Evaluation of the shadowgraph method for the convective flow in a side-heated cavity

The shadowgraph method is used to visualize the convective flow in a water-filled square cavity, which is differentially heated and cooled from the opposing vertical sidewalls. Since in this system a quantitative recovery of the temperature field from the observed shadowgraph images is not possible, we apply a somewhat reverse procedure. The numerical solution of the cavity flow yields the field of the refractive index. By numerically integrating the path of light through this field, artificial shadowgraph images are constructed. This makes a comparison of the numerical and the experimental temperature fields possible and also leads to a clearer interpretation of the shadowgraph images and a better understanding of the way in which certain features are generated. The procedure is not restricted to the cavity flow, but can be applied whenever the field of the refractive index is available.     

Application of the boundary-element method to calculate subsonic flow around a profile

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 5, pp. 94–97, September–October, 1993.     

A velocity minimum in a potential fluid flow

An example of three-dimensional potential flow of an inviscid incompressible fluid is presented, in which the point of a strict non-zero local minimum of velocity is an internal point of the flow. This proves the impossibility to extend to a three-dimensional flow the two-dimensional velocity minimum principle, according to which in plane potential flows of incompressible fluid the flow velocity cannot have a local non-zero minimum at an internal point.     

Particle interaction in a flow with a parabolic velocity profile

The hydrodynamic interaction of two rigid spherical particles in a viscous incompressible fluid with the velocity at infinity represented by a second-degree polynomial in the coordinates is considered. An analytical solution of the problem is suggested. The forces and torques exerted on the particles and also the linear and angular particle velocities are calculated. The results are compared with previous theoretical and experimental data. Saransk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 84–91, January–February, 2000. The work received financial support from the Russian Foundation for Basic Research (project No. 98-01-03295).     

输液管道临界流速的傅里叶级数法

傅里叶级数法被用于计算输液管道的临界流速，与有限元等数值法相比，更为简单可靠。     

Effect of the measurement volume in turbulent pipe flow measurement by the ultrasonic velocity profile method (mean velocity profile and Reynolds stress measurement)

 The ultrasonic velocity profile measurement method has some favorable advantages over the conventional flow measurement methods, such as measurement of the instantaneous velocity profile over the measuring line and its applicability to opaque liquids. The method has another advantage of being non-intrusive. Hence, it is applicable to various flow conditions, although it requires a relatively large measurement volume. In this paper, the effects of the measurement volume on the mean velocity profile and the Reynolds stress measurement have been investigated for fully developed turbulent flows in a vertical pipe. The results were then compared with data obtained by direct numerical simulation. Received: 9 March 2000 / Accepted: 27 March 2001 Published online: 29 November 2001     

Instability of a plane axisymmetric flow with a shear discontinuity in the velocity profile

It is proposed to investigate the stability of a plane axisymmetric flow with an angular velocity profile (r) such that the angular velocity is constant when r < r_O – L and r > r_O + L but varies monotonically from ₁ to ₂ near the point r_O, the thickness of the transition zone being small L r_O, whereas the change in velocity is not small ¦₂ – ₁¦ ₂, ₁. Obviously, as L O short-wave disturbances with respect to the azimuthal coordinate (k=m/r_O 1/r_O) will be unstable with a growth rate-close to the Kelvin—Helmholtz growth rate. In the case L=O (i.e., for a profile with a shear-discontinuity) we find the instability growth rate _O and show that where the thickness of the discontinuity L is finite (but small) the growth rate does not differ from _O up to terms proportional to kL 1 and 1/m 1. Using this example it is possible to investigate the effect of rotation on the flow stability. It is important to note that stabilization (or destabilization) of the flow in question by rotation occurs only for three-dimensional or axisymmetric perturbations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 111–114, January–February, 1985.     

Velocity profile measurement of the Taylor vortex flow of a magnetic fluid using the ultrasonic Doppler method

 A successful application of the ultrasound velocity profile (UVP) measuring technique to investigations on the flow of magnetic fluids is described. The flow structure of a magnetic fluid in a concentric annular geometry with a large aspect ratio of 20 and a radius ratio of 0.65 was investigated for a inner cylinder rotation. Axial velocity distributions were measured using the UVP measuring technique. A non-uniform magnetic field was applied to the flow field using a permanent magnet located on the outside of the cylinders. The energy spectral density was calculated from the periodic axial velocity profiles. The critical Reynolds number was obtained for various magnetic field strengths, and the apparent viscosity caused by the applied magnetic field was estimated. The UVP method was demonstrated to provide useful information on the structure of Taylor vortex flow in a magnetic fluid. Received: 27 May 1997/Accepted: 21 July 1998     

A novel formula to describe the velocity profile of free jet flow

Having a potential core, the velocity profile in initial zone of incompressible submerged jet flow is different from that in fully developed region. In the former researches, the two regions were studied separately, even a short part between the two regions being considered as a transition region. The velocity profile in fully developed region looked as a Gaussian distribution, which is valid when jet initial region is comparatively short. But when the size of initial zone is long enough not to be able to be neglected, especially for large-size exit, this kind of assumption is not acceptable. Based on the analysis of flow structure of jet flow, a new velocity profile formula of submerged jet flow was proposed, which unites the initial, transition, fully developed regions of jet flow via modifying Gaussian distribution with a radial adjusting coefficient. For the round jet with the medium or high range of Reynolds number, the radial adjusting coefficient is a power function of reciprocal of jet distance. And then some literature experimental data were applied in verification, and the new formula exhibited a good calculation result. This work opened that the jet flow velocity profile at any site along the flow distance can be described via a same formula.     

The shadowgraph method in convection experiments

The shadowgraph method is applied to thermal convection experiments and electro-hydrodynamic convection (EHC) in nematic liquid crystals. In both cases convection leads to a spatially periodic field of the refractive index causing a spatially periodic intensity modulation of parallel light passing the cell. Close to the onset of convection the temperature or director field is given by linear stability analysis. Knowing these functions the determination of their amplitudes becomes possible by means of the shadowgraph method. The method is demostrated using various examples of thermal and EHC convection experiments.     

Calculation by the Krylov-Bogolyubov method of the velocity profile and fluxes in the nonisothermal flow of a rarefied gas in a cylindrical capillary

The Krylov-Bogolyubov numerical method is used to solve integral transfer equations obtained from the kinetic equation with the BHC (Bhatnagar—Cross—Krook) model of the collision operator. The velocity profiles and the thermal-creep flows and Poiseuille flow are calculated in different modes of flow under conditions of incomplete accommodation of the tangential momentum of molecules at the wall.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 143–150, November–December, 1978.     

Theory of steady waves in horizontal flow with a linear velocity profile

The structure and characteristics of nonlinear steady waves on the surface of horizontal shear flow of an ideal homogeneous incompressible fluid of finite depth with a linear velocity profile are studied using two-dimensional theory and the Euler approach. The wave motion is considered irrotational. A modification of the first Stokes method is proposed that allows algebraic calculations of terms of perturbation series. Nonlinear dispersion relations are obtained and analyzed for both upstream and downstream traveling waves. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 43–48, May–June, 2006.     

Solution of the perturbation problem for a shear flow with nonmonotonic velocity profile

Novosibirsk State University, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 36, No. 5, pp. 7–15, September–October, 1995.     

Application of the ultrasonic velocity profile method to the mapping of liquid metal flows under the influence of a non-uniform magnetic field

An ultrasonic velocity profile (UVP) method has been successfully applied to the investigation of a liquid metal channel flow under the influence of an inhomogeneous magnetic field. Using velocity profiles obtained by the ultrasonic velocimeter and their numerical post processing, two-dimensional time-averaged flow maps were efficiently produced. A single transducer immersed directly into the working fluid was used in order to simplify alignment of measurement lines and avoid the undesirable refraction of the acoustic beam on the walls. An M-shaped flow and wake behind a magnetic obstacle were reconstructed as the patterns of shear and large-scale vortical flows.     

A velocity formulation for flow past a symmetric profile with a wake

A model having velocity components as basic unknowns is presented for calculation of two-dimensional flow past a symmetric profile with a wake in a channel. A modified least squares functional is used for the finite element solution of velocities. The determination of the position of the free streamline is treated as an optimum design problem. The concepts of cost function, geometry parameter and sensitivity derivative are employed. Numerical results are compared with published results obtained with streamfunction formulations.