[Paper Review] Numerical investigation of high-pressure combustion in rocket engines using Flamelet/Progress-variable models

Alessandro Coclite, Luigi Cutrone+2 more|arXiv (Cornell University)|Dec 2, 2014

Combustion and flame dynamics23 references3 citations

TL;DR

This paper proposes a novel flamelet/progress-variable (FPV) model for high-pressure H₂/LO₂ rocket combustion that uses the Statistically Most Likely Distribution (SMLD) framework to eliminate assumptions about the joint probability density function (PDF) of mixture fraction and progress variable. By integrating a real-gas equation of state (Peng-Robinson) and detailed kinetic mechanisms, the model improves prediction accuracy of flame structure and temperature, especially near injectors, outperforming conventional FPV models in capturing flame length, thickness, and vortex entrainment effects in the MASCOTTE V03 test case.

ABSTRACT

The present paper deals with the numerical study of high pressure LOx/H2 or LOx/hydrocarbon combustion for propulsion systems. The present research effort is driven by the continued interest in achieving low cost, reliable access to space and more recently, by the renewed interest in hypersonic transportation systems capable of reducing time-to-destination. Moreover, combustion at high pressure has been assumed as a key issue to achieve better propulsive performance and lower environmental impact, as long as the replacement of hydrogen with a hydrocarbon, to reduce the costs related to ground operations and increase flexibility. The current work provides a model for the numerical simulation of high- pressure turbulent combustion employing detailed chemistry description, embedded in a RANS equations solver with a Low Reynolds number k-omega turbulence model. The model used to study such a combustion phenomenon is an extension of the standard flamelet-progress-variable (FPV) turbulent combustion model combined with a Reynolds Averaged Navier-Stokes equation Solver (RANS). In the FPV model, all of the thermo-chemical quantities are evaluated by evolving the mixture fraction Z and a progress variable C. When using a turbulence model in conjunction with FPV model, a probability density function (PDF) is required to evaluate statistical averages of chemical quantities. The choice of such PDF must be a compromise between computational costs and accuracy level. State- of-the-art FPV models are built presuming the functional shape of the joint PDF of Z and C in order to evaluate Favre-averages of thermodynamic quantities. The model here proposed evaluates the most probable joint distribution of Z and C without any assumption on their behavior.

Motivation & Objective

• To develop a more accurate turbulent combustion model for high-pressure rocket engines, particularly under supercritical conditions.
• To reduce reliance on assumed PDFs in flamelet/progress-variable (FPV) models by introducing the Statistically Most Likely Distribution (SMLD) framework.
• To assess the impact of real-gas effects and detailed kinetic mechanisms on combustion prediction accuracy in high-pressure H₂/LO₂ systems.
• To evaluate the performance of the proposed model against experimental data from the MASCOTTE V03 test case.

Proposed method

• The study employs a Reynolds-Averaged Navier-Stokes (RANS) solver with a low-Reynolds-number k-ω turbulence model to simulate high-pressure turbulent flows.
• A flamelet/progress-variable (FPV) model is used, where thermochemical quantities are tracked via mixture fraction (Z) and progress variable (C).
• The SMLD framework is applied to compute the most probable joint distribution of Z and C without assuming a functional form for the PDF, improving statistical accuracy.
• The Peng-Robinson equation of state is implemented to account for real-gas effects at supercritical pressures, crucial for accurate density and transport property modeling.
• Four kinetic mechanisms—two reduced (Li and Warnatz) and two detailed (Li and Warnatz)—are used to evaluate sensitivity to chemical mechanism choice.
• The model is validated against experimental data from the MASCOTTE V03 test case, focusing on temperature and OH mass fraction distributions.

Experimental results

Research questions

• RQ1 How does the SMLD-based FPV model improve prediction accuracy compared to conventional FPV models that assume a PDF shape?
• RQ2 To what extent do real-gas effects influence flame structure and combustion efficiency in high-pressure H₂/LO₂ rocket engines?
• RQ3 How do different kinetic mechanisms (reduced vs. detailed) affect the prediction of ignition delay, flame length, and reaction zone thickness?
• RQ4 Can the proposed model accurately capture complex flow features such as corner vortex entrainment and flame front deformation?

Key findings

• Model B, based on the SMLD framework, predicts a shorter and more realistic flame length compared to Model A, showing better agreement with experimental data.
• The SMLD-based model captures the characteristic flame front bump due to corner vortex entrainment more accurately, particularly near the injector (x ≤ 0.03 m).
• Flame thickness increases more slowly in the initial region with Model B, correctly representing the thin, hot layer near the cold LO₂ core.
• The detailed Li-scheme produces more accurate temperature and flame structure predictions than reduced schemes, which overpredict combustion speed and underestimate ignition delay.
• The model with the SMLD framework and real-gas effects shows improved prediction of temperature and OH mass fraction distributions, especially in the first 0.1 m downstream of the injector.
• The combination of detailed kinetics, real-gas effects, and SMLD-based PDF modeling significantly enhances the fidelity of high-pressure combustion simulations.