Effect of Turbulent Prandtl Number on Convective Heat Transfer to Turbulent Flow of a Supercritical Fluid in a Vertical Round Tube

2011 ◽  
Vol 133 (7) ◽  
Author(s):  
Mahdi Mohseni ◽  
Majid Bazargan

A two-dimensional numerical model is developed to study the effect of the turbulent Prandtl number Prt on momentum and energy transport in a highly variable property flow of supercritical fluids in a vertical round tube. Both regimes of enhanced and deteriorated heat transfer have been investigated. The equations of the Prt leading to the best agreement with the experiments in either regime of heat transfer were specified. The results of this study show that the increase in the Prt causes the heat transfer coefficients to decrease. When the buoyancy force increases, a better agreement with the experimental data is reached if values lower than 0.9 are used for the Prt. A decrease in the Prt values results in an increase in turbulent activities. From the effect that the Prt has on heat transfer coefficients, it may be deduced that the buoyancy effects in the upward flow of a supercritical fluid lead to the decrease in the Prt value and hence to the increase in the heat transfer coefficients. Furthermore, the value of the Prt in the laminar viscous sublayer as expected does not have a significant effect on heat transfer rate. The effect of the turbulence model on the extent to which the Prt influences the rate of heat transfer is also examined. The results obtained are shown to be valid regardless of the turbulence model used.

1996 ◽  
Vol 118 (3) ◽  
pp. 562-569 ◽  
Author(s):  
G. K. Morris ◽  
S. V. Garimella ◽  
R. S. Amano

The local heat transfer coefficient distribution on a square heat source due to a normally impinging, axisymmetric, confined, and submerged liquid jet was computationally investigated. Numerical predictions were made for nozzle diameters of 3.18 and 6.35 mm at several nozzle-to-heat source spacings, with turbulent jet Reynolds numbers ranging from 8500 to 13,000. The commercial finite-volume code FLUENT was used to solve the thermal and flow fields using the standard high-Reynolds number k–ε turbulence model. The converged solution obtained from the code was refined using a post-processing program that incorporated several near-wall models. The role of four alternative turbulent Prandtl number functions on the predicted heat transfer coefficients was investigated. The predicted heat transfer coefficients were compared with previously obtained experimental measurements. The predicted stagnation and average heat transfer coefficients agree with experiments to within a maximum deviation of 16 and 20 percent, respectively. Reasons for the differences between the predicted and measured heat transfer coefficients are discussed.


Author(s):  
Majid Bazargan ◽  
Mahdi Mohseni

A two-dimensional model is developed to simultaneously solve the momentum and energy equations and thus predict convection heat transfer to an upward flow of supercritical carbon dioxide in a round tube. The effect of the turbulent Prandtl number, Prt, on heat transfer coefficients has been extensively studied. A number of constant values of Prt, as well as a number of suggested equations accounting for variations of Prt with flow conditions, have been examined. The investigation has been carried out for both regimes of enhanced and deteriorated heat transfer. The results of this study show that the increase of Prt, even in the viscous sublayer, cause the heat transfer coefficients to decrease. The models of Prt leading to best agreement with experiments in either regimes of heat transfer were recognized. From the effect Prt has on heat transfer coefficients, it has been deduced that the buoyancy effects in upward flow of a supercritical fluid causes the Prt to decrease and hence the heat transfer coefficients to increase.


Author(s):  
M. E. Taslim ◽  
A. Nongsaeng

Trailing edge cooling cavities in modern gas turbine airfoils play an important role in maintaining the trailing edge temperature at levels consistent with airfoil design life. In this study, local and average heat transfer coefficients were measured in a test section simulating the trailing edge cooling cavity of a turbine airfoil using the steady-state liquid crystal technique. The test rig was made up of two adjacent channels, each with a trapezoidal cross sectional area. The first channel, simulating the cooling cavity adjacent to the trailing-edge cavity, supplied the cooling air to the trailing-edge channel through a row of racetrack-shaped slots on the partition wall between the two channels. Eleven crossover jets, issued from these slots entered the trailing-edge channel and exited from a second row of race-track shaped slots on the opposite wall in staggered or inline arrangement. Two jet angles were examined. The baseline tests were for zero angle between the jet axis and the trailing-edge channel centerline. The jets were then tilted towards one wall (pressure or suction side) of the trailing-edge channel by five degrees. Results of the two set of tests for a range of local jet Reynolds number from 10,000 to 35,000 were compared. The numerical models contained the entire trailing-edge and supply channels with all slots to simulate exactly the tested geometries. They were meshed with all-hexa structured mesh of high near-wall concentration. A pressure-correction based, multi-block, multi-grid, unstructured/adaptive commercial software was used in this investigation. Standard high Reynolds number k–ε turbulence model in conjunction with the generalized wall function for most parts was used for turbulence closure. Boundary conditions identical to those of the experiments were applied and several turbulence model results were compared. The numerical analyses also provided the share of each cross-over and each exit hole from the total flow for different geometries. The major conclusions of this study were: a) except for the first and last cross-flow jets which had different flow structures, other jets produced the same heat transfer results on their target surfaces, b) jets tilted at an angle of 5 degrees produced higher heat transfer coefficients on the target surface. The tilted jets also produced the same level of heat transfer coefficients on the wall opposite the target wall and c) the numerical predictions of impingement heat transfer coefficients were in good agreement with the measured values for most cases thus CFD could be considered a viable tool in airfoil cooling circuit designs.


Author(s):  
Fifi N. M. Elwekeel ◽  
Qun Zheng ◽  
Antar M. M. Abdala

This study investigated heat transfer characteristics on various shaped ribs on the lower channel wall using steam and steam/mist as cooling fluid. The lower wall is subjected to a uniform heat flux condition while others walls are insulated. Calculations are carried out for ribs with square ribs (case A), triangular ribs (case B), trapezoidal ribs (case C) and (case D) cross sections over a range of Reynolds numbers (14000–35000), constant mist mass fraction (6%) and fixed rib height and pitch. To investigate turbulence model effects, computations based on a finite volume method, are carried out by utilizing three turbulence models: the standard k-ω, Omega Reynolds Stress (ωRS) and Shear Stress Transport (SST) turbulence models. The predicted results from using several turbulence models reveal that the SST turbulence model provide better agreement with available measurements than others. It is found that the heat transfer coefficients are enhanced in ribbed channels with injection of a small amount of mist. The steam/mist provides the higher heat transfer enhancement over steam when trapezoidal shaped ribs (38°, case C).


2011 ◽  
Vol 133 (4) ◽  
Author(s):  
M. E. Taslim ◽  
A. Nongsaeng

Trailing edge cooling cavities in modern gas turbine airfoils play an important role in maintaining the trailing-edge temperature at levels consistent with airfoil design life. In this study, local and average heat transfer coefficients were measured in a test section, simulating the trailing-edge cooling cavity of a turbine airfoil using the steady-state liquid crystal technique. The test rig was made up of two adjacent channels, each with a trapezoidal cross-sectional area. The first channel, simulating the cooling cavity adjacent to the trailing-edge cavity, supplied the cooling air to the trailing-edge channel through a row of racetrack-shaped slots on the partition wall between the two channels. Eleven crossover jets issued from these slots entered the trailing-edge channel and exited from a second row of race-track shaped slots on the opposite wall in staggered or inline arrangement. Two jet angles were examined. The baseline tests were for zero angle between the jet axis and the trailing-edge channel centerline. The jets were then tilted toward one wall (pressure or suction side) of the trailing-edge channel by 5 deg. Results of the two set of tests for a range of local jet Reynolds number from 10,000 to 35,000 were compared. The numerical models contained the entire trailing-edge and supply channels with all slots to simulate exactly the tested geometries. They were meshed with all-hexa structured mesh of high near-wall concentration. A pressure-correction based, multiblock, multigrid, unstructured/adaptive commercial software was used in this investigation. Standard high Reynolds number k−ε turbulence model in conjunction with the generalized wall function for most parts was used for turbulence closure. Boundary conditions identical to those of the experiments were applied and several turbulence model results were compared. The numerical analyses also provided the share of each cross-over and each exit hole from the total flow for different geometries. The major conclusions of this study were (a) except for the first and last cross-flow jets which had different flow structures, other jets produced the same heat transfer results on their target surfaces, (b) jets tilted at an angle of 5 deg produced higher heat transfer coefficients on the target surface. The tilted jets also produced the same level of heat transfer coefficients on the wall opposite the target wall, and (c) the numerical predictions of impingement heat transfer coefficients were in good agreement with the measured values for most cases; thus, computational fluid dynamics could be considered a viable tool in airfoil cooling circuit designs.


2013 ◽  
Vol 135 (5) ◽  
Author(s):  
M. E. Taslim ◽  
M. K. H. Fong

Local and average heat transfer coefficients were measured in a test section simulating a rib-roughened trailing edge cooling cavity of a turbine airfoil. The test rig was made up of two adjacent channels, each with a trapezoidal cross sectional area. The first channel, simulating the cooling cavity adjacent to the trailing-edge cavity, supplied the cooling air to the trailing-edge channel through a row of racetrack-shaped slots on the partition wall between the two channels. Eleven crossover jets, issued from these slots entered the trailing-edge channel, impinged on eleven radial ribs and exited from a second row of race-track shaped slots on the opposite wall in staggered or inline arrangement. Two jet angles of 0 deg and 5 deg and a range of jet Reynolds number from 10,000 to 35,000 were tested and compared. The numerical models contained the entire trailing-edge and supply channels with all slots and ribs to simulate exactly the tested geometries. They were meshed with all-hexa structured mesh of high near-wall concentration. A pressure-correction based, multiblock, multigrid, unstructured/adaptive commercial software was used in this investigation. The realizable k-ε turbulence model was employed in combination with an enhanced wall treatment approach for the near wall regions. Boundary conditions identical to those of the experiments were applied and several turbulence model results were compared. The numerical analyses also provided the share of each crossover and each exit hole from the total flow for different geometries. The major conclusions of this study were: (a) except for the first and last cross-flow jets, which had different flow structures, other jets produced the same heat transfer results on their target surfaces; (b) tilted crossover jets produced higher heat transfer coefficients on the target surface towards which they were tilted and lower values on the opposite surface, and (c) the numerical predictions of impingement heat transfer coefficients were in good agreement with the measured values for most cases thus CFD could be considered a viable tool in airfoil cooling circuit designs.


1960 ◽  
Vol 82 (2) ◽  
pp. 125-136 ◽  
Author(s):  
E. R. G. Eckert ◽  
T. F. Irvine

Friction factors have been measured for a duct whose cross section has the shape of an isosceles triangle with a side ratio 5 to 1 in the fully developed flow region for laminar, transitional, and turbulent conditions. In addition, local and average heat-transfer coefficients and the temperature field in the duct wall have been determined for the condition of constant heat generation per unit volume of the duct walls. Friction factors in laminar flow agreed well with analytical predictions. In the turbulent flow range they were by 20 per cent lower than values calculated from relations for a round tube with the use of the “hydraulic diameter.” Heat-transfer coefficients averaged over the circumference of the duct were only half as large as values calculated from round tube relations in the Reynolds number range from 4300 to 24,000. The measurements also revealed that thermal starting lengths were in excess of 100 diameters. In round tubes a length of 10 to 20 diameters has been found sufficient to develop the temperature field.


Author(s):  
M. E. Taslim ◽  
X. Huang

Hot and harsh environments, sometimes experienced by gas turbine airfoils, can create undesirable effects such as clogging of the cooling holes. Clogging of the cooling holes along the trailing edge of an airfoil on the tip side and its effects on the heat transfer coefficients in the cooling cavity around the clogged holes is the main focus of this investigation. Local and average heat transfer coefficients were measured in a test section simulating a rib-roughened trailing edge cooling cavity of a turbine airfoil. The rig was made up of two adjacent channels, each with a trapezoidal cross sectional area. The first channel supplied the cooling air to the trailing-edge channel through a row of racetrack-shaped slots on the partition wall between the two channels. Eleven cross-over jets, issued from these slots entered the trailing-edge channel, impinged on eleven radial ribs and exited from a second row of race-track shaped slots on the opposite wall that simulated the cooling holes along the trailing edge of the airfoil. Tests were run for the baseline case with all exit holes open and for cases in which 2, 3 and 4 exit holes on the airfoil tip side were clogged. All tests were run for two cross-over jet angles. The first set of tests were run for zero angle between the jet axis and the trailing-edge channel centerline. The jets were then tilted towards the ribs by five degrees. Results of the two set of tests for a range of jet Reynolds number from 10,000 to 35,000 were compared. The numerical models contained the entire trailing-edge and supply channels with all slots and ribs to simulate exactly the tested geometries. They were meshed with all-hexa structured mesh of high near-wall concentration. A pressure-correction based, multi-block, multi-grid, unstructured/adaptive commercial software was used in this investigation. The realizable k – ε turbulence model in combination with enhanced wall treatment approach for the near wall regions were used for turbulence closure. Boundary conditions identical to those of the experiments were applied and several turbulence model results were compared. The numerical analyses also provided the share of each cross-over and each exit hole from the total flow for different geometries. The major conclusions of this study were: a) Clogging of the exit holes near the airfoil tip alters the distribution of the coolant mass flow rate through the crossover holes and changes the flow structure. Depending on the number of clogged exit holes (from 3 to 6, out of 12), the tip-end crossover hole experienced from 35% to 49% reductions in its mass flow rate while the root-end crossover hole, under the same conditions, experienced an increase of the same magnitude in its mass flow rate, b) up to 64% reduction in heat transfer coefficients on the tip-end surface areas around the clogged holes were observed which might have devastating effects on the airfoil life. At the same time, a gain in heat transfer coefficient of up 40% was observed around the root-end due to increased crossover flows, c) Numerical heat transfer results with the use of the realizable k – ε turbulence model in combination with enhanced wall treatment approach for the near wall regions were generally in a reasonable agreement with the test results. The overall difference between the CFD and test results was about 10%.


1985 ◽  
Vol 107 (3) ◽  
pp. 570-574 ◽  
Author(s):  
R. S. Kane ◽  
R. Pfeffer

Heat transfer coefficients of air-glass, argon-glass, and argon-aluminum suspensions were measured in horizontal and vertical tubes. The glass, 21.6 and 36.0-μ-dia particles, was suspended at gas Reynolds numbers between 11,000 and 21,000 and loading ratios between 0 and 2.5. The presence of particles generally reduced the heat transfer coefficient. The circulation of aluminum powder in. the 0.870-in.-dia closed loop system produced tenacious deposits on protuberances into the stream. In the vertical test section, the Nusselt number reduction was attributed to viscous sublayer thickening; in the horizontal test section to particle deposition.


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