scholarly journals Theory of Heat Transfer in Straight Round Pipes with Square and Triangular Turbulators Under High Reynolds Criteria

2021 ◽  
Vol 5 (2) ◽  
Keyword(s):  
Heat Transfer ◽  
Shear Stress ◽  
Cross Section ◽  
Stress Transfer ◽  
Reynolds Numbers ◽  
Structured Grids ◽  
Reynolds Equations ◽  
Multi Scale ◽  
High Reynolds ◽  
Energy Equations

Objectives: To carry out mathematical modeling of the structure of vortex zones between periodic flow turbulators with a surface arrangement of triangular and square transverse profiles on the basis of multi-block computing technologies based on solutions of the Reynolds equations (closed by means of the Menter shear stress transfer model) and energy equations (on multi-scale intersecting structured grids) with high Reynolds criteria Re = 106 with an exhaustive analysis of the corresponding current lines. Method: The calculations were carried out on the basis of a theoretical method based on the solution of the Reynolds equations by the factorized finite-volume method, which are closed using the low-Reynolds model of the Menter shear stress transfer, and the energy equation on multi -scale intersecting structured grids (FCOM). Result: Mathematical simulations of the heat exchange process in straight and round pipes with turbulators with d / D = 0.95 ... 0.90 and t / D = 0.25 ... 1.00 square and triangular cross-sections at large Reynolds numbers (Re = 106) on a foundation with multi-block computing technologies, which are based on solutions of the Reynolds equations and energy equations in a finite-volume and factorized way. It is found that the relative intensification of heat transfer [(Nu / Nusm) | Re = 106] / [(Nu / Nusm) | Re = 105] in round pipes with square air turbulators for large Reynolds numbers (Re = 106), which may well be relevant in the channels used in heat exchangers, may be higher with a large-scale increment of hydraulic resistance than for slightly smaller numbers (Re = 105), for relatively high flow turbulators d / D = 0. 90 for the entire range under consideration for the parameter of the relative step between them t / D = 0.25 ... 1.00 a little more than 3%; for turbulators of triangular cross-section, similar indicators are approximately the same. For lower square turbulators with d / D = 0.95, this increase in relative heat transfer for large Reynolds numbers (Re = 106) compared to smaller numbers (Re = 105) does not exceed 6%; for triangular cross-section turbulators, similar indicators are slightly more than 4%. Conclusion: According to the results of calculations based on the developed model, it is possible to optimize the intensification of double turbulators, as well as to control the process of heat transfer intensification. It is shown that for higher square turbulators and at higher Reynolds numbers, a slight increase in the relative Nusselt number Nu / Nusm is accompanied by a significant increase in the relative hydraulic resistance due to the very significant influence of return currents, which can flow directly on the turbulator itself to the greater extent, the higher the Reynolds number; for triangular turbulators, the above trend persists and even deepens.

scholarly journals Theory of Heat Exchange in Pipes With Turbulators With d/D = 0.95 ÷ 0.90 And t/D = 0.25 ÷ 1.00, and Also in Rough Pipes, by Air With Great Reynold’s Numbers Re = 106

2020 ◽  
Vol 2 (4) ◽  
Author(s):  
Lobanov Igor Evgenjevich
Keyword(s):  
Heat Exchange ◽  
Cross Section ◽  
Energy Equation ◽  
Stress Transfer ◽  
Reynolds Numbers ◽  
Transfer Model ◽  
Computational Studies ◽  
Structured Grids ◽  
Multi Scale ◽  
Semicircular Cross Section

Mathematical modeling of heat exchange in air in pipes with turbulators with d / D = 0.95 ÷ 0.90 and t / D = 0.25 ÷ 1.00, as well as in rough pipes, with large Reynolds numbers (Re = 106). The solution of the heat exchange problem for semicircular cross-section flow turbulizers based on multi-block computing technologies based on the factorized Reynolds equations (closed using the Menter shear stress transfer model) and the energy equation (on multi-scale intersecting structured grids) was considered. This method was previously successfully applied and verified by experiment in [1-4] for lower Reynolds numbers. The article continues the computational studies initiated in [1-4,25-27].

scholarly journals MODELING HEAT EXCHANGE DEPENDING ON THE PRANDTL NUMBER FOR VARIOUS GEOMETRIC AND REGIME PARAMETERS

2020 ◽  
Vol 46 (4) ◽  
pp. 91-101
Author(s):  
I. E. Lobanov
Keyword(s):  
Heat Transfer ◽  
Shear Stress ◽  
Prandtl Number ◽  
Energy Equation ◽  
Transport Model ◽  
Reynolds Numbers ◽  
Structured Grids ◽  
Shear Stress Transport Model ◽  
Small Reynolds Numbers ◽  
Prandtl Numbers

Objectives. The aim is to study the dependency of the distribution of integral heat transfer during turbulent convective heat transfer in a pipe with a sequence of periodic protrusions of semicircular geometry on the Prandtl number using the calculation method based on a numerical solution of the system of Reynolds equations closed using the Menter’s shear stress transport model and the energy equation on different-sized intersecting structured grids.Method. A calculation was carried out on the basis of a theoretical method based on the solution of the Reynolds equations by factored finite-volume method closed with the help of the Menter shear stress transport model, as well as the energy equation on different-scaled intersecting structured grids (fast composite mesh method (FCOM)).Results. The calculations performed in the work showed that with an increase in the Prandtl number at small Reynolds numbers, there is an initial noticeable increase in the relative heat transfer. With additional increase in the Prandtl number, the relative heat transfer changes less: for small steps, it increases; for median steps it is almost stabilised, while for large steps it declines insignificantly. At large Reynolds numbers, the relative heat transfer decreases with an increase in the Prandtl number followed by its further stabilisation.Conclusion. The study analyses the calculated dependencies of the relative heat transfer on the Pr Prandtl number for various values of the relative h/D height of the turbulator, the relative t/D pitch between the turbulators and for various values of the Re Reynolds number. Qualitative and quantitative changes in calculated parameters are described all other things being equal. The analytical substantiation of the obtained calculation laws is that the height of the turbuliser is less for small Reynolds numbers, while for large Reynolds numbers, it is less than the height of the wall layer. Consequently, only the core of the flow is turbulised, which results in an increase in hydroresistance and a decrease in heat transfer. In the work on the basis of limited calculation material, a tangible decrease in the level of heat transfer intensification for small Prandtl numbers is theoretically confirmed. The obtained results of intensified heat transfer in the region of low Prandtl numbers substantiate the promising development of research in this direction. The theoretical data obtained in the work have determined the laws of relative heat transfer across a wide range of Prandtl numbers, including in those areas where experimental material does not currently exist. 

Numerical Prediction of Heat Transfer in a Channel With Ribs and Bleed

1997 ◽  
Author(s):  
David L. Rigby ◽  
E. Steinthorsson ◽  
A. A. Ameri
Keyword(s):  
Heat Transfer ◽  
Cross Section ◽  
Turbulence Model ◽  
Comparative Evaluation ◽  
Reynolds Numbers ◽  
Structured Grids ◽  
Complicated Geometries ◽  
Block Approach ◽  
Number Of Cells ◽  
Good Agreement

In the present work numerical simulations for flow in a straight channel with square cross section is presented. While three of the walls of the channel are smooth the remaining wall was simulated to possess a combination of ribs and bleed holes. To allow for a comparative evaluation of the said heat transfer promoters that same wall was also simulated with holes only; ribs only; or simply smooth. Reynolds numbers from 10,000 to 38,000 based on the hydraulic diameter were considered. Very general multi-block structured grids were used to allow good grid quality around ribs and into the holes, and also to minimize the number of cells required. Turbulence was accounted for by a k-ω turbulence model which does not require reference to distance to a wall. Good agreement with experimental results demonstrate that the structured multi-block approach with the k-ω turbulence model is efficient and viable even for very complicated geometries.

An Experimental and Numerical Study of Heat Transfer and Pressure Loss in a Rectangular Channel With V-Shaped Ribs

2006 ◽  
Author(s):  
Michael Maurer ◽  
Jens von Wolfersdorf ◽  
Michael Gritsch
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Enhancement ◽  
Thermal Performance ◽  
Pressure Loss ◽  
Numerical Study ◽  
Rectangular Channel ◽  
Reynolds Numbers ◽  
Transfer Enhancement ◽  
High Reynolds Numbers ◽  
High Reynolds

An experimental and numerical study was conducted to determine the thermal performance of V-shaped ribs in a rectangular channel with an aspect ratio of 2:1. Local heat transfer coefficients were measured using the steady state thermochromic liquid crystal technique. Periodic pressure losses were obtained with pressure taps along the smooth channel sidewall. Reynolds numbers from 95,000 to 500,000 were investigated with V-shaped ribs located on one side or on both sides of the test channel. The rib height-to-hydraulic diameter ratios (e/Dh) were 0.0625 and 0.02, and the rib pitch-to-height ratio (P/e) was 10. In addition, all test cases were investigated numerically. The commercial software FLUENT™ was used with a two-layer k-ε turbulence model. Numerically and experimentally obtained data were compared. It was determined that the heat transfer enhancement based on the heat transfer of a smooth wall levels off for Reynolds numbers over 200,000. The introduction of a second ribbed sidewall slightly increased the heat transfer enhancement whereas the pressure penalty was approximately doubled. Diminishing the rib height at high Reynolds numbers had the disadvantage of a slightly decreased heat transfer enhancement, but benefits in a significantly reduced pressure loss. At high Reynolds numbers small-scale ribs in a one-sided ribbed channel were shown to have the best thermal performance.

Heat Transfer and Pressure Drop Correlations for Square Channels With 45 Deg Ribs at High Reynolds Numbers

2009 ◽  
Vol 131 (7) ◽  
Author(s):  
Akhilesh P. Rallabandi ◽  
Huitao Yang ◽  
Je-Chin Han
Keyword(s):  
Heat Transfer ◽  
Local Heat Transfer ◽  
Reynolds Numbers ◽  
Local Heat ◽  
Transfer Coefficients ◽  
Turbine Blade Cooling ◽  
Square Channel ◽  
Heat Transfer Coefficients ◽  
High Reynolds ◽  
Cooling Passage

Systematic experiments are conducted to measure heat transfer enhancement and pressure loss characteristics on a square channel (simulating a gas turbine blade cooling passage) with two opposite surfaces roughened by 45 deg parallel ribs. Copper plates fitted with a silicone heater and instrumented with thermocouples are used to measure regionally averaged local heat transfer coefficients. Reynolds numbers studied in the channel range from 30,000 to 400,000. The rib height (e) to hydraulic diameter (D) ratio ranges from 0.1 to 0.18. The rib spacing (p) to height ratio (p/e) ranges from 5 to 10. Results show higher heat transfer coefficients at smaller values of p/e and larger values of e/D, though at the cost of higher friction losses. Results also indicate that the thermal performance of the ribbed channel falls with increasing Reynolds numbers. Correlations predicting Nusselt number (Nu) and friction factor (f¯) as a function of p/e, e/D, and Re are developed. Also developed are correlations for R and G (friction and heat transfer roughness functions, respectively) as a function of the roughness Reynolds number (e+), p/e, and e/D.

Comparisons of Pins/Dimples/Protrusions Cooling Concepts for a Turbine Blade Tip-Wall at High Reynolds Numbers

2010 ◽  
Author(s):  
Gongnan Xie ◽  
Bengt Sunde´n ◽  
Weihong Zhang
Keyword(s):  
Heat Transfer ◽  
Turbine Blade ◽  
Computational Models ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Gas Leakage ◽  
Leakage Flows ◽  
Blade Tip ◽  
High Reynolds ◽  
The Cost

The blade tip region encounters high thermal loads because of the hot gas leakage flows, and it must therefore be cooled to ensure a long durability and safe operation. A common way to cool a blade tip is to design serpentine passages with 180° turn under the blade tip-cap inside the turbine blade. Improved internal convective cooling is therefore required to increase blade tip lifetime. Pins, dimples and protrusions are well recognized as effective devices to augment heat transfer in various applications. In this paper, enhanced heat transfer of an internal blade tip-wall has been predicted numerically. The computational models consist of a two-pass channel with 180° turn and arrays of circular pins or hemispherical dimples or protrusions internally mounted on the tip-wall. Inlet Reynolds numbers are ranging from 100,000 to 600,000. The overall performance of the two-pass channels is evaluated. Numerical results show that the heat transfer enhancement of the pinned tip is up to a factor of 3.0 higher than that of a smooth tip while the dimpled-tip and protruded-tip provide about 2.0 times higher heat transfer. These augmentations are achieved at the cost of an increase of pressure drop by less than 10%. By comparing the present cooling concepts with pins, dimples and protrusions, it is shown that the pinned-tip exhibit best performance to improve the blade tip cooling. However, when disregarding the added active area and considering the added mechanical stress, it is suggested that the usage of dimples is more suitable to enhance blade tip cooling, especially at low Reynolds numbers.

scholarly journals CONSTRUCTAL DESIGN OF FINS IN COOLED CAVITIES BY NON-NEWTONIAN FLUIDS

2019 ◽  
Vol 18 (1) ◽  
pp. 85
Author(s):  
J. F. Bueno ◽  
A. R. S. Silva ◽  
T. A. Hirt ◽  
G. F. C. Bogo ◽  
F. S. F. Zinani ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Aspect Ratio ◽  
Newtonian Fluids ◽  
Rheological Parameters ◽  
Flow Index ◽  
Pseudoplastic Fluid ◽  
High Reynolds ◽  
Energy Equations ◽  
Rayleigh Numbers

The present work investigates the Construtal Design of fins inserted in cavities submitted to mixed convection by non-Newtonian fluids. The objective is to obtain the optimum aspect ratio for the fin considering different flow conditions and variations in the rheological parameters of the fluid. The phenomena of flow and heat transfer are modeled by mass balance, momentum and energy equations, and by the generalized Newtonian liquid constitutive equation. The viscosity is modeled as that of a pseudoplastic fluid, using the Carreau function. The optimization problem consists in maximizing heat transfer from the fin using the average Nusselt number. The investigated project variable is the aspect ratio between the edges of the rectangular plane fin profile. The restrictions are the volume of the cavity and the fin. The results are obtained numerically using a finite volume code and a two-dimensional geometry, through exhaustive searching. The results show that the fin geometry influences the maximum Nusselt number mainly for the cases with high Reynolds and Rayleigh numbers, such as was shown in previous studies. The results show that the fin geometry influences the maximum Nusselt number mainly for the cases with high Reynolds and Rayleigh numbers, as was shown in previous studies. It was also found that the Nusselt number increases as the increase in flow intensity, represented by the parameter p, and that the result of the maximum Nusselt number does not change monotonically with the non-Newtonian dimensionless viscosity and with the flow index, showing that the pseudoplasticity of the fluid implies optimal configurations very different from those predicted for Newtonian fluids.

Temperature Control of Blow-Down, Supersonic Tunnels

1956 ◽  
Vol 60 (541) ◽  
pp. 67-70
Author(s):  
T. A. Thomson
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Mach Number ◽  
Reynolds Numbers ◽  
Stagnation Temperature ◽  
Blow Down ◽  
High Reynolds Numbers ◽  
Experimental Errors ◽  
High Reynolds

The blow-down type of intermittent, supersonic tunnel is attractive because of its simplicity and because relatively high Reynolds numbers can be obtained for a given size of test section. An adverse characteristic, however, is the fall of stagnation temperature during runs, which can affect experiments in several ways. The Reynolds number varies and the absolute velocity is not constant, even if the Mach number and pressure are; heat-transfer cannot be studied under controlled conditions and the experimental errors arising from the effect of heat-transfer on the boundary layer vary in time. These effects can become significant in quantitative experiments if the tunnel is large and the variation of temperature very rapid; the expense required to eliminate them might then be justified.

Correlated Compressible and Incompressible Channel Flows

1997 ◽  
Vol 119 (4) ◽  
pp. 911-915 ◽  
Author(s):  
C. Crnojevic´ ◽  
V. D. Djordjevic´
Keyword(s):  
Cross Section ◽  
High Reynolds Number ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Isothermal Flow ◽  
Governing Equations ◽  
Adiabatic Flow ◽  
High Reynolds Numbers ◽  
High Reynolds ◽  
Reynolds Number Flows

Compressible flow in channels of slowly varying cross section at moderately high Reynolds numbers is treated in the paper by employing some Stewartson-type transformations that convert the problem into an incompressible one. Both adiabatic flow and isothermal flow are considered, and a Poiseuille-type incompressible solution is mapped onto compressible plane in order to generate some exact solutions of the compressible governing equations. The results show striking effects that viscosity may have upon the flow characteristics in this case, in comparison with more conventional high Reynolds number flows.

Investigation of Buoyancy Effects on Heat Transfer Characteristics of Supercritical Carbon Dioxide in Heating Mode

2015 ◽  
Vol 1 (3) ◽  
Author(s):  
Sandeep R. Pidaparti ◽  
Jacob A. McFarland ◽  
Mark M. Mikhaeil ◽  
Mark H. Anderson ◽  
Devesh Ranjan
Keyword(s):  
Heat Transfer ◽  
Carbon Dioxide ◽  
Shear Stress ◽  
Wall Temperature ◽  
Reynolds Numbers ◽  
Turbulent Shear ◽  
Heat Transfer Characteristics ◽  
Transfer Characteristics ◽  
Turbulent Shear Stress ◽  
Heating Mode

Experiments were performed to investigate the effects of buoyancy on heat transfer characteristics of supercritical carbon dioxide in heating mode. Turbulent flows with Reynolds numbers up to 60,000, at operating pressures of 7.5, 8.1, and 10.2 MPa, were tested in a round tube. Local heat transfer coefficients were obtained from measured wall temperatures over a large set of experimental parameters that varied inlet temperature from 20 to 55°C, mass flux from 150 to 350  kg/m2s, and a maximum heat flux of 65  kW/m2. Horizontal, upward, and downward flows were tested to investigate the unusual heat transfer characteristics due to the effect of buoyancy and flow acceleration caused by large variation in density. In the case of upward flow, severe localized deterioration in heat transfer was observed due to reduction in the turbulent shear stress and is characterized by a sharp increase in wall temperature. In the case of downward flow, turbulent shear stress is enhanced by buoyancy forces, leading to an enhancement in heat transfer. In the case of horizontal flow, flow stratification occurred, leading to a circumferential variation in wall temperature. Thermocouples mounted 180° apart on the tube revealed that the wall temperatures on the top side are significantly higher than the bottom side of the tube. Buoyancy factor calculations for all the test cases indicated that buoyancy effects cannot be ignored even for horizontal flow at Reynolds numbers as high as 20,000. Experimentally determined Nusselt numbers are compared to existing correlations available in the literature. Existing correlations predicted the experimental data within ±30%, with maximum deviation around the pseudocritical point.

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