Unsteady fluid flow in tubes and thinwall envelopes

Classical and new mathematical models describing the phenomenon of hydraulic shock are considered.Belarusian State University of Transport, Gomel. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 6, pp. 960–967, November–December, 1995.     

Unsteady Stokes' flow in two dimensions

Some simple problems are considered which indicate how transient effects lead to the development of slow viscous flows. Explicit solutions are obtained for situations when a source, rotlet or stokeslet is impulsively introduced at a particular time, and the manner by which such flows, which are initially harmonic, are transformed into those satisfying the biharmonic equation is clearly displayed. Conclusions regarding the formation of separated regions are presented.     

Unsteady,turbulent flow in pipes

Summary The method of multiple scales is utilized to calculate the propagation of small-amplitude, finite-rate waves in tubes. It is assumed that the flow generated by the wave is quasi-one-dimensional and furthermore that the effects of turbulence can be modeled by a constant friction coefficient. A simple analytical expression for shocks which propagate into still air is derived and the asymptotic structure of the wave-properties is discussed in detail.

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Instationäre, turbulente Strömung in Rohren

Zusammenfassung Mittels der Methode der mehrfachen Veränderlichen wird die Ausbreitung von Wellen kleiner, jedoch endlicher, Amplituden in Rohren berechnet. Dabei wird die Strömung näherungsweise als eindimensional behandelt und weiters vorausgesetzt, daß der Einfluß der Turbulenz durch eine konstante Widerstandszahl erfaßt werden kann. Für in ruhendes Medium laufende Stöße ergibt sich eine einfache analytische Beziehung. Das asymptotische Verhalten der Welle für große Zeiten wird im Detail behandelt.

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With 4 Figures     

A simple method for measuring wire tension in drift tubes

Measuring the tension of wires in drift tubes after construction is an important procedure because sometimes the wires get loose after soldering. The method described here uses a simple circuit for observing the change in the Lissajous pattern of a wire resonating with an external magnetic field. The vibration of the wire causes a fundamental harmonic component in the current and results in a periodic change of the Lissajous pattern. Measurement of this fundamental harmonic signal provides a precise determination of the resonance frequency and the wire tension.     

Unsteady swirled flow in a cylindrical channel

We show the effect of the non-steady-state problem of a working medium on the evolution of the parameters of translational-rotational flow in a cylindrical channel.Translated from InzhenernoFisicheskii Zhurnal, Vol. 46, No. 1, pp. 21–24, January, 1984.     

Unsteady convective heat transfer in potential flow

Analytical relations are obtained for the unsteady temperature field in potential flow over a flat plate and a cylinder.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 32, No. 1, pp. 109–115, January, 1977.     

A simple wide-band sine wave quadrature oscillator

A simple sine wave oscillator delivering two signals in quadrature has been developed. It covers the frequency range from below 1 Hz to 100 MHz and is voltage-controllable over each frequency decade. The circuit consists of two 90° phase shift stages using active allpass filters and an inverter, all arranged in a feedback loop. Although general application is envisaged, the design is particularly suitable in particle electrorotation studies     

Unsteady hydromagnetic couette flow in a rotating system

Unsteady hydromagnetic flow of an electrically conducting viscous incompressible fluid in a rotating system under the influence of a uniform transverse magnetic field is investigated when one of the plates is set into motion with the time dependent velocity $\text{U(t)}$ in its own plane. Two cases of interest, namely, impulsive start as well as accelerated start of the moving plate are discussed. The asymptotic behaviour of the solution is also analysed for both small and large time to highlight the transient approach to the final steady state and effects of rotation parameter as well as Hartmann number. The shear stresses at the moving plate due to the primary and secondary flows are derived in both cases. It is found that the shear stress components due to the primary flow decrease, whereas that due to the secondary flow increase with the increase in rotation parameter.     

Approximations to flow in slender tubes

Summary A tube of circular cross section whose radius is a function of a slow variable Z=(1/R)z, where z is the co-ordinate in the axial direction and R is a large streamwise Reynolds number, may be designated a slender tube. An elementary approximation to the flow in such tubes is obtained and results compared with an approximation based on the profiles obtained by Daniels and Eagles [7] for exponential slender tubes.     

Viscous flow in oscillating angulated tubes

Summary.  The motion of a Newtonian liquid contained in an angulated tube, which oscillates under the effect of external stimulation and gravity, was studied. It was experimentally established that the one-dimensional theory developed in the present study predicts satisfactorily the meniscus position, for frequencies of oscillation below 0.5 Hz and tube radius above 2.5 mm. Received February 11, 2002; revised April 19, 2002 Published online: January 16, 2003     

Nonlinear wave modulation in fluid filled distensible tubes

Summary The present work considers one dimensional wave propagation in an infinitely long, straight and homogeneous nonlinear viscoelastic or elastic tube filled with an incompressible, inviscid fluid. Using the reductive perturbation technique, and assuming the weakness of dissipative effects, the amplitude modulation of weakly nonlinear waves is examined. It is shown that the amplitude modulation of these waves is governed by a dissipative nonlinear Schrödinger equation (NLS). In the absence of dissipative effects, this equation reduces to the classical NLS equation. The examination of the coefficients of the dissipative and classical NLS equations reveals the significance of the tube wall inertia to obtain a balance between nonlinearity and dispersion. Some special solutions of the NLS equation are given and the modulational instability of the plane wave solution is discussed for various incompressible hyperelastic materials.     

A numerical method for flexible airfoils in incompressible inviscid flow

Summary The paper deals with the aerodynamic analysis of flexible airfoils, based on a quasi-lattice vortex method (QVLM). The analysis is formulated in matrix form and leads, as in other similar studies, to a linear algebraic system when the angle of attack is nonzero, and to an eigenvalue problem when the incidence angle is zero. The aerodynamic characteristic curvesC _L -,C _m - are presented. Finally, the airfoil shapes for several values of the tension coefficient and angles of attack are drawn. The results obtained with the present method are in good agreement with those reported in previous studies and evidentiate the flexibility of the QVLM as applied to flexible airfoils.Notation A aerodynamic matrix, defined in QVL method, (8) - B matrix, see Eq. (18) - c chord of airfoil - C matrix defined asAB - C _L lift coefficient, 2L/V ² c) - C _p moment coefficient, 2M/(V ² c ²) - C _p pressure coefficient,C _p =2p/(V ² ) - C _T tension coefficient, 2T/(V ² c) - D matrix, see Eq. (11) - I unit matrix - l curvilinear length of the flexible airfoil - N number of collocation points on the airfoil shape - q dynamic pressure, V ² /2 - T tension force in the sail - V freestream velocity - w downwash - x nondimensional coordinate,x/c - X _i control points, Eq. (9) - X _max dimensionless position of the maximum camber - Y _k source points, Eq. (9) - z coordinate normal tox axis - Z nondimensional coordinate,z/c - Z _s camber equation in dimensionless form,z _s /c - incidence with respect to the upstream flow velocity - column vector of the local curvatures {₁, ₂,..., _N } ^T - nondimensional membrane excess ratio - eigenvalue of the problem (23) - _k zeroes of the Chebyshev polynomia of the first kind, 1kN - column vector of the local slopes, {₀, ₁, ₂,..., _N } ^T - column vector, {₁, ₂,..., _N } ^T - ₀ slope at airfoil leading edge     

Unsteady pressure waves and shock waves in elastic tubes containing bubbly air-water mixtures

Summary The flow of a two-phase fluid through elastic tubes is more complex than that of a single phase fluid. The mathematical model is based on an one-dimensional approach to the flow of a liquid-gas mixture. The one-dimensional equations for transient two-phase flow through elastic tubes are a system of nonlinear hyperbolic partial differential equations if the bubbles and the liquid particles move with the same velocity. Included in the model are the effects of wall elasticity, compressibility of the gas and the liquid, the surface tension and the variable area change. The propagation of finite pressure waves and shock waves in a liquid containing gas bubbles has been investigated. The results show a differently strong influence of the parameters on the wave propagation speed and on the shock wave relations.

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Zur Ausbreitung von Druck- und Stoßwellen in instationären Blasen-Flüssigkeitsströmungen durch elastische Leitungen

Zusammenfassung Es ist bekannt, daß bei der mathematischen Beschreibung einer Zweiphasenströmung insofern Schwierigkeiten auftreten können, als unter bestimmten Voraussetzungen sowohl reelle als auch komplexe charakteristische Richtungen auftreten können. Für den Fall gleicher Geschwindigkeiten von Blasen und Flüssigkeit erhält man aus den instationären Gleichungen ein nichtlineares hyperbolisches Differentialgleichungssystem. Berücksichtigt werden die Elastizität der Wandungen, die Kompressibilität des Gases und der Flüssigkeit sowie die Oberflächenspannung. Wellenausbreitungsgeschwindigkeiten und Stoßrelationen werden angegeben. Die Resultate zeigen einen unterschiedlich starken Einfluß der verschiedenen Parameter auf die Wellenaus-breitungsgeschwindigkeit und die Stoßrelationen.

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With 13 Figures     

A simple non-associated flow model for sand

 This paper proposes a simple non-associated plasticity model for sand. The yield surface is taken to be a member of a recently derived family of yield loci, requiring the specification of a single parameter in addition to the stress ratio at the peak value of deviatoric stress on the yield surface in deviatoric:mean effective stress space. This simple equation, can easily be fitted to given sand data. The flow rule also has a simple equation, such that the critical state is not at the top of the yield locus in stress space. The equation of the flow rule requires the specification of the critical state dissipation constant, plus one additional parameter. This permits realistic modelling of the undrained behaviour of sand in states looser and denser than critical. The parameter controlling the flow rule can, for convenience, be taken to be equal to the parameter governing the shape of the yield surface. However, since the two parameters are not required to be equal, the flow rule can easily be adjusted to model more accurately the rate of change of direction of the plastic strain increment vector with changing stress ratio around the yield surface. The model resembles more complex models based on the mathematical theory of envelopes, but the equations of the yield loci and flow rules are much simpler. The contribution in this paper is therefore to provide a model similar to those derived based on micro mechanical considerations, but which is more useful to geotechnical engineers, in that the number of parameters is kept to a minimum, the constitutive equations are simple, and the flow rule can easily be controlled. The model is easy to apply in geotechnical analysis, and would be easy to implement in a finite element program. Received: 11 January 2002     

Unsteady flow from a source in a rotating fluid

Summary A source, which is situated on the axis of a rotating fluid, commences to expel fluid with constant rate at the time t=0. We describe how the geostrophic forces lead to the formation of a narrow column along the axis, before the eventual development of the viscous Stewartson column along the axis, and how the final steady state is achieved. An understanding of the role of the non-linear inertial forces in the neighbourhood of the source is given. The results are also extended by considering the effect of placing the source between two infinite discs situated perpendicular to the axis of rotation.     

Oscillatory liquid flow in elastic porous tubes

Summary An analytical method of solution of some problems of laminar, oscillatory flow in elastic porous tubes is given. The mathematical model is based on an one-dimensional approach to the liquid motion. The derived formulae describe the main flow characteristics: pressure, velocity, local and surface outflow of fluid. Influence of geometric dimensions, mechanical properties of elastic tubes, local outflow and filtration through the porous wall, on liquid motion durability is analysed. A simple method of experimental determination of functional parameters is shown.     

Calculation of He II flow in tubes

The flow of superfluid helium through a tube with different temperatures at the ends differs considerably from that of a Newtonian fluid. The strong dependence of the thermodynamic properties on temperature, the internal convection mechanism and the structure of superfluid turbulence causes unusual flows. The equations for the flow of He II are integrated using a new one-dimensional, steady state model to study the flow in a tube. A wide range of driving conditions is studied. The temperature and pressure profiles along the tube fall into four classes. A dimensionless parameter called is defined which determines the progression through the four classes of behavior. The deviation of the flow from Newtonian is measured by . Significant maxima of the temperature and pressure can occur between the ends of the tube for large values of . The shapes of the profiles and the mass flux depend primarily on , the geometry and the boundary conditions. Formulas are presented which relate the variables of interest to the boundary conditions. These formulas result from averaging the equations of motion along the tube. A general and unified approach, based on , is presented for analyzing experimental data and designing new experiments. It is shown that the common practice of neglecting the pressure term in the energy equation results in poor prediction for many situations. The occurrence of large maxima of pressure and temperature imply that the interpretation of some of the experimental data of the literature should be reconsidered.