Experimental study and mathematical simulation of the characteristics of a turbulent flow in a straight circular pipe rotating about its longitudinal axis

The vorticity formed in the cross section of a turbulent flow in a straight circular pipe rotating about its longitudinal axis decreases the values of the turbulent stresses, turbulence energy, and dissipation rate along the pipe. The results of laboratory experiments and calculations by the second-order closure model of turbulent transfer are presented. On the whole, the model using a system of transport equations yields better agreement with experimental data than the models with algebraic relations for second-order moments. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 103–116, March–April, 1998.     

Experimental investigation of a rapidly rotating turbulent duct flow

Rapidly rotating duct flow is studied experimentally with Rotation numbers in the interval [0, 1]. To achieve this, in combination with relatively high Reynolds numbers (5,000-30,000 based on the hydraulic radius), water was used as the working medium. Square and rectangular duct cross-sections were used and the angle between the rotation vector and the main axis of the duct was varied. The influence of the rotation on the pressure drop in the duct was investigated and suitable scalings of this quantity were studied.     

Experimental study of spectra corresponding to some two-point fourth-order moments in a developed turbulent flow in a tube

Moscow Physico-Technical Institute, Dolgoprudnyi Moscow Region 111700. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 36, No. 3, pp. 87–91, May–June, 1995     

Experimental study of convective heat transfer from a rotating finned tube in transverse air flow

 The convective heat transfer from fins to air has been evaluated using rotating annular fins subjected to an air flow parallel to the fins. The fin cooling is studied using infrared thermography. The thermal balance in a fin during its cooling process allows us to obtain the heat transfer coefficient from the temperature time evolution of the fin. Moreover, Particle Image Velocimetry allows us to obtain the flow field in the mid-plane between two fins. The influence of the fin spacing on the convective heat transfer is studied for various velocities of the superposed air flow and various fin rotational speeds. These tests were carried out for air flow Reynolds numbers (based on the shaft diameter and the velocity of the superposed air flow) between 2550 and 18200 and rotational Reynolds numbers (based on the shaft diameter and the peripheral speed) between 800 and 2.9 × 10⁴, for different fin spacings. Received: 14 May 1999/Accepted: 8 October 1999     

Friction drag and energy loss in a turbulent pulsating flow in a tube

The results of an experimental investigation of the kinematic structure and tangential wall stresses are used for an analysis of the time-dependent friction drag and loss of mechanical energy in a turbulent pulsating flow in a round tube. The question of the applicability of the quasistationary approach to calculation of the friction and the dissipative loss in unsteady flow is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 160–162, January–February, 1977.We thank O. F. Vasil'ev, on whose initiative and with whose support this work was carried out, and also E. M. Romanov, V. V. Zykov, and P. A. Drozhzhin for their great contribution to the. design of the experimental apparatus and provision of apparatus for the investigations.     

Variational model of a turbulent rotating flow

A model of effectively viscous turbulent flows satisfying the Navier-Stokes equations and certain slip conditions at the walls is analyzed. The turbulent viscosity is determined on the basis of the principle of minimum energy dissipation rate, whose significance and conditions of applicability are discussed in detail. A new separated turbulent flow model is outlined. The problem of turbulent flow in a porous rotating tube is solved. The existence of two metastable flow regimes is predicted: one with an axial circulation zone, the other straight-through. In the case of a strongly swirled flow the first of these has a greater probability of realization; however, as the rotation weakens, in a certain critical situation the circulation zone collapses, after which the flow can only be straight-through. Despite the absence of empirical content, every aspect of the proposed theory is in good agreement with the experimental research on vortex chamber flows.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 22–32, May–June, 1985.     

The turbulent wake of a circular cylinder rotating about the streamwise axis

This paper presents measurements in the turbulent wake of a circular cylinder rotating with its axis normal to the free-stream velocity; in other words, the axis of rotation was parallel to the streamwise direction. All three mean velocities and six Reynolds stresses were obtained at three positions downstream of the cylinder, with and without rotation of the free-stream. Most emphasis is given to the latter results because of the better flow quality. The ratio of the circumferential velocity of the cylinder to the free-stream velocity — the swirl number — had a maximum value of 0.6. Measurements for two combinations of the free-stream and angular velocities showed the velocity deficit in the wake to be a multi-valued function of the swirl number, implying that the rotation affected the separation of the cylinder's boundary layer in a complex manner. In the turbulent wake, the rotation did not significantly alter the magnitudes of the normal stresses, but caused large changes to the shape of the profiles of the axial and cross-stream normal stresses. Eventually, the primary (cross-stream) shear stress became almost entirely positive, but there was no corresponding change to the (cross-stream) gradient of the streamwise mean velocity. Despite these alterations to the turbulence, the rotationally-activated generation terms in the Reynolds transport equations never dominated the terms that are common to the wakes of rotating and non-rotating cylinders.This work was supported by the Australian Research Council. Most of the data acquisition software was written by Mr J. J. Smith.     

Experimental investigation of instabilities in flow through a long square channel rotating about the transverse axis

The results of an experimental investigation of bifurcation phenomena in a laminar flow through a rotating square channel approximately 50 channel widths long are presented. A comparison with known results of the numerical modeling of bifurcations of developed steady-state flow is carried out. A map of the steady and unsteady flow regimes is plotted. The effect of artificially generated input perturbations on the conditions of onset of longitudinally oriented vortex structures in the neighborhood of the elevated-pressure side of channels of lesser length is investigated.St. Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 87–93, March–April, 1996.     

Finite element study of free surface turbulent flow in rotating channels

Under certain conditions of liquid flow through rotating channels, the Coriolis force can induce a free surface to be formed. This problem is of practical importance in a Coriolis wear tester, which is used for determining the sliding wear coefficient of wear materials in slurry handling equipment. A deforming Galerkin finite element method is presented for predicting two‐dimensional turbulent free surface mean flow in rotating channels. Reynolds‐averaged Navier–Stokes (RANS) equations are cast into weak(algebraic) form using primitive variables (velocity and pressure). Eddy viscosity is determined via a mixing length model. Velocity is interpolated biquadratically, while pressure is interpolated bilinearly. The kinematic condition is used to form the Galerkin residual for the free surface. The free surface is represented by Hermite polynomials of zeroeth order for continuity of position and slope. Combined Newton's iteration is used to simultaneously solve for the free surface and the field variables. Results of velocity and pressure fields, as well as the free surface are shown to converge with mesh‐size refinement. There is excellent respect for mass conservation. Results are presented for various values of Rossby number (Ro) and height‐based Reynolds number (Re_H). Parameter continuation in Ro and Re_H space is used to compute solutions at higher values of flow rate and angular velocity. Copyright © 2002 John Wiley & Sons, Ltd.     

Predicting turbulent flow in a staggered tube bundle

This paper presents the results of calculations performed for the turbulent, incompressible flow around a staggered array of tubes for which carefully obtained experimental results are available as part of an established ERCOFTAC-IAHR test case. The Reynolds-averaged Navier–Stokes equations are solved using a pressure-based finite volume algorithm, using collocated cell vertex store on an unstructured and adaptive mesh of tetrahedra. Turbulence closure is obtained with a truncated form of a low-Reynolds number k– model developed by Yang and Shih. The computational domain covers all seven rows of tubes used in the experimental study and periodic flow is allowed to develop naturally. The results of the computations are surprisingly good and compare favourably with results obtained by others using a wide range of alternative k– models for a single cylinder with periodic inflow and outflow boundaries on structured meshes.     

Experimental study of turbulent axisymmetric cavity flow

An experimental study is made of turbulent axisymmetric cavity flow. The flow configuration consists of a sudden expansion and contraction pipe joint. In using the LDV system, in an effort to minimize refraction of laser beams at the curved interface, a refraction correction formula for the Reynolds shear stress is devised. Three values of the cavity length (L = 300, 600 and 900 mm) are chosen, and the cavity height (H) is fixed at 55 mm. Both open and closed cavities are considered. Special attention is given to the critical case L = 600 mm, where the cavity length L is nearly equal to the reattachment length of the flow. The Reynolds number, based on the inlet diameter (D = 110 mm) is 73,000. Measurement data are presented for the static wall pressure, mean velocity profiles, vorticity thickness distributions, and turbulence quantities.List of symbols C _f velocity correction factor - C _p static wall pressure coefficient - D diameter of inlet pipe = 110 mm - H step height or difference in radii of two pipes = 55 mm - L cavity length = 300, 600 and 900 mm - n _a , n _w , n _f refraction indices of the medium between the transmitting lens and window, the window itself, and the working fluid - signal validation rate in LDV, Hz - P wall static pressure, Pa - P _ref wall static pressure at x = -70 mm, Pa - r radial distance from centreline, m - r _a radial position of the virtual intersection, m - r _d radial location of the dividing streamline, m - r _f radial position of the real beam intersection, m - Re Reynolds number based on the inlet diameter - R _i inner radius of the cylindrical cavity=110 mm - t thickness of the window, m - T ₁ integral time scale, s - U streamwise mean velocity, m/s - U _c centreline mean velocity, m/s - U _ref maximum upstream velocity at x= -70 mm, m/s - r.m.s. intensity of streamwise, radial and circumferential velocity fluctuations respectively, m/s - Reynolds shear stress, m²/s² - x distance in the streamwise direction, m - x _a streamwise position of virtual intersection, m - x _f streamwise position of real beam intersection, m - x _r mean reattachment length, m - x nondimensional streamwise distance - y distance normal to the wall=R–r, m Greek symbols vorticity thickness - stream function of dividing streamline      

LES of turbulent flow in a concentric annulus with rotating outer wall

Fully-developed turbulent flow in a concentric annulus, r₁/r₂ = 0.5, Re_h = 12,500, with the outer wall rotating at a range of rotation rates N = U_θ,wall/U_b from 0.5 up to 4 is studied by large-eddy simulations. The focus is on the effects of moderate to very high rotation rates on the mean flow, turbulence statistics and eddy structure. For N up to ∼2, an increase in the rotation rate dampens progressively the turbulence near the rotating outer wall, while affecting only mildly the inner-wall region. At higher rotation rates this trend is reversed: for N = 2.8 close to the inner wall turbulence is dramatically reduced while the outer wall region remains turbulent with discernible helical vortices as the dominant turbulent structure. The turbulence parameters and eddy structures differ significantly for N = 2 and 2.8. This switch is attributed to the centrifuged turbulence (generated near the inner wall) prevailing over the axial inertial force as well as over the counteracting laminarizing effects of the rotating outer wall. At still higher rotation, N = 4, the flow gets laminarized but with distinct spiralling vortices akin to the Taylor–Couette rolls found between the two counter-rotating cylinders without axial flow, which is the limiting case when N approaches to infinity. The ratio of the centrifugal to axial inertial forces, Ta/Re² ∝ N² (where Ta is the Taylor number) is considered as a possible criterion for defining the conditions for the above regime change.     

Numerical analysis of turbulent flow in a rotating U-bend with roughened walls

A numerical analysis has been performed for a developing turbulent flow in a rotating U-bend of strong curvature with rib-roughened walls using an anisotropic turbulent model. In this calculation, an algebraic Reynolds stress model is used to precisely predict Reynolds stresses, and a boundary-fitted coordinate system is introduced as a method of coordinate transformation to set the exact boundary conditions along the complicated shape of U-bend with rib-roughened walls. Calculated results for mean velocity and Reynolds stresses are compared to the experimental data in order to validate the proposed numerical method and the algebraic Reynolds stress model. Although agreement is certainly not perfect in all details, the present method can predict characteristic velocity profiles and reproduce the separated flow generated near the outer wall, which is located just downstream of the curved duct. The Reynolds stresses predicted by the proposed turbulent model agree well with the experimental data, except in regions of flow separation.     

Experimental study of the mean wake of a tidal stream rotor in a shallow turbulent flow

The mean wake of a three-bladed horizontal axis tidal stream turbine operating at maximum power coefficient has been investigated experimentally in a wide flume with width 11 times the depth, providing minimal restriction to transverse wake development and behaviour of large-scale horizontal turbulence structures. This is an important first stage for understanding wake interaction in turbine arrays and hence large-scale power generation. The rotor diameter has a typical value of 60% of the depth and the thrust coefficient is representative of a full-scale turbine. The shear layers originating from the rotor tip circumference show classic linear expansion downstream, with the rate of a plane shear layer vertically and 1.5 times that horizontally. These shear layers merge by around 2.5 diameters downstream forming a self-similar two-dimensional wake beyond eight diameters downstream with a virtual origin at two diameters downstream of the rotor plane. The spreading rate is somewhat less than that for solid bodies. The detailed velocity measurements made in the near wake show rotation and vorticity similar to that measured previously for wind and marine turbines although with asymmetry associated with bed and surface proximity. The longitudinal circulation in a transverse plane is conserved at about 1% of the swept circulation from the blade tip within two diameters downstream, the extent of detailed measurement. Turbines are usually designed using blade element momentum theory in which velocities at the rotor plane are characterised by axial and tangential induction factors and it is now possible to see how this idealisation relates to actual velocities. The axial induction factor corresponds to velocity deficits at 0.4–0.8 radii from the rotor axis across the near wake while the tangential induction factor at the rotor plane corresponds to velocities at 0.4–0.6 radii between 1–2 diameters downstream, indicating some general correspondence. For the two-dimensional self-similar far wake the two parameters defining the centreline velocity deficit and the transverse velocity profiles are likely to be insensitive to Reynolds number in turbulent conditions.     

Influence of suspended particles on the structure of a turbulent flow in a tube

The results of an experimental investigation into the dispersed flow of a system subject to negative pressure gradients are presented. The measurements were based on an optical time-of-flight method in a water channel, using polystyrene spheres as the solid phase. The average and pulsational characteristics of the dispersed flow were obtained in the boundary (wall) region and also in the center (core) of the flow. For zero pressure gradient the influence of the solid phase expressed itself as a reduction in the level of turbulence and an increase in the extent of the viscous sublayer, leading to a fall in the coefficient of friction. For a negative pressure gradient the pressure of the solid phase generated small-scale vortices, reduced the extent of the viscous sublayer, and hence increased the coefficient of surface friction.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 111–118, March–April, 1976.The author wishes to thank Yu. A. Buevich for interest in this work and V. L. Zalukaev for participation in the experiments.