Streamwise Heat Flux Research Articles

Technique for calculating streamwise local fluxes in general flows

This paper presents a new technique for calculating microscopic local fluxes that provides a robust and accessible way to obtain the streamwise fluxes in general flows. Flux calculation is one of the fundamental elements in molecular simulations. Several-decades-long research efforts on the subject made significant progresses since the pioneering work of Irving and Kirkwood [J. Chem. Phys, (1950) 18, 817–829]. However, some issues remain regarding the fluxes in the flow direction. The streaming velocity (SV) and the fluxes independent of SV are difficult to manage during computation. For example, the local fluxes and SV that vary in more than one direction are not well represented despite being prevalent in the microscopic phenomena such as nanofluidics, biotechnologies, and energy conversions. The technique presented in this paper is based on the instantaneous microscopic conservation equations and depends only on the total fluxes that include the convective contributions. This allows a calculation of all the fluxes at the end of a simulation run, with no complication arising in terms of defining and collecting SV, pressure tensor, and heat flux vector. Widely-used methods such as the method of planes and volume-average method were adapted, respectively. This study then investigated a planar shear flow in a highly confined channel, where a flow is unknown at the beginning of a simulation, and the controversial streamwise heat flux with no temperature gradient was present. The flow and fluxes were structured, and the streamwise heat flux evolved significantly and slowly over a few tens of nano-seconds even with steady boundary conditions.

Continuum breakdown in compressible mixing layers.

Gas-kinetic simulations of rarefied and compressible mixing layers are performed to characterize continuum breakdown and the effect on the Kelvin-Helmholtz instability. The unified gas-kinetic scheme (UGKS) is used to perform the simulations at different Mach and Knudsen numbers. The UGKS stress tensor and heat-flux vector fields are compared against those given by the Navier-Stokes-Fourier constitutive equations. The most significant difference is seen in the shear stress and transverse heat flux. The study demonstrates the existence of two distinct continuum breakdown regimes, one at low and the other at high convective Mach numbers. Overall, at low convective Mach numbers, the deviation from continuum stress and heat flux appears to scale exclusively with the micro-macro length scale ratio given by the Knudsen number. On the other hand, at high convective Mach numbers, the deviation depends on the global micro-macro timescale ratio given by the product of Mach and Knudsen numbers. We further demonstrate that, unlike shear stresses and transverse heat flux, the deviations in normal stresses and the streamwise heat flux depend separately on Knudsen and Mach numbers. A local parameter called the gradient Knudsen number is proposed to characterize the rarefaction effects on the local momentum and thermal transport. Noncontinuum aspects of gas-kinetic stress-tensor and heat-flux behavior that Grad's 13-moment equationmodel reasonably captures are identified.

Wall shear stress, pressure, and heat flux fluctuations in compressible wall-bounded turbulence, part I: One-point statistics

This two-part study investigates the effects of Mach number and wall temperature on the statistics of wall shear stress, pressure, and heat flux fluctuations in compressible wall-bounded turbulence. In the first part, we focus on their one-point statistics, including the root mean square (r.m.s.), skewness factor (third-order moment), flatness factor (fourth-order moment), and their correlations. By exploiting the direct numerical simulation databases, we found that the r.m.s. of the streamwise wall shear stress and pressure, the skewness factor of all the flow quantities considered, and the flatness factor of streamwise wall shear stress monotonically vary with the friction Mach number (Mτ), while for the rest, the wall heat flux and global temperature parameters should be taken into account as well for a monotonic trend of variation. The correlation coefficients between wall shear stress, pressure, and heat flux fluctuations increase with the Mach number Mτ, suggesting the underlying interactions between dynamic and thermodynamic processes. The distributions of spectra and probability density functions indicate that the increased correlation is induced by the highly intermittent traveling wave packets among the streaky structures, as reflected by the “double-peak” feature of the spectra that gradually emerges with the increasing compressibility effects. The probability density distribution also manifests the alteration of the occurrence of extreme events caused by these structures. By accordingly decomposing the fluctuations with cutoff filtering, it is found that the root mean squares of streamwise wall shear stress and heat flux fluctuations related to the streaky structures are Mach number-independent, while those related to the traveling wave packets monotonically increase with the friction Mach number.

Infrared thermography of hypersonic boundary layer transition induced by isolated roughness elements

Roughness element induced hypersonic boundary layer transition on a flat plate is investigated using infrared thermography at Ma = 5 and 6 flow condition. Surface Stanton number is acquired to analyze the effect of roughness element shape and height on the transition process. The correlation between the vortex structure induced by roughness element and the wall heat streaks is established. The results indicate that higher roughness element would induce stronger streamwise heat flux streaks, lead to transition advance in streamwise centerline and increase the width of spanwise wake. Moreover, for low roughness element, the effect of the shape is not obvious, and the height plays a leading role in the transition; for tall roughness element, the effect on accelerating transition for the diamond roughness element is the best, the square is the worst, and the shape plays a leading role in the transition.

Theoretical analysis of convective heat flux structure in the incompressible turbulent boundary layer on a porous plate with uniform injection and suction

Although many experimental and numerical studies on thermal convection exist for turbulent transpiration boundary layer flows on a porous structure, the general convective heat flux formula is urgently needed to clarify the influence of injection or suction on the energy transfer mechanism of turbulent heat convection. The two-dimensional (2D) theoretical convective heat flux structure obtained previously is therefore applied to the incompressible turbulent thermal boundary layer on a porous flat plate with uniform injection and suction. The energy balance relationship between the streamwise and wall-normal heat flux components is established and the effects of injection and suction on turbulent convective heat fluxes are analyzed. The explicit analytical expressions of turbulent skin friction factor, convective heat transfer coefficient and Stanton number are obtained based on the heat flux theory and verified by the previously experimental measurements. The turbulence characteristics of convective heat transfer with uniform injection and suction are revealed by the proposed key parameters. A hybrid control volume analysis for energy transfer inside the porous media plate is performed and applied to the cases of transpiration cooling and enhancing heat transfer, respectively, and a novel calculation formula for convective heat transfer is proposed in the form of heat flux instead of the heat transfer coefficient. It is also found that the direction of the resultant convective heat flux combining the conduction with advection is not always to remain that of the negative temperature gradient, and it depends not only on the temperature difference direction as well as velocity direction, but also on the magnitude contrast of the conductive and advective heat fluxes.

Unsteady effects in a hypersonic compression ramp flow with laminar separation

Abstract

Simulations of Unsteady Three-Dimensional Hypersonic Double-Wedge Flow Experiments

Hypersonic flow over a three-dimensional 30–55 deg double wedge is investigated for three different conditions of varying enthalpy and Reynolds number with nitrogen as the test gas. Streamwise and spanwise wall heat flux are compared to the experimental data that were obtained at the University of Illinois at Urbana–Champaign and the California Institute of Technology. In previous studies, there were concerns that portions of the flowfield were rarefied; however, after an in-depth analysis, we find the flowfield to be firmly in the continuum regime. Comparisons of heat flux at an instant of time in the simulations show good agreement with the experiments. However, averaged heat flux over a long period of time relative to the experimental test time are underpredicted and develop low-frequency periodic motion. To better understand the unsteadiness and three-dimensionality of the flowfield, we analyze the mass flux through a spanwise plane, and we perform sparsity-promoting dynamic mode decomposition for the wall heat flux and midplane pressure. Finally, we analyze the effect of vibrational nonequilibrium on the flowfield. It is found that the flowfield dynamics vary with increasing enthalpy and Reynolds number. Furthermore, the flowfield is found to be three dimensional, unsteady, and asymmetric for all cases.

Experimental Investigation on Velocity and Temperature Field in a Rotating Non-isothermal Turbulent Boundary Layer using Hot-wire

This experiment measured the instantaneous temperature and velocity field synchronously in non-isothermal turbulent boundary layer in a rotating straight channel with a parallel-array hot-wire probe. The Reynolds number based on the bulk mean velocity (U) and hydraulic diameter (D) is 19000, and the rotation numbers are 0, 0.07, 0.14, 0.21 and 0.28. The mean velocity u and mean temperature T as well as their fluctuating quantity u’ and T’ were measured at three streamwise locations (x/D = 4.06, 5.31, 6.56). A method for temperature-changing calibration with constant temperature hot-wire anemometers was proposed. It achieved the calibration in operational temperature range (15.5 °C–50 °C) of the hot-wire via a home-made heating section. The measurement system can obtain the velocity and temperature in a non-isothermal turbulent boundary layer at rotating conditions. The result analysis mainly contains the dimensionless mean temperature, temperature fluctuation as well as its skewness and flatness and streamwise turbulent heat flux. For the trailing side, the rotation effect is more obvious, and makes the dimensionless temperature profiles lower than that under static conditions. The dimensionless streamwise heat flux shows a linear decrease trend in the boundary layer. It is hoped that this research can improve our understanding of the flow and heat transfer mechanism in the internal cooling passages of turbine rotor blades.

Numerical Investigation of a Confined Laminar Jet Impingement Cooling of Heat Sources Using Nanofluids

Abstract The thermal and fluid dynamic behavior of a confined two-dimensional steady laminar nanofluid jet impinging on a horizontal plate embedded with five discrete heating elements subjected to a constant surface heat flux has been studied for a range of Reynolds number (Re) from 100 to 400 with Prandtl number, Pr = 6.96, of the base fluid. Variation of inlet Reynolds number produces a significant change of the flow and heat transfer characteristics in the domain. Increasing the nanoparticle concentration (ϕ) from 0% to 4% exhibits discernible change in equivalent Re and Pr caused by the modification of dynamic viscosity, effective density, thermal conductivity, and specific heat of the base fluid. Considerable improvement in heat transfer from the heaters is observed as the maximum temperature of the impingement wall is diminished from 0.95 to 0.55 by increasing Re from 100 to 400; however, the result of increasing ϕ on cooling of the heaters is less appreciable. Self-similar behavior has been depicted by cross-stream variation of temperature and streamwise heat flux in the developed region along the impingement wall up to Re = 300 for ϕ=0% to 4%. But the spread of the respective quantities shows strong dependence on ϕ at Re = 300 with sudden attenuation in magnitude in the developed region of flow. Substantial influence of Re is evident on Eckert number and pumping power. Eckert number decreases, whereas pumping power increases with an increase in Re, and the respective variations exhibit correspondence with power fit correlations.

Effect of the wall properties on the shock wave / laminar boundary layer interaction

The CFD calculations have been performed based on RANS approach with the Menter transition model [1]. The boundary layer developing on a flat plate was considered. To generate the incident shock wave, a wedge was installed over the plate. The wall was represented by one cm thick solid flat plate made from aluminum and polyacetal. Flow parameters were M∞=1.41, P0=0.7 bar, T0=293K. As a result of solving the conjugate heat transfer problem, the SWBLI flow was studied. The temperature and pressure distributions on the wall for different surface materials were obtained. It was found that the streamwise heat fluxes inside the wall can lead to a change of the separation zone length.

Slip effects on turbulent heat transport over post and ridge structured superhydrophobic surfaces

Forced convection and turbulent scalar transport over a structured superhydrophobic walls composed of periodic arrays of square posts and ridges textures are numerically investigated in a periodic channel. The flow physics and thermal transport within the fluid are studied using Direct numerical simulation (DNS), assuming the plastrons are flat. Slip velocities, Nusselt number, turbulent Prandtl number and turbulent heat fluxes are determined for both square posts and streamwise ridge shaped feature geometry configurations at a friction Reynolds number of Reτ=180. This article provides an insight that superhydrophobic surfaces enhance turbulent heat fluxes and thermal fluctuations in the laminar-sublayer region. With increasing feature wavelength, the turbulent heat fluxes in the buffer layer and outer layer drop for both square posts and streamwise ridges. When compared with a smooth no-slip channel, the diffusion term in the budget of thermal fluxes pointed to the role of organized lateral flow motions in enhancing wall-normal heat-flux, and a reduction in large scale transport of streamwise heat fluxes by near-wall coherent structures.

Experimental investigation of Görtler vortices in hypersonic ramp flows

A sharp leading-edge ramp model with 15°, 20°, and 25° ramp angles is experimentally investigated at a freestream Mach number 7.7 and a unit Reynolds number 4.2 × 106 m−1 in the Aachen Shock Tunnel TH2. The objective of this paper is to analyze Gortler vortices in terms of shear layer length, flow curvature, and vortex related parameters. The spanwise heat flux variation caused by it and the streamwise heat flux enhancement during its tenure are also studied. Thermocouples, pressure sensors, schlieren imagery, and infrared imaging are used for the investigation. The boundary layer on the flat plate until separation is laminar. An important outcome is that the arc length at reattachment is constant irrespective of the ramp angle. Characteristic boundary layer thicknesses at different Mach number show that the momentum thickness is insensitive to compressibility and is used to determine the Gortler number. A model is presented to determine the Gortler number in terms of ramp angle and a constant based on separation angle, arc length, momentum thickness, and Reynolds number. The half of the vortex wavelength is equal to the boundary layer thickness just before reattachment. The length scale required for breakdown of Gortler vortices decreases with rising ramp angle and is analogous to peak heating length. The streamwise heat flux enhancement occurs during the tenure of Gortler vortices and the enhancement rises with ramp angle. Although the visibility of Gortler vortices through temperature variation is distinct, the spanwise heat flux variation is not too high. Moreover, the spanwise heat flux variation rises marginally with ramp angle.

Structures of scalar transport in a turbulent channel

Direct numerical simulation (DNS) of a turbulent channel with temperature treated as a passive scalar at a moderate Reynolds number (Reτ=395) was performed to investigate the large scale motions (LSMs) responsible for scalar transport. Structures are elicited by using three dimensional maps of two-point correlations. Complete three-dimensional structure of cross-correlations between velocity and scalar fluctuations was evaluated for the first time. The results show that the organized motions which are responsible for transporting streamwise component of the turbulence kinetic energy, scalar variance, and streamwise heat flux are very similar only in the viscous sublayer. However, LSMs which transport streamwise component of the turbulence kinetic energy, scalar variance, and streamwise heat flux are clearly distinct to each other beyond the buffer region. In addition, comprehensive three-dimensional two-point correlation data implied that LSMs which are responsible for carrying most of the Reynolds stresses are not exactly the same as those that transport most of the scalar fluxes in both inner and outer regions of the turbulent boundary layer. Analysis of the length scales of correlations revealed that the growth of LSMs which influence both momentum and thermal transport is linear. Comparison of physical extents of LSMs which are responsible for transporting Reynolds stresses and wall-normal heat fluxes revealed that Reynolds analogy holds for scalar transport by the LSMs in the boundary layer.

Numerical investigation of gas–surface scattering dynamics on the rarefied gas flow through a planar channel caused by a tangential temperature gradient

A numerical analysis of the rarefied gas flow caused by a temperature gradient in the direction tangential to a wall through a planar channel of finite length is carried out based on the nonlinear Shakhov model of the Boltzmann kinetic equation. The Maxwell diffuse and Cercignani–Lampis gas–surface interaction models are provided as a boundary condition at solid walls. An implicit scheme for solution of the S-model kinetic equation was applied and the algorithm has been optimized for the use of massive parallelization in both physical and velocities spaces. The competition between rarefaction, gas–surface scattering model and temperature gradient effects on a gas flow is discussed in terms of both mass flow rate and streamwise heat flux. A comparison with available literature results has been carried out and showed a good agreement. It was found that the temperature gradient as well as the gas–surface scattering dynamics play a significant role for the highly rarefied gas flow, beginning from the transition flow regime. At the same time, under certain gas–surface scattering conditions a change of the value of temperature gradient does not affect the heat flux. For the weakly rarefied flow the temperature gradient effect on the mass flow rate is small for any gas–surface scattering condition, while the heat flux does not depend neither on value of temperature gradient nor choice and details of gas–surface scattering dynamics.

Dissimilarity of Turbulent Fluxes of Momentum and Heat in Perturbed Turbulent Flows

The dissimilarity between the Reynolds stresses and the heat fluxes in perturbed turbulent channel and plane Couette flows was studied using direct numerical simulation. The results demonstrate that the majority of the dissimilarity was due to the difference between the wall-normal fluxes, while the difference between the streamwise fluxes was lower. The main causes for the dissimilarity were the production terms, followed by the velocity-pressure interaction terms. Further insights into the importance of the velocity-pressure interaction in the origin of the dissimilarity are provided using two-point correlation. Furthermore, an octant conditional averaged dataset reveals that not only the wall-normal heat flux but also the streamwise heat flux is strongly related to the wall-normal gradient of the mean temperature. A simple Reynolds-averaged Navier–Stokes (RANS) heat flux model is proposed as a function of the Reynolds stresses. A comparison of the direct numerical simulation data with an “a priori” prediction suggests that this simple model performs reasonably well.

Large eddy simulation of thermal driven cavity: Evaluation of sub-grid scale models and flow physics

Three eddy-viscosity and one non-eddy-viscosity type sub-grid scale models have been evaluated in large eddy simulations of buoyant turbulent flows in the three-dimensional thermal driven cavity of aspect ratio 4. The eddy-viscosity models considered include the traditional dynamic Smagorinsky model, and the recently developed dynamic Vreman and constant coefficient Sigma models. The non-eddy-viscosity Stretched Vortex model has also been evaluated. A high-order numerical framework has been used for the present LES of buoyant turbulent flows. Excellent comparison to DNS data has been obtained using dynamic Smagorinsky, Sigma and Stretched Vortex models, while more tests are required to ascertain the applicability of the dynamic Vreman model for buoyant turbulent flows. The use of WENO advective scheme for scalars has been established by comparing to results using BQUICK scalar advective scheme. Finally, the flow structure in the thermal cavity has been examined in detail, and features such as inhomogeneity, wave-vortical interactions, the turbulent kinetic energy budget, and the boundary layer dynamics have been studied. In particular, the near wall behavior of the turbulent shear stress and the turbulent streamwise heat flux has been studied in conjunction with their respective production terms.

Algebraic Modeling of the Turbulent Heat Fluxes Using the Elliptic Blending Approach—Application to Forced and Mixed Convection Regimes

The present paper focuses on the application of the elliptic blending approach to the modeling of turbulent heat fluxes, in order to account for the influence of solid boundaries. The analytical justification of the extension to the temperature–pressure gradient correlation term of this approach, originally applied to the velocity–pressure gradient, is given. The assumption of weak equilibrium enables the derivation of two new algebraic flux models valid down to the wall. It is shown, with both a priori tests and computations in forced and mixed convection regimes, that the predictions of the streamwise heat-flux and the temperature variance are significantly improved by the use of elliptic blending. A particular attention is devoted to the issue of the modeling of the correlation length scale involved in the elliptic blending for the heat fluxes, which is shown to have a significant influence on the predictions.

Structure of turbulent heat flux in a flow over a heated wavy wall

A particle image thermometry technique is proposed to determine the turbulent heat flux in a water channel between a sinusoidal heated bottom and a flat top wall. Reynolds numbers between 2400 and 20,500 are considered. A proper orthogonal decomposition of combined velocity and temperature fields reveals a quantitative agreement between large-scale thermal and momentum structures. The distribution of budget terms of the streamwise and wall-normal heat fluxes are similar to those for the two Reynolds stress components. Co-spectra indicate that larger scale structures make a significant contribution to the streamwise heat flux and smaller scales are more important to the wall-normal heat flux.

Subgrid Scale Modeling of Turbulence for the Dynamic Procedure Using Finite Difference Method and Its Assessment on the Thermally Stratified Turbulent Channel Flow

Abstract Previously proposed methods for subgrid-scale (SGS) stress modeling were re-investigated and extended to SGS heat-flux modeling, and various anisotropic and isotropic eddy viscosity/diffusivity models were obtained. On the assumption that they are used in a finite-difference (FD) simulation, the models were constructed in such a way that they are insensitive to numerical parameters on which calculated flows are strongly dependent in the conventional Smagorinsky model. The models obtained, as well as those previously proposed, were evaluated a priori in a stably stratified open channel flow, which is considered to be a challenging application of large eddy simulation and suitable for testing both SGS stress and heat-flux models. The most important feature of the models proposed is that they are insensitive to the discretized test filtering parameter required in the dynamic procedure of Germano et al. (1991, Phys. Fluids, 3, pp. 1760–1765) in FD simulation. We also found in SGS heat-flux modeling that the effect of the grid (resolved)-scale (GS) velocity gradient plays an important role in the estimation of the streamwise heat flux, and an isotropic eddy diffusivity model with the effect of the GS velocity is proposed.

Passive scalar transport in polymer drag‐reduced turbulent channel flow

AbstractPassive scalar transport in turbulent channel flow of viscoelastic dilute polymer solutions exhibiting drag reduction (DR) is studied using direct numerical simulations for DR values up to 74.0%. DR is accompanied by the stabilization of low‐speed streaks in the buffer layer that are primarily responsible for the streamwise heat transport. Moreover, as DR increases, the Reynolds stress and the root mean square fluctuations in the wall‐normal and spanwise velocity components decrease. Thus, as DR is increased, streamwise heat flux increases, whereas both wall‐normal and spanwise heat fluxes decrease. Consequently, for large DR values, the flow acts as a highly efficient heat pump. The turbulent Prandtl number, defined as the ratio of the eddy diffusivities of momentum to heat, increases from its Newtonian limit of unity to a value that exceeds the molecular Prandtl number for DR = 74.0%. This experimentally well documented phenomenon is predicted using first‐principle simulations for the first time in this work. © 2005 American Institute of Chemical Engineers AIChE J, 2005