to .618 : 'fli h/bfl.6t8 to .554 .... ...

.... t./bo.554 to .490 VLfl'.AiL .....h/bO. 190 to .?

Il. s sure histories, presented in Fig. 14 indicate an initial ---- shedding frequency of St. 0.53 at the jet exit, drop- I 0.00 0.00 0.05 0.10 ping to a vortex passage frequency in the range of 0.1 Strouhal Number to 0.2 by four diameters downstream. Although the initial shedding frequency is lower than the experi- Fig. 11: Power spectra of lift history for the descent mentally observed frequencies (probably due to the case.

large time-step and inadequate grid resolution), the These spectra indicate that preferred frequencies are observed passage frequency (0.1 to 0.2) near the end confined in the narrow range of Strouhal number = of the potential core is within the range of experi- 0.015 to 0.030. (St. = f Dj/Uj, where Dj and Uj are mentally observed ring vortex Strouhal numbers, as jet diameter and velocity respectively) compiled by Gutmark.' 5 The reduction in frequency Flow visualizations indicate a number of flow fea- as the probe is lowered from the jet lip to four di- tures that could cause large temporal variations and ameters downstream is attributed to vortex pairings increased amplitude in lift oscillation with ground observed in flow visualizations. Because the range of proximity. For example, vortices shedding from the observed frequencies due to the ring vortex dynamics is much higher than the observed time period in the jet lip interact in non-periodic, almost random pair- ings; as a result the jet strength and trajectory vary lift variations, it is unlikely that the ring vortex struc- tures are the dominant cause of the lift oscillations.

with time. The jet oscillates both laterally, to- To determine if the lift oscillations are related to wards and away from the symmetry plane, and in the streamwise direction. There is also evidence of a com- the lateral /streamwise jet oscillations, the temporal plex Kármán vortex street shedding behind the dual variation of the pressure field on the under surface

32-7 the jet and jet-induced flow structures.

Polo Pow 0. 0.2 0.4 0.6 0.8 1.0 Strouhal Number 0. 0.05 0.10 0.15 0.20 Fig. 14: Power spectra of pressure sampled at the jet Strouhal Number probe locations.

Fig. 16: Power spectra of pressure sampled at the ground probe locations.

of the delta wing is visualized. Concentric pressure waves emanating from the jet region move along the The very low frequency ground vortex oscillations under-surface of the delta wing (Plate 2). Pressure (St. = f Dj/Uj = 0.006) observed by Cimbala et.

distribution on the under-surface of the delta wing aL 17 suggest that lift oscillations could be related to is shown at two different steps corresponding to in- ground vortex oscillations. These low-frequency os- stances when the under-surface is dominated by the cillations, referred to as "ground vortex puffing," are high pressure and low pressure regions respectively caused when the ground vortex first grows and then, of the pressure wave (Plate 2). Flow visualizations when it can no longer retain its structure, collapses.

indicate that lift oscillates in synchrony with the However, in these computations, the ground vortex movement of peaks (high-pressure) and troughs (low- appears only at lower heights (Fig. 17, 18), yet the pressure) of the pressure wave on the under-side of same narrow range of low-level-frequency lift oscilla- the delta wing. Based on this, it appears that the lift tions occur over the range of computed heights. For oscillations are related to these pressure waves. These this reason, it appears the lift oscillations are not re- waves are similar in shape and magnitude to the pres- lated to ground vortex puffing.

sure waves observed on the ground plane (Plate 1) as well.

The history of the pressure variations at four points on the ground plane are presented in Fig. 15. These pressure histories were extracted as the delta wing descended through h/b = 0.35. Spectra analysis of PrE 0. 1.0 2.0 3.0 4.0 5.0 Fig. 17: Front view of the ground vortex.

Time There is evidence of a Kármán vortex street be- Fig. 15: Pressure samples at the ground probe loca- hind the dual jet. The frequency of this vortex tions.

street has yet to be determined, however, the shed- these histories, presented in Fig. 16, show a preferred ding frequency for a Kármán vortex street for flow frequency of St. = 0.015, which is within the range past a circular cylinder (jet in this case) for simi- of lift oscillation frequency. Because of this match lar Reynolds numbers (jet-diameter-based) is in the in frequency, and the observation that the pressure range of St. = 0.18 to 0.20.16 The computed lift os- waves only exist when the jets are present, and also cillation frequency range corresponds to free-stream they emanate from the jet vicinity, it appears that velocity based St. = 0.23 to 0.46. This frequency the lift oscillations are due to large scale motions of range is very close to the expected vortex street fre-

CL

C2 '—'U, CD _I CL co cu Oca cps c —I C2 cts

I')

C"

Ob) cm c'J a, I-.

CO) I- CIO a, o ( —

G)

CO) — a, V C c 4-.

ci

32-9 may not be captured. The time-step used in these simulations was sufficiently small to capture the de- scent related flow features.

The time-accurate computations for the straight- and-level flight were performed for a number of heights (h/b=1.0, 0.5, 0.35, and 0.25) above the ground. The computations over-predict the lift co- efficient, however flow physics corresponding to lift loss with increased ground proximity is captured.

- The time-accurate simulation of the descent from h/b = 1.0 to h/b = 0.25 captures the initial increased lift due to the conventional ground cushion effect fol- lowed by lift loss due to the suck-down effect as the Fig. 18: Side view of the ground vortex.

delta wing approaches the ground. The computed lift coefficients are in fair agreement with the experimen- tal values.

quency. However, the position of the Kármán vortex Both the straight-and-level flight and descent simu- street past the trailing edge of the delta wing makes lations exhibit high levels of unsteadiness. Spectra of it an unlikely feature that can affect the lift oscil- the lift histories indicate preferred frequencies in the lations. Further, no correlation has been found be- narrow range of St. = . 015 to .03 for the straight-and- tween the wave-like nature of the pressure field on level flight over all computed heights. The same range the under-surface of the delta wing and the Kármán of frequencies is preferred when spectra are computed vortex street.

over segments of the descent.

The computational simulation captures the quali- Efforts were made to understand the unsteady flow tative physics, as indicated by typical lift-coefficients structures which produce the lift oscillations. The at high h/b values and low lift-coefficient values at ring vortex shedding frequencies were deemed too lower heights indicating suck-down (Fig. 6). Com- high to cause the lift oscillations. Kármán vortex puted values fall within the data discrepancy band street was ruled out as the feature causing lift oscil- in the two experimental facilities (note C1 difference lations due to its position beyond the trailing edge between the VRF and W/T results for h/b = 1.0 of the delta wing. Further, no correlation could be and h/b = 0.25). Quantitatively, the CFD simula- found between the wave-like nature of the pressure tion under-estimates the lift loss for straight-and-level distribution on the under-surface of the delta wing flight cases. This could be due to the lack of a turbu- and the ground, and the vortex street.

lence model in these simulations. Inclusion of a tur- Presence of a "wave-like" pressure field in the vicin- bulence model would have increased the jet spreading ity of the jet indicates that the jet oscillations result and resulted in increased flow entrainment. No turbu- in moving pressure waves. It was shown that the lence model was included in these simulations due to lift oscillation frequency is related to the frequency of lack of a rational approach to apply an algebraic tur- these waves. Analysis of the temporal variations of bulence model to a flow of this complexity. A higher pressure at various locations on the ground indicated order two-equation model, for example a k - € model, frequencies within the range of the lift oscillation fre- would have pushed the computational cost beyond quencies. Based on this, it was concluded that the what could be accommodated.

lift oscillations are due to large scale motions of the jet and jet-induced flow structures.

Ground vortex was ruled out as the cause of lift 5. CONCLUSIONS oscillations as it appears only at lower heights. Lift oscillations, however, over same range of preferred fre- quencies appear even at higher heights (e.g. h/b = Lift loss in ground proximity, as may be encoun- 1.0). It is conjectured that ground-vortex-puffing tered during STOL operations, was computed by type of flow physics occurs in the vortex formed be- solving flow past a delta wing with thrust reverser hind the jet causing its size to oscillate, and resulting jets in the straight-and-level and descent flight pro- in lift oscillations.

files.

Efforts were made to minimize numerical errors due to grid resolution and time step. Overset grids were used to capture the jet trajectory. Two-dimensional parametric studies were carried out to determine the effect of time step At on simulations involving moving grids. The computed unsteady result (descent case) showed convergence for smaller values of At and in- dicates that for higher At, the ground cushion effect

32-10 6. References Kemmerly, G. T. and Paulson, J. W., "Investiga- 1 tion of a Moving-Model Technique for Measuring Paulson, J. W. and Kemmerly, G. T., "An Assess- Ground Effects," NASA Technical Memorandum ment of Ground Effects Determined by Static and 4080, January 1989.

Dynamic Testing Techniques," Ground Vortex Workshop, NASA Conference Publication 10008, 15 Gutmark, E. and Ho, C. M., "Preferred Modes NASA Ames Research Center, 1987.

and the Spreading Rates of Jets," Physics of Flu- ids, 26, pp. 2932-2938, 1983.

Van Dalsem, W. R., "Study of Jet in Ground Ef- fect with Crossfiow Using the Fortified Navier- 16 Schlichting, H., Boundary Layer Theory, McGraw Stokes Scheme," AIAA Paper 87-2279, 1987.

Hill Book Company, pp. 32, 1979.

Van Dalsem, W. R., Panaras, A. G., and Ste- Cimbala, J. M., Billet, M. L., and Gaublomme, D.

ger, J. L., "Numerical Investigation of a Jet in P., "Experiments on the Unsteadiness Associated Ground Effect with a Crossfiow," SAE Paper with a Ground Vortex," Journal of Aircraft, 28, 872344, 1987.

No. 4, pp. 261-267, 1991.

' Stewart, V. R., Kuhn, R. E., and Walters, M. M., "Characteristics of the Ground Vortex Developed by Various V/STOL Jets at Forward Speed," AIAA Paper 83-2494, 1983.

Chawla, K., Van Dalsem, W. It., and Rao, K.

V., "Simulation of a Delta Wing with Two Jets in Ground Effect," Computing Systems in Engi- neering, 1, pp. 483-494, 1990.

Chawla, K., Van Dalsem, W. R., and Rao, K. V., "Numerical Study of a Delta Planform with Mul- tiple Jets in Ground Effect," SAE Paper 892283, 1989. Also in SAE 1989 Transactions, Journal of Aerospace, Section I, pp. 1555-1567.

Chawla, K., Van Dalsem, W. R., and Rao, K.V., "Simulation and Analysis of a Delta Planform with Multiple Jets in Ground Effect," AIAA Pa- per 90-0299, 1990.

Dougherty, F. C. and Kuan, J. H., "Transonic Store Separation Using a Three-Dimensional Chimera Grid Scheme," AIAA Paper 89-0637, 1989.

Meakin, R. L. and Suhs, N. E., "Unsteady Aero- dynamic Simulation of Multiple Bodies in Rela- tive Motion," AIAA Paper 89-1996, 1989.

Meakin, R. L., "A New Method for Establish- ing Inter-Grid Communication among Systems of Overset Grids," AIAA Paper 91-1586, 1991.

Benek, J. A., Buning, P. G., and Steger, J. L., "A 3-D Chimera Grid Embedding Technique," AIAA Paper 85-1523, 1985.

Buning, P. G. and Chan, W. M., "OVER- FLOW/F3D User's Manual," NASA Internal Memorandum, NASA Ames Research Center, Moffett Field, CA, March 1991.

Pulliam, T. H. and Chaussee, D. S., "A Diagnol Form of an Implicit Approximate Factorization Algorithm," Journal of Computational Physics 39, pp. 347-363, 1981.

Appendix 11

A jw^ - AIAA 93-0197 Tracking Flow Features Using Overset Grids K. Chawla MCAT Institute NASA Ames Research Center Moffett Field, CA and D. W. Banks University of California Davis, CA 31st Aerospace Sciences Meeting & Exhibit January 11-14, 1993 / Reno, NV r permission to copy or republish, contact the American institute of Aeronautics and Astronautics 0 LEnlant Promenade, S.W., Washington, D.C. 20024

TRACKING FLOW FEATURES USING OVERSET GRIDS Kalpana Chawla* MCAT Institute NASA Ames Research Center Moffett Field, CA and David W. Banks University of California at Davis Davis, CA Abstract methods can be classified into two approaches. In the first approach, new grid points are added in the re- A method is proposed to use overset grid topology gions of high gradients, and in the second approach to track dynamic flow features. Features of interest grid points are moved to cluster in the regions of high such as moving shock waves and vortices are over- gradients.

set with relatively fine tracker grids. Solutions are In the adaptive mesh refinement technique, regions computed on the various grids and information is ex- of the global grid are refined, and re-refined to provide changed at intergrid boundaries. A grid track-sensor additional points so as to resolve the flow gradients variable such as pressure is used to track the position accurately.' This approach seems to be well suited for of the flow feature to be resolved. The tracker grid problems with moving flow features. However, gen- is moved to the position where the track-sensor vari- erally, explicit methods are used in conjunction with able has the desired value (generally a maximum or a this approach, thus inhibiting the time-step size. This minimum) and new interpolation coefficients are com- approach has been exploited efficiently in conjunction puted for information exchange across grid bound- with unstructured grids where explicit approaches are aries. Solutions are computed at the current loca- more efficient.'

tion and time-step, and grid motion is brought into Grid movement based adaption methods are more the solution via time metrics. The method is demon- popular in the structured-grid arena. The points are strated by tracking a moving shock and vortices shed moved either 1) based on minimization of some error behind a circular cylinder. It is conjectured that the measure or 2) based on a measure of artificial forces method would show significant benefits in resolving acting between nodes.3 features such as wakes behind oscillating airfoils and The error measures in the minimization method are trajectories of jets issuing from rotating nozzles as en- computed, amongst other approaches, using modified countered during thrust-vectoring.

equation analysis. In modified equation analysis, the discrete equations are expanded using Taylor series to obtain the original differential equation plus error Introduction terms. The grid is then adapted to minimize the trun- cation error terms. Truncation error based measures Engineering Computational Fluid Dynamics (CFD) have been used successfully to adapt grids to moving simulations routinely require the use of adaption pro- shocks.4 cedures to resolve flow fields of interest by providing Methods utilizing artificial forces to move grid denser grids in areas of high gradients. The existing points make use of, amongst other approaches, the spring analogy. In the methods utilizing spring anal- *Research Scientist, Member AIAA.

ogy, it is imagined that the grid points are connected tResearch Assistant, Member AIAA.

Copyright © 1992 by the American Institute of Aeronautics to each other with springs and that flow variables and Astronautics, Inc. No copyright is asserted in the United to which the grid is adapted are equivalent to forces States under Title 17, U.S. Code. The U.S. Government has acting at grid points. Equations are formulated so a royalty-free license to exercise all rights under the copyright that a uniform spring force distribution is achieved.

claimed herein for Governmental purposes. All other rights are reserved by the copyright owner.

This approach has been used to solve complex three-

dimensional flows. 5 '6 A number of variants of this method exist and the reader is referred to Ref. 3 for more details on this and other adaption methods.

Most of the structured-grid based adaption meth- ods require that once the grid has been adapted, the solution be updated on the adapted grid by an in- terpolation method. For problems requiring time- accurate analysis, subiterations have to be carried out Fig. 2: An overset grid to resolve the jet.

as the interpolated solution is not necessarily a solu- tion of the governing equations. Alternatively, time wing, which is possible if the jet trajectory is simu- metrics may be used to obtain solution on the de- lated correctly. The overset grid is just fine enough formed (adapted) grid. Flow fields consisting of dy- to allow correct prediction of jet trajectory and hence namic features do not lend themselves very well to air-loads, but too coarse to simulate unnecessary fea- this adaption procedure. Frequent grid adaptions are tures such as modes of jet deformation.

required as the flow features move around. Further, adaption to flow variables generally results in grids of poor quality. Modified equation analysis indicates that grids with skewed, high stretching and high as- .4 pect ratio cells may result in solution errors As a result, grids that have been adapted to solution vari- ables, now, in addition, have to be adapted to grid Fig. 3: Jet trajectory with an overset grid.

quality functions such as skewness, straightness, and .7 orthogonality as well The adaption problem with these constraints may be very stiff, and may not con- In the present study, overset grids are used to re- verge.

solve large, distinct, dynamic flow features such as moving shocks and vortices by oversetting the rela- In this paper, a method is proposed to adapt the static flow features such as wall jets and shear lay- tively coarse background and component grids with ers via conventional adaption methods, and tracking finer grids; thus allowing grid enrichment in the re- the dynamic flow features such as vortices and mov- gions of high gradients. These grids are then used to ing shocks by using dynamic overset grids, termed track the dynamic flow features. It is conjectured that "tracker grids" here. Overset grids have been used the proposed approach will show promise in track- ing flow features associated with bodies in motion, successfully in the past to provide grid enrichment in regions of high gradients to resolve jets' ,', and to re- e.g., wakes behind oscillating airfoils and trajectories solve shear layers and wake flows10 . The grid den- of jets issuing from rotating nozzles as encountered during thrust-vectoring.

sities used in these overset grid examples to resolve static flow features were determined based on para- metric studies. Sample two-dimensional problems Approach were solved to determine grid densities that would provide desired resolution of frequencies and flow fea- Tracker Grid Motion Procedure: tures. The structured grids used were solved implic- itly allowing for the corresponding benefits of large The approach to track the flow features is very sim- time-step size. Fig. 1, for example, shows a result from ilar to the simulation of moving bodies using over- the simulation of a delta wing with thrust-reverser jets set grid technology. ' 2 " 3 First, the problem is solved in ground effect.8 '11 Particle traces starting at the jet on the global and component grids. Then Cartesian tracker grids are introduced at locations where the chosen track steering variable, or its gradient (termed "sensor variable" here) has the minimum or maximum value. Centroids of these grids are placed exactly over locations where sensor variables have desired values.

The solutions on the tracker grids are initially inter- Fig. 1: Jet trajectory without an overset grid polated from the solution in the existing domain. The flow solution is then carried out on all the grids for a exit in Fig. 1 do not reach the ground. However, when few steps so that the solutions on the tracker grids the solution is obtained with an additional overset grid match the solutions on the underlying grids. After (Fig. 2) to resolve the jet, the jet is able to reach the this, solution is computed for a desired number of time ground (Fig. 3). The engineering requirement of this steps, and a search is initiated at the centroid of the simulation is to predict correct air-loads on the delta tracker grid. A stencil-walk from this location leads

to the new position where the sensor variable has the component grids to resolve boundary layers and im- local maximum/minimum value. This new position plement turbulence models, and 3) Cartesian tracker is written to a file which is then read by a grid com- grids to follow the dynamic flow features.

munication package to determine new interpolation Other advantages of choosing Cartesian tracker coefficients for transferring solutions at grid hole and grids include: outer boundaries. Holes are regions within which the 1) Cartesian grids would lend themselves to grid re- solution is not ccmputed. The region within the hole finement much more easily, if it was desired to relate boundary is either overset by a solid body or a finer the grid density to a rigorous error measure as opposed grid. Once the intergrid communication process has to parametric studies. Techniques such as Richard- been completed, the solution process is begun once son's extrapolation to perform grid-sensitivity studies again. Time metrics are used to bring the effect of could be carried out relatively easily.

grid motion into the solution. The above-mentioned 2) Search routines to locate the sensor variable's procedure is summarized in Fig. 4.

maxima/minima are simple and inexpensive on these grids.

Once tracker grids have been introduced, 3) Once a grid family is chosen, advance knowledge initialize tracker grid solution, of the size of the grid can be used to ensure that run flow solver for n time steps, tracker grids do not come closer than a certain dis- determine new positions of tance (which would imply a waste of points).

flow features being tracked 4) In other scenarios, the size of the grid helps in spec- ifying minimum overlap that must exist between two tracker grids. Without this specification, the holes Move tracker grids to new locations caused by tracker grids may not overlap, resulting in and update global grid field points between tracker grids as shown grid communication coefficients in Fig. 5.

Run flow solver; Use time metrics to bring in effect of movina arids Determine new positions of flow features being tracked No New position = Old Fig. 5: Insufficient overlap between tracker grids.

Yes Track Sensor Variable: Stop The choice of the sensor variable to track the flow feature is problem-dependent. For example, pressure gradient may be chosen as the sensor variable for a Fig. 4: Tracking procedure.

moving shock. One should choose variables that are representative of the features that need to be resolved.

Tracker Grid Type: These variables should offer a wide variation in values with the surrounding flow field so that they have dis- The choice of Cartesian or analytically defined tinct minima or maxima on the tracker grids to en- tracker grids offers a number of advantages, however able accurate tracking. Flow fields with very small tracker grids are not limited to this family alone. Since flow features or dynamic features with weak gradients the nature of the flow feature is generally not known a scattered all over may not be suitable for this tracking priori, a Cartesian grid would be the simplest choice.

approach.

Not only are the grid quality issues absent with this choice, but also Cartesian flow solvers could be used Errors: to obtain solutions on these grids at relatively cheaper costs."' In the proposed simulation, one could use The most common errors associated with overset 1) a global Cartesian background grid, 2) curvilinear grids occur when a fine grid transfers a large flow gra-

dient onto a coarse grid. These errors can be min- a large number of engineering problems require finer imized by ensuring that flow gradients are small at grids in regions of the computed domain to yield so- intergrid boundaries if grid densities of communicat- lutions of desired accuracy. However, in both of these ing grids are widely different. If large gradients exist problems, grid arrangements are chosen such that only at the intergrid boundaries, then both the global and the tracking procedure is validated. No effort is made the overset grid should be capable of resolving the to demonstrate solutions of higher accuracy with the gradient at that location. This is generally ensured use of tracker grids. For the shock problem, validation by providing grids of similar densities. For example, will be successful if the shock is tracked at the correct shear-layer studies of Ref. 10 carried out on overset shock speed. The shock speed is known a priori as it grids indicate that it is possible to simulate unsteady is the solution of the analytical problem correspond- flow features accurately on static overset grids, sug- ing to the specified initial conditions. For the vortex gesting that once proper attention is paid to positions tracking problem, the tracking procedure is started and densities of grids, space-conservation errors are after the vortex is positioned more than a diameter probably minimal.

downstream of the cylinder. The method will be vali- Time-conservation error studies of Ref. 15, for mov- dated if it can be shown that tracking does not change ing grids, show that a small phase error can occur in the vortex shedding rate and the relative positions of the solution. If all grid communication boundaries the vortices.

are updated at the end of a solution step, some of this error may diminish. For global space-time related The Moving Shock Problem conservation errors associated with overset grids, the An initial condition corresponding to a shock speed reader is referred to Ref. 16. Rigorous analysis of of Mach number of 2.81 was prescribed on a Carte- conservation errors associated with overset grids is in progress at NASA Ames. sian grid. A fine Cartesian grid was introduced at the shock position. Fig. 6 shows the background Carte- sian grid and the boundary of the overset, fine, shock- Examples tracker grid. The location of the left-moving shock is The motivational problem for tracking flow features The outer boundary of using overset grids is the simulation of a descend- ing delta wing with thrust reverser jets in ground environment. 13 When the delta wing is more than one wing span above the ground, the thrust reverser jets do not strike the ground. Instead, the free-stream causes the jets to move downstream. However, as the delta wing approaches the ground, the jet trajectory starts to change. At heights of about one-half wing span above the ground, the jet is able to strike the ground and spreads into a thin wall jet that can be resolved properly by the fine grids used in the vicin- ity of the ground to resolve boundary layers. In an ideal scenario, one would require only the grid in the jet vicinity to be refined so as to predict correct jet trajectory, as opposed to using a fine background grid that could be computationally expensive. In the pro- posed approach, one grid would be introduced in the jet vicinity at the beginning of the simulation. Af- ter the jet has developed in this grid, other tracker The background grid Hole boundary In the background grid grids would be added so that the jet trajectory could develop in these grids. This problem is deemed too Fig. 6: The grid setup for the left moving shock complicated to test the tracking method; instead sim- pler demonstration problems are tested and discussed shown by the vertical thick solid line passing through below.

the blanked area of the background grid. Interpo- lation coefficients for grid communication across the Validation Cases two grids were obtained using Domain Connectivity Two demonstration problems, namely tracking a Function (DCF).' 7 OVERFLOW,' 8 a flow solver, shock, and tracking a vortex are used for validating was then used to obtain the solution on this grid ar- the tracking procedure. Past experience indicates that rangement for ten time steps. Finally, a new routine

in the program was used to determine the location of late over longer lengths of time and show the effect of the highest pressure gradient in the fine tracker grid.

errors more clearly.

The location of the tracker grid is stored in a file and used by DCF to generate new interpolation coefficient Flow Past a Circular Cylinder files. The flow solver was then run again, and the time metrics were computed so that effect of grid motion The previous example is essentially a one dimen- could be brought into the solution. Figure 7 shows the sional dynamic flow feature. In this example, two- location of the moving shock (pressure jump) and also dimensional features, namely vortices behind a cir- the location of the tracker (solid line) and background cular cylinder, are tracked. A similar procedure as grids (dashed line). It can be seen that the tracker described above is followed, however, now the sen- grid is able to follow the moving shock automatically.

sor used to position the tracker grid is vorticity. The The computed shock speed with and without tracker tracker grid is searched for maximum vorticity after the solution has been carried out for some time-steps, and then moved to this new location. Figure 9 shows the grid setup for this case consisting of a background Cartesian grid, a body-conforming grid around the cylinder and a Cartesian tracker grid. Fig. 10 shows

^J=JJ7'

Hole boundarl..

1 17

Tracker grid - - - - Background grid Fig. 7: A tracker grid following a shock.

grid matches the analytical shock speed. Comparison of shock positions with and without tracker grids is shown in Fig. 8. It should be pointed out that shocks vorticity contours at a Reynolds number of 200, and the tracker grid position as it follows a vortex. The results with and without tracker grid are similar, indi- cating that Strouhal number is not affected with this approach.

Another case was tried by tracking two vortices, yielding very similar results, as shown in Fig. 11. The positions of the vortices, and thus the Strouhal num- ber, are almost identical to the one tracker grid case.

This problem is a motivation for developing automatic introduction and removal of grids. Grids could be re- moved when the associated gradients have weakened - Tracker grid - - - - Background grid such that the global grid can resolve them.

Fig. 8: Shock speed comparison without (1-3a) and with (1-3b) tracker grid.

Conclusions of speeds as low as Mach 0.06 were tracked correctly The overset grid methodology has been successfully using this procedure. The low shock speed cases are used to track one-dimensional and two-dimensional important because they allow the errors to accumu- flow features in time and space. It is expected that the

Fig. 10: Vorticity contours (white = large vorticity, black small vorticity) for flow past a circular cylinder at a Reynolds number of 200 showing a tracker grid following a vortex.

Fig. 11: Vorticity contours (white = large vorticity, black small vorticity) for flow past a circular cylinder at a Reynolds number of 200 showing tracker grids following two vortices.

tracking approach will minimize grid-quality-related " Klopfer, G. H. and McRae, D. S., "The Nonlinear solution errors by allowing Cartesian tracker grids to Modified Equation Approach to Analyzing Finite track flow features as opposed to deforming the grid Difference Schemes," AIAA Paper 81-1029, 1981.

to meet the same objective.

Djomehri, M. J. and Deiwert, G. S., "Solution This approach uses tools very similar to those used Adaptive Program SADAP3D," AIAA Paper 91- in overset moving body simulations. Solutions are 2903, 1991.

computed on the various grids and information is ex- changed at various boundaries. A sensor variable such 6 Davies, C. B. and Venkatapathy, E., "A Simplified as pressure is used to track the position of the flow Self-Adaptive Grid Method, SAGE," NASA-TM- feature to be resolved. The tracker grid is moved to 102198,1989.

the position where the sensor variable has the desired Lee, K. D. and Loellbach, J. M., "A Mapping value (generally a maximum or a minimum) and new Technique for Solution Adaptive Grid Control," interpolation coefficients are computed for informa- AIAA 89-2178-CP, 1989.

tion exchange across grid boundaries. Solutions are computed at the current tracker locations and time- Chawla, K., Van Dalsem, W. R., and Rao, K.V., step, while grid motion is brought into the solution "Simulation and Analysis of a Delta Planform via time metrics. The method is demonstrated by with Multiple Jets in Ground Effect," AIAA Pa- tracking a moving shock, and vortices shed behind a per 90-0299, 1990.

circular cylinder.

The grid steering is automated at this stage as il- Smith, M., Chawla, K., and Van Dalsem, W., lustrated by the examples shown. Work is in progress "Numerical Simulation of a Complete Aircraft in to automate the process of introduction and removal Ground Effect," AIAA Paper 91-3293, 1991.

of tracker grids. It is conjectured that the method Atwood, C. A. and Van Dalsem, W. R., "Flow- would show significant benefits in resolving features field Simulation about the SOFIA Airborne Ob- such as wakes behind oscillating airfoils and trajecto- servatory," AIAA Paper 92-0656, 1992.

ries of jets issuing from rotating nozzles as encoun- tered during thrust-vectoring.

Chawla, K., Van Dalsem, W. R., and Rao, K.V., "Simulation of a Delta Wing with Two Jets in Ground Effect," Computing Systems in Engineer- Future Work ing, Vol. 1, Nos 2-4, pp. 483-494, 1990.

A strategy is being formulated to introduce and Meakin, R. L., "Unsteady Aerodynamic Simula- remove tracker grids automatically. Tracker grids will tion of Multiple Bodies in Relative Motion," AIAA be discarded once global grid density is sufficient to Paper 89-1996, 1989.

resolve the flow gradient. A method may be developed to change the size of the tracker grids based on the Chawla, K. and Van Dalsem, W. IL, "Numerical value of the gradient they are trying to resolve. Also, a Simulation of STOL Operations Using Thrust Re- method may be evaluated to track flow features based versers," AIAA Paper 92-4254, 1992.

on error estimates. The new methodologies will be Joseph L. Steger, private communication.

tested on analytic/simple two-dimensional problems initially. Once the method has matured, it will be Dougherty, F. C. and Kuan, J. H., "Transonic applied to a realistic three-dimensional problem.

Store Separation Using a Three Dimensional Chimera Grid Scheme," AIAA Paper 89-0637, References 1989.

Berger, M. J. and Colella, P., "Local Adap- Steger, J. L., "Chimera Simulation of Viscous and tive Mesh Refinement for Shock Hydrodynamics," Vortical Flows about Aircraft," Appendix-1, Ma- Journal of Computational Physics, Vol. 82, pp. 64- trix Analysis, IBM CFD Short Course, April 29 84, May 1989.

to May 3, 1991.

Mavriplis, D. J., "Accurate Multigrid Solution of Meakin, R. L., "A New Method for Establish- the Euler Equations on Unstructured and Adap- ing Inter-Grid Communication among Systems of tive Meshes," AIAA Journal, Vol. 28, No. 2, pp.

Overset Grids," AIAA Paper 91-1586, 1991.

213-221, 1990.

Buning, P. G., Chan, W. M. et. al., "OVER- Hawken, D. F., "Review of Adaptive-Grid Tech- FLOW/F3D User's Manual," NASA Internal niques for Solution of Partial Differential Equa- Memorandum, NASA Ames Research Center, tions," Progress in Aerospace Sciences, Vol. 24, Moffett Field, CA, March 1991.

pp. 29-49, 1987.

Appendix III

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