# What is VBT theory

### Description

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#### Table of Contents

- introduction
- General characterization of turbulence
- Features of turbulent flows
- Turbulence generation, turbulence categories
- Turbulent currents in nature and technology

- Basics in the field of laminar flows
- Field-local flow field kinematics / deformation and rotation tensor
- Representation of the local kinematic state in Cartesian coordinates
- Rotation and deformation tensor from the decomposition of the tensor of the local state of relative motion
- Field-local kinematic state as a superposition of translation, rotation and deformation
- Volume dilation and divergence

- Flow field differential equations from mass and momentum balances
- Mass balance / continuity equation
- Momentum balance equation, frictional stresses

- Energy analysis of laminar, incompressible flows / energy dissipation
- Flow field equations of energy and mass transport
- Transport equation for thermal energy
- Transport equation for substance species

- Laminar and turbulent flows / Reynolds number as a discrimination parameter

- Field-local flow field kinematics / deformation and rotation tensor
- Turbulent impulse, heat and mass transport
- Decomposition of turbulent flow quantities into mean values and fluctuation values
- Turbulent momentum and scalar exchange
- Gradient approaches for turbulent-diffusive transport quantities / transport flow densities
- Reynolds equations
- Reynolds decomposition of turbulent field quantities
- Reynolds’s equations of flow for incompressibility
- Turbulent scalar transport equation for incompressibility

- Reynolds number dependence of the turbulent, incompressible, time-averaged transport equations
- Turbulent transport equations for flow fields of varying density using Favre averaging
- Favre averaging and Favre fluctuation components / definition
- Favre decomposition applied to mass flux terms / continuity equation
- Favre decomposition applied to momentum current density terms / momentum balance equation
- Favre decomposition applied to the scalar transport terms and the scalar transport equation

- Mode of action of
- Analogy between molecular and fluidic viscosity
- Molecular toughness (internal friction)
- Prandtl’s mixing path approach

- Dynamics of turbulence
- Equation of the kinetic energy of the main flow
- Equation of the kinetic energy of the turbulent oscillatory motion
- Equation for the vortex strength (vortex transport equation)
- Reynolds equation for turbulent flow layers
- Current near solid walls

- The energy cascade
- Premix flames
- Laminar flame propagation - thermal theory
- Turbulent premix combustion
- Parameters and key figures of the Borghi diagram
- Mathematical flame model for premixed flames according to Hans-Peter Schmid

#### comment

The script will be handed out to accompany the lecture.

#### application areas

The lecture material is the basis of many scientific and industrial applications, especially in the field of gas turbines and internal combustion engines.

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