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.

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.

A Numerical Study of Thermodynamic Effects of Sheet Cavitation

2002 ◽  
Author(s):  
Takashi Tokumasu ◽  
Kenjiro Kamijo ◽  
Yoichiro Matsumoto
Keyword(s):  
Reynolds Number ◽  
Numerical Study ◽  
Strong Dependence ◽  
Cavitation Model ◽  
Sheet Cavitation ◽  
Cryogenic Fluids ◽  
Hydraulic Equipment ◽  
Thermodynamic Effects ◽  
Temperature Depression ◽  
Latent Heat Of Vaporization

In cryogenic fluids such as LH2 or LOX, temperature depression of liquids due to latent heat of vaporization suppresses the growth of cavitation, which is called “thermodynamic effects of cavitation.” Thermodynamic effects of cavitation are significant in these fluids, because they are generally operated close to the critical point and are also characterized by a strong dependence of vapor pressure on temperature. Owing to this phenomenon, the performance of the rocket pump, inducer and other hydraulic equipment is sustained. In this paper, the thermodynamic effects of cavitation are investigated numerically. To predict these effects, a cavitation model introduced by Deshpande et al. is improved. Using this model a sheet cavity around a 2-D hydrofoil is simulated and the dependence of the properties of fluids or Reynolds number on the thermodynamic effects of cavitation is analyzed. The numerical results explain the thermodynamic effects well.

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.

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.

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.

scholarly journals Peristaltic motion of a Johnson-Segalman fluid in a planar channel

2003 ◽  
Vol 2003 (1) ◽  
pp. 1-23 ◽  
Author(s):  
T. Hayat ◽  
Y. Wang ◽  
A. M. Siddiqui ◽  
K. Hutter
Keyword(s):  
Characteristic Time ◽  
Numerical Solutions ◽  
Pressure Rise ◽  
Travelling Wave ◽  
Weissenberg Number ◽  
Planar Channel ◽  
Two Dimensional ◽  
Peristaltic Motion ◽  
Two Dimensional Flow ◽  
Large Wavelength

This paper is devoted to the study of the two-dimensional flow of a Johnson-Segalman fluid in a planar channel having walls that are transversely displaced by an infinite, harmonic travelling wave of large wavelength. Both analytical and numerical solutions are presented. The analysis for the analytical solution is carried out for small Weissenberg numbers. (A Weissenberg number is the ratio of the relaxation time of the fluid to a characteristic time associated with the flow.) Analytical solutions have been obtained for the stream function from which the relations of the velocity and the longitudinal pressure gradient have been derived. The expression of the pressure rise over a wavelength has also been determined. Numerical computations are performed and compared to the perturbation analysis. Several limiting situations with their implications can be examined from the presented analysis.

The structure of two-dimensional separation

1990 ◽  
Vol 220 ◽  
pp. 397-411 ◽  
Author(s):  
Laura L. Pauley ◽  
Parviz Moin ◽  
William C. Reynolds
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Adverse Pressure Gradient ◽  
Navier Stokes ◽  
Stream Velocity ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Shedding Frequency

The separation of a two-dimensional laminar boundary layer under the influence of a suddenly imposed external adverse pressure gradient was studied by time-accurate numerical solutions of the Navier–Stokes equations. It was found that a strong adverse pressure gradient created periodic vortex shedding from the separation. The general features of the time-averaged results were similar to experimental results for laminar separation bubbles. Comparisons were made with the ‘steady’ separation experiments of Gaster (1966). It was found that his ‘bursting’ occurs under the same conditions as our periodic shedding, suggesting that bursting is actually periodic shedding which has been time-averaged. The Strouhal number based on the shedding frequency, local free-stream velocity, and boundary-layer momentum thickness at separation was independent of the Reynolds number and the pressure gradient. A criterion for onset of shedding was established. The shedding frequency was the same as that predicted for the most amplified linear inviscid instability of the separated shear layer.

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