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 Analysis of Laminar Forced Convection in Sinusoidal-Wavy-, Rounded-Ellipse-, and Rounded-Vee-Shaped Corrugated-Plate Channels

2010 ◽  
Author(s):  
Dean Ferley ◽  
Scott J. Ormiston
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Numerical Analysis ◽  
Prandtl Number ◽  
Friction Factor ◽  
Forced Convection ◽  
Reynolds Numbers ◽  
Ansys Cfx ◽  
Prandtl Numbers ◽  
Laminar Forced Convection

Numerical analysis of steady, two-dimensional, laminar forced convection in corrugated-plate channels is performed using a commercial CFD code: ANSYS CFX. The flow domain consists of six modules in each of three wall corrugations: sinusoidal-wavy-shaped (SWS), rounded-ellipse-shaped (RES), and rounded-vee-shaped (RVS). One ratio of minimum-to-maximum plate spacings and one module length-to-height ratio is considered. Fluid flow and heat transfer are repeating in the modules and the results are examined in a typical module in the fully-developed region for Reynolds numbers in the range of 25 to 300 for Prandtl numbers of 0.7 (air), 2.29 (water), and 34.6 (ethylene glycol). The RES corrugation produced the highest peak value of local Nusselt number as well as the highest friction factor. The SWS corrugation produced the highest average Nusselt number, except at a Prandtl number of 34.6 at higher Reynolds number where the RES corrugation had the highest value. The RVS corrugation had the lowest friction factor for the geometric configuration considered. The highest heat transfer rate per unit pumping power was found at the highest Prandtl number for the RES corrugation.

scholarly journals MATHEMATICAL LOW-REYNOLDS MODELING OF HEAT EXCHANGE IIN TURBULENT FLOW IN FLAT CHANNELS WITH TURBULATORS SYMMETRICALLY LOCATED ON BOTH SIDES

2018 ◽  
Vol 45 (2) ◽  
pp. 70-93 ◽  
Author(s):  
I. E. Lobanov
Keyword(s):  
Heat Exchange ◽  
Hydraulic Resistance ◽  
Energy Equation ◽  
Transport Model ◽  
Theoretical Method ◽  
Flat Channel ◽  
Structured Grids ◽  
Calculation Results ◽  
Shear Stress Transport Model ◽  
Volume Method

ObjectivesThe aim of the study was to simulate the heat transfer in flat channel with turbulators, symmetrically located on its both sides, depending on the channel's geometric parameters and the coolant flow modes followed by the verification of the obtained calculated data by the existing experiment.MethodsThe calculation was carried out on the basis of a theoretical method based on the solution of the Reynolds equations, closed with the help of the Menter shear stress transport model, by factored finite-volume method, as well as the energy equation on multiscale intersecting structured grids (Fast COmposite Mesh method, FCOM).ResultsA theoretical mathematical calculation model for intensified heat exchange in turbulent flow for a flat channel with turbulators, symmetrically located on both sides, depending on the channel's geometric parameters and coolant flow modes was generated. The calculation results of the intensified heat exchange in flat channels with double turbulators, depending on the determining parameters, are in very good agreement with the existing experimental material and have an undeniable advantage over the latter, since the assumptions made in their derivation cover a much wider range of determining parameters than the limitations of the experiments (Pr = 0.7 ч 100; Re = 103ч 106; h / dЭ= 0.005 ч 0.2; t / h= 1 ч 200). ConclusionAccording to the calculation results based on the developed model, it is possible to optimise the heat exchange intensification in flat channels with double turbulators, as well as to control the process of heat exchange intensification. The comparative calculations of the intensified hydraulic resistance and heat exchange for flat channels with two-sided symmetrical flow turbulators with corresponding data for round channels with turbulators were carried out and analysed. From the point of view of heat exchange intensification, all other conditions being equal, the reduction of a flat channel with two-sided symmetrical turbulators with respect to a round tube with turbulators takes place because a smaller increase in heat exchange is achieved with a greater increase in hydraulic resistance. It was established by calculation that the relative hydraulic resistance ξП/ ξT for channels with turbulators is always higher than for smooth channels; however, the relative heat exchange NuП/ NuT for channels with turbulators can be higher than for smooth channels. Therefore, there is an enhanced redistribution of the temperature drop over the channel section with an intensified heat exchanger. The developed theoretical method based on the solution of the Reynolds equations by the factored finite-volume method, combined with the energy equation on multiscale intersecting structured grids and closed by means of the Menter shear stress transport model, makes it possible, with reasonable accuracy, to calculate heat exchange coefficients and hydraulic resistance in flat channels of practically any forms of double symmetrically located flow turbulators.

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 Modelling boundary-layer transition on wings operating in ground effect at low Reynolds numbers

2018 ◽  
Vol 233 (11) ◽  
pp. 2820-2837 ◽  
Author(s):  
LS Roberts ◽  
MV Finnis ◽  
K Knowles
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Wind Tunnel ◽  
Transport Model ◽  
Three Dimensional ◽  
Ground Effect ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Shear Stress Transport Model ◽  
Low Reynolds

The transition-sensitive, three-equation k- kL- ω eddy-viscosity closure model was used for simulations of three-dimensional, single-element and multi-element wing configurations operating in close proximity to the ground. The aim of the study was to understand whether the model correctly simulated the transitional phenomena that occurred in the low Reynolds number operating conditions and whether it offered an improvement over the classical fully turbulent k-ω shear stress transport model. This was accomplished by comparing the simulation results to experiments conducted in a 2.7 m × 1.7 m closed-return, three-quarter-open-jet wind tunnel. The model was capable of capturing the presence of a laminar separation bubble on the wing and predicted sectional forces and surface-flow structures generated by the wings in wind tunnel testing to within 2.5% in downforce and 4.1% in drag for a multi-element wing. It was found, however, that the model produced insufficient turbulent kinetic energy during shear-layer reattachment, predicted turbulent trailing-edge separation prematurely in areas of large adverse pressure gradients, and was found to be very sensitive to inlet turbulence quantities. Despite these deficiencies, the model gave results that were much closer to wind-tunnel tests than those given by the fully turbulent k-ω shear stress transport model, which tended to underestimate downforce. Significant differences between the transitional and fully turbulent models in terms of pressure field, wake thickness and turbulent kinetic energy production were found and highlighted the importance of using transitional models for wings operating at low Reynolds numbers in ground effect. The k- kL- ω model has been shown to be appropriate for the simulation of separation-induced transition on a three-dimensional wing operating in ground effect at low Reynolds number.

Analytical Study of the Convection Heat Transfer From an Isothermal Wedge Surface to Fluids

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
M. Bachiri ◽  
A. Bouabdallah
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Ad Hoc ◽  
Convection Heat Transfer ◽  
Analytical Approximation ◽  
Numerical Results ◽  
Convection Heat ◽  
Governing Equations ◽  
Wedge Surface ◽  
Prandtl Numbers

In this work, we attempt to establish a general analytical approximation of the convection heat transfer from an isothermal wedge surface to fluids for all Prandtl numbers. The flow has been assumed to be laminar and steady state. The governing equations have been written in dimensionless form using a similarity method. A simple ad hoc technique is used to solve analytically the governing equations by proposing a general formula of the velocity profile. This formula verifies the boundary conditions and the equilibrium of the governing equations in the whole spatial region and permits us to obtain analytically the temperature profiles for all Prandtl numbers and for various configurations of the wedge surface. A comparison with the numerical results is given for all spatial regions and in wide Prandtl number values. A new Nusselt number expression is obtained for various configurations of the wedge surface and compared with the numerical results in wide Prandtl number values.

Convective Heat Transfer of the Flow through a Rotating Circular Straight Pipe

2001 ◽  
Vol 17 (2) ◽  
pp. 79-91
Author(s):  
U. Lei ◽  
Arthur C. Y. Yang
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Reynolds Numbers ◽  
Straight Pipe ◽  
Constant Wall Temperature ◽  
Fully Developed Flow ◽  
Flow Through ◽  
Prandtl Numbers ◽  
Scaling Analyses ◽  
Gradient Condition

ABSTRACTLaminar heat transfer for large ranges of Reynolds numbers, rotational Reynolds numbers, and Prandtl numbers are studied numerically for incompressible fully developed flow in a circular straight pipe, which is rotating constantly about an axis perpendicular to its own axis under the constant wall temperature gradient condition. There exist four types of local Nusselt number distributions associated with the four different flow regimes for different parameters depending on the relative importance of different forces. Correlations of the averaged Nusselt number are also provided. When the Prandtl number is sufficiently large, the temperature distribution in the core is determined essentially by the secondary flow. Scaling analyses are provided for understanding the essential physics of the problem.

Validation and Development of DNS Database for Low Prandtl Numbers in Rod Bundle

2019 ◽  
Author(s):  
Jonathan K. Lai ◽  
Elia Merzari ◽  
Yassin A. Hassan ◽  
Aleksandr Obabko
Keyword(s):  
Heat Transfer ◽  
Thermal Diffusivity ◽  
Prandtl Number ◽  
Liquid Metals ◽  
Heat Transfer Characteristics ◽  
Reynolds Analogy ◽  
Transfer Characteristics ◽  
Rod Bundle ◽  
High Thermal Diffusivity ◽  
Prandtl Numbers

Abstract Difficulty in capturing heat transfer characteristics for liquid metals is commonplace because of their low molecular Prandtl number (Pr). Since these fluids have very high thermal diffusivity, the Reynolds analogy is not valid and creates modeling difficulties when assuming a turbulent Prandtl number (Prt) of near unity. Baseline problems have used direct numerical simulations (DNS) for the channel flow and backward facing step to aid in developing a correlation for Prt. More complex physics need to be considered, however, since correlation accuracy is limited. A tight lattice square rod bundle has been chosen for DNS benchmarking because of its presence of flow oscillations and coherent structures even with a relatively simple geometry. Calculations of the Kolmogorov length and time scales have been made to ensure that the spatial-temporal discretization is sufficient for DNS. In order to validate the results, Hooper and Wood’s 1984 experiment has been modeled with a pitch-to-diameter (P/D) ratio of 1.107. The present work aims at validating first- and second-order statistics for the velocity field, and then analyzing the heat transfer behavior at different molecular Pr. The effects of low Pr flow are presented to demonstrate how the normalized mean and fluctuating heat transfer characteristics vary with different thermal diffusivity. Progress and future work toward creating a full DNS database for liquid metals are discussed.

Conjugated Heat Transfer in 2-Dimensional Mini and Micro Channels: Influence of Axial Conduction in the Walls

2004 ◽  
Author(s):  
G. Maranzana ◽  
I. Perry ◽  
D. Maillet
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer Coefficient ◽  
Reynolds Numbers ◽  
Analytical Models ◽  
Conductive Heat ◽  
Axial Conduction ◽  
Micro Channels ◽  
Small Reynolds Numbers ◽  
Conjugated Heat Transfer ◽  
Axial Heat

For small Reynolds numbers, conductive heat transfer in the wall of mini-micro channels can become quite multidimensional: the wall heat flux density does not stay uniform and heat transfer mainly occurs at the entrance of the channels. The use of a ID model to invert measurements designed for estimating the convective heat transfer coefficient can lead to misinterpretations such as a variation of the Nusselt number with the Reynolds number. Three analytical models of conjugated heat transfer in channels are proposed, and the potential inversion of measurements is considered. A non-dimensional number M quantifying the relative part of conductive axial heat transfer in walls is introduced.

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