Incompressible Navier-Stokes Computation of the NREL Airfoils Using a Symmetric Total Variational Diminishing Scheme

1994 ◽  
Vol 116 (4) ◽  
pp. 174-182 ◽  
Author(s):  
S. L. Yang ◽  
Y. L. Chang ◽  
O. Arici
Keyword(s):  
Turbulence Model ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Wind Tunnel Test ◽  
Factorization Method ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Approximate Factorization ◽  
Two Dimensional Flow ◽  
Good Agreement

The purpose of this paper is to present a numerical study of flow fields for the NREL S805 and S809 airfoils using a spatially second-order symmetric total variational diminishing scheme. The steady two-dimensional flow is modeled as turbulent, viscous, and incompressible and is formulated in the pseudo-compressible form. The turbulent flow is closed by the Baldwin-Lomax algebraic turbulence model. Numerical solutions are obtained by the implicit approximate-factorization method. The accuracy of the numerical results is compared with the Delft two-dimensional wind tunnel test data. For comparison, the Eppler code results are also included. Numerical solutions of pressure and lift coefficients show good agreement with the experimental data, but not the drag coefficients. To properly simulate the post-stall flow field, a better turbulence model should be used.

scholarly journals Structure and stability of non-symmetric Burgers vortices

1998 ◽  
Vol 363 ◽  
pp. 199-228 ◽  
Author(s):  
AURELIUS PROCHAZKA ◽  
D. I. PULLIN
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Structure And Stability ◽  
Two Dimensional Flow ◽  
Steady Solutions ◽  
Pseudo Spectral Method ◽  
Burgers Vortices

We investigate, numerically and analytically, the structure and stability of steady and quasi-steady solutions of the Navier–Stokes equations corresponding to stretched vortices embedded in a uniform non-symmetric straining field, (αx, βy, γz), α+β+γ=0, one principal axis of extensional strain of which is aligned with the vorticity. These are known as non-symmetric Burgers vortices (Robinson & Saffman 1984). We consider vortex Reynolds numbers R=Γ/(2πv) where Γ is the vortex circulation and v the kinematic viscosity, in the range R=1−104, and a broad range of strain ratios λ=(β−α)/(β+α) including λ>1, and in some cases λ[Gt ]1. A pseudo-spectral method is used to obtain numerical solutions corresponding to steady and quasi-steady vortex states over our whole (R, λ) parameter space including λ where arguments proposed by Moffatt, Kida & Ohkitani (1994) demonstrate the non-existence of strictly steady solutions. When λ[Gt ]1, R[Gt ]1 and ε≡λ/R[Lt ]1, we find an accurate asymptotic form for the vorticity in a region 1<r/(2v/γ)1/2[les ]ε1/2, giving very good agreement with our numerical solutions. This suggests the existence of an extended region where the exponentially small vorticity is confined to a nearly cat's-eye-shaped region of the almost two-dimensional flow, and takes a constant value nearly equal to Γγ/(4πv)exp[−1/(2eε)] on bounding streamlines. This allows an estimate of the leakage rate of circulation to infinity as ∂Γ/∂t =(0.48475/4π)γε−1Γ exp (−1/2eε) with corresponding exponentially slow decay of the vortex when λ>1. An iterative technique based on the power method is used to estimate the largest eigenvalues for the non-symmetric case λ>0. Stability is found for 0[les ]λ[les ]1, and a neutrally convective mode of instability is found and analysed for λ>1. Our general conclusion is that the generalized non-symmetric Burgers vortex is unconditionally stable to two-dimensional disturbances for all R, 0[les ]λ[les ]1, and that when λ>1, the vortex will decay only through exponentially slow leakage of vorticity, indicating extreme robustness in this case.

Numerical Modeling of the Thermodynamic Effects of Cavitation

1997 ◽  
Vol 119 (2) ◽  
pp. 420-427 ◽  
Author(s):  
Manish Deshpande ◽  
Jinzhang Feng ◽  
Charles L. Merkle
Keyword(s):  
Numerical Solutions ◽  
Strong Dependence ◽  
Numerical Approach ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Sheet Cavitation ◽  
Cryogenic Fluids ◽  
Cavity Profile ◽  
Two Dimensional Flow ◽  
Thermodynamic Effects

A Navier-Stokes solver based on artificial compressibility and pseudo-time stepping, coupled with the energy equation, is used to model the thermodynamic effects of cavitation in cryogenic fluids. The analysis is restricted to partial sheet cavitation in two-dimensional cascades. Thermodynamic effects of cavitation assume significance in cryogenic fluids because these fluids are generally operated close to the critical point and also because of the strong dependence of the vapor pressure on the temperature. The numerical approach used is direct and fully nonlinear, that is, the cavity profile evolves as part of the solution for a specified cavitation pressure. This precludes the necessity of specifying the cavity length or the location of the inception point. Numerical solutions are presented for two-dimensional flow problems and validated with experimental measurements. Predicted temperature depressions are also compared with measurements for liquid hydrogen and nitrogen. The cavitation procedure presented is easy to implement in engineering codes to provide satisfactory predictions of cavitation. The flexibility of the formulation also allows extension to more complex flows and/or geometries.

Numerical Solutions of the Navier-Stokes Equations in Inlet Regions

1972 ◽  
Vol 39 (4) ◽  
pp. 873-878 ◽  
Author(s):  
J. W. McDonald ◽  
V. E. Denny ◽  
A. F. Mills
Keyword(s):  
Reynolds Number ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Improved Method ◽  
Navier Stokes Equations ◽  
Two Dimensional Flow ◽  
Vorticity Equations

Numerical solutions of the Navier-Stokes equations are obtained for steady two-dimensional flow in the inlet region of both a tube and a channel. The entering flow is considered to be either uniform (u = constant, v = 0) or irrotational (u = constant, ω = 0). Values of Reynolds number Re = u0a/ν range from 0.75 to 2 × 106. An improved method for solving the stream function-vorticity equations of hydrodynamics has been developed. The method is stable at all Reynolds numbers and appears to be computationally superior to previous methods.

Flow Past a Forced Oscillating Cylinder: A Three-Dimensional Numerical Study

2019 ◽  
Author(s):  
Huan Ping ◽  
Yan Bao ◽  
Dai Zhou ◽  
Zhaolong Han
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Flow Dynamics ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Flow Past ◽  
Flow Past A Cylinder ◽  
Two Dimensional Flow

Abstract In this paper, we conducted a three-dimensional investigation of flow past a cylinder undergoing forced oscillation. The flow configuration is similar to the work of Blackburn & Henderson (1999) [1], in which Reynolds number equals to 500 and a fixed motion amplitude of A/D = 0.25. The oscillation frequencies are varied in the range near to the natural shedding frequency of a stationary cylinder. The flow dynamics are governed by Navier-Stokes equations and the solutions are obtained by employing high-order spectral/hp element method. It is found that the flow dynamics are significantly distinguished from the study of two-dimensional flow by Blackburn & Henderson (1999) [1]. The values of hydrodynamic forces are smaller compared to that in the two-dimensional study. However, lock-in boundary we identified is broader. In addition, a different type of hysteresis loop of energy transfer coefficient is obtained.

scholarly journals A Comparison of Simplified Two-dimensional Flow Models Exemplified by Water Flow in a Cavern

2017 ◽  
Vol 64 (3-4) ◽  
pp. 141-154
Author(s):  
Dzmitry Prybytak ◽  
Piotr Zima
Keyword(s):  
Water Flow ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Flow Models ◽  
Two Dimensional Flow ◽  
Flow Through ◽  
Potential Flow Model

AbstractThe paper shows the results of a comparison of simplified models describing a two-dimensional water flow in the example of a water flow through a straight channel sector with a cavern. The following models were tested: the two-dimensional potential flow model, the Stokes model and the Navier-Stokes model. In order to solve the first two, the boundary element method was employed, whereas to solve the Navier-Stokes equations, the open-source code library OpenFOAM was applied. The results of numerical solutions were compared with the results of measurements carried out on a test stand in a hydraulic laboratory. The measurements were taken with an ADV probe (Acoustic Doppler Velocimeter). Finally, differences between the results obtained from the mathematical models and the results of laboratory measurements were analysed.

A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

1989 ◽  
Vol 209 ◽  
pp. 285-308 ◽  
Author(s):  
R. J. Bodonyi ◽  
W. J. C. Welch ◽  
P. W. Duck ◽  
M. Tadjfar
Keyword(s):  
Numerical Solutions ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Surface Geometry ◽  
Navier Stokes Equations ◽  
S Waves ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

Computational Fluid Dynamics Evaluation of Heat Transfer Correlations for Sodium Flows in a Heat Exchanger

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Seok-Ki Choi ◽  
Seong-O Kim ◽  
Hoon-Ki Choi
Keyword(s):  
Heat Transfer ◽  
Heat Exchanger ◽  
Turbulence Model ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Cross Flow ◽  
Turbulence Models ◽  
Parallel Flow ◽  
Sst Model ◽  
Heat Transfer Correlations

A numerical study for the evaluation of heat transfer correlations for sodium flows in a heat exchanger of a fast breeder nuclear reactor is performed. Three different types of flows such as parallel flow, cross flow, and two inclined flows are considered. Calculations are performed for these three typical flows in a heat exchanger changing turbulence models. The tested turbulence models are the shear stress transport (SST) model and the SSG-Reynolds stress turbulence model by Speziale, Sarkar, and Gaski (1991, “Modelling the Pressure-Strain Correlation of Turbulence: An Invariant Dynamical System Approach,” J. Fluid Mech., 227, pp. 245–272). The computational model for parallel flow is a flow past tubes inside a circular cylinder and those for the cross flow and inclined flows are flows past the perpendicular and inclined tube banks enclosed by a rectangular duct. The computational results show that the SST model produces the most reliable results that can distinguish the best heat transfer correlation from other correlations for the three different flows. It was also shown that the SSG-RSTM high-Reynolds number turbulence model does not deal with the low-Prandtl number effect properly when the Peclet number is small. According to the present calculations for a parallel flow, all the old correlations do not match with the present numerical solutions and a new correlation is proposed. The correlations by Dwyer (1966, “Recent Developments in Liquid-Metal Heat Transfer,” At. Energy Rev., 4, pp. 3–92) for a cross flow and its modified correlation that takes into account of flow inclination for inclined flows work best and are accurate enough to be used for the design of the heat exchanger.

Numerical Prediction of Turbulent Wakes Behind a Square Cylinder

1998 ◽  
Vol 14 (1) ◽  
pp. 23-29
Author(s):  
Robert R. Hwang ◽  
Sheng-Yuh Jaw
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Wall Region ◽  
Square Cylinder ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Turbulent Vortex Shedding ◽  
Model Equations ◽  
Good Agreement

ABSTRACTThis paper presents a numerical study on turbulent vortex shedding flows past a square cylinder. The 2D unsteady periodic shedding motion was resolved in the calculation and the superimposed turbulent fluctuations were simulated with a second-order Reynolds-stress closure model. The calculations were carried out by solving numerically the fully elliptic ensemble-averaged Navier-Stokes equations coupled with the turbulence model equations together with the two-layer approach in the treatment of the near-wall region. The performance of the computations was evaluated by comparing the numerical results with data from available experiments. Results indicate that the present study gives good agreement in the shedding frequency and mean drag as well as in some phase profiles of the mean velocity.

An Exact Solution of the Unsteady Navier-Stokes Equations Resulting From a Stretching Surface

1994 ◽  
Vol 61 (3) ◽  
pp. 629-633 ◽  
Author(s):  
S. H. Smith
Keyword(s):  
Exact Solution ◽  
Stokes Equations ◽  
Limited Range ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Stretching Surface ◽  
Navier Stokes Equations ◽  
Short Period ◽  
Two Dimensional Flow ◽  
Surrounding Fluid

When a stretching surface is moved quickly, for a short period of time, a pulse is transmitted to the surrounding fluid. Here we describe an exact solution in terms of a similarity variable for the Navier-Stokes equations which represents the effect of this pulse for two-dimensional flow. The unusual feature is that this solution is only valid for a limited range of the Reynolds number; outside this domain unbounded velocities result.

Numerical Study on Supersonic Combustor with an Allotype Cavity

2014 ◽  
Vol 694 ◽  
pp. 187-192
Author(s):  
Jin Xiang Wu ◽  
Jian Sun ◽  
Xiang Gou ◽  
Lian Sheng Liu
Keyword(s):  
Alternative Model ◽  
Numerical Study ◽  
Reverse Flow ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Experimental Result ◽  
Navier Stokes ◽  
Cold Flow ◽  
Hypersonic Inlet ◽  
Good Agreement

The three-dimensional coupled explicit Reynolds Averaged Navier–Stokes (RANS) equations and the two equation shear-stress transport k-w (SST k-w) model has been employed to numerically simulate the cold flow field in a special-shaped cavity-based supersonic combustor. In a cross-section shaped rectangular, hypersonic inlet with airflow at Mach 2.0 chamber, shock structures and flow characteristics of a herringbone-shaped boss and a herringbone-shaped cavity models were discussed, respectively. The results indicate: Firstly, according to the similarities of bevel-cutting shock characteristics between the boss case and the cavity case, the boss structure can serve as an ideal alternative model for shear-layer. Secondly, the eddies within cavity are composed of herringbone-spanwise vortexes, columnar vortices in the front and main-spanwise vortexes in the rear, featuring tilting, twisting and stretching. Thirdly, the simulated bottom-flow of cavity is in good agreement with experimental result, while the reverse flow-entrainment resulting from herringbone geometry and pressure gradient. However, the herringbone-shaped cavity has a better performance in fuel-mixing.

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