A new reaction rate source term
ω
m
(
c
)
for modelling of premixed combustion with a single progress variable
c
is proposed.
ω
m
(
c
)
mimics closely the Arrhenius source term
ω
A
(
c
)
for a large ...range of activation energies and density ratios while admitting analytic evaluation of many quantities of interest. The analytic flame profile
c
m
(
ξ
)
very closely approximates the numerically integrated Arrhenius flame profiles
c
A
(
ξ
)
. An important feature of
c
m
(
ξ
)
is that it is analytically invertible into a
ξ
m
(
c
)
. Analytic estimates of the laminar flame Eigenvalue
Λ
and of the
Le
dependence of the laminar flame speed
s
L
are derived, which are more accurate than classic results based on asymptotic analyses. The flamelet pdf
p
(
c
)
=
1
/
(
Δ
∗
c
∗
(
1
-
c
m
)
)
for a flat laminar flame front in a LES cell of width
Δ
is derived. The exact mean of the reaction rate
ω
(
c
)
¯
is compared to a beta pdf result, which is shown to be inaccurate for large ratios of filter width to flame thickness
Δ
/
δ
f
and particularly for high activation energy flames. For multidimensional flame wrinkling we derive the exact relationship
p
(
c
)
=
p
1
D
(
c
)
I
(
c
)
Ξ
(
c
)
between the 3D pdf
p
(
c
), the 1D flat flame pdf
p
1
D
(
c
)
, a correction factor
I
(
c
) for change of inner flame structure and a geometrical wrinkling factor
Ξ
(
c
)
. We show that the
c
dependence of these quantities cannot be neglected for small
Δ
/
δ
f
. A simple model of a sinusoidally wrinkled flame front qualitatively demonstrates the effect of flame wrinkling on
p
(
c
). We show that for large
Δ
/
δ
f
, a wrinkling of the reaction zone almost constantly increases
p
(
c
) in the reaction zone by a wrinkling factor
Ξ
∗
(defined for the surface of the isosurface of maximum heat release) while reducing it near
c
=
0
,
1
as required for normalisation of
p
(
c
). The 1D
p
(
c
) evaluated using a reduced filter width
Δ
′
=
Δ
/
Ξ
∗
may be a good approximation of the wrinkled flame pdf for evaluation of
ω
(
c
)
¯
for such cases.
Mixing under high pressure conditions plays a central role in several engineering applications, such as direct-injection engines and liquid rocket engines. Numerical flow simulations have become a ...complementary tool to study the mixing process under these conditions but require complex thermodynamic modeling as well as validation with accurate experimental data. For this reason, we use experiments of supercritical single-phase jet mixing from the literature, where the mixing is quantified by the mixture speed of sound, as a reference for our work. We here focus on the thermodynamic modeling of multi-component flows under high pressure conditions and the analytical calculation of the mixture speed of sound. Our thermodynamic model is based on cubic equations of state extended for multi-components. Using an extension of OpenFOAM, we perform large-eddy simulations of hexane and pentane injections and compare our results with the experimentally measured mixture speed of sound at specific positions. The simulation results show the same characteristic trends, indicating that the mixing effects are well reproduced in the simulations. Additionally, the effect of the sub-grid scale modeling is assessed by comparing results using different models (Smagorinsky, Vreman, and Wall-Adapting Local Eddy-viscosity). The comprehensive simulation data presented here, in combination with the experimental data, provide a benchmark for numerical simulations of jet mixing in high pressure conditions.
A probabilistic data-driven approach that models the filtered reaction rate in large-eddy simulation (LES) is investigated. We propose a novel framework that incorporates a conditional generative ...adversarial network and a Gaussian mixture model to take into account the statistical fluctuations that are present in LES of turbulent reacting flows due to non-resolved subgrid structures, which cannot be predicted by purely deterministic models and machine learning algorithms. The data from a direct numerical simulation of turbulent premixed combustion are spatially filtered using a wide range of filter widths and employed for the training. We extract physically relevant parameters from the database and reduce the input features to the network to the most influential ones based on the result of feature importance analysis. The trained model is then tested on unseen timesteps and untrained LES filter widths, where it is able to accurately predict the distribution of the filtered reaction rate.
The data provided allows other research groups to numerically investigate the flame wall interactions of an experimental test bench at the University of the Bundeswehr Munich. Numerical simulations ...can then be compared to the experimental results to test new models. Three data sets are available. The first data set contains the inflow boundary conditions created by the burner into the test section. The fields of interest are the velocity and RMS-velocity fields. Large-Eddy-Simulation (LES) using ANSYS Fluent was used to collect this data. The second data set provides the inflow boundary condition from the fuel injector into the test section using methane at a momentum ratio of I = 10. LES using OpenFOAM was used to create this data. The third data set provides the temperature distribution at the wall of the test section when injecting methane at a momentum ratio of I = 10. The temperature is provided along the wall ranging from +/- 25 mm in the lateral and 0 - 220 mm in the axial direction. The data was derived from wall-embedded thermocouples by applying the inverse heat conduction method using MATLAB and COMSOL.
Large Eddy Simulations (LES) of film cooling flows were conducted to investigate the impact of high turbulence intensity in the main flow, representative of jet-engine combustor conditions. A ...comparison was made with LES simulations at zero turbulence at the main flow inlet boundary. The study investigated three different film cooling configurations, which involved cylindrical holes and two variations with holes embedded in trenches known as transverse and segmented trench. Different momentum ratios (I=3.5 and 8.3) relevant to combustor flows in jet-engines were applied. The LES simulations utilized OpenFOAM and solved the energy and passive scalar transport equations to determine film cooling efficiency (η), heat transfer coefficient (hf), and net heat flux reduction (NHFR). The numerical results were validated through comparison with experimental data. The mean and instantaneous results revealed that high turbulence intensity in the main flow significantly influenced film cooling performance. The film cooling efficiency was found to decrease with increased turbulence intensity, while for the ordinary film cooling design exhibiting jet lift-off, the increased mixing led to higher η. The heat transfer coefficient increased with turbulence intensity and momentum ratio, with turbulence intensity having a greater impact on ordinary designs and momentum ratio on trenched designs. Moreover, increasing turbulence intensity or momentum ratio resulted in lower NHFR for all designs. Hot spots were observed in the instantaneous results, with spatial variations depending on the film cooling design.
•Unsteady high turbulence boundary condition.•Ordinary and trenched film cooling designs.•Heat transfer coefficient.•Net heat flux reduction.•Unsteady effects near the wall.
A new chemical reaction rate source term in the transport equation of a single progress variable is proposed and implications for premixed flame modelling are discussed. This surrogate source term ...approximates the Arrhenius one over a large range of activation energies and density ratios almost perfectly. An analytic, invertible flame profile and the corresponding 1D laminar flame pdf are derived. The laminar flame Eigenvalue is evaluated analytically for unity and non-unity Lewis number and compared to classical results. A method to evaluate the progress variable pdf from DNS data is introduced. It is based on regularized delta functions and a transformation of the DNS progress variable field with the inverse of the 1D laminar flame profile, which behaves like a signed distance function. The pdf factorizes into the flat flame pdf, a geometrical wrinkling factor and a correction factor accounting for changes in the inner flame structure. The pdfs of RANS-like filter volumes and their ingredients are evaluated from DNS datasets of statistically flat turbulent flames featuring different turbulence intensity levels. For all DNS cases the wrinkling and correction factors vary little with progress variable. The wrinkling factor rises with turbulence intensity. The pdf is similar to that of a 1D laminar flame pdf, scaled by the wrinkling factor. Opportunities for improvements to premixed turbulent flame modelling are discussed.
In the present paper, the behaviour of an oxy-fuel non-premixed jet flame is numerically investigated by using a novel approach which combines a transported joint scalar probability density function ...(T-PDF) following the Eulerian Stochastic Field methodology (ESF) and a Flamelet Progress Variable (FPV) turbulent combustion model under consideration of detailed chemical reaction mechanism. This hybrid ESF/FPV approach overcomes the limitations of the presumed- probability density function (P-PDF) based FPV modelling along with the solving of associated additional modelled transport equations while rendering the T-PDF computationally less demanding. In Reynolds Averaged Navier-Stokes (RANS) context, the suggested approach is first validated by assessing its general prediction capability in reproducing the flame and flow properties of a simple piloted jet flame configuration known as Sandia Flame D. Second, its feasibility in capturing CO2addition effect on the flame behaviour is demonstrated while studying a non-premixed oxy-flame configuration. This consists of an oxy-methane flame characterized by a high CO2 amount in the oxidizer and a significant content of H2 in the fuel stream, making it challenging for combustion modelling. Comparisons of numerical results with experimental data show that the complete model reproduces the major properties of the flame cases investigated and allows achieving the best agreement for the temperature and different species mass fractions once compared to the classical presumed PDF approach.
We use analytical, numerical and experimental methods to characterize the laminar flow inside a Tesla turbine rotor gap. A comparison based on one particular set of operating conditions mutually ...validates the three approaches. The simplicity of the analytical flow model allows for a cost efficient optimization of the underlying turbine parameters. Performance charts exhibit general trends and serve as a guide for preliminary turbine design and optimization. In terms of the ratio of half the gap width to inlet radius and the ratio of outletto inlet radius, the designer of a tesla turbine has to find a compromise between optimal efficiency and optimal power output.
•Presentation of a robust and efficient CFD framework for CH4-O2 rocket engines.•Assessment of three near-wall LES treatments regarding wall-heat flux predictions.•Validation with experimental data ...(heat flux, chamber pressure and OH∗ emission).•Analysis of the instantaneous and time-averaged reacting flow field.•Investigation of spatial and temporal wall-heat flux variations.
This work presents Large Eddy Simulations of a single-element GOx-GCH4 combustion chamber at elevated pressure. A robust and efficient flamelet model accounting for heat losses is applied to represent the hydrocarbon combustion process at affordable computational effort. Three different near-wall treatments are used: wall-resolved LES, wall-modeled LES and a hybrid RANS/LES approach. The results are compared to experimental data in terms of wall heat fluxes, chamber pressure profile and optical OH∗emission images. Generally, a good agreement with respect to the measurements is observed. In addition, different features of the flow field, like, e.g., the near-injector region and the axial development of the flame, are thoroughly discussed. Finally, a detailed a priori assessment of the different modeling assumptions – regarding the combustion model and relevant transport processes – is carried out to derive possible areas for future improvements.
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