High Reynolds Number Case Research Articles

Investigations of angle bias errors in laser velocimetry measurements

Fig. 3 Ice shapes for 15,30, and 60 s on the leading edge of the NACA 0012 airfoil. Recent studies with the calculation method of Ref. 1 also indicate excellent agreement between calculations and measurements on clean airfoils where the Reynolds number is low. It will be interesting to extend this study to an iced airfoil operating at low Reynolds numbers. For example, typical Reynolds numbers for the blades of a rotorcraft near the hub may be around 2 x 10. For the NACA 0012 airfoil, the stall angle without ice accretion is 11 deg at this Reynolds number (Fig. 1). The question would be, will a small leading-edge ice reduce the stall angle as drastically as it does in the higher Reynolds number case, and what will that stall angle be?

Studies of Wake-Affected Heat Transfer arounda Leading Edge of Turbine Rotors. lst Report, Heat Transfer Augmentation by Incident Wakes.

Detailed measurements are performed on time-averaged pressure and heat transfer distributions around a blunt body which is affected by periodically incoming wakes from the upstream moving bars. The blunt body is a test model of a front portion of a turbine blade in gas turbines and consists of a semicircular cylindrical leading edge and a flat plate afterbody. A wide range of steady and unsteady flow conditions, such as Reynolds numbers based on the diameter of the leading edge and the bar-passing Strouhal numbers, are investigated. The measurement of the surface pressure distribution, in conjunction with the corresponding numerical analysis by BEM (Boundary Element Method), reveals the existence of the separation bubble around the junction between the semicircular cylinder and the flat plate, which is emphasized especially in higher Reynolds number cases. The wake-affected heat transfer distributions indicated that the wake passing over the leading edge caused significant increase in heat transfer in that area, and such phenomena become more pronounced in the higher Strouhal number cases.

Turbulence Measurements of High Shear Flow Fields in a Turbomachine Seal Configuration

The mean velocity and Reynolds stress tensor throughout a whirling annular seal are presented. The data were collected with a three-dimensional laser Doppler velocimeter using phase averaging. Two axial flow conditions (Re = 12,000 and 24,000) were studied at one shaft speed (Ta = 6,600). The eccentricity and whirl ratios were 50 percent and 100 percent, respectively. There is a region of high axial momentum at the inlet on the pressure side of the clearance that migrates around the seal to the suction side at the exit. The normalized axial momentum in this region is higher in the low Reynolds number case due to an axial recirculation zone that occurs on the suction side of the rotor at the inlet. The recirculation zone does not occur in the high Reynolds number case. At both Reynolds numbers there is a recirculation zone on the rotor surface in the pressure side of the inlet. This recirculation zone extends from 20 to 200 deg past the rotor zenith in the tangential direction, and is one third of a clearance wide radially. The high Reynolds number circulation zone is 1.5 mean clearances long, while the low Reynolds number zone extends two mean clearances downstream. When compared to previous studies, it is apparent that the tangential momentum is no greater for a seal with whirl than for one without if other parameters are constant. Areas of high tangential momentum occur in the clearance where the axial momentum is low. Average exit plane tangential velocities in the low Reynolds number case are 1.5 times greater than those in the other flow case. These results are in general agreement with predictions made by other investigators.

Velocity of cavitation bubbles in uniform flowfield high and low Reynolds number

AGASEOUS bubble caused by the tip cavitation of a propeller blade operating in a uniform flowfield environment experiences a drag force in relation to its angular velocity and a thrust force in the axial direction. In this paper, a mathematical model is presented that studies propagation of the gaseous bubble at low and high Reynolds number cases. The temporal and the spatial profile velocity variations are presented. The time constants involved in both regimes are obtained. The velocity variations are shown to be exponential for the low Reynolds number case and algebraic for the high Reynolds number case. Contents When a propeller operates in an underwater environment at high revolutions, cavitation will occur. Three different types of cavitation can occur: 1) hub cavitation, 2) blade cavitation, and 3) tip cavitation. In this paper, tip cavitation will be considered. Tip cavitation produces tip vortices of entrained gases that propagate downstream in a helical motion. The rate at which the cavitation gases propagate downstream is a function of propeller geometry, flowfield, and the geometry of the cavitation gases. The three different types of cavitation that can exist are 1) individual spherical bubbles of equal size, 2) individual bubbles of different sizes, and 3) train of gas shaped in cylindrical form. In this paper, it will be assumed that the cavitation bubbles are spherical and the shape does not change as a function of time. The motion of air bubbles in a fluid has been investigated by a variety of authors with numerous articles being presented by Lauterborn.1 Individual gaseous bubbles will be assumed to be moving in a flowfield, and interactions between successive bubbles will be neglected. The bubble is assumed to move with velocity V, whereas the flowfield has a velocity U. The effect of the added mass and the mass of the displaced fluid have to be considered in the general governing equation. The governing equation of motion is the conservation of momentum equation as given by Newman2 dV dV

Drag and Inertia Forces on Circular Cylinders in Harmonic Flow

A review of the Morison‐equation approach to the evaluation of wave loads on cylindrical members in harmonic flow is presented. The results presented show the most comprehensive picture to date of the Reynolds number‐displacement ratio dependence of the drag and inertia coefficient in the small‐displacement‐ratio range and demonstrate the important effect of the Reynolds number in the case of both smooth and rough cylinders. Results from oscillating‐cylinder tests are compared with wave‐tank results for both regular and random waves. Finally, a wake model applied to the high Reynolds number case is shown to correlate the drag coefficient for both rough and smooth cylinders quite well.

Pressure Gradient method for solving incompressible Navier-Stokes equations with curvilinear coordinate system

A nonstaggered Pressure Gradient (PG) method, one of the finite difference schemes using primitive variables, is applied to solve the 3-D, unsteady incompressible Navier-Stokes equations based on a curvilinear coordinate system. The PG method, in contrast to conventional methods, uses pressure gradient instead of pressure as the field variable. The most prominent contribution of this method is its adoption of a modified nonstaggered grid which eliminates the troublesome calculation of the pressure boundary conditions and any special treatment for velocities near the boundary. Another advantage is that the discretization error of the convection terms is relatively insensitive to the magnitude of the convecting flow in the high Reynolds number cases. A variety of test problems have been studied, including Couette flow, flow past a cylinder, transient buoyancy convection, and 3-D unsteady cavity flow driven by shear and body forces. The comparisons between the present numerical results and the existing data are shown to be in good agreement.

Anisotropic magnetohydrodynamic turbulence in a strong external magnetic field

A strong external dc magnetic field introduces a basic anisotropy into incompressible magnetohydrodynamic turbulence. The modifications that this is likely to produce in the properties of the turbulence are explored for the high Reynolds number case. The conclusion is reached that the turbulent spectrum splits into two parts: an essentially two-dimensional spectrum with both the velocity field and magnetic fluctuations perpendicular to the dc magnetic field, and a generally weaker and more nearly isotropic spectrum of Alfvén waves. A minimal characterization of the spectral density tensors is given. Similarities to measurements from the Culham–Harwell Zeta pinch device and the University of California, Los Angeles Macrotor tokamak are remarked upon, as are certain implications for the Belcher and Davis measurements of magnetohydrodynamic turbulence in the solar wind.

Rotation of a cylinder about an eccentric parallel axis in a viscous fluid

A circular cylinder in an infinite fluid rotates rigidly about a fixed axis which is parallel to, but does not coincide with, its geometric axis. It is found that, depending on the relative magnitude of the Reynolds number R and eccentricity ε, the flow may have two, one or no boundary layers. General solutions for R [Lt ] are obtained. It is found that owing to eccentricity there exist both a flow periodic in the circumferential direction and a non-periodic flow which is a function only of the radial distance from the centre of the cylinder. The non-periodic flow is caused by the nonlinear Reynolds stress and contributes to the torque experienced by the cylinder. The high Reynolds number case, \[ 1 \Lt R \Lt\epsilon^{-\frac{3}{2}}, \] is solved by matched asymptotic expansions. The stream function can be represented by Hankel functions of order 1/3 and a slight decrease in torque is found. In the low Reynolds number case, R [Lt ] 1, the torque is increased owing to eccentricity when R < 0·145 and decreased when R > 0·145. A physical explanation is presented.