scholarly journals On the prediction of equilibrium states in homogeneous turbulence

1989 ◽  
Vol 209 ◽  
pp. 591-615 ◽  
Author(s):  
Charles G. Speziale ◽  
Nessan Mac Giolla Mhuiris
Keyword(s):  
Kinetic Energy ◽  
Numerical Simulations ◽  
Turbulent Kinetic Energy ◽  
Time Evolution ◽  
Dissipation Rate ◽  
Flow Instability ◽  
Turbulence Models ◽  
Second Order ◽  
Equilibrium States ◽  
Unstable Flow

A comparison of several commonly used turbulence models (including the K–ε model and three second-order closures) is made for the test problem of homogeneous turbulent shear flow in a rotating frame. The time evolution of the turbulent kinetic energy and dissipation rate is calculated for these models and comparisons are made with previously published experiments and numerical simulations. Particular emphasis is placed on examining the ability of each model to predict equilibrium states accurately for a range of the parameter Ω/S (the ratio of the rotation rate to the shear rate). It is found that none of the commonly used second-order closure models yield substantially improved predictions for the time evolution of the turbulent kinetic energy and dissipation rate over the somewhat defective results obtained from the simpler K–ε model for the unstable flow regime. There is also a problem with the equilibrium states predicted by the various models. For example, the K–ε model erroneously yields equilibrium states that are independent of Ω/S while the Launder, Reece & Rodi model and the Shih-Lumley model predict a flow relaminarization when Ω/S > 0.39 - a result that is contrary to numerical simulations and linear spectral analyses, which indicate flow instability for at least the range 0 [les ] Ω/S [les ] 0.5. The physical implications of the results obtained from the various turbulence models considered herein are discussed in detail along with proposals to remedy the deficiencies based on a dynamical systems approach.

Assessment of the Turbulent Prandtl Number Effect on Simulating Heat Transfer Characteristics of Supercritical Water Flow in Bare Tubes

2017 ◽  
Author(s):  
Amjad Farah ◽  
Glenn Harvel ◽  
Igor Pioro
Keyword(s):  
Heat Transfer ◽  
Fluid Dynamics ◽  
Kinetic Energy ◽  
Prandtl Number ◽  
Turbulent Kinetic Energy ◽  
Supercritical Water ◽  
Dissipation Rate ◽  
Turbulence Models ◽  
Turbulent Prandtl Number ◽  
Wide Range

Computational Fluid Dynamics (CFD) is a numerical approach to modelling fluids in multidimensional space using the Navier-Stokes equations and databases of fluid properties to arrive at a full simulation of a fluid dynamics and heat transfer system. The turbulence models employed in CFD are a set of equations that determine the turbulence transport terms in the mean flow equations. They are based on hypotheses about the process of turbulence, and as such require empirical input in the form of constants or functions, in order to achieve closure. By introducing a set of empirical constants to a model, that model then becomes valid for certain flow conditions, or for a range of flows. Of those constants, the turbulent Prandtl number appears in multiple equations; energy, momentum, turbulent kinetic energy, turbulent kinetic energy dissipation rate, etc. and the value it takes in each equation is different and chosen empirically to fit a wide range of flows in the subcritical region. The studies that attempt to find the effect of varying the turbulent Pr number on simulation results, often only mention one number; presumably the one that appears in the energy equation (although it is never explicitly explained). The rest of the constants are treated as universally acceptable for generalized flow and not tested for their effect on flow parameters. A numerical study on heat transfer to supercritical water flowing in a vertical tube is carried out using the ANSYS FLUENT code and employing the Realizable k-ε (RKE) and the SST k-ε turbulence models. The 3-D mesh consists of a 1/8 slice (45° radially) of a bare tube. The study explored the effects of turbulent Pr numbers, and their variations, in order to understand their significance, and to build on previous knowledge to modify the turbulence models and achieve higher accuracy in simulating experimental conditions. The numerical results of 3D flow and thermal distributions under normal and deteriorated heat transfer conditions are compared to experimental results. The distributions of temperature and turbulence levels are used to understand the underlying phenomena of the heat transfer deterioration in supercritical water flows. Reducing the energy turbulent Pr number produced the most accurate prediction of the deterioration in heat transfer, by altering the production term due to buoyancy, which appears in the equations for turbulent kinetic energy as well as its dissipation rate. The buoyancy forces in upward flows act to reduce the turbulent shear stress, resulting in localized increase in wall temperatures.

Characteristics of Turbulence in a Turbofan Stage

2012 ◽  
Vol 135 (2) ◽  
Author(s):  
Jeremy Maunus ◽  
Sheryl Grace ◽  
Douglas Sondak ◽  
Victor Yakhot
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Dissipation Rate ◽  
Turbulence Models ◽  
Energy Dissipation Rate ◽  
Scale Model ◽  
Length Scale ◽  
Experimental Measurements ◽  
Hot Wire ◽  
Turbofan Engine

Two-equation turbulence models are commonly used in the simulation of turbomachinery flow fields, but there are limited experimental data available to validate the resulting turbulence quantities. Experimental measurements are available from NASA’s Source Diagnostic Test (SDT), a 1/5th scale model representation of the bypass stage of a turbofan engine. Detailed unsteady hot-wire anemometer data were taken at two axial locations between the rotor and fan exit guide vanes (FEGVs). Here, an accurate and consistent procedure is used to obtain the turbulent kinetic energy, dissipation rate, and integral length scale from structure functions calculated using the SDT data. These results are compared to the solutions provided by four proprietary CFD codes that employ two-equation turbulence models. The simulations are shown to predict the turbulent kinetic energy and length scale reasonably well as well as the trend in mean dissipation. The actual mean dissipation rates differ by nearly two orders of magnitude due to a difference in interpretation between the classical definition and what is used in CFD.

scholarly journals Sensitivity analysis of nuclear main pump annular casing tongue blend

2017 ◽  
Vol 9 (7) ◽  
pp. 168781401770659 ◽  
Author(s):  
Xiaorui Cheng ◽  
Wenrui Bao ◽  
Li Fu ◽  
Xiaoting Ye
Keyword(s):  
Kinetic Energy ◽  
Numerical Simulations ◽  
Turbulent Kinetic Energy ◽  
Stokes Equations ◽  
Flow Instability ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Simple Algorithm ◽  
Operating Conditions ◽  
Navier Stokes

Based on the Reynolds-averaged Navier–Stokes equations of relative coordinates and the RNG k-ε turbulence model, using our SIMPLE algorithm, we performed numerical simulations for an AP1000 nuclear main pump model with water as the medium. By changing the size of the tongue blend in the annular casing, seven different schemes were designed. Three-dimensional numerical simulations were conducted for the flow within the pump under various settings, and the flow characteristics of the annular casing using different tongue blends were obtained. The results show that for different operating conditions, there is a specific tongue blend that optimizes pump performance. Based on the calculation results, a larger tongue blend leads to a larger flow rate. Off-design conditions caused flow instability, which in turn caused the tongue blend to have a certain impact on the performance of the impeller. However, the performance of the pump was not primarily affected by changes in the impeller performance, but was instead affected by the performance of the annular casing, which was itself affected by tongue blend. When changing the tongue blend, the change in static pressure and total pressure of the annular casing was larger under the condition of 0.6 Qd and was smaller under the conditions of 1.0 Qd and 1.4 Qd. The turbulent kinetic energy in the annular casing changed mainly in the tongue impact zone and outlet diffuser under the condition of 1.0 Qd; furthermore, the turbulent kinetic energy in the whole of the annular casing demonstrated significant changes under the conditions of 0.6 Qd and 1.4 Qd.

scholarly journals Numerical Modelling of Wave Fields and Currents in Coastal Area

Water ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1582
Author(s):  
Francesco Gallerano
Keyword(s):  
Kinetic Energy ◽  
Numerical Simulations ◽  
Turbulent Kinetic Energy ◽  
Turbulence Model ◽  
Wave Motion ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Wave Fields ◽  
Induced Velocity ◽  
Wave Induced

The design and management of coastal engineering, like harbors and coastal defense structures, requires the simulation of hydrodynamic phenomena. This special issue collects five original papers that address state of the art numerical simulations of wave fields and wave-induced velocity fields in coastal areas. The first paper proposes a turbulence model for wave breaking simulation, which is expressed in terms of turbulent kinetic energy and dissipation rate of turbulent kinetic energy (k − ε); the proposed turbulence model is a modification of the standard k − ε turbulence models. The second paper investigates modalities by which wind interacts with wave motion, modifying the wave propagation dynamic. The third paper proposes a study on waves overtopping over coastal barriers. The fourth paper details the numerical simulation of a tsunami wave that propagates over an artificial reservoir, caused by a landslide that creates a solid mass to detach from the slopes and to slide into the reservoir. The fifth paper examines an application case concerning Cetraro harbor (Italy), which is carried out using three-dimensional numerical simulations of wave motion.

Evaluation of Turbulent Kinetic Energy Dissipation Rate in a Free Jet Flow from PIV Measurements

2012 ◽  
Vol 7 (1) ◽  
pp. 53-69
Author(s):  
Vladimir Dulin ◽  
Yuriy Kozorezov ◽  
Dmitriy Markovich
Keyword(s):  
Energy Dissipation ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Turbulent Velocity ◽  
Small Scale ◽  
Velocity Fluctuations ◽  
Piv Measurements ◽  
Free Jet

The present paper reports PIV (Particle Image Velocimetry) measurements of turbulent velocity fluctuations statistics in development region of an axisymmetric free jet (Re = 28 000). To minimize measurement uncertainty, adaptive calibration, image processing and data post-processing algorithms were utilized. On the basis of theoretical analysis and direct measurements, the paper discusses effect of PIV spatial resolution on measured statistical characteristics of turbulent fluctuations. Underestimation of the second-order moments of velocity derivatives and of the turbulent kinetic energy dissipation rate due to a finite size of PIV interrogation area and finite thickness of laser sheet was analyzed from model spectra of turbulent velocity fluctuations. The results are in a good agreement with the measured experimental data. The paper also describes performance of possible ways to account for unresolved small-scale velocity fluctuations in PIV measurements of the dissipation rate. In particular, a turbulent viscosity model can be efficiently used to account for the unresolved pulsations in a free turbulent flow

K–ϵ model for rotating homogeneous decaying turbulence

2016 ◽  
Vol 94 (11) ◽  
pp. 1200-1204 ◽  
Author(s):  
Hamed Marzougui
Keyword(s):  
Kinetic Energy ◽  
Numerical Simulations ◽  
Decay Rate ◽  
Rate Equation ◽  
Rotation Rate ◽  
Dissipation Rate ◽  
Direct Numerical Simulations ◽  
Uniform Rotation ◽  
Axis Of Rotation ◽  
Decaying Turbulence

In the present work, we propose a modification to the standard K–ϵ model for simulating homogeneous decaying turbulence subjected to uniform rotation. In this modification, the dissipation rate equation is formulated in terms of the rotation rate Ω, the integral length scales along the axis of rotation [Formula: see text], and its isotropic value [Formula: see text]. The comparison of our results with the corresponding direct numerical simulations proves that the new model reproduces in an excellent way the decay rate of the turbulent kinetic energy.

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