Streamwise Heat Flux Research Articles

Heat Flux Reduction From Film Cooling and Correlation of Heat Transfer Coefficients From Thermographic Measurements at Enginelike Conditions

Heat transfer coefficients and the resulting heat flux reduction due to film cooling on a flat plate downstream a row of cylindrical holes are investigated. Highly resolved two-dimensional heat transfer coefficient distributions were measured by means of infrared thermography and carefully corrected for local internal testplate conduction and radiation effects. These locally acquired data are processed to lateral average heat transfer coefficients for a quantitative assessment. A wide range variation of the flow parameters blowing rate and density ratio as well as the geometrical parameters streamwise ejection angle and hole spacing is examined. The effects of these dominating parameters on the heat transfer augmentation from film cooling are discussed and interpreted with the help of highly resolved surface results of effectiveness and heat transfer coefficients presented earlier. A new method of evaluating the heat flux reduction from film cooling is presented. From a combination of the lateral average of both the adiabatic effectiveness and the heat transfer coefficient, the lateral average heat flux reduction is processed according to the new method. The discussion of the total effect of film cooling by means of the heat flux reduction reveals important characteristics and constraints of discrete hole ejection. The complete heat transfer data of all measurements are used as basis for a new correlation of lateral average heat transfer coefficients. This correlation combines the effects of all the dominating parameters. It yields a prediction of the heat transfer coefficient from the ejection position to far downstream, including effects of extreme blowing angles and hole spacing. The new correlation has a modular structure to allow for future inclusion of additional parameters. Together with the correlation of the adiabatic effectiveness it provides an immediate determination of the streamwise heat flux reduction distribution of cylindrical hole film-cooling configurations.

THEORY OF TURBULENCE: ANOMALOUS THERMAL FLUX SPECTRUM

A recent theory of fully-developed 3D hydrodynamic turbulence, involving dynamical response functions for turbulent thermal shear flow, yields analytical results for the anomalous Kolmogorov spectrum of streamwise heat flux.

Numerical study of a buoyancy-induced flow along a vertical plate with discretely heated integrated circuit packages

Abstract A numerical study by the multigrid technique has been performed to investigate the laminar natural convection air cooling of a vertical plate with five wall-attached protruding, discretely heated integrated circuit (IC) packages. This study is of great practical importance because it shows the influence of the blockages (IC package) dimension, and of their power distribution on the buoyancy-induced flow and thermal field in such a configuration. A two-dimensional, steady state model is used to describe the conjugate natural convection/conduction heat transfer. The fluid physical properties are assumed uniform except for the buoyancy terms which are computed using the Boussinesq approximation of Navier Stokes equations. The development of the buoyancy-induced flow has been studied through the evolution of the streamwise velocity, temperature and heat flux fields.

An explicit algebraic heat-flux model for the temperature field

An explicit algebraic heat-flux (EAHF) model is derived by invoking the assumption of equilibrium turbulence for both the velocity and the thermal fields. Further modifications are achieved by applying an approximation technique to render the implicit heat flux vector relation explicit. Thus derived, the heat flux vector yields two terms. The first term is identical to that given by a simple thermal eddy diffusivity model, while the second term provides a correction to the streamwise heat flux. This second term is non-zero even when the streamwise mean temperature gradient is zero. It allows the modeling of the generation of a streamwise heat flux due to the interaction of the turbulent eddies with the mean temperature gradient normal to the streamwise direction. Previously derived near-wall corrections to the equations of the temperature variance and its dissipation rate are found to be equally valid for the EAHF model. The near-wall EAHF model is validated against direct numerical simulation data and experimental measurements. In addition, the calculations are also compared with those obtained from a second-order model and the simple thermal eddy diffusivity model. Two different near-wall Reynolds-stress models are used to calculate the velocity field and they are found to have little effect on the thermal field predicted by the EAHF model. In general, the results for the temperature field are in good agreement with data and are essentially unaffected by the second term in the EAHF model. On the other hand, the prediction of the streamwise heat flux is in good agreement with that given by a second-order model which correlates well with data.

Conjugate heat transfer in solar collector panels with internal longitudinal corrugated fins-Part II: Local results

A computational study is conducted to determine, for laminar flow in a solar collector panel or a parallel-plate channel with an internal, longitudinal, corrugated fin, the effects of varying the fin angle (or the fin pitch), the fin thickness, the wall-to-fluid thermal conductivity ratio, and the thermal boundary condition on the local surface temperature and heat flux distributions. The corrugated fin and the two walls form individual triangular flow passages in the collector panel or parallel-plate channel. The results of the investigation show that the variation of the local surface temperature is large when the fin is thin and when the wall/fluid thermal conductivity ratio is small. The local surface heat flux is low near the corners of both the upper and lower triangular flow passages. Near the point of fin attachment on the heated wall, heat may be transferred from the fluid to the fin. Heat may also be transferred from the fluid to the unheated wall near the point of fin attachment. When the thermal conductivity ratio is small, the temperature field in the flow cross section is predominantly stratified. In the limit as the thermal conductivity ratio approaches infinity, the temperature field is that of the thermally fully developed laminar flow in a triangular duct with a streamwise uniform heat flux and peripheral uniform surface temperature boundary condition.

Direct Numerical Simulation of Passive Scalar Field in a Turbulent Channel Flow

A direct numerical simulation (DNS) of the fully developed thermal field in a two-dimensional turbulent channel flow of air was carried out. The isoflux condition was imposed on the two walls so that the local mean temperature increased linearly in the streamwise direction. With any buoyancy effect neglected, temperature was considered as a passive scalar. The computation was executed on 1,589,248 grid points by using a spectral method. The statistics obtained were root-mean-square temperature fluctuations, turbulent heat fluxes, turbulent Prandtl number, and dissipation time scales. They agreed fairly well with existing experimental and numerical simulation data. Each term in the budget equations of temperature variance, its dissipation rate, and turbulent heat fluxes was also calculated. It was found that the temperature fluctuation θ′ was closely correlated with the streamwise velocity fluctuation u′, particularly in the near-wall region. Hence, the distribution of budget terms for the streamwise and wall-normal heat fluxes, u′θ′ and v′θ′, were very similar to those for the two Reynolds stress components, u′u′ and u′v′.

Measurement of turbulent dispersion behind a fine cylindrical heat source in a weakly sheared flow

Turbulent structure in a turbulent scalar dispersion field behind a fine cylindrical heat source in a weakly sheared flow is experimentally investigated and previous computational turbulence models for third-order scalar transport terms in the second-order turbulence equations are assessed with the present data.The mean temperature and r.m.s. temperature profiles are found to be almost Gaussian even in the uniform shear layer. Decay of the peak temperature, mean dispersion and half-widths of the mean temperature and the r.m.s. temperatures are well correlated with corresponding data on the scalar dispersion behind an elevated line heat source in the turbulent boundary layer.Normalized streamwise heat flux .In addition, since the experiment isolates the effect of uniform mean shear on the turbulent scalar transport, experimental data accumulated by the present study will be useful for further development of more refined second-order turbulence models for non-isothermal turbulent flows.

Experiments on scalar dispersion within a model plant canopy part II: An elevated plane source

An experiment is reported in which heat was released as a passive tracer from an elevated lateral line source within a model plant canopy, with hs = 0.85 hc (hs and hc being the source and canopy heights, respectively). A sensor assembly consisting of three coplanar hot wires and one cold wire was used to measure profiles of mean temperature % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikamaana% aabaGaeqiUdehaaiaacMcaaaa!390C!\[(\overline \theta )\], temperature variance (Σθ2), vertical and streamwise turbulent heat fluxes, and third moments of wind and temperature fluctuations. Conclusions were: (i) Despite the very heterogeneous flow within the canopy, the observed dispersive heat flux (due to spatial correlation between time-averaged temperature and vertical velocity) was small. However, there is evidence from the plume centroid (which was lower than hs at the source) of systematic recirculating motions within the canopy. (ii) The ratio % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS% baaSqaaiabeI7aXjaab2gacaqGHbGaaeiEaaqabaGccaGGVaWaa0aa% aeaacqaH4oqCaaWaaSbaaSqaaiaab2gacaqGHbGaaeiEaaqabaaaaa!41DF!\[\sigma _{\theta {\text{max}}} /\overline \theta _{{\text{max}}} \] (of maximum values on vertical profiles) decreased from 1 near the source to an asymptotic value of 0.4 far downstream, in good agreement with previous experimental and theoretical work for concentration fluctuations in the surface layer well above the canopy. (iii) The eddy diffusivity for heat from the line source (KHL) increased, downstream of the source, to a nearly constant ‘far-field’ vertical profile. Within the canopy, the far-field KHL was an order of magnitude larger than KHP, the equivalent diffusivity for a plane source; well above the canopy, the two were equal. The time scale defined by (far-field KHL)/(vertical velocity variance) was independent of height within the canopy. (iv) Budgets for temperature variance, vertical heat flux and streamwise heat flux are remarkably similar to the equivalent budgets for an elevated line source in the surface layer well above the canopy, except in the lower part of the canopy in the far field, where vertical transport is much more important than in the surface layer. (v) A random flight simulation of the mean height and depth of the temperature plume was generally in good agreement with experiment. However, details of the temperature and streamwise turbulent heat flux profiles were not correct, suggesting that the model formulation needs to be improved.

Turbulent flow with heat transfer in plane and curved wall jets

Extensive single-point turbulence measurements made in a heated wall jet on a convex wall, and in an equivalent plane flow, show that the turbulence structure and the transfer of heat and momentum are affected by wall curvature. In the curved wall jet the points of zero shear stress and zero streamwise heat flux are displaced further from the point of maximum velocity, the Stanton number for heat transfer from the surface is reduced more than the skin-friction coefficient, and temperature profiles in the inner layer depart from the flat-flow wall law. The shear stress, turbulent intensities and turbulent heat fluxes are reduced by stabilizing curvature in the inner layer and increased by destabilizing curvature in the outer flow. The largest changes occur in the triple products, which are nearly doubled by destabilizing curvature.

Turbulent boundary layer on a mildly curved convex surface

Extensive single point turbulence measurements made in the boundary layer on a mildly curved heated convex wall show that the turbulence heat fluxes and Stanton number are more sensitive to a change in wall curvature than the Reynolds stresses and skinfriction coefficient, and that downstream, as the flow adjusts to new curved conditions, the St/cf ratio of Reynolds analogy is appreciably lower than in plane wall flow for the same conditions. Details of the turbulence structure in unheated flow have been documented in an earlier paper; temperature field measurements now described comprise mean temperature distributions, the streamwise variation of wall heat flux, profiles of the temperature variance, transverse and streamwise heat fluxes, and triple correlations. Turbulent diffusion of heat flux is drastically reduced even by mild curvature; changes in the heat fluxes are of the same order as changes in the shear stress, that is, an order of magnitude greater than the ratio of boundary layer thickness to wall radius of curvature. The data include plane flow measurements taken in a developed boundary layer upstream of a change in wall curvature.

Streamwise heat flux budget in the atmospheric surface layer

Atmospheric surface-layer measurements of terms in the equation for the streamwise heat flux confirm previous results in both laboratory and atmosphere that the temperature-pressure gradient correlation acts as a sink, approximately equal in magnitude to the production term. The measured viscous dissipation term is independent of stability and represents less than 10% of the production term over the range of experimental stability conditions. Models for the temperature-pressure gradient correlation are compared with the measurements.

The periodic thermally developed regime in ducts with streamwise periodic wall temperature or heat flux

When a tube or duct flow is subjected to a streamwise periodic variation of wall temperature or wall heat flux, a periodic thermally developed regime is established at sufficient distances from the inlet. In the developed regime, similar heat-transfer characteristics occur in successive streamwise modules whose length is equal to the period of the imposed variation. A methodology was developed for obtaining universal solutions for the periodic fully developed regime. The end result of the development enables the wall heat flux distribution corresponding to any given wall temperature variation to be determined via the summing of a simple series. A similar series enables the wall temperature to be determined when the heat flux distribution is given. The series contains influence coefficients which represent the solution for an array of pulses. A procedure for determining these influence coefficients is presented which circumvents the need to solve the differential energy equation. The use of the methodology was illustrated by application to sine wave wall temperature and heat flux distributions.