On Difference Methods for Shock Wave Propagation in Variable Area Ducts Including Wall Friction

1973 ◽  
Vol 95 (2) ◽  
pp. 327-332
Author(s):  
R. H. Fashbaugh ◽  
A. Widawsky
Keyword(s):  
Shock Wave ◽  
Wave Attenuation ◽  
Fluid Dynamic ◽  
Finite Difference Methods ◽  
Wall Friction ◽  
Variable Cross ◽  
Viscous Effects ◽  
Cross Sectional ◽  
Basic Fluid ◽  
Difference Methods

Results are presented of an analytical study concerned with the prediction of the propagation of shock waves through air ducting systems. The solution is one-dimensional but is appropriate for ducts which have a variable cross-sectional area and includes attenuation due to viscous effects at the wall of the duct. Finite-difference methods are utilized to obtain an approximate solution to the basic fluid dynamic equations. Comparisons are given between analytical results and shock tube experimental data which validate the capabilities of the methods used to predict shock wave attenuation and the effect of duct area variation on shock strength.

A simple constitutive model for predicting the pressure histories developed behind rigid porous media impinged by shock waves

2013 ◽  
Vol 718 ◽  
pp. 507-523 ◽  
Author(s):  
O. Ram ◽  
O. Sadot
Keyword(s):  
Shock Wave ◽  
Porous Medium ◽  
Porous Media ◽  
Shock Waves ◽  
Constitutive Model ◽  
Wave Attenuation ◽  
Front Face ◽  
Viscous Effects ◽  
Pressure History ◽  
Target Wall

AbstractShock wave attenuation by means of rigid porous media is often applied when protective structures are dealt with. The passage of a shock wave through a layer of porous medium is accompanied by diffractions and viscous effects that attenuate and weaken the transmitted shock, thus reducing the load that develops on the target wall that is placed behind the protective layer. In the present study, the parameters governing the pressure build-up on the target wall are experimentally investigated using a shock tube facility. Different porous samples are impinged by normal shock waves of various strengths and the subsequent pressure histories that are developed on the target wall are recorded. In addition, different standoff distances from the target wall are investigated. Assuming that the flow through the porous medium is close to being isentropic enabled us to develop a general constitutive model for predicting the pressure history developed on the target wall. This model can be applied to predict the pressure build-up on the target wall for any pressure history that is imposed on the front face of the porous sample without the need to conduct numerous experiments. Results obtained by other investigators are found to be in very good agreement with the predictions of the presently developed constitutive model.

Fluid Dynamics

2017 ◽  
pp. 94-139
Keyword(s):  
Fluid Dynamics ◽  
Pressure Drop ◽  
Static Loading ◽  
Fluid Dynamic ◽  
Transition To Turbulence ◽  
Viscous Effects ◽  
Basic Fluid ◽  
Free Shear Layers ◽  
Present Context ◽  
Loss Coefficients

A review of basic fluid dynamics is presented in this chapter. Fluid static loading of hydraulic gates is examined. The focus in the present context will be on one-dimensional, incompressible flow of Newtonian fluids (air and water). Viscous effects will be included as loss coefficients in pressure drop calculations through ducts and channels. Discharge coefficients of hydraulics gates are presented to account for viscous effects in the flow past these gates. More advanced concepts related to the instabilities of boundary layers and free shear layers, and transition to turbulence will be introduced briefly and references provided for further investigation by the interested reader. Readers are encouraged to review additional fluid dynamic concepts using the text with which they are most comfortable.

scholarly journals Obtaining the Efficiency and Effectiveness of Fin in Unsteady State Conditions Using Explicit Finite Difference Method

2021 ◽  
Vol 03 (01) ◽  
pp. 111-124
Author(s):  
Petrus Kanisius Purwadi ◽  
◽  
Budi Setyahandana ◽  
R.B.P. Harsilo ◽  
◽  
...  
Keyword(s):  
Finite Difference ◽  
Finite Difference Methods ◽  
Convection Heat Transfer ◽  
Computation Method ◽  
Unsteady State ◽  
Cross Sectional ◽  
Fin Efficiency ◽  
Efficiency And Effectiveness ◽  
Difference Methods ◽  
Explicit Finite Difference

This paper discusses the search for fin efficiency and effectiveness in unsteady state conditions using numerical computation methods. The straight fin under review has a cross-sectional area that changes with the position x. The cross section of the fin is rectangular. The fins are composed of two different metal materials. The computation method used is the explicit finite difference methods. The properties of the fin material are assumed to be fixed, or do not change with changes in temperature. When the stability requirements are met, the use of the explicit finite difference methods yields satisfactory results. The use of the explicit finite difference methods can be developed for various other fin shapes, which are composed of two or more different materials, time-varying convection heat transfer coefficient, and the properties of the fin material that change with temperature.

Influence Analysis of Roadway Friction on Shock Wave Attenuation

2012 ◽  
Vol 178-181 ◽  
pp. 1619-1622
Author(s):  
Ning He ◽  
Bin Qin
Keyword(s):  
Shock Wave ◽  
Friction Coefficient ◽  
Wave Attenuation ◽  
Calculation Model ◽  
Wall Friction ◽  
Tunnel Wall ◽  
Shock Wave Attenuation ◽  
Roughness Elements ◽  
Simulation Calculation ◽  
The Impact

Friction is the extremely important factor when considering the interaction between the shock wave and the tunnel wall. But so far, the impact of wall friction on the shock wave is mainly measured by experimental methods. This paper mainly discusses the effect of wall friction on the shock wave attenuation, without considering roughness, roughness elements, the viscosity of air, and the complex relationship between them; the numerical simulation calculation model is established with DYNA calculation software; the influence law of friction coefficient on tunnel shock wave propagation and attenuation is given based on friction coefficient between air medium and tunnel wall, so as to provide guidance to mining, reduce the impact of tunnel explosion shock wave on personnel and equipment and provide a design basis for shaft safety works.

scholarly journals Effects of a Logistic Reaction to Finite Difference Numerical Solutions of the Inviscid Burgers Equation

2020 ◽  
Vol 2 (2) ◽  
pp. 11
Author(s):  
Sudi Mungkasi
Keyword(s):  
Shock Wave ◽  
Finite Difference ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Finite Difference Methods ◽  
Research Results ◽  
Difference Methods ◽  
Inviscid Burgers Equation ◽  
Nonstandard Finite Difference

We solve the inviscid Burgers equation involving a logistic reaction. The goal is to investigate the effects of the logistic reaction to numerical solutions of the inviscid Burgers equation. We use standard and nonstandard finite difference methods. Based on our research results, the logistic reaction in the inviscid Burgers equation makes the shock wave propagates faster.

DETERMINATION OF THE FUNCTION OF THE ROD’S CROSS-SECTIONAL AREA USING VIBRATION EIGENFREQUENCIES

2020 ◽  
Vol 0 (4) ◽  
pp. 19-24
Author(s):  
I.M. UTYASHEV ◽  
◽  
A.A. AITBAEVA ◽  
A.A. YULMUKHAMETOV ◽  
◽  
...  
Keyword(s):  
Cross Sectional Area ◽  
Variable Cross ◽  
Sectional Area ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Method Error ◽  
Various Boundary Conditions ◽  
Elastic Fixation ◽  
Crosssectional Area

The paper presents solutions to the direct and inverse problems on longitudinal vibrations of a rod with a variable cross-sectional area. The law of variation of the cross-sectional area is modeled as an exponential function of a polynomial of degree n . The method for reconstructing this function is based on representing the fundamental system of solutions of the direct problem in the form of a Maclaurin series in the variables x and λ. Examples of solutions for various section functions and various boundary conditions are given. It is shown that to recover n unknown coefficients of a polynomial, n eigenvalues are required, and the solution is dual. An unambiguous solution was obtained only for the case of elastic fixation at one of the rod’s ends. The numerical estimation of the method error was made using input data noise. It is shown that the error in finding the variable crosssectional area is less than 1% with the error in the eigenvalues of longitudinal vibrations not exceeding 0.0001.

Longitudinal oscillation of a rod with a variable cross section

2019 ◽  
Vol 14 (2) ◽  
pp. 138-141
Author(s):  
I.M. Utyashev
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Liouville Problem ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Independent Functions ◽  
The Cross ◽  
The Right

Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of longitudinal vibrations. The paper presents a method that allows numerically finding the natural frequencies of longitudinal vibrations of an elastic rod with a variable cross section. This method is based on representing the cross-sectional area as an exponential function of a polynomial of degree n. Based on this idea, it was possible to formulate the Sturm-Liouville problem with boundary conditions of the third kind. The linearly independent functions of the general solution have the form of a power series in the variables x and λ, as a result of which the order of the characteristic equation depends on the choice of the number of terms in the series. The presented approach differs from the works of other authors both in the formulation and in the solution method. In the work, a rod with a rigidly fixed left end is considered, fixing on the right end can be either free, or elastic or rigid. The first three natural frequencies for various cross-sectional profiles are given. From the analysis of the numerical results it follows that in a rigidly fixed rod with thinning in the middle part, the first natural frequency is noticeably higher than that of a conical rod. It is shown that with an increase in the rigidity of fixation at the right end, the natural frequencies increase for all cross section profiles. The results of the study can be used to solve inverse problems of restoring the cross-sectional profile from a finite set of natural frequencies.

Biharmonic navigation using radial basis functions

Robotica ◽  
2021 ◽  
pp. 1-12
Author(s):  
Xu-Qian Fan ◽  
Wenyong Gong
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Radial Basis Functions ◽  
Real World ◽  
Biharmonic Equation ◽  
Finite Difference Methods ◽  
Basis Functions ◽  
Large Size ◽  
Radial Basis ◽  
Difference Methods

Abstract Path planning has been widely investigated by many researchers and engineers for its extensive applications in the real world. In this paper, a biharmonic radial basis potential function (BRBPF) representation is proposed to construct navigation fields in 2D maps with obstacles, and it therefore can guide and design a path joining given start and goal positions with obstacle avoidance. We construct BRBPF by solving a biharmonic equation associated with distance-related boundary conditions using radial basis functions (RBFs). In this way, invalid gradients calculated by finite difference methods in large size grids can be preventable. Furthermore, paths constructed by BRBPF are smoother than paths constructed by harmonic potential functions and other methods, and plenty of experimental results demonstrate that the proposed method is valid and effective.

scholarly journals Reliable Efficient Difference Methods for Random Heterogeneous Diffusion Reaction Models with a Finite Degree of Randomness

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 206
Author(s):  
María Consuelo Casabán ◽  
Rafael Company ◽  
Lucas Jódar
Keyword(s):  
Stochastic Process ◽  
Finite Difference ◽  
Coming Out ◽  
Finite Difference Methods ◽  
Diffusion Reaction ◽  
Finite Difference Schemes ◽  
Finite Degree ◽  
Mean Square Stability ◽  
Reaction Models ◽  
Difference Methods

This paper deals with the search for reliable efficient finite difference methods for the numerical solution of random heterogeneous diffusion reaction models with a finite degree of randomness. Efficiency appeals to the computational challenge in the random framework that requires not only the approximating stochastic process solution but also its expectation and variance. After studying positivity and conditional random mean square stability, the computation of the expectation and variance of the approximating stochastic process is not performed directly but through using a set of sampling finite difference schemes coming out by taking realizations of the random scheme and using Monte Carlo technique. Thus, the storage accumulation of symbolic expressions collapsing the approach is avoided keeping reliability. Results are simulated and a procedure for the numerical computation is given.

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