Water-Channel Analog to High-Velocity Combustion

1953 ◽  
Vol 20 (1) ◽  
pp. 115-121
Author(s):  
A. K. Oppenheim
Keyword(s):  
Flow Field ◽  
Boundary Conditions ◽  
Combustion Front ◽  
Water Channel ◽  
Combustion System ◽  
Dynamic Boundary Conditions ◽  
Proper Selection ◽  
Dynamic Boundary ◽  
Analogous System ◽  
Selection Of

Abstract This paper is a sequel to one presented in 1951, by the author (1). It was shown that during the development of detonation, the combustion zone which appears first in a unidimensional flow field as a single discontinuity, is later transformed into an unsteady, double discontinuity system, and it was demonstrated that such a transformation is necessary because of the restrictions imposed on the system by the dynamic boundary conditions. In the water channel the combustion-front discontinuity is simulated by a unidimensional source formed by admitting water from the bottom. By a proper selection of state parameters analogous relationships are derived to those between pressure and specific volume in a gaseous combustion system. Thus the consequences of restrictions imposed by dynamic boundary conditions on the propagation of combustion are illustrated in an analogous system which, being simpler in nature, is easier to understand. Moreover, the water-channel analog is utilized as an illustrative model of a system where controlled, stationary detonation could be achieved.

The coupled Cahn–Hilliard/Allen–Cahn system with dynamic boundary conditions

2021 ◽  
pp. 1-27
Author(s):  
Ahmad Makki ◽  
Alain Miranville ◽  
Madalina Petcu
Keyword(s):  
Fractal Dimension ◽  
Boundary Conditions ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Dynamic Boundary Conditions ◽  
Finite Dimensional ◽  
Dynamic Boundary ◽  
Long Time ◽  
Finite Fractal Dimension

In this article, we are interested in the study of the well-posedness as well as of the long time behavior, in terms of finite-dimensional attractors, of a coupled Allen–Cahn/Cahn–Hilliard system associated with dynamic boundary conditions. In particular, we prove the existence of the global attractor with finite fractal dimension.

scholarly journals An inverse problem of radiative potentials and initial temperatures in parabolic equations with dynamic boundary conditions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
El Mustapha Ait Ben Hassi ◽  
Salah-Eddine Chorfi ◽  
Lahcen Maniar
Keyword(s):  
Inverse Problem ◽  
Boundary Conditions ◽  
Parabolic Equations ◽  
Stability Result ◽  
Stability Estimate ◽  
Lipschitz Stability ◽  
Dynamic Boundary Conditions ◽  
Logarithmic Convexity ◽  
Dynamic Boundary ◽  
Logarithmic Stability

Abstract We study an inverse problem involving the restoration of two radiative potentials, not necessarily smooth, simultaneously with initial temperatures in parabolic equations with dynamic boundary conditions. We prove a Lipschitz stability estimate for the relevant potentials using a recent Carleman estimate, and a logarithmic stability result for the initial temperatures by a logarithmic convexity method, based on observations in an arbitrary subdomain.

Boundaries Influence on the Flow Field Around an Oscillating Sphere

2013 ◽  
Author(s):  
Domenica Mirauda ◽  
Antonio Volpe Plantamura ◽  
Stefano Malavasi
Keyword(s):  
Free Surface ◽  
Flow Field ◽  
Boundary Conditions ◽  
Damping Ratio ◽  
Water Channel ◽  
Open Water ◽  
Free Surface Flows ◽  
The Body ◽  
Sphere Diameter ◽  
Oscillating Sphere

This work analyzes the effects of the interaction between an oscillating sphere and free surface flows through the reconstruction of the flow field around the body and the analysis of the displacements. The experiments were performed in an open water channel, where the sphere had three different boundary conditions in respect to the flow, defined as h* (the ratio between the distance of the sphere upper surface from the free surface and the sphere diameter). A quasi-symmetric condition at h* = 2, with the sphere equally distant from the free surface and the channel bottom, and two conditions of asymmetric bounded flow, one with the sphere located at a distance of 0.003m from the bottom at h* = 3.97 and the other with the sphere close to the free surface at h* = 0, were considered. The sphere was free to move in two directions, streamwise (x) and transverse to the flow (y), and was characterized by values of mass ratio, m* = 1.34 (ratio between the system mass and the displaced fluid mass), and damping ratio, ζ = 0.004. The comparison between the results of the analyzed boundary conditions has shown the strong influence of the free surface on the evolution of the vortex structures downstream the obstacle.

Updating Substructure Models With Dynamic Boundary Conditions

1995 ◽  
Author(s):  
Michael Link ◽  
Zheng Qian
Keyword(s):  
Boundary Conditions ◽  
Dynamic Stiffness ◽  
Design Parameters ◽  
Physical Parameters ◽  
Model Parameters ◽  
Dynamic Boundary Conditions ◽  
Main Structure ◽  
Modal Data ◽  
Residual Structure ◽  
Dynamic Boundary

Abstract In recent years procedures for updating analytical model parameters have been developed by minimizing differences between analytical and preferably experimental modal analysis results. Provided that the initial analysis model contains parameters capable of describing possible damage these techniques could also be used for damage detection. In this case the parameters are updated using test data before and after the damage. Looking at complex structures with hundreds of parameters one generally has to measure the modal data at many locations and try to reduce the number of unknown parameters by some kind of localization technique because the measurement information is generally not sufficient to identify all the parameters equally distributed all over the structure. Another way of reducing the number of parameters shall be presented here. This method is based on the idea of measuring only a part of the structure and replacing the residual structure by dynamic boundary conditions which describe the dynamic stiffness at the interfaces between the measured main structure and the remaining unmeasured residual structure. This approach has some advantage since testing could be concentrated on critical areas where structural modifications are expected either due to damage or due to intended design changes. The dynamic boundary conditions are expressed in Craig-Bampton (CB) format by transforming the mass and stiffness matrices of the unmeasured residual structure to the interface degrees of freedom (DOF) and to the modal DOFs of the residual structure fixed at the interface. The dynamic boundary stiffness concentrates all physical parameters of the residual structure in only a few parameters which are open for updating. In this approach damage or modelling errors within the unmeasured residual structure are taken into account only in a global sense whereas the measured main structure is parametrized locally as usual by factoring mass and stiffness submatrices defining the type and the location of the physical parameters to be identified. The procedure was applied to identify the design parameters of a beam type frame structure with bolted joints using experimental modal data.

scholarly journals Asymptotic Behavior of Solutions to Reaction-Diffusion Equations with Dynamic Boundary Conditions and Irregular Data

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Yonghong Duan ◽  
Chunlei Hu ◽  
Xiaojuan Chai
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Conditions ◽  
Reaction Diffusion ◽  
Large Time Behavior ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Time Behavior ◽  
Dynamic Boundary Conditions ◽  
Dynamic Boundary

This paper is concerned with the asymptotic behavior of solutions to reaction-diffusion equations with dynamic boundary conditions as well as L1-initial data and forcing terms. We first prove the existence and uniqueness of an entropy solution by smoothing approximations. Then we consider the large-time behavior of the solution. The existence of a global attractor for the solution semigroup is obtained in L1(Ω¯,dν). This extends the corresponding results in the literatures.

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