Turbulent Pipe Flow of an Internally Heat Generating Fluid

1966 ◽  
Vol 88 (3) ◽  
pp. 314-321 ◽  
Author(s):  
R. B. Kinney ◽  
E. M. Sparrow
Keyword(s):  
Heat Transfer ◽  
Satisfactory Agreement ◽  
Reynolds Numbers ◽  
Turbulent Heat Transfer ◽  
Working Fluid ◽  
Bulk Temperature ◽  
Chloride Salt ◽  
Turbulent Regime ◽  
Number Range ◽  
Prandtl Numbers

Experimental measurements, supported by analysis, were performed to determine the heat-transfer characteristics of an internally heat generating fluid in the fully turbulent regime. Heat was generated uniformly within the flow by electrical dissipation, the working fluid being an aqueous solution of sodium chloride salt. Measurements were made of the fully developed wall-to-bulk temperature differences for flow in an adiabatic pipe; data were also collected in the thermal entrance region. The Reynolds numbers and the Prandtl numbers, respectively, ranged from 10,000 to 80,000 and from 3 to 4. The small wall-to-bulk temperature differences (between 1 and 2 deg F) necessitated special care and instrumentation beyond that required in conventional turbulent heat-transfer measurements. The fully developed wall-to-bulk temperature differences were in very satisfactory agreement with the analytical calculations. The consistent scatter in the data was no more than ±7 percent over the entire Reynolds number range. The analytical solutions were found to be very sensitive to the choice of the eddy diffusivity for heat. The assumption of equal diffusivities for heat and momentum led to the most satisfactory agreement between the experimental and analytical results. Additional numerical results are presented which include fluids with Prandtl numbers ranging from 1 to 100 for Reynolds numbers from 10,000 to 150,000.

Effect of Plenum Length and Diameter on Turbulent Heat Transfer in a Downstream Tube and on Plenum-Related Pressure Losses

1981 ◽  
Vol 103 (3) ◽  
pp. 415-422 ◽  
Author(s):  
S. C. Lau ◽  
E. M. Sparrow ◽  
J. W. Ramsey
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Pressure Loss ◽  
Reynolds Numbers ◽  
Turbulent Heat Transfer ◽  
Working Fluid ◽  
Turbulent Heat ◽  
Turbulent Regime ◽  
Transfer Coefficients ◽  
Pressure Loss Coefficient

A systematic experimental study was carried out to determine how the heat transfer characteristics of a turbulent tube flow are affected by the length and diameter of a cylindrical plenum chamber which delivers fluid to the tube. The net pressure loss due to the presence of the plenum was also measured. The experimental arrangement was such that the fluid experiences a consecutive expansion and contraction in the plenum before entering the electrically heated test section. Air was the working fluid, and the Reynolds number was varied over the range from 5,000 to 60,000. It was found that at axial stations in the upstream portion of the tube, there are substantially higher heat transfer coefficients in the presence of longer plenums. Thus, a longer plenum functions as an enhancement device. On the other hand, the plenum diameter appears to have only a minor influence in the range investigated (i.e., plenum diameters equal to three and six times the tube diameter). The fully developed Nusselt numbers are independent of the plenum length and diameter. With longer plenums in place, the thermal entrance length showed increased sensitivity to Reynolds number in the fully turbulent regime. The pressure loss coefficient, which compares the plenum-related pressure loss with the velocity head in the tube, increases more or less linearly with the plenum length. With regard to experimental technique, it was demonstrated that guard heating/cooling of the electrical bus adjacent to the tube inlet is necessary for accurate heat transfer results at low Reynolds numbers but, although desirable, is less necessary at higher Reynolds numbers.

Evaporation of Pure Liquids at High Prandtl Numbers in a Scale-Up Capable Falling Film Evaporator

2010 ◽  
Author(s):  
Stefanie Arndt ◽  
Stephan Scholl
Keyword(s):  
Heat Transfer ◽  
Scale Up ◽  
Reynolds Numbers ◽  
Temperature Sensitive ◽  
Turbulent Regime ◽  
Falling Film ◽  
Film Evaporator ◽  
Laminar And Turbulent Flow ◽  
Falling Film Evaporation ◽  
Prandtl Numbers

In industrial application heat transfer to temperature sensitive products in falling film evaporation is often linked to the evaporation at elevated viscosities. In the present study a scale-up capable falling film evaporator has been used to investigate the heat transfer to liquids with Prandtl numbers up to 150. The focus was on heated falling films during surface evaporation. Film-Reynolds numbers were varied from 48 to 10,000. As pure liquids water and cyclohexanol were used. In the results a distinct transition zone between laminar and turbulent flow can be observed for elevated Prandtl numbers. The comparison to literature models shows that more parameters have to be taken into account to properly predict the heat transfer in falling film evaporators for different equipment and fluids. The optical monitoring of the film on the inside of the evaporation tube through an endoscope showed that the fully turbulent regime could not been reached for high viscosities.

Turbulent Heat Transfer Downstream of an Unsymmetric Blockage in a Tube

1978 ◽  
Vol 100 (4) ◽  
pp. 588-594 ◽  
Author(s):  
K. K. Koram ◽  
E. M. Sparrow
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Turbulent Heat Transfer ◽  
Working Fluid ◽  
Initial Increase ◽  
Turbulent Heat ◽  
Transfer Coefficients ◽  
Tube Cross Section ◽  
Nusselt Numbers ◽  
Prandtl Numbers

Pipe flow experiments were performed to study the heat transfer in the separation, reattachment, and redevelopment regions downstream of a wall-attached blockage in the form of a segmental orifice plate. Water was the working fluid, and the Reynolds number encompassed the range from about 10,000–60,000. The extent of the flow blockage was varied from one-fourth to three-fourths of the tube cross section. Heat transfer coefficients were determined both around the circumference of the uniformly heated tube and along its length. The axial distributions of the circumferential average Nusselt numbers show an initial increase, then attain a maximum, and subsequently decrease toward the fully developed regime. These Nusselt numbers are much higher than those for a conventional thermal entrance region. The unsymmetric blockage induces variations of the Nusselt number around the circumference of the tube. Axial distributions of the Nusselt number at various fixed angular positions reveal the presence of two types of maxima. One of these is associated with the reattachment of the flow and the other occurs due to the impingement of flow deflected by the blockage onto the tube wall. The circumferential variations decay with increasing downstream distance, but the rate of decay for the case of the smallest blockage is remarkably slow. Although most of the tests were performed for Pr = 4, supplementary experiments for Pr = 8 showed that the results are valid for a range of Prandtl numbers.

scholarly journals Nusselt number correlation for turbulent heat transfer of helium–xenon gas mixtures

2021 ◽  
Vol 32 (11) ◽  
Author(s):  
Biao Zhou ◽  
Yu Ji ◽  
Jun Sun ◽  
Yu-Liang Sun
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Prandtl Number ◽  
Liquid Metals ◽  
Turbulent Heat Transfer ◽  
Working Fluid ◽  
Turbulent Heat ◽  
Heat Transfer Correlation ◽  
Heat Transfer Correlations ◽  
Prandtl Numbers

AbstractA gas-cooled nuclear reactor combined with a Brayton cycle shows promise as a technology for high-power space nuclear power systems. Generally, a helium–xenon gas mixture with a molecular weight of 14.5–40.0 g/mol is adopted as the working fluid to reduce the mass and volume of the turbomachinery. The Prandtl number for helium–xenon mixtures with this recommended mixing ratio may be as low as 0.2. As the convective heat transfer is closely related to the Prandtl number, different heat transfer correlations are often needed for fluids with various Prandtl numbers. Previous studies have established heat transfer correlations for fluids with medium–high Prandtl numbers (such as air and water) and extremely low-Prandtl fluids (such as liquid metals); however, these correlations cannot be directly recommended for such helium–xenon mixtures without verification. This study initially assessed the applicability of existing Nusselt number correlations, finding that the selected correlations are unsuitable for helium–xenon mixtures. To establish a more general heat transfer correlation, a theoretical derivation was conducted using the turbulent boundary layer theory. Numerical simulations of turbulent heat transfer for helium–xenon mixtures were carried out using Ansys Fluent. Based on simulated results, the parameters in the derived heat transfer correlation are determined. It is found that calculations using the new correlation were in good agreement with the experimental data, verifying its applicability to the turbulent heat transfer for helium–xenon mixtures. The effect of variable gas properties on turbulent heat transfer was also analyzed, and a modified heat transfer correlation with the temperature ratio was established. Based on the working conditions adopted in this study, the numerical error of the property-variable heat transfer correlation was almost within 10%.

Heat Transfer for High Aspect Ratio Rectangular Channels in a Stationary Serpentine Passage With Turbulated and Smooth Surfaces

2013 ◽  
Author(s):  
Matthew A. Smith ◽  
Randall M. Mathison ◽  
Michael G. Dunn
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Aspect Ratio ◽  
Flow Behavior ◽  
Reynolds Numbers ◽  
Hydraulic Diameter ◽  
Internal Cooling ◽  
Number Range ◽  
Aspect Ratios ◽  
Parallel Configuration

Heat transfer distributions are presented for a stationary three passage serpentine internal cooling channel for a range of engine representative Reynolds numbers. The spacing between the sidewalls of the serpentine passage is fixed and the aspect ratio (AR) is adjusted to 1:1, 1:2, and 1:6 by changing the distance between the top and bottom walls. Data are presented for aspect ratios of 1:1 and 1:6 for smooth passage walls and for aspect ratios of 1:1, 1:2, and 1:6 for passages with two surfaces turbulated. For the turbulated cases, turbulators skewed 45° to the flow are installed on the top and bottom walls. The square turbulators are arranged in an offset parallel configuration with a fixed rib pitch-to-height ratio (P/e) of 10 and a rib height-to-hydraulic diameter ratio (e/Dh) range of 0.100 to 0.058 for AR 1:1 to 1:6, respectively. The experiments span a Reynolds number range of 4,000 to 130,000 based on the passage hydraulic diameter. While this experiment utilizes a basic layout similar to previous research, it is the first to run an aspect ratio as large as 1:6, and it also pushes the Reynolds number to higher values than were previously available for the 1:2 aspect ratio. The results demonstrate that while the normalized Nusselt number for the AR 1:2 configuration changes linearly with Reynolds number up to 130,000, there is a significant change in flow behavior between Re = 25,000 and Re = 50,000 for the aspect ratio 1:6 case. This suggests that while it may be possible to interpolate between points for different flow conditions, each geometric configuration must be investigated independently. The results show the highest heat transfer and the greatest heat transfer enhancement are obtained with the AR 1:6 configuration due to greater secondary flow development for both the smooth and turbulated cases. This enhancement was particularly notable for the AR 1:6 case for Reynolds numbers at or above 50,000.

Heat Transfer in Rotating Serpentine Coolant Passage With Ribbed Walls at Low Mach Numbers

2015 ◽  
Vol 7 (1) ◽  
Author(s):  
Shang-Feng Yang ◽  
Je-Chin Han ◽  
Salam Azad ◽  
Ching-Pang Lee
Keyword(s):  
Heat Transfer ◽  
Mach Number ◽  
Reynolds Numbers ◽  
Working Fluid ◽  
Transfer Coefficients ◽  
Low Mach Number ◽  
Heat Transfer Coefficients ◽  
Rotation Numbers ◽  
Wide Range ◽  
Mach Numbers

This paper experimentally investigates the effect of rotation on heat transfer in typical turbine blade serpentine coolant passage with ribbed walls at low Mach numbers. To achieve the low Mach number (around 0.01) condition, pressurized Freon R-134a vapor is utilized as the working fluid. The flow in the first passage is radial outward, after the 180 deg tip turn the flow is radial inward to the second passage, and after the 180 deg hub turn the flow is radial outward to the third passage. The effects of rotation on the heat transfer coefficients were investigated at rotation numbers up to 0.6 and Reynolds numbers from 30,000 to 70,000. Heat transfer coefficients were measured using the thermocouples-copper-plate-heater regional average method. Heat transfer results are obtained over a wide range of Reynolds numbers and rotation numbers. An increase in heat transfer rates due to rotation is observed in radially outward passes; a reduction in heat transfer rate is observed in the radially inward pass. Regional heat transfer coefficients are correlated with Reynolds numbers for nonrotation and with rotation numbers for rotating condition, respectively. The results can be useful for understanding real rotor blade coolant passage heat transfer under low Mach number, medium–high Reynolds number, and high rotation number conditions.

Heat Transfer And Pressure Drop Of An Angled Discrete Turbulator At Elevated Reynolds Numbers Up To 900,000

2021 ◽  
pp. 1-29
Author(s):  
Sam Ghazi-Hesami ◽  
Dylan Wise ◽  
Keith Taylor ◽  
Peter Ireland ◽  
Étienne Robert
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Pressure Drop ◽  
Friction Factor ◽  
Rectangular Channel ◽  
Reynolds Numbers ◽  
Enhance Heat Transfer ◽  
Near Surface ◽  
Number Range ◽  
Smooth Channel

Abstract Turbulators are a promising avenue to enhance heat transfer in a wide variety of applications. An experimental and numerical investigation of heat transfer and pressure drop of a broken V (chevron) turbulator is presented at Reynolds numbers ranging from approximately 300,000 to 900,000 in a rectangular channel with an aspect ratio (width/height) of 1.29. The rib height is 3% of the channel hydraulic diameter while the rib spacing to rib height ratio is fixed at 10. Heat transfer measurements are performed on the flat surface between ribs using transient liquid crystal thermography. The experimental results reveal a significant increase of the heat transfer and friction factor of the ribbed surface compared to a smooth channel. Both parameters increase with Reynolds number, with a heat transfer enhancement ratio of up to 2.15 (relative to a smooth channel) and a friction factor ratio of up to 6.32 over the investigated Reynolds number range. Complementary CFD RANS (Reynolds-Averaged Navier-Stokes) simulations are performed with the κ-ω SST turbulence model in ANSYS Fluent® 17.1, and the numerical estimates are compared against the experimental data. The results reveal that the discrepancy between the experimentally measured area averaged Nusselt number and the numerical estimates increases from approximately 3% to 13% with increasing Reynolds number from 339,000 to 917,000. The numerical estimates indicate turbulators enhance heat transfer by interrupting the boundary layer as well as increasing near surface turbulent kinetic energy and mixing.

scholarly journals Numerical study of flow patterns and heat transfer in mini twisted oval tubes

2015 ◽  
Vol 26 (12) ◽  
pp. 1550140 ◽  
Author(s):  
Amin Ebrahimi ◽  
Ehsan Roohi
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Performance ◽  
Numerical Study ◽  
Critical Role ◽  
Reynolds Numbers ◽  
Flow Patterns ◽  
Working Fluid ◽  
Transfer Performance ◽  
Temperature Dependent ◽  
Overall Performance

Flow patterns and heat transfer inside mini twisted oval tubes (TOTs) heated by constant-temperature walls are numerically investigated. Different configurations of tubes are simulated using water as the working fluid with temperature-dependent thermo-physical properties at Reynolds numbers ranging between 500 and 1100. After validating the numerical method with the published correlations and available experimental results, the performance of TOTs is compared to a smooth circular tube. The overall performance of TOTs is evaluated by investigating the thermal-hydraulic performance and the results are analyzed in terms of the field synergy principle and entropy generation. Enhanced heat transfer performance for TOTs is observed at the expense of a higher pressure drop. Additionally, the secondary flow generated by the tube-wall twist is concluded to play a critical role in the augmentation of convective heat transfer, and consequently, better heat transfer performance. It is also observed that the improvement of synergy between velocity and temperature gradient and lower irreversibility cause heat transfer enhancement for TOTs.

CFD Aided Design of Heat Transfer Plates for Gasketed Plate Heat Exchangers

2014 ◽  
Author(s):  
Ece Özkaya ◽  
Selin Aradag ◽  
Sadik Kakac
Keyword(s):  
Heat Transfer ◽  
Pressure Drop ◽  
Heat Exchangers ◽  
Three Dimensional ◽  
Separate Flow ◽  
Working Fluid ◽  
Number Range ◽  
Plate Heat ◽  
Pressure Distributions ◽  
Cfd Analyses

In this study, three-dimensional computational fluid dynamics (CFD) analyses are performed to assess the thermal-hydraulic characteristics of a commercial Gasketed Plate Heat Exchangers (GPHEx) with 30 degrees of chevron angle (Plate1). The results of CFD analyses are compared with a computer program (ETU HEX) previously developed based on experimental results. Heat transfer plate is scanned using photogrammetric scan method to model GPHEx. CFD model is created as two separate flow zones, one for each of hot and cold domains with a virtual plate. Mass flow inlet and pressure outlet boundary conditions are applied. The working fluid is water. Temperature and pressure distributions are obtained for a Reynolds number range of 700–3400 and total temperature difference and pressure drop values are compared with ETU HEX. A new plate (Plate2) with corrugation pattern using smaller amplitude is designed and analyzed. The thermal properties are in good agreement with experimental data for the commercial plate. For the new plate, the decrease of the amplitude leads to a smaller enlargement factor which causes a low heat transfer rate while the pressure drop remains almost constant.

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. 

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