Optimization of the deflagration to detonation transition: reduction of length and time of transition

The aim of this experimental investigation is the study of Deflagration to Detonation Transition (DDT) in tubes in order to (i) reduce both run-up distance and time of transition (L _DDT and t _DDT) in connection with Pulsed Detonation Engine applications and to (ii) attempt to scale L _DDT with λ_CJ (the detonation cellular structure width). In DDT, the production of turbulence during the long flame run-up can lead to L _DDT values of several meters. To shorten L _DDT, an experimental set-up is designed to quickly induce highly turbulent initial flow. It consists of a double chamber terminated with a perforated plate of high Blockage Ratio (BR) positioned at the beginning of a 26 mm inner diameter tube containing a “Shchelkin spiral” of BR ≈ 0.5. The study involves stoichiometric reactive mixtures of H₂, CH₄, C₃H₈, and C₂H₄ with oxygen and diluted with N₂ in order to obtain the same cell width λ_CJ≈10 mm at standard conditions. The results show that a shock-flame system propagating with nearly the isobaric speed of sound of combustion products, called the choking regime, is rapidly obtained. This experimental set-up allows a L _DDT below 40 cm for the mixtures used and a ratio L _DDT/λ_CJ ranging from 23 to 37. The transition distance seems to depend on the reduced activation energy (E _a/RT _c) and on the normalized heat of reaction (Q/a ₀ ²). The higher these quantities are, the shorter the ratio L _DDT/λ_CJ is. PACS 47.40.Rs · 47.60.+i · 47.70.Pq · 47.80.CbThis paper was based on the work that was presented at the 19th International Colloquium on the Dynamics of Explosions and Reactive Systems, Hakone, Japan, July 27–August 1, 2003.     

Experimental investigations of the stability limit of the helical flow of pseudoplastic liquids

The stability of the laminar helical flow of pseudoplastic liquids has been investigated with an indirect method consisting in the measurement of the rate of mass transfer at the surface of the inner rotating cylinder. The experiments have been carried out for different values of the geometric parameter = R ₁/R ₂ (the radius ratio) in the range of small values of the Reynolds number,Re < 200. Water solutions of CMC and MC have been used as pseudoplastic liquids obeying the power law model. The results have been correlated with the Taylor and Reynolds numbers defined with the aid of the mean viscosity value. The stability limit of the Couette flow is described by a functional dependence of the modified critical Taylor number (including geometric factor) on the flow indexn. This dependence, general for pseudoplastic liquids obeying the power law model, is close to the previous theoretical predictions and displays destabilizing influence of pseudoplasticity on the rotational motion. Beyond the initial range of the Reynolds numbers values (Re>20), the stability of the helical flow is not affected considerably by the pseudoplastic properties of liquids. In the range of the monotonic stabilization of the helical flow the stability limit is described by a general dependence of the modified Taylor number on the Reynolds number. The dependence is general for pseudoplastic as well as Newtonian liquids.Nomenclature C _i concentration of reaction ions, kmol/m³ - d = R ₂ –R ₁ gap width, m - F _M () Meksyn's geometric factor (Eq. (1)) - F ₀ Faraday constant, C/kmol - i _l density of limit current, A/m³ - k _c mass transfer coefficient, m/s - n flow index - R ₁,R ₂ inner, outer radius of the gap, m - Re = V _m ·2d·/µ _m Reynolds number - Ta _c = _c ·d^3/2·R ₁ ^1/2 ·/µ _m Taylor number - Z _i number of electrons involved in electrochemical reaction - = R ₁/R ₂ radius ratio - µ apparent viscosity (local), Ns/m² - µ _m mean apparent viscosity value (Eq. (3)), Ns/m² - µ _i apparent viscosity value at a surface of the inner cylinder, Ns/m² - density, kg/m³ - _c angular velocity of the inner cylinder (critical value), 1/s     

Investigation of the stability problems of elastic bodies using the method of mathematical theory of elasticity

In this paper, using the equilibrium equations and boundary conditions of elastic stability problem of and the method of mathematical theory of elasticity, we solve some elastic stability problems, which were studied by Ишлынский^[2] and Войцеховская^[3,4],and obtained more reasonable results than theirs.     

Experimental study of sedimentation characteristics of spheroidal particles

The drag of non-spherical particles is a basic, important parameter for multi-phase flow. As the first step in research in this area, the terminal velocities, Ut, of hemispherical and spherical segment particles with maximal diameters of 6-21 mm were measured in static fluids by using a high-speed video camera. The drag coefficient, CD, measured for Reynolds number, Re of 10^1-10^5, has been obtained and compared with those for a sphere. The Re based on the terminal velocity has a logarithmic linear relationship with Ar number for both the facet facing upwards or downwards for the two experimental spheroidal particles, and their Co values are greater than those of spheres. A shape function that depends on the initial orientation of the particle facet is presented to correct for the shape effects.     

Explicit integration of one problem of motion of the generalized Kowalevski top

In the problem of motion of the Kowalevski top in a double force field the four-dimensional invariant submanifold of the phase space was pointed out by [Kharlamov, M.P., 2002. Mekh. Tverd. Tela 32, 33–38]. We show that the equations of motion on this manifold can be separated by the appropriate change of variables, the new variables s₁, s₂ being elliptic functions of time. The natural phase variables (components of the angular velocity and the direction vectors of the forces with respect to the movable basis) are expressed via s₁, s₂ explicitly in elementary algebraic functions.     

A formulation of PANS capable of mimicking IDDES

The partially averaged Navier–Stokes (PANS) model, proposed in Girimaji (2006), allows to simulate turbulent flows either in RANS, LES or DNS mode. The PANS model includes $f_k$ which denotes the ratio of modeled to total kinetic energy. In RANS, $f_k=1$ while in DNS it tends to zero. In the present study we propose an improved formulation for $f_k$ based on the H-equivalence introduced by Friess et al. (2015). In this formulation the expression of $f_k$ is derived to mimic Improved Delayed Detached Eddy Simulation (IDDES). This new formulation behaves in a very similar way as IDDES, even though the two formulations use different mechanisms to separate modeled and resolved scales. They show very similar performance in separated flows as well as in attached boundary layers. In particular, the novel formulation is able to (i) treat attached boundary layers as properly as IDDES, and (ii) “detect” laminar initial/boundary conditions, in which case it enforces RANS mode. Furthermore, it is found that the new formulation is numerically more stable than IDDES.     

Initiation of fracture at the interface corner of bi-material joints

Within the context of linear elasticity, a stress singularity of the form Hr^λ−1 may exist at the interface corner of a bi-material joint, where r is the radial distance from the corner, H is the stress intensity factor and λ−1 is the order of the singularity. Recent experimental results in the literature support the use of a critical value of the intensity factor H=H_c as a fracture initiation criterion at the interface corner. In this paper, we examine the validity and limitations of this criterion for predicting the onset of fracture in a butt joint consisting of a thin layer of an elastic-plastic adhesive layer sandwiched between two elastic adherends. The evolution of plastic deformation at the corner is determined theoretically and by the finite element method, and the solution is compared with the extent of the elastic singular field. It is shown that H_c is a valid fracture parameter if h>B(H_c/σ_Y)^1/(1−λ) where the non-dimensional constant B=100 for β=0 and B=13 for β=α/4. Here, h is the thickness of the adhesive layer, σ_Y is the uniaxial yield stress of the bulk adhesive and (α,β) are Dundurs’ parameters (Dundurs, J., J. Appl. Mech. 36 (1969) 650). Experimental results for aluminium/epoxy/aluminium and brass/solder/brass sandwiched joints are used to assess the role of plastic deformation on the validity of the failure criterion.     

Anisotropy of elastic properties of materials

Papers dealing with the generalized Hooke’s law for linearly elastic anisotropic media are reviewed. The papers considered are based on Kelvin’s approach disclosing the structure of the generalized Hooke’s law, which is determined by six eigenmoduli of elasticity and six orthogonal eigenstates. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 131–151, November–December, 2008.     

Stability of Couette flow of liquids with power law viscosity

The stability of the Couette flow of the liquid with the power law viscosity in a wide annular gap has been investigated theoretically in this work with the aid of the method of small disturbances. The Taylor number, being a criterion of the stability, has been defined using the mean apparent viscosity value in the main flow. In the whole range of the radius ratio, R _i /R _o and the flow index, n, considered (R _i /R _o 0.5, n = 0.25–1.75 ), the critical value of the Taylor number Ta _c is an increasing function of the flow index, i.e., shear thinning has destabilizing influence on the rotational flow, and dilatancy exhibits an opposite tendency.In the wide ranges of the flow index, n > 0.5, and the radius ratio, R _i /R _o > 0.5, the wide-gap effect on the stability limit is predicted to be almost the same for non-Newtonian fluids as for Newtonian ones. The ratio on the critical Taylor numbers for non-Newtonian and Newtonian fluids: Ta _c (n) and Ta _c (n = 1) obey a generalized functional dependence: Ta _c (n)/Ta _c (n = 1) = g(n), where g(n) is a function corresponding to the solution for the narrow gap approximation.Theoretical predictions have been compared with experimental results for pseudoplastic liquids. In the range of the radius ratio R _i /R _o > 0.6 the theoretical stability limit is in good agreement with the experiments, however, for R _i /R _o < 0.6, the critical Taylor number is considerably lower than predicted by theory.     

Degree of branching of polypropylene measured from Fourier-transform rheology

In this study, linear and branched polypropylenes (PP) were compared under medium strain amplitude oscillatory shear (usually strain amplitude range from 10 to 100%) with Fourier-transform rheology (FT rheology). On a log–log diagram, the third relative intensity (I ₃/I ₁), which is a parameter to represent nonlinearity, shows a linear relationship with the strain amplitude in the range of medium strain amplitude. The slope of I ₃/I ₁ of linear PP with various molecular weight and molecular weight distribution was 2 as most constitutive equations predict, while that of branched PP was 1.64, which is lower than that of linear PP. When the linear and branch PP were blended, the slope of I ₃/I ₁ was proportional to the composition of the branch PP. Therefore, it is suggested that the degree of branching can be defined in terms of the slope of I ₃/I ₁ under medium amplitude oscillatory shear.     

A Critique of Atomistic Definitions of the Stress Tensor

Current interest in nanoscale systems and molecular dynamical simulations has focussed attention on the extent to which continuum concepts and relations may be utilised meaningfully at small length scales. In particular, the notion of the Cauchy stress tensor has been examined from a number of perspectives. These include motivation from a virial-based argument, and from scale-dependent localisation procedures involving the use of weighting functions. Here different definitions and derivations of the stress tensor in terms of atoms/molecules, modelled as interacting point masses, are compared. The aim is to elucidate assumptions inherent in different approaches, and to clarify associated physical interpretations of stress. Following a critical analysis and extension of the virial approach, a method of spatial atomistic averaging (at any prescribed length scale) is presented and a balance of linear momentum is derived. The contribution of corpuscular interactions is represented by a force density field f. The balance relation reduces to standard form when f is expressed as the divergence of an interaction stress tensor field, T ⁻. The manner in which T ⁻ can be defined is studied, since T ⁻ is unique only to within a divergence-free field. Three distinct possibilities are discussed and critically compared. An approach to nanoscale systems is suggested in which f is employed directly, so obviating separate modelling of interfacial and edge effects.      

Characteristics and suppression of flow-induced vibrations of two side-by-side circular cylinders

A free-vibration experiment was conducted to examine flow-induced vibration (FIV) characteristics of two identical circular cylinders in side-by-side arrangements at spacing ratio T^⁎ (=T/D)=0.1–3.2, covering all possible flow regimes, where T is the gap spacing between the cylinders and D is the cylinder diameter. Each of the cylinders was two-dimensional, spring mounted, and allowed to vibrate independently in the cross-flow direction. Furthermore, an attempt to suppress flow-induced vibrations was undertaken by attaching flexible sheets at the rear stagnation lines of the cylinders. Based on the vibration responses of the two cylinders, four vibration patterns I, II, III and IV are identified at 0.1≤T^⁎<0.2, 0.2≤T^⁎≤0.9, 0.9<T^⁎<2.1 and 2.1≤T^⁎≤3.2, respectively. Pattern I is characterized by the two cylinders vibrating inphase^, with the maximum amplitudes occurring at the same reduced velocity Ur=10.47 almost two times that (Ur=5.25) for an isolated cylinder. Pattern II features no vibration generated for either cylinder. Pattern III exemplifies the occurrence of the maximum vibration amplitude of a cylinder at a smaller Ur and that of the other cylinder at a higher Ur compared to its counterpart in an isolated cylinder. Pattern IV represents each cylinder response resembling an isolated cylinder response; the vibrations of the two cylinders are, however, coupled inphase or antiphase. Linking maximum vibration amplitudes to fluctuating lift forces acting on fixed cylinders reveals that fluid–structure interactions between two fixed cylinders and between two elastic cylinders are not the same, even though vibration is not significant. As such, while two fixed cylinders generate narrow and wide wakes at 0.2≤T^⁎<1.7, two elastic cylinders do the same for a longer range of T^⁎ (0.2≤T^⁎<2.1). The flexible sheets effectively suppress FIV of the two cylinders in patterns III and IV, and reduce the vibration amplitude in pattern I. For the effectively controlled cases (patterns III and IV), the flexible sheet of each cylinder folds into a semicircle at the base, forming two free edges.     

An investigation of the viscoelastic properties of molten polypropylene

Two series of polypropylene samples of different molecular weight, the first obtained directly from polymerization reactions and the second from controlled thermal degradation, were studied by dynamic testing in the melt state. Several viscoelastic parameters were determined, and correlated with weight-average molecular weightM _w . It is found that theM _w -dependence of the two series is rather different.     

Slow Eigenvalues of Self-similar Solutions of the Dafermos Regularization of a System of Conservation Laws: an Analytic Approach

The Dafermos regularization of a system of n hyperbolic conservation laws in one space dimension has, near a Riemann solution consisting of n Lax shock waves, a self-similar solution u = u _ε(X/T). In Lin and Schecter (2003, SIAM J. Math. Anal. 35, 884–921) it is shown that the linearized Dafermos operator at such a solution may have two kinds of eigenvalues: fast eigenvalues of order 1/ε and slow eigenvalues of order one. The fast eigenvalues represent motion in an initial time layer, where near the shock waves solutions quickly converge to traveling-wave-like motion. The slow eigenvalues represent motion after the initial time layer, where motion between the shock waves is dominant. In this paper we use tools from dynamical systems and singular perturbation theory to study the slow eigenvalues. We show how to construct asymptotic expansions of eigenvalue-eigenfunction pairs to any order in ε. We also prove the existence of true eigenvalue-eigenfunction pairs near the asymptotic expansions.     

Analysis of the squeezing flow of dusty fluids

The current investigation deals with the study of the effect of introducing a small fraction of dust, by volume, to the fluid in a squeeze film on the viscous resistance to a steady moving disc. Expressions are obtained for the fluid-phase and the dust-phase velocity distributions and the dust particle number density. Analysis based on an iterative procedure indicates that the resistance to motion experienced by the moving disc increases due to the presence of dust.Nomenclature A arbitrary function of integration - B bulk concentration - F resistance to motion experienced by the disc (dusty fluid case) - F _c resistance to motion experienced by the disc (clean fluid case) - F* difference in resistance between the clean fluid and dusty fluid films - f mass concentration - h thickness of the squeeze film - K Stokes coefficient of resistance - m mass of a single dust particle - fluid viscosity coefficient - N dust particles number density - N ₀ dust particles number density at r=R - n iteration level - p fluid pressure in the squeeze film - P pressure in the surrounding - R radius of the disc - fluid density - (r, , y) cylindrical coordinates - t time - U fluid-phase velocity vector - V dust-phase velocity vector - ₁ fluid-phase radial velocity component - U ₂ dust-phase radial velocity component     

Effects of incompressible surfactant on thermocapillary interactions of spherical drops

Collision efficiencies are determined for two surfactant-covered spherical drops in the limit of nearly uniform surface coverage in thermocapillary motion. The problem is linearized by assuming dilute surfactant concentration, with the effect of surfactant controlled by a single retardation parameter A  . The mobility function _LA$L_A$ along the drops’ line of centers is much less than zero over a wide range of parameters, so that the smaller drop can move faster than the larger one at moderate to large separations. At surface Péclet numbers less than 10, the incompressible surfactant model agrees well with solution of the full convective-diffusion equation for the minimum separation between drops. With the exception of non-conducting drops, the collision efficiencies become zero at moderate values of A. A model system of contaminated ethyl salicylate (ES) drops in diethylene glycol (DEG) is studied in thermocapillary motion. Population dynamics simulations confirm the coalescence-inhibiting effect of incompressible surfactant on the evolution of the ES/DEG drop-size distribution.     

Influence of M w of LDPE and vinyl acetate content of EVA on the rheology of polymer modified asphalt

Asphalt binder was modified by low-density polyethylene (LDPE) and ethyl vinyl acetate (EVA) polymers to investigate the structure–property relationships of polymer-modified asphalt (PMA). The PMA was prepared in a high-shear blender at 160 °C. The optimum blending time (OBT) for each polymer was determined following a separate investigation. OBT was influenced by M_w, MWD, and polymer structure. The influence of M_w of LDPE and vinyl acetate (VA) content of EVA on PMAs was studied by rheological tools. Polymer modification improved the rheological properties of base asphalt. EVA–PMAs were found to be less temperature sensitive than LDPE-modified asphalts. LDPE modification increased flow activation energy (E_a) but EVA modification decreased E_a. Both VA content and M_w of LDPE have influenced the storage stability of PMAs. The low-temperature properties of PMAs and short ageing tests were not influenced by polymer type. On the other hand, the high-temperature properties of PMAs were strongly influenced by M_w of LDPE and VA content of EVA. Overall, EVA with low VA content showed the best temperature resistance to high- temperature deformations, the highest upper service temperature as well as the best storage stability.