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Effect of Nozzle Burn-through on CLV Booster Controllability

Terry L. Holst* and Shishir A. Pandya† NASA Ames Research Center, Moffett Field, CA, 94035

The CART3D flow solver is used to compute the flow field about the Crew Launch Vehicle (CLV) with various burn-through failures in the booster’s nozzle. The purpose of these computations is to determine if the CLV with a nozzle burn-through will remain controllable during the launch phase using standard nozzle gimbaling. Emphasis in this study is upon understanding how the various physical parameters—for example, hole size, hole position or mission elapsed time—affect the computed results. The final application of these results will be made in the CLV design phase for risk assessment. In all scenarios studied, the loss in thrust was less than 1%, and the burn-through normal force was less than the potential side force generated via nozzle gimbaling. Thus, the nozzle burn-through failure mode will not produce a loss of controllability, providing the burn-through does not produce any additional failures in the gimbaling control mechanism.

Nomenclature CA = Force coefficient in the axial direction CN = Force coefficient in the normal direction MET = Mission Elapsed Time M∞ = Free-stream Mach number P∞ = Free-stream pressure T∞ = Free-stream temperature XP = Distance from the nozzle exit in the upstream direction h = Altitude q∞ = Dynamic pressure x = Distance downstream of the coordinate system’s origin z = Distance in the pitch plane away from the coordinate system’s origin α = Angle of attack γ = Ratio of specific heats

I. Introduction N the utilization of solid rocket motors one mode of failure occurs when the nozzle wall is breached by the thermal and mechanical loads that are present during nozzle operation. This failure mode, among others, was

studied in Refs. 1-2 for the Space Shuttle and Ares-I-X launch vehicles, respectively, using a flight dynamics program to produce statistical information for a range safety malfunction analysis. As stated in Ref. 1, a burn-through can potentially occur in numerous nozzle locations. It would most likely start as a small breach and then grow in size until a complete circumferential joint failure. Thus, the burn through scenario utilized in Refs. 1-2 consisted of a full circumferential burn through in which the entire aft half of the supersonic-portion of the nozzle was instantaneously expelled, resulting in a 12.6% reduction of axial thrust and loss of thrust vector control (TVC).

The present study differs from Refs. 1-2 in several important ways. First, only a partial burn-through of the nozzle is considered. With such a failure it is highly likely that additional failures, including hole growth as described in Refs. 1-2, will follow after the initial burn-through, resulting in loss of the TVC system and eventually the entire launch vehicle. Nevertheless, for the present study no additional failures have been assumed and the size

* Branch Chief, Applications Branch, NASA Advanced Supercomputing Division, MS T27B, and AIAA fellow. † Aerospace Engineer, NASA Advanced Supercomputing Division, MS T27B, AIAA Senior member.

I

26th AIAA Applied Aerodynamics Conference18 - 21 August 2008, Honolulu, Hawaii

AIAA 2008-6575

This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.

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of the nozzle wall breach is assumed to be fixed. The primary purpose of the present study is to analyze the resulting flow field around the entire launch vehicle, especially the portion in the nozzle base flow, and to provide a preliminary quantification of the loss in axial thrust and the generation of a side force that might overtax TVC control authority.

The computational methodology utilized in this study is discussed next, followed by a series of computed results. The first results are from a grid refinement study, which is used to determine the distribution of grid cells that will minimize truncation errors arising from coarse grid effects, especially with regard to the normal force that is generated by the nozzle burn-through failure. The next series of results is used to demonstrate key features of the CLV nozzle burn-through flow field. These results are highlighted by a series of contour and streamline plots that focus on the flow field in the vicinity of the CLV nozzle. Finally, the effect of hole size, hole position and mission elapsed time (MET) on axial thrust loss and normal-force generation are presented. These results can be used to assess the risk to crew and vehicle from a burn-through failure in a rocket nozzle.

III. Computational Methodology In the present study, nozzle burn-through results are computed using the CART3D flow solution package.3-4 The basic embedded-boundary method used in CART3D is presented in Aftosmis, et al.3-4 This flow solver utilizes a highly efficient multi-grid approach to solve the inviscid flow equations (Euler equations) about general three-dimensional configurations. The Cartesian unstructured grids utilized by CART3D are automatically generated and adapted to the geometry in question. These grids are generated from watertight surface triangulation files, which are automatically obtained from CAD.5

A detailed description of the CART3D boundary condition implementation procedure for nozzle flows is presented in Ref. 6 and will not be reproduced herein. In addition, an extensive set of validation comparisons for a variety of nozzle flows computed using the CART3D code is presented in this reference. In all cases presented herein the entire ascent-mode CLV launch vehicle is included in the simulation (Figure 1) with enhanced grid refinement in the vicinity of the nozzle—both internal and external flow. An early version of the CLV external-line geometry is used for all computations. The nozzle burn-through geometry is assumed to be elliptical in shape with the semi-major axis aligned with the direction of flow. Two geometric parameters have been varied: the area of the ellipse and the ellipse position. Using these two parameters, a total of ten geometrical variations were evaluated in this study. Figure 2 shows three of these variations; the smallest hole at the forward most position, the mid-size hole at the mid position and the largest hole in the aft posion. Only hole positions that are downstream of the nozzle throat are considered.

Figure 1. CLV launch vehicle

Figure 2. Burn-through hole size and location (3 sizes and 3 locations are shown)

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In addition to hole geometry, the position along the CLV flight trajectory is varied. Each free-stream flight condition is taken from the CLV due east reference trajectory. Four sets of data along this trajectory corresponding to four different mission elapsed times (MET) are presented. More on the precise trajectory points utilized in this study will be presented in the section on computed results.

Rocket nozzle boundary conditions are set inside a truncated plenum chamber to produce the approximate thrust corresponding to the point on the trajectory being simulated6. A perfect gas assumption associated with the air in the plenum-chamber/nozzle flow field is used in conjunction with each computation. Despite the inadequacies of the inviscid and perfect gas assumptions for the present nozzle burn-through flow problem, they were deemed appropriate for the engineering nature of the present calculations. If the issue of CLV controllability had turned out to be marginal, a more accurate simulation with viscous and real-gas/reacting flow assumptions would have been required.

IV. Grid Refinement Study The first issue is to determine the effect of grid refinement on the physical attributes of current interest—axial thrust and normal force. Figure 3 shows results obtained from such a grid refinement study for a typical transonic case: M∞ = 0.89, α = 0°, MET = 35 sec, h = 4622 m and Thrust = 11.5x106 N. The nozzle burn-through hole was arbitrarily selected to be a 0.4 m x 0.25 m ellipse with an area of 0.314 m2. The center of the burn-through ellipse for this computation was located 26.5 m downstream of the coordinate system origin (x = 26.5 m), which is approximately 0.6 m downstream of the nozzle throat and 3.5 m upstream of the nozzle exit (XP = 3.5 m). The different levels of grid refinement for this series of computations were generated by changing the maximum number of grid refinement levels within the CUBES grid generator, by utilizing a variety of grid refinement boxes in the nozzle’s vicinity and by varying the number of transition cells that are utilized in going from one grid level to the next.

As can be seen from Figure 3, the level of grid refinement had little effect on the axial thrust coefficient (CA), as each grid, ranging from 106 cells to 5x107 cells, produced CA values within ±2% of the CA average value. Conversely, the level of grid refinement had a large effect on the normal force coefficient (CN). Values of CN computed on the finer grids (>107 cells) produced a variation that was generally bounded by ±8%. As a result, a minimum grid of 1.1x107 cells was used for each of the remaining computations.

Figure 3. Grid refinement study showing the effect of grid variation on the axial force and normal force coefficients, M∞ = 0.89, α = 0°, MET = 35 sec, h = 4622 m and Thrust = 11.5x106 N. Elliptical burn-through dimensions ~ 0.4 m x 0.25 m (0.314 m2) and XP = 3.

0

10

20

30

40

0

0.5

1

1.5

2

105 106 107 108 109

CA

CN

AX

IAL

FO

RC

E C

OE

FF

ICIE

NT

(T

HR

US

T -

DR

AG

) --

CA

NO

RM

AL

FO

RC

E C

OE

FF

ICIE

NT

--

CN

NUMBER OF GRID CELLS

± 8% VARIATION

± 2% VARIATION

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V. Computed Results Results from a numerical study to determine the effects of nozzle burn-through on CLV controllability during flight of the solid-rocket booster with a variety of nozzle-burn-through failures are now presented and discussed. For all computations performed in this study the x-coordinate is aligned with the flow direction, positive downstream; the y-coordinate is normal to x in the pitch plane; and z is normal to both x and y, forming a right-handed coordinate system. The coordinate system origin is centered along the vehicle axis at a position 30 m upstream of the nozzle exit, that is, the nozzle exit is located at x = 30 m. Each burn-through hole is elliptical in shape with the semi-major axis aligned with the x-coordinate direction. It is centered in the z = 0 pitch plane such that the burn-through jet issues in the negative y-direction.

The next several results are intended to demonstrate the general flow field features for the CLV nozzle in which a burn-through hole has developed in the side of the CLV solid rocket motor. All burn-through scenarios in this study have been chosen to lie downstream of the nozzle throat, that is, in the supersonic section of the nozzle. For all simulations performed herein, none of the apparatus placed between the nozzle external wall and the booster skirt, for example, the gimbaling actuators, was modeled. In addition, the shroud covering the gap between the side of the nozzle and the booster skirt was not modeled. Despite the fact that additional damage to the CLV booster could result from a nozzle burn-through, for example, damage to the booster skirt, the effect of additional damage on booster controllability was not considered in this study. For all results presented in this section, those in which flow field details are depicted in the form of contour plots, a 5x107 cell grid was used with heavy clustering in the vicinity of the booster nozzle. Figure 4 shows axial-velocity component contours for a series of cutting planes from the transonic solution used in the grid refinement study shown in Figure 3. The nozzle exit is located at x = 30 m, the skirt ends at x = 28 m, and the elliptic burn-through is centered at x = 26.5 m, which is 3.5 m upstream of the nozzle exit (XP = 3.5 m). Orange contours represent the highest values for the axial-component of velocity, followed by yellow, green and finally; the blue contours represent the lowest values. The effect of the jet created by the nozzle exhaust gases issuing through

Figure 4. Axial-velocity-component contours in and around the CLV solid rocket nozzle with a burn-through hole centered at x = 26.5 m in the z = 0 plane, M∞ = 0.89, α = 0°, MET = 35 sec, h = 4622 m and Thrust = 11.5x106 N. The elliptical burn-through dimensions are 0.4 m x 0.25 m (0.314 m2).

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the burn-through hole on the surrounding flow field can be seen in the longitudinal and various cross-sectional views shown in this figure. The main nozzle is ideally expanded (or nearly so) for this trajectory point. The burn-through affects the main plume to only a small degree. With the burn-through hole in this location, a jet is created just downstream of the nozzle throat that impacts and is deflected by the booster skirt. This can be seen in the cross-sectional plots at x = 27 and 28 m. The deflected jet then flows downstream, paralleling the main nozzle plume. Details associated with the deflected jet can be seen in the cross-sectional views at x = 28, 29, 30 and 33 m. Figure 5 shows axial-velocity component contours for the same series of cutting planes as shown in Figure 4, but for a supersonic case near booster separation: M∞ = 4.49, α = 12.87°, MET = 114 sec, h = 45526 m and Thrust = 4.5x106 N. For this case the elliptic burn-through is centered at x = 27.5 m (XP = 2.5 m)—one meter downstream from the location used in Figure 4. Orange contours represent the highest values for the axial velocity component, followed by yellow, green and finally; the blue contours represent the lowest values. The main nozzle for this set of conditions is highly under expanded. The jet created by the nozzle exhaust gases issuing through the burn-through hole has a larger effect on the surrounding flow field than in Figure 4. The cross-sectional views presented at x = 28, 29 and 30 m, show details of the developing jet flow field. The flow between the nozzle and booster skirt is low speed and highly recirculatory.

A blow-up of the axial-velocity component contours shown for the x = 28 m cutting plane from Figure 5 is displayed in Figure 6 with in-plane particle traces included. This view is just downstream of the nozzle skirt. The cross-flow created by the 12.87 deg angle-of-attack is clearly evident. The jet created by the nozzle burn-through flows in the negative y-direction where it encounters the opposite-flowing cross flow. The low-speed recirculation between the nozzle and the skirt is also clearly evident in this figure.

Figure 5. Axial velocity component contours in and around the CLV solid rocket nozzle with an elliptic-shaped burn-through hole centered at x = 27.5 m in the z = 0 plane, M∞ = 4.49, α = 12.87°, MET = 114 sec, h = 44526 m and Thrust = 4.5x106 N. The elliptical burn-through dimensions are 0.4 m x 0.25 m (0.314 m2).

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Figure 6. Axial velocity component contours in the cross-sectional plane at x = 28 m from the solution shown in Figure 5. The elliptic-shaped burn-through hole is centered at x = 26.5 m in the z = 0 plane, M∞ = 4.49, α = 12.87°, MET = 114 sec, h = 44526 m and Thrust = 4.5x106 N. The burn-through hole dimensions are 0.4 m x 0.25 m (0.314 m2).

Figure 7 shows temperature contours for the same series of cutting planes as shown in Figure 4 and Figure 5, but for a supersonic case corresponding to the trajectory’s maximum dynamic pressure: M∞ = 1.31, α = 0°, MET = 49 sec, h = 9065 m, Thrust = 10.2x106 N, T∞ = 240 °K and γ = 1.4. For this case the elliptic burn-through hole is centered at x = 26.5 m (XP = 3.5 m)—the same location used in Figure 4. Red contours represent the highest temperatures, followed by yellow, green and finally; the blue contours are the lowest temperatures. As can be seen, the main nozzle for this set of conditions is slightly under expanded. The jet created by the nozzle exhaust gases issuing through the burn-through hole creates an interesting flow pattern in the region between the nozzle and the booster skirt and in the region beside the main plume downstream of the burn-through hole.

As seen from the cross-sectional view at x = 27 m, the jet impinges on the skirt, causing the temperature to dramatically increase in this location. As the present simulation utilizes a perfect gas assumption for both the external and internal flows and does not include viscous effects, it is impossible to determine how hot the actual skirt becomes, but it is clear from this simulation that the thermal loads on the skirt would be significant. In addition to the high temperatures experienced on the inside of the booster skirt, there is an elevated temperature created between the booster skirt and the nozzle. This region can be seen in the cross-sectional plot at x = 28 m and will be discussed in more detail subsequently.

Influence of the burn-through jet on the flow surrounding the booster nozzle is also clearly visible in this set of temperature contours. Instead of staying tightly coalesced, the burn-through flow spreads laterally around the main nozzle in the region downstream of the skirt and the nozzle/nozzle plume. This can be seen in the cross-sectional contour plots located at x = 28, 29, 30 and 33 m. Roll-up of the flow can be seen in various locations in this region of the flow field.

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The forward facing lip of the burn-through hole, which produces an elevated temperature due to the stagnation

point that forms in that location, can be seen in the main longitudinal view of Figure 7 just upstream of x = 27 m. This lip also creates a bow shock wave, which intersects the skirt on one side of the lip and emanates downstream inside the nozzle on the other side. The faint bow shock wave can be seen in the main longitudinal view, as well as in the cross-sectional views at x = 29, 30 and 33 m.

Figure 8 shows pressure contours for the same case as that displayed in Figure 7. Red contours represent the highest pressures, followed by orange, yellow, green and finally; the blue contours are the lowest pressures. Many of the same features that were prevalent in the temperature contours of Figure 7, can also be seen in Figure 8. For example, details of the burn-through hole lip shock can be seen in the main longitudinal view as well as several of the cross-sectional views, especially the cross-sectional plot at x = 29 m. An additional feature displayed in Figure 8 is the series of external shock waves that are created by the booster’s supersonic velocity.

Figure 7. Non-dimensional temperature contours at maximum dynamic pressure in and around the CLV solid rocket nozzle with an elliptical burn-through hole centered at x = 26.5 m in the z = 0 plane, M∞ = 1.31, α = 0°, MET = 49 sec, h = 9065 m, Thrust = 10.2x106 N, T∞ = 240 °K and γ = 1.4. The elliptical burn-through dimensions are 0.4 m x 0.25 m (0.314 m2).

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Figure 9 presents a blow-up view of the temperature contours from Figure 7, showing additional detail of the

flow in the vicinity of the burn-through hole. The contour labels to the right of the figure correspond to temperature values nondimensionalized by γT∞. In addition to the temperature contours, selected in-plane particle traces are plotted, which serve to define the direction of flow from the main nozzle through the hole and into the skirt region of the CLV booster geometry. The particle traces also help to define the jet created by the burn-through hole and the system of shock waves that are generated by the burn-through jet secondary flow. The bow shock from the hole lip reflects off the skirt and interacts with a second shock from the external nozzle wall to form a strong Mach disk between the nozzle and skirt. For the present ideal gas approximation, the temperature downstream of the Mach disk is nearly as high as that of the main nozzle flow.

Figure 8. Non-dimensional pressure contours at maximum dynamic pressure in and around the CLV solid rocket nozzle with an elliptical burn-through hole centered at x = 26.5 m in the z = 0 plane, M∞ = 1.31, α = 0°, MET = 49 sec, h = 9065 m, Thrust = 10.2x106 N, P∞ = 32.3 KPa and γ = 1.4. The elliptical burn-through dimensions are 0.4 m x 0.25 m (0.314 m2).

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Figure 9. Blow up of Figure 7 showing the non-dimensional temperature contours as well as streamlines constrained to the z = 0 plane in the region surrounding the burn-through hole.

Figure 10 presents a blow-up view of the pressure contours from Figure 8, showing additional detail of the flow

in the vicinity of the burn-through hole. The contour labels to the right of the figure correspond to pressure values nondimensionalized by γP∞. Note that these contour levels are not distributed in a linear fashion. They were selected so as to enhance the information content of the figure. In addition to the pressure contours, selected in-plane particle traces are plotted, which serve to define the direction of flow from the main nozzle through the hole and into the skirt region of the booster. This view is the same as that presented in Figure 8, except that the contours are pressure instead of temperature and that the particle traces have been selected in slightly different locations. The burn-through lip bow shock wave is more easily seen in this view, as it intersects the skirt on one side and extends downstream inside the nozzle on the other side. Note the large pressure load on the skirt, which is induced by the impinging burn-through jet.

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Figure 10. Blow up of Figure 8 showing the non-dimensional pressure contours as well as streamlines constrained to the z = 0 plane in the region surrounding the burn-through hole.

A. Summary of Force Data The next topic of discussion is associated with the force coefficient changes that are caused by the burn-through failure and whether or not the control authority provided by nozzle gimbaling will be sufficient to maintain control during the CLV boost phase. To answer this question four hole sizes have been considered at four different positions as displayed in Table 1. The parameter XP is the center of the hole measured along the x-coordinate direction from the nozzle exit plane in meters. The largest hole—corresponding to 3.142 m2 of area (case no. 10)—is only considered for one hole position—at XP = 0.0. A value of XP = 0.0 places the middle of the hole on the CLV main nozzle exit plane. Only half of the case 10 ellipse actually intersects the nozzle. Thus, only half of the area for this ellipse is actually removed from the nozzle’s surface. That’s why the hole area for case 10 appears to be a factor of two too low.

Computations were performed at four points along the launch trajectory in this study: a transonic point, the maximum dynamic pressure point, a supersonic point and a point near boost phase termination. The conditions at these four trajectory points are summarized in Table 2. Burn-through computations were performed at an additional trajectory point associated with subsonic flow (M∞ = 0.31), but are not included in this study because the results were unsteady, making conclusions at this speed difficult to discern.

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Table 1. Summary of burn-through hole geometries all elliptical in shape with the semi-major axis aligned with the free-stream direction and centered in the vehicle pitch plane (z = 0). XP is the distance upstream from the nozzle exit plane.

Case No. Position (XP) Semi-major axis Semi-minor axis Area

m m m m2

1 1.5 0.2 0.125 0.0785 2 1.5 0.3 0.1875 0.177 3 1.5 0.4 0.25 0.314 4 2.5 0.2 0.125 0.0785 5 2.5 0.3 0.1875 0.177 6 2.5 0.4 0.25 0.314 7 3.5 0.2 0.125 0.0785 8 3.5 0.3 0.1875 0.177 9 3.5 0.4 0.25 0.314

10 0.0 2.0 1.0 3.142

Table 2. Summary of flight conditions at each trajectory point for which computations were performed.

Parameter

units

Transonic flow

(point 1)

Max dynamic pressure (point 2)

Supersonic flow

(point 3)

Near booster cut off

(point 4)

Mission elapsed time, MET

sec 35 49 83 114

Mach number, M∞ — 0.89 1.31 3.00 4.49 Angle of attack, α deg 0 0 0 12.87 Dynamic pressure,

q∞ N/m2 lb/ft2

32506 679.0

39070 816.2

17475 365.6

2377.2 49.66

Altitude, h m ft

4622 15163

9065 29741

10865 80372

44526 146081

Thrust N lb

11.5 x106 2.59 x106

10.2 x106 2.30 x106

10.9 x106 2.44 x106

4.51 x106 1.01x106

Figure 11 shows a summary of the force coefficients computed in this study. The top row of plots shows axial force coefficient, normalized using a no-burn-through result, as a function of hole size with hole position (XP value) as a parameter. In nearly all cases there is a loss in axial thrust caused by the nozzle burn-through, but the amount of thrust loss is always less that 1% for the cases tested.

The bottom row of plots displayed in Fig. 11 shows the normal force coefficient (CN) minus the no-burn-through normal force coefficient (CN_NOBT) normalized by the axial force coefficient times 100. Thus, a value of 1.0 corresponds to a burn-through-produced normal force that is equal to 1% of the axial force. Because trajectory point 4 carries a significant normal force due to angle of attack, it was necessary to subtract the no-burn-through normal force (CN_NOBT) so that this trajectory point could be compared on the same basis as the other three trajectory points.

As can be seen from Fig. 11, the normal force is highest for trajectory points 2, 3 and 4 for case 10 (the largest burn-through hole area). It approaches but does not exceed 3% of the axial thrust, and thus, is easily controllable by the ability of the main nozzle to gimbal (assuming gimbal authority is not lost as a result of the failure). The reason the normal force for trajectory point 1 (transonic point) is not higher is due to the fact that the nozzle for this trajectory point is ideally expanded (or nearly so). The pressure difference across the burn-through hole, which is near the nozzle exit, is not as large for this case. Thus, the production of flow in the normal direction and the associated normal force is not as great.

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For the other cases considered in this study—cases 1 through 9—it can be seen that the transonic and maximum dynamic pressure trajectory points generally produce the largest normal forces and that these maximums occur for the largest burn-through holes that are closest to the nozzle throat (XP = 3.5). Nevertheless, the maximum normal force for these cases does not exceed 2% of the axial force.

As the free-stream Mach number increases the most critical hole position (for cases 1 through 9) shifts from XP

= 3.5 m (throat region) to a position near the end of the skirt (XP = 2.5 m). This is because the booster skirt blocks the burn-through jet flow, creating loads on the booster skirt that counteract the burn-through jet normal force. These counteracting skirt loads are largest when the burn-through hole is closest to the nozzle throat. If the skirt were to fail, as part of the nozzle burn-through failure, the resulting normal force distribution as a function of hole size and position that is presented in Fig. 11 would most likely be different, especially for the burn-through holes that were closest to the nozzle throat. Studying failures of the booster skirt in conjunction with the nozzle burn-through mode of failure was not part of the present study.

In all cases computed, the gimbal authority is easily sufficient to counteract the pitching moment caused by the nozzle burn-through side force, providing the ability to gimbal the nozzle is not disrupted by the burn-through failure.

VI. Concluding Remarks The CART3D flow solver has been used to compute the flow field about the Crew Launch Vehicle (CLV) with

various burn-through-failures in the booster’s nozzle. The purpose of these computations was to determine if the CLV with a nozzle burn-through will remain controllable during the launch phase by using standard nozzle gimbaling. Emphasis in this study is upon understanding how the various physical parameters—for example, hole size, hole position or mission elapsed time—affect the computed results. The final application of these results will be made in the CLV crew and vehicle risk assessment. In all scenarios studied the loss in axial thrust was less than 1%, and the burn-through normal force was less than 3% of the axial force, which is less than the maximum normal force generated via nozzle gimbaling. Thus, the nozzle burn-through failure mode will not produce a loss of

a) M∞ = 0.89 b) M∞ = 1.31 c) M∞ = 3.00 d) M∞ = 4.49

Figure 11. Axial and side force coefficient variation with burn-through hole size and position for four selected locations along the CLV trajectory, as indicated by Mach number.

0.98

0.99

1

1.01

XP = 1.5 mXP = 2.5 mXP = 3.5 mXP = 0.0

NO

RM

AL

IZE

D A

XIA

L F

OR

CE

XP = 1.5 m

XP = 2.5 m

XP = 3.5 m

XP = 0.0 m

XP = 1.5 m

XP = 2.5 m

XP = 3.5 m

XP = 0.0 m

XP = 1.5 m

XP = 2.5 m

XP = 3.5 m

XP = 0.0 m

-1

0

1

2

3

0.01 0.1 1 10

XP = 1.5 m

XP = 2.5 m

XP = 3.5 m

XP = 0.0 m

(CN

-CN

_N

OB

T)

/ C

Ax100

HOLE AREA -- m2

0.01 0.1 1 10

XP = 1.5 m

XP = 2.5 m

XP = 3.5 m

XP = 0.0 m

HOLE AREA -- m2

0.01 0.1 1 10

XP = 1.5 m

XP = 1.5 m

XP = 3.5 m

XP = 0.0 m

HOLE AREA -- m2

0.01 0.1 1 10

XP = 1.5 m

XP = 2.5 m

XP = 3.5 m

XP = 0.0 m

HOLE AREA -- m2

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controllability, providing the burn-through does not produce any additional failures in the gimbaling control mechanism.

Acknowledgments The authors wish to thank Veronica Hawke and Alexander Te for CAD support. Thanks also go to Jerry Yan and

Donovan Mathias for supporting this work.

References 1Gowan, Jr., J. W., “Ascent Trajectory Simulation for the Space Shuttle Launch Area Risk Assessment,” AIAA Paper No.

2005-6505, Aug. 2005. 2Beaty, J. R., Starr, B. R. and Gowan, Jr., J. W., “Ares-I-X Vehicle Preliminary Range Safety Malfunction Turn Analysis”,

AIAA Paper No. 2008-191, Jan. 2008. 3Aftosmis, M. J., Melton, J. E., and Berger, M. J., “Adaptation and Surface Modeling for Cartesian Mesh Methods,” AIAA

Paper No. 95-1725, June 1995. 4Aftosmis, M. J., Berger, J. J., and Melton, J. E., “Robust and Efficient Cartesian Mesh Generation for Component-Based

Geometry,” AIAA Journal, Vol. 36, No. 6, Jun. 1998, pp. 952-960. Proceedings

5Haimes, R. and Aftosmis, M. J., “On Generating High Quality ‘Water-Tight’ Triangulations Directly from CAD,” Proceedings of the International Society for Grid Generation 2002, ISGG, Jun. 2002.

6Pandya, S. A., Murman, S. M. and Aftosmis, M. J., “Validation of Inlet and Exhaust Boundary Conditions for a Cartesian Method”, AIAA Paper 2004-4837, Aug. 2004.