TURBULENT HEAT TRANSFER AND TEMPERATURE FLUCTUATIONS IN A FIELD WITH UNIFORM VELOCITY AND TEMPERATURE GRADIENTS
Velocity and temperature correlation in homogeneous turbulent field
TEMPERATURE↗
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Internal low Reynolds number turbulent heat transfer
The results of a semi-analytical and experimental study of adiabatic tube flow and an analytical and experimental investigation of the thermal entrance region for gas flowing through electrically heated circular tubes are presented. Emphasis is placed on the low Reynolds number turbulent flow regime--defined as fully turbulent flow at bulk Reynolds numbers from 3,000 to about 15,000. Adiabatic air velocity and friction data and localized heat transfer measurements for air and helium, at low heating rates, are presented for this range. The adiabatic data were obtained in a 1.61 inch 1D tube for flow at bulk Reynolds numbers from 3,000 to 15,000. A continuous, Reynolds number-dependent, profile is developed from the data by using a modification of Reichardts' wall and middle law eddy diffusivity expressions. The velocity profile satisfies continuity. It is valid for all Reynolds numbers in excess of 3,000 for which the flow is fully turbulent and the Blasius friction factor expression is valid. The thermal entrance problem for a fully developed velocity profile is solved analytically by the method of Sparrow, Hallman, and Siegel. The solution is based on the profile developed from the velocity study. Tabular values of the eigenvalues and normalized Nusselt numbers for gases are presented for it range of Reynolds numbers from 3,000 to 50,000. The axial variation of Nusselt number is found to be correlated by [Nu/Nu_(∞)] = 1 + 0.8 (1+ 70,000 Re^(-3/2)) ((x/D)^(-1)) to within ± 5 per cent for x/D ≥2. The fully developed value agrees with the Dittus - Boelter correlation, Nu_(∞) = 0.021 Re^(0.8) Pr^(0.4) For the eigenvalues, λ^(2)_(n), and the associated constants, A_(n), correlations of the form λ^(2)_(n) =A_(1,n) Re^(-b_(1,n) + C_(1,n) Re^(-d_(1,n)) A_(n) = -A_(2,n) Re^(-b_(2,n) + C_(2,n) Re^(-d_(2,n)) are obtained. The coefficients and powers are presented in tabular form. Heat transfer data are presented, primarily for helium, for the low Reynolds number turbulent range. A one-quarter inch, resistively heated, vertical, circular tube was used for the study. The data cover an axial range from 1.2 to 96 diameters; wall-to-bulk temperature ratios vary from 1 to 1.4. In the low Reynolds number turbulent regime, these data clearly support the present analytical solution rather than the prediction obtained by applying the eddy diffusivity distribution used by Sparrow, Hallman, and Siegel.
Harold C. Reynolds, Jr.↗
Investigation of the influence of a step change in surface roughness on turbulent heat transfer
The use is studied of smooth heat flux gages on the otherwise very rough SSME fuel pump turbine blades. To gain insights into behavior of such installations, fluid mechanics and heat transfer data were collected and are reported for a turbulent boundary layer over a surface with a step change from a rough surface to a smooth surface. The first 0.9 m length of the flat plate test surface was roughened with 1.27 mm hemispheres in a staggered, uniform array spaced 2 base diameters apart. The remaining 1.5 m length was smooth. The effect of the alignment of the smooth surface with respect to the rough surface was also studied by conducting experiments with the smooth surface aligned with the bases or alternatively with the crests of the roughness elements. Stanton number distributions, skin friction distributions, and boundary layer profiles of temperature and velocity are reported and are compared to previous data for both all rough and all smooth wall cases. The experiments show that the step change from rough to smooth has a dramatic effect on the convective heat transfer. It is concluded that use of smooth heat flux gages on otherwise rough surfaces could cause large errors.
Taylor, Robert P.↗
Distributed Roughness Effects on Blunt-Body Transition and Turbulent Heating
An experimental program has been conducted to obtain data on the effects of surface roughness on blunt bodies at laminar, transitional, and turbulent conditions. Wind tunnel models with distributed surface roughness heights from 0.06 mm to 1.75 mm were tested and heating data were obtained using global surface thermography. Heating rates of up to 85% higher than predicted, smooth-surface turbulent levels were measured.
Hollis, Brian R.↗
Teleconnections, Midlatitude Cyclones and Aegean Sea Turbulent Heat Flux Variability on Daily Through Decadal Time Scales
We analyze daily wintertime cyclone variability in the central and eastern Mediterranean during 1958-2001, and identify four distinct cyclone states, corresponding to the presence or absence of cyclones in each basin. Each cyclone state is associated with wind flows that induce characteristic patterns of cooling via turbulent (sensible and latent) heat fluxes in the eastern Mediterranean basin and Aegean Sea. The relative frequency of occurrence of each state determines the heat loss from the Aegean Sea during that winter, with largest heat losses occurring when there is a storm in the eastern but not central Mediterranean (eNOTc), and the smallest occurring when there is a storm in the central but not eastern Mediterranean (cNOTe). Time series of daily cyclone states for each winter allow us to infer Aegean Sea cooling for winters prior to 1985, the earliest year for which we have daily heat flux observations. We show that cyclone states conducive to Aegean Sea convection occurred in 1991/1992 and 1992/1993, the winters during which deep water formation was observed in the Aegean Sea, and also during the mid-1970s and the winters of 1963/1964 and 1968/1969. We find that the eNOTc cyclone state is anticorrelated with the North Atlantic Oscillation (NAO) prior to 1977/1978. After 1977/1978, the cNOTe state is anticorrelated with both the NAO and the North Caspian Pattern (NCP), showing that the area of influence of large scale atmospheric teleconnections on regional cyclone activity shifted from the eastern to the central Mediterranean during the late 1970s. A trend toward more frequent occurrence of the positive phase of the NAO produced less frequent cNOTe states since the late 1970s, increasing the number of days with strong cooling of the Aegean Sea surface waters.
cyclones↗
Turbulent Heating in Collisionless Low-beta Plasmas: Imbalance, Landau Damping, and Electron–Ion Energy Partition
An understanding of how turbulent energy is partitioned between ions and electrons in weakly collisional plasmas is crucial for modeling many astrophysical systems. Using theory and simulations of a four-dimensional reduced model of low-beta gyrokinetics (the “Kinetic Reduced Electron Heating Model”), we investigate the dependence of collisionless heating processes on plasma beta and imbalance (normalized cross-helicity). These parameters are important because they control the helicity barrier, the formation of which divides the parameter space into two distinct regimes with remarkably different properties. In the first, at lower beta and/or imbalance, the absence of a helicity barrier allows the cascade of injected power to proceed to small (perpendicular) scales, but its slow cascade rate makes it susceptible to significant electron Landau damping, in some cases leading to a marked steepening of the magnetic spectra on scales above the ion Larmor radius. In the second, at higher beta and/or imbalance, the helicity barrier halts the cascade, confining electron Landau damping to scales above the steep “transition-range” spectral break, resulting in dominant ion heating. We formulate quantitative models of these processes that compare well to simulations in each regime, and combine them with results of previous studies to construct a simple formula for the electron–ion heating ratio as a function of beta and imbalance. This model predicts a “winner takes all” picture of low-beta plasma heating, where a small change in the fluctuations' properties at large scales (the imbalance) can cause a sudden switch between electron and ion heating.
Interplanetary turbulence↗
Turbulent heat transfer in a channel with two right-angled bends
A numerical study is reported on the flow and heat transfer in a channel with two right-angled bends. The k-epsilon turbulence model with a refined near-wall model is adopted for the computation of the flow field for step ratios ranging H/W = 1-4 and for Reynolds numbers Re = 3,000-10,000. The solution method of the governing transport equations is based on the modified hybrid scheme which produces very small truncation error. As a result of extensive computations, the complex flow patterns in the channel with two bends are clarified and the mechanisms of heat transfer are explained relating to the flow behaviors of separation, deflection, recirculation, and reattachment.
Amano, R. S.↗
Uniform distortion of a heated turbulent wake
Digital sampling and processing techniques are used to assess the effect of a uniform and constant strain rate on a slightly heated cylinder-generated wake which had undergone a prestrain development distance of 115 cylinder diameters. The wake is generated by a circular heating element (6.6-mm-diam cylinder) mounted horizontally in the center of a low-speed open return wind tunnel. The strain field is produced by a distortion duct oriented in such a way as to accentuate any periodic interface structure which might be present in the undistorted wake. Interface statistics are presented for both the undistorted (near) wake and the uniformly strained wake, and conditional (point) averages of the streamwise velocity and passive temperature fields of the strained wake. The results suggest that the interface thickness is fairly uniform along the back but decreases along the front with distance from the wake center.
Kawall, J. G.↗
A comparison of estimated and directly measured turbulent heat fluxes in the lower stratosphere
The contribution of small-scale motions to the vertical heat flux in the lower stratosphere is determined from wind and temperature fluctuation statistics obtained during the High Altitude Clear Air Turbulence investigation. Analysis of the cospectra suggests a horizontal wavelength of 3 km as the appropriate long-wave cutoff of small-scale motion. With this scale restriction, the measured vertical heat fluxes are in good agreement with the values of heat flux estimated by Lilly et al. (1974) from the kinetic energy dissipation rate. Hence, the hypothesis of Lilly et al. for estimating heat flux from the dissipation rate is considered to be reliable. It follows that, in the lower stratosphere, subsynoptic vertical transport is small compared to large-scale transport.
Heck, W.↗
A three-dimensional turbulent heat transfer analysis for advanced tubular rocket thrust chambers
Heat transfer was analyzed in the throat region of a plug and spool rocket engine for both smooth and corrugated walls. A three-dimensional, Navier-Stokes code was used for the analysis. The turbulence model in the code was modified to handle turbulence suppression in the crevice region of the corrugated wall. The overall heat transfer at the throat for the corrugated wall was 34 percent higher than it was for the smooth wall for comparable rocket flow conditions.
Kacynski, Kenneth J.↗
Analysis of turbulent heat transfer, mass transfer, and friction in smooth tubes at high Prandtl and Schmidt numbers
The expression for eddy diffusivity from a previous analysis was modified in order to account for the effect of kinematic viscosity on the turbulence in the region close to a wall. By using the modified expression, good agreement was obtained between predicted and experimental results for heat and mass transfer at Prandtl and Schmidt numbers between 0.5 and 3000. The effects of length-to-diameter ratio and of variable viscosity were also investigated for a wide range of Prandtl numbers.
Deissler, Robert G↗
A Three-Dimensional Turbulent Heat Transfer Analysis for Advanced Tubular Rocket Thrust Chambers
Heat transfer was analyzed in the throat region of a plug and spool rocket engine for both smooth and corrugated walls. A three-dimensional, Navier-Strokes code was used for the analysis. The turbulence model in the code was modified to handle turbulence suppression in the crevice region of the corrugated wall. Circumferential variations in the wall heat transfer was predicted for the corrugated wall. The overall heat transfer at the throat of the corrugated wall was 34 percent higher than it was for the smooth wall for comparable rocket flow conditions.
Kacynski, Kenneth J.↗
Laminar, Transitional, and Turbulent Heating on Mid Lift-to-Drag Ratio Entry Vehicles
The boundary-layer transition characteristics and convective aeroheating levels on mid lift-to-drag ratio entry vehicle configurations have been studied through wind-tunnel testing. Several configurations were investigated, including elliptically blunted cylinders with both circular and elliptically flattened cross sections, biconic geometries based on launch vehicle dual-use shrouds, and parametrically optimized analytic geometries. Vehicles of this class have been proposed for high-mass Mars missions, such as sample return and crewed exploration, for which the conventional sphere-cone entry-vehicle geometries of previous Mars missions are insufficient. Testing was conducted at Mach 6 over a range of Reynolds numbers sufficient to generate laminar, transitional, and turbulent flow. Transition onset locations, both straight-line and cross-flow, and heating rates were obtained through global phosphor thermography. Supporting computations were performed to obtain heating rates for comparison with the data. Laminar data and predictions agreed to well within the experimental uncertainty. Fully turbulent data and predictions also agreed well. However, in transitional flow regions, greater differences were observed.
Hollis, Brian R.↗
Laminar, Transitional, and Turbulent Heating on Mid Lift-to-Drag Ratio Entry Vehicles
The boundary-layer transition characteristics and convective aeroheating levels on mid lift-to-drag ratio entry vehicle configurations have been studied through wind tunnel testing. Several configurations were investigated, including elliptically-blunted cylinders with both circular and elliptically-flattened cross sections, biconic geometries based on launch vehicle dual-use shrouds, and parametrically-optimized analytic geometries. Vehicles of this class have been proposed for high-mass Mars missions, such as sample return and crewed exploration, for which the conventional sphere-cone entry-vehicle geometries of previous Mars missions are insufficient. Testing was conducted at Mach 6 over a range of Reynolds numbers sufficient to generate laminar, transitional, and turbulent flow. Transition onset locations - both straight-line and cross-flow - and heating rates were obtained through global phosphor thermography. Supporting computations were performed to obtain heating rates for comparison with the data. Laminar data and predictions agreed to well within the experimental uncertainty. Fully-turbulent data and predictions also agreed well. However, in transitional flow regions, greater differences were observed. Additional aerodynamic performance data were also generated through Modified-Newtonian analyses of the geometries.
Hollis, Brian R.↗
Turbulent heat and mass transfers across a thermally stratified air-water interface
Rates of heat and mass transfer across an air-water interface were measured in a wind-wave research facility, under various wind and thermal stability conditions (unless otherwise noted, mass refers to water vapor). Heat fluxes were obtained from both the eddy correlation and the profile method, under unstable, neutral, and stable conditions. Mass fluxes were obtained only under unstable stratification from the profile and global method. Under unstable conditions the turbulent Prandtl and Schmidt numbers remain fairly constant and equal to 0.74, whereas the rate of mass transfer varies linearly with bulk Richardson number. Under stable conditions the turbulent Prandtl number rises steadily to a value of 1.4 for a bulk Richardson number of about 0.016. Results of heat and mass transfer, expressed in the form of bulk aerodynamic coefficients with friction velocity as a parameter, are also compared with field data.
Papadimitrakis, Y. A.↗
Further Experiments on the Flow and Heat Transfer in a Heated Turbulent Air Jet
Measurements have been made of the mean total-head and temperature fields in a round turbulent jet with various initial temperatures. The results show that the jet spreads more rapidly as its density becomes lower than that of the receiving medium, even when the difference is not sufficiently great to cause measurable deviations from the constant-density, dimensionless, dynamic-pressure profile function. Rough analytical considerations have given the same relative spread. The effective "turbulent Prandtl number" for a section of the fully developed jet was found to be equal to the true (laminar) Prandtl number within the accuracy of measurement. (author)
FLOW - JETS↗
On the calculation of turbulent heat transport downstream from an abrupt pipe expansion
A numerical study of flow and heat transfer in the separated flow region produced by an abrupt pipe explosion is reported, with emphasis on the region in the immediate vicinity of the wall where turbulent transport gives way to molecular conduction and diffusion. The analysis is based on a modified TEACH-2E program with the standard k-epsilon model of turbulence. Predictions of the experimental data of Zemanick and Dougall (1970) for a diameter ratio of 0.54 show generally encouraging agreement with experiment. At a diameter ratio of 0.43 different trends are discernable between measurement and calculation, though this appears to be due to effects unconnected with the wall region studied here.
Chieng, C. C.↗