scholarly journals Determination of Critical Reynolds Number for the Flow Near a Rotating Disk on the Basis of the Theory of Stochastic Equations and Equivalence of Measures

Fluids ◽  
2020 ◽  
Vol 6 (1) ◽  
pp. 5
Author(s):  
Artur Dmitrenko
Keyword(s):  
Reynolds Number ◽  
Power Plants ◽  
Critical Reynolds Number ◽  
Thermal State ◽  
Rotating Disk ◽  
Stochastic Equations ◽  
Analytical Dependence ◽  
Steam Turbines ◽  
Equivalence Of Measures

The determination of the flow regime of liquid and gas in power plants is the most important design task. Performing the calculations based on modern calculation methods requires a priori knowledge of the initial and boundary conditions, which significantly affect the final results. The purpose of the article is to present the solution for the critical Reynolds number for the flow near a rotating disk on the basis of the theory of stochastic equations of continuum laws and equivalence of measures between random and deterministic motions. The determination of the analytical dependence for the critical Reynolds number is essential for the study of flow regimes and the thermal state of disks and blades in the design of gas and steam turbines. The result of the calculation with using the new formula shows that for the flow near a wall of rotating disk, the critical Reynolds number is 325,000, when the turbulent Reynolds is 5 ÷ 10 and the degree of turbulence is 0.01 ÷ 0.02. Therefore, the result of solution shows a satisfactory correspondence of the obtained analytical dependence for the critical Reynolds number with the experimental data.

Determination of Incompressible Flow Friction in Smooth Circular and Noncircular Passages: A Generalized Approach Including Validation of the Nearly Century Old Hydraulic Diameter Concept

1988 ◽  
Vol 110 (4) ◽  
pp. 431-440 ◽  
Author(s):  
N. T. Obot
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Critical Reynolds Number ◽  
Pressure Coefficient ◽  
Hydraulic Diameter ◽  
Length Scale ◽  
The Difference ◽  
Friction Method ◽  
Reduced Data

It has been demonstrated conclusively that the widely observed differences in data for frictional pressure coefficient between circular and noncircular passages derive from the inseparably connected effects of transition and the choice of a length scale. A relatively simple approach, the critical friction method (CFM), has been developed and when applied to triangular, rectangular, and concentric annular passages, the reduced data lie with remarkable consistency on the circular tube relations. In accordance with the theory of dynamical similarity, it has also been shown that noncircular duct data can be reduced using the hydraulic diameter or any arbitrarily defined length scale. The proposed method is what is needed to reconcile such data with those for circular tubes. With the hydraulic diameter, the critical friction factor almost converges to a universal value for all passages and the correction is simply that required to account for the difference in critical Reynolds number. By contrast, with any other linear parameter, two corrections are needed to compensate for variations in critical friction factor and Reynolds number. Application of the method to roughened passages is discussed.

Numerical and Analytical Investigation of Heat Transfer Mechanisms and Flow Phenomena in an IP Steam Turbine Blading During Startup

2020 ◽  
Author(s):  
Dieter Bohn ◽  
Christian Betcher ◽  
Karsten Kusterer ◽  
Kristof Weidtmann
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Steam Turbine ◽  
Convective Heat ◽  
Power Plants ◽  
Thermal Stresses ◽  
Analytical Investigation ◽  
Computational Effort ◽  
Steam Turbines ◽  
Transfer Mechanisms

Abstract As a result of an ever-increasing share of volatile renewable energies on the world wide power generation, conventional power plants face high technical challenges in terms of operational flexibility. Consequently, the number of startups and shutdowns grows, causing high thermal stresses in the thick-walled components and thus reduces lifetime and increases product costs. To fulfill the lifetime requirements, an accurate prediction of the metal temperature distribution inside these components is crucial. The objective of this paper is to understand the predominant basic heat transfer mechanisms during an IP steam turbine startup. Convective heat transport is described by means of HTC's as a function of dimensionless parameters, considering predominant flow structures. Based on steady-state and transient CHT- simulations the HTC's are derived during startup and compared to correlations from the literature. The simulations outline that the local HTC generally increases with increasing axial and circumferential Reynolds' number and is mostly influenced by vortex systems such as passage and horseshoe vortices. The HTC's at the turbine stage surfaces can be modeled with a high accuracy using a linear relation with respect to the total Reynolds' number. The comparison illustrates that the correlations underestimate the convective heat transfer by approx. 40% on average. Results show that special correlation-based approaches from the literature are a particularly efficient procedure to predict the heat transfer within steam turbines. in the design process. Overall, the computational effort can be significantly reduced by applying analytical correlations while maintaining a satisfactory accuracy.

Experimental Determination of Transition Reynolds Number for Unsteady Film Cooling

1981 ◽  
Author(s):  
F. K. Tsou ◽  
L. T. Smith ◽  
S. J. Chen
Keyword(s):  
Reynolds Number ◽  
Film Cooling ◽  
Critical Reynolds Number ◽  
Subsonic Flow ◽  
Gas Injection ◽  
Wedge Flow ◽  
Ludwieg Tube ◽  
Order Of Magnitude ◽  
Unsteady Effect

In order to investigate the unsteady effect on transition in film cooling, an 11-m long Ludwieg Tube, consisting of a test section placed between the high pressure and low pressure sections of a shock tube, has been constructed. With this device, a controlled unsteady, low subsonic flow lasting for a period of several milliseconds is obtained. The transition Reynolds Number is determined from the output of thin film heat flux transducers having a response time of a fraction of a microsecond. The results indicate that, in the case of flow without gas injection into the boundary layer, the transition Reynolds Number is one order of magnitude smaller than the critical Reynolds Number for steady wedge flow with the same pressure gradient. With injection, the transition Reynolds Number is small near the injection slot; far downstream, it increases asymptotically to the value for flow without injection.

Experimental Determination of Transition to Turbulence in a Rectangular Channel With Eddy Promoters

1994 ◽  
Vol 116 (3) ◽  
pp. 484-487 ◽  
Author(s):  
J. S. Kapat ◽  
J. Ratnathicam ◽  
B. B. Mikic´
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Rectangular Channel ◽  
Transition To Turbulence ◽  
Channel Height ◽  
Laminar To Turbulent Transition ◽  
Turbulent Transition ◽  
Power Spectral ◽  
Unstable Configuration

We report on laminar-to-turbulent transition in a rectangular channel in the presence of periodically placed cylindrical eddy promoters. Transition is identified through the analysis of power spectral density (PSD) of velocity fluctuations. Placement of the eddy promoters in the channel, depending on the geometric configuration, can significantly reduce the value of Reynolds number at transition. The critical Reynolds number (based on the average velocity and the channel height) ranges from 1500 (for an unobstructed channel) to about 400 (for the most unstable configuration we have deployed). For all the configurations tested, demarcation of transition can be correlated with the expression: Reτ≡τ¯w,αv/ρH/2/ν=44˜51, where τw,αv is the spatially averaged value of mean wall shear stress and H is the channel height.

Further Experiments and Investigations for Discharge Coefficient of PTC 6 Flow Nozzle in a Wide Range of Reynolds Number

2015 ◽  
Vol 138 (4) ◽  
Author(s):  
Noriyuki Furuichi ◽  
Yoshiya Terao ◽  
Shinichi Nakao ◽  
Keiji Fujita ◽  
Kazuo Shibuya
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Power Plants ◽  
Discharge Coefficient ◽  
High Accuracy ◽  
Steam Turbines ◽  
Number Range ◽  
Accurate Evaluation ◽  
Discharge Coefficients ◽  
Wide Range

The discharge coefficients of the flow nozzles based on ASME PTC 6 are measured in a wide range of Reynolds number from Red = 5.8 × 104 to Red = 1.4 × 107, and the equations of the discharge coefficients are developed for the laminar, the transitional, and the turbulent flow ranges. The equation of the discharge coefficient consists of a nominal discharge coefficient and the tap effect. The nominal discharge coefficient is the discharge coefficient without tap, which is experimentally determined from the discharge coefficients measured for different tap diameters. The tap effects are correctly obtained by subtracting the nominal discharge coefficient from the discharge coefficient measured. The deviation of the present experimental results from the equations developed is from −0.06% to 0.04% for 3.0 × 106 < Red < 1.4 × 107 and from −0.11% to 0.16% for overall Reynolds number range examined. The developed equations are expected to be capable of estimating the discharge coefficient of the throat tap nozzle defined in PTC 6 with a high accuracy and contribute for the high accurate evaluation of steam turbines in power plants.

An Experimental Determination of the Minimum Reynolds Number for Instability in a Free Jet

1962 ◽  
Vol 29 (3) ◽  
pp. 506-508 ◽  
Author(s):  
Andrus Viilu
Keyword(s):  
Reynolds Number ◽  
Experimental Determination ◽  
Critical Reynolds Number ◽  
Free Jet

The critical Reynolds number for instability of a circular jet is found to lie between 10.5 and 11.8. This result was obtained experimentally, observing a jet of water into water.

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