Pseudo-turbulent heat flux and average gas–phase conduction during gas–solid heat transfer: flow past random fixed particle assemblies

2016 ◽  
Vol 798 ◽  
pp. 299-349 ◽  
Author(s):  
Bo Sun ◽  
Sudheer Tenneti ◽  
Shankar Subramaniam ◽  
Donald L. Koch
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Gas Phase ◽  
Volume Fraction ◽  
Turbulent Heat Flux ◽  
Turbulent Heat ◽  
Fluid Temperature ◽  
Bulk Fluid ◽  
The Mean ◽  
Temperature Equation

Fluctuations in the gas-phase velocity can contribute significantly to the total gas-phase kinetic energy even in laminar gas–solid flows as shown by Mehrabadi et al. (J. Fluid Mech., vol. 770, 2015, pp. 210–246), and these pseudo-turbulent fluctuations can also enhance heat transfer in gas–solid flow. In this work, the pseudo-turbulent heat flux arising from temperature–velocity covariance, and average fluid-phase conduction during convective heat transfer in a gas–solid flow are quantified and modelled over a wide range of mean slip Reynolds number and solid volume fraction using particle-resolved direct numerical simulations (PR-DNS) of steady flow through a random assembly of fixed isothermal monodisperse spherical particles. A thermal self-similarity condition on the local excess temperature developed by Tenneti et al. (Intl J. Heat Mass Transfer, vol. 58, 2013, pp. 471–479) is used to guarantee thermally fully developed flow. The average gas–solid heat transfer rate for this flow has been reported elsewhere by Sun et al. (Intl J. Heat Mass Transfer, vol. 86, 2015, pp. 898–913). Although the mean velocity field is homogeneous, the mean temperature field in this thermally fully developed flow is inhomogeneous in the streamwise coordinate. An exponential decay model for the average bulk fluid temperature is proposed. The pseudo-turbulent heat flux that is usually neglected in two-fluid models of the average fluid temperature equation is computed using PR-DNS data. It is found that the transport term in the average fluid temperature equation corresponding to the pseudo-turbulent heat flux is significant when compared to the average gas–solid heat transfer over a significant range of solid volume fraction and mean slip Reynolds number that was simulated. For this flow set-up a gradient-diffusion model for the pseudo-turbulent heat flux is found to perform well. The Péclet number dependence of the effective thermal diffusivity implied by this model is explained using a scaling analysis. Axial conduction in the fluid phase, which is often neglected in existing one-dimensional models, is also quantified. As expected, it is found to be important only for low Péclet number flows. Using the exponential decay model for the average bulk fluid temperature, a model for average axial conduction is developed that verifies standard assumptions in the literature. These models can be used in two-fluid simulations of heat transfer in fixed beds. A budget analysis of the mean fluid temperature equation provides insight into the variation of the relative magnitude of the various terms over the parameter space.

Heat Transfer Scaling Close to the Wall for Turbulent Channel Flows

2013 ◽  
Vol 65 (3) ◽  
Author(s):  
Chiranth Srinivasan ◽  
Dimitrios V. Papavassiliou
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Turbulent Flow ◽  
Turbulent Heat Flux ◽  
Turbulent Heat Transfer ◽  
Wall Region ◽  
Turbulent Heat ◽  
Mean Temperature ◽  
Scaling Parameters ◽  
The Mean

This work serves a two-fold purpose of briefly reviewing the currently existing literature on the scaling of thermal turbulent fields and, in addition, proposing a new scaling framework and testing its applicability. An extensive set of turbulent scalar transport data for turbulent flow in infinitely long channels is obtained using a Lagrangian scalar tracking approach combined with direct numerical simulation of turbulent flow. Two cases of Poiseuille channel flow, with friction Reynolds numbers 150 and 300, and different types of fluids with Prandtl number ranging from 0.7 to 50,000 are studied. Based on analysis of this database, it is argued that the value and the location of the maximum normal turbulent heat flux are important scaling parameters in turbulent heat transfer. Implementing such scaling on the mean temperature profile for different fluids and Reynolds number cases shows a collapse of the mean temperature profiles onto a single universal profile in the near wall region of the channel. In addition, the profiles of normal turbulent heat flux and the root mean square of the temperature fluctuations appear to collapse on one profile, respectively. The maximum normal turbulent heat flux is thus established as a turbulence thermal scaling parameter for both mean and fluctuating temperature statistics.

An explicit algebraic Reynolds-stress and scalar-flux model for stably stratified flows

2013 ◽  
Vol 723 ◽  
pp. 91-125 ◽  
Author(s):  
W. M. J. Lazeroms ◽  
G. Brethouwer ◽  
S. Wallin ◽  
A. V. Johansson
Keyword(s):  
Heat Flux ◽  
Kinetic Energy ◽  
Temperature Gradient ◽  
Reynolds Stress ◽  
Turbulent Heat Flux ◽  
Turbulent Heat ◽  
Homogeneous Shear ◽  
Self Consistent ◽  
The Mean ◽  
Homogeneous Shear Flow

AbstractThis work describes the derivation of an algebraic model for the Reynolds stresses and turbulent heat flux in stably stratified turbulent flows, which are mutually coupled for this type of flow. For general two-dimensional mean flows, we present a correct way of expressing the Reynolds-stress anisotropy and the (normalized) turbulent heat flux as tensorial combinations of the mean strain rate, the mean rotation rate, the mean temperature gradient and gravity. A system of linear equations is derived for the coefficients in these expansions, which can easily be solved with computer algebra software for a specific choice of the model constants. The general model is simplified in the case of parallel mean shear flows where the temperature gradient is aligned with gravity. For this case, fully explicit and coupled expressions for the Reynolds-stress tensor and heat-flux vector are given. A self-consistent derivation of this model would, however, require finding a root of a polynomial equation of sixth-order, for which no simple analytical expression exists. Therefore, the nonlinear part of the algebraic equations is modelled through an approximation that is close to the consistent formulation. By using the framework of a$K\text{{\ndash}} \omega $model (where$K$is turbulent kinetic energy and$\omega $an inverse time scale) and, where needed, near-wall corrections, the model is applied to homogeneous shear flow and turbulent channel flow, both with stable stratification. For the case of homogeneous shear flow, the model predicts a critical Richardson number of 0.25 above which the turbulent kinetic energy decays to zero. The channel-flow results agree well with DNS data. Furthermore, the model is shown to be robust and approximately self-consistent. It also fulfils the requirements of realizability.

Use of Algebraic Heat Flux Models to Improve Heat Transfer Predictions for Supercritical Pressure Fluids

2016 ◽  
Author(s):  
Vera Papp ◽  
Andrea Pucciarelli ◽  
Medhat Sharabi ◽  
Walter Ambrosini
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Turbulent Heat Flux ◽  
Supercritical Pressure ◽  
Internal Diameter ◽  
Inlet Temperature ◽  
Turbulent Heat ◽  
Commercial Code ◽  
Simplifying Assumptions ◽  
Flux Model

This work proposes simulations of heat transfer under supercritical pressure conditions showing improvements with respect to previous works. This is obtained by the introduction of the Algebraic Heat Flux Model (AHFM) for evaluating the turbulent heat flux in turbulence production terms, using the in-house code THEMAT and the STAR-CCM+ code. The first code makes use of the AHFM also in the energy balance equations, while for the commercial code simplifying assumptions are considered in the implementations. Custom sets of parameters for every condition of inlet temperature and internal diameter are tuned in some cases, driven by the opinion that a single set of parameters cannot be suitable in every flow conditions, considering the complexity of the variables that concur in the heat transfer deterioration phenomenon. The AHFM model gives promising results with new sets of parameters in order to model the deterioration and the recovery phases because of its term related to the variance of temperature.

Characterization of Turbulent Heat Transfer in Ribbed Pipe Flow

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Changwoo Kang ◽  
Kyung-Soo Yang
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Pipe Flow ◽  
Temperature Fields ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Mean Flow ◽  
Transfer Enhancement ◽  
Pitch Ratio ◽  
The Mean

In the current investigation, we performed large eddy simulation (LES) of turbulent heat transfer in circular ribbed-pipe flow in order to study the effects of periodically mounted square ribs on heat transfer characteristics. The ribs were implemented on a cylindrical coordinate system by using an immersed boundary method, and dynamic subgrid-scale models were used to model Reynolds stresses and turbulent heat flux terms. A constant and uniform wall heat flux was imposed on all the solid boundaries. The Reynolds number (Re) based on the bulk velocity and pipe diameter is 24,000, and Prandtl number is fixed at Pr = 0.71. The blockage ratio (BR) based on the pipe diameter and rib height is fixed with 0.0625, while the pitch ratio based on the rib interval and rib height is varied with 2, 4, 6, 8, 10, and 18. Since the pitch ratio is the key parameter that can change flow topology, we focus on its effects on the characteristics of turbulent heat transfer. Mean flow and temperature fields are presented in the form of streamlines and contours. How the surface roughness, manifested by the wall-mounted ribs, affects the mean streamwise-velocity profile was investigated by comparing the roughness function. Local heat transfer distributions between two neighboring ribs were obtained for the pitch ratios under consideration. The flow structures related to heat transfer enhancement were identified. Friction factors and mean heat transfer enhancement factors were calculated from the mean flow and temperature fields, respectively. Furthermore, the friction and heat-transfer correlations currently available in the literature for turbulent pipe flow with surface roughness were revisited and evaluated with the LES data. A simple Nusselt number correlation is also proposed for turbulent heat transfer in ribbed pipe flow.

Two-Phase Heat Transfer in a Wall-Driven Cubical Heat Sink

2016 ◽  
Author(s):  
Majid Molki
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Sink ◽  
Volume Fraction ◽  
Turbulent Heat Transfer ◽  
Liquid Volume ◽  
Turbulent Heat ◽  
Fluid Temperature ◽  
Complex Flow ◽  
Liquid Volume Fraction

Turbulent heat transfer for flow of water-air mixture driven by moving walls in a cubical heat sink is investigated. One wall is maintained at an elevated temperature, while the vertical walls are at a low temperature. The cubical enclosure functions as a heat sink using water-air mixture with no phase change. Different arrangements for wall motion are considered, which include 1 to 4 moving walls. As the number of moving walls increases, the flow and heat transfer become more complex. In general, the flow reveals complex and multi-scale structures with an unsteady and evolving nature. The larger structure of the flow is resolved using Large Eddy Simulation, while the sub-grid scales are captured by the dynamic k-equation eddy-viscosity model. The focus of this work is on thermal field and heat transfer as affected by the complex flow field generated by multiple moving walls. The results indicate that the Nusselt number for the heat sink varies from 5202.8 to 7356.1, depending on the number of moving walls. Contours of fluid temperature, liquid volume fraction, local and average values of Nusselt number are among the results presented in this paper.

An Explicit Algebraic Model for Turbulent Heat Transfer in Wall-Bounded Flow With Streamline Curvature

2006 ◽  
Vol 129 (4) ◽  
pp. 425-433 ◽  
Author(s):  
B. A. Younis ◽  
B. Weigand ◽  
S. Spring
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Flux ◽  
Algebraic Model ◽  
Heat Fluxes ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Streamline Curvature ◽  
Turbulent Heat Fluxes ◽  
The Mean

Fourier’s law, which forms the basis of most engineering prediction methods for the turbulent heat fluxes, is known to fail badly in capturing the effects of streamline curvature on the rate of heat transfer in turbulent shear flows. In this paper, an alternative model, which is both algebraic and explicit in the turbulent heat fluxes and which has been formulated from tensor-representation theory, is presented, and its applicability is extended by incorporating the effects of a wall on the turbulent heat transfer processes in its vicinity. The model’s equations for flows with curvature in the plane of the mean shear are derived and calculations are performed for a heated turbulent boundary layer, which develops over a flat plate before encountering a short region of high convex curvature. The results show that the new model accurately predicts the significant reduction in the wall heat transfer rates wrought by the stabilizing-curvature effects, in sharp contrast to the conventional model predictions, which are shown to seriously underestimate the same effects. Comparisons are also made with results from a complete heat-flux transport model, which involves the solution of differential transport equations for each component of the heat-flux tensor. Downstream of the bend, where the perturbed boundary layer recovers on a flat wall, the comparisons show that the algebraic model yields indistinguishable predictions from those obtained with the differential model in regions where the mean-strain field is in rapid evolution and the turbulence processes are far removed from local equilibrium.

Heat Transfer in the Accelerated Fully Rough Turbulent Boundary Layer

1981 ◽  
Vol 103 (1) ◽  
pp. 153-158 ◽  
Author(s):  
H. W. Coleman ◽  
R. J. Moffat ◽  
W. M. Kays
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Flux ◽  
Turbulent Boundary Layer ◽  
Prandtl Number ◽  
Pressure Gradient ◽  
Turbulent Heat Flux ◽  
Test Surface ◽  
Turbulent Heat ◽  
Turbulent Prandtl Number

Heat transfer behavior of a fully rough turbulent boundary layer subjected to favorable pressure gradients was investigated experimentally using a porous test surface composed of densely packed spheres of uniform size. Stanton numbers and profiles of mean temperature, turbulent Prandtl number, and turbulent heat flux are reported. Three equilibrium acceleration cases (one with blowing) and one non-equilibrium acceleration case were studied. For each acceleration case of this study, Stanton number increased over zero pressure gradient values at the same position or enthalpy thickness. Turbulent Prandtl number was found to be approximately constant at 0.7–0.8 across the layer, and profiles of the non-dimensional turbulent heat flux showed close agreement with those previously reported for both smooth and rough wall zero pressure gradient layers.

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