Laminar Source Flow Between Two Parallel Coaxial Disks Rotating at Different Speeds

1967 ◽  
Vol 34 (3) ◽  
pp. 541-547 ◽  
Author(s):  
F. Kreith ◽  
H. Viviand
Keyword(s):  
Series Expansion ◽  
Stokes Equations ◽  
Double Series ◽  
Navier Stokes ◽  
Large Radius ◽  
Laminar Regime ◽  
Navier Stokes Equations ◽  
Pressure Distributions ◽  
Flow Configurations ◽  
Source Flow

This article presents an analysis of the flow in the gap between two parallel coaxial disks rotating at different velocities, with a source in the center. The Navier-Stokes equations are solved by double series expansion about a known solution at a large radius, and velocity and pressure distributions are calculated for the laminar regime. The interaction between the source flow and the rotational effects is investigated by a method valid for small rotational Taylor numbers of the disks. Several flow configurations are shown to be physically possible, and the magnitude of the parameters delineating the different flow regimes are calculated.

scholarly journals 3D Hydrodynamic Modelling Enhances the Design of Tendaho Dam Spillway, Ethiopia

Water ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 82
Author(s):  
Getnet Kebede Demeke ◽  
Dereje Hailu Asfaw ◽  
Yilma Seleshi Shiferaw
Keyword(s):  
Stokes Equations ◽  
Flow Behavior ◽  
Fluid Flows ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Hydraulic Structures ◽  
Hydrodynamic Modelling ◽  
Navier Stokes Equations ◽  
Pressure Distributions ◽  
Computational Fluid Dynamics Cfd

Hydraulic structures are often complex and in many cases their designs require attention so that the flow behavior around hydraulic structures and their influence on the environment can be predicted accurately. Currently, more efficient computational fluid dynamics (CFD) codes can solve the Navier–Stokes equations in three-dimensions and free surface computation in a significantly improved manner. CFD has evolved into a powerful tool in simulating fluid flows. In addition, CFD with its advantages of lower cost and greater flexibility can reasonably predict the mean characteristics of flows such as velocity distributions, pressure distributions, and water surface profiles of complex problems in hydraulic engineering. In Ethiopia, Tendaho Dam Spillway was constructed recently, and one flood passed over the spillway. Although the flood was below the designed capacity, there was an overflow due to superelevation at the bend. Therefore, design of complex hydraulic structures using the state-of- art of 3D hydrodynamic modelling enhances the safety of the structures. 3D hydrodynamic modelling was used to verify the safety of the spillway using designed data and the result showed that the constructed hydraulic section is not safe unless it is modified.

Inertial effect on gas squeeze film for large radius disc excited by standing waves with complex modal shapes

2019 ◽  
Vol 33 (24) ◽  
pp. 1950282 ◽  
Author(s):  
Yi Qiang Fan ◽  
M. Miyatake ◽  
S. Kawada ◽  
Bin Wei ◽  
S. Yoshimoto
Keyword(s):  
Reynolds Equation ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Standing Waves ◽  
Inertial Effect ◽  
Squeeze Film ◽  
Navier Stokes ◽  
Large Radius ◽  
Navier Stokes Equations ◽  
Sinusoidal Functions

In order to investigate the gas inertial effect on bearing capacity of acoustic levitation on condition of complex exciting shapes, a new kind of numerical model including inertial effect in cylindrical coordinates was proposed. The inertial terms in Navier–Stokes equations are packaged to derive modified Reynolds equations. The amplitudes of standing waves were tested by distance probe in experiment and film thickness equation were reconstructed by sum of the sinusoidal functions. The theoretical and experimental results implied that the inertial effect is strongly related to the exciting modal shapes. It is concluded that the proposal of modified Reynolds equation can provide more optimized numerical solutions to solve the problems about the deviation between theoretical and experimental data.

Numerical Study on Impeller Performance of Mini Hydro Turbine

2015 ◽  
Vol 772 ◽  
pp. 552-555 ◽  
Author(s):  
Kyu Han Kim ◽  
Joni Cahyono
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Flow Behavior ◽  
Three Dimensional ◽  
Horizontal Axis ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Hydro Turbine ◽  
Pressure Distributions ◽  
Power Outputs

The aim of this paper is to numerically explore the feasibility of designing a Mini-Hydro turbine. The interest for this kind of horizontal axis turbine relies on its versatility. In the present study, the numerical solution of the discredited three-dimensional, incompressible Navier-Stokes equations over an unstructured grid is accomplished with an ANSYS program. In this study, a mini hydro turbine (3kW) has been considered for utilization of horizontal axis impeller. The turbine performance and flow behavior have been evaluated by means of numerical simulations. Moreover, the performance of the impeller varied in the pressure distribution, torque, rotational speed and power generated by the different number of blades and angles. The results trends are similar between the highest pressure distributions at the impeller also produced highest power outputs on 6 numbers of blades at impeller. The model has been validated, comparing numerical results with available experimental data.

scholarly journals Viscous Flow Calculations in Turbomachinery Channels

1989 ◽  
Author(s):  
Francesco Martelli ◽  
Vittorio Michelassi
Keyword(s):  
Stokes Equations ◽  
Turbulent Viscosity ◽  
Axisymmetric Flow ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Algebraic Expression ◽  
Two Dimensional ◽  
Approximate Factorization ◽  
Navier Stokes Equations ◽  
Flow Configurations

An implicit procedure based on the artificial compressibility formulation is presented for the numerical solution of the two-dimensional incompressible steady Navier-Stokes equations in the presence of large separated regions. Turbulence effects are accounted for by the Chien low Reynolds number form of the K-ε turbulence model and the Baldwin-Lomax algebraic expression for turbulent viscosity. The governing equations are written in conservative form and implicitly solved in fully coupled form using the approximate factorization technique. Preliminary tests were carried out in a laminar flow regime to check the accuracy and stability of the method in two-dimensional and cylindrical axisymmetric flow configurations. After testing in laminar and turbulent flow regimes and comparing the two turbulence models, the code was successfully applied to an actual gas turbine diffuser at low Mach numbers.

Aerodynamic Origin of Rotor-Rotor Interaction Noise From Unducted Propulsors

2013 ◽  
Author(s):  
Florian Danner ◽  
Christofer Kendall-Torry ◽  
Hans-Peter Kau
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Propagation Characteristics ◽  
Propulsion Systems ◽  
Navier Stokes Equations ◽  
Pressure Distributions ◽  
Blade Row ◽  
Open Rotor ◽  
Blade Row Interaction ◽  
Insight Into

The sound arising from blade row interaction in open rotor propulsion systems is known to significantly contribute to overall noise emissions. The present paper therefore addresses the origination of rotor-rotor interaction noise from a pair of unducted counter-rotating fans. The focus is on the aerodynamic mechanisms that involve sound generation, in order to provide the physical understanding required to find noise-reducing means. Detailed insight into the underlying phenomena is provided on the basis of numerical simulations applying the unsteady Reynolds-averaged Navier-Stokes equations. The interaction mechanisms are identified by extracting the time-dependent disturbances of the flow field in the respective rotor relative frame of reference. Conclusions on the sources of interaction noise and potential noise-reducing means are drawn by evaluating polar directivities, blade surface pressure distributions and propagation characteristics.

The Interaction Between the Impeller and Casing in a Small-Size Turbo-Compressor

2002 ◽  
Author(s):  
D.-W. Kim ◽  
Youn J. Kim
Keyword(s):  
Static Pressure ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reference Method ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Pressure Distributions ◽  
Loss Coefficients ◽  
Compressible Turbulent Flow ◽  
Turbo Compressor

The effects of casing shape on the performance and the interaction between the impeller and casing in a small-size turbo-compressor are investigated. Numerical analysis is conducted for the compressor with circular and single volute casings from inlet to discharge nozzle. In order to predict the flow pattern inside the entire impeller, vaneless diffuer and casing, calculations with multiple frames of reference method between the rotating and stationery parts of the domain are carried out. For compressible turbulent flow fields, the continuity and three-dimensional time-averaged Navier-Stokes equations are employed. To evaluate the performance of two types of casings, the static pressure and loss coefficients are obtained with various flow rates. Also, static pressure distributions around casings are studied for different casing shapes, which are very important to predict the distribution of radial load. To prove the accuracy of numerical results, measurements of static pressure around casing and pressure difference between the inlet and outlet of the compressor are performed for the circular casing. Comparison of these results between the experimental and numerical analyses are conducted, and reasonable agreement is obtained.

scholarly journals Accurate RANS Simulation of Wind Turbine Stall by Turbulence Coefficient Calibration

2018 ◽  
Vol 8 (9) ◽  
pp. 1444 ◽  
Author(s):  
Wei Zhong ◽  
Hongwei Tang ◽  
Tongguang Wang ◽  
Chengyong Zhu
Keyword(s):  
Experimental Data ◽  
Wind Turbine ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Maximum Torque ◽  
Simulation Accuracy ◽  
Navier Stokes Equations ◽  
Pressure Distributions ◽  
Sst Turbulence Model ◽  
Better Than

Stall, a complex phenomenon related to flow separation, is difficult to be predicted accurately. The motivation of the present study is to propose an approach to improve the simulation accuracy of Reynolds Averaged Navier–Stokes equations (RANS) for wind turbines in stall. The approach is implemented in three steps in simulations of the S809 airfoil and the NREL (National Renewable Energy Laboratory) Phase VI rotor. The similarity between airfoil and rotor simulations is firstly investigated. It is found that the primary reason for the inaccuracy of rotor simulation is not the rotational effect or the 3-D effect, but the turbulence-related problem that already exists in airfoil simulation. Secondly, a coefficient of the SST turbulence model is calibrated in airfoil simulation, ensuring the onset and development of the light stall are predicted accurately. The lift of the airfoil in the light stall, which was overestimated about 30%, is reduced to a level consistent with experimental data. Thirdly, the calibrated coefficient is applied to rotor simulation. That makes the flow patterns on the blade properly simulated and the pressure distribution of the blade, as well as the torque of the rotor, are predicted more accurately. The relative error of the predicted maximum torque is reduced from 34.4% to 3.2%. Furthermore, the procedure of calibration is applied to the MEXICO (Model Experiments in Controlled Conditions) rotor, and the predicted pressure distributions over blade sections are better than the CFD (Computational Fluid Dynamics) results from the Mexnext project. In essence, the present study provides an approach for calibrating rotor simulation using airfoil experimental data, which enhances the potential of RANS in accurate simulation of the wind turbine aerodynamic performance.

Understanding subsonic and transonic cavity flows

2001 ◽  
Vol 105 (1044) ◽  
pp. 77-84 ◽  
Author(s):  
J. Henderson ◽  
K. J. Badcock ◽  
B. E. Richards
Keyword(s):  
Acoustic Pressure ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Cavity Flows ◽  
Computational Investigation ◽  
Oscillatory Flows ◽  
Navier Stokes Equations ◽  
Open Flow ◽  
Pressure Distributions ◽  
Cavity Floor

AbstractA computational investigation of the subsonic and transonic turbulent open flow over cavities was conducted. Simulations of these oscillatory flows were generated through time-accurate solutions of the Reynolds-averaged form of the Navier-Stokes equations. The effect of turbulence was included through the k–ω model. The results presented include calculations of the acoustic pressure distributions along the cavity floor, which compare well with experiment. The results are then used to describe the behaviour of the flow.

Study on the Clearance of Impeller and Draft-Tube on Stamping and Welding Multistage Centrifugal Pump

2010 ◽  
Vol 43 ◽  
pp. 434-437
Author(s):  
Yuan Yi Liu ◽  
Rui Guang Li
Keyword(s):  
Centrifugal Pump ◽  
Design Theory ◽  
Stokes Equations ◽  
Draft Tube ◽  
Outer Edge ◽  
Navier Stokes ◽  
Centrifugal Pumps ◽  
Navier Stokes Equations ◽  
Pressure Distributions ◽  
Multistage Centrifugal Pump

Based on the Renault-averaged Navier-Stokes equations and a standard turbulence model, the different clearance of the outer edge on the impeller and the draft-tube is simulated by the commercial software CFX, in order to achieve optimal performance. The velocity distributions and pressure distributions within the stamping and welding multistage centrifugal pumps are analyzed. The reasonable clearance value which impact on its performance and properties have been discovered. This paper is helpful to improve the design theory of stamping and welding multistage centrifugal pumps.

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