SGP_HeatSinkIcon

Use the Heat Sink component to model heat transfer among gas path components or with the ambient environment. Add a heat sink component to the model and connect gas path components to the heat sink in the Heat Sink tab sheet of the gas path component. In the gas path component heat sink table, specify the specific heat transfer model data, one connection per row.

General tab sheet

•Enabled
Enable/disable the Heat Sink. Disabling means all heat transfer with this heat sink is inhibited.

•Dynamics
Define the Effective mass and Specific Heat of the heat sink. Note that these data only affect transient performance, similar to the heat soakage effect model.

•Iteration control
Define a Temperature 1st guess and a Q total error normalization factor to optimize iteration performance and stability. Since the heat sink temperature is a state variable, For the temperature, take the expected material temperature of the structures between the components, for example the gas path temperature averaged over the connected components. For the Q total factor, take a value in the order of the expected heat flux in order to have well conditioned Jacobian matrix for the solver; this is because the error equation for the heat sink is the sum of all heat fluxes being equal to zero

External heat transfer tab sheet

Here the heat transfer model data to the ambient environment and to other heat sink components can be specified in two separate tables, one per table row. See information below on parameters.

When the Heat Sink option is activated in the Heat Sink tab of a gas path component, a heat flux to or from the attached Heat Sink component is calculated. The Heat Sink component itself must also be activated. It is possible for a component to have more than one Heat Sink connected to it. This can be seen as different heat transfers that occur with different components. Heat Sink components can also be interfaced with multiple gas turbine components as well as with other Heat Sink components and the ambient environment.

Using Heat Sink components, complex thermal network models can be built connecting multiple heat sinks and gas path components. For steady state calculations, the heat capacity (mass and specific heat) does not affect the results since the system is in a thermal equilibrium. For transient calculations, the dynamic effects of heat transfer (heat soakage) is determined by the effective mass and the specific heat assigned to the Heat Sink component. Note that this heat soakage effect is in addition to the heat soakage effect that can be applied in the gas path component itself.

The heat sink model parameters are specified at two locations:

•Heat sink tab sheet of the connected Gas path component. Here the heat transfer model data for the heat transfer between the specific component and the heat sink are given in the table in the Heat sink tab sheet.

•Heat Sink component itself: here the general heat sink properties (mass, specific heat) and data for heat transfer data with the ambient environment and other heat sinks are specified.

An overview of the generic equations used is given in Heat sink equations. For a glossary on parameter names, also used in the sections below, see Heat sink parameters.

External heat transfer

In the External heat transfer tab sheet the data for modeling heat transfer to ambient can be specified. In the table rows multiple heat transfer models can be specified. Total heat transfer is the sum of all rows. Per row, either Ambient conditions as specified in the global model Ambient/Flight conditions can be selected or custom conditions can be selected in which case Temperature, Density, Mu and Cp must be user specified in the adjacent columns. A shaft suffix, D, Mu and density can be specified to calculate a Re number for rotating disks or cylinders. This option can be used to represent heat transfer with rotating elements in the gas turbine. Without a shaft suffix, Re will be 0 and the Re D or Nu L parameter now will represent the characteristic length L for the Nusselt relation. Next parameters to calculate Prantl number Pr (k gas) and the Nusselt expression for convective heat transfer is specified. This expression may include the 'Re' and 'Pr' parameters calculated before. Avoid Re being 0 (no shaft) if Re is used in the expression.

From the Nusselt expression Nu number is calculated. The convection heat transfer is then calculated using h_conv = Nu * k_gas / L. The conduction heat transfer coefficient is calculated with h_cond = k mat / d mat. Total heat transfer coefficient for convection and conduction then is h total = 1 / ( 1/h_conv + 1/h_cond). Corresponding heat flux Qconvcond = h total * Aht * (Tambient - Theatsink). Note that Qconvcond is negative when heat flows from the heatsink to ambient.

A wall surface temperature is calculated using Twall = Theatsink + Qconvcond / Aht / h_cond.

With an emissivity index Eps rad > 0, a radiation heat flux is calculated using

Qrad = (Twall^4 - Tambient^4) * Cstefanboltzmann * Eps rad * Aht.

Finally, total heat flux Qtotal then is the sum of Qconvcond and Qrad.

User specified heat flux

Heat transfer with the Heat Sink component also allows for a user specified heat flux. If the option is enabled a value can be specified in the field of the total heat rate “Qtotal” column at the far right of the table (check the User spec Q column) and calculations to determine the heat transfer coefficient are performed only for reference is possible and results are overridden by the user specified value. The GSP solver will iterate towards an operating point including heat sink and wall temperatures where this condition can be met. For example, if heat transfer of the heat sink with the ambient environment is user specified, then the heat sink temperature will go to a level where this heat flux can be realized by convection and/or radiation. Consequently, the heat transfer between gas path components and the heat sink will be affected.

Heat transfer among Heat Sink components

Heat Sink components can also exchange thermal energy among each other. This is an option that resides in the Heat Sink component. If heat transfer between two Heat Sink components is enable in a Heat Sink component, this is automatically enabled in the target Heat Sink. A user defined heat transfer coefficient with the unit [W/K] can be specified for a heat flux proportional with the temperature difference between the heat sinks. This corresponds to heat transfer by conduction between solids. Therefore, the heat transfer coefficient can be estimated by:

Only in one of the 2 heat sink components a value for the heat transfer coefficient must be defined. The other heat sink automatically accepts this heat transfer and does not require additional input.

After calculation, the total of the External conditions heat transfers heat fluxes and the Heat fluxes to other heat sinks is summed up to provide the total heat flux to/from the component. During steady state this sum must be 0, during transient, it can be non-zero only if a heat sink mass and Cp has been specified in the Dynamics box in the General tab sheet. This heat balance is added to the GSP equation system while the heat sink temperature is added as a state variable.