# UFR 3-06 Description

# Natural and mixed convection boundary layers on vertical heated walls (A)

Underlying Flow Regime 3-06 © copyright ERCOFTAC 2004

# Description

## Introduction

The flow under consideration is a low mach number flow of a strongly heated gas inside a vertical circular tube. The experimental work of A.M.Shehata and D.M.McEligot (3) which is used to define this UFR supplements and extends earlier data for internal flows in small tubes (D<13mm) with temperature dependent transport properties that could only provide integralparameters.

These recent data are used to assess turbulence models by comparing measures and computed distributions of the mean streamwise velocity and temperature in this well defined experiment involving strong influence on the initial turbulent field, of the variation of the gas transport properties and the thickening of the viscous layer (the so called laminarization effect) which are caused by intense heating at the wall. Intense heating is defined here by a ratio wall to bulk absolute temperatures greater than 2.5.

This UFR is of particular relevance for the design of gas cooled nuclear reactors and the use of a gas as a coolant in power generation systems.

## Review of UFR studies and choice of test case

A variety of basic studies has been conducted examining turbulence structure in simple boundary layers with constant properties and uniform wall temperatures. A strong heating atthe wall induced by a nearly constant high heat flux boundary condition involves significant transport property variation and buoyancy effects and makes necessary to further assess the predictive capabilities of turbulence models in that situation. Experiments for air flowing upwards in small heated vertical tubes with temperature dependent transport properties were made by Humble, Lowdermilk and Desmon (4), Jackson (5), McEligot, Magee and Leppert (6), Perkins and Worsoe-Schmidt (7) and others. These studies were lacking of internal profile measurements for temperature and velocities but they provided some average data to make preliminary tests of turbulence models accounting for temperature-dependent transport properties and the influence of intense heating on turbulent flows in tubes.

In (3) Shehata and McEligot have provided new data on mean velocity profiles along with mean temperature profiles, wall temperature and axial pressure distributions in a carefully controlled experiment. These data have been compared in (1) to the computational results of a number of two equations turbulence models for turbulence kinetic energy and its dissipation rate <ε or the related quantity ω. The definition of this UFR makes an extensive use and summarizes these two recent publications.

**Non dimensional Parameters**

The Reynolds number Re = G*D/μ and the non dimensional heating rate q^{+}_{in} = q′′w/G*Cp_{in}*T_{in} evolve naturally from non-dimensionalizing the governing equations and boundary conditions in pipe flow with an imposed wall heat flux distribution (8).G is the mean mass flux (mass flow-rate divided by the cross sectional area) D is the tube diameter, μ the absolute viscosity q′′ is the prescribed heat flux at the wall, , Cp the specific heat at constant temperature, T the absolute temperature.

The “in” index means that the value is related to the inlet.
The “w” index means that the value is related to the wall. The experimental data reported in (3) are available for the following set of parameters: Low Reynolds numbers (4260 and 6080), moderate, high and intense heating rates (q^{+}_{in} = 0.0018, 0.0035, 0.0045) yielding flows ranging from turbulent to laminarized

**Computational Studies of Mixed Convection in circular tubes with intense heating**

The various two equations models used in the study reported in (1) are of the Low Reynolds number (k, ε) type, they differ in respect of the coefficients of the diffusive terms and also in respect of additional source terms which are introduced in some of them to account for pressure diffusion of k and production of ε.

These models are detailed in the references cited hereunder:JL: Low Reynolds number (k, ε) turbulence model proposed by Jones and Launder(10)LS: Low Reynolds number (k, ε) turbulence model proposed by Launder and Sharma (11)CH: Low Reynolds number (k, v) turbulence model proposed by Chien (12)LB: Low Reynolds number (k, ε) turbulence model proposed by Lam and Bremhorst (13)MRS: Low Reynolds number (k, ε) turbulence model proposed by Michelassi et al. (14)SH: Low Reynolds number (k, ε) turbulence model proposed by Shi and Hsu (15)TAS: Low Reynolds number (k, τ) turbulence model proposed by Thangan et al (16)

**Choice of UFR**

Three experiments described Shin-ichi Satake, Tomoaki Kunugi, Mohsen Shehata and D.M.McEligot in (3) are chosen as a test case. They are called runs 445, 635 and 618. Run 445 is for Re= 4260 ,
q^{+}_{in} = 0.0045Run 635 is for Re= 6080 , q^{+}_{in} = 0.0035 Run 618 is for Re= 6080 , q^{+}_{in} = 0.0018

These runs are used because they cover a wide range of heating rates and the Reynolds number is representative of the Reynolds number used in real power generation units. The flow conditions at the entrance of the heated section are fully established as it comes after a long enough adiabatic section. The wall heat flux distribution is given with a claimed accuracy of 3%.

© copyright ERCOFTAC 2004

Contributors: André Latrobe - CEA / DRN / Department de Thermohydraulique