scholarly journals A Constitutive Equation of Turbulence

Fluids ◽  
2021 ◽  
Vol 6 (11) ◽  
pp. 414
Author(s):  
Peter W. Egolf ◽  
Kolumban Hutter
Keyword(s):  
Constitutive Equation ◽  
Turbulence Model ◽  
Turbulence Models ◽  
Turbulent Shear ◽  
Fractional Dynamics ◽  
Physics First ◽  
First Order ◽  
Flow Problems ◽  
Closure Scheme ◽  
Theoretical Considerations

Even though applications of direct numerical simulations are on the rise, today the most usual method to solve turbulence problems is still to apply a closure scheme of a defined order. It is not the case that a rising order of a turbulence model is always related to a quality improvement. Even more, a conceptual advantage of applying a lowest order turbulence model is that it represents the analogous method to the procedure of introducing a constitutive equation which has brought success to many other areas of physics. First order turbulence models were developed in the 1920s and today seem to be outdated by newer and more sophisticated mathematical-physical closure schemes. However, with the new knowledge of fractal geometry and fractional dynamics, it is worthwhile to step back and reinvestigate these lowest order models. As a result of this and simultaneously introducing generalizations by multiscale analysis, the first order, nonlinear, nonlocal, and fractional Difference-Quotient Turbulence Model (DQTM) was developed. In this partial review article of work performed by the authors, by theoretical considerations and its applications to turbulent flow problems, evidence is given that the DQTM is the missing (apparent) constitutive equation of turbulent shear flows.

scholarly journals Analysis of Flow Characteristics and Effects of Turbulence Models for the Butterfly Valve

2021 ◽  
Vol 11 (14) ◽  
pp. 6319
Author(s):  
Sung-Woong Choi ◽  
Hyoung-Seock Seo ◽  
Han-Sang Kim
Keyword(s):  
Turbulence Model ◽  
Dissipation Rate ◽  
Flow Characteristics ◽  
Turbulence Models ◽  
Flow Properties ◽  
Nominal Diameter ◽  
Large Pressure ◽  
Sst Model ◽  
Turbulence Effect ◽  
Valve Opening

In the present study, the flow characteristics of butterfly valves with different sizes DN 80 (nominal diameter: 76.2 mm), DN 262 (nominal diameter: 254 mm), DN 400 (nominal diameter: 406 mm) were numerically investigated under different valve opening percentages. Representative two-equation turbulence models of two-equation k-epsilon model of Launder and Sharma, two-equation k-omega model of Wilcox, and two-equation k-omega SST model of Menter were selected. Flow characteristics of butterfly valves were examined to determine turbulence model effects. It was determined that increasing turbulence effect could cause many discrepancies between turbulence models, especially in areas with large pressure drop and velocity increase. In addition, sensitivity analysis of flow properties was conducted to determine the effect of constants used in each turbulence model. It was observed that the most sensitive flow properties were turbulence dissipation rate (Epsilon) for the k-epsilon turbulence model and turbulence specific dissipation rate (Omega) for the k-omega turbulence model.

scholarly journals Turbulence model performance for ventilation components pressure losses

2021 ◽  
Author(s):  
Karsten Tawackolian ◽  
Martin Kriegel
Keyword(s):  
Reynolds Number ◽  
Turbulence Model ◽  
Pressure Loss ◽  
Low Reynolds Number ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Test Case ◽  
Pressure Losses ◽  
Loss Coefficients ◽  
Near Wall

AbstractThis study looks to find a suitable turbulence model for calculating pressure losses of ventilation components. In building ventilation, the most relevant Reynolds number range is between 3×104 and 6×105, depending on the duct dimensions and airflow rates. Pressure loss coefficients can increase considerably for some components at Reynolds numbers below 2×105. An initial survey of popular turbulence models was conducted for a selected test case of a bend with such a strong Reynolds number dependence. Most of the turbulence models failed in reproducing this dependence and predicted curve progressions that were too flat and only applicable for higher Reynolds numbers. Viscous effects near walls played an important role in the present simulations. In turbulence modelling, near-wall damping functions are used to account for this influence. A model that implements near-wall modelling is the lag elliptic blending k-ε model. This model gave reasonable predictions for pressure loss coefficients at lower Reynolds numbers. Another example is the low Reynolds number k-ε turbulence model of Wilcox (LRN). The modification uses damping functions and was initially developed for simulating profiles such as aircraft wings. It has not been widely used for internal flows such as air duct flows. Based on selected reference cases, the three closure coefficients of the LRN model were adapted in this work to simulate ventilation components. Improved predictions were obtained with new coefficients (LRNM model). This underlined that low Reynolds number effects are relevant in ventilation ductworks and give first insights for suitable turbulence models for this application. Both the lag elliptic blending model and the modified LRNM model predicted the pressure losses relatively well for the test case where the other tested models failed.

Assessment of turbulence models for bubbly flows: Toward a five-equation turbulence model

2020 ◽  
Vol 220 ◽  
pp. 115425
Author(s):  
Ghazi Bellakhal ◽  
Fathia Chaibina ◽  
Jamel Chahed
Keyword(s):  
Turbulence Model ◽  
Turbulence Models ◽  
Bubbly Flows

Evaluation of Different Turbulence Models Applied in Turbopump’s Hydraulic Turbine

2021 ◽  
Author(s):  
Daniel Ferreira Corrêa Barbosa ◽  
Daniel da Silva Tonon ◽  
Luiz Henrique Lindquist Whitacker ◽  
Jesuino Takachi Tomita ◽  
Cleverson Bringhenti
Keyword(s):  
Boundary Conditions ◽  
Turbulence Model ◽  
Rotor Blade ◽  
Space Shuttle ◽  
Turbulence Models ◽  
Tip Clearance ◽  
Test Facility ◽  
Speed Ratio ◽  
Computational Domain ◽  
Axial Turbine

Abstract The aim of this work is an evaluation of different turbulence models applied in Computational Fluid Dynamics (CFD) techniques in the turbomachinery area, in this case, in an axial turbine stage used in turbopump (TP) application. The tip clearance region was considered in this study because it has a high influence in turbomachinery performance. In this region, due to its geometry and the relative movement between the rotor row and casing, there are losses associated with vortices and secondary flow making the flowfield even more turbulent and complex. Moreover, the flow that leaks in the tip region does not participate in the energy transfer between the fluid and rotor blades, degradating the machine efficiency and performance. In this work, the usual flat tip rotor blade geometry was considered. The modeling of turbulent flow based on Reynolds Averaged Navier-Stokes (RANS) equations predicts the variation of turbine operational characteristics that is sufficient for the present turbomachine and flow analysis. Therefore, the appropriate choice of the turbulence model for the study of a given flow is essential to obtain adequate results using numerical approximations. This comparison become important due to the fact that there is no general turbulence model for all engineering applications that has fluid and flow. The turbomachine considered in the present work, is the first stage of the hydraulic axial turbine used in the Low Pressure Oxidizer Turbopump (LPOTP) of the Space Shuttle Main Engine (SSME), considering the 3.0% tip clearance configuration relative to rotor blade height. The turbulence models evaluated in this work were the SST (Shear Stress Transport), the k-ε Standard and the k-ε RNG. The computational domain was discretized in several control volumes based on unstructured mesh. All the simulations were performed using the commercial software developed by ANSYS, CFX v15.0 (ANSYS). All numerical settings and how the boundary conditions were imposed at different surfaces are explained in the work. The boundary conditions settings follow the same rule used in the test facility and needs some attention during the simulations to vary the Blade-Jet-Speed ratio parameter adequately. The results from numerical simulations, were synthesized and compared with the experimental data published by National Aeronautics and Space Administration (NASA), in which the turbine efficiency and its jet velocity parameter are analyzed for each turbulence model result. The work fluid considered in this work was water, the same fluid used in the NASA test facility.

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.

Calculation of Flow in Mixing Vessels With Various Turbulence Models

Volume 4 ◽  
2004 ◽  
Author(s):  
Branislav Basara ◽  
Ales Alajbegovic ◽  
Decan Beader
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Turbulence Model ◽  
Unstructured Grids ◽  
Turbulence Models ◽  
Cfd Applications ◽  
Volume Method ◽  
Rushton Impeller

The paper presents calculations of flow in a mixing vessel stirred by a six-blade Rushton impeller. Mathematical model used in computations is based on the ensemble averaged conservation equations. An efficient finite-volume method based on unstructured grids with rotating sliding parts composed of arbitrary polyhedral elements is used together with various turbulence models. Besides the standard k-ε model which served as a reference, k-ε-v2 model (Durbin, 1995) and the recently proposed hybrid EVM/RSM turbulence model (Basara & Jakirlic, 2003) were used in the calculations. The main aim of the paper is to investigate if more advanced turbulence models are needed for this type of CFD applications. The results are compared with the available experimental data.

scholarly journals Development of a Numerical Investigation Framework for Ground Vehicle Platooning

Fluids ◽  
2021 ◽  
Vol 6 (11) ◽  
pp. 404
Author(s):  
Charles Patrick Bounds ◽  
Sudhan Rajasekar ◽  
Mesbah Uddin
Keyword(s):  
Turbulence Model ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Ground Vehicle ◽  
Simulation Methodology ◽  
Vehicle Platooning ◽  
Length Separation ◽  
Dynamics Simulations ◽  
The Impact ◽  
Far Wake

This paper presents a study on the flow dynamics involving vehicle interactions. In order to do so, this study first explores aerodynamic prediction capabilities of popular turbulence models used in computational fluid dynamics simulations involving tandem objects and thus, ultimately presents a framework for CFD simulations of ground vehicle platooning using a realistic vehicle model, DrivAer. Considering the availability of experimental data, the simulation methodology is first developed using a tandem arrangement of surface-mounted cubes which requires an understanding on the role of turbulence models and the impacts of the associated turbulence model closure coefficients on the prediction veracity. It was observed that the prediction accuracy of the SST k−ω turbulence model can be significantly improved through the use of a combination of modified values for the closure coefficients. Additionally, the initial validation studies reveal the inability of the Unsteady Reynolds-Averaged Navier-Stokes (URANS) approach to resolve the far wake, and its frailty in simulating tandem body interactions. The Improved Delayed Detached Eddy Simulations (IDDES) approach can resolve the wakes with a reasonable accuracy. The validated simulation methodology is then applied to the fastback DrivAer model at different longitudinal spacing. The results show that, as the longitudinal spacing is reduced, the trailing car’s drag is increased while the leading car’s drag is decreased which supports prior explanations of vortex impingement as the reason for drag changes. Additionally, unlike the case of platooning involving Ahmed bodies, the trailing model drag does not return to an isolated state value at a two car-length separation. However, the impact of the resolution of the far wake of a detailed DrivAer model, and its implication on the CFD characterization of vehicle interaction aerodynamics need further investigations.

scholarly journals Assessment of CFD turbulence models for free surface flow simulation and 1-D modelling for water level calculations over a broad-crested weir floodway

Water SA ◽  
2019 ◽  
Vol 45 (3 July) ◽  
Author(s):  
Ahmed M Helmi
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Water Level ◽  
Dimensional Analysis ◽  
Turbulence Model ◽  
Turbulence Models ◽  
Cfd Simulations ◽  
One Dimensional ◽  
The Mean ◽  
The One

Floodways, where a road embankment is permitted to be overtopped by flood water, are usually designed as broad-crested weirs. Determination of the water level above the floodway is crucial and related to road safety. Hydraulic performance of floodways can be assessed numerically using 1-D modelling or 3-D simulation using computational fluid dynamics (CFD) packages. Turbulence modelling is one of the key elements in CFD simulations. A wide variety of turbulence models are utilized in CFD packages; in order to identify the most relevant turbulence model for the case in question, 96 3-D CFD simulations were conducted using Flow-3D package, for 24 broad-crested weir configurations selected based on experimental data from a previous study. Four turbulence models (one-equation, k-ε, RNG k-ε, and k-ω) ere examined for each configuration. The volume of fluid (VOF) algorithm was adopted for free water surface determination. In addition, 24 1-D simulations using HEC-RAS-1-D were conducted for comparison with CFD results and experimental data. Validation of the simulated water free surface profiles versus the experimental measurements was carried out by the evaluation of the mean absolute error, the mean relative error percentage, and the root mean square error. It was concluded that the minimum error in simulating the full upstream to downstream free surface profile is achieved by using one-equation turbulence model with mixing length equal to 7% of the smallest domain dimension. Nevertheless, for the broad-crested weir upstream section, no significant difference in accuracy was found between all turbulence models and the one-dimensional analysis results, due to the low turbulence intensity at this part. For engineering design purposes, in which the water level is the main concern at the location of the flood way, the one-dimensional analysis has sufficient accuracy to determine the water level.

The Simulation Study of Turbulence Models for Conjugate Heat Transfer Analysis of a High Pressure Air-Cooled Gas Turbine

2010 ◽  
Author(s):  
Zhenfeng Wang ◽  
Peigang Yan ◽  
Hongfei Tang ◽  
Hongyan Huang ◽  
Wanjin Han
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Gas Turbine ◽  
Turbulence Model ◽  
Conjugate Heat Transfer ◽  
Turbulence Models ◽  
Turbulence Characteristic ◽  
The Heat Transfer Coefficient

The different turbulence models are adopted to simulate NASA-MarkII high pressure air-cooled gas turbine. The experimental work condition is Run 5411. The paper researches that the effect of different turbulence models for the flow and heat transfer characteristics of turbine. The turbulence models include: the laminar turbulence model, high Reynolds number k-ε turbulence model, low Reynolds number turbulence model (k-ω standard format, k-ω-SST and k-ω-SST-γ-θ) and B-L algebra turbulence model which is adopted by the compiled code. The results show that the different turbulence models can give good flow characteristics results of turbine, but the heat transfer characteristics results are different. Comparing to the experimental results, k-ω-SST-θ-γ turbulence model results are more accurate and can simulate accurately the flow and heat transfer characteristics of turbine with transition flow characteristics. But k-ω-SST-γ-θ turbulence model overestimates the turbulence kinetic energy of blade local region and makes the heat transfer coefficient higher. It causes that local region temperature is higher. The results of B-L algebra turbulence model show that the results of B-L model are accurate besides it has 4% temperature error in the transition region. As to the other turbulence models, the results show that all turbulence models can simulate the temperature distribution on the blade pressure surface except the laminar turbulence model underestimates the heat transfer coefficient of turbulence flow region. On the blade suction surface with transition flow characteristics, high Reynolds number k-ε turbulence model overestimates the heat transfer coefficient and causes the blade surface temperature is high about 90K than the experimental result. Low Reynolds number k-ω standard format and k-ω-SST turbulence models also overestimate the blade surface temperature value. So it can draw a conclusion that the unreasonable choice of turbulence models can cause biggish errors for conjugate heat transfer problem of turbine. The combination of k-ω-SST-γ-θ model and B-L algebra model can get more accurate turbine thermal environment results. In addition, in order to obtain the affect of different turbulence models for gas turbine conjugate heat transfer problem. The different turbulence models are adopted to simulate the different computation mesh domains (First case and Second case). As to each cooling passages, the first case gives the wall heat transfer coefficient of each cooling passages and the second case considers the conjugate heat transfer course between the cooling passages and blade. It can draw a conclusion that the application of heat transfer coefficient on the wall of each cooling passages avoids the accumulative error. So, for the turbine vane geometry models with complex cooling passages or holes, the choice of turbulence models and the analysis of different mesh domains are important. At last, different turbulence characteristic boundary conditions of turbine inner-cooling passages are given and K-ω-SST-γ-θ turbulence model is adopted in order to obtain the effect of turbulence characteristic boundary conditions for the conjugate heat transfer computation results. The results show that the turbulence characteristic boundary conditions of turbine inner-cooling passages have a great effect on the conjugate heat transfer results of high pressure gas turbine.

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