Introduction to CFX -Heat Transfer

Introduction to CFX -Heat Transfer

Governing Equations

Conservation Equations

Heat transfer in a fluid domain is governed by the Energy Transport Equation:

The Heat Transfer Model relates to the above equation as follows

-None: Energy Transport Equation not solved

-Isothermal: The Energy Transport Equation is not solved but a temperature is required to evaluated fluid properties (e.g. when using an Ideal Gas)

-Thermal Energy: An Energy Transport Equation is solved which neglects variable density effects. It is suitable for low speed liquid flow with constant specific heats. An optional viscous dissipation term can be included if viscous heating is significant.

-Total Energy: This models the transport of enthalpy and includes kinetic energy effects. It should be used for gas flows where the Mach number exceeds 0.2, and high speed liquid flows where viscous heating effects arise in the boundary layer, where kinetic energy effects become significant.

For multicomponent flows, reacting flows and radiation modeling additional terms are included in the energy equation

Heat transfer in a solid domain is modeled using the following conduction equation

Selecting a Heat Transfer Model

The Heat Transfer model is selected on the Domain > Fluid Models panel

Enable the Viscous Work term (Total Energy), or Viscous Dissipation term (Thermal Energy), if viscous shear in the fluid is large (e.g. lubrication or high speed compressible flows)

Enable radiation model / submodels if radiative heat transfer is significant

Radiation

Radiation effects should be accounted for when is significant compared to convective and conductive heat transfer rates

To account for radiation, Radiative Intensity Transport Equations (RTEs) are solved

-Local absorption by fluid and at boundaries couples these RTEs with the energy equation

Radiation intensity is directionally and spatially dependent

Transport mechanisms for radiation intensity:

-Local absorption

-Out-scattering (scattering away from the direction)

-Local emission

-In-scattering (scattering into the direction)

Radiation Models

Several radiation models are available which provide approximate solutions to the RTE

Each radiation model has its assumptions, limitations, and benefits

Choosing a Radiation Model

The optical thickness should be determined before choosing a radiation model

-Optically thin means that the fluid is transparent to the radiation at wavelengths where the heat transfer occurs

The radiation only interacts with the boundaries of the domain

-Optically thick/dense means that the fluid absorbs and re-emits the radiation

For optically thick media the P1 model is a good choice

-Many combustion simulations fall into this category since combustion gases tend to absorb radiation

-The P1 models gives reasonable accuracy without too much computational effort

For optically thin media the Monte Carlo or Discrete Transfer models may be used

-DTM can be less accurate in models with long/thin geometries

-Monte Carlo uses the most computational resources, followed by DTM

-Both models can be used in optically thick media, but the P1 model uses far less computational resources

Surface to Surface Model

-Available for Monte Carlo and DTM

-Neglects the influence of the fluid on the radiation field (only boundaries participate)

-Can significantly reduce the solution time

Radiation in Solid Domains

-In transparent or semi-transparent solid domains (e.g. glass) only the Monte Carlo model can be used

-There is no radiation in opaque solid domains

Heat Transfer Boundary Conditions

Inlet

-Static Temperature

-Total Temperature

-Total Enthalpy

Outlet

-No details (except Radiation, see below)

Opening

-Opening Temperature

-Opening Static Temperature

Wall

-Adiabatic

-Fixed Temperature

-Heat Flux

-Heat Transfer Coefficient

Radiation Quantities

-Local Temperature (Inlet/Outlet/Opening)

-External Blackbody Temperature (Inlet/Outlet/Opening)

-Opaque

Specify Emissivity and Diffuse Fraction

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