scholarly journals A New Anisotropic Four-Parameter Turbulence Model for Low Prandtl Number Fluids

Fluids ◽  
2021 ◽  
Vol 7 (1) ◽  
pp. 6
Author(s):  
Giacomo Barbi ◽  
Valentina Giovacchini ◽  
Sandro Manservisi
Keyword(s):  
Heat Flux ◽  
Prandtl Number ◽  
Turbulence Model ◽  
Liquid Metals ◽  
Plane Channel ◽  
Turbulent Heat Flux ◽  
Heat Fluxes ◽  
Turbulent Heat ◽  
Reynolds Analogy ◽  
Wide Range

Due to their interesting thermal properties, liquid metals are widely studied for heat transfer applications where large heat fluxes occur. In the framework of the Reynolds-Averaged Navier–Stokes (RANS) approach, the Simple Gradient Diffusion Hypothesis (SGDH) and the Reynolds Analogy are almost universally invoked for the closure of the turbulent heat flux. Even though these assumptions can represent a reasonable compromise in a wide range of applications, they are not reliable when considering low Prandtl number fluids and/or buoyant flows. More advanced closure models for the turbulent heat flux are required to improve the accuracy of the RANS models dealing with low Prandtl number fluids. In this work, we propose an anisotropic four-parameter turbulence model. The closure of the Reynolds stress tensor and turbulent heat flux is gained through nonlinear models. Particular attention is given to the modeling of dynamical and thermal time scales. Numerical simulations of low Prandtl number fluids have been performed over the plane channel and backward-facing step configurations.

scholarly journals A Logarithmic Turbulent Heat Transfer Model in Applications with Liquid Metals for PR = 0.01-0.025

2020 ◽  
Author(s):  
Roberto Da Vià ◽  
Sandro Manservisi ◽  
Valentina Giovacchini
Keyword(s):  
Heat Transfer ◽  
Turbulence Model ◽  
Liquid Metals ◽  
Turbulence Models ◽  
Turbulent Heat Flux ◽  
Turbulent Heat Transfer ◽  
Transfer Model ◽  
Turbulent Heat ◽  
Reynolds Analogy ◽  
Wide Range

The study of turbulent heat transfer in liquid metal flows has gained interest because of applications in several industrial fields. The common assumption of similarity between the dynamical and thermal turbulence, namely the Reynolds analogy, has been proven to be not valid for these fluids. Many methods have been proposed in order to overcome the difficulties encountered in a proper definition of the turbulent heat flux, such as global or local correlations for the turbulent Prandtl number or four parameter turbulence models. In this work we assess a four parameter logarithmic turbulence model for liquid metals based on RANS approach. Several simulation results considering fluids with Pr = 0.01 and Pr = 0.025 are reported in order to show the validity of this approach. The Kays turbulence model is also assessed and compared with integral heat transfer correlations for a wide range of Peclet numbers.

scholarly journals A Logarithmic Turbulent Heat Transfer Model in Applications with Liquid Metals for Pr = 0.01–0.025

2020 ◽  
Vol 10 (12) ◽  
pp. 4337
Author(s):  
Roberto Da Vià ◽  
Valentina Giovacchini ◽  
Sandro Manservisi
Keyword(s):  
Heat Transfer ◽  
Turbulence Model ◽  
Liquid Metals ◽  
Turbulence Models ◽  
Turbulent Heat Flux ◽  
Turbulent Heat Transfer ◽  
Transfer Model ◽  
Turbulent Heat ◽  
Reynolds Analogy ◽  
Wide Range

The study of turbulent heat transfer in liquid metal flows has gained interest because of applications in several industrial fields. The common assumption of similarity between the dynamical and thermal turbulence, namely, the Reynolds analogy, has been proven to be invalid for these fluids. Many methods have been proposed in order to overcome the difficulties encountered in a proper definition of the turbulent heat flux, such as global or local correlations for the turbulent Prandtl number and four parameter turbulence models. In this work we assess a four parameter logarithmic turbulence model for liquid metals based on the Reynolds Averaged Navier-Stokes (RAN) approach. Several simulation results considering fluids with P r = 0.01 and P r = 0.025 are reported in order to show the validity of this approach. The Kays turbulence model is also assessed and compared with integral heat transfer correlations for a wide range of Peclet numbers.

scholarly journals Air–Sea Turbulent Heat Fluxes in Climate Models and Observational Analyses: What Drives Their Variability?

2019 ◽  
Vol 32 (8) ◽  
pp. 2397-2421 ◽  
Author(s):  
R. Justin Small ◽  
Frank O. Bryan ◽  
Stuart P. Bishop ◽  
Robert A. Tomas
Keyword(s):  
Heat Flux ◽  
Climate Models ◽  
Climate Model ◽  
Turbulent Heat Flux ◽  
Heat Fluxes ◽  
Small Scale ◽  
Turbulent Heat ◽  
Realistic Representation ◽  
Frontal Zones ◽  
The Tropics

Abstract A traditional view is that the ocean outside of the tropics responds passively to atmosphere forcing, which implies that air–sea heat fluxes are mainly driven by atmosphere variability. This paper tests this viewpoint using state-of-the-art air–sea turbulent heat flux observational analyses and a climate model run at different resolutions. It is found that in midlatitude ocean frontal zones the variability of air–sea heat fluxes is not predominantly driven by the atmosphere variations but instead is forced by sea surface temperature (SST) variations arising from intrinsic oceanic variability. Meanwhile in most of the tropics and subtropics wind is the dominant driver of heat flux variability, and atmosphere humidity is mainly important in higher latitudes. The predominance of ocean forcing of heat fluxes found in frontal regions occurs on scales of around 700 km or less. Spatially smoothing the data to larger scales results in the traditional atmosphere-driving case, while filtering to retain only small scales of 5° or less leads to ocean forcing of heat fluxes over most of the globe. All observational analyses examined (1° OAFlux; 0.25° J-OFURO3; 0.25° SeaFlux) show this general behavior. A standard resolution (1°) climate model fails to reproduce the midlatitude, small-scale ocean forcing of heat flux: refining the ocean grid to resolve eddies (0.1°) gives a more realistic representation of ocean forcing but the variability of both SST and of heat flux is too high compared to observational analyses.

The importance of including sea surface current when estimating air-sea turbulent heat fluxes and wind stress in the Gulf Stream region

2020 ◽  
Author(s):  
Xiangzhou Song
Keyword(s):  
Heat Flux ◽  
Wind Stress ◽  
Gulf Stream ◽  
Turbulent Heat Flux ◽  
Heat Fluxes ◽  
Turbulent Heat ◽  
Surface Currents ◽  
Mean Flow ◽  
Geostrophic Currents ◽  
Turbulent Heat Fluxes

AbstractUsing buoy observations from 2004 to 2010 and newly released atmospheric reanalysis and satellite altimetry-derived geostrophic currents from 1993 to 2017, the quantitative contribution of daily mean surface currents to air-sea turbulent heat flux and wind stress uncertainties in the Gulf Stream (GS) region is investigated based on bulk formulas. At four buoy stations, the daily mean latent (sensible) heat flux difference between the estimates with and without surface currents ranges from -18 (-4) to 20 (4) Wm-2, while the daily mean wind stress difference ranges from -0.04 to 0.02 Nm-2. The positive values indicate higher estimates with opposite directions between surface currents and absolute winds. The transition between positive and negative differences is significantly associated with synoptic-scale weather variations. The uncertainties based on buoy observations are approximately 7% and 3% for wind stress and turbulent heat fluxes, respectively. The new reanalysis and satellite geostrophic currents confirm the uncertainties identified by buoy observations with acceptable discrepancies and provide a spatial view of the uncertainty fields. The mean geostrophic currents are aligned with the surface wind along the GS; therefore, the turbulent heat fluxes and wind stress will be ‘underestimated’ with surface currents included. However, on both sides of the GS, the surface flow can be upwind due to possible mechanisms of eddy-mean flow interactions and recirculations, resulting in higher turbulent heat flux estimations. The wind stress and turbulent heat flux uncertainties experience significant seasonal variations and show long-term trends.

Direct Numerical Simulation and RANS Modeling of Turbulent Natural Convection for Low Prandtl Number Fluids

2004 ◽  
Author(s):  
I. Otic´ ◽  
G. Gro¨tzbach
Keyword(s):  
Numerical Simulation ◽  
Heat Flux ◽  
Kinetic Energy ◽  
Prandtl Number ◽  
Direct Numerical Simulation ◽  
Turbulent Heat Flux ◽  
Turbulent Heat ◽  
Temperature Variance ◽  
Flux Model ◽  
Heat Flux Model

Results of direct numerical simulation (DNS) of turbulent Rayleigh-Be´nard convection for a Prandtl number Pr = 0.025 and a Rayleigh number Ra = 105 are used to evaluate the turbulent heat flux and the temperature variance. The DNS evaluated turbulent heat flux is compared with the DNS based results of a standard gradient diffusion turbulent heat flux model and with the DNS based results of a standard algebraic turbulent heat flux model. The influence of the turbulence time scales on the predictions by the standard algebraic heat flux model at these Rayleigh- and Prandtl numbers is investigated. A four equation algebraic turbulent heat flux model based on the transport equations for the turbulent kinetic energy k, for the dissipation of the turbulent kinetic energy ε, for the temperature variance θ2, and for the temperature variance dissipation rate εθ is proposed. This model should be applicable to a wide range of low Prandtl number flows.

Effects of spatial resolution and temporal offset of air-sea boundary-layer variables on turbulent heat flux estimates

2021 ◽  
Author(s):  
Tong Lee ◽  
Chelle Centemann ◽  
Carol Anne Clayson ◽  
Mark Bourassa ◽  
Shannon Brown ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
High Resolution ◽  
Surface Wind ◽  
Turbulent Heat Flux ◽  
Heat Fluxes ◽  
Sea Surface ◽  
Turbulent Heat ◽  
Input Variables ◽  
Temporal Offset

<p>Air-sea turbulent heat fluxes and their spatial gradients are important to the ocean, climate, weather, and their interactions. Satellite-based estimation of air-sea latent and sensible fluxes, providing broad coverage, require measurements of sea surface temperature, ocean-surface wind speed, and air temperature and humidity above sea surface. Because no single satellite has been able to provide simultaneous measurements of these input variables, they typically come from various satellites with different spatial resolutions and sampling times that can be offset by hours. These factors introduce errors in the estimated heat fluxes and their gradients that are not well documented. As a model-based assessment of these errors, we performed a simulation using a Weather Research and Forecasting (WRF) model forced by high-resolution blended satellite SST for the Gulf Stream extension region with a 3-km resolution and with 30-minute output. Latent and sensible heat fluxes were first computed from input variables with the original model resolutions and at coincident times. We then computed the heat fluxes by (1) decimating the input variables to various resolutions from 12.5 to 50 km, and (2) offsetting the “sampling” times of some input variables from others by 3 hours. The resultant estimations of heat fluxes and their gradients from (1) and (2) were compared with the counterparts without reducing resolution and without temporal offset of the input variables. The results show that reducing input-variable resolutions from 12.5 to 50 km weakened the magnitudes of the time-mean and instantaneous heat fluxes and their gradients substantially, for example, by a factor of two for the time-mean gradients. The temporal offset of input variables substantially impacted the instantaneous fluxes and their gradients, although not their time-mean values. The implications of these effects on scientific and operational applications of heat flux products will be discussed. Finally, we highlight a mission concept for providing simultaneous, high-resolution measurements of boundary-layer variables from a single satellite to improve air-sea turbulent heat flux estimation.</p>

Heat Flux Measurements in Homogeneous Curved Shear Flow

1999 ◽  
Vol 121 (1) ◽  
pp. 190-194 ◽  
Author(s):  
A. G. L. Holloway ◽  
S. A. Ebrahimi-Sabet
Keyword(s):  
Heat Flux ◽  
Shear Flow ◽  
Turbulent Heat Flux ◽  
Heat Fluxes ◽  
Turbulent Shear ◽  
Turbulent Heat ◽  
Curvature Effects ◽  
Turbulent Shear Stress ◽  
Uniform Shear ◽  
Flow Curvature

Turbulent heat fluxes were measured far downstream of a fine heating wire stretched spanwise across a curved, uniform shear flow. The turbulence was approximately homogeneous and the overheat small enough to be passive. Strong destabilizing and stabilizing curvature effects were produced by directing the shear toward the center of curvature and away from the center of curvature, respectively. The dimensionless turbulent shear stress was strongly affected by the flow curvature, but the dimensionless components of the turbulent heat flux were found to be relatively insensitive.

scholarly journals Explicit Algebraic Reynolds-stress Modelling of a Convective Atmospheric Boundary Layer Including Counter-Gradient Fluxes

2020 ◽  
Author(s):  
Velibor Želi ◽  
Geert Brethouwer ◽  
Stefan Wallin ◽  
Arne V. Johansson
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Atmospheric Boundary Layer ◽  
Reynolds Stress ◽  
Turbulent Heat Flux ◽  
Gradient Term ◽  
Turbulent Heat ◽  
Bound Layer Meteorol ◽  
Wide Range ◽  
Stable Atmospheric Boundary Layer

AbstractIn a recent study (Želi et al. in Bound Layer Meteorol 176:229–249, 2020), we have shown that the explicit algebraic Reynolds-stress (EARS) model, implemented in a single-column context, is able to capture the main features of a stable atmospheric boundary layer (ABL) for a range of stratification levels. We here extend the previous study and show that the same formulation and calibration of the EARS model also can be applied to a dry convective ABL. Five different simulations with moderate convective intensities are studied by prescribing surface heat flux and geostrophic forcing. The results of the EARS model are compared to large-eddy simulations of Salesky and Anderson (J Fluid Mech 856:135–168, 2018). It is shown that the EARS model performs well and is able to capture the counter-gradient heat flux in the upper part of the ABL due to the presence of the non-gradient term in the relation for vertical turbulent heat flux. The model predicts the full Reynolds-stress tensor and heat-flux vector and allows us to compare other important aspects of a convective ABL such as the profiles of vertical momentum variance. Together with the previous studies, we show that the EARS model is able to predict the essential features of the ABL. It also shows that the EARS model with the same model formulation and coefficients is applicable over a wide range of stable and moderately unstable stratifications.

scholarly journals Assessment of Turbulence Models in a Hypersonic Cold-Wall Turbulent Boundary Layer

Fluids ◽  
2019 ◽  
Vol 4 (1) ◽  
pp. 37 ◽  
Author(s):  
Junji Huang ◽  
Jorge-Valentino Bretzke ◽  
Lian Duan
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Prandtl Number ◽  
Eddy Viscosity ◽  
Turbulence Models ◽  
Turbulent Heat Flux ◽  
Turbulent Heat ◽  
Cold Wall

In this study, the ability of standard one- or two-equation turbulence models to predict mean and turbulence profiles, the Reynolds stress, and the turbulent heat flux in hypersonic cold-wall boundary-layer applications is investigated. The turbulence models under investigation include the one-equation model of Spalart–Allmaras, the baseline k - ω model by Menter, as well as the shear-stress transport k - ω model by Menter. Reynolds-Averaged Navier-Stokes (RANS) simulations with the different turbulence models are conducted for a flat-plate, zero-pressure-gradient turbulent boundary layer with a nominal free-stream Mach number of 8 and wall-to-recovery temperature ratio of 0.48 , and the RANS results are compared with those of direct numerical simulations (DNS) under similar conditions. The study shows that the selected eddy-viscosity turbulence models, in combination with a constant Prandtl number model for turbulent heat flux, give good predictions of the skin friction, wall heat flux, and boundary-layer mean profiles. The Boussinesq assumption leads to essentially correct predictions of the Reynolds shear stress, but gives wrong predictions of the Reynolds normal stresses. The constant Prandtl number model gives an adequate prediction of the normal turbulent heat flux, while it fails to predict transverse turbulent heat fluxes. The discrepancy in model predictions among the three eddy-viscosity models under investigation is small.

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