Analytic solution for secondary flow with heat transfer in a square duct

1984 ◽  
Vol 5 (3) ◽  
pp. 167-177 ◽  
Author(s):  
M. Rahman ◽  
P. Colbourne
Keyword(s):  
Heat Transfer ◽  
Secondary Flow ◽  
Analytic Solution ◽  
Square Duct

scholarly journals Effects of Rotation on Transient Fluid Flow and Heat Transfer Through a Curved Square Duct: The Case of Negative Rotation

2021 ◽  
Vol 26 (4) ◽  
pp. 29-50
Author(s):  
Mohammad Sanjeed Hasan ◽  
Md. Tusher Mollah ◽  
Dipankar Kumar ◽  
Rabindra Nath Mondal ◽  
Giulio Lorenzini
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Secondary Flow ◽  
Flow Behavior ◽  
Square Duct ◽  
Curvature Effects ◽  
Flow And Heat Transfer ◽  
Curved Duct ◽  
Wide Range ◽  
Mechanical Devices

Abstract The fluid flow and heat transfer through a rotating curved duct has received much attention in recent years because of vast applications in mechanical devices. It is noticed that there occur two different types of rotations in a rotating curved duct such as positive and negative rotation. The positive rotation through the curved duct is widely investigated while the investigation on the negative rotation is rarely available. The paper investigates the influence of negative rotation for a wide range of Taylor number (−10 ≤ Tr ≤ −2500) when the duct itself rotates about the center of curvature. Due to the rotation, three types of forces including Coriolis, centrifugal, and buoyancy forces are generated. The study focuses and explains the combined effect of these forces on the fluid flow in details. First, the linear stability of the steady solution is performed. An unsteady solution is then obtained by time-evolution calculation and flow transition is determined by calculating phase space and power spectrum. When Tr is raised in the negative direction, the flow behavior shows different flow instabilities including steady-state, periodic, multi-periodic, and chaotic oscillations. Furthermore, the pattern variations of axial and secondary flow velocity and isotherms are obtained, and it is found that there is a strong interaction between the flow velocities and the isotherms. Then temperature gradients are calculated which show that the fluid mixing and the acts of secondary flow have a strong influence on heat transfer in the fluid. Diagrams of unsteady flow and vortex structure are further sketched and precisely elucidate the curvature effects on unsteady fluid flow. Finally, a comparison between the numerical and experimental data is discussed which demonstrates that both data coincide with each other.

Large Eddy Simulation of Flow and Heat Transfer in an Internal Cooling Duct With High Blockage Ratio 45° Staggered Ribs

2005 ◽  
Author(s):  
Aroon K. Viswanathan ◽  
Danesh K. Tafti ◽  
Samer Abdel-Wahab
Keyword(s):  
Heat Transfer ◽  
Secondary Flow ◽  
Flow Direction ◽  
Outer Wall ◽  
Internal Cooling ◽  
Square Duct ◽  
Square Channel ◽  
Heat Transfer Augmentation ◽  
Eddy Simulation ◽  
Numerical Predictions

Numerical predictions of a hydrodynamic and thermally developed turbulent flow are presented for a unit period of a stationary duct with square ribs aligned at 45° to the main flow direction. The rib height to channel hydraulic diameter (e/Dh) is 0.375 and the rib pitch to rib height (P/e) is 10. The domain under consideration is a rectangular passage of aspect ratio 1:2.5 with 45° ribs on the top and bottom walls arranged in a staggered fashion. The computations are carried out for a bulk Re of 27,000. The rib geometry introduces a strong secondary flow along the rib. A large helical vortex develops behind the rib which breaks down before it reaches the outer wall. This results in higher heat transfer at the inner wall as compared to the outer wall, which is in contrast to the trend observed in a square channel with low blockage ribs. In a square duct with low blockage ribs the secondary flow has two counter-rotating cells which do not change direction through the channel. However in this case only one rotating cell is observed in this case, which changes direction as it passes over successive ribs. The average friction and the heat transfer augmentation ratios are consistent with the experimental results [1], predicting values within 15% of the measured quantities.

Secondary Flow and Entropy Generation of Laminar Mixed Convection in the Entrance Region of a Horizontal Square Duct

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Y. Y. Huang ◽  
L. J. Zhang ◽  
G. Yang ◽  
J. Y. Wu
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Mixed Convection ◽  
Secondary Flow ◽  
Flow Structure ◽  
Entropy Generation ◽  
Entrance Region ◽  
Square Duct ◽  
Uniform Wall Temperature ◽  
Laminar Mixed Convection

The flow structure, heat transfer, and entropy generation characteristics in the entrance region of mixed convection under the effect of transverse buoyancy force are investigated numerically. Results are obtained for laminar flow of uniform inlet velocity and temperature through a square duct with uniform wall temperature. The buoyancy induced-secondary flow is observed in the entrance region where flow structure and heat transfer are significantly affected. The flow entrance region is extended by buoyancy, while the thermal entrance region is shortened. The developments of Nusselt number and local entropy generation are discussed in detail for Richardson numbers of 0 ≤ Ri ≤ 10, Reynolds number Re = 100 and Prandtl number Pr = 0.7. The total heat transfer rate and global entropy generation by friction increase with buoyancy, while global entropy generation by heat convection changes a little. The effect of Reynolds number on entropy generation is also discussed.

Detached Eddy Simulation of Flow and Heat Transfer in a Stationary Internal Cooling Duct With Skewed Ribs

2005 ◽  
Author(s):  
Aroon K. Viswanathan ◽  
Danesh K. Tafti
Keyword(s):  
Heat Transfer ◽  
Secondary Flow ◽  
Navier Stokes ◽  
Internal Cooling ◽  
Detached Eddy Simulation ◽  
Square Duct ◽  
Eddy Simulation ◽  
Flow And Heat Transfer ◽  
Numerical Predictions ◽  
Flow Features

Numerical predictions of a hydrodynamic and thermally developed turbulent flow for a unit period of a stationary duct using Detached Eddy Simulation (DES) and Unsteady Reynolds Averaged Navier-Stokes (URANS) are presented. The domain under consideration is a square duct with 45° ribs on the top and bottom walls arranged in a staggered fashion. Computations are carried out for a bulk Re of 47,000. The rib height to channel hydraulic diameter (e/Dh) is 0.1 and the rib pitch to rib height (P/e) is 10. DES is applied on two grids 80 × 80 × 80 and 128 × 80 × 80 and the initial results are compared with the experimental results and LES computations. Based on this the 128 × 80 × 80 grid is chosen for the comprehensive study. DES and URANS computations are carried out on the grid. The rib geometry introduces a strong secondary flow along the rib. The presence of the secondary flow introduces a spanwise variation in the heat transfer. DES predicts flow features and heat transfer distribution which is consistent with the experimental observations and LES computations. The average friction and the augmentation ratios predicted by DES also concur with the earlier observations.

Local Heat Transfer Measurements in Turbulent Flow Around a 180-deg Pipe Bend

1987 ◽  
Vol 109 (1) ◽  
pp. 43-48 ◽  
Author(s):  
J. W. Baughn ◽  
H. Iacovides ◽  
D. C. Jackson ◽  
B. E. Launder
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Turbulent Flow ◽  
Transfer Coefficient ◽  
Secondary Flow ◽  
Local Heat Transfer ◽  
Reynolds Numbers ◽  
Local Heat ◽  
Pipe Bend ◽  
Streamline Curvature

The paper reports extensive connective heat transfer data for turbulent flow of air around a U-bend with a ratio of bend radius:pipe diameter of 3.375:1. Experiments cover Reynolds numbers from 2 × 104 to 1.1 × 105. Measurements of local heat transfer coefficient are made at six stations and at five circumferential positions at each station. At Re = 6 × 104 a detailed mapping of the temperature field within the air is made at the same stations. The experiment duplicates the flow configuration for which Azzola and Humphrey [3] have recently reported laser-Doppler measurements of the mean and turbulent velocity field. The measurements show a strong augmentation of heat transfer coefficient on the outside of the bend and relatively low levels on the inside associated with the combined effects of secondary flow and the amplification/suppression of turbulent mixing by streamline curvature. The peak level of Nu occurs halfway around the bend at which position the heat transfer coefficient on the outside is about three times that on the inside. Another feature of interest is that a strongly nonuniform Nu persists six diameters downstream of the bend even though secondary flow and streamline curvature are negligible there. At the entry to the bend there are signs of partial laminarization on the inside of the bend, an effect that is more pronounced at lower Reynolds numbers.

Rotating Effect on Fluid Flow in a Smooth Duct With a 180-Deg Sharp Turn

2000 ◽  
Author(s):  
Chung-Chu Chen ◽  
Tong-Miin Liou
Keyword(s):  
Heat Transfer ◽  
Kinetic Energy ◽  
Secondary Flow ◽  
Turbulent Kinetic Energy ◽  
Turbine Blades ◽  
Outer Part ◽  
Intensity Level ◽  
Mean Velocity ◽  
High Heat Transfer ◽  
Sharp Turn

Laser-Doppler velocimetry (LDV) measurements are presented of turbulent flow in a two-pass square-sectioned duct simulating the coolant passages employed in gas turbine blades under rotating and non-rotating conditions. For all cases studied, the Reynolds number characterized by duct hydraulic diameter (Dh) and bulk mean velocity (Ub) was fixed at 1 × 104. The rotating case had a range of rotation number (Ro = ΩDh/Ub) from 0 to 0.2. It is found that both the skewness of streamwise mean velocity and magnitude of secondary-flow velocity increase linearly, and the magnitude of turbulence intensity level increases non-linearly with increasing Ro. As Ro is increased, the curvature induced symmetric Dean vortices in the turn for Ro = 0 is gradually dominated by a single vortex most of which impinges directly on the outer part of leading wall. The high turbulent kinetic energy is closely related to the dominant vortex prevailing inside the 180-deg sharp turn. For the first time, the measured flow characteristics account for the reported spanwise heat transfer distributions in the rotating channels, especially the high heat transfer enhancement on the leading wall in the turn. For both rotating and non-rotating cases, the direction and strength of the secondary flow with respect to the wall are the most important fluid dynamic factors affecting local heat transfer distributions inside a 180-deg sharp turn. The role of the turbulent kinetic energy in affecting the overall enhancement of heat transfer is well addressed.

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