Glossary

Adiabatic combustion temperature depends on the type of fuel, the fuel to air ratio and the temperature of the mixture prior to combustion.

and compute the adiabatic combustion temperature yourself.

AEF < 1 |
fuel rich |

AEF = 1 |
stoichiometric |

AEF > 1 |
fuel lean |

AEF is the reciprocal value of equivalence ratio (EQR). Whether AEF or EQR is used, often depends on the industry and its engineering environment.

The AFR is the reciprocal value of the fuel to air ratio (FAR). Mathematically there is no reason why to choose one over or the other since they express exactly the same thing. However, when dealing with fuel-lean combustion a value of the AFR of 40 is much more handy than a value of the FAR of 0.025. Otherwise it is often a question of tradition and practice in an engineering environment whether to use AFR or FAR.

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.

and make chemical equilbrium calculations yourself.

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 CO_{2}, all of the fuel hydrogen is transformed into H_{2}O and
all of the fuel sulfur is transformed into SO_{2}.

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.

Complete combustion will result in the adiabatic combustion temperature.

and make complete combustion calculations yourself.

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.

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).

and compute convective heat transfer yourself.

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

- Convective cooling
- Film cooling
- Riblet cooling
- Impingement cooling
- Effusion cooling
- Pedestal cooling

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.

In aerothermal modelling correlations are used to compute a desired quantity using known quantities. Correlations are mostly derived from experiments.

Example: flat plate correlation

$$ Nu = 0.023 \cdot Re^{0.8} \cdot Pr^{0.4} $$ The correlation formulated 1930 by Dittus and Boelter relates the Nusselt number (Nu) to the Reynolds (Re) and Prandtl (Pr) numbers of the fluid. If we know the Reynolds and Prandtl numbers of the fluid flowing past a flat plate, we can work out the Nusselt number and hence the heat transfer coefficient.

Diffusion flames are to a greater extent determined by fluid mechanics, molecular diffusion and flow turbulence than by chemical kinetics. The simplified approach "mixed equals burnt" for diffusion flames basically means that the time scale of fluid mechanics is much larger than the chemical timescale.

Different configurations can be compared with respect to certain physical effects by looking at their appropriate dimensionless numbers.

Example: Reynolds number

It is defined as $$ area_{eff} = \frac{\dot{m}}{\sqrt{2 \cdot \rho \cdot (p_{total,1} - p_{static,2})}} $$

\( \dot{m}\)= massflow, \( p_{total,1} \)= total pressure upstream, \( p_{static,2}\): static pressure downstream, \( \rho \): density (assumed constant)

Effective area, discharge coefficient and loss coefficient can be converted into each other.

Effective area does not depend on the boundary conditions. It only depends on the geometry of the flow element.

The concept of effective area can also be applied to the entire flow network of a combustor.

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.

EQR < 1 |
fuel lean |

EQR = 1 |
stoichiometric |

EQR > 1 |
fuel rich |

The advantage of using EQR instead of FAR is that the above table is true for any fuel. The value of the stoichiometric fuel to air ratio varies from fuel to fuel, but EQR=1 always means stoichiometric conditions.

Specific enthalpy hhx for a species can be calculated from H(T) \[\begin{aligned} hhx(T) = \frac{H(T)}{M} \cdot R_{gen} \cdot T \\ [ \frac{1}{\frac{kg}{kmol}} \cdot \frac{kJ}{kmol \cdot K} = \frac{kJ}{kg} ] \end{aligned} \]

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.

80 + 20 = 40 + 60

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:

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.

Examples (in mass percent)

- dry air:

- 23.2% O
_{2} - 76.8% N
_{2}

- 23.2% O
- pure hydrogen:
- 100% H
_{2}

- 100% H

FAR=0 means pure air whereas FAR=infinity means pure fuel. The stoichiometric FAR is a specific value for each fuel somewhere inbetween zero and infinity and means that the amount of oxygen in the air is just sufficient to burn all of the fuel. If the FAR is less than the stoichiometric value the case is fuel lean which means that we have more oxygen available than is needed to burn the fuel. Some oxygen remains after combustion.

If the FAR exceeds the stoichiometric value the case is fuel rich which means that there is not enough oxygen to burn the fuel, i.e. fuel, but not oxygen is left after combustion.

The FAR is the reciprocal value of the air to fuel ratio (AFR)

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.

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 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.

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

- Change of cross section
- Heat exchange
- Pressure drop.

Mass balance applies both to a flow element and a network node.

For a flow element it means that the massflow entering a flow element equals the massflow leaving the flow element. This is true for all flow elements at any time during the iteration.

For a network node it means that the sum of massflows flowing into the node equals the sum of massflows leaving the node. In a converged solution all nodes will have a mass balance within a specified tolerance.

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:

Any intermediate between a pure diffusion flame and a pure premixed flame is also possible.

A premixed flame is more sensitive to the stoichiometry than a diffusion flame. A premixture may be too fuel lean to burn, whereas a diffusion flame with the same stoichiometric ratio between fuel and oxidant streams may still burn.

- Friction
- Area change
- Flow curvature
- Mixing
- Swirl
- Combustion.

$$ Re = \frac{U \cdot L}{\nu} [ \frac {\frac{m}{s} \cdot m}{\frac{m^2}{s}} = 1 ] $$ Two fluid systems with different dimensions, different velocities and different fluids will behave similar with respect to turbulence when their Reynolds numbers are similar.

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.

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

Characteristics:

- Molecular weight
- volumetric content of carbon (C), hydrogen (H), sulfur (S) which can be burnt
- volumetric content of oxygen (O)
- volumetric content of inerts
- transport properties
- thermal properties

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 O_{2} or CH_{4} may be produced or consumed. Hence there is only a conservation of atoms like N,H,O,C,S.

and compute a species balance yourself.

Species transport means that in the flow network model individual chemical species like CH_{4} or O_{2} are modelled. This allows for more advanced combustion modelling like Chemical equilibrium, Perfectly stirred reactor (PSR) or Plug flow reactor (PFR).

Species transport is also a prerequisite for an enthalpy balance.

Species transport requires a species balance for flow elements and nodes

Thermal diffusivity is the diffusivity of heat in the heat conduction equation.

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.

Viscosity \(\mu\) is a transport property of a fluid which quantitatively describes how momentum is transferred within the fluid on a molecular level. For a fluid with higher viscosity (honey) more momentum is exchanged between adjacent fluid regions than for a fluid with lower viscosity (water). Just imagine dragging a spoon through a pot of honey and a pot of water and how the spoon moves the fluid.

Viscosity has the unit of kg / m / s.