Keith A. Gonthier

Reaction zone structure for strong, weak overdriven, and weak underdriven oblique detonations

A simple dynamic systems analysis is used to give examples of strong, weak overdriven, and weak underdriven oblique detonations. Steady oblique detonations consisting of a straight lead shock attached to a solid wedge followed by a resolved reaction zone structure are admitted as solutions to the reactive Euler equations. This is demonstrated for a fluid that is taken to be an inviscid, calorically perfect ideal gas that undergoes a two‐step irreversible reaction with the first step exothermic and the second step endothermic. This model admits solutions for a continuum of shock wave angles for two classes of solutions identified by a Rankine–Hugoniot analysis: strong and weak overdriven waves. The other class, weak underdriven, is admitted for eigenvalue shock‐wave angles. Chapman–Jouguet waves, however, are not admitted. These results contrast those for a corresponding one‐step model that, for detonations with a straight lead shock, only admits strong, weak overdriven, and Chapman–Jouguet solutions.

Formulations, predictions, and sensitivity analysis of a pyrotechnically actuated pin puller model

This article presents an analysis for pyrotechnic combustion and pin motion in the NASA Standard Initiator (NSI) actuated pin puller. The conservation principles and constitutive relations for a multiphase system are posed and reduced to a set of five ordinary differential equations which are solved to predict the system`s performance. The model tracks the interactions of the unreacted, incompressible solid pyrotechnic, incompressible condensed phase combustion products, and gas phase combustion products. Predicted pressure histories for the firing of an NSI into (1) the pin puller device, (2) a 10 cm(sup 3) closed vessel, and (3) an apparatus known as the Dynamic Test Device compare well with experimental results. A sensitivity analysis reveals large regions in parameter space where system performance is insensitive to particular parametric values; smaller regions of high sensitivity are also found. 15 refs.

A numerical investigation of transient detonation in granulated material

A two-phase model based upon principles of continuum mixture theory is numerically solved to predict the evolution of detonation in a granulated reactive material. Shock to detonation transition (SDT) is considered whereby combustion is initiated due to compression of the material by a moving piston. In particular, this study demonstrates the existence of a SDT event which gives rise to a steady two-phase Chapman-Jouguet (CJ) detonation structure consisting of a single lead shock in the gas and an unshocked solid; this structure has previously been independently predicted by a steadystate theory. The unsteady model equations, which constitute a non-strictly hyperbolic system, are numerically solved using a modern high-resolution method. The numerical method is based on Godunovs method, and utilizes an approximate solution for the two-phase Riemann problem. Comparisions are made between numerical predictions and known theoretical results for 1) an inert two-phase shock tube problem, 2) an inert compaction wave structure, and 3) a reactive two-phase detonation structure; in all cases, good agreement exists.

System Modeling of Explosively Actuated Valves

A model is formulated to describe time-dependent operation of an explosively actuated valve. The model accounts for burning of solid explosive to form product gas within an actuator, transport of product gas from the actuator to an expansion chamber, and insertion of an initially tapered piston into a constant diameter bore by gas pressure within the expansion chamber. A cutter attached to the piston punctures a diaphragm enabling the desired gas flow. An important model feature is the coupling of combustion energy to piston-housing deformation resulting from gas pressure and geometric interference during piston insertion. The model is correlated with quasi-static compression tests, and combustion bomb data for the explosive HMX (C 4 H 8 N 8 O 8 ), that provide estimates for the valve work requirements, and the pressure dependent burning rate, respectively. The model is then used to predict operation of a baseline valve configuration and to assess how variations in explosive mass and valve geometry affect performance. Predictions indicate that 150 mg of HMX routinely used with the baseline valve induces far greater piston kinetic energy than needed for successful operation. The appropriateness of key assumptions about stress and deformation fields within the piston and housing are examined based on a rate-independent finite-element analysis.

Performance Modeling for Explosively Actuated Valves

A mathematical model is formulated for the time-dependent operation of an explosively actuated valve that can be used as an engineering tool to quickly assess leading order eects of design modications on performance. The model tracks the evolution of explosive and gas product mass and thermal energy in response to combustion, gas o w between internal components, heat transfer with the surroundings, and work performed by the gas in pushing an initially tapered, deformable piston into a constant area bore enabling the desired uid o w through a conduit. An important model feature is the coupling of explosive combustion energy to the elasto-plastic structural deformation mechanics arising from high pressure gas and piston-housing interactions. The deformation model is correlated with inert quasistatic compression data that provide an estimate for the force and work required to actuate the valve. Preliminary predictions for peak combustion pressure within the expansion chamber ( 250 MPa), nal piston velocity ( 150 m/s), and valve actuation time ( 75 s) agree well with experimental observations. The strain hardening behavior of the piston, gas pressure within the expansion chamber, and sliding friction at the piston-housing interface are shown to strongly inuence device operation.

Analysis of Gas-Dynamic Effects in Explosively Actuated Valves

A quasi-one-dimensional model is formulated to assess unsteady gas dynamics occurring within axisymmetric explosively actuated valves. The model accounts for pressure-dependent explosive burn within an actuator, compressible product-gas flow through a narrow port connecting the actuator to a gas expansion chamber, and piston motion due to the combined effects of gas-dynamic forces within the expansion chamber and structural deformation forces between the piston and valve bore. The initial boundary-value problem is posed in terms of generalized coordinates to facilitate numerical computations on a domain that volumetrically expands due to combustionandpistonmotion.Predictionsforabaselineconfigurationthatisrepresentative ofaconventionalvalve indicate that gas-dynamic waves do not result in irregular operation, implying that spatially homogeneous models may be adequate for describing its performance. However, small changes in valve geometry and explosive mass can produce large variations in gas-dynamic fields that significantly affect both the magnitude and frequency of the pyrotechnic shock transmitted to the valve’s supporting structure. Port diameter is shown to control the rates of explosive energy release andacoustic energy transport, which can significantly affect pistonmotion andstroke time.

Modeling of an Explosively Driven Micro-Valve

An analysis is given which demonstrates how the performance of a well-characterized explosively actuated valve conguration (length L 2:5 cm) varies with a linear reduction in size. The analysis is based on a time-dependent, system-level model that tracks the evolution of explosive and product mass and energy within the actuator due to combustion, product gas o w from the actuator to an expansion chamber due to a pressure imbalance, work performed by gas within the expansion chamber in pushing a deformable piston into a constant area bore during stroke, and heat transfer with the surroundings. Predictions indicate that the baseline valve is signican tly overdriven by the 150 mg of HMX (C4H8N8O8) contained in the actuator; consequently, little variation in performance is predicted for a reduction in valve size over the range 0:44 s < 1, where s = l=L is a scale factor. Performance variations are predicted for approximately s < 0:44 due to unrestricted compressible gas o w through the actuator port that reduces the pressurization rate within both the actuator and expansion chamber, and results in irregular piston motion. The analysis demonstrates how product gas o w between internal valve components may adversely aect the performance of small valves.

Reaction zone structure of weak underdriven oblique detonations

Steady weak underdriven oblique detonations consisting of a lead shock attached to a solid wedge followed by a resolved reaction zone structure are admitted as solutions to the reactive Euler equations for eigenvalue shock wave angles. This is demonstrated for a fluid which is taken to be an inviscid, calorically perfect ideal gas which undergoes a two-step irreversible reaction with the first step exothermic and the second step endothermic. These solutions represent two-dimensional extensions of one-dimensional weak detonations. In addition, this model admits solutions to the other two classes of solutions identified by a Rankine-Hugoniot analysis, namely weak overdriven and strong waves. Chapman-Jouguet waves, however, are not admitted. These results contrast those for a corresponding one-step model which, for detonations with a lead shock, only admits weak overdriven, strong, and Chapman-Jouguet solutions.

Analysis for steady propagation of a generic ram accelerator/obliquedetonation wave engine configuration

This study describes a methodology and gives analyses to determine the steady propagation speed of a projectile fired into a gaseous mixture of fuel and oxidizer. For tractability, the steady supersonic flow of an inviscid calorically perfect ideal reacting gas with high activation energy over a symmetric double wedge, unconfined by a cowl, is considered. Propagation speeds are found which give rise to shocks of such strength which induce a reaction zone to be in a region which allows the combustion-induced thrust to balance the wave drag. For a fixed heat release greater than a critical value, two steady propagation speeds are predicted. The solution at the higher Mach number is stable to quasi-static perturbations while the solution at the lower Mach number is unstable. This methodology can be applied to analyze devices which have more complex geometries such as the ram accelerator or oblique detonation wave engine. This paper gives both a simple proof of concept analysis based on Rankine-Hugoniot jump conditions and a detailed numerical analysis of the governing partial differential equations. The simple analysis and numerical analysis are shown to be in qualitative agreement.