Redistribution of Energy during Interaction of a Shock Wave with a Temperature Layered Plasma Region at Hypersonic Speeds

The paper is devoted to the problem of the interaction between a shock wave and a thermally stratified energy source for the purpose of supersonic/hypersonic flow control realization. The effect of the thermally stratified energy source on a shock wave with the Mach number in the range of 6–12 is researched numerically based on the Navier-Stokes system of equations. Redistribution of specific internal energy and volume density of kinetic energy behind the wave front is investigated. Multiple manifestations of the Richtmyer-Meshkov instability has been obtained which has caused the blurring and disappearance of shock wave and contact discontinuity fronts in density fields. A study of the efficiency of using a stratified energy source instead of a homogeneous one with the same value of the full energy is carried out. The agreement with the available experimental data for the shock wave Mach number 6 has been obtained.

Study on Mechanical Properties of Water Mist Acting on Plane Shock Wave

The fine water mist has a significant effect in dealing with fire, gas explosion and other disasters of ships and offshore platforms. In this paper, the correlation formula of water mist acting on the plane shock wave front is derived. By combining with the correlation formula of shock wave tube flow parameters, the classical theory of solving shock wave tube flow parameters is improved, so that it can be applied to the action of water mist on plane shock wave without considering the amount of evaporation. The results of shock wave pressure and wave velocity calculated by the above theoretical formula are compared with experimental data, and the errors are all within 10%, thus verifying the applicability and reliability of the above formula. On this basis, the effects of water mist mass concentration and specific internal energy of droplet after wave on shock wave pressure and shock wave velocity are studied, and different heat absorption methods are compared. The results show that the greater the mass concentration of water mist is, the stronger the weakening effect on the shock wave, indicating that the fine water mist can weaken the strength of shock wave; and specific internal energy of droplet after wave is an important parameter that affects the degree to which the water mist weakens the shock wave. In the case of a small amount of evaporation, sensible heat absorption is the main mechanism for the water mist to weaken the shock wave.

Extreme Foaming Modes for SCF-Plasticized Polylactides: Quasi-Adiabatic and Quasi-Isothermal Foam Expansion

The experimental evidence on depressurization foaming of the amorphous D,L-polylactide, which is plasticized by subcritical (initial pressures below the critical value) or supercritical (initial pressures above the critical value) carbon dioxide at a temperature above the critical value, relates to two extreme cases: a slow quasi-isothermal foam expansion, and a rapid quasi-adiabatic expansion. Under certain conditions, the quasi-isothermal mode is characterized by the non-monotonic dependencies of the foam volume on the external pressure that are associated with the expansion-to-shrinkage transition. The quasi-adiabatic and quasi-isothermal expansions are characterized by a significant increase in the degree of foam expansion under conditions where the CO2 initial pressure approaches the critical value. The observed features are interpreted in terms of the energy balance in the foam volume and the phenomenological model based on the equation of the foam state. The expansion-to-shrinkage condition is based on the relationship between the average bubble radius and the pressure derivative of the surface tension for the plasticized polylactide. The maximum expansion ratio of the rapidly foamed polylactide in the vicinity of the critical point is interpreted in terms of the maximum decrement of the specific internal energy of the foaming agent (carbon dioxide) in the course of depressurization.

Derivation of the physical parameters of the jet in S5 0836+710 from stability analysis

Context. A number of extragalactic jets show periodic structures at different scales that can be associated with growing instabilities. The wavelengths of the developing instability modes and their ratios depend on the flow parameters, so the study of those structures can shed light on jet physics at the scales involved. Aims. In this work, we use the fits to the jet ridgeline obtained from different observations of S5 B0836+710 and apply stability analysis of relativistic, sheared flows to derive an estimate of the physical parameters of the jet. Methods. Based on the assumption that the observed structures are generated by growing Kelvin–Helmholtz (KH) instability modes, we ran numerical calculations of stability of a relativistic, sheared jet over a range of different jet parameters. We spanned several orders of magnitude in jet-to-ambient medium density ratio, and jet internal energy, and checked different values of the Lorentz factor and shear layer width. This represents an independent method to obtain estimates of the physical parameters of a jet. Results. By comparing the fastest growing wavelengths of each relevant mode given by the calculations with the observed wavelengths reported in the literature, we have derived independent estimates of the jet Lorentz factor, specific internal energy, jet-to-ambient medium density ratio, and Mach number. We obtain a jet Lorentz factor γ ≃ 12, specific internal energy of ε ≃ 10−2 c2, jet-to-ambient medium density ratio of η ∼ 10−3, and an internal (classical) jet Mach number of Mj ∼ 12. We also find that the wavelength ratios are better recovered by a transversal structure with a width of ≃10% of the jet radius. Conclusions. This method represents a powerful tool to derive the jet parameters in all jets showing helical patterns with different wavelengths.

The temporal behaviour of MHD waves in a partially ionized prominence-like plasma: Effect of heating and cooling

Context. During heating or cooling processes in prominences, the plasma microscopic parameters are modified due to the change of temperature and ionization degree. Furthermore, if waves are excited on this non-stationary plasma, the changing physical conditions of the plasma also affect wave dynamics. Aims. Our aim is to study how temporal variation of temperature and microscopic plasma parameters modify the behaviour of magnetohydrodynamic (MHD) waves excited in a prominence-like hydrogen plasma. Methods. Assuming optically thin radiation, a constant external heating, the full expression of specific internal energy, and a suitable energy equation, we have derived the profiles for the temporal variation of the background temperature. We have computed the variation of the ionization degree using a Saha equation, and have linearized the single-fluid MHD equations to study the temporal behaviour of MHD waves. Results. For all the MHD waves considered, the period and damping time become time dependent. In the case of Alfvén waves, the cut-off wavenumbers also become time dependent and the attenuation rate is completely different in a cooling or heating process. In the case of slow waves, while it is difficult to distinguish the slow wave properties in a cooling partially ionized plasma from those in an almost fully ionized plasma, the period and damping time of these waves in both plasmas are completely different when the plasma is heated. The temporal behaviour of the Alfvén and fast wave is very similar in the cooling case, but in the heating case, an important difference appears that is related with the time damping. Conclusions. Our results point out important differences in the behaviour of MHD waves when the plasma is heated or cooled, and show that a correct interpretation of the observed prominence oscillations is very important in order to put accurate constraints on the physical situation of the prominence plasma under study, that is, to perform prominence seismology.

Nonlinear waves in solids with slow dynamics: an internal-variable model

In heterogeneous solids such as rocks and concrete, the speed of sound diminishes with the strain amplitude of a dynamic loading (softening). This decrease, known as ‘slow dynamics’, occurs at time scales larger than the period of the forcing. Also, hysteresis is observed in the steady-state response. The phenomenological model by Vakhnenko et al. (2004 Phys. Rev. E 70, 015602. ( doi:10.1103/PhysRevE.70.015602 )) is based on a variable that describes the softening of the material. However, this model is one dimensional and it is not thermodynamically admissible. In the present article, a three-dimensional model is derived in the framework of the finite-strain theory. An internal variable that describes the softening of the material is introduced, as well as an expression of the specific internal energy. A mechanical constitutive law is deduced from the Clausius–Duhem inequality. Moreover, a family of evolution equations for the internal variable is proposed. Here, an evolution equation with one relaxation time is chosen. By construction, this new model of the continuum is thermodynamically admissible and dissipative (inelastic). In the case of small uniaxial deformations, it is shown analytically that the model reproduces qualitatively the main features of real experiments.

CFD Analysis of Steam Turbines With the IAPWS Standard on the Spline-Based Table Look-Up Method (SBTL) for the Fast Calculation of Real Fluid Properties

Accurate simulations of non-stationary processes in steam turbines by means of Computational Fluid Dynamics (CFD) require precise and extremely fast algorithms for computing real fluid properties. To fulfill these requirements, the International Association for the Properties of Water and Steam (IAPWS) issues the “Guideline on the Fast Calculation of Steam and Water Properties with the Spline-Based Table Look-Up Method (SBTL)” as an international standard. Through the use of this method, spline functions for the independent variables specific volume and specific internal energy (v,u) are generated for water and steam based on the industrial formulation IAPWS-IF97. With these spline functions, thermodynamic and transport properties can be computed. The desired backward functions of the variables pressure and specific volume (p,v), and specific internal energy and specific entropy (u,s) are numerically consistent with the spline functions from (v,u). The properties calculated from these SBTL functions are in agreement with those of IAPWS-IF97 within a maximum relative deviation of 10 to 100 ppm depending on the property and the range of thermodynamic states spanned under the given conditions (range of state). Consequently, the differences between the results of process simulations using the SBTL method and those obtained through the use of IAPWS-IF97 are negligible. Moreover, the computations from the (v,u) spline functions are more than 200 times faster than the iterative calculations with IAPWS-IF97. In order to demonstrate the efficiency and applicability of the SBTL method, the SBTL functions have been implemented into the CFD software TRACE, developed by the German Aerospace Center (DLR). As a result, the computing times required for the simulations of steam flow in a turbine cascade considering real fluid behavior are reduced by a factor of 6–10 in comparison to the calculations based on IAPWS-IF97. Furthermore, computing times are increased by a factor of 1.4 only with respect to CFD calculations where steam is considered to be an ideal gas, through the use of the SBTL method.

Behavior of Internal Energy and Enthalpy of Fluids Along Isotherms and Isentropic Lines in the Compressed Liquid Region

It is a common practice to approximate the thermodynamics properties of fluids in the compressed liquid regions from their saturation properties. Most thermodynamics textbooks state that the specific volume, specific internal energy, and specific entropy in the compressed liquid region are functions of temperature only and are independent of pressure. Therefore, compressed liquid property tables are not provided for any substance, except for water, and compressed liquid properties are approximated by their saturated liquid properties at a given temperature. Recent examination of current practice in approximating compressed liquid properties has shown that the internal energy of fluids exhibits growing dependency on pressure with increases in temperature. This paper compares the behavior of internal energy and enthalpy four compressed fluids along isotherms with those behaviors along isentropic lines. Water, ammonia, methane, and propane are examined in this study. It is shown that effects of pressure on the internal energy and enthalpy of compressed liquids are much lower along isentropic lines than those along isotherms.

Staggered Lagrangian Discretization Based on Cell-Centered Riemann Solver and Associated Hydrodynamics Scheme

The aim of the present work is to develop a general formalism to derive staggered discretizations for Lagrangian hydrodynamics on two-dimensional unstructured grids. To this end, we make use of the compatible discretization that has been initially introduced by E. J. Caramana et al., in J. Comput. Phys., 146 (1998). Namely, momentum equation is discretized by means of subcell forces and specific internal energy equation is obtained using total energy conservation. The main contribution of this work lies in the fact that the subcell force is derived invoking Galilean invariance and thermodynamic consistency. That is, we deduce a general form of the sub-cell force so that a cell entropy inequality is satisfied. The subcell force writes as a pressure contribution plus a tensorial viscous contribution which is proportional to the difference between the nodal velocity and the cell-centered velocity. This cell-centered velocity is a supplementary degree of freedom that is solved by means of a cell-centered approximate Riemann solver. To satisfy the second law of thermodynamics, the local subcell tensor involved in the viscous part of the subcell force must be symmetric positive definite. This subcell tensor is the cornerstone of the scheme. One particular expression of this tensor is given. A high-order extension of this discretization is provided. Numerical tests are presented in order to assess the efficiency of this approach. The results obtained for various representative configurations of one and two-dimensional compressible fluid flows show the robustness and the accuracy of this scheme.

Dynamic Mechanical Properties of Steel Fiber-Reinforced Concrete Subjected to Shock Loading

One-stage light gas gun is used to study the dynamic mechanical properties of reinforced concrete (SFRC) subjected to shock loading. The material of projectile is the same as of the target. The stress-time curves are recorded by three manganin pressure transducers embedded in the targets beforehand. The data of experiment are analyzed by self-designed program using the path line principle of Lagrangian analysis method. With the stress records, complete histories of particle velocity, density (and thus strain) and specific internal energy can be obtained at any point within the gaged region of the material. Moreover, the numerical constitutive relations of RC are obtained and the strain rate ranges from 104 to 105 per second. The result of experiment indicates that the stress-strain curves of SFRC present stagnant-return properties. And some other dynamic properties can be gained, such as rate dependent, waveform dissipation etc.