A Neural Network based Calculation of Exchange Factor for a CO₂/H₂O/N₂/Soot Mixture Between Two Perpendicular Rectangular Surfaces

Introduction

RAD-NNET-SSPD computes the exchange factor between two perpendicular rectangular areas with an intervening CO₂/H₂O/N₂/soot mixture at arbitrary mixture conditions (temperature, partial pressure of the participating gas and soot concentration) and wall temperature of the emitting surface.

The absorption of the mixture is computed using RAD-NNET which is a neural network developed based on narrow band spectral data provide by RADCAL. The detail of RAD-NNET and its associated references are presented in the RADNNET website.

The zonal method is the basic computational scheme. The concept of point mean beam length (PMBL) is used to enhance the computational efficiency of the geometric integration. A detailed description of the PMBL concept can be find in the paper "Point Mean Beam Length, a New Concept to Enhance the Computational Efficiency of Multi-Dimensional Non-Gray Radiative Heat Transfer". (As of 8/1/2020, this paper is under reviewed for publication by Numerical Heat Transfer. The manuscript is available from W. W. Yuen upon request.)

The calculation for exchange factors between two parallel rectangular areas of a CO₂/H₂O/N₂/soot mixture can be found in the RADNNET-SSPP website.

Instructions for Run

The software requires two sets of input parameters:

1^st input set is the mixture properties
2^nd input set is the geometric parameters of A₁ (emitting area), A₂ (receiving area), and their relative positions.

The outputs of the software are:

View Factor between A₁ and A₂

Exchange Factor between A₁ and A₂

Geometric Mean Transmittance between the two surfaces

Heat Transfer (based on the total energy emitted from A₁ at temperature T_w) received by A₂.

Note that the program will give the "exact" result when the convergence criteria is set to be 1% or less. However, it will take a few minutes to complete the calculation. The user can generate approximate results within a few seconds by setting higher convergence criteria (say 10%).

Fill in Input Values: (Total Pressure = 1 atm (101 kPa))

Mixture Properties		Valid Range	Units
Soot Volume Fraction	f_v	0 to 0.000001	(-)
Absorbing Temperature	T_g	300 to 2000	(K)
Mole Fraction of CO₂	CO₂/(CO₂+H₂O)	0.0 to 1.0	(-)
Pressure	P_g	0 to 101	(kPa)
Emitting Temperature	T_w	300 to 1500	(K)

Geometric Properties
Source	X₁	(m)
Source	Y₁	(m)
Target	Y₂	(m)
Target	Z₂	(m)
Offset	ΔX	(m)
	ΔY	(m)
	ΔZ	(m)

Download Results to File

Example 1

This is a classic view factor calculation for two finite sqaures of same length, having one common edge and having an angle of 90° to each other. The anayltical solution can be found in Siegel & Howell.

Taking the following inputs for mixture properties:

Soot volume fraction = 0
Gas temperature = 300K
Molar fraction of carbon dioxide = 0
Total pressure for the participating species (water vapor and carbon dioxide) = 0kPa
Emitting temperature = 300K

with the geometric configurations:

X₁ = 1m
Y₁ = 1m
X₂ = 1m
Y₂ = 1m
ΔX = 0m
ΔY = 0m
ΔZ = 0m

You will have the following outputs.

	Mixture Properties					Geometric Properties							Outputs
Units	(-)	(K)	(-)	(kPa)	(K)	(m)	(m)	(m)	(m)	(m)	(m)	(m)	(-)	(m²)	(-)	(W)
Symbols	f_v	T_g	Mole Fraction of CO₂	P_g	T_w	X₁	Y₁	Y₂	Z₂	ΔX	ΔY	ΔZ	View Factor	Exchange Fractor	Gemoemtric Mean Transmittance	Heat Transfer
Values	0	300	0	0	300	1	1	1	1	0	0	0	1.9986E-1	1.9986E-1	1.0000E+0	9.1796E+1

Example 2

This example is intended to demonstrate the radiation calculation with a participating medium consisted of water vapor, carbon dioxide, and soot particulates.

Using the geometric configuration given in Example 1, when we have mixtures properties as:

Soot volume fraction = 1E-7
Gas temperature = 500K
Molar fraction of carbon dioxide = 0.5
Total pressure for the participating species (water vapor and carbon dioxide) = 30kPa
Emitting temperature = 1000K,

We can determine:

View factor
Exchange factor
Geometric transmittance
Heat transfer to the receiving surface due to emission from the hot surface.

	Mixture Properties					Geometric Properties							Outputs
Units	(-)	(K)	(-)	(kPa)	(K)	(m)	(m)	(m)	(m)	(m)	(m)	(m)	(-)	(m²)	(-)	(W)
Symbols	f_v	T_g	Mole Fraction of CO₂	P_g	T_w	X₁	Y₁	Y₂	Z₂	ΔX	ΔY	ΔZ	View Factor	Exchange Fractor	Gemoemtric Mean Transmittance	Heat Transfer
Values	0.0000001	500	0.5	30	1000	1	1	1	1	0	0	0	1.9708E-1	1.5589E-1	7.9098E-1	8.8394E+3

Example 3

The last example demonstrates the calculation capibilities to account for arbritary emitting and receiving rectangular surfaces with arbritary relative distance between the two surfaces when the medium bounded by the two surface is consisted of water vapor, carbon dioxide, and soot particulates.

As shown in below figure, the emitting surface (A₁) is situated at z = 0m.

The dimensions of A₁ are 0.43m and 0.96m (X₁, Y₁).
The dimensions of A₂ are 1.93m and 1.26m (Y₂, Z₂).
The relative distance in between A₁ and A₂ in x, y, and z direction is 2.31m, -0.81m, and 1.34m, respectively.

With mixture properties to be:

Soot volume fraction = 1E-8,
Gas temperature = 350K
Molar fraction of carbon dioxide = 0.12
Total pressure for the participating species (water vapor and carbon dioxide) = 5.31kPa
Emitting temperature = 986K.

You should have the following outputs.

	Mixture Properties					Geometric Properties							Outputs
Units	(-)	(K)	(-)	(kPa)	(K)	(m)	(m)	(m)	(m)	(m)	(m)	(m)	(-)	(m²)	(-)	(W)
Symbols	f_v	T_g	Mole Fraction of CO₂	P_g	T_w	X₁	Y₁	Y₂	Z₂	ΔX	ΔY	ΔZ	View Factor	Exchange Fractor	Gemoemtric Mean Transmittance	Heat Transfer
Values	0.00000001	350	0.12	5.31	986	0.43	0.96	1.93	1.26	2.31	-0.81	1.34	3.2937E-2	1.0545E-2	7.7560E-1	5.6516E+2

References

Other related publications:

Walter W. Yuen, "RAD-NNET, a neural network based correlation developed for a realistic simulation of the non-gray radiative heat transfer effect in three-dimensional gas-particle mixtures", International Journal of Heat and Mass Transfer Volume 52, Issues 13-14, June 2009, Pages 3159-3168

Walter W. Yuen, W. C. Tam and W. K. Chow, "Assessment of radiative heat transfer characteristics of a combustion mixture in a three-dimensional enclosure using RAD-NETT (with application to a fire resistance test furnace)", International Journal of Heat and Mass Transfer Volume 68, January 2014, Pages 383-390

Walter W. Yuen, "On the utilization of the mean beam length concept in the evaluation of radiative heat transfer in isothermal three-dimensional non-gray system", International Journal of Heat and Mass Transfer Volume 84, May 2015, Pages 809-820

Walter W. Yuen, W. C. Tam and W. K. Chow, "A Realistic Radiation Heat Transfer Model for Builidng Energy Simulation Program", accepted for publicatin in Numerical Heat Transfer, also AIAA Paper 2014-2389, the 11th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, June, 2014

Walter W. Yuen, L. C. Chow and W. C. Tam, "An Exact Analysis of Radiative Heat Transfer in Three-Dimensional Inhomogeneous Non-Isothermal Media Using Neural Networks", AIAA Journal of Thermophysics and Heat Transfer, Volume 30, Issue 4, May 2016, Pages 897-911

A Neural Network based Calculation of Exchange Factor for a CO2/H2O/N2/Soot Mixture Between Two Perpendicular Rectangular Surfaces