Shallow wakes generated on smooth and rough surfaces

This study deals with the behavior of shallow turbulent wakes generated on smooth and rough surfaces. The wake generator used is a flat plate placed normal to the flow. Experiments were conducted at flow depths of 40 and 80 mm. The boundary layer thickness in the approaching flow occupies 60–75% of the flow depth. The Reynolds number based on the plate width and approaching freestream velocity varies from 13.0 × 10³ to 14.5 × 10³. Velocity measurements were carried out in the near-wake region (1–10 plate widths) using a laser-Doppler anemometer. The mean velocity distributions at various axial stations collapse onto a single curve by a proper choice of the length and velocity scales. It is important to note that a sense of self-similarity is attained even in the near-wake region. Attempts were made to clarify the relative effects of the transverse shear and bed friction in shallow open channel wakes. Received: 11 February 1999/Accepted: 30 August 2000     

Numerical modeling of the rotation of a solid body with a liquid-filled cavity having radial ribs

The boundary-value problem of unsteady vortex flow of a viscous incompressible fluid in a cylindrical vessel with radial ribs rotating at a variable angular velocity is solved using a finite-difference method. The results of the solution are used to calculate the motion of a system of a solid body and a cavity filled with a liquid. The results are compared with available experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 135–139, March–April, 2007.     

Receptivity of the boundary layer on a flat plate with a blunted leading edge to steady nonuniformity of the free stream

The flow past a flat plate with a blunted leading edge by a flow of a viscous incompressible fluid with a small spanwise-periodic, steady nonuniformity of the velocity profile is considered. Such a flow simulates the interaction of one type of vortex disturbances of a turbulent external flow with the boundary layer. The solution obtained predicts generation of strong disturbances in the boundary layer, which are similar to the streaky structure observed in the case of high free-stream turbulence. It is shown that the boundary-layer flow on blunted bodies is more sensitive to vortex disturbances than on a plate with a sharp leading edge. Central Aerohydrodynamic Institute, Zhukovskii, 140160. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 93–100, July–August, 2000.     

Scanning PIV investigation of the laminar separation bubble on a SD7003 airfoil

A laminar separation bubble occurs on the suction side of the SD7003 airfoil at an angle of attack α =  4–8° and a low Reynolds number less than 100,000, which brings about a significant adverse aerodynamic effect. The spatial and temporal structure of the laminar separation bubble was studied using the scanning PIV method at α =  4° and Re = 60,000 and 20,000. Of particular interest are the dynamic vortex behavior in transition process and the subsequent vortex evolution in the turbulent boundary layer. The flow was continuously sampled in a stack of parallel illuminated planes from two orthogonal views with a frequency of hundreds Hz, and PIV cross-correlation was performed to obtain the 2D velocity field in each plane. Results of both the single-sliced and the volumetric presentations of the laminar separation bubble reveal vortex shedding in transition near the reattachment region at Re = 60,000. In a relatively long distance vortices characterized by paired wall-normal vorticity packets retain their identities in the reattached turbulent boundary layer, though vortices interact through tearing, stretching and tilting. Compared with the restricted LSB at Re = 60,000, the flow at Re = 20,000 presents an earlier separation and a significantly increased reversed flow region followed by “huge” vortical structures.     

An inviscid model for vortex shedding from a deforming body

An inviscid vortex sheet model is developed in order to study the unsteady separated flow past a two-dimensional deforming body which moves with a prescribed motion in an otherwise quiescent fluid. Following Jones (J Fluid Mech 496, 405–441, 2003) the flow is assumed to comprise of a bound vortex sheet attached to the body and two separate vortex sheets originating at the edges. The complex conjugate velocity potential is expressed explicitly in terms of the bound vortex sheet strength and the edge circulations through a boundary integral representation. It is shown that Kelvin’s circulation theorem, along with the conditions of continuity of the normal velocity across the body and the boundedness of the velocity field, yields a coupled system of equations for the unknown bound vortex sheet strength and the edge circulations. A general numerical treatment is developed for the singular principal value integrals arising in the solution procedure. The model is validated against the results of Jones (J Fluid Mech 496, 405–441, 2003) for computations involving a rigid flat plate and is subsequently applied to the flapping foil experiments of Heathcote et al. (AIAA J, 42, 2196–2204, 2004) in order to predict the thrust coefficient. The utility of the model in simulating aquatic locomotion is also demonstrated, with vortex shedding suppressed at the leading edge of the swimming body.      

Linear problem of a hydrofoil moving under the free surface of a finite-depth fluid

A method of solving the plane linear problem of a steady-state irrotational flow about a body under the free surface of a heavy fluid of finite depth is developed. The boundary-value problem is formulated for a complex perturbed velocity and is reduced to a singular integral equation relative to the intensity of a vortex layer that models the hydrofoil. The kernel of the equation is the exact solution of the corresponding boundary-value problem for a vortex of unit intensity. The equation is solved by the discrete-vortex method. The effect of the parameters of the problem on the hydrodynamic characteristics of the elliptical hydrofoil and the shape of the free surface are estimated numerically. Omsk Division of the Sobolev Institute of Mathematics, Omsk 644099. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 85–90, November–December, 1998.     

Ideal incompressible flow around a wedge tip

A planar analog of conical flows is considered: an inviscid incompressible fluid flow around a wedge tip. A class of conical flows is found where vorticity is transported along streamlines by the potential component of velocity. Problems of a wave “locked” in the corner region and of a flow accelerating along the rib of a dihedral angle are considered. By analogy with an axisymmetric quasi-conical flow, a planar quasi-conical flow of the fluid is determined, namely, the flow inside and outside the region bounded by tangent curves described by a power law. Conditions are found where vorticity and swirl produce a significant effect. An approximate solution of the problem of the fluid flow inside a “zero” angle is obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 57–65, March–April, 2007.     

Development of steady-state mixing in an aerodynamic wake

We consider the unsteady, isothermal flow in the wake behind a body on which a shock wave has impinged. This flow is studied for sufficiently large distance from the body, when the effect of the latter on the external flow, as in the corresponding steady problem [1, 2], may be neglected. The analysis is performed for laminar and turbulent mixing with planar and axial symmetry.In § 1 we use the characteristics of the system of equations consisting of the momentum equation written on the wake centerline and an integral equation to determine approximately the boundary separating the steady and unsteady flows. It is noted that the unsteady flow takes place between this boundary and the tagged particle line, which at the moment of detachment of the shock wave from the body coincided with it.In §2 we show the possibility of calculating the flow in this region using the characteristics of the system of equations noted above. Some particular solutions of the latter are obtained.Then, in §§ 3 and 4 the exact solutions corresponding to the flow regions identified in §§1 and 2 are presented.Section 3 presents the exact solutions of the linear system of equations for large values of the time, when the velocity in the wake is close to the velocity of the particles behind the shock wave.On the basis of the analysis made in §2, and previously in [3], §4 obtains the exact solution of the nonlinear system of equations which describes the development of the mixing near the tagged particle line for planar turbulent flow. This solution is compared with the corresponding approximate solution of §2. The accuracy of the latter is noted. Comparison of the horizontal component velocity profiles with the profiles obtained in the preceding section and used in [4] in the method of integral relations shows satisfactory agreement between them     

Investigation of turbulence structures in a drag-reduced turbulent channel flow with surfactant additive by stereoscopic particle image velocimetry

In the present study, we employed stereoscopic particle image velocimetry (PIV) to investigate the characteristics of turbulence structures in a drag-reduced turbulent channel flow with addition of surfactant. The tested drag-reducing fluid was a CTAC/NaSal/Water (CTAC: cetyltrimethyl ammonium chloride; NaSal: sodium salicylate) system at 25°C. The weight concentration of CTAC was 30 ppm. Stereoscopic PIV measurement was performed for a water flow (Re=1.1×10⁴) and a CTAC solution flow (Re=1.5×10⁴ with 54% drag reduction) in both the streamwise–spanwise and wall-normal-spanwise planes, respectively. The three-dimensionality of hairpin vortex structures in the near-wall region for wall-bounded turbulent flow was reproduced by conditionally averaging the stereoscopic two-dimensional-three-component velocity fields. A series of wall-normal vortex cores were found to align with the near-wall low-speed streaks with opposite vorticity signals at both sides of the streaks and with the vorticity decreased on average by about one order of magnitude in CTAC solution flow compared with water flow; the spanwise spacing between the near-wall low-speed streaks in the solution flow is increased by about 46%. The streamwise vorticity of the vortex cores appearing in the wall-normal-spanwise plane was also decreased by the use of drag-reducing surfactant additives.     

Nonstationary hydrodynamic characteristics of a double grid of profiles

The flow about a double grid of solid profiles of arbitrary shape which vibrate in a stream of an ideal incompressible fluid is considered. Behind the grid profiles, the nonstationary vortex traces simulated by the lines of contact velocity discontinuity are taken into account. The problem is reduced to the solution of a system of two integral equations relative to the fluid velocity on the initial profiles of the double grid under the assumption that the vibration amplitudes are small. Formulas for calculating the nonstationary forces and moments are derived. The dependences of these forces on the shape, mutual positions, and laws of vibration of the grid profiles are studied. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 150–155, July–August, 1999.     

The turbulent boundary layer on the moving surface of a cylindrical body

A study is made of the problem of a two-dimensional turbulent boundary layer on the moving surface of a cylindrical body (a Rankine oval with a relative elongation of four) moving at constant velocity in an incompressible fluid. For the numerical simulation of the turbulent flow of the fluid, the boundary layer is divided into exterior and interior regions in accordance with a two-layer model, using different expressions for the coefficients of turbulent transfer for each region. A study was nade of the development of the boundary layer on the body at different speeds of the body surface and different Reynolds numbers. The following integral characteristics were found by numerical calculation: the work of friction as the body is displaced; the work expended on the movement of its surface; and, for a flow regime with separation, the work of the pressure force. In this case the following model of separation flow is assumed: beyond the singular point in the solution of the boundary layer equations that indicates the appearance of a region of reverse flow, the pressure and friction stress on the wall are constant and are determined by their values at the singular point.Translated from Izvestiya Akademii Nauk SSSH, Mekhanika Zhidkosti i Gaza, No. 5, pp. 61–67, September–October, 1984.Finally, the author would like to thank G. G. Chernyi and Yu. D. Shevelev for useful discussions and for their interest in this work.     

Spontaneous swirling in axisymmetric MHD flows of an ideally conducting fluid with closed streamlines

The region of instability of the Hill-Shafranov viscous MHD vortex with respect to azimuthal axisymmetric perturbations of the velocity field is determined numerically as a function of the Reynolds number and magnetization in a linear formulation. An approximate formulation of the linear stability problem for MHD flows with circular streamlines is considered. The further evolution of the perturbations in the supercritical region is studied using a nonlinear analog model (a simplified initial system of equations that takes into account some important properties of the basic equations). For this model, the secondary flows resulting from the instability are determined. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 40–50, May–June, 2007.     

An approximate solution of the problem of the axially symmetric flow of a viscous incompressible fluid in an angular region

An approximate solution of the axially symmetric problem of the flow of a viscous incompressible fluid in the vicinity of the point of contact between a uniformly moving plunger and a channel wall is obtained. Tomsk (Tomsk Branch of the Institute of Structural Macrokinetics, Russian Academy of Sciences). Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 157–160, January–February, 1999.     

An Attempt to Combine Large Eddy Simulation with the k-ε Model in a Channel-Flow Calculation

Large eddy simulation (LES) is combined with the Reynolds-averaged Navier–Stokes (RANS) equation in a turbulent channel-flow calculation. A one-equation subgrid-scale model is solved in a three-dimensional grid in the near-wall region whereas the standard k–ε model is solved in a one-dimensional grid in the outer region away from the wall. The two grid systems are overlapped to connect the two models smoothly. A turbulent channel flow is calculated at Reynolds numbers higher than typical LES and several statistical quantities are examined. The mean velocity profile is in good agreement with the logarithmic law. The profile of the turbulent kinetic energy in the near-wall region is smoothly connected with that of the turbulent energy for the k–ε model in the outer region. Turbulence statistics show that the solution in the near-wall region is as accurate as a usual LES. The present approach is different from wall modeling in LES that uses a RANS model near the wall. The former is not as efficient as the latter for calculating high-Reynolds-number flows. Nevertheless, the present method of combining the two models is expected to pave the way for constructing a unified turbulence model that is useful for many purposes including wall modeling. Received 11 June 1999 and accepted 15 December 2000     

Using the perturbation method to solve the problem of separated incompressible flow past thin airfoils

A model for separated incompressible flow past thin airfoils in the neighborhood of the “shockless entrance” condition is constructed based on the averaging of the vortex shedding flow past the airfoil edges. By approximation of the vortex shedding by two vortex curves, determination of the average hydrodynamic parameters is reduced to a twofold solution of an integral singular equation equivalent to the equation describing steady-state nonseparated airfoil flow. In this case, the calculation time is two orders of magnitude smaller than the time required for the solution of the corresponding evolution problem. The results of a test calculation using the proposed method are in fair agreement with available results of calculations and experiments. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 49–63, May–June, 2006.     

Determination of the aerodynamic characteristics of aircraft in the transonic velocity range

The problem of determining the integral aerodynamic characteristics of aircraft as a whole in the transonic velocity range is considered. An approximate method of their calculation is developed using the nonlinear transonic theory of small perturbations for three-dimensional flow over a body. The method of investigation consists in separating the flow region into two subregions (outer and inner), applying numerical methods of integrating the equations in those regions, and joining the solutions. The Murman-Cole method of calculating the pressure drag of an isolated wing is generalized to the case of a combination of wing and fuselage. Central Aerohydrodynamics Institute, Zhukovskii 140160. Translated from Prikladnaya Mekhanika i Tekhnicheskaya fizika, Vol. 39, No. 4, pp. 91–101, July–August, 1998.     

Velocity distributions in a hydrocyclone separator

 The internal three-dimensional flow field in a hydrocyclone was studied using laser velocimetry. Seven axial planes were investigated for three different inlet flow rates and three independent and different rejects rates. Results at each measurement plane showed that the measured tangential velocity profile behaves like a forced vortex at the region near the air core, and like a free vortex in the outer portion of the flow. The peak nondimensional tangential velocity decreases as the distance from the inlet region increases, however, the peak dimensional tangential velocity increases as the distance from the inlet region increases. The nondimensional peak tangential velocities are approximately equal for all of the flow rates. The magnitude of the tangential velocity increased in the inner forced vortex region as the rejects rate was increased. Backflows exist in the axial velocity profile near the inlet region, but these reversed flows disappear in the exit region. The dimensional vorticity is proportional to inlet flow rate and decreases with increasing rejects flow rates. Received: 27 February 2001/Accepted: 19 June 2001     

Self-similar problem of separated ideal-fluid flow over an expanding plate

The research carried out in [1–8] is developed by considering the self-similar problem of the unsteady separated flow over a plate expanding from a point with the constant velocity D of a plane-parallel stream of ideal fluid with velocity V_∞. At infinity the flow is uniform, steady and normal to the surface of the plate. A wide range of values of the parameter α=V_∞/D is investigated. On the value of α there depends, in particular, the direction of shedding of the vortex sheets (VS) which, in accordance with the Joukowsky-Chaplygin condition, occur in separated flow over a plate. A comparison is made with the results obtained when the sheets are replaced by vortex filaments (VF). In accordance with [9] the choice of the intensity of the VF ensures, like the introduction of VS, the finiteness of the flow velocity at the edges of the plate. Within the framework of the unsteady analogy and the law of plane sections the problem of the flow over a delta wing at an angle of attack reduces to the unsteady flow over an expanding plate investigated. In addition to [3, 9], this question was also examined in [10–15]. In [11–15] and in [3] the analysis is based on VS and in [9, 10] on VF. Special attention is paid to the topology of the flow, in particular, to the structure of the so-called conical streamlines and their points of convergence and divergence (this was done in [3] for a special, nonlinear law of expansion of the plate and a variable free-stream velocity). The results obtained for the models with VS and VF are compared over a broad range of values of α, not only with respect to the integral characteristics, as in [12], but also with respect to the flow patterns. Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 62–69, September–October, 1988.     

Three-dimensional flow structures and associated turbulence in the tip region of a waterjet pump rotor blade

Stereo particle image velocimetry measurements focus on the flow structure and turbulence within the tip leakage vortex (TLV) of an axial waterjet pump rotor. Unobstructed optical access to the sample area is achieved by matching the optical refractive index of the transparent pump with that of the fluid. Data obtained in closely spaced planes enable us to reconstruct the 3D TLV structure, including all components of the mean vorticity and strain-rate tensor along with the Reynolds stresses and associated turbulence production rates. The flow in the tip region is highly three-dimensional, and the characteristics of the TLV and leakage flow vary significantly along the blade tip chordwise direction. The TLV starts to roll up along the suction side tip corner of the blade, and it propagates within the passage toward the pressure side of the neighboring blade. A shear layer with increasing length connects the TLV to the blade tip and initially feeds vorticity into it. During initial rollup, the TLV involves entrainment of a few vortex filaments with predominantly circumferential vorticity from the blade tip. Being shed from the blade, these filaments also have high circumferential velocity and appear as swirling jets. The circumferential velocity in the TLV core is also substantially higher than that in the surrounding passage flow, but the velocity peak does not coincide with the point of maximum vorticity. When entrainment of filaments stops in the aft part of the passage, newly forming filaments wrap around the core in helical trajectories. In ensemble-averaged data, these filaments generate a vortical region that surrounds the TLV with vorticity that is perpendicular to that in the vortex core. Turbulence within the TLV is highly anisotropic and spatially non-uniform. Trends can be traced to high turbulent kinetic energy and turbulent shear stresses, e.g., in the shear layer containing the vortex filaments and the contraction region situated along the line where the leakage backflow meets the throughflow, causing separation of the boundary layer at the pump casing. Upon exposure to adverse pressure gradients in the aft part of the passage, at 0.65–0.7 chord fraction in the present conditions, the TLV bursts into a broad turbulent array of widely distributed vortex filaments.     

Time-resolved and volumetric PIV measurements of a transitional separation bubble on an SD7003 airfoil

To comprehensively understand the effects of Kelvin–Helmholtz instabilities on a transitional separation bubble on the suction side of an airfoil regarding as to flapping of the bubble and its impact on the airfoil performance, the temporal and spatial structure of the vortices occurring at the downstream end of the separation bubble is investigated. Since the bubble variation leads to a change of the pressure distribution, the investigation of the instantaneous velocity field is essential to understand the details of the overall airfoil performance. This vortex formation in the reattachment region on the upper surface of an SD7003 airfoil is analyzed in detail at different angles of attack. At a Reynolds number Re _c < 100,000 the laminar boundary layer separates at angles of attack >4°. Due to transition processes, turbulent reattachment of the separated shear layer occurs enclosing a locally confined recirculation region. To identify the location of the separation bubble and to describe the dynamics of the reattachment, a time-resolved PIV measurement in a single light-sheet is performed. To elucidate the spatial structure of the flow patterns in the reattachment region in time and space, a stereo scanning PIV set-up is applied. The flow field is recorded in at least ten successive light-sheet planes with two high-speed cameras enclosing a viewing angle of 65° to detect all three velocity components within a light-sheet leading to a time-resolved volumetric measurement due to a high scanning speed. The measurements evidence the development of quasi-periodic vortex structures. The temporal dynamics of the vortex roll-up, initialized by the Kelvin–Helmholtz (KH) instability, is shown as well as the spatial development of the vortex roll-up process. Based on these measurements a model for the evolving vortex structure consisting of the formation of c-shape vortices and their transformation into screwdriver vortices is introduced.