Motion of shock waves in a channel of variable cross section in the presence of a steady flow regime

The motion of shock waves against a steady flow in a channel of variable cross section is considered. Situations for which Chisnell's hypothesis [1] or a quasistationary flow model are valid are considered. The problem is of interest, in particular, in connection with the investigation of the starting of shock wind tunnels.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 103–110, July–August, 1981.I am very grateful to A. N. Kraiko and V. T. Grin' for valuable advice and support during the work.     

Numerical modeling of jet flow in a slot channel in the transition regime

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 6, pp. 108–112, November–December, 1991.     

Rotational inviscid flow with circulation zones in a channel of variable cross section

The development of the theory of rotational motion of inviscid fluids for the purposes of describing channel flow encounters certain difficulties in connection with the appearance of viscosity effects near the walls. In the potential-rotational model [1], in which the vorticity is nonzero only in a closed circulation zone surrounded by potential flow, it is assumed that the separation and attachment points are known in advance. For example, for flow around a cavity these points coincide with the extreme corner points of the contour. The problem of determining the vorticity in a closed zone for the potential-rotational model has been investigated in a number of studies [2, 3], etc. In the case of an incompressible fluid the vorticity in the circulation zone is constant for two-dimensional flow and proportional to the distance from the axis for axisymmetric flow. The value of the constant is found from the steady-state condition for the adjoining viscous layers. If the channel walls have a smooth profile without corner points, then for determining the boundaries of the circulation zones additional conditions must be used. This study employs another scheme, in which the vorticity is formed outside the region of flow and in a particular problem is specified in the form of a boundary condition. An analytic solution describing the rotational flow of an inviscid fluid in a channel with a slightly varying cross section is obtained. Three types of entrance flow nonuniformity are considered: 1) uniform shear flow, 2) wake-type flow, and 3) potential flow with a narrow wall boundary layer. Streamline patterns with circulation zones are constructed for flows in diffuser channels with the above-mentioned types of entrance nonuniformity. A model of flow separation in a channel with a turbulent boundary layer on the walls is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 31–37, March–April, 1985.In conclusion the author wishes to thank E. Yu. Shal'man, A. N. Kraiko, and A. B. Vatazhin for useful discussions and advice.     

Simple waves on a shear gas flow in a channel of constant cross section

The plane-parallel unsteady-state shear gas flow in a narrow channel of constant cross section is considered. The existence theorem of solutions in the form of simple waves of a set of equations of motion is proved for a class of isentropic flows with a monotone velocity profile over the channel depth. The exact solution described by incomplete beta-functions is found for a polytropic equation of state in a class of isentropic flows. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 36–43, January–February, 1999.     

Velocity characteristics of the flow around a square cross section cylinder placed near a channel wall

Laser-Doppler measurements are reported of the flow around a square cross section cylinder placed at various heights (Y ₀) above a plane channel wall for a Reynolds number Re _H = 1.36 × 10⁴.The thickness of the turbulent boundary layer on the channel wall at the obstacle position, but with it removed from the water tunnel, was equal to 0.8 H, being H the square obstacle height and the free stream turbulence intensity was 6%. The periodic character of the flow in the near wake was characterized by measurements of turbulence spectra in the range 0 Y ₀/H 3.3 and the results revealed that regular vortex shedding was suppressed for a gap height less than 0.35 H. Detailed results of time averaged mean flow properties, turbulence intensities and Reynolds stresses revealed the structural differences of the near wakes with and without vortex shedding for Y _O = 0.5 and Y _O = 0.25 respectively.List of symbols R _e Reynolds number Re = U ₀ H/v - H Square obstacle height - Y Normal coordinate - Y ₀ Gap distance between the plane wall and obstacle face - C _f Skin friction coefficient - k Turbulent kinetic energy - u Friction velocity - Turbulent boundary layer thickness - y ⁺ Non-dimensional log law coordinate - X _r Separated flow length behind the obstacle - U Mean axial velocity - V Mean radial velocity - u² Axial turbulent stress - ² Normal turbulent stress - u Turbulent shear stress - U ₀ Mean bulk velocity - E Power spectrum energy - f Predominant frequency - h Distance between inner shear layers behind the obstacle - s Distance from the wall to the shear layer behind the obstacle - C _D Drag coefficient     

变截面悬链线无铰拱应变影响线的解析解

针对变截面悬链线无铰拱应变影响线尚无解析解的现状,通过弹性中心法对其力法方程进行简化,利用Ritter截面变化规律简化变截面悬链线无铰拱的曲线积分,从而推导出变截面悬链线无铰拱应变影响线的闭合解表达式,再将解析结果与有限元分析结果进行对比研究,并对轴力参数展开对比分析。研究结果表明,本文推导得到变截面悬链线无铰拱应变影响线的解析解,数值解析解同有限元结果间最大相对误差小于2%,其轴力影响随矢跨比和测点位置变化而变化,本文公式具有较高的工程精度和计算分析参考价值。     

Acoustic waves in a cylindrical duct with periodically varying cross section

The null field approach is used to study the propagation of acoustic waves in a rotationally symmetric hard-walled duct with a periodically varying cross section. For a radius that varies sinusoidally along the axial distance, numerical computations give the axial wave number and the passbands and stopbands of the modes of the duct. In particular, small passbands are seen to exist even for very large variations in radius, and probably all the way to the point where the duct is cut off. We also present some plots which show the pressure pattern inside the duct.     

Visualisation and modelling studies of churn flow in a vertical pipe

Churn flow is an important flow regime intermediate between slug flow and annular flow. A feature of this regime is the occurrence of very large waves travelling upwards over a liquid film substrate which may intermittently travel downwards. These waves are often formed close to the liquid inlet where their behaviour is usually difficult to observe. This paper describes a series of experiments using a test section with a specially constructed transparent liquid inlet. High-speed video recordings show clearly the process of wave formation and analysis of the recordings gave data on wave frequencies and typical velocities. Also, predictions of velocity and distance travelled by the waves were obtained via the application of a simple mathematical model that takes into account the forces acting on a circumferentially coherent wave.     

Friction factor in micropipe gas flow under laminar,transition and turbulent flow regime

The present work deals with the compressible flow of nitrogen gas inside microtubes ranging from 30 to 500 μm and with different values of the surface roughness (<1%), for different flow regimes. The first part of the work is devoted to a benchmark of friction factor data obtained at DIENCA (University of Bologna) and the ENEA laboratories, using fused silica pipes of 50 and 100 μm. Data overlapping is excellent thus evidencing how the agreement of the experimental data with the classic theory is independent of the measurement system. The second part of the work demonstrates that classic correlations can predict friction factor in laminar flow without revealing any evident influence of the surface roughness. The laminar-to-turbulent transition starts for Reynolds number not lower than 2000 for smooth pipes, while tending to larger values (3200–4500) for rough pipes. Anyway, contrarily to other available results, no dependence of the critical Reynolds number on the L/D has been observed. Changes in the flow regime have been found of the sharp and smooth type, like for larger pipes; smooth transition looks typical of smooth pipes while the sharp transition in the flow pattern is associated with rough pipes. In the fully developed turbulent regime, obtained for both smooth and rough pipes, an agreement between experimental data and the Blasius correlation has been verified for smooth pipes, while for rough pipes the agreement with predictions given by the Colebrook equation is rather modest.     

Specific momentum of a flow in the minimal cross section of a laval nozzle and in the outlet cross section of a contracting nozzle

The article discusses the question of the effect of nonuniformity of the parameters, brought about by the two-dimensional character of the flow on the value of the specific momentum of the flow under supercritical conditions. It is shown, that, in the approximation of an ideal (nonviscous and non-heat-conducting) gas, the corresponding value with a continuous flow always exceeds the value calculated in accordance with the one-dimensional theory for the same nozzle and the same stagnation parameters of the gas.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 186–188, January–February, 1976.     

Fluid flow in a rotating channel of square section

Laminar flow in a channel rotating about a transverse axis has been studied numerically [1–3] and analytically [4–7] at small Reynolds numbers. The drag coefficient of rotating channels with straight and curvilinear axes has been measured [4, 8, 9]. The present paper gives the results of an experimental investigation into the kinematics of water flow in a channel rotating with different intensities. The flow was visualized by means of hydrogen bubbles and a dye. A study was made of the process of flow separation in a rapidly rotating channel into a core with homogeneous velocity distribution in the direction parallel to the rotation axis and thin shear layers on the walls normal to this axis. The values of the dimensionless numbers were found that correspond to flow rearrangement accompanied by formation of longitudinally oriented vortex structures in the region of higher pressure, and also the values of the rotation parameter needed for the almost complete suppression of turbulence in the region of lower pressure. A general analysis is made of the forms of instability in the different regions of the flow and of the possible flow regimes in a rotating channel.     

Fission of solitons in a symmetric triangular channel with variable cross section

In this paper, we study the disintegration of a soliton in a symmetric triangular channel when it propagates from one uniform cross section of the channel into another through a transition region. A criterion under which a soliton is split into n solitons is given. Numerical results for n = 3 are presented to confirm the analytical predictions.     

Investigation of the flow around a circular cylinder under the influence of an electromagnetic force

An investigation of the effect of the local electromagnetic body force on the flow behavior around a circular cylinder is conducted. The electromagnetic force is applied locally on the cylinder surface in the range of 70–130° from the stagnation point along the cylinder circumference in both clockwise and counterclockwise directions. The numerical results predict that the Lorentz force applied in the circumferential direction on the cylinder moves the separation point rearward, and reduces the drag. To validate the numerical results, an experiment is conducted with a circular cylinder of 5 cm diameter. The electrodes and permanent magnets are flush mounted on the cylinder in such a way that the Lorentz force is generated in the circumferential direction. Flow visualization with polystyrene particles and direct drag measurement using strain gages are made. The fluid used is natural sea water of electric conductivity of about 4 (Ω m)^-1. Induction effect can be neglected in the present investigation due to the low flow speed and the Lorentz force is proportional to E×B where E is an applied electric field and B is a magnetic field. Received: 7 June 1998/Accepted: 28 April 1999     

Seiche oscillations in a rectangular channel with an abrupt expansion of the cross section

The natural frequencies and modes of seiche oscillations in a closed water reservoir consisting of a long narrow channel connected to a wide basin were investigated theoretically and experimentally. Calculations were made using linear shallow-water theory in two-dimensional and one-dimensional formulations. The spectral properties of free-surface oscillations at points lying on the nodal lines of the first four modes of seiche oscillations were studied experimentally. The one-dimensional model adequately predicts lower-mode frequencies, but the data on the positions of the nodal points of seiche oscillations obtained using this model are somewhat different from those obtained experimentally and using the two-dimensional model.