A General Macroscopic Turbulence Model for Flows in Packed Beds, Channels, Pipes, and Rod Bundles

2008 ◽  
Vol 130 (10) ◽  
Author(s):  
A. Nakayama ◽  
F. Kuwahara
Keyword(s):  
Porous Media ◽  
Kinetic Energy ◽  
Turbulent Flows ◽  
Turbulence Model ◽  
Packed Bed ◽  
Volume Averaging ◽  
Packed Beds ◽  
Mean Flow ◽  
Rod Bundles ◽  
And Performance

This study focuses on Nakayama and Kuwahara’s two-equation turbulence model and its modifications, previously proposed for flows in porous media, on the basis of the volume averaging theory. Nakayama and Kuwahara’s model is generalized so that it can be applied to most complex turbulent flows such as cross flows in banks of cylinders and packed beds, and longitudinal flows in channels, pipes, and rod bundles. For generalization, we shall reexamine the extra production terms due to the presence of the porous media, appearing in the transport equations of turbulence kinetic energy and its dissipation rate. In particular, we shall consider the mean flow kinetic energy balance within a pore, so as to seek general expressions for these additional production terms, which are valid for most kinds of porous media morphology. Thus, we establish the macroscopic turbulence model, which does not require any prior microscopic numerical experiments for the structure. Hence, for the given permeability and Forchheimer coefficient, the model can be used for analyzing most complex turbulent flow situations in homogeneous porous media without a detailed morphological information. Preliminary examination of the model made for the cases of packed bed flows and longitudinal flows through pipes and channels reveals its high versatility and performance.

Experimental Study on CH4 / Air Diffusion Combustion on the Upper Surface of Porous Media Packed Beds

2012 ◽  
Vol 516-517 ◽  
pp. 62-65 ◽  
Author(s):  
Xin Zhang Huang ◽  
Xiu Li Zhang ◽  
Jun Rui Shi ◽  
Zhi Jia Xue ◽  
You Ning Xu ◽  
...  
Keyword(s):  
Experimental Study ◽  
Porous Media ◽  
Packed Bed ◽  
Flame Height ◽  
Diffusion Combustion ◽  
Packed Beds ◽  
Flame Shape ◽  
Air Diffusion

This paper experimentally study on CH4/ air co-flow diffusion combustion on the upper surface of porous media packed beds. The flame height and flame shape were reconstructed from the upper and the side of the combustor. The influence of the height of the packed bed on the flame height and flame shape is reported. It is shown that the flame height decreases rapidly and the circular diameter increases rapidly with increase the height of the packed beds.

scholarly journals Biases in Thorpe-Scale Estimates of Turbulence Dissipation. Part II: Energetics Arguments and Turbulence Simulations

2015 ◽  
Vol 45 (10) ◽  
pp. 2522-2543 ◽  
Author(s):  
Alberto Scotti
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Turbulent Flows ◽  
Companion Paper ◽  
Mean Flow ◽  
Available Potential Energy ◽  
Ozmidov Scale ◽  
Thorpe Scale ◽  
The Mean ◽  
Shear Driven Flows

AbstractThis paper uses the energetics framework developed by Scotti and White to provide a critical assessment of the widely used Thorpe-scale method, which is used to estimate dissipation and mixing rates in stratified turbulent flows from density measurements along vertical profiles. This study shows that the relevant displacement scale in general is not the rms value of the Thorpe displacement. Rather, the displacement field must be Reynolds decomposed to separate the mean from the turbulent component, and it is the turbulent component that ought to be used to diagnose mixing and dissipation. In general, the energetics of mixing in an overall stably stratified flow involves potentially complex exchanges among the available potential energy and kinetic energy associated with the mean and turbulent components of the flow. The author considers two limiting cases: shear-driven mixing, where mixing comes at the expense of the mean kinetic energy of the flow, and convective-driven mixing, which taps the available potential energy of the mean flow to drive mixing. In shear-driven flows, the rms of the Thorpe displacement, known as the Thorpe scale is shown to be equivalent to the turbulent component of the displacement. In this case, the Thorpe scale approximates the Ozmidov scale, or, which is the same, the Thorpe scale is the appropriate scale to diagnose mixing and dissipation. However, when mixing is driven by the available potential energy of the mean flow (convective-driven mixing), this study shows that the Thorpe scale is (much) larger than the Ozmidov scale. Using the rms of the Thorpe displacement overestimates dissipation and mixing, since the amount of turbulent available potential energy (measured by the turbulent displacement) is only a fraction of the total available potential energy (measured by the Thorpe scale). Corrective measures are discussed that can be used to diagnose mixing from knowledge of the Thorpe displacement. In a companion paper, Mater et al. analyze field data and show that the Thorpe scale can indeed be much larger than the Ozmidov scale.

A Turbulence Model for Pulsatile Arterial Flows

2004 ◽  
Vol 126 (5) ◽  
pp. 578-584 ◽  
Author(s):  
B. A. Younis ◽  
S. A. Berger
Keyword(s):  
Turbulent Flows ◽  
Turbulence Model ◽  
Solid Wall ◽  
Flow Behavior ◽  
Local Equilibrium ◽  
Fluid Motion ◽  
Circulatory System ◽  
Wave Form ◽  
Mean Flow ◽  
Law Of The Wall

Difficulties in predicting the behavior of some high Reynolds number flows in the circulatory system stem in part from the severe requirements placed on the turbulence model chosen to close the time-averaged equations of fluid motion. In particular, the successful turbulence model is required to (a) correctly capture the “nonequilibrium” effects wrought by the interactions of the organized mean-flow unsteadiness with the random turbulence, (b) correctly reproduce the effects of the laminar-turbulent transitional behavior that occurs at various phases of the cardiac cycle, and (c) yield good predictions of the near-wall flow behavior in conditions where the universal logarithmic law of the wall is known to be not valid. These requirements are not immediately met by standard models of turbulence that have been developed largely with reference to data from steady, fully turbulent flows in approximate local equilibrium. The purpose of this paper is to report on the development of a turbulence model suited for use in arterial flows. The model is of the two-equation eddy-viscosity variety with dependent variables that are zero-valued at a solid wall and vary linearly with distance from it. The effects of transition are introduced by coupling this model to the local value of the intermittency and obtaining the latter from the solution of a modeled transport equation. Comparisons with measurements obtained in oscillatory transitional flows in circular tubes show that the model produces substantial improvements over existing closures. Further pulsatile-flow predictions, driven by a mean-flow wave form obtained in a diseased human carotid artery, indicate that the intermittency-modified model yields much reduced levels of wall shear stress compared to the original, unmodified model. This result, which is attributed to the rapid growth in the thickness of the viscous sublayer arising from the severe acceleration of systole, argues in favor of the use of the model for the prediction of arterial flows.

Implementation of k-kL-ω Turbulence Model for Compressible Flow into OpenFOAM

2016 ◽  
Vol 821 ◽  
pp. 63-69 ◽  
Author(s):  
Martin Kožíšek ◽  
Jiří Fürst ◽  
Jaromír Příhoda ◽  
Piotr Doerffer
Keyword(s):  
Kinetic Energy ◽  
Flat Plate ◽  
Compressible Flow ◽  
Turbulent Flows ◽  
Turbulence Model ◽  
Transitional Flow ◽  
Flow Simulations ◽  
Flow Through ◽  
Turbine Cascades ◽  
Laminar And Turbulent Flows

The article deals with results of the implementation of the k-kL-ω turbulence model for compressible transitional flow into OpenFOAM. This model was firstly proposed by Walters and Leylek [2] and utilizes the approach of the laminar kinetic energy in order to predict the transition between laminar and turbulent flows. The performance of the implemented model has been tested for the case of flow over a flat plate and the flow through VKI and SE 1050 turbine cascades. The properties of the implementation of the model for compressible flow simulations into OpenFOAM are discussed.

Prediction of Turbulent Source Flow Between Corotating Disks With an Anisotropic Two-Equation Turbulence Model

1988 ◽  
Vol 110 (2) ◽  
pp. 187-194 ◽  
Author(s):  
S. A. Shirazi ◽  
C. R. Truman
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulence Model ◽  
Ad Hoc ◽  
Low Reynolds Number ◽  
Wall Region ◽  
Mixing Length ◽  
Mean Flow ◽  
Low Reynolds

An anisotropic form of a low-Reynolds-number two-equation turbulence model has been implemented in a numerical solution for incompressible turbulent flow between corotating parallel disks. Transport equations for turbulent kinetic energy and dissipation rate were solved simultaneously with the governing equations for the mean-flow variables. Comparisons with earlier mixing-length predictions and with measurements are presented. Good agreement between the present predictions and the measurements of velocity components and turbulent kinetic energy was obtained. The low-Reynolds-number two-equation model was found to model adequately the near-wall region as well as the effects of rotation and streamline divergence, which required ad hoc assumptions in the mixing-length model.

Steady and Unsteady Computations of Turbulent Flows Induced by a 4/45° Pitched-Blade Impeller

1999 ◽  
Vol 121 (2) ◽  
pp. 318-329 ◽  
Author(s):  
K. Wechsler ◽  
M. Breuer ◽  
F. Durst
Keyword(s):  
Steady State ◽  
Turbulent Flows ◽  
Turbulence Model ◽  
High Performance ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Computational Effort ◽  
Stirred Tank ◽  
Mean Flow ◽  
Stirred Vessel

The present paper summarizes steady and unsteady computations of turbulent flow induced by a pitched-blade turbine (four blades, 45° inclined) in a baffled stirred tank. Mean flow and turbulence characteristics were determined by solving the Reynolds averaged Navier-Stokes equations together with a standard k-ε turbulence model. The round vessel had a diameter of T = 152 mm. The turbine of diameter T/3 was located at a clearance of T/3. The Reynolds number (Re) of the experimental investigation was 7280, and computations were performed at Re = 7280 and Re = 29,000. Techniques of high-performance computing were applied to permit grid sensitivity studies in order to isolate errors resulting from deficiencies of the turbulence model and those resulting from insufficient grid resolution. Both steady and unsteady computations were performed and compared with respect to quality and computational effort. Unsteady computations considered the time-dependent geometry which is caused by the rotation of the impeller within the baffled stirred tank reactor. Steady-state computations also considered neglect the relative motion of impeller and baffles. By solving the governing equations of motion in a rotating frame of reference for the region attached to the impeller, the steady-state approach is able to capture trailing vortices. It is shown that this steady-state computational approach yields numerical results which are in excellent agreement with fully unsteady computations at a fraction of the time and expense for the stirred vessel configuration under consideration.

Reynolds Stress Field and Turbulent Kinetic Energy Budget in a Repeating Compressor Stage

2020 ◽  
Author(s):  
Ahmad Nawab ◽  
Feng Wang ◽  
Luca di Mare ◽  
John J. Adamczyk
Keyword(s):  
Kinetic Energy ◽  
Pressure Gradient ◽  
Turbulent Kinetic Energy ◽  
Turbulence Model ◽  
Turbulence Modelling ◽  
Compressor Stage ◽  
Mean Flow ◽  
Rans Simulation ◽  
Dissipation Rates ◽  
The Mean

Abstract Turbulence modelling in compressor passages continues to be a challenging problem. In order to better understand the shortcomings of turbulence modelling, a LES and a RANS computation were performed of a repeating compressor stage. The computation was carried out near the aerodynamic design point of the compressor stage, in order to minimise the challenge posed to the turbulence model. The use of a repeating stage configuration removes the need to specify the statistics of the incoming turbulent field; the statistics become an output of the simulation and not an input. This is a critical fact that greatly increases the credibility of the current LES compressor simulation over many previous simulations. As the computations are performed at mid-span, radial gradients can safely be assumed to be small, thus removing issues associated with capturing flow features attributed to 3D geometry. The flow field is assumed to be incompressible, which is required in order to achieve a true repeating stage environment. The RANS computation is based on a state-of-the-art turbulence model. At the same flow coefficient, the RANS simulation yielded a total pressure rise very near that of the LES simulation. However, there are nontrivial differences in the flow details. The mean flow and Reynolds shear stress boundary layer profiles are in good agreement in regions of favourable pressure gradient, but significant differences exist in the presence of adverse pressure-gradients. The turbulent kinetic energy profiles however are in poor agreement throughout the flow. The mean flow production rates predicted by the RANS computation are largely similar to those of the LES simulation forward of mid-chord where the pressure gradient is favourable. A notable exception is the leading-edge region where the LES predicts negative production i.e. a net transfer of energy to the time-mean flow, and the region aft of mid-chord where the pressure gradient is adverse. Outside of the viscous sub-layer, the dissipation rates are also predicted correctly by the RANS simulation forward of midchord where the pressure gradient is favourable. Aft of mid-chord however, there are significant differences in the dissipation rates.

Multidimensional Predictions of In-Cylinder Turbulent Flows: Contribution to the Assessment of k-ε Turbulence Model Variants for Bowl-in-Piston Engines

2003 ◽  
Author(s):  
Andrea E. Catania ◽  
Mirko Baratta ◽  
Ezio Spessa ◽  
Rui L. Liu
Keyword(s):  
Turbulent Flows ◽  
Turbulence Model ◽  
Fluid Motion ◽  
Combustion Process ◽  
Turbulence Models ◽  
Algebraic Equations ◽  
Mean Flow ◽  
Wall Functions ◽  
Simpler Algorithm ◽  
Model Engine

As is well known, the in-cylinder flow phenomena can strongly affect the engine combustion process and the related emission sources. Therefore, a better understanding of the fluid motion is critical for developing new engine concepts with the most attractive operation and emission characteristics. To that end, multidimensional flow computational codes with reliable turbulence models are useful investigation and design tools. This paper is concerned with mean-flow and turbulence simulation in a motored model engine with a compression ratio of 6.7. The flow configurations comprise an axisymmetric combustion chamber with one centrally located valve and each of a flat piston and cylindrical bowl-in-piston arrangements. The calculations are performed using a non-commercial CFD code that was originally developed by the authors. A finite volume conservative implicit method, applying various order-of-accuracy schemes, is employed for the discretization of the partial differential equations modeling the in-cylinder turbulent flow, and the resultant algebraic equations are linearized and sequentially solved by an iterative procedure. Velocity-pressure coupling is ensured by a pressure correction method similar to that of the SIMPLER algorithm. Results of the simulation are presented at the model engine speed of 200 rpm throughout the engine cycle. They were obtained using three versions of the k-ε turbulence model (Standard, Two Scale and RNG) which differ from each other for underlying concepts, complexity and accuracy in capturing flow features. Modified boundary conditions with respect to logarithmic wall-functions were applied. Insight was also gained into the nonlinear effects of stress-strain constitutive relation on turbulence modeling. The effects of the equation differencing schemes and computational grid spacing on flow predictions were tested. Then the numerical results were compared to those of LDV measurements and the influence of the k-ε model variants on the flow field features were examined during the induction stroke and around compression TDC.

The formulation of the RANS equations for supersonic and hypersonic turbulent flows

2020 ◽  
pp. 1-31
Author(s):  
H. Zhang ◽  
T.J. Craft ◽  
H. Iacovides
Keyword(s):  
Kinetic Energy ◽  
Pressure Gradient ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
High Speed ◽  
Mean Flow ◽  
Rans Equations ◽  
Flow Equations ◽  
The Mean ◽  
The Impact

Abstract Accurate prediction of supersonic and hypersonic turbulent flows is essential to the design of high-speed aerospace vehicles. Such flows are mainly predicted using the Reynolds-Averaged Navier–Stokes (RANS) approach in general, and in particular turbulence models using the effective viscosity approximation. Several terms involving the turbulent kinetic energy (k) appear explicitly in the RANS equations through the modelling of the Reynolds stresses in such approach, and similar terms appear in the mean total energy equation. Some of these terms are often ignored in low, or even supersonic, speed simulations with zero-equation models, as well as some one- or two-equation models. The omission of these terms may not be appropriate under hypersonic conditions. Nevertheless, this is a widespread practice, even for very high-speed turbulent flow simulations, because many software packages still make such approximations. To quantify the impact of ignoring these terms in the RANS equations, two linear two-equation models and one non-linear two-equation model are applied to the computation of five supersonic and hypersonic benchmark cases, one 2D zero-pressure gradient hypersonic flat plate case and four shock wave boundary layer interaction (SWBLI) cases. The surface friction coefficients and velocity profiles predicted with different combinations of the turbulent kinetic energy terms present in the transport equations show little sensitivity to the presence of these terms in the zero-pressure gradient case. In the SWBLI cases, however, comparisons show that inclusion of k in the mean flow equations can have a strong effect on the prediction of flow separation. Therefore, it is highly recommended to include all the turbulent kinetic energy terms in the mean flow equations when dealing with simulations of supersonic and hypersonic turbulent flows, especially for flows with SWBLIs. As a further consequence, since k may not be obtained explicitly in zero-equation, or certain one-equation, models, it is debatable whether these models are suitable for simulations of supersonic and hypersonic turbulent flows with SWBLIs.

scholarly journals Voltage rise anemometry in turbulent flows applied to internal combustion engines

2021 ◽  
Vol 62 (6) ◽  
Author(s):  
Michael Wörner ◽  
Gregor Rottenkolber
Keyword(s):  
Turbulent Flows ◽  
Internal Combustion Engines ◽  
Clear Correlation ◽  
Combustion Engines ◽  
Mean Flow ◽  
Voltage Rise ◽  
Mathematical Correlation ◽  
Thermodynamic Conditions ◽  
Secondary Voltage ◽  
Cylinder Flow

AbstractIn an experimental procedure, a voltage rise anemometry is developed as a measurement technique for turbulent flows. Initially, fundamental investigations on a specific wind tunnel were performed for basic understanding and calibration purpose. Thus, a mathematical correlation is derived for calculating flow from measured secondary voltage of an ignition system under different thermodynamic conditions. Subsequently, the derived method was applied on a spark-ignited engine to measure in-cylinder flow. Therefore, no changes on combustion chamber were necessary avoiding any interferences of the examined flow field. Comparing four different engine configurations, a study of mean flow and turbulence was performed. Moreover, the results show a clear correlation between measured turbulence and analysed combustion parameters. Graphic abstract

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