Method of contour dynamics for plane flows of an ideal fluid

The method of contour dynamics is generalized for plane flows of a general form when, apart from vortices, distributed mass sources (or sinks) are present in the fluid. The laws of variation of the vorticity and divergence of the fluid particles with time are obtained for this case which makes it possible to use the method of contour dynamics for piecewise-constant vortex sink distributions.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 16–19, September–October, 1993.     

A contour integral approach to some cavity flows of elastic fluids

This papers considers a contour integral approach to some cavity flows of elastic fluids. The fluids are described by integral constitutive equations and therefore require consideration of strain history. Strain calculations can consume a large amount of computer resource and so we develop an efficient approach to this aspect. Both slider and calender driven flows are considered.     

Conformal contour dynamics in bounded domains

A contour dynamics algorithm is presented for vortex patches in unbounded domains and in simply connected bounded domains. It is based on conformal mapping and spectral analysis. The inside and outside of a vortex patch are analytically mapped onto the inside and outside of the unit circles of two different complex planes. The flow field is determined by matching the inner and outer flows on the patch boundary. Following the Legras and Zeitlin conformal dynamics concept, the time evolution of the patch boundary is expressed by means of the time derivatives of the mapping functions. The presence of a bounding wall, which can be permeable and movable, is considered. The geometry and dynamics of the patch and the flow velocity on the bounding wall are represented by Fourier series; by assuming their coefficients as control parameters, the proposed formulation can be appealing for optimization and control purposes. Two numerical examples of the proposed technique are presented.     

Tomographic reconstruction of shock layer flows

The tomographic reconstruction of supersonic flows faces two challenges. Firstly, techniques used in the past, such as the direct Fourier method (DFM) (Gottlieb and Gustafsson in On the direct Fourier method for computer tomography, 1998; Morton in Tomographic imaging of supersonic flows, 1995) or various backprojection (Kak and Slaney in Principles of computerized tomographic imaging, vol. 33 in Classics in Applied Mathematics, 2001) techniques, have only been able to reconstruct areas of the flow which are upstream of any opaque objects, such as a model. Secondly, shock waves create sharp discontinuities in flow properties, which can be difficult to reconstruct both in position and in magnitude with limited data. This paper will present a reconstruction method, matrix inversion using ray-tracing and least squares conjugate gradient (MI-RLS), which uses geometric ray-tracing and a sparse matrix iterative solver (Paige and Saunders in ACM Trans. Math. Softw. 8(1):43–71, 1982) to overcome both of these challenges. It will be shown, through testing with a phantom object described in tomographic literature, that the results compare favourably to those produced by the DFM technique. Finally, the method will be used to reconstruct three-dimensional density fields from interferometric shock layer images, with good resolution (Faletič in Tomographic reconstruction of shock layer flows, 2005). This paper was based on work that was presented at the 3rd International Symposium on Interdisciplinary Shock Wave Research, Canberra, Australia, March 1–3, 2006.     

Inviscid gas flows in nozzles with a steeply converging contour

Inviscid gas flows in nozzles with a uniform exit flow and contours profiled starting from the lower point of a steeply converging region with an angle θ = −90° are analyzed. It is shown that there exists a class of convergent-divergent contours, within which the flow is characterized by the fact that the line θ = 0 of zero angle of the velocity vector inclination to the x axis consists of two oppositely-directed regions located partially or even completely ahead of the minimum section, while near the minimum sections their regions convex inward the gas stream are in decelerated flow. The minimum sections of the nozzles with M _e → 1 approach the center of the nozzle from the right.     

Boundary layer interaction in three-dimensional flows

An approach known from the theory of matched asymptotic expansions involving the isolation of subregions with different scales is used to study flows which are assumed to be described by the boundary layer equations almost everywhere near the surface except for a fairly narrow zone in which the inflowing boundary layers interact. Two characteristic types of interaction are identified. An approximate theory describing the flow in the interaction zone, which makes it possible to locate the position of the interaction zone on the surface, is proposed. The interaction flow on the end wall of a vane channel is calculated subject to certain simplifications. The results of an experimental investigation of this flow are presented and it is shown that the theoretical model proposed describes the three-dimensional corner separation which occurs in the neighborhood of the line of intersection of the end wall and the convex edge of the vane.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 116–123, May–June, 1988.     

The fundamental equations of two-dimensional layer flows

In many studics on two-dimensional flows in field of atmosphere and ocean theequations which are extension of river-hydraulic equationsor Navier-Stokes equationsare usually used.In these equations stand forturbulent resistance.Obviously use of these equations in practice may lead to contradiction.In this paper the average of Reynolds equations over depth is taken.The motion equations,continuity equation and diffusion equation are obtained for the average physical variables.     

Horizontal mixing layer in shallow water flows

Horizontal-shear thin-layer homogeneous fluid flow in the open channel is considered. A one-dimensional mathematical model of the development and evolution of the horizontal mixing layer is derived within the framework of the three-layer scheme. The steady-state solutions of the equations of motion are constructed and investigated. In particular, supercritical (subcritical)-in-average flow concepts are introduced and the problem of the mixing layer structure is solved. The proposed model is verified on the basis of comparison with a numerical solution of two-dimensional equations of shallow water theory.     

Droplet dynamics in sub-critical complex flows

A newly designed eccentric cylinder device has been used to study the deformation and orientation of single Newtonian droplets immersed in an immiscible Newtonian liquid in a controlled complex flow field. Optical microscopy coupled with image acquisition analysis allows monitoring the dynamics of droplets flowing in the gap between the eccentric cylinders. Throughout the experiments, the flow intensity was kept below the critical conditions for droplet break-up. The experimental results are compared with predictions which are obtained using the transient form of the phenomenological model of Maffettone and Minale (J Non-Newtonian Fluid Mech 78:227–241, 1998; J Non-Newtonian Fluid Mech 84:105–106, 1999), incorporating a flow type parameter that accounts for the relative amount of elongational effects in the flow field and adapting the capillary number to mixed flows. For all the sub-critical flows studied here, good agreement was found between model predictions and experimental data, providing, for the first time, a quantitative assessment of drop shape predictions in complex flows.     

Experimental study of boundary layer separation in truncated ideal contour nozzles

DLR Lampoldshausen carried out a cold flow test series to study the boundary layer separation and the related flow field in a truncated ideal contour nozzle. A special focus was set on low nozzle pressure ratios to identify the origin of a locally re-attached flow condition that was detected in previous test campaigns. A convex shaped Mach disc was found for nozzle pressure ratios less than 10 and a slight concave one for nozzle pressure ratios more than 20. Due to boundary layer transition at low nozzle pressure ratios the convex Mach disc is temporary tilted and redirects the flow towards the nozzle wall. A simple separation criterion for turbulent nozzle flows is presented that fits well for both cold and hot flows. It is shown that the oblique separation shock recompresses the flow to 90% of the ambience. The separation zone of the presented film cooled nozzle is compared with a conventional one around 40% longer. Furthermore a relation between shear layer shape and forced side loads is described.      

Effects of dissipation on heat transfer due to second order boundary layer flows

Heat and Mass Transfer - Effects of dissipation on heat transfer due to second order effects of longitudinal curvature, transverse curvature, displacement speed, external vorticity and stagnation...     

Vectored injection into isobaric laminar boundary layer flows

The results of a systematic study of self-similar solutions of the Blasius equation are presented for a wide range of both normal and tangential surface injection velocities. Only flows with non-vanishing shear are considered; however, an arbitrary orientation of the injection vector is allowed. It is found that a positive tangential component of injection (downstream vectoring) significantly increases the mass transfer rate required to blow off the boundary layer. For upstream vectoring, a new group of solutions is found over a certain range of the tangential wall velocity wherein the wall shear is doublevalued.

---

Zusammenfassung Es wird eine systematische Untersuchung ähnlicher Lösungen der Blasius-Gleichung in einem weiten Bereich der normalen und tangentialen Ausblasgeschwindigkeit vorgelegt, wobei nur Strömungen mit nicht-verschwindender Schubspannung, aber beliebiger Ausblasrichtung betrachtet werden. Man findet, daß eine positive tangentiale (stromabwärts gerichtete) Komponente der Ausblasgeschwindigkeit den Stoff-übergangsstrom beträchtlich erhöht, der zum Wegblasen der Grenzschicht erforderlich ist. Für stromaufwärts gerichtetes Ausblasen wird eine neue Gruppe von Lösungen in einem gewissen Bereich der tangentialen Wandgeschwindigkeit gefunden, innerhalb dessen die Wandschubspannung verdoppelt wird.

     

Finite element analysis of incompressible laminar boundary layer flows

A numerical procedure was developed to solve the two-dimensional and axisymmetric incompressible laminar boundary layer equations using the semi-discrete Galerkin finite element method. Linear Lagrangian, quadratic Lagrangian, and cubic Hermite interpolating polynomials were used for the finite element discretization; the first-order, the second-order backward difference approximation, and the Crank-Nicolson method were used for the system of non-linear ordinary differential equations; the Picard iteration and the Newton-Raphson technique were used to solve the resulting non-linear algebraic system of equations. Conservation of mass is treated as a constraint condition in the procedure; hence, it is integrated numerically along the solution line while marching along the time-like co-ordinate. Among the numerical schemes tested, the Picard iteration technique used with the quadratic Lagrangian polynomials and the second-order backward difference approximation case turned out to be the most efficient to achieve the same accuracy. The advantages of the method developed lie in its coarse grid accuracy, global computational efficiency, and wide applicability to most situations that may arise in incompressible laminar boundary layer flows.     

Applications of a higher‐order bounded numerical scheme to turbulent flows

This paper applies the higher‐order bounded numerical scheme Weighted Average Coefficients Ensuring Boundedness (WACEB) to simulate two‐ and three‐dimensional turbulent flows. In the scheme, a weighted average formulation is used for interpolating the variables at cell faces and the weighted average coefficients are determined from a normalized variable formulation and total variation diminishing (TVD) constraints to ensure the boundedness of the solution. The scheme is applied to two turbulent flow problems: (1) two‐dimensional turbulent flow around a blunt plate; and (2) three‐dimensional turbulent flow inside a mildly curved U‐bend. In the present study, turbulence is evaluated by using a low‐Reynolds number version of the k–ω model. For the flow simulation, the QUICK scheme is applied to the momentum equations while either the WACEB scheme (Method 1) or the UPWIND scheme (Method 2) is used for the turbulence equations. The present study shows that the WACEB scheme has at least second‐order accuracy while ensuring boundedness of the solutions. The present numerical study for a pure convection problem shows that the ‘TVD’ slope ranges from 2 to 4. For the turbulent recirculating flow, two different mixed procedures (Method 1 and Method 2) produce a substantial difference for the mean velocities as well as for the turbulence kinetic energy. Method 1 predicts better results than Method 2 does, comparing the analytical solution and the experimental data. For the turbulent flow inside the mildly curved U‐bend, although the predictions of velocity distributions with two procedures are very close, a noticeable difference of turbulence kinetic energy is exhibited. It is noticed that the discrepancy exists between numerical results and the experimental data. The reason is the limit of the two‐equation turbulence model to such complex turbulent flows with extra strain‐rates. Copyright © 2001 John Wiley & Sons, Ltd.     

模糊随机有限元在转子动力学分析中的应用

综合考虑转子系统的模糊和随机不确定性,根据信息熵理论,在保证模糊熵不变的前提下将模糊量转化为随机变量.然后,采用基于Neumann展开式的随机有限元法分析转子系统动力学问题.将Neumann展开式与Newmark-β法结合起来,从而使基于Neumann展开式的随机有限元法可以应用于分析非线性转子系统.以考虑模糊和随机因素的转子系统的临界转速和非线性响应为例,验证了模糊随机有限元方法在转子系统动力学分析中的适用性.     

Electrical measurement of sediment layer thickness under suspension flows

 This paper reports a new technique to measure the thickness of a layer of deposited sediment as a function of time, independent of the flow conditions or presence of suspended sediment above the layer. Small electrodes on the bottom and a reference electrode in the fluid above were used to measure the resistance of the layer with a small AC current and a bridge circuit. Using a multiplexer and an Analog-to-Digital converter the growth of the layer can be accurately monitored at many locations on the tank bottom. In a trial experiment the sedimentation under a stagnant column of a monodisperse suspension was examined. The results show that changes in the sediment layer thickness of less than 0.3% can be measured for layers up to 0.2 g/cm². Received: 8 February 1998/Accepted: 19 July 1998