Critical transition Reynolds number for plane channel flow

The determination of the critical transition Reynolds number is of practical importance for some engineering problems. However, it is not available with the current theoretical method, and has to rely on experiments. For supersonic/hypersonic boundary layer flows, the experimental method for determination is not feasible either. Therefore, in this paper, a numerical method for the determination of the critical transition Reynolds number for an incompressible plane channel flow is proposed. It is basically aimed to test the feasibility of the method. The proposed method is extended to determine the critical Reynolds number of the supersonic/hypersonic boundary layer flow in the subsequent papers.

从亚临界到临界雷诺数圆柱绕流和分离泡的大涡模拟

A large eddy simulation of wall-adapting local eddy-viscosity model(LES-WALE)is used to simulate the threedimensional flow around a circular cylinder with a diameter of 0.25 m from sub-critical to super-critical Reynolds numbers at 1×10^(5),2.5×10^(5),and 7.2×10^(5),respectively.The present results such as drag crisis,surface pressure distribution,and Strouhal number are in good agreement with the classical experimental data.When entering the critical region,a small plateau was found on the pressure distribution curves,corresponding to the appearance of laminar separation bubbles,and the separation point is delayed and the recirculation bubbles become narrowed and shortened.The tangential velocity of the cylinder surface changes from positive to negative at the separation point.The instantaneous vorticity and timeaveraging separation bubbles embody an unstable feature.Within the separation bubble,the pressure varies dramatically with time,but not with position.The surface pressure fluctuates greatly after the laminar separation bubble appears,and it is gradually stabilized until the basic pressure is reached.The process of laminar separation,transition from laminar flow to turbulent flow and turbulent reattachment is also shown.The three-dimensional Q criterion of vortex structure and the two-dimensional spanwise vorticity reveal the phenomenon that the wake structure narrows with the increase of the Reynolds number.

Critical Transition Reynolds Number for the Incompressible Flat-plate Boundary Layer as Searched by Numerical Simulation

The critical transition Reynolds number is the lowest value at which the turbulent flow can hold in real flows.The determination of the critical transition Reynolds number not only is a scientific problem,but also is important for some engineering problems.However,there is no available theoretical method to search the critical value.For the hypersonic boundary layer with significant importance for engineering problems,there is no available experimental method to search the critical value so far.Consequently,it is imperative to take numerical method to search it.In this paper,direct numerical simulations(DNS)method is employed to determine the critical transition Reynolds number for the incompressible flat-plate boundary layer.Firstly,under the assumption of parallel flow,the temporal mode DNS is performed to determine the critical value as Re_(xpcr)=43767,which is quite close to the numerical results of other people.Secondly,under the condition of nonparallel flow,the spatial mode DNS is performed to determine the critical transition Reynolds number as Re_(xcr)=3×10^(5),which is well consistent with the experimental results.In principle,the proposed method in this paper can be extended to the supersonic/hypersonic boundary layer,and that problem will be discussed in the subsequent papers.

The Analysis of Stability of Bingham Fluid Flowing Down an Inclined Plane

In this paper, the stability problem of Bingham fluids flowing down an inclinedplane is studied with respect to two dimensional disturbances. The crilical Reynolodsnumber is given in ihe case of long waves, and the effect of yield stress on stability isanalysed.

Viscous Fluid Flowing around the Plate: Turbulence

Diffusion of momentum gives rise to viscosity. This article presents a solution in the explicit form of the equation of the momentum diffusion for a viscous fluid flowing around a plate taking into account deceleration. Three characteristic regions of a viscous flow have been described: the mantle, the body of the boundary layer, the viscous sublayer. In the mantle, the effect of viscosity is significant at a considerable distance from the plate. The momentum diffusion is focused in the body of the boundary layer. The diffusion force that produces the momentum of force giving rise to eddies is localized in the viscous sublayer. At the beginning of the plate, a moment of force twists the liquid along the flow, creating eddies that roll along the plate. For this reason, they are pressed against the surface of the plate. But at some distance from the beginning of the plate, the moment of force changes its orientation to the opposite and twists the vortices in the opposite direction, causing the vortices to roll along the plate against the flow. This causes the liquid to detach from the surface of the plate. This is the beginning of turbulence. The diameter of the vortex produced in the viscous sublayer is small being of the order of the thickness of the viscous sublayer. The vortex possesses a large angular velocity. Due to the momentum diffusion and the effect of the eddies combined in passing along the plate, its diameter increases up to the size of the thickness of the boundary layer and even more, whereas its angular velocity decreases down to the values really observed. The value of the critical Reynolds number of the transition from the laminar flow to the turbulent one has been found, and it agrees with the experimental data. The value of the shear stress produced by the viscous fluid on the plate surface has also been obtained. The way of measurement of the friction coefficient characterizing the effect of the plate on the flow has been proposed. It has been shown that the boundary condition of adhesion to the surface of a body flown around, that is applied in the estimation of viscous flows, contradicts the real processes of the flow.

EXPERIMENTAL STUDY OF FRICTION FACTOR FOR GROUNDWATER FLOW IN A SINGLE ROUGH FRACTURE

To study the relationships between the friction factor f and the flow type in a single rough fracture, the formulae of f for both unconfined and confined flows are deduced based on previous studies. The relationships between f and the Reynolds number （Re） for different relative roughnesses are investigated experimentally. The Moody-type diagram, based on the deduced formula of f, is also plotted and the hydraulic characteristics of the flow in a rough fracture are analyzed. Results show that the Moody-type diagram of the experiment has a similar distribution to that of the conventional Moody diagram. It is found that the value of f in the experiment is much smaller than that of the conventional Moody diagram and turbulent flow appears easier for rough fractures, which can be explained by the separation phenomenon in boundary layers. The critical Re ranging from 650 to 700 in rough fractures is concluded based on the experimental results. It also can be concluded that the friction factor f is related not only with the Re and the relative roughness but also with the absolute roughness.

The numerical investigation of flow and heat transfer characteristics of flow past a slit-cylinder

The flow and heat transfer characteristics, including transition critical Reynolds number from two-dimensional to three-dimensional, the influence of slit-cylinder geometric parameter on Strouhal number, Nusselt number and forces acting on the slit-cylinder are numerically investigated. It's found that transition critical Reynolds number from two-dimensional(flow wake deforms in two directions) to three-dimensional(flow wake deforms in three directions) increases with the augment of the slit width ratio in the range of present considered Reynolds number. The present results indicate that the three-dimensional vortex structures resulting from the deformation of the vortex shedding have significant effects on flow and heat transfer features such as Strouhal number, Nusselt number and forces acting on the cylinders with different ratios of slit width. It's observed that the drag and lift coefficients reduce as the increase of slit width ratio, and vortex shedding is effectively suppressed by the slits.Moreover, the comprehensive heat transfer performance of the cylinder with the slits is significantly improved with the increase of the slit width ratio.

Experimental Study of the Flow in Helical Circular Pipes:Torsion Effect on the Flow Velocity and Turbulence

An objective of the present paper is to experimentally clarify the torsion effect on the flow in helical circular pipes. We have made six helical circular pipes having different pitches and common non-dimensional curvature δ of about 0.1. The torsion parameter β0, which is defined by β0 = τ/（2δ）1/2 with non-dimensional torsion r, are taken to be 0.02, 0.45, 0.69, 1.01, 1.38 and 1.89 covering from small to very large pitch. The velocity distributions and the turbulence of the flow are measured using an X-type hot-wire anemometer in the range of the Reynolds number from 200 to 20000. The results obtained are summarized as follows： The mean secondary flow pattern in a cross section of the pipe changes from an ordinary twin-vortex type as is seen in a curved pipe without torsion （toroidal pipe） to a single vortex type after one of the twin-vortex gradually disappears as β0 increases. The circulation direction of the single vortex is the same as the direction of torsion of the pipe. The mean velocity distribution of the axial flow is similar to that of the toroidal pipe at small β0, but changes its shape as β0 increases, and attains the shape similar to that in a straight circular pipe when ,β0 = 1.89. It is also found that the critical Reynolds number, at which the flow shows a marginal behavior to turbulence, decreases as ,β0 increases for small ,β0, and then increases after taking a minimum at ,β0 ≈ 1.4 as ,β0 increases. The minimum of the critical Reynolds number experimentally obtained is about 400 at ,β0 ≈ 1.4.