Some Comments on Reynolds Number

1964 ◽  
Vol 86 (3) ◽  
pp. 225-226 ◽  
Author(s):  
L. H. Smith
Keyword(s):  
Reynolds Number ◽  
Viscous Fluid ◽  
Dimensional Analysis ◽  
Flow Parameter ◽  
Incompressible Viscous Fluid ◽  
Physical Variables ◽  
Real Fluids ◽  
Physical Laws ◽  
Real Test

The physical laws that govern fluid motions are examined to gain justification for the grouping of physical variables that we call Reynolds number. First, a perfect incompressible viscous fluid is considered, and it is shown that Reynolds number is the only flow parameter of its kind upon which the performance of a turbomachine can depend. The extent to which Reynolds number loses this uniqueness when real fluids are employed in real test situations is then discussed. The necessity of the use of educated engineering judgment, not furnished by dimensional analysis, is pointed out.

On the flow past a sphere at low Reynolds number

1969 ◽  
Vol 37 (4) ◽  
pp. 751-760 ◽  
Author(s):  
W. Chester ◽  
D. R. Breach ◽  
Ian Proudman
Keyword(s):  
Reynolds Number ◽  
Viscous Fluid ◽  
Low Reynolds Number ◽  
Incompressible Viscous Fluid ◽  
Euler’S Constant ◽  
Stokes Drag ◽  
Flow Past ◽  
Low Reynolds ◽  
Euler's Constant ◽  
Flow Past A Sphere

The flow of an incompressible, viscous fluid past a sphere is considered for small values of the Reynolds number. In particular the drag is found to be given by \[ D = D_s\{1+{\textstyle\frac{3}{8}}R+{\textstyle\frac{9}{40}}R^2(\log R+\gamma + {\textstyle\frac{5}{3}}\log 2 - {\textstyle\frac{323}{360}})+{\textstyle\frac{27}{80}}R^3\log R+O(R^3)\}, \] where Ds is the Stokes drag, R is the Reynolds number and γ is Euler's constant.

Creeping flow around a deforming sphere

1972 ◽  
Vol 56 (1) ◽  
pp. 61-71 ◽  
Author(s):  
S. P. Lin ◽  
A. K. Gautesen
Keyword(s):  
Reynolds Number ◽  
Viscous Fluid ◽  
Strouhal Number ◽  
Creeping Flow ◽  
Incompressible Viscous Fluid

The flow of an incompressible viscous fluid past a deforming sphere is studied for small values of the Reynolds number. The deformation is assumed to be radial but is otherwise quite general. The case of S = O(l), where S is the Strouhal number, is investigated in detail. In particular, the drag is obtained up to O(R2 In R), where R is the Reynolds number.

scholarly journals Numerical Method in Two Dimensional Boundary Layer Theory for Incompressible Viscous Fluid

2013 ◽  
Vol 38 ◽  
pp. 61-73
Author(s):  
MA Haque
Keyword(s):  
Boundary Layer ◽  
Viscous Fluid ◽  
Initial Value Problem ◽  
Shooting Method ◽  
Boundary Layer Equation ◽  
Incompressible Viscous Fluid ◽  
Initial Value ◽  
Box Scheme ◽  
Runge Kutta Method ◽  
Dimensional Boundary

In this paper laminar flow of incompressible viscous fluid has been considered. Here two numerical methods for solving boundary layer equation have been discussed; (i) Keller Box scheme, (ii) Shooting Method. In Shooting Method, the boundary value problem has been converted into an equivalent initial value problem. Finally the Runge-Kutta method is used to solve the initial value problem. DOI: http://dx.doi.org/10.3329/rujs.v38i0.16549 Rajshahi University J. of Sci. 38, 61-73 (2010)

Physical Interpretation of Flow and Heat Transfer in Preswirl Systems

2006 ◽  
Vol 129 (3) ◽  
pp. 769-777 ◽  
Author(s):  
Paul Lewis ◽  
Mike Wilson ◽  
Gary Lock ◽  
J. Michael Owen
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Turbulent Flow ◽  
Gas Turbines ◽  
Flow Parameter ◽  
Rotating Disk ◽  
Turbine Rotor ◽  
Scaled Model ◽  
Flow Rates

This paper compares heat transfer measurements from a preswirl rotor–stator experiment with three-dimensional (3D) steady-state results from a commercial computational fluid dynamics (CFD) code. The measured distribution of Nusselt number on the rotor surface was obtained from a scaled model of a gas turbine rotor–stator system, where the flow structure is representative of that found in an engine. Computations were carried out using a coupled multigrid Reynolds-averaged Navier-Stokes (RANS) solver with a high Reynolds number k-ε∕k-ω turbulence model. Previous work has identified three parameters governing heat transfer: rotational Reynolds number (Reϕ), preswirl ratio (βp), and the turbulent flow parameter (λT). For this study rotational Reynolds numbers are in the range 0.8×106<Reϕ<1.2×106. The turbulent flow parameter and preswirl ratios varied between 0.12<λT<0.38 and 0.5<βp<1.5, which are comparable to values that occur in industrial gas turbines. Two performance parameters have been calculated: the adiabatic effectiveness for the system, Θb,ad, and the discharge coefficient for the receiver holes, CD. The computations show that, although Θb,ad increases monotonically as βp increases, there is a critical value of βp at which CD is a maximum. At high coolant flow rates, computations have predicted peaks in heat transfer at the radius of the preswirl nozzles. These were discovered during earlier experiments and are associated with the impingement of the preswirl flow on the rotor disk. At lower flow rates, the heat transfer is controlled by boundary-layer effects. The Nusselt number on the rotating disk increases as either Reϕ or λT increases, and is axisymmetric except in the region of the receiver holes, where significant two-dimensional variations are observed. The computed velocity field is used to explain the heat transfer distributions observed in the experiments. The regions of peak heat transfer around the receiver holes are a consequence of the route taken by the flow. Two routes have been identified: “direct,” whereby flow forms a stream tube between the inlet and outlet; and “indirect,” whereby flow mixes with the rotating core of fluid.

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