scholarly journals Effect of spatial discretization of energy on detonation wave propagation

2017 ◽  
Vol 817 ◽  
pp. 306-338 ◽  
Author(s):  
XiaoCheng Mi ◽  
Evgeny V. Timofeev ◽  
Andrew J. Higgins
Keyword(s):  
Wave Propagation ◽  
Equilibrium State ◽  
Specific Heat ◽  
Energy Release ◽  
Reference Frame ◽  
Delay Time ◽  
Wave Speed ◽  
Specific Heat Ratio ◽  
Average Wave ◽  
Sonic Surface

Detonation propagation in the limit of highly spatially discretized energy sources is investigated. The model of this problem begins with a medium consisting of a calorically perfect gas with a prescribed energy release per unit mass. The energy release is collected into sheet-like sources that are embedded in an inert gas that fills the spaces between them. The release of energy in the first sheet results in a planar blast wave that propagates to the next source, which is triggered after a prescribed delay, generating a new blast, and so forth. The resulting wave dynamics as the front passes through hundreds of such sources is computationally simulated by numerically solving the governing one-dimensional Euler equations in the laboratory-fixed reference frame. Two different solvers are used: one with a fixed uniform grid and the other using an unstructured, adaptively refined grid enabling the limit of highly concentrated, spatially discrete sources to be examined. The two different solvers generate consistent results, agreeing within the accuracy of the measured wave speeds. The average wave speed for each simulation is measured once the wave propagation has reached a quasi-periodic solution. The effect of source delay time, source energy density, specific heat ratio and the spatial discreteness of the sources on the wave speed is studied. Sources fixed in the laboratory reference frame versus sources that convect with the flow are compared. Simulations using an Arrhenius-rate-dependent energy release are performed as well. The average wave speed is compared to the ideal Chapman–Jouguet (CJ) speed of the equivalent homogenized media. Velocities in excess of the CJ speed are found as the sources are made increasingly discrete, with the deviation above CJ being as great as 15 %. The deviation above the CJ value increases with decreasing values of specific heat ratio $\unicode[STIX]{x1D6FE}$. The total energy release, delay time and whether the sources remain laboratory-fixed or are convected with the flow do not have a significant influence on the deviation of the average wave speed away from CJ. A simple, ad hoc analytic model is proposed to treat the case of zero delay time (i.e. source energy released at the shock front) that exhibits qualitative agreement with the computational solutions and may explain why the deviation from CJ increases with decreasing $\unicode[STIX]{x1D6FE}$. When the sources are sufficiently spread out so as to make the energy release of the media nearly continuous, the classic CJ solution is obtained for the average wave speed. Such continuous waves can also be shown to have a time-averaged structure consistent with the classical Zel’dovich–von Neumann–Döring (ZND) structure of a detonation. In the limit of highly discrete sources, temporal averaging of the wave structure shows that the effective sonic surface does not correspond to an equilibrium state. The average state of the flow leaving the wave in this case does eventually reach the equilibrium Hugoniot, but only after the effective sonic surface has been crossed. Thus, the super-CJ waves observed in the limit of highly discretized sources can be understood as weak detonations due to the non-equilibrium state at the effective sonic surface. These results have implications for the validity of the CJ criterion as applied to highly unstable detonations in gases and heterogeneous detonations in condensed phase and multiphase media.

Analysis of the Impact of Specific Heat Ratio on Two-Dimensional Low Maher Number Nozzle Design

2014 ◽  
Vol 590 ◽  
pp. 546-550
Author(s):  
Zhi Qiang Fan ◽  
Hai Bo Yang ◽  
Fei Zhao ◽  
Rong Zhu ◽  
Dong Bai Sun
Keyword(s):  
Specific Heat ◽  
Supersonic Nozzle ◽  
Two Dimensional ◽  
Nozzle Design ◽  
Scheme Design ◽  
Specific Heat Ratio ◽  
Nozzle Contour ◽  
Ratio Change ◽  
Change Impact ◽  
The Impact

The practical requirements of the project the nozzle entrance temperature is high, the gas specific heat ratio varies greatly, so it must consider the specific heat ratio change impact on two-dimensional nozzle contour design. Divided into consideration specific heat ratio change and not consider two kinds of scheme design of 1.4Ma nozzle profile and build the model using the arc line method, numerical simulation is carried out through the CFD software Fluent, analysis of two kinds of design scheme comparison. The results show that, in the supersonic nozzle at low Maher numbers, two schemes of nozzle design profile similarity, parameters change little flow tube, export the Maher number and the flow quality can meet the design requirements, proof of specific heat ratio has little effect on the design results in the design of the nozzle under the condition of low Maher number.

scholarly journals A novel semi-implicit scheme for elastodynamics and wave propagation in nearly and truly incompressible solids

2021 ◽  
Author(s):  
Chennakesava Kadapa
Keyword(s):  
Wave Propagation ◽  
Wave Speed ◽  
Critical Time ◽  
Incompressible Material ◽  
Implicit Scheme ◽  
Bulk Wave ◽  
Lumped Mass ◽  
Time Step ◽  
Material Models ◽  
Shear Wave Speed

AbstractThis paper presents a novel semi-implicit scheme for elastodynamics and wave propagation problems in nearly and truly incompressible material models. The proposed methodology is based on the efficient computation of the Schur complement for the mixed displacement-pressure formulation using a lumped mass matrix for the displacement field. By treating the deviatoric stress explicitly and the pressure field implicitly, the critical time step is made to be limited by shear wave speed rather than the bulk wave speed. The convergence of the proposed scheme is demonstrated by computing error norms for the recently proposed LBB-stable BT2/BT1 element. Using the numerical examples modelled with nearly and truly incompressible Neo-Hookean and Ogden material models, it is demonstrated that the proposed semi-implicit scheme yields significant computational benefits over the fully explicit and the fully implicit schemes for finite strain elastodynamics simulations involving incompressible materials. Finally, the applicability of the proposed scheme for wave propagation problems in nearly and truly incompressible material models is illustrated.

Speed of stress wave propagation in lung

1986 ◽  
Vol 61 (2) ◽  
pp. 701-705 ◽  
Author(s):  
R. T. Yen ◽  
Y. C. Fung ◽  
H. H. Ho ◽  
G. Butterman
Keyword(s):  
Wave Propagation ◽  
Stress Wave ◽  
Impact Loading ◽  
Wave Speed ◽  
Dynamic Pressure ◽  
Transpulmonary Pressure ◽  
Lung Parenchyma ◽  
Surface Velocity ◽  
Stress Wave Propagation ◽  
Rabbit Lung

The speed of stress waves in the lung parenchyma was investigated to understand why, among all internal organs, the lung is the most easily injured when an animal is subjected to an impact loading. The speed of the sound is much less in the lung than that in other organs. To analyze the dynamic response of the lung to impact loading, it is necessary to know the speed of internal wave propagation. Excised lungs of the rabbit and the goat were impacted with water jet at dynamic pressure in the range of 7–35 kPa (1–5 psi) and surface velocity of 1–15 m/s. The stress wave was measured by pressure transducer. The distance between the point of impact and the sensor at another point on the far side of the lung and the transit time of the stress wave were measured. The wave speed in the goat lung was found to vary from 31.4 to 64.7 m/s when the transpulmonary pressure Pa-Ppl was varied from 0 to 20 cmH2O where Pa represents airway pressure and Ppl represents pleural pressure. In rabbit lung the wave speed varied from 16.5 to 36.9 m/s when Pa-Ppl was varied from 0 to 16 cmH2O. Using measured values of the bulk modulus, shear modulus, and density of the parenchyma, reasonable agreement between theoretical and experimental wave speeds were obtained.

Modelling and Simulation of Transient Performance of the Semi-Closed O2/CO2 Gas Turbine Cycle for CO2-Capture

2003 ◽  
Author(s):  
Ragnhild E. Ulfsnes ◽  
Olav Bolland ◽  
Kristin Jordal
Keyword(s):  
Water Vapor ◽  
Specific Heat ◽  
Gas Turbine ◽  
Transient Behavior ◽  
Cycle Performance ◽  
Working Fluid ◽  
Transient Event ◽  
Co2 Gas ◽  
Specific Heat Ratio ◽  
Gas Turbine Cycle

One of the concepts proposed for capture of CO2 in power production from gaseous fossil fuels is the semi-closed O2/CO2 gas turbine cycle. The semi-closed O2/CO2 gas turbine cycle has a near to stoichiometric combustion with oxygen, producing CO2 and water vapor as the combustion products. The water vapor is condensed and removed from the process, the remaining gas, primarily CO2, is mainly recycled to keep turbine inlet temperature at a permissible level. A model for predicting transient behavior of the semi-closed O2/CO2 gas turbine cycle is presented. The model is implemented in the simulation tool gPROMS (Process System Enterprise Ltd.), and simulations are performed to investigate two different issues. The first issue is to see how different cycle performance variables interact during transient behavior; the second is to investigate how cycle calculations are affected when including the gas constant and the specific heat ratio in compressor characteristics. The simulations show that the near to stoichiometric combustion and the working fluid recycle introduce a high interaction between the different cycle components and variables. This makes it very difficult to analytically predict the cycle performance during a transient event, i.e. simulations are necessary. It is also found that, except for the shaft speed calculation, the introduction of gas constant and specific heat ratio dependence on the compressor performance map will have only a minor influence on the process performance.

Specific Heat Ratio of High Methane Fraction Natural Gas/Air in Confined Vessel

2015 ◽  
Author(s):  
Chenglong Tang ◽  
Zhanbo Si ◽  
Shuang Zhang ◽  
Zuohua Huang ◽  
Shiyi Pan ◽  
...  
Keyword(s):  
Natural Gas ◽  
Specific Heat ◽  
Specific Heat Ratio

Sensitivity of the Shear Wave Speed-Stress Relationship to Soft Tissue Material Properties and Fiber Alignment

2021 ◽  
Author(s):  
Jonathon Blank ◽  
Darryl Thelen ◽  
Matthew S. Allen ◽  
Joshua Roth
Keyword(s):  
Wave Propagation ◽  
Shear Modulus ◽  
Shear Wave ◽  
Wave Speed ◽  
Axial Stress ◽  
Beam Model ◽  
Fiber Alignment ◽  
Wave Speeds ◽  
Shear Wave Speed ◽  
Constitutive Properties

The use of shear wave propagation to noninvasively gauge material properties and loading in tendons and ligaments is a growing area of interest in biomechanics. Prior models and experiments suggest that shear wave speed primarily depends on the apparent shear modulus (i.e., shear modulus accounting for contributions from all constituents) at low loads, and then increases with axial stress when axially loaded. However, differences in the magnitudes of shear wave speeds between ligaments and tendons, which have different substructures, suggest that the tissue’s composition and fiber alignment may also affect shear wave propagation. Accordingly, the objectives of this study were to (1) characterize changes in the apparent shear modulus induced by variations in constitutive properties and fiber alignment, and (2) determine the sensitivity of the shear wave speed-stress relationship to variations in constitutive properties and fiber alignment. To enable systematic variations of both constitutive properties and fiber alignment, we developed a finite element model that represented an isotropic ground matrix with an embedded fiber distribution. Using this model, we performed dynamic simulations of shear wave propagation at axial strains from 0% to 10%. We characterized the shear wave speed-stress relationship using a simple linear regression between shear wave speed squared and axial stress, which is based on an analytical relationship derived from a tensioned beam model. We found that predicted shear wave speeds were both in-range with shear wave speeds in previous in vivo and ex vivo studies, and strongly correlated with the axial stress (R2 = 0.99). The slope of the squared shear wave speed-axial stress relationship was highly sensitive to changes in tissue density. Both the intercept of this relationship and the apparent shear modulus were sensitive to both the shear modulus of the ground matrix and the stiffness of the fibers’ toe-region when the fibers were less well-aligned to the loading direction. We also determined that the tensioned beam model overpredicted the axial tissue stress with increasing load when the model had less well-aligned fibers. This indicates that the shear wave speed increases likely in response to a load-dependent increase in the apparent shear modulus. Our findings suggest that researchers may need to consider both the material and structural properties (i.e., fiber alignment) of tendon and ligament when measuring shear wave speeds in pathological tissues or tissues with less well-aligned fibers.

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