Army Research LagorATORY m| Extended-Range 5-in Navy Gun: | Theoretical Thermal and Erosion Investigations by Paul J. Conroy, Paul Weinacht, Michael J. Nusca, and Kirk Rice ARL-TR-2473 May 2001 Approved for public release; distribution is unlimited 20010508 028‘The findings in this report are not to be construed as an official Department of the Army position unless so designated by othe: authorized documents. tation of manufacturer's or trade names does not constitute an official endorsement or approval of the use thereof. Destroy this report when itis no longer needed. Do not return itto the originator.Army Research Laboratory Aberdeen Proving Ground, MD 21005-5066 ARL-TR-2473. ‘May 2001 Extended-Range 5-in Navy Gun: Theoretical Thermal and Erosion Investigations Paul J. Conroy, Paul Weinacht, and Michael J. Nusca ‘Weapons and Materials Research Directorate, ARL Kirk Rice Formerly of the U.S. Naval Surface Warfare Center “Approved for public release; distribution is unlimited,a EES GEEEEIeeeeeeeee Abstract Barrel heating and erosion concems for the Navy are being brought to light by new extended-range munitions. These munitions have, in general, higher performance requirements and use new propellants. In light of these concems, the following investigation was performed to determine the thermal and erosion characteristics of the current and proposed munitions. In this report, the calculation methodology governing both the thermal and erosion work is described. Six thermal scenarios were computed to compare the thermal load from various combinations of charges. Single-shot erosion predictions are presented for three charges: MK67 with NACO propellant, MK73 with ‘M3OAI propellant, and EX167 extended-range guided munitions (ERGM) propelling charge with EX99 propellant. A fourth single-shot erosion calculation was made using the product gas-state variables and gas velocity of the MK73 charge with chemical constituents of EX99 propellant. The erosion results highlight propellant combustion product differences at the surface between the current and newer propellants. The primary conclusion is that carburization leading to iron carbide formation may be an important contributing factor for much of the material lost from the steel barrel once it is exposed through cracks or chips in the surface coating2. 21 2.2 23 24 25 3. Table of Contents List of Figures.. List of Tables... Introduction Mechanistic Descriptions... Heat Transfer : Erosion Methodology. Surface Description. Erosion Calculations. Thermal Calculations. Conclusions... References. Distribution List.. Report Documentation Page iii x Bevan 7 19 2 29INTENTIONALLY LEFT BLANK.10. List of Figures Conceptual Tube Surface Illustration .... Contrel Valine Description Showing Solid Phase Dependence Upon Carbon Diffusion Depth .. a Single-Shot Surface Temperatures for MK67, MK73, EX167, and MK73 With EX99 Rounds.. — ss coos Single-Shot Surface Regression for MK67, MK73, EX167, and MK73 With EX99 Rounds.. Inner-Bore Residual Surface Temperatures for Scenario No. 1: 10 EX167 Rounds at 9 Rounds/min, Followed by 240 EX167 Rounds at 4 Rounds/min, Followed by 250 Rounds of MK67 at 10 Rounds/min... Inner-Bore Residual Surface Temperatures for Scenario No. 2: 20 MK67 Rounds at 18 Rounds/min, Followed by 230 MK67 Rounds at 10 Rounds/mi Followed by 250 Rounds of EX167 at 4 Rounds/min. Inner-Bore Residual Surface Temperatures for Scenario No. 3: 10 MK67 Rounds at 10 Rounds/min, Followed by 10 EX167 Rounds at 4 Rounds/min, Altemating Until 500 Total Rounds Are Fired... Inner-Bore Residual Surface Temperatures for Scenario No. 4: 600 MK67 Charges at a Firing Rate of 10 Rounds/min.. Inner-Bore Residual Surface Temperatures for Scenario No. 5: 600 EX167 Charges at a Firing Rate of 4 Rounds/min...... z Inner-Bore Residual Surface Temperatures for Scenario No. Charges at a Firing Rate of 10 Rounds/min.. u u 14 14 15 15 16 16INTENTIONALLY LEFT BLANK. vi1 1 2. List of Tables Modeled Propelling Charges. Six Firing Scenarios for Thermal Considerations.. viiINTENTIONALLY LEFT BLANK. viii1. Introduction ‘The Navy's requirement for extended-range ordnance using shipboard cannons has led to the development of a new S-in, 62-cal. MK-45, mod-4 gun system capable of firing both conventional ammunition and extended-range guided munitions (ERGM). The methods involved enabling increased range performance are higher muzzle velocity, the inclusion of a rocket in the projectile with tail fins and forward canards, and improved airframe aerodynamics. The requirement to be able to shoot the current ammunition inventory fixed the gun chamber geometry. Several other constraints limited what could be done with the gun mount, barrel, and propelling charge, ‘The length and weight of the barrel were governed by many factors: gun mount slew rate requirements, barrel droop and whip considerations, the physical envelope available onboard ship, blast overpressure effects on ship structures, maximum trunnion loads, recoil load-handling capability, and barrel yield strength, among others. For the propelling charge, since the chamber volume was already fixed, other means were used to achieve higher muzzle velocity: increasing projectile travel due to a longer gun barrel, operating the propelling charge at a higher chamber pressure, and increasing the system chemical energy by utilizing a propellant of greater density and impetus. Unfortunately, the latter usually resulted in an increase in the adiabatic flame temperature of the propellant. The modifications related to the propelling charge are expected to create an increased thermal load upon the gun and may result in an increase in the erosion rate. Previously, Navy ‘guns were fatigue limited due to the extremely low adiabatic flame temperature of the Navy cool (NACO) single-based propellant. With the newer, higher energy propellant, it is expected that the gun barrel’s life will be erosion limited. This report investigates the effects of candidate new charges on the system’s thermal load for specific firing scenarios, as well as the erosion differences between the older and newer propelling charges. Navy 5-in gun barrels are normally plated with a 5-mil-thick layer of chrome. While this layer can afford dramatic protection from erosion, it tends to crack, flake, and peel during the first few hundred firings. In the erosion portion of this investigation, the chrome layer was assumed absent.Historically, the propellant adiabatic flame temperature was used as an indicator of the erosivity of a propellant. Unfortunately, flame temperature was not the only factor (1, 2] Mitigation of the erosion was a mystery, with the exception of the obvious solution of applying surface coatings or ablatives. Attempts to model erosion using first principles have been and are currently being made [3-6], although it is believed that significant additional work is required to understand the fundamental physics involved. 2. Mechanistic Descriptions 2.1 Heat Transfer, The U.S. Army Research Laboratory (ARL) XBR two-dimensional (2-D) heat-transfer/conduction code used in this report is an extension of the Veritay XBR-2D heat-transfer/conduction code (7, 8] and consists of a 2-D axisymetric implicit finite-difference heat-conduction model. Required inputs include barrel geometry and physical properties, as well as a single-round interior ballistic history of the propellant product gas velocity, pressure, and temperature. ‘The inner boundary condition consists of forced convective heat transfer over flat plates [8] or or ay where k is the conductivity, Tyes is the combustion product gas temperature, and Tyau is the wall temperature. The coefficient h is provided from a correlation of correlations [9] and given as 037 pers Se, x Cp Q) where j1" is the viscosity computed from a form of Sutherland’s law, 7, represents the equivalent flat-plate length to the axial position of interest, Re is the Reynolds number, Re = xpw/p", and Cy is the specific heat of the wall material. The compressible skin friction ratio C-/Cj, where y isthe specific heat ratio and M is the Mach number, is given by [Cy = f+ - ae] @) ‘The outer boundary condition consists of both convective and radiative heat transfer and is expressed as hom Tout ~Te) + 02(fon = Te), @) where ¢ is the emissivity of the wall, o is the Boltzmann constant, and Tz is the temperature of the surroundings. The convection coefficient, Hon, is represented by one of two models, depending on the value of the Reynolds number. For buoyant laminar flow, the convection coefficient is expressed as ieee Poon = 1.39 Beet = Te tow = 134 . 6) for air, where OD is the outer diameter of the barre] wall. The units are accounted for in the coefficient. For buoyant turbulent cross flow in air, the convection coefficient is Irogs = 12 Tout ~To)"? + © where, again, the units are accounted for in the coefficient. This heat-transfer model has been validated with differing gun systems and differing ammunition, such as 120-mm M256 with M829 [10, 11] and M865 (10, 11]; 155 mm with M203 [8], MACS, [12] and LP zones 1~7 [13]; 25-mm Bushmaster with M919 and M791 [14]; and 27-mm caseless [8]. The results agree with the experimentally measured values,2.2 Erosion Methodology. The erosion representation consists of three fully coupled portions, including thermal ablation and heat conduction with an iterative solution for the surface regression, independent heat and multicomponent species mass transport to the surface, and full equilibrium thermochemistry. The contributions due to mechanical wear and abrasion, however, are not included. A surface control volume treatment is also included to ensure conservation of ‘mass of the solid-phase product species due to the solid-gas interface. The core flow gas-phase velocity, as well as state variables pressure and temperature of the gun tube from the XKTC [15] or NGEN [16] interior ballistic codes are used, as well as species data from IBBLAKE [17-19]. The thermochemistry calculation incorporates the NASA Lewis [20] thermochemical database. Primary features of the model have been described [6, 13] and are cursorily presented here. The model, shown conceptually in Figure 1, enables the surface to heat convectively. A surface control volume is defined, and surface reactions occur, which release additional energy into the system as a surface source term. Various gas, solid, or liquid products are produced, which either remain as solids or are removed in the case of gases and liquids. Gas Phase Solid Phase Interior Balisic Supplied PT Convective Heat Interior Ballistic Mass Removal- lied Species Liquid Species — Melt Wipe) Speces Mass FF “rranser Lennard-Jones Mixtare Ditfosion and Mixture Viscosity = [New Gas Species se Figure 1. Conceptual Tube Surface Illustration.The in-depth temperature response of the unablated (solid) material is modeled using the one-dimensional (1-D) heat conduction equation: a By setting 8 = 0 or B = 1, the planar or axisymmetric form of the governing equation can be obtained. The relevant material properties are density,p; specific heat, C,; and conductivity, k. The conductivity and specific heat vary with temperature. The surface energy balance, while gross melting is not occurring, includes the same convective surface heat input used in the thermal calculations, along with the possible contribution due to the surface reaction (shown in equation 8). This source term is balanced with the energy conducted through the material: ® However, when the system is melting, the energy balance includes the fixed surface temperature condition, as well as the unknown surface location. The surface temperature cannot rise beyond the specified melting value because any additional energy is applied to the material-phase ‘transition (melting) as shown: ao Tag = Togs pres = h (Cpe —Teat) + eZ = Source. 0 Prior to the onset of melting, the governing equations and boundary conditions are linear, and solutions are obtained in a direct (noniterative) fashion, During the melting process, the equations become nonlinear since the computational domain dimensions are coupled to the regression rate. An iterative approach is utilized during melting to address the nonlinearity. Because the boundary of the computational domain moves during the erosion event, atransformed version of the governing equation is employed. This allows the equations to be solved in a fixed computational space, even though the physical boundary is moving. A generalized transformation between the computational coordinate, é, and the physical coordinate, 7, is utilized, as shown in the transformed equations: ar, © pc, g +&, . and 7 (10) In this form, the nonlinear nature of the governing equation produced by the moving boundary is evident because the metric terms, &, and &, are not constant and are dependent on the erosion rate when the grid is moving. This methodology compares very well to the semi-analytical solutions of Landau in test cases [20]. The species mass transport to the surface from the core flow of the propellant product gases is assumed frozen and is provided through a concentration potential @ : cor flow ~ wat for each species i, and a mass transport coefficient ty derived from Sherwood number correlations integrated over space and time [6]: Mass, = {fMtm (Prcore= pow ~ Pivas)4A dt an The surface control volume reaction is governed by equilibrium kinetics because the actual reactions and rates are not well known at this time. Equilibrium chemical processes are considered to dominate whenever the characteristic time for a fluid element to traverse the flow field of interest is much longer than the characteristic time for chemical reactions to approachequilibrium. As the pressure and temperature increase, the molecular collision frequency and energy per collision increases, leading to smaller characteristic chemical times, and the chemical processes approach equilibrium. The condition for chemical equilibrium may be stated as the minimization of the Gibbs free energy [21]. For a mixture of N species (e.g., atoms or molecules) with the number of moles of species denoted as m, the Gibbs free energy per mole of mixture is given in terms of the Gibbs free energy of the individual species, gi; the internal energy, e; the temperature, 7; the entropy, s; the pressure, p; and the specific volume, v: G=Eng, =e-Ts+ pv. (a2y 23 Surface Description. The full equilibrium control volume approach, as shown in Figure 2, results in many product mass fractions that are physically impossible due to the constraints of diffusion into the solid phase. Mainly, the carbon that results from CO and/or CO, breakdown will react with as much iron as possible to form Fe;C if permitted. To treat this deficiency, the amount of carbon available for a reaction with the steel is diffusion limited. Gas diffusion/EOS. Carbon diffusion depth (function of temperature) | Gas Phase —_—— — Gas and liquid Residual: Steel, Fresh steel (if needed) products removed FexC, C(GR), Fe0s Figure 2. Control Volume Description Showing Solid-Phase Dependence Upon Carbon Diffusion Depth.‘A surface exposed to a carbon concentration G per unit surface area for a specified length of time ¢ has a carbon concentration C(x) at a specified depth of x given by the following relationship: Ch) = Lew , (13) abt where D is the diffusion coefficient over the a and phases (body-centered cubic [BCC] and face-centered cubic [FCC] lattice structure, respectively). The diffusion of carbon into ot iron (T<1,118 °C) is given by the following function in Smithells Metals Reference Handbook [22] in square centimeters per second, were R, is the universal gas constant in (kilo-calories per mole per Kelvin) D=0008e%7 + 2.2¢*, 4) while the diffusion of carbon into y iron (T < 1,300 °C) is provided by =e D = 0.366%" , as) To find the total amount of carbon that has diffused in time ¢, the concentration function can be integrated and has an error function solution as a= | je ax = Ger (x). (16) Integrating the concentration profile to the maximum depth to which material can diffuse in time t provides the carbon diffused into the material over the time period. To treat the reactant products from the full equilibrium calculation, a subset reaction is created consisting of the