- Numerical Modeling of Explosives and Propellants, Third Edition
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- Numerical Modeling of Explosives and Propellants - Charles L. Mader - Google Books
The surface reaction of these VOCs and their chemical kinetics parameters are listed in Table 3. The parameters listed in Table 3 were used in the models involving oxidation of 2-propanol. Chemical kinetic parameters for heterogeneous surface reaction of acetone and 2-propanol. Catalysts are substances that accelerate reactions without being consumed.
Catalysts change reaction rates by offering different paths or mechanisms for the reaction. Catalysts change the speed of reactions.
Numerical Modeling of Explosives and Propellants, Third Edition
However, they do not affect the equilibrium. As shown in Equation 6 , the reaction rate is a function of the pre-exponential factor and the activation energy. The pre-exponential factor, A s , is usually determined from experimental measurements. Three different approaches i. The values of A s for partial oxidation of 2-propanol i. A simulation model was developed and used to perform a parametric study of the coupled electro-thermo-mechanical models of the microcantilever platform used in this study. Correct estimation of the temperature profile of the microcantilevers is a key factor in characterizing chemo-mechanical sensing of explosives.
The numerical model developed in this study can be used to predict the mechanical deflection of a bimorph structure in response to a change in the temperature distribution of the structure due to a chemical reaction. The main assumptions underlying the numerical model are as follows: i the flow remains laminar during the entire combustion process laminar finite-rate model ; ii the multi-step chemical kinetics in the gas-phase volumetric and complete or deep reaction models for catalytic surface reactions occur with rate constants that exhibit Arrhenius-type dependence Equation 6 ; and iii explosives of constant concentrations are present in the control volume of the mixture with air.
In this UDF code, the electrical conductivity values were defined as the diffusivity of the solid phase potential in the solid zones. Thermal analyses of catalytic oxidation based on species transport and the gas phase coupled with the surface oxidation models were then performed. Numerical simulations were performed using a three-dimensional 3-D model, assuming steady-state conditions for laminar flow, coupled with the species transport equations in the gas phase, along with surface reaction.
Hexagonal and gradient meshing techniques were used to discretize the equations. The size of the simulation volume was determined by estimating the thickness of the thermal boundary layer due to natural convection over the heated surface, using the following equation [ 24 ]:. For the temperature at the maximum actuation current e.
The CFD tool provides a powerful and flexible numerical framework for modeling fluid flow and performing associated convection heat transfer calculations, but it does not have built-in advanced solid mechanics analysis capabilities for performing thermo-mechanical stress analysis. On the other hand, the FEA tool provides advanced solid mechanics analysis capabilities. The temperature dependence of the thermo-physical properties e. In the 3-D models, the binary diffusion coefficient Equations 11 — 15 is calculated using the relationships provided by Reid et al.
This theoretical model relies on the values of the hard-sphere collision diameter and the Lennard-Jones energy parameters, which are summarized in Table 4. Hard-sphere collision diameter and Lennard—Jones energy parameter for various species. The mixture viscosity and thermal conductivity were determined using the kinetic theory of gases and the ideal gas mixing law, respectively.
The fabrication process of the thermal bimorph microcantilever array Active Pen TM platform is illustrated in Figure 3. For the tip wafer Figure 3 e—h , the oxidized wafer is patterned into small squares and used as a mask in an anisotropic silicon etching process to form a pyramidal tip.
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After a low-stress and low-stress-gradient Si 3 N 4 film is deposited on an oxidized silicon wafer a priori by low pressure chemical vapor deposition LPCVD , it is patterned and dry-etched. The resist is then applied and patterned. Finally, the two wafers are aligned by infrared IR alignment, clamped together using a Suss MA-6 platform, and bonded by thermal compression bonding at a high temperature e. The handle and tip wafers were etched in tetramethylammonium-hydroxide TMAH , and the sharpening oxide layer was removed using buffered oxide etching BOE.
The thermal stresses induced during bonding can exceed the elastic limit and are not completely relieved when the substrates are returned to room temperature. That is, cooling down to room temperature generates residual stresses. An initial curvature is therefore induced in the microcantilevers by the residual stresses that are generated during cooling down to room temperature after thermal bonding. Figure 4 shows the micro-fabricated microcantilever array, which is hooked up to a flexible printed circuit board PCB courtesy of NanoInk, Inc.
Each cantilever can be actuated individually by a separate electrical connection.
Optical microscopy image of micro-fabricated bimorph microcantilever array integrated with heating element at their base. This technology was developed in for use in atomic force microscopy AFM [ 28 ]. The experimental setup consists of an airtight acrylic chamber an environmental control chamber , a platform to support and control the movement of the laser source, a platform for the microcantilever array, and a position-sensitive detector PSD to detect the laser beam spot reflected from the surface of each microcantilever.
To render the acrylic chamber airtight, silicone was used to seal the edges inside the box, and an aluminum tape insert was used to seal the edges along the exterior of the box.
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Weather stripping was used as a sealant between the door and the front wall of the chamber. Inside the chamber, a low-power laser 1 mW, nm was affixed to a semi-automated stage with four axes of motion assembled from Newport components. The Newport stage system Figure 5 supports the laser and can be actuated remotely for laser beam alignment with the cantilever axes in the nano-calorimeter apparatus. To alter the position of the laser, a remote-controlled stage can also be used to rotate the cantilever array.
Hence, laser alignment and cantilever positioning can be accomplished without perturbing the environmental chamber.
Schematic of the experimental apparatus based on the optical-lever method used in this study for explosive detection: a experimental setup for detection; and b sensing of reflected light using PSD. Each experiment was performed in two separate steps. First, a control baseline experiment was performed under ambient atmospheric conditions, and second, an experiment was performed in the presence of explosive vapors at the equilibrium vapor concentration. The bending response of the microcantilever as a function of the actuation current in the uncontaminated air environment was compared to that in air saturated with the vapor of the explosive materials or VOCs chosen for use in this study.
As shown in Figure 5 , the laser beam incident on the microcantilever surface is reflected by the gold coating onto the PSD.
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The actuation current for heating the micro-heaters and therefore for actuating the microcantilever beam was increased from 0 to 20 mA at 2 mA intervals. The resulting deflection of the microcantilever beam was tracked by measuring the voltage values corresponding to the position of the reflected laser beam obtained from the PSD.
Once the data were collected for the control experiment, the explosive sample was placed in a small bowl that was placed inside the chamber. The sample was placed in the environmental control chamber for approximately thirty minutes to ensure saturation conditions for the vapor emanating from the explosive sample. The results were then recorded and compared to the results obtained from the control experiments. The change in the deflection angle of the microcantilevers was measured as a function of the actuation current.
The total experimental error in the angle measurement is given by [ 10 ]:. In this study, the experimental error in measuring the change in angular deflection was found to be less than 0. Oxidation of VOCs with air was numerically studied at specific initial concentrations in a finite control volume. The chemical kinetics, expressed in Arrhenius form according to Equation 6 , were used to model the temperature dependence of the reaction rate and the activation energy for oxidation. The higher surface area-to-volume ratio at the nano-scale was expected to expedite the kinetics of the area-limited catalytic reactions, which means that the chemical reactions were expected to occur only on the catalyst surface provided by the gold coatings on the microcantilevers [ 15 ].
The catalytic reaction on the surface of the microcantilevers depends on the core temperature of the heating element. Figure 6 shows the surface temperature range of the electrically preheated microcantilevers in air. In the kinetic-controlled region, the concentration of explosives over the surface is obtained as the general solution to the diffusion equation given by Equation 5.
Prior to the 3-D simulations conducted using the multi-step reaction model and the temperature-dependent material properties, a simple 1-D calculation was performed to verify the theoretical model. The global one-step oxidation model for propane C 3 H 8 was used in this calculation. The equation given by Hayes et al. A comparison of the concentration profiles over the heated surface obtained from the 1-D analysis and the CFD simulation is shown in Figure 7.
Numerical Modeling of Explosives and Propellants - Charles L. Mader - Google Books
In the 1-D analysis, the concentrations of the explosive vapor varied only with the height. Nevertheless, the predictions obtained from the 1-D analytical model were found to be in good agreement with the results of the CFD simulations. Concentration profiles over the microcantilever surface in the longitudinal direction.
The species of the explosive vapor are assumed to be uniformly distributed throughout the control volume. The initial conditions for concentration and the enthalpy for phase change are listed in Table 1. The oxidation reactions of explosives are highly exothermic; hence, the surface temperature is increased by the additional thermal energy generated by the catalytic combustion reactions i. Accordingly, a downward bending response of the microcantilevers is caused by the thermal bimorph effect, as shown in Figure 8.
Figure 9 shows the resultant deflection and temperature distribution of the microcantilever as a function of the actuation current. The amount of gas consumed during the oxidation reactions is proportional to the concentration of the explosive vapor around the cantilever. The difference in the heat of combustion between acetone and 2-propanol is not significant. However, because the vapor pressure of acetone is higher than that of 2-propanol, the surface temperature enhancement due to combustion reactions is augmented in the case of acetone.
Surface temperature profile by nano-scale combustion reactions on the surface of the microcantilevers and bending response caused by bimetallic effect at 20 mA a acetone and b 2-propanol note: translucent images represent the deflection in air. Simulation of the resultant deflection and temperature changes due to nano-scale combustion as a function of actuation current from 6 mA to 20 mA at 2mA intervals a acetone and b 2-proapnol.
Larger deflections are achieved by design optimization, but the noise signal produced by flow or thermally induced excitations can reduce the deflection sensitivity [ 30 ].