# «THE DEVELOPMENT OF AN EROSIVE BURNING MODEL FOR SOLID ROCKET MOTORS USING DIRECT NUMERICAL SIMULATION A Thesis Presented to The Academic Faculty by ...»

## THE DEVELOPMENT OF AN EROSIVE BURNING MODEL FOR SOLID

## ROCKET MOTORS USING DIRECT NUMERICAL SIMULATION

A Thesis

Presented to

The Academic Faculty

by

Brian A. McDonald

In Partial Fulfillment

of the Requirements for the Degree

of Doctor of Philosophy in the

School of Aerospace Engineering

Georgia Institute of Technology

April 2004

## THE DEVELOPMENT OF AN EROSIVE BURNING MODEL FOR SOLID

## ROCKET MOTORS USING DIRECT NUMERICAL SIMULATION

**Approved By:**

Dr. Suresh Menon, Adivisor Dr. Jeff Jagoda Dr. Jerry Seitzman Dr. Tim Lieuwen Dr. Robert Hackett April 21, 2004 Date Approved DEDICATION "Worthy are you, our Lord and God, to receive glory and honor and power, for you created all things, and by your will they existed and were created."

Rev. 4:11 (English Standard Version)

## ACKNOWLEDGEMENTS

I am greatly indebted to Dr. Menon and Dr. Jagoda for their willingness to allow me to pursue this degree from a remote location.I appreciate the countless emails Dr. Menon has answered in advising me in my work. His support and advice in the completion of this research has been most valuable.

I would like to thank Dr. Seitzman for the tutorial session he gave me in preparation of the oral exams. Those two hours were as vital and beneficial as any I received in my educational career.

Thanks to Dr. Lieuwen for serving on my committee.

I am very grateful for Dr. Robert Hackett serving on my committee. He has given support at several key junctures in my career, for which I am much appreciative.

I am also indebted to Eggenspieler Gilles for his ability to take excellent class notes and willingness to share them.

Thank you to Scott Michaels of the U.S. Army Aviation and Missile Command’s Propulsion Laboratory for the use of the CKEM data.

I am indebted to Dr. Bill and Anne Stone, of Stone Engineering for all of the mentoring, support, and opportunity they have offered to me at Stone Engineering over the last 15 years.

Special thanks to Dr. Tom Tytula for agreeing to review this Thesis.

I would like to thank my parents, Parris and Arlene McDonald, who provided the means and support to begin this educational journey many years ago.

my three daughters, Kaleigh, Kelsey, and Sarah. Their love, support, and understanding through many frustrations during the pursuit of this degree have been invaluable.

ACKNOWLEDGEMENTS

LIST OF TABLES

LIST OF FIGURES

LIST OF SYMBOLS

SUMMARY

CHAPTER 1

INTRODUCTION

1.0 Background of Erosive Burning

1.1 Problem Definition

1.2 Erosive Burning Mechanisms

1.3 Literature Review

1.4 Opportunity for DNS

1.5 Summary of Content

CHAPTER 2

PRESENTATION OF OBJECTIVES

2.0 Overview of Objectives

2.1 Objective-1 Develop a Calibrated DNS Computer Code.

2.2 Objective-2 Infinite Rate Chemistry Erosive Burning Model

2.3 Objective-3 Examination of Constant Surface Temperature Assumption.......... 12

2.4 Objective-4 Interior Ballistics Analysis

2.5 Objective-5 Thermal Boundary Layer Growth Impact

2.7 Objective-7 Finite Rate Chemistry Model.

CHAPTER 3

DNS COMPUTER CODE DEVELOPMENT

3.0 Introduction

3.1 Overview of DNS Code

3.2 Governing Equations

3.3 Gas Phase Boundary Conditions

3.4 Thermal Transport Model

3.5 Gas-Solid Interface

3.6 Numerical Schemes

3.7 Code Verification

CHAPTER 4

INTERIOR BALLISTICS CODE DESCRIPTION

4.0 Introduction

4.1 Overview of the Interior Ballistics Code

4.2 Governing Equations

4.3 Solution Methodology

4.4 Code Verification

CHAPTER 5

EROSIVE BURNING NUMERICAL ANALYSIS

5.0 Introduction

5.1 Overview of Analysis

5.3.0 Infinite Rate Chemistry Model

5.3.1 Rocket Motor Configuration

5.3.2 Constant Surface Temperature Analysis

5.3.3 Ballistics Analysis Using the Infinite Rate DNS Model

5.4 Varying Surface Temperature Analysis

5.5 Universalism of the Infinite Rate Chemistry Model

5.6 Thermal Boundary Layer Profile Dependency

5.7.0 Finite Rate Chemistry Model Overview

5.7.1 Model Definition and Boundary Conditions

5.7.2 Chemical Mechanism

5.7.3 Model Calibration Procedure

5.7.4 Finite Rate Model Results

5.7.5 Reduced Base Burn Rate Analysis

5.7.6 Interior Ballistics Results for Finite Rate Model

CHAPTER 6

CONCLUSIONS AND FUTURE WORK

APPENDIX

TIME DEPENDENT DATA

REFERENCES

VITA

Table 1 Physical Properties of The CKEM Solid Propellant and Combustion Gases...... 40 Table 2 Heats of Formation of Considered Species

Table 3 Finite Rate Model Gas Properties

Table 4 Finite Rate Chemistry Model Input

Table 5 Finite Rate Model Results

Table 6 Results of the Low Rate Analysis

Figure 1 Window Bomb Strand Burner

Figure 2 Burn Rate Data for AP/HTPB Propellant with Catocene

Figure 3 CKEM Measured Chamber Pressure

Figure 4 Entrance Axial Velocity Profile (m/s)

Figure 5 Converged Exit Velocity Profile (m/s)

Figure 6 Axial Velocity Contours (m/s)

Figure 7 Pressure Contours (Pa)

Figure 8 Convergence History of Exit Pressure

Figure 9 Ballistics Code Regression Model Schematic

Figure 10 Comparison of 3DGE to Static Test Data

Figure 11 Cross-Flow Computational Domain Schematic

Figure 12 CKEM Rocket Motor Schematic

Figure 13 Normalized Burn Rate versus Mach Number

Figure 14 Internal Ballistics Calculations Using DNS Results

Figure 15 Thermal Boundary Layer Profiles

Figure 16 Temperature (K) Contours (M=0.)

Figure 17 Temperature (K) Contours (M=.1)

Figure 18 Temperature (K) Contours (M=.5)

Figure 19 Temperature Profile in the Solid

Figure 20 Expected Surface Temperature versus Normalized Burn Rate

Figure 22 Ballistics Analysis of CKEM-9 Using DNS Model

Figure 23 Normalized Surface Values for the 50% Width Case

Figure 24 Normalized Surface Values for the 2% Width Case

Figure 25 Thermal Contours at the Leading Edge of the Propellant (K)

Figure 26 Fixed Surface Temperature Burn Rate Profile

Figure 27 Entrance Temperature Profile from Isentropic Flow Relationships................. 57 Figure 28 Entrance Temperature Profile with Wall Heat Transfer

Figure 29 Burn Rate Comparison for Isentropic and Modified Entrance Temperature Profiles

Figure 30 Near Wall Temperature Profile

Figure 31 Temperature Profiles out to Thermal Boundary Layer Edge

Figure 32 Comparison of the AP Decomposition and APd-Binder Flame Thicknesses for M=0.0

Figure 33 APd-Binder Flame Thickness Comparison for Various Free-Stream Mach Numbers

Figure 34 AP Decomposition Flame Thickness Comparison for Various Free-Stream Mach Numbers

Figure 35 Near-Wall Vorticity for Various Free-Stream Mach Numbers

Figure 36 APd-Binder Flame and Vorticity for M=0.8

Figure 37 Near Wall Tangential Velocity Profiles

Figure 38 Comparison of Reaction Rate Gradients to Thermal Gradients

Rate and Low Rate Propellant

Figure 40 Comparison of Vorticity Through the APd-Binder Flame for a High Rate and Low Rate Propellant

Figure 41Comparison of Thermal Gradients at the Solid-Gas Interface for a High Rate and Low Rate Propellant

Figure 42 Temperature Contours for M=0.0 (K)

Figure 43 APd-Binder Reaction Rate Contours for M=0.0 (K)

Figure 44 Temperature Contours for M=0.3 (K)

Figure 45 APd-Binder Reaction Rate Contours for M=0.3 (K)

Figure 46 Interior Ballistics Results with Finite Rate Model

Figure 47 Erosive Burning Rate Compared to the Base Rate

Figure 48 Entrance Velocity Profile in Y+ Coordinate System

Figure 49 Velocity Fluctuations at y+=15, M=0.1, Over Center of Propellant................ 88 Figure 50 Velocity Fluctuations at y+=30, M=0.1, Over Center of Propellant................ 88 Figure 51 Velocity Fluctuations at y+=15, M=0.1, Near Entrance

Roman Letters a Speed of Sound (Characteristic Wave Equations) Burn Rate Coefficient (cPn) c Cp Gas Specific Heat at Constant Pressure Cs Solid Propellant Specific Heat di Characteristic Wave Velocities (i=1-5)

kg Gas Conductivity ks Solid Propellant Conductivity lI Integral Scale Dimension lη Dissipation Scale Li Characteristic Wave Amplitudes (i=1-5)

Tad Adiabatic Flame Temperature To Stagnation Temperature TSurf Propellant Surface Temperature TSurfo Propellant Surface Temperature – Zero Cross-Flow

A method for developing an erosive burning model for use in solid propellant design-and-analysis interior ballistics codes is described and evaluated. Using Direct Numerical Simulation, the primary mechanisms controlling erosive burning (turbulent heat transfer, and finite rate reactions) have been studied independently through the development of models using finite rate chemistry, and infinite rate chemistry. Both approaches are calibrated to strand burn rate data by modeling the propellant burning in an environment with no cross-flow, and adjusting thermophysical properties until the predicted regression rate matches test data. Subsequent runs are conducted where the cross-flow is increased from M=0.0 up to M=0.8. The resulting relationship of burn rate increase versus Mach Number is used in an interior ballistics analysis to compute the chamber pressure of an existing solid rocket motor. The resulting predictions are compared to static test data.

Both the infinite rate model and the finite rate model show good agreement when compared to test data. The propellant considered is an AP/HTPB with an average AP particle size of 37 microns. The finite rate model shows that as the cross-flow increases, near wall vorticity increases due to the lifting of the boundary caused by the side injection of gases from the burning propellant surface. The point of maximum vorticity corresponds to the outer edge of the APd-binder flame. As the cross-flow increases, the APd-binder flame thickness becomes thinner; however, the point of highest reaction rate moves only slightly closer to the propellant surface. As such, the net increase of heat transfer to the propellant surface due to finite rate chemistry affects is small. This leads

transfer increase due to turbulence dominates over combustion chemistry in the erosive burning problem. This conclusion is advantageous in the development of future models that can be calibrated to heat transfer conditions without the necessity for finite rate chemistry. These results are considered applicable for propellants with small, evenly distributed AP particles where the assumption of premixed APd-binder gases is reasonable.

1.0 Background of Erosive Burning The development of erosive burning models for interior ballistics purposes dates back to the 1950’s. The primary purpose of these models is to better predict or simulate rocket motor chamber pressure and performance in motors with erosive burning. In most design phases of solid rocket motors, subscale burn rate data, either from strand data, or standard 2x4 inch motors is all that is available. Typically, the burn rate behavior of a given propellant in cross-flow is unknown. Subscale propellant burn rate data is typically collected in a closed bomb such as shown in Figure 1 [1].

The bombs are pre-pressurized with an inert gas to a selected pressure, and provide a convenient means of characterizing a propellant’s burn rate versus pressure. However, the environment is relatively stagnant, and provides no means for inducing a cross-flow at the burning surface. Typical strand burning data is shown in Figure 2A.

A CKEM test data used by permission of the U.S. Army Aviation and Missile Command, Huntsville, AL, 2001, CKEM Program. Program Manager- Mr. George Snyder, Chief Engineer – Mr. Steve Casan, and Propulsion Lead – Mr. Scott Michaels.

Figure 2 Burn Rate Data for AP/HTPB Propellant with Catocene Many small SRM’s have high propellant volumetric loading fractions for weight efficiency. For these motors, the port to throat area (ratio of the aft end propellant grain diameter to the throat area) is reduced driving the internal flow Mach Numbers upward.

Thus, significant cross-flow velocities at the propellant surface are induced.

As the chamber Mach Number increases the resulting cross-flow velocity at the propellant surface results in heat transfer conditions that deviate considerably from the condition in the strand burner test. The burn rate experienced at a local static pressure condition in the full scale motor is greater than the strand burner data at the same pressure, and can be attributed to the increased heat transfer from the hot combustion gases in cross-flow to the propellant [2]. This increase in burn rate, called erosive burning, can be clearly seen in full scale motor tests as shown in Figure 3.