A New Nusselt Number for Complicated Configurations

Convective heat transfer over surfaces is generally presented in the form of the heat-transfer coefficient (h) or its nondimensional form, the Nusselt number (Nu). Both require the specification of the free-stream temperature (Too) or the bulk (Tb) temperature, which are clearly defined only for simple configurations. For complicated configurations with flow separation and multiple temperature streams, the physical significance of Too and Tb becomes unclear. In addition, their use could cause the local h to approach positive or negative infinity if Too or Tb is nearly the same as the local wall temperature (Twall). In this paper, a new Nusselt number, referred to as the SCS number, is proposed, that provides information on the local heat flux but does not use h and hence by-passes the need to define Too or Tb. CFD analysis based on steady RANS with the shear-stress transport model is used to compare and contrast the SCS number with Nu for two test problems: (1) compressible flow and heat transfer in a straight duct with a circular cross section and (2) compressible flow and heat transfer in a high-aspect ratio rectangular duct with a staggered array of pin fins. Parameters examined include: Reynolds number at the duct inlet (3,000 to 15,000 for the circular duct and 15,000 and 150,000 for the rectangular duct), wall temperature (Twall = 373 K to 1473 K for the circular duct and 313 K and 1,173 K for the rectangular duct), and distance from of the inlet of the duct (up to 100D for the circular duct and up to 156D for the rectangular duct). For the circular duct, Nu was found to decrease rapidly from the duct inlet until reaching a minimum and then to rise until reaching a nearly constant value in the “fully” developed region if the wall is heating the gas. If the wall is cooling the gas, then Nu has a constant positive slope in the “fully” developed region. The location of the minimum in Nu and where Nu becomes nearly constant in value or in slope are strong functions of Twall. For the SCS number, the decrease from the duct inlet is monotonic with a negative slope, whether the wall is heating or cooling the gas. Also, different SCS curves for different Twall approach each other as the distance from the inlet increases. For the rectangular duct, Nu tends to oscillate about a constant value in the pin-fin region, whereas SCS tends to oscillate about a line with a negative slope. For both test problems, the variation of SCS is not more complicated than Nu, but SCS yields the local heat flux without need for Tb, a parameter that is hard to define and measure for complicated problems.

A Parametric Numerical Study of the Effects of Freestream Turbulence Intensity and Length Scale on Anti-Vortex Film Cooling Design at High Blowing Ratio

An advanced, high-effectiveness film-cooling design, the anti-vortex hole (AVH) has been investigated by several research groups and shown to mitigate or counter the vorticity generated by conventional holes and increase film effectiveness at high blowing ratios and low freestream turbulence levels. [1, 2] The effects of increased turbulence on the AVH geometry were previously investigated and presented by researchers at West Virginia University (WVU), in collaboration with NASA, in a preliminary CFD study [3] on the film effectiveness and net heat flux reduction (NHFR) at high blowing ratio and elevated freestream turbulence levels for the adjacent AVH. The current paper presents the results of an extended numerical parametric study, which attempts to separate the effects of turbulence intensity and length-scale on film cooling effectiveness of the AVH. In the extended study, higher freestream turbulence intensity and larger scale cases were investigated with turbulence intensities of 5, 10 and 20% and length scales based on cooling hole diameter of Λx/dm = 1, 3 and 6. Increasing turbulence intensity was shown to increase the centerline, span-averaged and area-averaged adiabatic film cooling effectiveness. Larger turbulent length scales were shown to have little to no effect on the centerline, span-averaged and area-averaged adiabatic film-cooling effectiveness at lower turbulence levels, but slightly increased effect at the highest turbulence levels investigated.

A Validated Two-Phase Flow Large Eddy Simulation Methodology

A robust two-phase flow LES methodology is described, validated and applied to simulate primary breakup of a liquid jet injected into an airstream in either co-flow or cross-flow configuration. A Coupled Level Set and Volume of Fluid method is implemented for accurate capture of interface dynamics. Based on the local Level Set value, fluid density and viscosity fields are treated discontinuously across the interface. In order to cope with high density ratio, an extrapolated liquid velocity field is created and used for discretisation in the vicinity of the interface. Simulations of liquid jets discharged into higher speed airstreams with non-turbulent boundary conditions reveals the presence of regular surface waves. In practical configurations, both air and liquid flows are, however, likely to be turbulent. To account for inflowing turbulent eddies on the liquid jet interface primary breakup requires a methodology for creating physically correlated unsteady LES boundary conditions, which match experimental data as far as possible. The Rescaling/Recycling Method is implemented here to generate realistic turbulent inflows. It is found that liquid rather than gaseous eddies determine the initial interface shape, and the downstream turbulent liquid jet disintegrates much more chaotically than the non-turbulent one. When appropriate turbulent inflows are specified, the liquid jet behaviour in both co-flow and cross-flow configurations is correctly predicted by the current LES methodology, demonstrating its robustness and accuracy in dealing with high liquid/gas density ratio two-phase systems.

Modal Analysis of Inclined Jet Film Cooling Flows With Density Variation

Thermal and hydrodynamic flow field over a flat surface cooled with a single round inclined film cooling jet and fed by a plenum chamber is numerically investigated using Large Eddy Simulation (LES) and validated with published measurements. The calculations are done for a free stream Reynolds number Re = 16000, density ratio of coolant to free stream fluid ρj/ρ∞ = 2.0 and blowing ratio BR = ρjV/ρ∞V = 1.0. A short delivery tube with aspect ratio l/D = 1.75 and 35° inclination is considered. The evolution of the Kelvin-Helmholtz (K-H), hairpin and Counter-Rotating Vortex Pair (CVP) vortical structures are discussed to identify their origins. Modal analysis of the complete 3D flow and temperature field is carried out using a Dynamic Mode Decomposition (DMD) technique. The modal frequencies are identified, and the specific modal contribution towards the cooling wall temperature fluctuation is estimated on the film cooling wall. The low and intermediate frequency modes associated with streamwise and hairpin flow structures are found to have largest contribution (in-excess of 28%) towards wall temperature (or cooling effectiveness) fluctuations. The high frequency Kelvin-Helmholtz mode contributes towards initial mixing in the region of film cooling hole away from the wall. The individual modal temperature fluctuations on the wall and their corresponding hydrodynamic flow structures are presented and discussed.

Experimental Study of a Closed-Loop Thermosyphon Operating With Slurries of a Microencapsulated Phase-Change Material

An experimental investigation of steady, laminar, fluid flow and heat transfer in a vertical closed-loop thermosyphon operating with slurries of a microencapsulated phase-change material (MCPCM) suspended in distilled water is presented. The MCPCM particles consisted of a solid-liquid phase-change material (PCM) encapsulated in a thin polymer resin shell. Their effective diameter was in the range 0.5 to 12.5 micrometers, and had a mean value of 2.5 micrometers. The melting and freezing characteristics and the latent heat of fusion of the PCM were determined using a differential scanning calorimeter. The effective density of the MCPCM was measured, and the effective thermal conductivity of the slurries was determined using a published correlation. In the range of parameters considered, it was determined that the slurries exhibit non-Newtonian behavior. The closed-loop thermosyphon consisted of two vertical straight pipes, joined together by two vertical semi-circular 180-degree bends made of the same pipe. An essentially constant heat flux was imposed on a portion of one of the vertical pipes. The wall temperature of a portion of the other vertical pipe was maintained at a constant value. The outer surfaces of the entire thermosyphon were very well insulated. Calibrated thermocouples were used to measure the outer-wall-surface temperature at numerous points over the heated portion and the bulk temperature of the slurry at four different locations. A special procedure was formulated, benchmarked, and used to deduce the mass flow rate of the slurries in the thermosyphon. The investigation was conducted with slurries of MCPCM mass concentration 0% (pure distilled water), 7.471%, 9.997%, 12.49%, 14.95%, and 17.5%. The results are presented and discussed.

Heat Transfer Analysis of Two Pass Cooling Channel of Gas Turbine Blade With Analytical Wall Function Turbulence Approach

This paper reports experimental and computational studies of flow and heat transfer through a square duct with a sharp 180 degree turn. The main purpose of this research is to study flow and heat transfer predictions of the Analytical Wall-Function (AWF). To compare the predicting performance of the AWF, the standard Log-Law Wall-Function (LWF) and Low-Reynolds-number (LRN) k-ε model were applied. Their results were also compared with the experimental results for validation. In addition, three extended forms of the AWF were tested. Computational results showed better agreement with the experimental data, especially after the turn of the channel. It was also found that the wall-function (WF) models predicted more reasonable results as Reynolds number increased. The both wall-function models predicted similar results except for separation/reattachment regions where the LWF predicted lower Nusselt number than the other models.

A Numerical Model to Reduce Thermal Residual Stress During Cooling and Annealing Process of Large Optical Glass Production

Optical glass has been widely used in optical device manufacturing due to its high degree of physical and chemical homogeneity, which is considered as one of most important indicators of optical performance. Thermal stress during production has a significant impact on the optical homogeneity of the glass and it is primarily generated from temperature difference at different parts of the glass during annealing process which includes coarse and fine phases. Accumulation of thermal residual stress at early cooling stage will not only cause the cracking of the glass during process, but also affect the following fine annealing, especially, for the symmetric pattern of stress distribution. This paper focuses on mitigating of radiation influence and controlling cooling rate during coarse annealing in order to reduce thermal residual stress in the process. Numerical models are established to simulate the coarse process and investigate the homogeneity of temperature distribution at different conditions. Simulation results show that the coarse annealing process can be optimized through changing glass configuration and cooling rate.

Study of Deformation of Water-Cooled Laser Mirror Used in High Power Laser System

The transient thermal deformations of laser water-cooled mirror surface with minichannels have been numerically studied. The theoretical results show that fluid flow has a great influence on temperature distribution and thermal deformation. The maximum of temperature and thermal deformation appear in the downstream area, which is different from the previous research results. Meanwhile, experiments with different working conditions are conducted to validate the numerical simulation, and the numerical results agree well with the experimental data. The emulation method of thermal deformation of water-cooled mirror used in this study is proved to be effective research method.

The Effect of Upstream Thermal Boundary Condition on Convective Heat Transfer Coefficient on a Film-Cooled Flat Plate

The convection heat transfer coefficient on a film-cooled flat plate with and without upstream surface heating is investigated using liquid crystal thermography. The experiments were conducted with a turbulent boundary layer and low freestream turbulence at mass flux ratios of 0.5, 1.0, and 1.5 and density ratio of unity, using cylindrical holes at a 30° injection angle. Results show that upstream surface heating produces a lower convective heat transfer coefficient as expected, and the spanwise-averaged heat transfer enhancement factor is increased by up to 5% over approximately 60% of the film-cooled region. As blowing ratio increased, this area of increased enhancement factor moved further downstream of the holes.

Compact Gravity Driven and Capillary-Sized Thermosyphon Loop for Power Electronics Cooling

A novel two-phase thermosyphon based on automotive technology is presented as a valid solution for the cooling of power-electronic semiconductor modules. A horizontal evaporator configuration is investigated. This solution is based on a 90°-shaped thermosyphon that allows an optimal geometrical arrangement of the cooler with limited volume occupancy, reduced air pressure drop, and weight as well as optimal thermal performance compared to standard heat-sink technology. The 90°-shape refers to the mutual arrangement of the evaporator body and the condenser; which are in a horizontal and vertical position, respectively. The evaporator cools three power modules with a total power loss between 500 and 1500 W. Experimental results are presented for inlet air temperatures ranging from 20 to 50 °C and for different air volume flow rates between 200 and 400 m3/h. The working fluid is refrigerant R245fa. The maximum thermal resistance (cooler base to air) attained values between 40 and 50 K/kW.