Martin

OPTIMAL VACUUM HOLE PLACEMENT IN BENT PIPE TO MAXIMIZE EXIT FLOW UNIFORMITY

A Masters Project Final Report

Presented to

The Designated Masters Project Committee

San José State University

In Partial Fulfillment

of the Requirements for the Degree

Masters of Science in Aerospace Engineering

by

Steven S. Martin

May 2011

© 2011

Steven S. Martin

ALL RIGHTS RESERVED

The Designated Masters Project Committee Approves the Thesis Titled

OPTIMAL VACUUM HOLE PLACEMENT IN BENT PIPE TO MAXIMIZE EXIT FLOW UNIFORMITY

by

Steven S. Martin

APPROVED FOR THE DEPARTMENT OF AEROSPACE ENGINEERING

SAN JOSÉ STATE UNIVERSITY

May 2011

ABSTRACT A computational investigation of supersonic flow in a bent pipe was conducted to assess the ability of a suction hole to decrease separation and improve exit flow uniformity. Many spacecraft and aircraft have a bent pipe feature included in the primary nozzle, the engine bleed or turbine exhaust redirect, or elsewhere in the plumbing. The flow’s difficulty in turning such bends is common knowledge, as separation and shock waves are easily and frequently observed. These phenomena have been shown to degrade and often decrease the predictability of the performance of the system. Thus, a means of improving the behavior would have extensive positive influence. The thrust vectoring literature was surveyed to develop a better understanding of internal flow behavior, and to learn about the various ways flow can be redirected. An exit “Flow Uniformity Parameter” (FUP) was established based on flow variables that have a direct impact on the thrust performance. Computational Fluid Dynamics (CFD) was employed to demonstrate that a suction hole can indeed improve the FUP in the pipe by bending the flow, similar to suction’s contribution in thrust vectoring. Automation and improved initialization and post-processing strategies were studied and implemented to reduce user-interface time as CFD was used to experimentally determine optimization of the FUP by varying certain geometric and flow parameters. Findings that improve the FUP include larger holes and smaller inlet pressures and bend angles. The optimal hole location only changed when the bend angle was decreased. As a result of this work, optimal placement and size of suction holes can be determined for a set of conditions and geometric dimensions. This technology can be implemented in countless aircraft and spacecraft to improve engine performance and predictability.

ACKNOWLEDGEMENTS

The author would like to acknowledge Adrienne Toh and Jerry Ockerman for the years of assistance they provided to Lockheed Martin employees who were pursuing a graduate degree through San Jose State University. They made application and enrollment easier to achieve, requirements and expectations easier to understand, and paperwork easier to complete.

Also of particular help were Yvette Fierro and Angela Wayfer who assisted with the completion and submission of forms relating to grades.

Lastly, the Committee deserves recognition for their insight and expertise, and their flexibility regarding timelines and geographic inconveniences.

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TABLE OF CONTENTS

1 INTRODUCTION…………………………………………………………......……..…1

2 GEOMETRIES……………………………………………………………………….....2 2.1 NOMINAL………………………………………………………………...……...2 2.2 BEND ANGLE……………………………………………………………………2 2.3 HOLE LOCATION AND SIZE…………………………………………………..3

3 METHODOLOGY…………………………………………………………………...…4 3.1 ANALYSIS MODELING………………………………………………………...5

3.1.1 LITERATURE……………………………………………………………...5 3.1.1.1 DEFINITION OF THRUST VECTORING……………………….…5 3.1.1.2 IMPORTANCE OF THRUST VECTORING………………….…….5 3.1.1.3 WAYS OF ACHIEVING THRUST VECTORING…………….……5 3.1.1.4 RESULTS AND COMPARISON……………………………………6

3.1.2 DETERMINATION OF FUP………………………………………………6 3.2 COMPUTATIONAL EXPERIMENT……………………………………...…….9

3.2.1 APPROACH………………………………………………………...……...9 3.2.2 ASSUMPTIONS…………………………………………………………..10 3.2.3 TOOLS…………………………………………………………………….11

3.2.3.1 MODELING AND MESHING………………………………….…..11 3.2.3.2 CFD…………………………………………………………….……11 3.2.3.3 DATA EXTRACTION AND PLOTTING FLOW FIELDS…….….11 3.2.3.4 DATA ORGANIZATION AND PLOTTING TRENDS…………...11

3.2.4 VALIDATION…………………………………………………………….11 3.2.5 RANGE OF MEASUREMENT……………………………………...…...11 3.2.6 MESH PARAMETERS…………………………………………………...12 3.2.7 FLUENT SETTINGS…………………………………………………......13

4 RESULTS AND DISCUSSION………………………………………………...……..15 4.1 OBJECTIVE 1: IMPROVE FLOW……………………………………………...15

4.1.1 RETARD SEPARATION…………………………………………………15 4.1.2 IMPROVE FLOW UNIFORMITY AT EXIT ……………………………17

4.2 OBJECTIVE 2: OPTIMIZATION…………………………………………...….18 4.2.1 DECREASING FUP FURTHER………………………………………….19 4.2.2 OPTIMIZING LOCATION……………………………………………….22

4.3 OBJECTIVE 3: IMPROVE CFD SKILLS……………………………...………24 4.3.1 BOUNDARY CONDITIONS……………………………………………..24 4.3.2 PATCH INITIALIZATION………………………………………….…....24 4.3.3 FMG INITIALIZATION……………………………………………….….25 4.3.4 INTERPOLATION INITIALIZATION……………………………….......26 4.3.5 AUTOMATION…………………………………………………………...27 4.3.6 CUSTOM FIELD FUNCTIONS…………………………………………..28

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5 CONCLUSIONS…………………….……………………………………….....……..29

6 FUTURE WORKS………………………………………………………………..…...30 6.1 OMISSIONS……………………………………………………………...……..30 6.2 ALTERNATIVES……………………………………………………………....30

REFERENCES……………………………………………………………………..……31

APPENDIX A: THE NEED FOR A 3D ANALYSIS………………………….………..32

APPENDIX B: SAMPLE BOUNDARY CONDITION FILE…………………………..33

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NOMENCLATURE A cross-sectional area Ae cross-sectional area at the exit CFD computational fluid dynamics COTS commercial off the shelf F/l effective force (per unit length) at exit node FMG full multigrid FUP flow uniformity parameter ID internal diameter Loc hole location M/l moment (per unit length) at exit node due to thrust m mass flow rate .

Nominal 15 deg, 0.075”ID, Pc 821 P static pressure, psi Pc chamber or inlet pressure, stagnation Pe static pressure at exit Pex thrust normalized by Ae q dynamic pressure T thrust TUI text user interface v velocity ve exit velocity y distance from exit center (in exit plane) θ pipe bend angle ρ density

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LIST OF EQUATIONS

2

21 vq ××= ρ (1)

vAm ××=•

ρ (2)

eeee APvAT ×+××= 2ρ (3)

eATPex = (4)

⎟⎠⎞

⎜⎝⎛ −

×= −+

211 ii

ii yy

PexlF

(5)

⎟⎠⎞

⎜⎝⎛ +

= −+

211 ii

fiyy

y (6)

fiii y

lF

lM

×= (7)

∑=

=n

i

iT

lM

lM

1 (8)

( ) TMPexstdevFUP ×= (9)

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LIST OF FIGURES Figure 1: Flow Problem in Bent Pipe……………………...………………………...……1 Figure 2: Nominal Geometry and Conditions……………………………………...…......2 Figure 3: The 10 Degree Bend………………………………………………………........2 Figure 4: The 15 Degree Bend………….…………………………………………...........3 Figure 5: The 20 Degree Bend ……………………………………………………...……3 Figure 6: Hole Location and 0.075” ID……...……………………………………...……3 Figure 7: Small 0.05” ID Holes……………………………………………………...…...4 Figure 8: Large 0.1” ID Holes………….…………………………….……………...…...4 Figure 9: Uneven Exit Thrust…………………..………………………………….....…..6 Figure 10: Exit Symmetry Line……………..……………………………………...…….7 Figure 11: Pex Along Exit Symmetry Line……………………………...………….....…8 Figure 12: Thrust/l Along Exit Symmetry Line…….……………………………...….....9 Figure 13: Mass Flow As Evidence of Convergence……..………………………….…10 Figure 14: The Mesh, from GAMBIT……….…………………………………….....…13 Figure 15: Separation After Bend…………………………………………………..…...15 Figure 16: Improved Separation Due to Hole………..……………………………….…16 Figure 17: Swirling in Separation Region with No Hole…………….……..……...……16 Figure 18: Hole Corrects Swirling…………………………………………...…….....…17 Figure 19: Exit Velocities without and with a Hole…………………………….........…17 Figure 20: Exit Pex without and with a Hole….…………………………………...…...18 Figure 21: FUP for Varying Hole Location, Nominal Conditions……………….......…19 Figure 22: Minimum Achievable FUP for Each Bend Angle…..………………………20 Figure 23: Minimum Achievable FUP for Each Inlet Pressure…….………..............…21 Figure 24: Minimum Achievable FUP for Each Hole Diameter……………..….......…21 Figure 25: Optimal Hole Location for Each Inlet Pressure……………...……………..22 Figure 26: Optimal Hole Location for Each Hole Diameter ……………………......…23 Figure 27: Optimal Hole Location for Each Bend Angle………………………………23 Figure 28: Case Initialized from Inlet………………………………………….….....…25 Figure 29: Case Patch Initialized…………………………………………………….....25 Figure 30: Case Initialized with FMG……………………………………………...…..26 Figure 31: Interpolation Initialization Misused……...………………………...…….....27 Figure 32: 2D vs 3D Geometry…………………………………………………….…..32

x

xi

LIST OF TABLES Table 1: The Run Matrix…………………………………………………………...…....12 Table 2: The Boundary Layer Specifications…….……………...…………………....…13 Table 3: The Volume Mesh Specifications ………………………………………..……13 Table 4: FUP Comparison Without and With Hole………..…………………………....18

1 INTRODUCTION

This paper presents the results of a study of supersonic flow in a slightly bent pipe, which demonstrates that a strategically placed vacuum hole is a viable technology for improving separation and exit flow uniformity. The difficulty of high speed flow turning a bend in a pipe has been observed in the working designs of several spacecraft’s propulsion plumbing systems. Figure 1 shows an example of this difficulty in a generic bent pipe.

850

450

exit non- uniformity

50

Figure 1: Flow Problem in Bent Pipe velocity vectors colored by total pressure (psi)

Measurable degradation in performance and predictability has been noted due to separation after the bend, off-axis thrust, and a lack of uniformity in exit flow. This behavior is undesirable, and thus, a method was sought that could improve it. The desired result of turning quasi-one-dimensional flow is essentially what thrust vectoring is. It was wondered if the same technology used to turn exhaust in a nozzle could be used to help flow turn in bent pipes, thus improving the performance and predictability of the familiar design.

So a literature review was conducted to identify the several ways thrust vectoring can be achieved, as well as to gain academic knowledge such as the benefits of a thrust-vectored aircraft and the associated losses in efficiency of engine performance. Several American Institute of Aeronautics and Astronautics (AIAA) journals and papers were reviewed to determine the methods for thrust vectoring include moving flaps and other surfaces, gimbaling the nozzle or entire engine, and mass injection or suction. The manipulation of pressure forces on the engine and the mass flow exit direction create a torque on the vehicle that improves maneuverability and reduces take off and landing distance. Additionally, thrust vectoring is a primary means of spacecraft orientation. The fluidic injection method requires minimal engine bleed, is capable of bending the exhaust up to 16 degrees, and can drastically reduce the weight of the engine compared to a gimbaled one.

Any of these methods seem to be capable of helping the pipe flow turn the bend. The fact that the pipe is bent means it could already be categorized as gimbaled, and indeed the flow does noticeably change directions along with the pipe. Yet there are still problems with the flow, so additional improvements are needed. Mass injection would probably accomplish the desired results, but as previously stated, it would require a

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percentage of bleed. The intended operating environment is outer space, so the suction method seems the most applicable to the bent pipe design because the lack of ambient pressure could be leveraged to create a vacuum. It is hypothesized that an appropriately placed suction hole has the ability to improve exit flow uniformity in a bent pipe by helping it turn, parameters can be determined to optimize this effect, and Computational Fluid Dynamcs (CFD) software can be employed to demonstrate this technology. The primary objective of this work is to show the effectiveness of the vacuum hole. The secondary objective is to show that there is an optimal location and size of such a hole, given certain flow and geometric parameters. The tertiary objective is to improve CFD skills, including efficiency.

2 GEOMETRIES

The bent pipe geometry has a circular cross section. A narrow inlet piece stair-steps up to the larger main portion, which is bent. A hole in the pipe wall is placed at various locations downstream of the bend.

2.1 NOMINAL

Figure 2 shows the nominal geometry and conditions. Nominal may refer to these parameters with no hole (Loc 0), or with a hole at Loc 1, depending on context.

821 psia 0.001 psia 2390 R 410 R 0.20” ID pressure inlet

0.001 psia 0.075” ID

hole

410 R 0.30” ID pressure outlet

0.375” 0.50” 0.90” 15° bend

Figure 2: Nominal Geometry and Conditions

2.2 BEND ANGLE Three different bend angles were analyzed. These were 10, 15, and 20°. Figures 3, 4, and 5 show these geometries. The bent section is deflected at the upper (or inner) corner, meaning the bottom length is based on the angle.

pivot

point 10°

Figure 3: The 10 Degree Bend

2

2.3 HOLE LOCATION AND SIZE

The four different possible hole locations are shown in Figure 6. Loc 1 places the hole just downstream of the bend. Loc 2 is one nominal ID (0.075”) downstream of Loc 1. Loc 3 is tangent to Loc 2 and so on. Only one hole is considered at a time. The no hole case is referred to as Loc 0.

0.075”

Figure 5: The 20 Degree Bend

Figure 4: The 15 Degree Bend

1 2 3 4

Figure 6: Hole Location and 0.075” ID

3

The position of the hole is dependent on the location number only, not the ID. The hole spacing is still 0.075” regardless of ID. Figure 7 shows the small holes’ locations and the gaps between them.

0.05” 0.075”

1 2 3 4

Figure 7: Small 0.05” ID Holes

Figure 8 shows the large holes and their overlap, due to the spacing being smaller than the ID. Note the hole centers are in the same position as the corresponding location number for the other IDs.

0.1” 0.075”

1 2 3 4

Figure 8: Large 0.1” ID Holes

3 METHODOLOGY

This section addresses the analytical and experimental approaches, including the literature review and how it was used to establish a relevant FUP, and the assumptions, tools, run matrix, and geometries for CFD.

4

3.1 ANALYSIS MODELING A literature review for thrust vectoring was conducted to establish expectations of performance and capabilities for various designs. Once the physics were sufficiently understood, a determination was solidified that flow uniformity would be the characteristic whose improvement was sought. A definition of a flow uniformity parameter (FUP) was developed, and a means of extracting the FUP from each case was decided.

3.1.1 LITERATURE Several AIAA journals and papers were reviewed to develop a background understanding of thrust vectoring, what it is, how it is achieved, and why it is important.

3.1.1.1 DEFINITION OF THRUST VECTORING Thrust vectoring is when exhaust gasses in an engine are manipulated to create a torque on an aircraft or spacecraft. This is achieved by an imbalance of pressure forces on the engine, as well as a redirection of mass flow direction at the exit5.

3.1.1.2 IMPORTANCE OF THRUST VECTORING Aircrafts are able to manipulate external aerodynamic control surfaces to create pressure differentials on the body, and thus are able to change direction and orientation. Thrust vectoring can be utilized to increase the torque that the aircraft experiences, increasing the maneuverability and agility4. It can enable post-stall control and can reduce takeoff and landing distances6. Additionally, the amount of necessary control surfaces can be reduced, decreasing drag and radar signature4. Thrust vectoring is essential to a spacecraft’s ability to orient itself in orbit, due to the lack of air in space2.

3.1.1.3 WAYS OF ACHIEVING THRUST VECTORING The original method for thrust vectoring was to use control surfaces inside the nozzle, or more extremely, to gimbal a large portion of the engine and nozzle. However, moving large masses of hardware requires additional weight and slows the response time5. More recently, fluidic injection has been implemented in either supersonic or subsonic portions of the nozzle2. Introducing small amounts of engine bleed or primary flow downstream of the throat not only changes the mass and energy of the system, but it produces a series of oblique shock waves that also alters the local wall pressure. Consequently, thrust is reduced through each of the shocks3. Throat shifting methods utilize inject just upstream of the throat, where the subsonic flow is more easily turned3. Opposite of fluidic injection is fluidic suction, which often leverages ambient low pressure conditions to draw minimal gas out of the nozzle, thereby altering local pressure and turbulence4. A variant of normal suction is counterflow, which uses suction at the throat to create a

5

secondary shear jet between the primary jet and the wall. Due to pressure loss, this bends the exhaust toward the secondary jet3.

3.1.1.4 RESULTS AND COMPARISON By employing fluidic methods rather than gimbaling, it is estimated that nozzle weight can be reduced by as much as 80%. The lack of complexity and mechanical demand may also save up to 50% of maintenance costs5. Response time may be as little as 20 milliseconds for fluidic methods2. Subsonic injection incurs lower losses in thrust than supersonic injection due to the avoidance of shocks3. Counterflow’s secondary jet isolates control surfaces and engine walls from the hot exhaust gas, which reduces observability and the need for an independence cooling system6. However, counterflow can lead to hysteresis and can be difficult to integrate in the design3. Depending on the thrust vectoring method, a fluidic injection rate of between 1.25-6% is needed, leading to around 4% loss in thrust. But the exhaust jet has been shown to be able to bend up to around 16 degrees6.

3.1.2 DETERMINATION OF FUP The intended goal was to improve flow uniformity at the exit of the pipe. There are a number of ways that the term “flow uniformity” can be defined. A major problem with flow in bent pipes is that the flow produces a moment about the exit due to imbalanced pressure forces and off-axis thrust angle. When designing a nozzle or exhaust pipe, the thrust is typically assumed or intended to be normal to the exit and symmetrical about that center, thus eliminating the need to consider torque. However, the thrust coming out of a bent pipe is not normal to the exit plane, nor is it evenly distributed about the center. See Figure 9 for an example.

140

135

larger thrust at the bottom

130 Figure 9: Uneven Exit Thrust

velocity vectors colored by static pressure (psi)

6

The most important effect a vacuum hole could have to make the bent pipe behave like a straight one is to minimize the moment at the exit. That is, the thrust curve would be symmetric about the exit centerline. The thrust near the edges would also be similar to the thrust at the center. Thrust can be calculated using Equation 3. However, defining this equation in the Custom Field Function menu option (CFF) in the COTS CFD tool ANSYS FLUENT is difficult because of the area term. Areas of established faces and surfaces can be calculated, but correlating the area of each individual cell in the exit face with its own density, velocity, and pressure values would be a daunting task. So the area term was divided out of Equation 3, and the result was Equation 4 for a new variable, Pex. Pex was defined in the CFF, and it was calculated at each node in the exit symmetry line as identified in Figure 10.

axis

exit plane

exit symmetry line

Figure 10: Exit Symmetry Line A text file of the Pex value at each node was written out for every case, and the data was manipulated and plotted in Microsoft Excel. Figure 11 shows an the plotted Pex data for the nominal case.

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0

100

200

300

400

500

600

700

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15

Distance (in Symmetry Plane) from Exit Axis (in)

Pex

(psi

)

Figure 11: Pex Along Exit Symmetry Line Pex has units of pressure, so Pex should be multiplied by an area to get a force (and ultimately a moment). Since the Pex data file organizes the Pex values according to the x-coordinate of each node on the exit symmetry line, the distance between nodes was easily determined. In the absence of cell area information, Pex was simply multiplied by the cell length (or local node spacing) using Equation 5. This resulted in units of force per length, which though technically not a force, is still effective in determining relative moments for FUP comparison sake. These “force” vectors were applied at their own respective nodes, resulting in a loading as demonstrated in Figure 12.

8

0

5

10

15

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15Distance (in Bend Plane) from Exit Axis (in)

F/l (

lb/in

) lever arm

“force” vector

Figure 12: Thrust/l Along Exit Symmetry Line Each F/l dot in Figure 12 should have a “force” vector pointing down, yet only two vectors were drawn to show the imbalance in forces, which causes a moment. This “moment” (taken from the center of the exit symmetry line) was calculated for each F/l using Equations 6 and 7. The individual moments were summed with Equation 8 to get the total moment, and the total moment was multiplied by the standard deviation of Pex in Equation 9 to determine the FUP.

3.2 COMPUTATIONAL EXPERIMENT The following sections describe the methodology for satisfying the objectives, the assumptions that were made, the software tools used to generate meshes and run CFD, and the run matrix.

3.2.1 APPROACH

The general approach to satisfying the three objectives was to use CFD to experimentally demonstrate a suction hole’s effectiveness at improving the FUP, and to determine optimal parameters. First, the nominal case was modeled, a mesh was generated, and CFD was run on it. A velocity vector plot of the converged solution qualitatively verified separation and exit non-uniformity. See Figure 1. A second case was converged, identical to the first except with a vacuum hole just downstream of the bend. The FUPs for both cases were calculated, and the suctioned case’s FUP was found to be lower. Then a list of features was determined such that parametrically varying them and noting the FUP for each case would yield trend lines from which optimization could be

9

identified. A run matrix was established that included all the desired parametric variations, while being small enough that completion time was realistic. The different geometries were all modeled, meshed, and solved with CFD, utilizing advanced time saving techniques whenever possible. The mass flow rate iteration history was selected as a measurement of convergence, and it was closely monitored for each case. Once converged, relevant variable data was extracted from a case. The data was manipulated and plotted, and trends and optimization were discovered.

3.2.2 ASSUMPTIONS The effectiveness of the suction hole increases with decreasing ambient pressure. Thus, the maximum effect would occur in space. Since CFD needs to model an actual fluid in order to solve the Navier-Stokes equations, the true vacuum of space is not solvable. Instead the pressure was approximated to 0.001 psia, and 410 R. These conditions were assumed to be a sufficient representation of space. A CFD solution was assumed to be converged when the mass flow rate through the exit was converged, or stopped noticeably changing with each iteration. Figure 13 shows a sample mass flow monitor.

0.065

0.066

0.067

0.068

0 5000 10000

Iterations ( )

Mas

s Fl

ow R

ate

Thro

ugh

Exit

(kg/

s)

flat-line indicates convergence

15000

Figure 13: Mass Flow as Evidence of Convergence

10

3.2.3 TOOLS

Software was used to create geometries, run CFD, and interpret the data.

3.2.3.1 MODELING AND MESHING All models and meshes were created using COTS ANSYS GAMBIT v. 2.4.6.

3.2.3.2 CFD All CFD computations were performed using COTS ANSYS FLUENT v.12.1. Processing was done in parallel using a:b = 3:8, 2:8, 1:8, and/or 1:4, where “a” is the number of nodes, and “b” is the number of processors per node. The processor allotment was based purely on availability.

3.2.3.3 DATA EXTRACTION AND PLOTTING FLOW FIELDS Because the FLUENT parallel licenses were consistently exhausted by the cases being iterated, much, if not all of the CFD data was extracted using COTS ANSYS FLUENT v. 6.3.26, as it was easily accessible in serial, which did not count against the allowable parallel license number.

3.2.3.4 DATA ORGANIZATION AND PLOTTING TRENDS

Data was stored, organized, and plotted using Microsoft Office Excel v. 2003. This includes monitoring the progress of the run matrix, calculating the FUP values, and interpolating or extrapolating to determine optimizations.

3.2.4 VALIDATION ANSYS FLUENT has extensive information on their validation on their website

3.2.5 RANGE OF MEASUREMENT Three different inlet total pressures, three vacuum hole diameters, three pipe bend angles, and four hole locations (plus a no-hole geometry) were considered. FUP trends were sought for each parameter individually, so not every combination of parameter pairings was required to satisfy the objective. The run matrix is included in Table 1. The grayed out cases, case 5 and case 25, were identical to case 19. Thus they were not rerun.

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Table 1: The run Matrix Case No Inlet Temperature Inlet Pressure Hole Diameter Bend Angle Hole Loc

( ) ( R) (PSI) (in) (deg) ( )1 1892.2 650 0.075 15 12 1892.2 650 0.075 15 23 1892.2 650 0.075 15 34 1892.2 650 0.075 15 45 2390 821 0.05 15 06 2390 821 0.05 15 17 2390 821 0.05 15 28 2390 821 0.05 15 39 2390 821 0.05 15 4

10 2390 821 0.075 10 011 2390 821 0.075 10 112 2390 821 0.075 10 213 2390 821 0.075 10 314 2390 821 0.075 10 415 2390 821 0.075 15 016 2390 821 0.075 15 117 2390 821 0.075 15 218 2390 821 0.075 15 319 2390 821 0.075 15 420 2390 821 0.075 20 021 2390 821 0.075 20 122 2390 821 0.075 20 223 2390 821 0.075 20 324 2390 821 0.075 20 425 2390 821 0.1 15 026 2390 821 0.1 15 127 2390 821 0.1 15 228 2390 821 0.1 15 329 2390 821 0.1 15 430 2911.1 1000 0.075 15 131 2911.1 1000 0.075 15 232 2911.1 1000 0.075 15 333 2911.1 1000 0.075 15 4

mesh?

xxxx

xxxx

xxxx

xxxx

xxxx

The inlet pressures were varied, and the ratio of inlet temperature to inlet pressure was held constant.

3.2.6 MESH PARAMETERS

A separate mesh was created for each of the various geometries, while varying inlet pressure did not require additional meshing. The no-hole cases also did not require their own meshes because the hole face boundary was changed to a wall in FLUENT. In all, 20 meshes were needed. See Table 1’s final column for a list. With the exception of the minor geometric differences, the meshes all used the

12

same strategy and parameters, and were thus nearly identical. Each mesh consisted of a triangular prism boundary layer, whose parameters are in Table 2.

Table 2: Boundary Layer Parameters Number First Cell Last Cell

of Rows Height (in) Percent20 1.00E-04 50

Internal EdgeContinuity? Corner?

yes yes

Mesh SF Growthon BL? Rate

yes 1.2

Unstructured tetrahedrons were grown from the final boundary layer row into the volume. Volume parameters are in Table 3.

Table 3: Volume Mesh Parameters Number

of Cells~400,000

Figure 14 shows an example of one of the meshes. Cells were concentrated at the bend, at the exit, and near the hole. Symmetry in the problem was leveraged in order to save time by only modeling, meshing, and solving half of each geometry.

Figure 14: The Mesh, from GAMBIT

3.2.7 FLUENT SETTINGS The following is a list of the settings used in FLUENT, tabbed to represent directory and menu location, and commented to explain rationale (where necessary).

13

File Autosave % automatically writes files for recovery purposes cas: 1000 iterations dat: 1000 iterations location: correct directory %directories organized according to

%run matrix parameters Grid scaled: (x,y,z) = (0.0254, 0.0254, 0.0254) %created in in., read as m reorder: domain %to reduce bandwidth and iterate faster Define Models Solver: density %Mach# ~ 3, pressure solver will diverge Green-Gauss node based implicit Energy: on %compressible flow Viscous: k-omega:

SST Materials: air: %technology demonstrated regardless of species density:

ideal gas %compressible, uninterested in real %gas effects

Operating Conditions: 0 psi %makes ambient pressure = gauge pressure Boundary Conditions pressure inlet: gauge total pressure: 821 PSI supersonic/initial gauge pressure: 791.44 PSI intensity and viscosity ratio: 10%, 10 total temperature: 2390 R pressure outlet gauge pressure 0.001 PSI %to simulate vaccum intensity and viscosity ratio: 10%, 10 backflow total temperature: 408.57 R Custom Field Functions

see section 4.3.6 Solve Controls Roe-FDS all first order upwind %speed up convergence,

%uninterested in 2nd order fidelity

14

Monitors Residuals: no convergence criteria %avoid iteration termination Surface Monitors: mdot through exit %converged mdot assumed

%converged solution

4 RESULTS AND DISCUSSION The run matrix was completed. Various qualitative observations and quantitative calculations were made that prove the viability of the suction hole as a means of improving flow.

4.1 OBJECTIVE 1: IMPROVE FLOW Two cases were run initially to prove that the flow could be improved with a vacuum hole. The nominal geometry (Loc 0) and conditions, and the nominal geometry (Loc 3) and conditions were compared.

4.1.1 RETARD SEPARATION

The flow in the pipe without the hole clearly separates just after the bend. There is a drop in velocity magnitude, and it changes direction. See Figure 15. The line at the separation region is used as a cutting plane for Figure 17.

800 cutting plane

separation

450

100

Figure 15: Separation After Bend velocity vectors colored by total pressure (psi)

The flow in Figure 16 with the addition of the hole is clearly more attached. The velocity does not experience a drastic decrease in magnitude, and the flow is moving parallel to the pipe.

15

800 cutting plane improved

separation

450

100

velocity vectors colored by total pressure (psi)

Figure 16: Improved Separation Due to Hole Also note the differences in velocity vectors of the cross section just after the bend, in Figures 17 and 18. Without a hole, the flow swirls perpendicular to the symmetry plane. Though it damps slightly as the flow moves down the pipe, some swirling is still present at the exit, meaning the exit flow is not uniform. These effects prevented the geometry from being modeled two-dimensionally.

1200

600

0

velocity vectors colored by magnitude (m/s)

Figure 17: Swirling in Separation Region with No Hole

16

Figure 18: Hole Corrects Swirling

velocity vectors colored by magnitude (m/s)

The suction of the hole keeps the flow going mostly axial, though some goes out the hole. This axial flow keeps thrust deviation at a minimum.

4.1.2 IMPROVE FLOW UNIFORMITY AT EXIT Both velocity magnitude and Pex were observed in the exit plane as a way of qualitatively observing improvement in exit uniformity. Figure 19 shows the velocities without and with a hole.

no hole

600

with hole

reduced “slow” region

1000 Figure 19: Exit Velocities without and with a Hole

velocity contours colored by magnitude (m/s)

17

Figure 20 compares the Pex contours with similar conclusions. The blue area of reduced Pex is greatly reduced with the addition of the hole. Due to the blue area being only on one side (the top) of the exit, the misbalance of thrust causes a moment. This moment is stronger without the hole.

Standard Dev Moment FUPPex (psi) M/l (lbf) (lbf/in)^2

Nom Loc 0 128.63 2.59 333.14Nom Loc 3 133.25 1.86 248.51

4.5

no hole

1

reduced “low thrust” region

Figure 20: Exit Pex without and with a Hole Pex contours x 1E6 (psi)

with hole

Table 4 quantifies the improvement in FUP with the addition of the hole (Loc 3).

Table 4: Hole Improves FUP

A smaller FUP for the case with the hole means the flow’s uniformity was improved, thus satisfying the first objective.

4.2 OBJECTIVE 2: OPTIMIZATION It has been shown that a suction hole does improve the exit flow uniformity. However, moving the hole’s locations changes the value of FUP. The optimal hole location was sought, so all four hole locations were analyzed for the nominal geometry and conditions. The FUP for each case was determined, and the results are plotted in Figure 21.

18

15 Deg, 0.075"ID, Pc 821

200

300

400

0 0.5 1 1.5 2 2.5

Hole Location ( )

FUP

(lb/in

)^2

333

minimum FUP, 250

3.1

3 3.5 4

Figure 21: FUP for Varying Hole Location, Nominal Conditions The minimum FUP (for this geometry and these conditions) is achieved with a hole placed between location 3 and location 4. By interpolating, a location of 3.1 seems appropriate. So 3.1 is the optimal hole location to maximize flow exit uniformity for the nominal conditions and geometry. The identification of such a relative minimum technically satisfies objective 2, but many additional trends can still be easily noted. The green dot in Figure 21 will be addressed in section 4.2.1.

4.2.1 DECREASING FUP FURTHER All four hole locations were analyzed for each of the three bend angles. The minimum FUP was determined for each bend angle (based on hole location as in Figure 21). These minimum FUPs are plotted in Figure 22. Not surprisingly, the smaller the bend angle, the smaller the FUP. This means that exit flow uniformity improves with a shallower bend.

19

0.075"ID, Pc 821400

200

100

200

300

10 15

Bend Angle (deg)

FUP

Min

(lb/

in)^

2310

Figure 22: Minimum Achievable FUP for Each Bend Angle

The green dot in Figure 21 represents the FUP for the nominal case, 15 degree bend, with no hole. The green dot in Figure 22 represents the FUP of a 20 degree bend with a 0.075” ID hole optimally placed. Notice that the 20 degree bend’s FUP with the hole (310) is less than the 15 degree bend’s FUP (333) without the hole. This means that a suction hole can enable a 20 degree bend to behave even better than a 15 degree bend, which is quite remarkable.

All four hole locations were analyzed for the three inlet pressures. The optimal FUP for each pressure is plotted in Figure 23. Larger inlet pressure values cause less uniform exit flow, most likely due to the fluid having a larger momentum, and thus, a more difficult time turning the bend. FUP is reduced when the inlet pressure is reduced.

20

21

15 Deg, 0.075"ID

0

100

200

300

400

500

500 600 700 800 900 1000

Pc (psi)

FUP

Min

(lb/

in)^

2

Figure 23: Minimum Achievable FUP for Each Inlet Pressure All four hole locations were analyzed for each of the three hole diameters. The optimal FUP for each diameter is plotted in Figure 24. Larger holes have a larger suction ability, meaning the FUP will be smaller.

15 Deg, Pc 821

200

250

300

0.05 0.06 0.07 0.08 0.09 0.1Hole ID (in)

FUP

Min

(lb/

in)^

2

Figure 24: Minimum Achievable FUP for Each Hole Diameter

Based on these curves, the minimum achievable FUP (for a given set of conditions, only one being allowed to vary) decreases when the hole ID is increased, and when the bend angle and inlet pressure are decreased.

4.2.2 OPTIMIZING LOCATION

The optimal hole location (for minimum FUP) was noted for each parametric series. Figure 25 shows the optimal location versus inlet pressure.

15 Deg, 0.075"ID

3

3.1

3.2

3.3

500 600 700 800 900 1000Pc (psi)

Opt

imal

Loc

atio

n ( )

Note that the best placement for the nominal geometry is near Loc 3, with the ideal spot moving slightly downstream with decreasing inlet pressure.

Figure 25: Optimal Hole Location for Each Inlet Pressure

The optimal hole location was found for each hole ID, and the results are plotted in Figure 26. There does not seem to be a strong correlation between these two. Interestingly though, the hole is still best placed near Loc 3.

22

15 Deg, Pc 8213.15

Opt

imal

Loc

atio

n ( )

3

3.05

3.1

0.05 0.06 0.07 0.08 0.09 0.1

Hole ID (in)

Figure 26: Optimal Hole Location for Each Hole Diameter Figure 27 plots optimal location against bend angle. As with the nominal geometric variations, the 20 degree bend’s best placement is near Loc 3. This means that for most geometries, the same hole location could be used without the need for much analysis. However, the 10 degree bend needs the hole somewhere near the theoretical Loc 6, which was determined by extrapolation.

0.075"ID, Pc 821

0

1

2

3

4

5

6

7

10 15 20

Bend Angle (deg)

Opt

imal

Loc

atin

( )

Figure 27: Optimal Hole Location for Each Bend Angle

23

It is interesting to note that the flatter the bend, the farther downstream the hole should be. An argument could be made that a Loc 3 could be employed indiscriminately because it would improve high bend angles’ FUP, while flatter bends’ flows are sufficiently uniform that they do not necessitate the hole technology. Or perhaps a mechanism to vary hole location for varying angle could be implemented.

4.3 OBJECTIVE 3: IMPROVE CFD SKILLS FLUENT has a number of features that had not previously been explored due to their remote access (TUI), or the required initial investment of time to learn them, which can only be justified by a large run matrix. Below are several features that were learned, all of which decreased time expenditures and reduced error in input.

4.3.1 BOUNDARY CONDITIONS There are many settings in FLUENT that reoccur in most cases, such as the inlet and outlet boundary conditions, the autosave information, and surface monitors. Rather than re-specify these reoccurrences each time, a TUI command was implemented to save time and eliminate error. These settings were written out to a text file, and then read in and applied for the next case. See Appendix B for a sample. The boundary condition file was still useful for the off-nominal inlet pressure cases, because all the settings but the autosave directory and the inlet conditions were the same. These two things were simply corrected after the file was read in.

4.3.2 PATCH INITIALIZATION For external flow cases, the flow field is typically initialized to the far field conditions. For internal flow cases, especially quasi one-dimensional cases, breaking the grid into zones in GAMBIT and then initializing each zone differently based on expected losses proved a worthy investment of time. This is known as patch initialization. For cases too dissimilar from already converged cases (different bend angle, different inlet pressure), patch initialization was the best choice. The pipe grid was broken into three zones, the horizontal inlet, the horizontal expanded pipe, and the bent piece. The first zone was patch initialized to pressure, temperature, and velocity marginally less than the inlet boundary condition. The second zone was initialized to pressure and temperature less, and velocity more (due to the expansion in area). The third zone was patch initialized to pressure and temperature marginally less again, while velocity was set marginally higher yet. See Figures 28 and 29 for the difference between a case initialized from the inlet and a case patch initialized.

24

791 791

Figure 28: Case Initialized from Inlet contours of static pressure (psi)

100

791 500 200

Note that temperature and velocity are similarly broken up.

Figure 29: Case Patched Initialized contours of static pressure (psi)

4.3.3 FMG INITIALIZATION After patch initializing, the solutions were further improved using the TUI command FMG-initialization. FMG has two features that speed up convergence. First, the flow is temporarily assumed to be inviscid, which reduces the number of equations being solved. Thus, less time is spent per iteration. Based on experimentation, time per iteration an inviscid case seems to be about half that of a turbulent case. Second, FMG utilizes a strategy known as multi-gridding. This temporarily merges adjacent cells into larger cells, and then combines those new cells into larger ones yet. The solver then converges (or partially converges) a solution for the coursest grid, splits to the intermediate refinement and reconverges, and finally restores the original grid and reconverges. This decreases the cell count, again making each iteration take less time. Five tetrahedral cells make up a larger tetrahedron, so the iteration time for each multi-grid level is on the order of 5 times faster than the level just finer. An FMG initialized solution is far closer to the final converged solution than a simple initialized one. See Figure 30 for an example.

25

800

450

100 Figure 30: Case Initialized with FMG contours of static pressure (psi)

4.3.4 INTERPOLATION INITIALIZATION Due to there being a relatively subtle difference in the flow contours between subsequent hole location cases, the solution from Loc 1 was “borrowed” and used to initialize Loc 2, and so on. Because a separate grid was used for each hole case, the boundary condition for the hole surface could not simply be changed from a wall to a pressure outlet, or vice versa. A new grid had to be read each time, which loses the solution data. However, prior to reading in the new grid, the solution data was written out to a single column text file with the following format for each cell:

pressure omega temperature k x-velocity y-velocity z-velocity value1 value2 value3 etc.

This data was then read back in and applied to the new case’s grid in a zero-order interpolation, or simply, “nearest to” cell. The first case to be run for a given bend angle or inlet pressure was initialized using the patch and FMG methods, but all others were interpolated. Though interpolation files were not shared between two different bend angles, Figure 31 shows a case that was interpolated using the wrong bend angle, just for visualization of what FMG initialization is.

26

800

400

0

velocity vectors colored by total pressure (psi)

Figure 31: Interpolation Initialization Misused

4.3.5 AUTOMATION Each of the 31 cases in the run matrix took on the order of a half a day to converge. Setting up every case individually proved highly inefficient for two reasons. First, the settings and path specifications were extremely tedious and easily mis-entered, making it necessary to re-run some erroneous cases. Second, there was down time in between case convergence, convergence recognition by the user, and subsequent case set up, due to conflicts in schedule. These prolonged the date of the final case’s convergence, and thus, delayed the date the complete data set could be utilized.

Certain patterns and behavior trends were noted after the first few cases, including settings that were omitted by the text boundary condition, appropriate courant number ramping rate, and necessary iterations to convergence.

The TUI was used as a test to set up one particular case, while each command was pasted into a text file to be used as a journal input. The journal file was then tested on a case that had not yet been set, and discrepancies were corrected. For example, the TUI allows for the [enter] key to be pressed, while the journal requires the text “enter” to be included. A sample journal file is found below.

rc !read case directory/name grid/scale .0254 !created in inches, read in m .0254 .0254 grid/reorder/reorder-domain !reduce bandwidth file/read-bc !read bc file to save time directory/name file/autosave/root-name

27

directory/name solve/monitors/surface/set mdot !already created in bc enter !accept current settings enter enter enter enter enter enter enter directory/name !to write to enter file/interpolate/read-data !read in interp directory/name solve/set/courant !CFL# .75 solve/iter 500 solve/set/courant 1 !ramp up CFL# solve/iter 1000 solve/set/courant 1.5 solve/iter 1000 solve/set/courant 2 solve/iter 10000 !would save, read in new case, and begin again

This journal file text was repeated for several cases in a row, yielding at times, days of unmonitored running. This freed up significant time for other aspects of this study.

4.3.6 CUSTOM FIELD FUNCTIONS Numerous variables were extracted from the solutions during post processing, but the custom field functions such Pex had to be recreated each time, even if the FLUENT window was not closed. To save time and eliminate errors, the TUI command

File/read-f-f Directory/name

28

was used to read in the previously created custom field function. Here is an example.

(custom-field-function/define '(((name pex) (display "density * (Vx * .965926 + Vy * .258819) ^ 2 + p") (syntax-tree ("+" ("*" "density" ("**" ("+" ("*" "x-velocity" 0.965926) ("*" "y-velocity" 0.258819)) 2)) "pressure")) (code (field-+ (field-* (field-load "density") (field-** (field-+ (field-* (field-load "x-velocity") 0.965926) (field-* (field-load "y-velocity") 0.258819)) 2)) (field-load "pressure")))) ((name v_ang) (display "(180 / pi) * atan (Vy / Vx)") (syntax-tree ("*" 57.295646 ("atan" ("/" "y-velocity" "x-velocity")))) (code (field-* 57.295646 (field-atan (field-/ (field-load "y-velocity") (field-load "x-velocity")))))) ))

5 CONCLUSIONS

Separation and exit flow non-uniformity occur in bent pipes often found in propulsion systems of aircraft and spacecraft. This faulty behavior can degrade the performance of the vehicle by creating forces where unexpected or unintended. After researching methods for vectoring thrust, it was hypothesized that an appropriately placed suction hole could retard separation and improve the exit flow. A generic bent pipe was modeled, and CFD was run for various conditions and geometric perturbations. Resulting contour and vector plots were studied, and data was interpreted to demonstrate the viability of the suction hole technology. In doing so, all three objectives were achieved.

The CFD run matrix included parametric variations of bend angle, hole location, hole diameter, and inlet pressure so as to plot trends and determine optimal points. For most bend angles, and seemingly all hole diameters and inlet pressures, the optimal hole placement is around Loc 3. The FUP can be improved by reducing bend angle, reducing inlet pressure, and enlarging the hole diameter. These will help the flow turn the bend, and remain uniform at the exit, minimizing unwanted torque.

29

6 FUTURE WORK

The expectation for this effort was that it should represent a culminating experience worthy of a semester’s work. The amount of research, analysis, and computation performed more than satisfied the requirement. Not surprisingly though, there are numerous related studies that were outside the scope of the project, and were thus omitted due to lack of time. There were also alternative methods that were equally valid, yet not chosen.

6.1 OMISSIONS Though grid refinement, turbulence model, and software independence studies are common (if not required) for a detailed CFD analysis in industry, no such evaluations were performed for this project. These would have postponed the project completion date, yet decreasing the uncertainty or error of the results was not a priority. The vacuum hole concept was proved viable, regardless of the accuracy of the results. If there was error, it would be systematic, not random. Though interesting, a transient flow analysis would have been too time-demanding. Also, there are an endless number of variations to the geometry, such as pipe aspect ratio or pipe ID. However, these were not needed for this demonstration. Perhaps a follow-on study can address some of these omissions.

6.2 ALTERNATIVES Other CFD tools could have been used, such as CFD++ or GASP. With enough budget, an actual pipe could be built and flow tested. Also, the FUP could be defined in countless ways, or perhaps the separation just after the bend could be quantified.

30

REFERENCES

1. ANSYS FLUENT 12.0 Validation Solution Files. November 2010. <http://www.fluentusers.com/fluent/doc/ori/v121/fluent/fluent12.1/help/valid/valid.htm>.

2. Case IV, E. Glenn, “Preliminary Design of a Hybrid Rocket Liquid Injection Thrust Vector Control System,” AIAA Paper 2008-1420, January 2008.

3. Deere, Karen A., Berrier, Bobby L., Flamm, Jeffrey D., and Johnson, Stuart K., “A Computational Study of a New Dual Throat Fluidic Thrust Vectoring Nozzle Concept,” AIAA Paper 2005-3502, July 2005.

4. Jaunet, V., Aymer, D., Collin, E., Bonnet, J. P., Lebedev, A., and Fourment, C., “3D Effects in a Supersonic Rectangular Jet Vectored by Flow Separation Control, a Numerical and Experimental Study,” AIAA Paper 2010-4976, June 2010.

5. Forliti, D. J., and Diaz-Guardamino, I. Echavarria, “Exploring Mechanisms of Fluidic Thrust Vectoring using a Transverse Jet and Suction,” AIAA Journal, Vol. 47, No. 10, October 2009.

6. Strykowski, P. J., Krothapalli, A., and Forliti, D. J., “Counterflow Thrust Vectoring of Supersonic Jets,” AIAA Journal, Vol. 34, No. 11, November 1996.

31

APPENDIX A: THE NEED FOR A 3D ANALYSIS It was initially thought that the study could be performed on a two-dimensional slice (the symmetry plane) of the bent pipe. However, the separation effects proved to be three-dimensional as shown in Figure 32. Also Also note the three-dimensional swirling in Figure 17. The unexpected need for three-dimensional grids greatly increased the amount of time allotted for computation.

800

attached flow

2D

100

separation

3D

Figure 32: 2D vs 3D Geometry contours of total pressure (psi)

32

APPENDIX B: SAMPLE BOUNDARY CONDITION FILE (rp ( (strategy/solution-strategy/modifications ((type . list-class) (min-length . 0) (max-length . #f) (curr-length . 0) (member-vars))) (strategy/solution-strategy/original-settings ((type . struct-class) (members-state (active? (value . #t) (type . boolean-class)) (name (value . "Original Settings") (type . string-class)) (command (value . "") (type . string-class)) (count (type . integer-class) (value . 1) (min . 0) (max . #f))))) (strategy/solution-strategy/before-init-modification ((type . struct-class) (members-state (active? (value . #f) (type . boolean-class)) (name (value . "Pre-Initialization") (type . string-class)) (command (value . "") (type . string-class)) (count (type . integer-class) (value . 0) (min . 0) (max . #f))))) (strategy/initialization-strategy ((selection . init-from-case) (type . union-class) (members-state (init-from-case . #f) (init-from-data-file (type . file-class) (value . "") (remote-file? . #t) (file-pattern . "*.dat*")) (init-from-solution (selection . init-from-case) (type . union-class) (members-state (init-from-case . #f) (init-from-data-file (type . file-class) (value . "") (remote-file? . #t) (file-pattern . "*.dat*"))))))) (domains (((1 geom-domain mixture) (children) (material . air)))) (monitor/surfaces ((mdot (print? . #f) (plot? . #t) (write? . #t) (unsteady? . #f) (freq . 10) (unit mass-flow) (report . "Mass Flow Rate") (surfaces exit) (sub-function . "Static Pressure") (domain . "mixture") (function . "Pressure...") (x-axis . "Iteration") (plot-attributes) (window . 1) (file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/mdot.out")))) (autosave/run-number 1) (autosave/solution-points ((1000 (unsteady? . #f) (flow-time . 0) (time-step . 0) (case-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-01000.cas.gz") (data-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-01000.dat.gz")) (2000 (unsteady? . #f) (flow-time . 0) (time-step . 0) (case-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-02000.cas.gz") (data-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-02000.dat.gz")) (3000 (unsteady? . #f) (flow-time . 0) (time-step . 0) (case-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-03000.cas.gz") (data-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-03000.dat.gz")) (4000 (unsteady? . #f) (flow-time . 0) (time-step . 0) (case-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-04000.cas.gz") (data-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-04000.dat.gz")) (5000 (unsteady? . #f) (flow-time . 0) (time-step . 0) (case-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-

33

05000.cas.gz") (data-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-05000.dat.gz")) (6000 (unsteady? . #f) (flow-time . 0) (time-step . 0) (case-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-06000.cas.gz") (data-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-06000.dat.gz")) (7000 (unsteady? . #f) (flow-time . 0) (time-step . 0) (case-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-07000.cas.gz") (data-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-07000.dat.gz")) (8000 (unsteady? . #f) (flow-time . 0) (time-step . 0) (case-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-08000.cas.gz") (data-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-08000.dat.gz")) (9000 (unsteady? . #f) (flow-time . 0) (time-step . 0) (case-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-09000.cas.gz") (data-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-09000.dat.gz")) (10000 (unsteady? . #f) (flow-time . 0) (time-step . 0) (case-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-10000.cas.gz") (data-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-10000.dat.gz")) (11000 (unsteady? . #f) (flow-time . 0) (time-step . 0) (case-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-11000.cas.gz") (data-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-11000.dat.gz")) (12000 (unsteady? . #f) (flow-time . 0) (time-step . 0) (case-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-12000.cas.gz") (data-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-12000.dat.gz")) (13000 (unsteady? . #f) (flow-time . 0) (time-step . 0) (case-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-13000.cas.gz") (data-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-13000.dat.gz")) (14000 (unsteady? . #f) (flow-time . 0) (time-step . 0) (case-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-14000.cas.gz") (data-file . "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter-1-14000.dat.gz")))) (autosave/save-case-preference 1) (autosave/file-suffix-type "iteration") (autosave/filename "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe_iter.gz") (autosave/frequency/data 1000) (amg-c/scheme 0)

34

(omega/default 33722766) (k/default 417.07717) (species/isat-file "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe") (temperature/default 1313.964) (viscous-energy-dissipation? #t) (pressure/default 5456786.4) (x-velocity/default 166.74875) (residuals/convergence-criterion-type 3) (residuals/window 0) (residuals/settings ((continuity #t 0 #t 0.001 0 0.05) (x-velocity #t 0 #t 0.001 0 0.05) (y-velocity #t 0 #t 0.001 0 0.05) (z-velocity #t 0 #t 0.001 0 0.05) (energy #t 0 #t 0.001 0 0.05) (k #t 0 #t 0.001 0 0.05) (omega #t 0 #t 0.001 0 0.05))) (mesh/grid-check-performed? #t) (dynamesh/motion-history/basename "/ctmp/ssmartin/SJSU/AEMasters/Tailpipe/Nov/T2/endpipe") (dynamesh/in-cyn/crank-period 1e+10) (dynamesh/in-cyn/crank-rpm 0.16666667) (dynamesh/remesh/repartition-interface-threshold 10) (dynamesh/remesh/repartition-interval 10) (sizing-function/zonal-edge-size-limits ((2 (0.0023490084 . 0.033402489)))) (sizing-function/boundary-threshold 0.7) (sizing-function/variation-rate 14.219825) (number-of-iterations 10000) (materials ((air fluid (chemical-formula . #f) (density (ideal-gas . #f) (constant . 1.225)) (specific-heat (constant . 1006.43) (polynomial piecewise-polynomial (100 1000 1161.4821 -2.3688189 0.014855111 -5.0349093e-05 9.9285696e-08 -1.1110966e-10 6.540196e-14 -1.5735877e-17) (1000 3000 -7069.8141 33.706051 -0.058127595 5.4216153e-05 -2.9366789e-08 9.2375332e-12 -1.5655534e-15 1.1123349e-19))) (thermal-conductivity (constant . 0.0242)) (viscosity (constant . 1.7894001e-05) (sutherland 1.716e-05 273.11 110.56) (power-law 1.716e-05 273.11 0.666)) (molecular-weight (constant . 28.966)) (lennard-jones-length (constant . 3.711)) (lennard-jones-energy (constant . 78.6)) (thermal-accom-coefficient (constant . 0.9137)) (velocity-accom-coefficient (constant . 0.9137)) (formation-entropy (constant . 194336)) (reference-temperature (constant . 298.15)) (critical-pressure (constant . 3758000)) (critical-temperature (constant . 132.3)) (acentric-factor (constant . 0.033)) (critical-volume (constant . 0.002857)) (therm-exp-coeff (constant . 0)) (speed-of-sound (none . #f))) (aluminum solid (chemical-formula . al) (density (constant . 2719)) (specific-heat (constant . 871)) (thermal-conductivity (constant . 202.4)) (formation-entropy (constant . 164448.08)) (electric-conductivity (constant . 35410000)) (magnetic-permeability (constant . 1.257e-06))))) (parallel/read-mesh? #t) (parallel/nprocs_string "24") (parallel/path "/app/FLUENT/v121/FLUENT") (parallel/function "FLUENT 3ddp -node -alnamd64 -r12.1.2 -t24 -pinfiniband -mpi=hp -cnf=./node_file ") (case-config ((rp-seg? . #f) (rp-acoustics? . #f) (rp-atm? . #f) (rp-axi? . #f) (rp-des? . #f) (rp-dpm-cache? . #t) (rp-unsteady? . #f) (rp-dual-time? . #f) (rp-amg? . #t) (rf-energy? . #t) (rp-hvac? . #f) (rp-

35

inviscid? . #f) (rp-ke? . #f) (rp-kklw? . #f) (rp-kw? . #t) (rp-lam? . #f) (rp-les? . #f) (rp-lsf? . #f) (rp-net? . #f) (rp-react? . #f) (rp-sa? . #f) (rp-sas? . #f) (rp-sge? . #f) (rp-spe? . #f) (rp-spe-part? . #f) (rp-spe-site? . #f) (rp-spe-surf? . #f) (rp-trans-sst? . #f) (rp-trb-scl? . #t) (rp-turb? . #t) (rp-absorbing-media? . #f) (rp-visc? . #t) (rp-v2f? . #f) (sg-cylindrical? . #f) (sg-disco? . #f) (sg-bee-gees? . #f) (sg-crev? . #f) (sg-dpm? . #f) (sg-dqmom-iem? . #f) (sg-dtrm? . #f) (sg-dynmesh? . #f) (sg-ecfm? . #f) (sg-hg? . #f) (sg-inert? . #f) (sg-ignite? . #f) (sg-network? . #f) (sg-node-udm? . #f) (sg-noniterative? . #f) (sg-nox? . #f) (sg-melt? . #f) (sg-micro-mix? . #f) (sg-mphase? . #f) (sg-p1? . #f) (sg-par-premix? . #f) (sg-pb? . #f) (sg-pdf? . #f) (sg-pdf-transport? . #f) (sg-premixed? . #f) (sg-pull? . #f) (sg-rosseland? . #f) (sg-rsm? . #f) (sg-s2s? . #f) (sg-soot? . #f) (sg-sox? . #f) (sg-spark? . #f) (sg-swirl? . #f) (sg-udm? . #f) (sg-uds? . #f) (sg-vfr? . #f) (sg-solar? . #f) (sg-wetsteam? . #f) (sg-moistair? . #f) (rp-3d? . #t) (rp-double? . #t) (rp-graphics? . #t) (rp-host? . #t) (rp-thread? . #t) (dpm-cache? . #t))) (iteration-chunk 10) (reference-thread 2) (reorder/reordered 24) (operating-pressure 0) (kw-sst-on? #t) (kw-std-on? #f) (des-sa-on? #f) (recon/cell-lsq? #f) (recon/node-lsq? #t) (courant-number/implicit 1) )) (dv ( )) (cx ( (unit-table ((pressure psi 6894.757 0) (temperature r 0.55555556 0) (length in 0.0254 0))) (surfaces/groups ((sym1 (7)) (sym2 (6)) (hole (5)) (exit (4)) (in (3)) (wall2 (2)) (wall1 (1)) (default-interior (0)))) (cx-virtual-id-list (4196 4197 4198 4199 4200 4201 4202 4203)) (cx-surface-id-map ((7 4203) (6 4202) (5 4201) (4 4200) (3 4199) (2 4198) (1 4197) (0 4196))) (cx-surface-type ((0 0) (1 0) (2 0) (3 0) (4 0) (5 0) (6 0) (7 0))) (cx-surface-def-list ((4203 () (zone-surface 4203 3) #f) (4202 () (zone-surface 4202 4) #f) (4201 () (zone-surface 4201 5) #f) (4200 () (zone-surface 4200 6) #f) (4199 () (zone-surface 4199 7) #f) (4198 () (zone-surface 4198 8) #f) (4197 () (zone-surface 4197 9) #f) (4196 () (zone-surface 4196 11) #f))) (cx-surface-list #((0 ((zid 11) (type zone-surf) (name default-interior) (status susp) (facet-info (0 0 0 0)))) (1 ((zid 9) (type zone-surf) (name wall1) (status susp) (facet-info (0 0 0 0)))) (2 ((zid 8) (type zone-surf) (name wall2) (status susp) (facet-info (0 0 0 0)))) (3 ((zid 7) (type zone-surf) (name in) (status susp) (facet-info (0 0 0 0)))) (4 ((zid 6) (type zone-surf) (name exit) (status active) (facet-info (0 0 1060 1049)))) (5 ((zid 5) (type zone-surf) (name hole) (status susp) (facet-info (0 0 0 0)))) (6 ((zid 4) (type zone-surf) (name sym2) (status active) (facet-info (0 0 3796 3523)))) (7 ((zid 3) (type zone-surf) (name sym1) (status active) (facet-info (0 0 4810

36

4498)))) #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f #f)) (xy/scale/fmt/y "%0.4f") (xy/scale/fmt/x "%0.4f") (xy/marker/symbol "") (xy/line/pattern "----") (view-list ((isometric ((2.9029067 3.4680982 2.4456811) (0.532248 0.115466 0.075022465) (-0.5000056 0.7071116 -0.5000056) 1.8965226 1.8965226 "perspective") #(1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1)) (front ((0.013519099 0.0029328364 0.12233476) (0.013519099 0.0029328364 0.0019055706) (0 1 0) 0.048171674 0.048171674 "perspective") #(1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1)) (back ((0.013519099 0.0029328364 -0.11852361) (0.013519099 0.0029328364 0.0019055706) (0 1 0) 0.048171674 0.048171674 "perspective") #(1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1)) (right ((0.13394828 0.0029328364 0.0019055706) (0.013519099 0.0029328364 0.0019055706) (0 1 0) 0.048171674 0.048171674 "perspective") #(1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1)) (left ((-0.10691009 0.0029328364 0.0019055706) (0.013519099 0.0029328364 0.0019055706) (0 1 0) 0.048171674 0.048171674 "perspective") #(1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1)) (top ((0.013519099 0.12336202 0.0019055706) (0.013519099 0.0029328364 0.0019055706) (0 0 1) 0.048171674 0.048171674 "perspective") #(1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1)) (bottom ((0.013519099 -0.11749635 0.0019055706) (0.013519099 0.0029328364 0.0019055706) (0 0 -1) 0.048171674 0.048171674 "perspective") #(1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1)))) (left-button-function mouse-rotate) (vector/style "filled-arrow") (vector/scale 2) (contour/filled? #t) (render/domain "mixture") (render/var-name "Total Pressure") (render/surfaces (7 6)) (render/grid/surfaces (16 17 15)) (render/range? #f) (hidden-surfaces? #t) (axes/visible? #t) (cx-case-version (12 1 2)) )) (bc (fluid fluid mixture) ( (material . air) (sources? . #f) (source-terms) (fixed? . #f) (cylindrical-fixed-var? . #f) (fixes) (motion-spec . 0) (grid-x-vel . 0) (grid-y-vel . 0) (grid-z-vel . 0) (omega . 0) (x-origin . 0)

37

(y-origin . 0) (z-origin . 0) (ai . 0) (aj . 0) (ak . 1) (deactivated? . #f) (laminar? . #f) (laminar-mut-zero? . #t) (porous? . #f) (conical? . #f) (direction-1/x (constant . 1) (profile "" "")) (direction-1/y (constant . 0) (profile "" "")) (direction-1/z (constant . 0) (profile "" "")) (direction-2/x (constant . 0) (profile "" "")) (direction-2/y (constant . 1) (profile "" "")) (direction-2/z (constant . 0) (profile "" "")) (cone-axis/x . 1) (cone-axis/y . 0) (cone-axis/z . 0) (cone-axis-pt/x . 1) (cone-axis-pt/y . 0) (cone-axis-pt/z . 0) (cone-angle . 0) (porous-r/1 (constant . 0) (profile "" "")) (porous-r/2 (constant . 0) (profile "" "")) (porous-r/3 (constant . 0) (profile "" "")) (porous-c/1 (constant . 0) (profile "" "")) (porous-c/2 (constant . 0) (profile "" "")) (porous-c/3 (constant . 0) (profile "" "")) (c0 . 0) (c1 . 0) (porosity (constant . 1) (profile "" "")) (solid-material . aluminum) )) (bc (sym1 symmetry mixture) ( )) (bc (sym2 symmetry mixture) ( )) (bc (hole pressure-outlet mixture) ( (p (constant . 6.8947568) (profile "" "")) (t0 (constant . 226.98334) (profile "" "")) (direction-spec . 1) (coordinate-system . 0) (ni (constant . 1) (profile "" "")) (nj (constant . 0) (profile "" "")) (nk (constant . 0) (profile "" "")) (ai . 1) (aj . 0) (ak . 0) (x-origin . 0) (y-origin . 0) (z-origin . 0) (ke-spec . 2) (k (constant . 1) (profile "" ""))

38

(o (constant . 1) (profile "" "")) (turb-intensity . 0.1) (turb-length-scale . 1) (turb-hydraulic-diam . 1) (turb-viscosity-ratio . 10) (mixing-plane-thread? . #f) (radial? . #f) (targeted-mf-boundary? . #f) (gen-nrbc? . #f) (gen-nrbc-spec . 0) (targeted-mf (constant . 1) (profile "" "")) (targeted-mf-pmax (constant . 5000000) (profile "" "")) (targeted-mf-pmin (constant . 1) (profile "" "")) )) (bc (exit pressure-outlet mixture) ( (p (constant . 6.8947568) (profile "" "")) (t0 (constant . 226.98334) (profile "" "")) (direction-spec . 1) (coordinate-system . 0) (ni (constant . 1) (profile "" "")) (nj (constant . 0) (profile "" "")) (nk (constant . 0) (profile "" "")) (ai . 1) (aj . 0) (ak . 0) (x-origin . 0) (y-origin . 0) (z-origin . 0) (ke-spec . 2) (k (constant . 1) (profile "" "")) (o (constant . 1) (profile "" "")) (turb-intensity . 0.1) (turb-length-scale . 1) (turb-hydraulic-diam . 1) (turb-viscosity-ratio . 10) (mixing-plane-thread? . #f) (radial? . #f) (targeted-mf-boundary? . #f) (gen-nrbc? . #f) (gen-nrbc-spec . 0) (targeted-mf (constant . 1) (profile "" "")) (targeted-mf-pmax (constant . 5000000) (profile "" "")) (targeted-mf-pmin (constant . 1) (profile "" "")) )) (bc (in pressure-inlet mixture) ( (frame-of-reference . 0) (p0 (constant . 5660595.4) (profile "" "")) (p (constant . 5456786.4) (profile "" "")) (t0 (constant . 1327.7778) (profile "" "")) (direction-spec . 1) (coordinate-system . 0) (ni (constant . 1) (profile "" "")) (nj (constant . 0) (profile "" "")) (nk (constant . 0) (profile "" ""))

39

(ni2 (constant . 1) (profile "" "")) (nj2 (constant . 0) (profile "" "")) (nk2 (constant . 0) (profile "" "")) (ai . 1) (aj . 0) (ak . 0) (x-origin . 0) (y-origin . 0) (z-origin . 0) (ke-spec . 2) (k (constant . 1) (profile "" "")) (o (constant . 1) (profile "" "")) (turb-intensity . 0.1) (turb-length-scale . 1) (turb-hydraulic-diam . 1) (turb-viscosity-ratio . 10) (mixing-plane-thread? . #f) )) (bc (wall2 wall mixture) ( (d . 0) (q-dot (constant . 0) (profile "" "")) (material . aluminum) (thermal-bc . 1) (t (constant . 300) (profile "" "")) (q (constant . 0) (profile "" "")) (h (constant . 0) (profile "" "")) (tinf (constant . 300) (profile "" "")) (motion-bc . 0) (shear-bc . 0) (relative? . #t) (rotating? . #f) (vmag . 0) (ni . 1) (nj . 0) (nk . 0) (components? . #f) (u (constant . 0) (profile "" "")) (v (constant . 0) (profile "" "")) (w (constant . 0) (profile "" "")) (ex-emiss (constant . 1) (profile "" "")) (trad (constant . 300) (profile "" "")) (roughness-height (constant . 0) (profile "" "")) (roughness-const (constant . 0.5) (profile "" "")) (omega . 0) (x-origin . 0) (y-origin . 0) (z-origin . 0) (ai . 0) (aj . 0) (ak . 1) (shear-x (constant . 0) (profile "" "")) (shear-y (constant . 0) (profile "" "")) (shear-z (constant . 0) (profile "" "")) (surf-tens-grad . 0)

40

41

(specular-coeff . 0) )) (bc (wall1 wall mixture) ( (d . 0) (q-dot (constant . 0) (profile "" "")) (material . aluminum) (thermal-bc . 1) (t (constant . 300) (profile "" "")) (q (constant . 0) (profile "" "")) (h (constant . 0) (profile "" "")) (tinf (constant . 300) (profile "" "")) (motion-bc . 0) (shear-bc . 0) (relative? . #t) (rotating? . #f) (vmag . 0) (ni . 1) (nj . 0) (nk . 0) (components? . #f) (u (constant . 0) (profile "" "")) (v (constant . 0) (profile "" "")) (w (constant . 0) (profile "" "")) (ex-emiss (constant . 1) (profile "" "")) (trad (constant . 300) (profile "" "")) (roughness-height (constant . 0) (profile "" "")) (roughness-const (constant . 0.5) (profile "" "")) (omega . 0) (x-origin . 0) (y-origin . 0) (z-origin . 0) (ai . 0) (aj . 0) (ak . 1) (shear-x (constant . 0) (profile "" "")) (shear-y (constant . 0) (profile "" "")) (shear-z (constant . 0) (profile "" "")) (surf-tens-grad . 0) (specular-coeff . 0) )) (bc (default-interior interior mixture) ( )) (ni ((2 fluid)(3 sym1)(4 sym2)(5 hole)(6 exit)(7 in)(8 wall2)(9 wall1)(11 default-interior)))