ConvectionAndRadiation tubeBank L2

Created Tuesday 23 March 2016

A model used to calculate the convective and radiative heat transfer inside a tube bank according to VDI-Wärmeatlas [1] chapter Gg.

1. Purpose of Model


A model used to calculate the convective and radiative heat transfer inside a tube bank. This model should be used for example to calculate the heat transfer to the first tube bundles inside a furnace where gas and particle radiation can not be neglected due to high temperatures.

2. Level of Detail, Physical Effects Considered and Physical Insight


2.1 Level of Detail


Referring to Brunnemann et al. [2], this model refers to the level of detail L2.

3. Limits of Validity


For the calculation of the radiative heat transfer no limits of validity known. According to [1] the convective heat transfer calculation is valid for Reynolds numbers in the range of 10¹ < Re < 10⁶ and for Prandtl numbers between 0.6 < Pr < 1000.

4. Interfaces


4.1 Physical Connectors


Basics:Interfaces:HeatPort a heat

5. Nomenclature



6. Governing Equations


The overall heat flow is the sum of convective and radiative heat transport:




Concective heat transfer:


The mean temperature difference is defined as follows, based on the user's choice in the boolean parameter temperature difference:



Please note that for the choice temperatureDifference="Logarithmic mean" a number of means is applied to make the equation regular also for zero heat flow and reversing heat flows. If an unsupported string for temperatureDifference is provided an assert would raise.

The uninfluenced velocity of the gas at inlet is calculated as follows:

The characteristic length is calculated as follows:

With the velocity, the characteristic length, dynamic viscosity and density the Reynolds number is calculated:

The Nusselt numbers are calculated with Reynolds and Prandtl number:



The arrangement factor is calculated depending on the tube arrangement:

The Nusselt number for the tube bank is then calculated as follows:


The heat transfer coefficient is then calculated as follows:

The convective heat flow is calculated as follows:



Radiative heat transfer:

The calculation is subdivided into three cases:

  1. Suspension_calculation_type = "Fixed": Fixed predefined values for emissivity and absorbance of the suspension are used
  2. Suspension_calculation_type = "Gas calculated, particles fixed": Particle emissivity is considered with a fixed value and emissivity and absorbance of H2O and CO2 are calculated temperature and composition dependent. This is a good choice if the needed parameters of the used coal (Rosin-Rammler-Distribution) are unknown.
  3. Suspension_calculation_type = "Calculated": Emissivity and absorbance of particles and gasses are calculated according to the chosen parameters as well as temperature and composition dependent.


The heat flow transferred by radiation is calculated for all three cases as follows:

The emissivity and absorbance for three cases is carried out in different ways depending on the three different cases.

Case 1: The emissivity and absorbance vales are set to the fixed parameter values:


Case 2: Emissivity and absorbance of the gas (H2O, CO2) are calculated, particle radiation is regarded with fixed parameter.

The equivalent thickness of the gas volume is calculated as follows:

The weighting factors at suspension and wall temperature:

The suspension emissivity factors are calculated with the partial pressure of H2O and CO2 and the equivalent thickness:

The emissivity of CO2 and H2O of the suspension is calculated as follows:

The emissivity of the suspension is now given as:

The absorbance of CO2 and H2O of the suspension is calculated with wall temperature:

And the absorbance of the suspension is given as:

Case 3: Emissivity and absorbance of the gas (H2O, CO2) and particles are calculated.

The values for emissivity and absorbance of the H2O and CO2 gasses are identical to case 2 but here we need to calculate the influence of particle radiation too.

The soot load of the flue gas is given as:

The coke load of the flue gas is given as:

The absorbance of the coke particles is calculated as follows:

The ash load of the flue gas is given as:

The absorbance of the ash particles is calculated as follows:

The suspension emissivity factors are calculated with the partial pressure of H2O and CO2, particle emissivities and the equivalent thickness:

The emissivity of the suspension is calculated as follows:

The absorbance of the suspension is calculated with wall temperature:


7. Remarks for Usage


8. Validation


9. References

[1] Johannes Brunnemann and Friedrich Gottelt, Kai Wellner, Ala Renz, André Thüring, Volker Röder, Christoph Hasenbein, Christian Schulze, Gerhard Schmitz, Jörg Eiden: "Status of ClaRaCCS: Modelling and Simulation of Coal-Fired Power Plants with CO2 capture", 9th Modelica Conference, Munich, Germany, 2012
[2] VDI Wärmeatlas, Verein Deutscher Ingenieure VDI-Gesellschaft Verfahrenstechnik und Chemieingenieurwesen (GVC), Springer Verlag, 10. Auflage, 2006

10. Authorship and Copyright Statement for original (initial) Contribution

Author:
DYNCAP/DYNSTART development team, Copyright 2011 - 2022.
Remarks:
This component was developed during DYNCAP/DYNSTART projects.
Acknowledgements:
ClaRa originated from the collaborative research projects DYNCAP and DYNSTART. Both research projects were supported by the German Federal Ministry for Economic Affairs and Energy (FKZ 03ET2009 and FKZ 03ET7060).
CLA:
The author(s) have agreed to ClaRa CLA, version 1.0. See https://claralib.com/pdf/CLA.pdf
By agreeing to ClaRa CLA, version 1.0 the author has granted the ClaRa development team a permanent right to use and modify his initial contribution as well as to publish it or its modified versions under the 3-clause BSD License.

11. Version History

25.06.2014 - v0.1 - initial implementation of the model - Lasse Nielsen, TLK-Thermo GmbH


Backlinks: ClaRa:Components:Furnace:FlameRoom:FlameRoomWithTubeBundle L2 Dynamic ClaRa:Components:Furnace:FlameRoom:FlameRoomWithTubeBundle L2 Static