A ballistic compressor-based experiment for the visualization of liquid propellant jet combustion above 100 MPa

 This paper describes the components and operation of an experimental setup for the visualization of liquid propellant (LP) jet combustion at pressures above 100 MPa. The apparatus consists of an in-line ballistic compressor and LP injector. The ballistic compressor, based on a modified 76 mm gun, provides high-pressure (ca. 55 MPa) clear hot gas for the jet ignition. A piston (projectile) is fired toward a test chamber beyond the barrel’s end, and its rebound is arrested in a transition section that seals the test chamber to the barrel. The LP jet is injected once the piston is restrained, and combustion of the jet further elevates the pressure. At a preset pressure, a disc in the piston ruptures and the combustion gas vents sonically into the barrel. If a monopropellant is used, the jet injection-combustion process then resembles liquid rocket combustion but at very high pressures (ca. 140 MPa). This paper discusses the ballistics of the compression and compares experimental results to those predicted by a numerical model of the apparatus. Experimentally, a pressure of 70 MPa was achieved upon a 12.5 volumetric compression factor by firing a 10 kg piston into 1.04 MPa argon using a charge of 75 g of small-grain M1 propellant. Received: 16 December 1996/Accepted: 15 July 1997     

Heat transfer during transient compression: Measurements and simulations

Experiments have been performed to assess the utility of unsteady one-dimensional heat conduction modelling for the calculation of heat losses during a free piston compression process. Heat transfer measurements have been obtained within a gun tunnel barrel using surface junction thermocouple instrumentation. The gun tunnel was operated with a relatively heavy piston such that the shock waves induced by the piston motion were weak. Peak heat transfer values are estimated reasonably well by the unsteady one-dimensional model. However, overall quantitative agreement between the measurements and calculations has not been achieved at this stage, principally because the development of turbulent heat transport was not properly modelled. Received 21 September 2001 / Accepted 11 March 2002 – Published online 11 June 2002     

Group classification of one-dimensional nonisentropic equations of fluids with internal inertia

A systematic application of the group analysis method for modeling fluids with internal inertia is presented. The equations studied include models such as the nonlinear one-velocity model of a bubbly fluid (with incompressible liquid phase) at small volume concentration of gas bubbles (Iordanski Zhurnal Prikladnoj Mekhaniki i Tekhnitheskoj Fiziki 3, 102–111, 1960; Kogarko Dokl. AS USSR 137, 1331–1333, 1961; Wijngaarden J. Fluid Mech. 33, 465–474, 1968), and the dispersive shallow water model (Green and Naghdi J. Fluid Mech. 78, 237–246, 1976; Salmon 1988). These models are obtained for special types of the potential function W(r,[(r)\dot],S){W(\rho,\dot \rho,S)} (Gavrilyuk and Teshukov Continuum Mech. Thermodyn. 13, 365–382, 2001). The main feature of the present paper is the study of the potential functions with W _S  ≠ 0. The group classification separates these models into 73 different classes.     

Nonlinear gas oscillations in a closed tube driven by the aperiodic motion of a piston

Nonlinear gas oscillations in a closed tube driven by the aperiodic motions of a piston as a result of the action of the external and internal pressure drop are studied. The external pressure takes two values alternating at the moment of change of direction of motion of the piston. Two models of the motion of the gas are considered. Model 1 is formed by a system of equations representing the mass, momentum, and entropy conservation laws. As distinct from model 1, model 2 includes the total energy conservation law in place of the entropy conservation laws. Kazan’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 134–142, March–April, 1998. The work was carried out with partial support from the Russian Foundation for Fundamental Research (project No. 96-01-00484).     

Slip coefficients and macroparameter jumps of a diatomic gas with rotational degrees of freedom on a weakly curved spherical surface

Using the half-space moment method, the problem of the slip of a diatomic gas along a rigid spherical surface is solved within the framework of a model kinetic equation previously proposed which takes into account the rotational degrees of freedom of the gas. Second-order slip coefficients (correctionsC _m ^′ , β _R ^′ , and β _R to the isothermal and thermal slip which are linear with respect to the Knudsen number Kn) are obtained. The gas macroparameter jump coefficientsC _v andC _q, which are of the second order in the Knudsen number and characterize the discontinuity of the normal mass and heat fluxes on the gas-rigid phase interface, are calculated. These coefficients are given as functions of the tangential momentum accommodation coefficient, the translational and rotational energy accommodation coefficients, and the Prandtl number. The coefficients are calculated for certain diatomic gases. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 163–173, January–February, 2000.     

Scalar mixing in the field of a gaseous laminar line vortex

An experimental study of scalar mixing in a laminar vortex is presented for vortices generated between two gas streams flowing parallel to each other in a rectangular flow channel. An isolated line vortex is initiated on demand by momentarily increasing one stream velocity in relation to the other using an electromagnetically actuated piston. The temporal piston motion profile is tailored to generate vortices of different strengths corresponding to vortex Reynolds numbers, Re≡Γ/2πν=130–210. Evolution of mixing is monitored by laser-induced fluorescence of acetone vapor premixed into one of the gas streams as the vortex structure evolves with increasing downstream distance from its point of origin. Vortex is generated by pulsing either of the gas streams (seeded or unseeded stream). Vortex initiation process affects the abundance of the gas in the vortex core from the pulsed stream. Spatial mixing statistics are obtained by determining scalar concentration probability density functions (pdf) and the mean mixed fluid concentrations obtained from these pdfs. It is found that the interfacial area generation as a result of vortex kinematics and molecular diffusion along this interface are principally responsible for mixing. The mean mixed fluid concentration in the vortex interaction region scales with the product of vortex circulation and the elapsed time of interaction. These results are similar to those found in liquid mixing experiments, but the rate of mixing is significantly higher due to higher diffusivity of gases.     

Use of high pressures for solving problems of hypersonic aerodynamics

The use of high pressures in a hypersonic aerodynamic experiment is founded on physical grounds. Calculation results of Mach and Reynolds numbers reachable at the line of gas condensation are given as functions of the temperature and pressure in the plenum chamber. Approaches to solving problems of designing ultrahigh-pressure facilities that ensure outflow with pressures up to20,000 atm are described. These problems include the stop of the first-stage piston at the point of maximum pressure, suppression of the reaction force, provision of normal operation of seals of the moving piston, and reduction of friction forces in the seals. The principles considered are used in an actually operating facility. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 103–114, September–October, 2000.     

Partially invariant solutions for a submodel of radial motions of a gas

All partially invariant solutions in terms of the group of extensions for a model of radial motions of an ideal gas are found. The solutions are obtained by the method of separation of variables in an equation containing functions of one variable but different functions of different independent variables. The solutions predict different continuous unsteady convergence or expansion of the gas under the action of a piston with a point sink or source. If the sink or source affects all particles simultaneously, a collapse or an explosion occurs. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 26–34, September–October, 2007.     

考虑活塞回复的侧向后喷武器两相流数值模拟

为研究活塞回复运动对火药燃气流动的影响,基于两相流理论对活塞控制侧向后喷武器的发射过程进行了数值模拟研究。考虑控制侧向后喷通道开闭的活塞-弹簧系统的往复运动,建立了结合膛内气固两相流、活塞腔内流固耦合和侧向排气管内气体瞬态流动的武器发射过程数学模型,并将数值模拟结果与相关文献进行了比较验证。得到了该武器发射过程中膛内流场分布与稀疏波传播特性,并与普通武器的膛内流场进行了对比分析。进一步研究了活塞回复运动对火药燃气流动和减后坐效率的影响。结果表明:相对于不考虑活塞的回复运动,在弹丸初速都降低1.52%的情况下,因为活塞回复关闭后喷通道,其减后坐效率由38.86%下降到32.88%,说明在此类武器研究中,不可忽视活塞回复运动。     

Laminar-turbulent transition in the boundary layer on cones in a hypersonic flow at high Reynolds numbers per meter

The laminar-turbulent transition is experimentally studied in boundary-layer flows on cones with a rectangular axisymmetric step in the base part of the cone and without the step. The experiments are performed in an A-1 two-step piston-driven gas-dynamic facility with adiabatic compression of the working gas with Mach numbers at the nozzle exit M _∞ = 12–14 and pressures in the settling chamber P₀ = 60–600 MPa. These values of parameters allow obtaining Reynolds numbers per meter near the cone surface equal to Re _1e = (53–200) · 10⁶ m ⁻¹. The transition occurs at Reynolds numbers Re _tr = (2.3–5.7) · 10⁶. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 76–83, May–June, 2007.     

Multibody Formulation with Large Bending Finite Elements (LBFE)

The goal of this paper is to present a flexible multibody formulation for Euler-Bernoulli beams involving large displacements. This method is based on a discretisation of internal and kinetic energies. The beam is represented by its line of centroids and each section is oriented by a frame defined by three Euler angles. We apply a finite element formulation to describe the evolution of these angles along the neutral fibre and describe the internal energy. The kinetic energy is approximated as the one of two rigid bars tangent to the neutral fibre at the ends of the beam. We derive the equations of motion from a Lagrange formulation. These equations are solved using the Newmark method or/and the Newton-Raphson technique. We solve some very classic problems taken from the literature as the curved beam presented by Simo [Simo, J. C., ‘A three-dimensional finite-strain rod model. the three-dimensional dynamic problem. Part I’, Comput. Meths. Appl. Mech. Engrg. 49, 1985, 55–70; Simo, J. C. and Vu-Quoc, L., ‘A three-dimensional finite-strain rod model, Part II: Computationals aspects’, Comput. Meths. Appl. Mech. Engrg. 58, 1988, 79–116] and Lee [Lee, Kisu, ‘Analysis of large displacements and large rotations of three-dimensional beams by using small strains and unit vectors’, Commun. Numer. Meth. Engrg. 13, 1997, 987–997] or the rotational rod presented by Avello [Avello, A., Garcia de Jalon, J., and Bayo, E., ‘Dynamics of flexible multibody systems using cartesian co-ordinates and large displacement theory’, Int. J. Num. Methods in Engineering 32, 1991, 1543–1563] and Simo [Simo, J. C. and Vu-Quoc, L., ‘On the dynamics of flexible beams under large overall motions – the planar case. Part I’ Jour. of Appl. Mech. 53, 1986, 849–854; Simo, J. C. and Vu-Quoc, L., ‘On the dynamics of flexible beams under large overall motions – the planar case. Part II’, Jour. of Appl. Mech. 53, 1986, 855–863].     

Heat and mass transfer for micropolar flow with radiation effect past a nonlinearly stretching sheet

In this study, an analysis has been performed for heat and mass transfer with radiation effect of a steady laminar boundary-layer flow of a micropolar flow past a nonlinearly stretching sheet. Parameters n, K, k ₀, Pr, Ec, and Sc represent the dominance of the nonlinearly effect, material effect, radiation effect, heat and mass transfer effects which have presented in governing equations, respectively. The similar transformation, the finite-difference method and Runge–Kutta method have been used to analyze the present problem. The numerical solutions of the flow velocity distributions, temperature profiles, the wall unknown values of θ′(0) and ϕ′(0) for calculating the heat and mass transfer of the similar boundary-layer flow are carried out as functions of n, Ec, k ₀, Pr, Sc. The value of n, k ₀, Pr and Sc parameters are important factors in this study. It will produce greater heat transfer efficiency with a larger value of those parameters, but the viscous dissipation parameter Ec and material parameter K may reduce the heat transfer efficiency. On the other hand, for mass transfer, the value of Sc parameter is important factor in this study. It will produce greater heat transfer efficiency with a larger value of Sc.     

Numerical Modeling of Interior Ballistics Processes in Light Gas Guns

An improved procedure for modeling the operation of a light-gas gun is proposed. The motion of working bodies in both the firing chamber and the light-gas chamber is studied within the framework of the mechanics of heterogeneous media. The problem of barrel heating taking into account its melting and removal of thermal ablation products into the medium inside the bore is solved in a coupled formulation. Heat and mass transfer and friction on the barrel surface are calculated using empirical dependences. The deformable piston is considered compressible and elastoviscoplastic. Allowance is made for the presence of a clearance between the lateral surface of the piston and the barrel bore walls and the associated gas flow between the firing and the light-gas chamber. Calculation results are given.     

Experimental Study of Seepage Properties of Broken Sandstone Under Different Porosities

In coal mining the water flow in broken rock is a very common phenomenon. Study of seepage properties of broken rock is one of the basic subjects required in order to understand the stability of rock surrounding roadways, preventing disasters such as water inrush and gas outbursts and developing underground resources. So far, quantitative studies on the nonlinear seepage properties of broken sandstone under different porosities are not extensive in the research literature. In this article, by means of an electro-hydraulic servo-controlled test system (MTS815.02) and a patent seepage device, the seepage properties under different conditions of porosity were tested on broken sandstone of five different grain sizes. Based on the loading method of controlling the axial compression displacement and steady permeating method, we obtained curves of the relation of pore pressure with time, as well as the relation curves between the pore pressure gradient for steady seepage and velocity. Furthermore, we calculated the permeability k and non-Darcy coefficient β corresponding to different porosities by fitting these curves with the binomial expression. This study indicates that: (1) the seepage properties of broken sandstone are closely related to grain size, load levels, and porosity structure; (2) the permeability k decreases, while the coefficient β increases with a decrease in porosity φ, but both the k − φ and the β − φ curves show some local fluctuations; (3) the permeability k of the broken sandstone has a magnitude of 10⁻¹⁴–10⁻¹² m², while the coefficient β ranges from 10¹⁰ to 10¹² m⁻¹. The results obtained provide some information for further study of the nonlinear seepage behavior of broken rock theoretically.     

Mass flow-rate control unit to calibrate hot-wire sensors

Hot-wire anemometry is a measuring technique that is widely employed in fluid mechanics research to study the velocity fields of gas flows. It is general practice to calibrate hot-wire sensors against velocity. Calibrations are usually carried out under atmospheric pressure conditions and these suggest that the wire is sensitive to the instantaneous local volume flow rate. It is pointed out, however, that hot wires are sensitive to the instantaneous local mass flow rate and, of course, also to the gas heat conductivity. To calibrate hot wires with respect to mass flow rates per unit area, i.e., with respect to (ρU), requires special calibration test rigs. Such a device is described and its application is summarized within the (ρU) range 0.1–25 kg/m² s. Calibrations are shown to yield the same hot-wire response curves for density variations in the range 1–7 kg/m³. The application of the calibrated wires to measure pulsating mass flows is demonstrated, and suggestions are made for carrying out extensive calibrations to yield the (ρU) wire response as a basis for advanced fluid mechanics research on (ρU) data in density-varying flows.     

Spatial distribution of the gas phase in an axisymmetric submerged impact jet

Experimental data on the spatial distribution of the gas phase in an axisymmetric impact jet are obtained by the particle image velocimetry/laser-induced fluorescence (PIV/LIF) method. It is shown that the distribution of bubbles in the flow is determined by the dynamics of vortex structures. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 33–38, July–August, 2009.     

Viscoelastic properties of ultra-high viscosity alginates

Ultra-high viscosity alginates were extracted from the brown seaweeds Lessonia nigrescens (UHV_N, containing 61% mannuronate (M) and 2% guluronate (G)) and Lessonia trabeculata (UHV_T, containing 22% M and 78% G). The viscoelastic behavior of the aqueous solutions of these alginates was determined in shear flow in terms of the shear stress σ ₂₁, the first normal stress difference N ₁, and the shear viscosity η in isotonic NaCl solutions (0.154 mol/L) at T = 298 K in dependence of the shear rate [(g)\dot]\dot{\gamma} for solutions of varying concentrations and molar masses (3–10 × 10⁵ g/mol, homologous series was prepared by ultrasonic degradation). Data obtained in small-amplitude oscillatory shear (SAOS) experiments obey the Cox–Merz rule. For comparison, a commercial alginate with intermediate chemical composition was additionally characterized. Particulate substances which are omnipresent in most alginates influenced the determination of the material functions at low shear rates. We have calculated structure–property relationships for the prediction of the viscosity yield, e.g., η–M _w–c–[(g)\dot]\dot{\gamma} for the Newtonian and non-Newtonian region. For the highest molar masses and concentrations, the elasticity yield in terms of N ₁ could be determined. In addition, the extensional flow behavior of the alginates was measured using capillary breakup extensional rheometry. The results demonstrate that even samples with the same average molar mass but different molar mass distributions can be differentiated in contrast to shear flow or SAOS experiments.     

Construction of piecewise-analytical gas flows joined through shock waves near the axis or center of symmetry

Analytical solutions of a quasilinear system of equations with partial derivatives are constructed in the case where the initial data for different functions are specified on different surfaces and the resultant problem has singularities of the form u/x and w/x. Conditions for existence and uniqueness of a solution in the form of formal power series for the problem posed and sufficient conditions for convergence of the series are indicated. A generalization of the problem considered is given. Results of the study are used to solve the problem of the focussing of a compression wave generated by a piston moving smoothly in a quiescent gas: a solution for t=0, including determination of the piston trajectory, and a solution for t<0, including unequivocal construction of the front of a reflected shock wave, are uniquely constructed from the distribution of gas-dynamic quantities for t>0. The solution of this problem is a generalization to the case of two independent variable self-similar Sedov's solutions. Ural State Academy of Communications, Ekaterinburg 620034. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 25–38, September–October, 1998.     

Rigorous Asymptotic Expansions for Critical Wave Speeds in a Family of Scalar Reaction-Diffusion Equations

We investigate traveling wave solutions in a family of reaction-diffusion equations which includes the Fisher–Kolmogorov–Petrowskii–Piscounov (FKPP) equation with quadratic nonlinearity and a bistable equation with degenerate cubic nonlinearity. It is known that, for each equation in this family, there is a critical wave speed which separates waves of exponential decay from those of algebraic decay at one of the end states. We derive rigorous asymptotic expansions for these critical speeds by perturbing off the classical FKPP and bistable cases. Our approach uses geometric singular perturbation theory and the blow-up technique, as well as a variant of the Melnikov method, and confirms the results previously obtained through asymptotic analysis in [J.H. Merkin and D.J. Needham, (1993). J. Appl. Math. Phys. (ZAMP) A, vol. 44, No. 4, 707–721] and [T.P. Witelski, K. Ono, and T.J. Kaper, (2001). Appl. Math. Lett., vol. 14, No. 1, 65–73].     

Projectile dynamics at low barrel pressures

A mathematical model for a projectile shot at low pressures in the space behind the projectile space is developed. The pressure rise is limited because of the nonsimultaneity of propellant ignition and combustion and the discharge of the propellant combustion products through the gap between the projectile and the walls of the gun barrel. The kinetic characteristics of flame propagation over the propellant particles are determined. A comparison of calculation and experimental data is performed. The calculation results are used in designing 2A85 self-propelled launchers and upgrading 2A30 self-propelled launchers. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 44–49, November–December, 2007.