Analysis and modelling of anisotropies in the dissipation rate of turbulence

1997 ◽  
Vol 344 ◽  
pp. 155-180 ◽  
Author(s):  
CHARLES G. SPEZIALE ◽  
THOMAS B. GATSKI
Keyword(s):  
Transport Equation ◽  
Dissipation Rate ◽  
Algebraic Model ◽  
Scalar Dissipation ◽  
Mean Velocity ◽  
Production Term ◽  
New Model ◽  
Symmetry Properties ◽  
The Mean ◽  
The Relationship

The modelling of anisotropies in the dissipation rate of turbulence is considered based on an analysis of the exact transport equation for the dissipation rate tensor. An algebraic model is systematically derived using integrity bases methods and tensor symmetry properties. The new model differs notably from all previously proposed models in that it depends nonlinearly on the mean velocity gradients. This gives rise to a transport equation for the scalar dissipation rate that is of the same general form as the commonly used model with one major exception: the coefficient of the production term is dependent on the invariants of both the rotational and irrotational strain rates. The relationship between the new model and other recently proposed models is examined in detail. Some basic tests and applications of the model are also provided along with a discussion of the implications for turbulence modelling.

Relationship between the heat transfer law and the scalar dissipation function in a turbulent channel flow

2017 ◽  
Vol 830 ◽  
pp. 300-325 ◽  
Author(s):  
Hiroyuki Abe ◽  
Robert Anthony Antonia
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Channel Flow ◽  
Dissipation Rate ◽  
Turbulent Channel Flow ◽  
Scalar Dissipation ◽  
Scalar Dissipation Rate ◽  
Mean Velocity ◽  
The Mean ◽  
Logarithmic Dependence

Integration across a fully developed turbulent channel flow of the transport equations for the mean and turbulent parts of the scalar dissipation rate yields relatively simple relations for the bulk mean scalar and wall heat transfer coefficient. These relations are tested using direct numerical simulation datasets obtained with two isothermal boundary conditions (constant heat flux and constant heating source) and a molecular Prandtl number Pr of 0.71. A logarithmic dependence on the Kármán number $h^{+}$ is established for the integrated mean scalar in the range $h^{+}\geqslant 400$ where the mean part of the total scalar dissipation exhibits near constancy, whilst the integral of the turbulent scalar dissipation rate $\overline{\unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}}$ increases logarithmically with $h^{+}$. This logarithmic dependence is similar to that established in a previous paper (Abe & Antonia, J. Fluid Mech., vol. 798, 2016, pp. 140–164) for the bulk mean velocity. However, the slope (2.18) for the integrated mean scalar is smaller than that (2.54) for the bulk mean velocity. The ratio of these two slopes is 0.85, which can be identified with the value of the turbulent Prandtl number in the overlap region. It is shown that the logarithmic $h^{+}$ increase of the integrated mean scalar is intrinsically associated with the overlap region of $\overline{\unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}}$, established for $h^{+}$ (${\geqslant}400$). The resulting heat transfer law also holds at a smaller $h^{+}$ (${\geqslant}200$) than that derived by assuming a log law for the mean temperature.

Implementation and Validation of a New Soot Model and Application to Aeroengine Combustors

2000 ◽  
Author(s):  
M. Balthasar ◽  
F. Mauss ◽  
M. Pfitzner ◽  
A. Mack
Keyword(s):  
Transport Equation ◽  
Gas Phase ◽  
Dissipation Rate ◽  
Soot Formation ◽  
Mixture Fraction ◽  
Scalar Dissipation ◽  
Scalar Dissipation Rate ◽  
Gas Phase Reactions ◽  
The Mean ◽  
Soot Model

The modelling of soot formation and oxidation under industrially relevant conditions has made significant progress in recent years. Simplified models introducing a small number of transport equations into a CFD code have been used with some success in research configurations simulating a reciprocating diesel engine. Soot formation and oxidation in the turbulent flow is calculated on the basis of a laminar flamelet library model. The gas phase reactions are modelled with a detailed mechanism for the combustion of heptane containing 89 species and 855 reactions developed by Frenklach and Warnatz and revised by Mauss. The soot model is divided into gas phase reactions, the growth of polycyclic aromatic hydrocarbons (PAH) and the processes of particle inception, heterogeneous surface growth, oxidation and condensation. The first two are modelled within the laminar flamelet chemistry, while the soot model deals with the soot particle processes. The time scales of soot formation are assumed to be much larger than the turbulent time scales. Therefore rates of soot formation are tabulated in the flamelet libraries rather than the soot volume fraction itself. The different rates of soot formation, e.g. particle inception, surface growth, fragmentation and oxidation, computed on the basis of a detailed soot model, are calculated in the mixture fraction / scalar dissipation rate space and further simplified by fitting them to simple analytical functions. A transport equation for the mean soot mass fraction is solved in the CFD-code. The mean rate in this transport equation is closed with the help of presumed probability density functions for the mixture fraction and the scalar dissipation rate. Heat loss due to radiation can be taken into account by including a heat loss parameter in the flamelet calculations describing the change of enthalpy due to radiation, but was not used for the results reported here. The soot model was integrated into an existing commercial CFD code as a post-processing module to existing combustion CFD flow fields and is very robust with high convergence rates. The model is validated with laboratory flame data and using a realistic 3-D BMW Rolls-Royce combustor configuration, where test data at high pressure are available. Good agreement between experiment and simulation is achieved for laboratory flames, whereas soot is overpredicted for the aeroengine combustor configuration by 1–2 orders of magnitude.

Implementation and Validation of a New Soot Model and Application to Aeroengine Combustors

2000 ◽  
Vol 124 (1) ◽  
pp. 66-74 ◽  
Author(s):  
M. Balthasar ◽  
F. Mauss ◽  
M. Pfitzner ◽  
A. Mack
Keyword(s):  
Transport Equation ◽  
Gas Phase ◽  
Dissipation Rate ◽  
Soot Formation ◽  
Mixture Fraction ◽  
Scalar Dissipation ◽  
Scalar Dissipation Rate ◽  
Gas Phase Reactions ◽  
The Mean ◽  
Soot Model

The modeling of soot formation and oxidation under industrially relevant conditions has made significant progress in recent years. Simplified models introducing a small number of transport equations into a CFD code have been used with some success in research configurations simulating a reciprocating diesel engine. Soot formation and oxidation in the turbulent flow is calculated on the basis of a laminar flamelet library model. The gas phase reactions are modeled with a detailed mechanism for the combustion of heptane containing 89 species and 855 reactions developed by Frenklach and Warnatz and revised by Mauss. The soot model is divided into gas phase reactions, the growth of polycyclic aromatic hydrocarbons (PAH) and the processes of particle inception, heterogeneous surface growth, oxidation, and condensation. The first two are modeled within the laminar flamelet chemistry, while the soot model deals with the soot particle processes. The time scales of soot formation are assumed to be much larger than the turbulent time scales. Therefore rates of soot formation are tabulated in the flamelet libraries rather than the soot volume fraction itself. The different rates of soot formation, e.g., particle inception, surface growth, fragmentation, and oxidation, computed on the basis of a detailed soot model, are calculated in the mixture fraction/scalar dissipation rate space and further simplified by fitting them to simple analytical functions. A transport equation for the mean soot mass fraction is solved in the CFD code. The mean rate in this transport equation is closed with the help of presumed probability density functions for the mixture fraction and the scalar dissipation rate. Heat loss due to radiation can be taken into account by including a heat loss parameter in the flamelet calculations describing the change of enthalpy due to radiation, but was not used for the results reported here. The soot model was integrated into an existing commercial CFD code as a post-processing module to existing combustion CFD flow fields and is very robust with high convergence rates. The model is validated with laboratory flame data and using a realistic three-dimensional BMW Rolls-Royce combustor configuration, where test data at high pressure are available. Good agreement between experiment and simulation is achieved for laboratory flames, whereas soot is overpredicted for the aeroengine combustor configuration by 1–2 orders of magnitude.

Closure of the scalar dissipation rate in the spray flamelet equations through a transport equation for the gradient of the mixture fraction

2019 ◽  
Vol 208 ◽  
pp. 330-350 ◽  
Author(s):  
Hernan Olguin ◽  
Arne Scholtissek ◽  
Sebastian Gonzalez ◽  
Felipe Gonzalez ◽  
Matthias Ihme ◽  
...  
Keyword(s):  
Transport Equation ◽  
Dissipation Rate ◽  
Mixture Fraction ◽  
Scalar Dissipation ◽  
Scalar Dissipation Rate

scholarly journals Measurements and numerical simulations of snow-particle saltation

1998 ◽  
Vol 26 ◽  
pp. 184-190 ◽  
Author(s):  
K. Nishimura ◽  
K. Sugiura ◽  
M. Nemoto ◽  
N. Maeno
Keyword(s):  
Friction Velocity ◽  
Laser Sheet ◽  
Impact Angle ◽  
Wind Tunnel Experiments ◽  
Mean Velocity ◽  
Measured Probability ◽  
The Mean ◽  
Snow Particle ◽  
The Relationship ◽  
Particle Saltation

First, wind-tunnel experiments were carried out to measure the trajectories of saltating snow particles with varying friction velocity. Trajectories of saltating particles were recorded by a video system with a laser sheet and trajectory statistics, such as ejection and impact velocities and angles, were obtained for each particle. Parabolic trajectories are considerably elongated with an increase in the friction velocity; impact angle was approximately the same but ejection angle decreased with increasing friction velocity. Furthermore, it should be noted that the gradient of flux decay with height decreased with friction velocity. In the experiments, a snow-particle counter, which can sense not only the number of particles but also their diameters, was introduced. The flux distribution and the transport rate obtained as a function of the particle size gave a new insight into the relationship with the friction velocity.Trajectories of saltating grains were computed, using the measurements of the initial ejection velocities, angles and the mean velocity profile of the air. The results agreed reasonably with our measurements. Using the measured probability distribution of the ejection velocities, an ensemble of trajectories was computed and thence the vertical profiles of stream-wise fluxes. The exponential decay of the flux on height was obtained in all cases and it supports the basic validity of the model, although agreement is less than expected.

Transport equation for the mean turbulent energy dissipation rate on the centreline of a fully developed channel flow

2015 ◽  
Vol 777 ◽  
pp. 151-177 ◽  
Author(s):  
S. L. Tang ◽  
R. A. Antonia ◽  
L. Djenidi ◽  
H. Abe ◽  
T. Zhou ◽  
...  
Keyword(s):  
Energy Dissipation ◽  
Transport Equation ◽  
Channel Flow ◽  
Dissipation Rate ◽  
Turbulent Energy ◽  
Energy Dissipation Rate ◽  
Grid Turbulence ◽  
Normal Velocity ◽  
Turbulent Energy Dissipation Rate ◽  
The Mean

The transport equation for the mean turbulent energy dissipation rate $\overline{{\it\epsilon}}$ along the centreline of a fully developed channel flow is derived by applying the limit at small separations to the two-point budget equation. Since the ratio of the isotropic energy dissipation rate to the mean turbulent energy dissipation rate $\overline{{\it\epsilon}}_{iso}/\overline{{\it\epsilon}}$ is sufficiently close to 1 on the centreline, our main focus is on the isotropic form of the transport equation. It is found that the imbalance between the production of $\overline{{\it\epsilon}}$ due to vortex stretching and the destruction of $\overline{{\it\epsilon}}$ caused by the action of viscosity is governed by the diffusion of $\overline{{\it\epsilon}}$ by the wall-normal velocity fluctuation. This imbalance is intrinsically different from the advection-driven imbalance in decaying-type flows, such as grid turbulence, jets and wakes. In effect, the different types of imbalance represent different constraints on the relation between the skewness of the longitudinal velocity derivative $S_{1,1}$ and the destruction coefficient $G$ of enstrophy in different flows, thus resulting in non-universal approaches of $S_{1,1}$ towards a constant value as the Taylor microscale Reynolds number, $R_{{\it\lambda}}$, increases. For example, the approach is slower for the measured values of $S_{1,1}$ along either the channel or pipe centreline than along the axis in the self-preserving region of a round jet. The data for $S_{1,1}$ collected in different flows strongly suggest that, in each flow, the magnitude of $S_{1,1}$ is bounded, the value being slightly larger than 0.5.

scholarly journals Relación entre la potencia y velocidad en press de banca y la velocidad de lanzamiento de balón en jugadores profesionales de balonmano (Relationship between barbell power and velocity in bench press exercise and ball throwing velocity in professional ha

Retos ◽  
2020 ◽  
pp. 53-59
Author(s):  
Iker Javier Bautista ◽  
Juan Vicente-Mampel ◽  
Luis Baraja-Vegas ◽  
Isidoro Martínez
Keyword(s):  
Bench Press ◽  
Average Power ◽  
Mean Velocity ◽  
Specific Performance ◽  
Relevant Variables ◽  
The Mean ◽  
Incremental Protocol ◽  
The One ◽  
The Relationship ◽  
Correlation Range

 Los objetivos de este estudio fueron (a) analizar la relación existente entre la una repetición máxima (1-RM) en press de banca y la velocidad de lanzamiento en jugadores de balonmano U18 de nivel internacional y, (b) analizar qué variables del ejercicio del press de banca son más relevantes en el rendimiento específico (velocidad de lanzamiento del balón) durante el test de velocidad de lanzamiento (T3-Step). Dieciséis jugadores de la Selección Española de Balonmano Juvenil participaron en la presente investigación. Todos los sujetos realizaron un protocolo incremental en el ejercicio del press de banca, además del T3-Step de velocidad de lanzamiento del balón. Por un lado, se analizó la relación existente entre la velocidad media (Velmedia), velocidad media de la fase propulsiva (VelMFP), velocidad pico (Velpico), potencia media (Potmedia), potencia media de la fase propulsiva (PotMFP), y potencia pico (Potpico) en todo el espectro de cargas en relación con la velocidad de lanzamiento. También se realizaron los mismos análisis con la carga en donde se obtuvo la máxima potencia media (CargaMP). Los resultados mostraron, por un lado que el rango de correlación de la CargaMP, PotmediaMP, PotMFPMP y PotpicoMP y la velocidad de lanzamiento fueron de .61 (p= .012), .702 (p< .01), .734 (p< .01) y .63 (p< .01), respectivamente. El coeficiente de correlación de Pearson entre la 1-RM y la velocidad de lanzamiento fue de r = .61 (p < .01). En conclusión, las variables relevantes a nivel de rendimiento específico con la velocidad de lanzamiento fueron la 1RM, la CargaMP, la PotMFPMP y la VelMFPMP. Todas estas analizadas en función del 60% de la 1-RM.  Abstract. The objectives of this study were (a) to analyze the relationship between one repetition maximum (1-RM) in free bench press exercise and ball throwing velocity in handball players U18 of international level and, (b) to analyze which variables of bench press exercise are more relevant in the specific performance during the ball throwing velocity test (T3-Step). Sixteen (n = 16) players of the Spanish Youth Handball Team participated in the present investigation. All subjects included performed an incremental protocol bench press exercise, in addition to the T3-Step. On the one hand, it analyzed the relationship between the mean velocity (Velmean), the mean velocity of propulsive phase (VelmeanPP), peak velocity (Velpeak), the average power (Powermean), the average power of the propulsive phase (PowermeanPP), and peak power (Powerpeak) over the entire spectrum of charges in relation to the launch speed. The same analyzes were also obtained with the load where the maximum average power (LoadMP). The results obtained, on the one hand that the correlation range of the LoadMP, PowermeanPP, PowerMPPMP and PowerpeakPP and ball throwing velocity were .61 (p = .012), .70 (p < .01), .73 (p < .01) and 0.63 (p < .01), respectively. The correlation coefficient between the 1-RM and ball throwing velocity was r = 0.61 (p< .01). In conclusion, the relevant variables at the specific performance level with the ball throwing velocity were 1-RM, LoadMP, PowerMFPMP and VelMFPMP. All these analyzed according to 60% of the 1-RM.

scholarly journals Measurements and numerical simulations of snow-particle saltation

1998 ◽  
Vol 26 ◽  
pp. 184-190 ◽  
Author(s):  
K. Nishimura ◽  
K. Sugiura ◽  
M. Nemoto ◽  
N. Maeno
Keyword(s):  
Friction Velocity ◽  
Laser Sheet ◽  
Impact Angle ◽  
Wind Tunnel Experiments ◽  
Mean Velocity ◽  
Measured Probability ◽  
The Mean ◽  
Snow Particle ◽  
The Relationship ◽  
Particle Saltation

First, wind-tunnel experiments were carried out to measure the trajectories of saltating snow particles with varying friction velocity. Trajectories of saltating particles were recorded by a video system with a laser sheet and trajectory statistics, such as ejection and impact velocities and angles, were obtained for each particle. Parabolic trajectories are considerably elongated with an increase in the friction velocity; impact angle was approximately the same but ejection angle decreased with increasing friction velocity. Furthermore, it should be noted that the gradient of flux decay with height decreased with friction velocity. In the experiments, a snow-particle counter, which can sense not only the number of particles but also their diameters, was introduced. The flux distribution and the transport rate obtained as a function of the particle size gave a new insight into the relationship with the friction velocity.Trajectories of saltating grains were computed, using the measurements of the initial ejection velocities, angles and the mean velocity profile of the air. The results agreed reasonably with our measurements. Using the measured probability distribution of the ejection velocities, an ensemble of trajectories was computed and thence the vertical profiles of stream-wise fluxes. The exponential decay of the flux on height was obtained in all cases and it supports the basic validity of the model, although agreement is less than expected.

scholarly journals Experiments on a round turbulent buoyant plume

1994 ◽  
Vol 275 ◽  
pp. 1-32 ◽  
Author(s):  
Aamir Shabbir ◽  
William K. George
Keyword(s):  
Velocity Field ◽  
Buoyancy Force ◽  
Turbulent Transport ◽  
Force Balance ◽  
Buoyant Plume ◽  
Hot Wire ◽  
Mean Velocity ◽  
Production Term ◽  
Vertical Advection ◽  
The Mean

This paper reports a comprehensive set of hot-wire measurements of a round buoyant plume which was generated by forcing a jet of hot air vertically up into a quiescent environment. The boundary conditions of the experiment were measured, and are documented in the present paper in an attempt to sort out the contradictory mean flow results from the earlier studies. The ambient temperature was monitored to ensure that the facility was not stratified and that the experiment was conducted in a neutral environment. The axisymmetry of the flow was checked by using a planar array of sixteen thermocouples and the mean temperature measurements from these are used to supplement the hot-wire measurements. The source flow conditions were measured to ascertain the rate at which the buoyancy was added to the flow. The measurements conserve buoyancy within 10%. The results are used to determine balances of the mean energy and momentum differential equations. In the mean energy equation it is found that the vertical advection of energy is primarily balanced by the radial turbulent transport. In the mean momentum equation the vertical advection of momentum and the buoyancy force balance the radial turbulent transport. The buoyancy force is the second largest term in this balance and is responsible for the wider (and higher) velocity profiles in plumes as compared to jets. Budgets of the temperature variance and turbulent kinetic energy are also determined in which thermal and mechanical dissipation rates are obtained as the closing terms. Similarities and differences between the two balances are discussed. It is found that even though the direct effect of buoyancy in turbulence, as evidenced by the buoyancy production term, is substantial, most of the turbulence is produced by shear. This is in contrast to the mean velocity field where the effect of the buoyancy force is quite strong. Therefore, it is concluded that in a buoyant plume the primary effect of buoyancy on turbulence is indirect, and enters through the mean velocity field (giving larger shear production).

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