Thermal Boundary Layer Profiles Research Articles

Comparison between two- and three-dimensional Rayleigh–Bénard convection

AbstractTwo-dimensional and three-dimensional Rayleigh–Bénard convection is compared using results from direct numerical simulations and previous experiments. The phase diagrams for both cases are reviewed. The differences and similarities between two- and three-dimensional convection are studied using $Nu(Ra)$ for $\mathit{Pr}= 4. 38$ and $\mathit{Pr}= 0. 7$ and $Nu(Pr)$ for $Ra$ up to $1{0}^{8} $. In the $Nu(Ra)$ scaling at higher $Pr$, two- and three-dimensional convection is very similar, differing only by a constant factor up to $\mathit{Ra}= 1{0}^{10} $. In contrast, the difference is large at lower $Pr$, due to the strong roll state dependence of $Nu$ in two dimensions. The behaviour of $Nu(Pr)$ is similar in two and three dimensions at large $Pr$. However, it differs significantly around $\mathit{Pr}= 1$. The Reynolds number values are consistently higher in two dimensions and additionally converge at large $Pr$. Finally, the thermal boundary layer profiles are compared in two and three dimensions.

Numerical Base Heating Sensitivity Study for a Four-Rocket Engine Core Configuration

In support of launch vehicle plume-induced base heating and pressure prediction efforts using the Loci-CHEM Navier–Stokes computational fluid dynamics solver, numerical simulations of a wind-tunnel test have been modeled and analyzed. This missile forebody test article is composed of four JP-4/LOX 500 lbf water-cooled rocket engines exhausting into a Mach 2–3.5 wind tunnel at various freestream pressure conditions. This study explores the base heating sensitivity for varying boundary conditions and various chemistry, turbulence, and thermodynamic models. The numerical solutions have been investigated at two freestream pressure conditions: (simulated low altitude) and (simulated high altitude). It is observed that the convective base heat flux and base temperature are most sensitive to the nozzle inner wall thermal boundary-layer profile, which is dependent on the wall temperature, boundary layer’s specific energy, jet expansion ratio, and chemical reactions. Recovery shock and wall jet dynamics and afterburning within the updraft plume also significantly influence convective base heating. Turbulence modeling shows less sensitivity to base heating characteristics. Base heating rates are validated for the highest-fidelity predictions, which show an agreement within with respect to test data.

Thermal and viscous boundary layers in turbulent Rayleigh–Bénard convection

AbstractWe present the results from numerical simulations of turbulent Rayleigh–Bénard convection for an aspect ratio (diameter/height) of 1.0, Prandtl numbers of 0.4 and 0.7, and Rayleigh numbers from $1\ensuremath{\times} 1{0}^{5} $ to $1\ensuremath{\times} 1{0}^{9} $. Detailed measurements of the thermal and viscous boundary layer profiles are made and compared to experimental and theoretical (Prandtl–Blasius) results. We find that the thermal boundary layer profiles disagree by more than 10 % when scaled with the similarity variable (boundary layer thickness) and likewise disagree with the Prandtl–Blasius results. In contrast, the viscous boundary profiles collapse well and do agree (within 10 %) with the Prandtl–Blasius profile, but with worsening agreement as the Rayleigh number increases. We have also investigated the scaling of the boundary layer thicknesses with Rayleigh number, and again compare to experiments and theory. We find that the scaling laws are very robust with respect to method of analysis and they mostly agree with the Grossmann–Lohse predictions coupled with laminar boundary layer theory within our numerical uncertainty.

Thermal boundary layer profiles in turbulent Rayleigh-Bénard convection in a cylindrical sample

We numerically investigate the structures of the near-plate temperature profiles close to the bottom and top plates of turbulent Rayleigh-Bénard flow in a cylindrical sample at Rayleigh numbers Ra = 10(8) to Ra = 2 × 10(12) and Prandtl numbers Pr = 6.4 and Pr = 0.7 with the dynamical frame method [Zhou and Xia, Phys. Rev. Lett. 104, 104301 (2010)], thus extending previous results for quasi-two-dimensional systems to three-dimensional systems. The dynamical frame method shows that the measured temperature profiles in the spatially and temporally local frame are much closer to the temperature profile of a laminar, zero-pressure gradient boundary layer (BL) according to Pohlhausen than in the fixed reference frame. The deviation between the measured profiles in the dynamical reference frame and the laminar profiles increases with decreasing Pr, where the thermal BL is more exposed to the bulk fluctuations due to the thinner kinetic BL, and increasing Ra, where more plumes are passing the measurement location.

Protuberances in a Turbulent Thermal Boundary Layer

Recent efforts to evaluate the effects of isolated protuberances within velocity and thermal boundary layers have been performed using transient heat transfer approaches. While these approaches provide accurate and highly resolved measurements of surface flux, measuring the state of the thermal boundary layer during transient tests with high spatial resolution presents several challenges. As such, the heat transfer enhancement evaluated during transient tests is presently correlated to a Reynolds number based either on the distance from the leading edge or on the momentum thickness. Heat flux and temperature variations along the surface of a turbine blade may cause significant differences between the shapes and sizes of the velocity and thermal boundary layer profiles. Therefore, correlations are needed which relate the states of both the velocity and thermal boundary layers to protuberance and roughness distribution heat transfer. In this study, a series of three experiments are performed for various freestream velocities to investigate the local temperature details of protuberances interacting with thermal boundary layers. The experimental measurements are performed using isolated protuberances of varying thermal conductivity on a steadily heated, constant flux flat plate. In the first experiment, detailed surface temperature maps are recorded using infrared thermography. In the second experiment, the unperturbed velocity profile over the plate without heating is measured using hot-wire anemometry. Finally, the thermal boundary layer over the steadily heated plate is measured using a thermocouple probe. Because of the constant flux experimental configuration, the protuberances provide negligible heat flux augmentation. Consequently, the variation in protuberance temperature is investigated using the velocity boundary layer parameters, the thermal boundary layer parameters, and the local fluid temperature at the protuberance apices. A comparison of results using plastic and steel protuberances illuminates the importance of the shape of the thermal and velocity boundary layers in determining the minimum protuberance temperatures.

Radial boundary layer structure and Nusselt number in Rayleigh–Bénard convection

Results from direct numerical simulation (DNS) for three-dimensional Rayleigh–Bénard convection in a cylindrical cell of aspect ratio 1/2 and Prandtl number Pr=0.7 are presented. They span five decades of Rayleigh number Ra from 2 × 106 to 2 × 1011. The results are in good agreement with the experimental data of Niemela et al. (Nature, vol. 404, 2000, p. 837). Previous DNS results from Amati et al. (Phys. Fluids, vol. 17, 2005, paper no. 121701) showed a heat transfer that was up to 30% higher than the experimental values. The simulations presented in this paper are performed with a much higher resolution to properly resolve the plume dynamics. We find that in under-resolved simulations the hot (cold) plumes travel further from the bottom (top) plate than in the better-resolved ones, because of insufficient thermal dissipation mainly close to the sidewall (where the grid cells are largest), and therefore the Nusselt number in under-resolved simulations is overestimated. Furthermore, we compare the best resolved thermal boundary layer profile with the Prandtl–Blasius profile. We find that the boundary layer profile is closer to the Prandtl–Blasius profile at the cylinder axis than close to the sidewall, because of rising plumes close to the sidewall.

Boundary layer and scaling properties in turbulent thermal convection

We describe an experiment which has been designed to measure both spatial and temporal features of turbulent thermal convection in a fluid layer heated from below. Specifically we have studied the dependence of the heat flowvs. the Rayleigh number, the thermal boundary layer profile, the temperature probability distribution function, the frequency and wave number power spectra. All the results have been compared with recent theories. The relevant scales of the problem, the Bolgiano and dissipative lengths, are also computed as a function of control parameters.

Parietal heat flux measurement in a nitrogen plasma jet

The local measurement of the net heat flux exchanged between a low-pressure plasma jet and a plate set along its flow direction is described. Manufactured and inserted in this plate are several flux gauges which have been calibrated by an original method based on the radial steepness of a Gaussian laser beam. These experimental results, when compared with information drawn from thermal boundary layer profiles, show the importance of the recombination term in the parietal energy equation.

Measurement of thermal conduction within a large fresh water ice block being towed in sea water

Large blocks (2500 kg) of fresh water ice were towed in sea water at speeds of approximately one knot. Thermocouples were frozen into the ice. The temperature profile was measured within the ablating ice block as a function of time and distance from the ice/water interface. A temperature gradient in the ice of 14.5°C/cm was found at the ice/water interface. A theory was developed which calculates the temperature within the ice in good agreement with measured values; agreement was usually to within a fraction of a degree Celsius. The thermal boundary layer was measured under turbulent flow conditions. At the ice/water interface, an average temperature gradient in the water of 62.9°C/cm was measured in one test. Using the measured temperature gradients and measured regréssion rates, an energy balance was calculated for the ice/water interface. The energies balanced within 0.3 per cent. A significant contribution of this paper is a set of thermal boundary layer profiles. The measurements are extremely valuable to theoreticians who want to model the problem of melting ice.

A Theoretical Investigation of Heat Transfer in the Laminar Flow Regions of Airfoils

An analysis is presented of the thermal boundary layer about a certain infinite cylinder having a chordwise pressure gradient. An incompressible fluid of Prandtl Number equal to unity is considered. The thermal boundary-layer profiles are obtained at various chordwise stations and are shown to differ appreciably from the existing velocity boundary-layer profiles. The method of solution is analogous to tha t used by Sears in calculating the spanwise flow in the boundary layer of a yawed infinite cylinder. Although use of this method is not feasible for an arbitrary cylinder, it presents a case in which the results of more approximate methods may be evaluated. Consequently, the heat transfer from the cylinder is calculated by several commonly used methods and is compared to the more exact solution. The results indicate that , of several available approximate methods applicable to the estimation of heat transfer in this case, only the one proposed by Squire gives good agreement with the more exact results. I N T R O D U C T I O N T PROBLEM OF theoretically calculating the thermal boundary-layer profiles, about an arbitrary airfoil having a chordwise pressure gradient, is at present too complicated for a rigorous solution. Therefore, in order to solve the dependent problem of heat transfer from an airfoil, various simplifying assumptions have been made as to the shape of the thermal layer. Consequently, several approximate methods are now available for calculating the heat transfer from an arbitrary airfoil. It was noted that the equation for the spanwise velocity component in a steady, incompressible flow over a yawed infinite cylinder is identical to the equation for the temperature distribution in a steady two-dimensional laminar boundary-layer flow, provided that the Prandtl Number is unity and the viscous heating is neglected. Therefore, the distribution of spanwise velocity near a yawed cylinder is the same as the distribution of temperature when the cylinder surface is maintained at a uniform temperature different from the stream temperature. Sears presented a rigorous solution to the spanwise velocity gradient distribution Received December 7, 1949. * An abstract of a thesis submitted in partial fulfillment of the requirements for the degree of M.Aero.E. in the Graduate School of Aeronautical Engineering, Cornell University, 1948. t Now, Associate Research Engineer, Cornell Aeronautical Laboratory, Inc. about a certain infinite yawed cylinder. Consequently, this solution is used here to obtain the thermal boundary-layer profiles about the same cylinder. These profiles are then used as a basis to evaluate the various simplifying assumptions made in the above references.