Simulation of Fully-Developed Average Turbulent MHD Pipe Flow With Heat Transfer

2012 ◽  
Author(s):  
K. Alammar ◽  
R. Vilagines ◽  
M. Shariff ◽  
Z. Kaneesamkandi ◽  
S. Abdullah
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Prandtl Number ◽  
Turbulence Model ◽  
Pipe Flow ◽  
Hartmann Number ◽  
Heat Transfer Characteristics ◽  
Enhance Heat Transfer ◽  
Prandtl Numbers ◽  
Grid Independence

Using a zero-equation turbulence model, fully-developed average turbulent MHD pipe flow with wall heating was simulated. Uncertainty was approximated through grid-independence and model validation. Effect of Reynolds, Hartmann, and Prandtl numbers on heat transfer characteristics was investigated. With increasing Hartmann number, heat transfer was shown to increase towards the side layer. Increasing the Prandtl number was shown to enhance heat transfer. Increasing the Reynolds number decreased the effect of the Hartmann number.

scholarly journals Effect of Prandtl number on heat transfer characteristics in an axisymmetric sudden expansion: A numerical study

2007 ◽  
Vol 11 (4) ◽  
pp. 171-178
Author(s):  
Khalid Alammar
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Prandtl Number ◽  
Turbulent Flow ◽  
Turbulence Model ◽  
Numerical Study ◽  
Sudden Expansion ◽  
Heat Transfer Characteristics ◽  
Transfer Characteristics ◽  
Simulated Effect

Using the standard k-e turbulence model, an incompressible, axisymmetric turbulent flow with a sudden expansion was simulated. Effect of Prandtl number on heat transfer characteristics downstream of the expansion was investigated. The simulation revealed circulation downstream of the expansion. A secondary circulation (corner eddy) was also predicted. Reattachment was predicted at approximately 10 step heights. Corresponding to Prandtl number of 7.0, a peak Nusselt number 13 times the fully-developed value was predicted. The ratio of peak to fully-developed Nusselt number was shown to decrease with decreasing Prandtl number. Location of maximum Nusselt number was insensitive to Prandtl number.

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.

scholarly journals Effect of Reynolds and Prandtl Numbers on Mixed Convection in an Obstructed Vented Cavity

2011 ◽  
Vol 3 (2) ◽  
pp. 271-281
Author(s):  
M. M. Rahman ◽  
M. M. Billah ◽  
M. A. Alim
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Reynolds Number ◽  
Finite Element ◽  
Free Convection ◽  
Prandtl Number ◽  
Mixed Convection ◽  
Forced Convection ◽  
Thermal Field ◽  
Heat Transfer Characteristics

A numerical investigation is conducted to analyze the steady flow and thermal fields as well as heat transfer characteristics in a vented square cavity with a built-in heat conducting horizontal solid circular obstruction. Hydrodynamic behavior, thermal characteristics and heat transfer results are obtained by solving the couple of Navier-Stokes and energy equations by using a weighted residuals Finite element method. The computation was made for different Reynolds number, Prandtl number ranging from 50 to 200 and from 0.71 to 7.1 at the three different convective regimes. Three different regimes are observed with increasing Ri: forced convection (with negligible free convection), mixed convection (comparable free and forced convection) and free convection dominated region (with higher free convection). The results are presented to show the effects of the Reynolds number, Prandtl number on flow pattern, thermal field and heat transfer characteristics at the three convective regimes. It is found that the flow and thermal field strongly depend on the Reynolds number, Prandtl number as well as Richardson number. As the Reynolds number and Prandtl number increase, the heat transfer rate increases but average fluid temperature in the cavity and temperature at the cylinder center decrease at the three convective regimes.Keywords: Mixed convection; Finite element method; Obstructed vented cavity; Prandtl number.© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi:10.3329/jsr.v3i2.4344                J. Sci. Res. 3 (2), 271-281 (2011)

scholarly journals Heat transfer from a rotating circular cylinder in the steady regime: Effects of Prandtl number

2012 ◽  
Vol 16 (1) ◽  
pp. 79-91 ◽  
Author(s):  
Varun Sharma ◽  
Kumar Dhiman
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Circular Cylinder ◽  
Prandtl Number ◽  
Rotation Rate ◽  
Average Nusselt Number ◽  
Steady Regime ◽  
Rotating Circular Cylinder ◽  
Prandtl Numbers

In this work, effects of Prandtl number on the heat transfer characteristics of an unconfined rotating circular cylinder are investigated for varying rotation rate (? = 0 - 5) in the Reynolds number range 1 - 35 and Prandtl numbers range 0.7 - 100 in the steady flow regime. The numerical calculations are carried out by using a finite volume method based commercial CFD solver FLUENT. The isotherm patterns are presented for varying values of Prandtl number and rotation rate in the steady regime. The variation of the local and the average Nusselt numbers with Reynolds number, Prandtl number and rotation rate are presented for the above range of conditions. The average Nusselt number is found to decrease with increasing value of the rotation rate for the fixed value of the Reynolds and Prandtl numbers. With increasing value of the Prandtl number, the average Nusselt number increases for the fixed value of the rotation rate and the Reynolds number; however, the larger values of the Prandtl numbers show a large reduction in the value of the average Nusselt number with increasing rotation rate.

Direct Numerical Simulation of the Flow in a Bare Rod Bundle at Different Prandtl Numbers

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Jonathan K. Lai ◽  
Giacomo Busco ◽  
Elia Merzari ◽  
Yassin A. Hassan
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Reynolds Number ◽  
Prandtl Number ◽  
Direct Numerical Simulation ◽  
Frequency Analysis ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Rod Bundle ◽  
Prandtl Numbers

Abstract A direct numerical simulation (DNS) of bare rod bundles with a low pitch-to-diameter ratio is performed with heat transfer at different Prandtl numbers. Turbulence statistics for temperature and velocity as well as the turbulent budgets have been collected. High-fidelity simulations are performed with the spectral element method (SEM) using Nek5000, a highly scalable code. To pertain to industrial-related flows, a rod bundle model is based on Hooper and Wood's (Hooper, J. D., and Wood, D., 1984, “Fully Developed Rod Bundle Flow Over a Large Range of Reynolds Number,” Nucl. Eng. Des., 83(1), pp. 31–46) experimental setup. Both wall normalized velocity profile and turbulent kinetic energy are validated with a Reynolds number of 22,600. Kolmogorov length scales and time scales are calculated to be within the simulation's spatial–temporal resolution. Moreover, gap vortices and coherent structures are quantified by using Lambda2 vortex criterion, frequency analysis, and two-point correlation. Heat transfer statistics are discussed with a constant heat flux for six different Prandtl numbers ranging from 2 to 0.002. This range shows significantly different characteristics in temperature for both mean and variance. Mean temperature profiles in the subchannel center are very sensitive to the Prandtl number when it becomes small. It is also found that the location of the local maxima for the variance of temperature fluctuations becomes very sensitive at larger Prandtl numbers. The temperature frequency analysis reveals a shift to lower frequencies for low Prandtl numbers. The DNS results provided in this work will contribute as benchmark for the improvement and development of existing and new turbulent heat transfer models at different Prandtl number regimes.

Heat Transfer in Magnetohydrodynamic Flow in an Entrance Section

1965 ◽  
Vol 87 (2) ◽  
pp. 231-236 ◽  
Author(s):  
A. M. Dhanak
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Prandtl Number ◽  
Flat Plate ◽  
Hartmann Number ◽  
Transverse Magnetic ◽  
Entrance Section ◽  
Pressure Distributions ◽  
Prandtl Numbers ◽  
Iterative Procedures

Based on the Ka´rma´n-Pohlhausen method and the associated iterative procedures developed herein the analysis shows that the presence of a transverse magnetic field in the entrance section of a channel has significant effects on the velocity and pressure distributions, and on the displacement and momentum thicknesses. The calculations further reveal that the heat transfer from the channel, in contrast with the flat plate case, increases with the Hartmann number. This increase is, however, significant only at high Prandtl numbers. The influence of Joulean dissipation appears to be negligible for a Joulean parameter up to 1.0 and at a Prandtl number of unity.

Stability of thermocapillary flows in non-cylindrical liquid bridges

2002 ◽  
Vol 458 ◽  
pp. 35-73 ◽  
Author(s):  
CH. NIENHÜSER ◽  
H. C. KUHLMANN
Keyword(s):  
Reynolds Number ◽  
Prandtl Number ◽  
Critical Reynolds Number ◽  
Volume Fraction ◽  
Thermocapillary Flow ◽  
Surface Shape ◽  
Liquid Bridges ◽  
Gravity Level ◽  
Neutral Curves ◽  
Prandtl Numbers

The thermocapillary flow in liquid bridges is investigated numerically. In the limit of large mean surface tension the free-surface shape is independent of the flow and temperature fields and depends only on the volume of liquid and the hydrostatic pressure difference. When gravity acts parallel to the axis of the liquid bridge the shape is axisymmetric. A differential heating of the bounding circular disks then causes a steady two-dimensional thermocapillary flow which is calculated by a finite-difference method on body-fitted coordinates. The linear-stability problem for the basic flow is solved using azimuthal normal modes computed with the same discretization method. The dependence of the critical Reynolds number on the volume fraction, gravity level, Prandtl number, and aspect ratio is explained by analysing the energy budgets of the neutral modes. For small Prandtl numbers (Pr = 0.02) the critical Reynolds number exhibits a smooth minimum near volume fractions which approximately correspond to the volume of a cylindrical bridge. When the Prandtl number is large (Pr = 4) the intersection of two neutral curves results in a sharp peak of the critical Reynolds number. Since the instabilities for low and high Prandtl numbers are markedly different, the influence of gravity leads to a distinctly different behaviour. While the hydrostatic shape of the bridge is the most important effect of gravity on the critical point for low-Prandtl-number flows, buoyancy is the dominating factor for the stability of the flow in a gravity field when the Prandtl number is high.

Numerical Study of Convective Heat Transfer From Expanding Annular Pipe Flows

2016 ◽  
Author(s):  
Khaled J. Hammad
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Prandtl Number ◽  
Convective Heat Transfer ◽  
Diameter Ratio ◽  
Wall Heat Transfer ◽  
Reattachment Point ◽  
Transfer Rates ◽  
Pipe Flows ◽  
Annular Pipe

Convective heat transfer from suddenly expanding annular pipe flows are numerically investigated within the steady laminar flow regime. A parametric study is performed to reveal the influence of the annular diameter ratio, k, the Prandtl number, Pr, and the Reynolds number, Re, over the following range of parameters: k = {0, 0.5, 0.7}, Pr = {0.7, 1, 7, 100}, and Re = {25, 50, 100}. Heat transfer enhancement downstream of the expansion plane is only observed for Pr > 1. Peak wall-heat-transfer-rates always appear downstream of the flow reattachment point, in the case of suddenly expanding round pipe flows, i.e. k = 0. However, for suddenly expanding annular pipe flows, i.e., k = 0.5 and 0.7, peak wall-heat-transfer-rates always appear upstream of the flow reattachment point. The observed heat transfer augmentation is more dramatic for suddenly expanding annular flows, in comparison with the one observed for suddenly expanding pipe flows. For a given annular diameter ratio and Reynolds number, increasing the Prandtl number, always results in higher wall-heat-transfer-rates downstream the expansion plane.

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.

Numerical Simulation on Heat Transfer Characteristics of Turbulent Gas Flow in Micro-Tubes

2011 ◽  
Author(s):  
Kyohei Isobe ◽  
Chungpyo Hong ◽  
Yutaka Asako ◽  
Ichiro Ueno
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Wall Temperature ◽  
Gas Flow ◽  
Tube Diameter ◽  
Turbulence Energy ◽  
Stagnation Temperature ◽  
Heat Transfer Characteristics ◽  
Transfer Characteristics ◽  
Turbulent Gas Flow

Numerical simulations were performed to obtain for heat transfer characteristics of turbulent gas flow in micro-tubes with constant wall temperature. The numerical methodology was based on Arbitrary-Lagrangian-Eulerinan (ALE) method to solve compressible momentum and energy equations. The Lam-Bremhorst Low-Reynolds number turbulence model was employed to evaluate eddy viscosity coefficient and turbulence energy. The tube diameter ranges from 100 μm to 400 μm and the aspect ratio of the tube diameter and the length is fixed at 200. The stagnation temperature is fixed at 300 K and the computations were done for wall temperature, which ranges from 305 K to 350 K. The stagnation pressure was chosen in such a way that the flow is in turbulent flow regime. The obtained Reynolds number ranges widely up to 10081 and the Mach number at the outlet ranges from 0.1 to 0.9. The heat transfer rates obtained by the present study are higher than those of the incompressible flow. This is due to the additional heat transfer near the micro-tube outlet caused by the energy conversion into kinetic energy.

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