Glossary see Flow network see Glossary see Flow network

Boundary conditions in an aerothermal network model are imposed via flow elements with no upstream node. These elements do not receive information from the network, but supply boundary conditions into the network.

Boundaries can be of pressure type or massflow/pressure type. In the first case the pressure in the network at the position of the boundary element determines the massflow into or out of the network through the boundary element. In the latter case the boundary fluid and temperature are also specified.

Chemical equilibrium means that for a reversible chemical reaction the rates of the forward reaction and the backward reaction are equal. The effect is that there are no net changes in the concentrations of reactants and products although both reactions still take place.

In order to reach chemical equilibrium a sufficient residence time time in the combustor is required.

Increasing pressure shifts the equilibrium towards a state with less volume and vice versa.

Increasing temperature in an exothermal reaction shifts the equilibrium towards the products.

The combustion model is the part of the overall physical model that describes the chemical reaction of fuel and oxidant to combustion products.

Depending on the species mass fractions entering into the combustion process the combustion model derives the species mass fractions leaving the combustion process.

Applying an enthapy balance, the change in species mass fractions will lead to a change in temperature.

Examples of combustion models:

Complete combustion means, sufficient oxygen provided, that all of the fuel carbon is transformed into CO2, all of the fuel hydrogen is transformed into H2O and all of the fuel sulfur is transformed into SO2.

If there is not enough oxygen available a part of the carbon, hydrogen and sulfur in the fuel will remain unburnt.

Complete combustion cannot deal with intermediate species such as CO, intermediate hydrocarbons or radicals such as OH.

Convective cooling is the most basic type of cooling. A stream of hot combustion products flows along one side of the combustor wall and the stream of cooling air flows along the other side of the wall.

convective_cooling.gif

In a stationary process with constant fluid temperatures and constant flow rates on both sides of the wall a heat transfer equilibrium will be reached. The resulting wall temperature profile not only depends on fluid temperatures and flow rates, but also on the wall material(s).

In order to prevent overheating and mechanical disintegration the combustor walls must be cooled. The heat transferred from the combustion process to the walls must be compensated.

Typical cooling technologies for gas turbine combustors are

In a 1d combustor network model each of the above cooling schemes requires special correlations that take the geometry and the various fluid streams into account and deliver heat transfer coefficients and wall temperatures.

Enthalpy balance for a node means that the total enthalpy entering the node equals the total enthalpy leaving the node.

$$ h_{t,in} = h_{t,out} \space \space \space [\frac{kJ}{kg \cdot s}] $$

For a flow element the total enthalpy at the outlet equals the total enthalpy at the inlet plus/minus the energy gained or lost by heat transfer across the element's walls.


$$ h_{t,outlet} = h_{t,inlet} + \dot{q} \space \space \space [\frac{kJ}{kg \cdot s}] $$

Film cooling is a means of reducing hot side heat transfer by injecting a film of cooling air alongside the hot side combustor wall.

Typically the cooling air enters from the combustor cold side through a number of holes and is deflected to form a cooling film that gradually mixes with the hot combustor flow.

Several stages of film cooling can be applied in series to achieve the desired wall temperature.

For heat transfer calculations there are correlations that allow the derivation of heat transfer coefficients from the film cooling geometry and the film mass flow.

The distribution of mass fluxes in the branches of a flow network. As massflow must be conserved the total massflow into a network node must be equal to the total massflow leaving the network node.

The flow split is a function of the resistance of the flow elements. In general terms high resistance in a flow element results in a high pressure drop along the element and accordingly in a low massflow through the element.

A 1d flow element is the ideal model of a real three dimensional geometry.

Characteristics:

A flow network consists of one or more 1d flow elements (circles) interconnected via nodes (squares). Both bifurcations and unifications of the flow path are possible. Boundary conditions are imposed via elements without an upstream node.


The basic aerodynamics (flowsplit, pressure drop, enthalpy balance) of combustion chambers like those of gas turbines can be modelled using a flow network. The effort for setting up a model and the computational effort for solving it are appreciably lower than with a full 3d CFD model. A fluid is a gaseous mixture of one or more species.

Examples (in mass percent) Fluids can be defined by the user.

A glossary lists relevant special terms of a specific field in alphabetical order and provides a short description for each term.

The maidhof.com glossary lists terms which are relevant to 1d combustion and aerothermal modelling.

A term in the glossary may have a different meaning in another scientific or technical field. It is therfore important to keep the context of the glossary in mind.

 = Graphical User Interface.

Via a GUI the user can interact with a computer program using a mouse and a keyboard. The GUI can contain various types of standardised input fields such as textfields, select lists or radio buttons as well as interactive graphics. Traditionally a GUI was a feature of stand-alone locally installed programs. With the advances in internet technology a GUI can nowadays be realised entirely in a web browser without any local installation. Heat flows from higher temperatures to lower temperatures. If the heat is not continuously supplied at the hot end and not continuously drained at the cold end, heat transfer will eventually lead to a temperature equilibrium.

Heat can be transferred by conduction and by radiation. The first necessitates physical contact between the hot and the cold part whereas the latter necessitates "sight contact" between the hot and the cold part. Please note that convection is a special case of conduction between a moving fluid and a solid.

The objective of heat transfer calculations in combustion is to obtain wall temperatures and to layout the cooling system. A secondary effect that can be taken into account is the transfer of heat from one flow element across a wall to another flow element leading to a change in temperature in both elements. This can be of interest for emissions calculations.

Impingement cooling uses double walls. One impermeable and the other perforated. The impermeable wall adjacent to the hot combustion stream is cooled by impingement jets that develop through the perforation holes of the outer wall.

riblet_cooling.gif

With a growing number of impingement jets a crossflow accumulates between the two walls and gradually makes the jets less efficient.

Correlations provide heat transfer coefficients as a function of hole sizes, hole spacing and hole pattern as well as wall distances.

 The Mach number is the ratio of flow velocity U to the speed of sound a. $$ Ma = \frac{U}{a} $$ The Mach number is an indication as to whether the flow is compressible. With a Mach number of <=0.3 the flow can be treated as incompressible whereas a higher Mach number requires the flow to be treated as compressible.

The evolution of the Mach number in a flow element depends on the following factors:

A node is a logical element with no geometric properties like a node in an electrical circuit. Flow elements can be connected upstream or downstream of a node.

At a node the first law of thermodynamics applies:

 The perfectly stirred reactor is a special flow element which can take chemical kinetics into account.

The reactants are assumed to have perfectly mixed upon entering the PSR. The reaction into products follows a chemical reaction mechanism and is primarily dependent on the reactor residence time. The longer the residence time the more the reaction will be completed. Pressure drop is the difference in total pressure across a single flow element or across an entire flow network. $$ \Delta p = p_{t,outlet} - p_{t , inlet} $$ Physical processes creating a pressure drop are: A pressure drop causes a change in Mach number. Residence time ($t_{res}$) for a flow element is a function of element volume (Vol), massflow through the element ($\dot{m}$) and the mean density ($\rho$) $$ t_{res} = \frac{Vol \cdot \rho}{\dot{m}} $$

Riblet cooling is a means of enhancing the heat transfer on the cold side of the combustor wall with turbulators.

The turbulators enhance flow turbulence and hence heat transfer and cooling.

riblet_cooling.gif

The turbulators increase the pressure drop as compared to a smooth wall.

Correlations allow the derivation of heat transfer coefficients as a function of the riblet geometry

 Species can be either atoms like C,O,H or molecules like O2, CH4 or C12H23.

Characteristics:

Species are the constituents of fluids and can be defined by the user.

Species balance for a node means that the sum of mass fractions x of species \( \alpha \) entering the node (branches,in) equals the sum of mass fractions of species \( \alpha \) leaving the node (branches out).

$$ \sum_{branches,in} x_{\alpha} = \sum_{branches,out} x_{\alpha} $$

Along a flow element, however, chemical reaction may occur. Species like O2 or CH4 may be produced or consumed. Hence there is only a conservation of atoms like N,H,O,C,S.

For an atom \( \beta \) we look into all species and sum up the mass content of atom \( \beta \) in the species $$ \sum_{\alpha,inlet} x_{\alpha} \cdot b_{\alpha\beta} = \sum_{\alpha,outlet} x_{\alpha} \cdot b_{\alpha\beta}. $$ \( \alpha \) are species like O2 or CH4 and \( \beta \) are atoms like N,H,O,C,S. \(b_{\alpha\beta}\) is the mass content of atom \( \beta \) in species \( \alpha \), e.g. 12/16 for C in CH4. \( x_{\alpha} \) is the mass fraction of species \( \alpha \).

Species transport means that in the flow network model individual chemical species like CH4 or O2 are modelled. This allows for more advanced combustion modelling like chemical equilibrium, perfectly stirred reactor or plug flow reactor.

Species transport is also a prerequisite for an enthalpy balance.

Species transport requires a species balance for flow elements and nodes

Thermal properties of a species are specific enthalpy [kJ/kg] and heat capacity [kJ/kg/K].

Thermal properties describe how molecules change their internal state as a function of temperature.

They are calculated for a single species as a polynomial function of temperature and for a fluid as a function of the participating species mass fractions.

Transport properties of a species are those properties that describe how momentum (viscosity) and heat (conductivity) are transported through molecular interaction.

Transport properties describe the interaction between molecules as a function of temperature.

They are calculated for a single species as a function of temperature and for a fluid as a function of the participating species mass fractions.