Numerical Solution of Lubrication’s Compressible Bulk Flow Equations: Applications to Annular Gas Seals Analysis

2001 ◽  
Author(s):  
Mihai Arghir ◽  
Jean Frene
Keyword(s):  
Compressible Flows ◽  
Reynolds Equation ◽  
Specific Treatment ◽  
Reynolds Numbers ◽  
Numerical Approach ◽  
Analytic Solutions ◽  
Bulk Flow ◽  
Flow Equations ◽  
The Family ◽  
Gas Seals

The appropriate theoretical model for lubrication flows characterized by reduced Reynolds numbers greater than unity (Re*=ρVH/μ·H/L≥l) is the so-called “bulk flow” system of equations. Its solution is more difficult than for the simple Reynolds equation because one has to deal with coupled pressure and velocity fields and the equations are of mixed elliptic-hyperbolic type. Adapting some methods borrowed from CFD can develop a suitable numerical approach. In the present work we introduce a pressure-based method belonging to the family of SIMPLE algorithms where compressibility is taken into account by coupling density corrections with pressure corrections. The method is capable of handling all compressible flows and doesn’t require any specific treatment of the incompressible flow regime. It is an adaptation for the bulk flow equations of Karki and Patankar’s (1989) work and is developed in conjunction with a triangular finite volume formulation. The present paper is focused on the description of the discretized equations, of the accompanying boundary conditions and of the solution algorithm. Comparisons with analytic solutions for subsonic and supersonic channel flows prove the ability of the method to handle all compressible flow regimes. Published results for gas (air) annular seals are further used to evaluate the proposed numerical model.

Essential Ingredients for the Computation of Steady and Unsteady Blade Boundary Layers

1991 ◽  
Vol 113 (4) ◽  
pp. 608-616 ◽  
Author(s):  
H. M. Jang ◽  
J. A. Ekaterinaris ◽  
M. F. Platzer ◽  
T. Cebeci
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Stokes Equations ◽  
Inviscid Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Transitional Region ◽  
Low Reynolds Numbers ◽  
Flow Equations ◽  
Low Reynolds

Two methods are described for calculating pressure distributions and boundary layers on blades subjected to low Reynolds numbers and ramp-type motion. The first is based on an interactive scheme in which the inviscid flow is computed by a panel method and the boundary layer flow by an inverse method that makes use of the Hilbert integral to couple the solutions of the inviscid and viscous flow equations. The second method is based on the solution of the compressible Navier–Stokes equations with an embedded grid technique that permits accurate calculation of boundary layer flows. Studies for the Eppler-387 and NACA-0012 airfoils indicate that both methods can be used to calculate the behavior of unsteady blade boundary layers at low Reynolds numbers provided that the location of transition is computed with the en method and the transitional region is modeled properly.

scholarly journals Radiation and Energetic Analysis of Nanofluid Based Volumetric Absorbers for Concentrated Solar Power

Nanomaterials ◽  
2018 ◽  
Vol 8 (10) ◽  
pp. 838 ◽  
Author(s):  
Jan Eggers ◽  
Eckart Lange ◽  
Stephan Kabelac
Keyword(s):  
Radiation Energy ◽  
Reynolds Numbers ◽  
Numerical Approach ◽  
Working Fluid ◽  
Concentrated Solar Power ◽  
Optical Efficiency ◽  
Solar Absorber ◽  
Energetic Analysis ◽  
High Reynolds ◽  
Very High

Recently, several publications gave attention to nanofluid based solar absorber systems in which the solar radiation energy is directly absorbed in the volume of the fluid. This idea could provide advantages over conventionally used surface absorbers regarding the optical and thermal efficiency. For the evaluation of this concept, a numerical approach is introduced and validated in this contribution. The results show that the optical efficiency of a volumetric absorber strongly depends on the scattering behavior of the nanofluid and can reach competitive values only if the particle size distribution is narrow and small. If this is achieved, the surface temperature and therefore the heat loss can be lowered significantly. Furthermore, the surface absorber requires very high Reynolds numbers to transfer the absorbed energy into the working fluid and avoid overheating of the absorber tube. This demand of pumping power can be reduced significantly using the concept of volumetric absorption.

scholarly journals On the propagation of diel signals in river networks using analytic solutions of flow equations

2015 ◽  
Vol 12 (8) ◽  
pp. 8175-8220 ◽  
Author(s):  
M. Fonley ◽  
R. Mantilla ◽  
S. J. Small ◽  
R. Curtu
Keyword(s):  
Analytic Solutions ◽  
River Network ◽  
Low Flow ◽  
River Networks ◽  
Signal Delay ◽  
Flow Conditions ◽  
Flow Equations ◽  
Linear Transport Equation ◽  
Daily Evapotranspiration ◽  
Self Similar

Abstract. Two hypotheses have been put forth to explain the magnitude and timing of diel streamflow oscillations during low flow conditions. The first suggests that delays between the peaks and troughs of streamflow and daily evapotranspiration are due to processes occurring in the soil as water moves toward the channels in the river network. The second posits that they are due to the propagation of the signal through the channels as water makes its way to the outlet of the basin. In this paper, we design and implement a theoretical experiment to test these hypotheses. We impose a baseflow signal entering the river network and use a linear transport equation to represent flow along the network. We develop analytic streamflow solutions for two cases: uniform and nonuniform velocities in space over all river links. We then use our analytic solutions to simulate streamflows along a self-similar river network for different flow velocities. Our results show that the amplitude and time delay of the streamflow solution are heavily influenced by transport in the river network. Moreover, our equations show that the geomorphology and topology of the river network play important roles in determining how amplitude and signal delay are reflected in streamflow signals. Finally, our results are consistent with empirical observations that delays are more significant as low flow decreases.

Airfoil Trailing Edge Noise Reduction Using a Boundary-Layer Bump

2019 ◽  
Vol 105 (5) ◽  
pp. 814-826 ◽  
Author(s):  
Yuejun Shi ◽  
Seongkyu Lee
Keyword(s):  
Boundary Layer ◽  
Noise Reduction ◽  
Suction Side ◽  
Reynolds Numbers ◽  
Numerical Approach ◽  
Trailing Edge ◽  
Velocity Deficit ◽  
Trailing Edge Noise ◽  
Field Noise ◽  
High Reynolds

This paper presents a new idea of reducing airfoil trailing edge noise using a small bump in the turbulent boundary layer. First, we develop and validate a new computational approach to predict airfoil trailing edge noise using steady RANS CFD, an empirical wall pressure spectrum model, and Howe's diff raction theory. This numerical approach enables fast and accurate predictions of trailing edge noise, which is used to study the noise reduction from the bump for various airfoil geometries and flow conditions at high Reynolds numbers. Three types of bumps, the suction-side bump, pressure-side bump, and both-side bumps, are studied. The results show that all types of bumps are able to reduce far-field noise up to 10 dB compared to clean airfoils, but their impacts are diff erent in terms of the eff ective frequency range. Also, bumps with four diff erent heights are compared with each other to investigate the eff ect of the height of bumps on noise reduction. It is demonstrated that a bump causes velocity deficit within the boundary layer near the wall. This velocity deficit results in reduced turbulence kinetic energy near the wall, which is responsible for trailing edge noise reduction. Overall, this paper demonstrates the potential of a boundary-layer bump in trailing edge noise reduction and sheds light on the physical mechanism of noise reduction with boundary-layer bumps.

Effect of corrugated skins on the aerodynamic performance of the cambered airfoils

2018 ◽  
Vol 35 (3) ◽  
pp. 1567-1582 ◽  
Author(s):  
Masoud Kharati-koopaee ◽  
Mahmood Fallahzadeh-abarghooee
Keyword(s):  
Drag Coefficient ◽  
Design Methodology ◽  
Reynolds Numbers ◽  
Numerical Approach ◽  
Aerodynamic Performance ◽  
Content Type ◽  
Lift Curve ◽  
Finite Volume Approach ◽  
Naca 0012 ◽  
Relative Curve

Purpose This paper aims to study the effect of corrugated skins on the aerodynamic performance of the cambered NACA 0012 airfoils at different corrugations parameters, maximum cambers, Reynolds numbers and maximum camber locations. Design/methodology/approach In this work, numerical approach is concerned, and results are obtained based on the finite volume approach. To characterize the effect of corrugated skins, the NACA 0012-corrugated airfoil section is chosen as the base airfoil, and different cambered corrugated airfoil sections are obtained by inclusion the camber to the base airfoil. In this research, the corrugation shape is a sinusoidal wave and corrugated skins are in the aft 30 per cent of airfoil chord. To investigate the effect of corrugations on the cambered sections, the drag coefficient and averaged lift curve slope for the corrugated airfoils are compared to those of the corresponding smooth sections. Findings Results indicate that the effect of increase in the maximum camber and also Reynolds number on the relative zero-incidence drag coefficient is of little importance at low corrugation amplitudes, whereas at high corrugation, amplitude results in different behaviors. It is found that as the maximum camber increases, the deterioration in the relative curve slope introduced by corrugated skins is reduced, and reduction in this deterioration is significant for high corrugation amplitudes airfoils. It is shown that an increase in the maximum camber location has nearly no effect on the relative zero-incidence drag coefficient and also relative lift curve slope. Originality/value The outcome of the present research provides the clues for better understanding of the effect of different corrugations parameters on the aerodynamic performance of the unmanned air vehicles to have as high aerodynamic performance as possible in different mission profiles of such vehicles.

Calculation of Surface Roughness Effects on Air-Riding Seals

2002 ◽  
Author(s):  
C. Guardino ◽  
J. W. Chew ◽  
N. J. Hills
Keyword(s):  
Surface Roughness ◽  
Compressible Flows ◽  
Reynolds Equation ◽  
Incompressible Flows ◽  
Numerical Solutions ◽  
Cfd Analysis ◽  
Roughness Effects ◽  
Stationary Wall ◽  
Comparative Results ◽  
Effect Of Surface

The effects of surface roughness on air-riding seals are investigated here using the Rayleigh-pad as an example. Both incompressible and compressible flows are considered using both CFD analysis and analytical/numerical solutions of the Reynolds equation for various 2D or 3D roughness patterns on the stationary wall. A ‘unit-based’ approach for incompressible flows has also been employed and is shown to be computationally much less expensive than the full-geometry solution. Results are presented showing the effect of surface roughness on the net lift force. The effects of varying the Reynolds number are demonstrated, as well as comparative results for static stiffness.

A Bulk-Flow Model of Angled Injection Lomakin Bearings

2002 ◽  
Author(s):  
Luis San Andre´s ◽  
Thomas Soulas ◽  
Florence Challier ◽  
Patrice Fayolle
Keyword(s):  
Flow Model ◽  
Control Volume ◽  
Dynamic Performance ◽  
Bulk Flow ◽  
Computational Method ◽  
Design Parameters ◽  
Dynamic Force ◽  
Injection Angle ◽  
Flow Equations ◽  
Force Coefficients

The paper introduces a bulk-flow model for prediction of the static and dynamic force coefficients of angled injection Lomakin bearings. The analysis accounts for the flow interaction between the injection orifices, the supply circumferential groove, and the thin film lands. A one control-volume model in the groove is coupled to a bulk-flow model within the film lands of the bearing. Bernoulli-type relationships provide closure at the flow interfaces. Flow turbulence is accounted for with shear stress parameters and Moody’s friction factors. The flow equations are solved numerically using a robust computational method. Comparisons between predictions and experimental results for a tangential-against-rotation injection water Lomakin bearing show the novel model predicts well the leakage and direct stiffness and damping coefficients. Computed cross-coupled stiffness coefficients follow the experimental trends for increasing rotor speeds and supply pressures, but quantitative agreement remains poor. A parameter investigation evidences the effects of the groove and land geometries on the Lomakin bearing flowrate and force coefficients. The orifice injection angle does not influence the bearing static performance, although it largely affects its stability characteristics through the evolution of the cross-coupled stiffnesses. The predictions confirm the promising stabilizing effect of the tangential-against-rotation injection configuration. Two design parameters, comprising the feed orifices area and groove geometry, define the static and dynamic performance of Lomakin bearing. The analysis also shows that the film land clearance and length have a larger impact on the Lomakin bearing rotordynamic behavior than its groove depth and length.

Turbulent Mixing With Density Differences

2011 ◽  
Author(s):  
Jos Derksen
Keyword(s):  
Turbulent Mixing ◽  
Richardson Number ◽  
Kinematic Viscosity ◽  
Three Dimensional ◽  
Flow Regimes ◽  
Reynolds Numbers ◽  
Flow Structures ◽  
Three Dimensional Flow ◽  
Flow Equations ◽  
Miscible Liquids

Homogenization of initially segregated and stably stratified systems consisting of two miscible liquids with different density and the same kinematic viscosity in an agitated tank was studied computationally. Reynolds numbers were in the range of 3,000 to 12,000 so that it was possible to solve the flow equations without explicitly modeling turbulence. The Richardson number that characterizes buoyancy was varied between 0 and 1. The stratification clearly lengthens the homogenization process. Two flow regimes could be identified. At low Richardson numbers large, three-dimensional flow structures dominate mixing, as is the case in non-buoyant systems. At high Richardson numbers the interface between the two liquids largely stays intact. It rises due to turbulent erosion, gradually drawing down and mixing up the lighter liquid.

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