scholarly journals Investigation of the Wall Scalar Fluctuations Effect on Passive Scalar Turbulent Fields at Several Prandtl Numbers by Means of Direct Numerical Simulations

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Bruno Chaouat ◽  
Christophe Peyret
Keyword(s):  
Boundary Condition ◽  
Heat Flux ◽  
Scalar Field ◽  
Boundary Conditions ◽  
Plane Channel ◽  
Passive Scalar ◽  
Wall Region ◽  
Turbulent Heat ◽  
The Mean ◽  
Prandtl Numbers

Abstract We investigate the effect of the wall-scalar fluctuations on passive scalar turbulent fields for a moderate Reynolds number Rτ = 395 and for several Prandtl numbers ranging from the very low value Pr = 0.01 to the high value Pr = 10 by means of direct numerical simulation (DNS) simulations. Several cases of plane channel flows are considered. Case I is a channel flow heated on both walls with a constant imposed heat flux qw. We consider for this case two different types of boundary conditions. For the first one, the isoscalar boundary condition θw = 0 is imposed at the wall implying that its fluctuation and therefore its rms scalar fluctuations θrms=⟨θ′θ′⟩ is zero at the wall whereas in the second type, θw is not prescribed to a fixed value so that it is fluctuating in time at the wall leading to nonzero rms fluctuations. In this latter case, as the heat flux is maintained constant in time at the wall, the fluctuating heat flux q′w reduces to zero at the wall. For illustration purpose, in addition to case I, we also consider case II, which is a plane channel heated only from one wall but cooled from the other one at the same rate taking into account of the freestream scalar boundary condition at the wall θ′w≠0 with q′w=0. The distributions of the mean scalar field, root-mean-square fluctuations, turbulent heat flux, correlation coefficient, turbulent Prandtl number, and Nusselt number are examined in detail. Moreover, some insights into the flow structure of the scalar fields are provided. As a result of interest, it is found that the mean scalar field ⟨θ⟩ is not affected by the scalar fluctuations at the wall. But owing to the different boundary conditions applied at the wall, significant differences in the evolution of the rms scalar fluctuations θrms are observed in the immediate vicinity of the wall. Surprisingly, the maximum rms intensity remains almost unchanged in the near wall region whatever the type of boundary condition is applied at the wall. In addition, the turbulent heat fluxes that play a major role in heat transfer are found to be independent of the wall scalar fluctuations. This study demonstrates that the impact of the wall scalar fluctuations is appreciable mainly in the near wall region. This outcome must be taken into account when simulating industrial flows with thermal boundary conditions involving different fluid/solid combinations.

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.

scholarly journals Bootstrapping boundary-localized interactions

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Connor Behan ◽  
Lorenzo Di Pietro ◽  
Edoardo Lauria ◽  
Balt C. van Rees
Keyword(s):  
Boundary Condition ◽  
Scalar Field ◽  
Boundary Conditions ◽  
Parameter Space ◽  
Three Dimensional ◽  
Conformal Boundary ◽  
Dimensional Boundary ◽  
Dirichlet And Neumann Conditions ◽  
Boundary Fields ◽  
Boundary Dynamics

Abstract We study conformal boundary conditions for the theory of a single real scalar to investigate whether the known Dirichlet and Neumann conditions are the only possibilities. For this free bulk theory there are strong restrictions on the possible boundary dynamics. In particular, we find that the bulk-to-boundary operator expansion of the bulk field involves at most a ‘shadow pair’ of boundary fields, irrespective of the conformal boundary condition. We numerically analyze the four-point crossing equations for this shadow pair in the case of a three-dimensional boundary (so a four-dimensional scalar field) and find that large ranges of parameter space are excluded. However a ‘kink’ in the numerical bounds obeys all our consistency checks and might be an indication of a new conformal boundary condition.

Fluid Mechanics and Heat Transfer Measurements in Transitional Boundary Layers Conditionally Sampled on Intermittency

1994 ◽  
Vol 116 (3) ◽  
pp. 405-416 ◽  
Author(s):  
J. Kim ◽  
T. W. Simon ◽  
M. Kestoras
Keyword(s):  
Heat Flux ◽  
Plate Boundary ◽  
Turbulent Heat Flux ◽  
Transitional Flow ◽  
Turbulent Heat ◽  
Mean Velocity ◽  
Power Spectral ◽  
Turbulent Characteristics ◽  
Transition Models ◽  
Prandtl Numbers

An experimental investigation of transition on a flat-plate boundary layer was performed. Mean and turbulence quantities, including turbulent heat flux, were sampled according to the intermittency function. Such sampling allows segregation of the signal into two types of behavior—laminarlike and turbulentlike. Results show that during transition these two types of behavior cannot be thought of as separate Blasius and fully turbulent profiles, respectively. Thus, simple transition models in which the desired quantity is assumed to be an average, weighted on intermittency, of the laminar and fully turbulent values may not be entirely successful. Deviation of the flow identified as laminarlike from theoretical laminar behavior is due to a slow recovery after the passage of a turbulent spot, while deviation of the flow identified as turbulentlike from fully turbulent characteristics is possibly due to an incomplete establishment of the fully turbulent power spectral distribution. Measurements were taken for two levels of free-stream disturbance—0.32 and 1.79 percent. Turbulent Prandtl numbers for the transitional flow, computed from measured shear stress, turbulent heat flux, and mean velocity and temperature profiles, were less than unity.

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.

Finite-Péclet-number effects on the scaling exponents of high-order passive scalar structure functions

2012 ◽  
Vol 713 ◽  
pp. 453-481 ◽  
Author(s):  
J. Lepore ◽  
L. Mydlarski
Keyword(s):  
Scalar Field ◽  
Boundary Conditions ◽  
Passive Scalar ◽  
Structure Functions ◽  
High Order ◽  
Field Boundary ◽  
Scaling Exponents ◽  
Heated Cylinder ◽  
Scalar Structure ◽  
The Difference

AbstractThe effect of scalar-field (temperature) boundary conditions on the inertial-convective-range scaling exponents of the high-order passive scalar structure functions is studied in the turbulent, heated wake downstream of a circular cylinder. The temperature field is generated two ways: using (i) a heating element embedded within the cylinder that generates the hydrodynamic wake (thus creating a heated cylinder) and (ii) a mandoline (an array of fine, heated wires) installed downstream of the cylinder. The hydrodynamic field is independent of the scalar-field boundary conditions/injection methods, and the same in both flows. Using the two heat injection mechanisms outlined above, the inertial-convective-range scaling exponents of the high-order passive scalar structure functions were measured. It is observed that the different scalar-field boundary conditions yield significantly different scaling exponents (with the magnitude of the difference increasing with structure function order). Moreover, the exponents obtained from the mandoline experiment are smaller than the analogous exponents from the heated cylinder experiment (both of which exhibit a significant departure from the Kolmogorov prediction). Since the observed deviation from the Kolmogorov $n/ 3$ prediction arises due to the effects of internal intermittency, the typical interpretation of this result would be that the scalar field downstream of the mandoline is more internally intermittent than that generated by the heated cylinder. However, additional measures of internal intermittency (namely the inertial-convective-range scaling exponents of the mixed, sixth-order, velocity–temperature structure functions and the non-centred autocorrelations of the dissipation rate of scalar variance) suggest that both scalar fields possess similar levels of internal intermittency – a distinctly different conclusion. Examination of the normalized high-order moments reveals that the smaller scaling exponents (of the high-order passive scalar structure functions) obtained for the mandoline experiment arise due to the smaller thermal integral length scale of the flow (i.e. the narrower inertial-convective subrange) and are not solely the result of a more intermittent scalar field. The difference in the passive scalar structure function scaling exponents can therefore be interpreted as an artifact of the different, finite Péclet numbers of the flows under consideration – an effect that is notably less prominent in the other measures of internal intermittency.

On Effects of Temperature Boundary Conditions on Heat Transfer in Turbulent Low-Prandtl-Number Flows

2020 ◽  
Author(s):  
Ivan Otic
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Boundary Conditions ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Flux Boundary Condition ◽  
Large Eddy ◽  
Heat Flux Boundary Condition ◽  
Effects Of Temperature

Abstract One important issue in understanding and modeling of turbulent heat transfer is the behavior of fluctuating temperature close to the wall. Common engineering computational approach assumes constant heat flux boundary condition on heated walls. In the present paper constant heat flux boundary condition was assumed and effects of temperature fluctuations are investigated using large eddy simulations (LES) approach. A series of large eddy simulations for two geometries is performed: First, forced convection in channels and second, forced convection over a backward facing step. LES simulation data is statistically analyzed and compared with results of direct numerical simulations (DNS) from the literature which apply three cases of heat flux boundary conditions: 1. ideal heat flux boundary condition, 2. non-ideal heat flux boundary condition, 3. conjugate heat transfer boundary condition. For low Prandtl number flows LES results show that, despite very good agreement for velocities and mean temperature, predictions of temperature fluctuations may have strong deficiencies if simplified boundary conditions are applied.

Nodal Topology in Compact Thermal Models

2007 ◽  
Author(s):  
D. H. Greisen ◽  
V. P. Manno
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Heat Transfer Coefficient ◽  
Boundary Conditions ◽  
Transfer Coefficient ◽  
Area Ratio ◽  
System Level ◽  
Thermal Models ◽  
Single Boundary

Compact Thermal Models (CTMs) utilize a few connected thermal nodes to represent the thermal characteristics of electronic packages. These models are preferable to highly discretized models in preliminary design and system level analysis because of their computational efficiency. Surface heat flux non-uniformities often make it necessary to subdivide the package surfaces into multiple CTM nodes. This division is often quantified as the surface area ratio. This work assesses CTM performance sensitivity to area ratio changes and variation in heat transfer coefficient boundary conditions. CTMs for benchmark TQFP and BGA packages are developed using an admittance matrix approach. While optimum area ratios are identified, a direct correlation between these optimal values and the heat flux distributions computed from fully-discretized models was not obtained. CTM performance was found to be sensitive to changes in the heat transfer coefficient used to generate the CTM parameter values. A critical generating heat transfer coefficient was determined such that the resulting CTM, when optimized for a single boundary condition, was relatively accurate over the whole set of boundary conditions considered. This single boundary condition also provided an upper bound for error. This finding could be significant in future CTM development procedures.

Turbulent Statistics of Rarefield Flows in Microchannel Flow and Heat Transfer

2004 ◽  
Author(s):  
G. X. Li ◽  
W. Q. Tao ◽  
Z. Y. Li ◽  
B. Yu
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Shear Stress ◽  
Reynolds Shear Stress ◽  
Wall Region ◽  
Turbulent Heat ◽  
Time Step ◽  
Temperature Variance ◽  
Flow And Heat Transfer ◽  
Turbulent Statistics

Direct numerical simulation has been carried out to investigate the effect of weak rarefaction on turbulent gas flow and heat transfer characteristics in mirochannel. The Reynolds number based on the friction velocity and the channel half width is 150. Grid number is 64×128×64. Fractional time step method is employed for the unsteady Navier-Stokes equations, and the governing equations are discretized with Finite Difference Method. Statistical quantities such as turbulent intensity, Reynolds shear stress, turbulent heat flux and temperature variance are obtained under various Knudsen number from 0 to 0.05. The results show that rarefaction can influence the turbulent flow and heat transfer statistics. The streamwise mean velocity and temperature increase with increase of Kn number. In the near wall region rarefaction can increase the turbulent intensities and temperature variance. The effect of rarefaction on Reynolds shear stress and wall-normal heat flux are presented. The instantaneous velocity fluctuations in the vicinity of the wall are visualized and the influence of Kn number on the flow structure is discussed.

Gradient Estimates for Spacelike Mean Curvature Flow with Boundary Conditions

2018 ◽  
Vol 62 (2) ◽  
pp. 459-469
Author(s):  
Ben Lambert
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Mean Curvature ◽  
Neumann Boundary Condition ◽  
Mean Curvature Flow ◽  
Neumann Boundary ◽  
Curvature Flow ◽  
Gradient Estimate ◽  
Gradient Estimates ◽  
The Mean

AbstractWe prove a gradient estimate for graphical spacelike mean curvature flow with a general Neumann boundary condition in dimension n = 2. This then implies that the mean curvature flow exists for all time and converges to a translating solution.

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.

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