In the mid-twentieth century, advances in rocket technology launched us into the Space Age, opening up a new galaxy of scientific discovery and exploration. Being able to operate in the vacuum of space is the defining characteristic of a rocket. Unlike aircraft propelled by air-breathing engines, rockets carry their fuel and oxidizer entirely onboard. 

There are three main categories of rocket engines: liquid, solid, and hybrid. All three types produce thrust by burning fuel and oxidizer in the combustion chamber and accelerating the combustion products out through a nozzle. What differs is how the fuel and oxidizer are stored, transported, and mixed. Liquid rockets rely on liquid fuel and oxidizer, which are injected into the combustion chamber where they are mixed and burned. Solid rockets, on the other hand, feature a solid fuel grain composed of fuel, oxidizer, and a binder, which is ignited and burned in the combustion chamber. Hybrid rockets, as their name suggests, combine some of the principles of both liquid and solid rockets, operating with a solid fuel grain and a liquid or gaseous oxidizer.

Each type of rocket engine comes with its own set of advantages and disadvantages and presents unique engineering challenges. These challenges include the safe storage of the fuel and oxidizer; ignition, combustion control, flame stabilization, and mixing and combustion efficiency; heat transfer and regenerative cooling of the components; and nozzle flow, shock interaction, acoustics, and efficiency over a range of operating conditions. 

CONVERGE CFD software contains a suite of powerful tools to help address these challenges:

  • Fully autonomous meshing: CONVERGE automatically generates a high-quality Cartesian mesh at runtime using a novel cut-cell technique that perfectly represents your geometry, no matter how complex.
  • Adaptive Mesh Refinement (AMR): AMR dynamically refines and coarsens the mesh throughout the simulation to efficiently capture the important physical phenomena.
  • Detailed chemistry solver: With an appropriate reaction mechanism, CONVERGE’s SAGE detailed chemistry solver provides predictive combustion results for a wide range of fuels and oxidizers.
    • Adaptive zoning: Used in conjunction with SAGE, adaptive zoning accelerates the chemistry calculations by grouping together similar computational cells and then invoking the chemistry solver once per group rather than once per cell.
  • Advanced physical models: CONVERGE includes a suite of state-of-the-art models for turbulence (RANS and LES), sprays, combustion, multi-phase flows, fluid-structure interaction, and much more.
  • Conjugate heat transfer (CHT) modeling: CONVERGE’s robust CHT model simultaneously predicts heat transfer in the fluid and solid portions of the domain. CONVERGE also offers the super-cycling feature, which significantly speeds up CHT calculations without sacrificing accuracy.

Liquid Rockets

Liquid rockets have their fuel and oxidizer stored in liquid form, typically under cryogenic conditions. Liquid rocket engines offer a few advantages over solid rockets, including a higher specific impulse and the ability to be throttled, shut down, and restarted. However, liquid propellants also require additional infrastructure, including pumps, piping, and storage tanks, which increases the complexity and the mass of the rocket. 

A vast range of temperatures and pressures are realized throughout the combustor during operation; combustion temperatures can be nearly 200 times higher than propellant storage temperatures, and pressures in the injector and combustion chamber can be orders of magnitude greater than at the nozzle exit. Furthermore, engineers must contend with various phase changes throughout the combustion cycle, from the liquid fuel and oxidizer to vapor-phase combustion products to potential ice formation near the nozzle. The plot below illustrates the wide spectrum of densities present in a rocket combustor for different fuel mixture fractions. It’s crucial to have an accurate description of the fluid properties under these extreme conditions to achieve meaningful simulation results. 

Scatter plot of density versus fuel mixture fraction for simulations of a single-element rocket combustor using various equations of state: Ideal Gas (IG; blue dots), Redlich-Kwong (RK; red dots), Soave-Redlich-Kwong (SRK; yellow dots), Peng-Robinson (PR; purple dots), and Tabulated Fluid Properties (TFP; green dots). The light blue circle indicates the oxidizer composition, the dark red circle indicates fuel composition, the dark blue circle indicates equilibrium combustion products, and the orange circle indicates perfectly expanded products.

CONVERGE features a real-fluid model (RFM) in which the mixing rules consider temperature, pressure, and species mass fraction for improved accuracy. With RFM, a table is constructed based on real fluid vapor-liquid equilibrium calculations to provide the thermodynamic and transport properties for a range of fluids, including common rocket fuel and oxidizer components. RFM allows you to more accurately model injection and mixing under the challenging conditions of a liquid rocket engine.

CONVERGE’s SAGE detailed chemistry solver with adaptive zoning is able to capture key combustion dynamics in liquid rocket engines, including flame characteristics and chamber pressure, which is primarily a function of combustion efficiency and heat loss through the walls. CONVERGE also includes the Flamelet Generated Manifold (FGM) model, a simplified approach that can provide a substantial reduction in computational cost compared to detailed chemistry. 

Additionally, CONVERGE is able to predict thermoacoustic instabilities in liquid rocket engines using detailed chemistry, LES turbulence modeling, and AMR. Instabilities related to the combustion chamber acoustics and flame interaction, or between the interior chamber and upstream propellant line, may occur in liquid rockets at various operating conditions. CONVERGE’s high-fidelity numerical models are designed to provide a good balance between accuracy and stability, sufficient to capture the frequency and amplitude of the pressure oscillations. 

Solid Rockets

While a solid rocket cannot be throttled like a liquid rocket, the advantage of a solid rocket lies in its simplicity—it does not require additional hardware to store and pump liquid propellants. Solid rockets are characterized by a composite mixture of fuel, oxidizer, and binder, which are contained within the grain. As the grain is heated, its components vaporize, mix, and react in a complex sublimation and ablation process. The material structure may give rise to non-premixed, premixed, and flame-flame interactions that must be captured for an accurate simulation. 

The grain regression rate is a key parameter for solid rockets. With an appropriate chemical mechanism, CONVERGE’s SAGE detailed chemistry solver with adaptive zoning is able to capture the combustion process and predict the burning rate as a function of pressure and/or temperature. Regressing the surface of the grain geometry is enabled by CONVERGE’s autonomous meshing, which automatically regenerates a high-quality cut-cell mesh at each time-step to accommodate complex moving boundaries.

Another challenge of solid rocket modeling is the wide range of timescales; the solid grain regression takes place orders of magnitude slower than the velocity of the flow through the nozzle. CONVERGE includes a variety of techniques to deal with disparate time scales by allowing the user to select when and where model equations are solved.

Hybrid Rockets

Hybrid rockets combine some of the advantages of both solid and liquid rockets. They typically feature a solid fuel grain with a liquid or gaseous oxidizer, which enables a robust burn with the ability to control the oxidizer flow rate. As with solid rockets, the grain regression rate is a key parameter in hybrid rocket engines. However, in hybrid rockets, the regression rate is a function of the oxidizer mass flux over the grain. 

As the fuel vaporizes and the surface regresses, the oxidizer flows over the fuel products and a diffusion flame stabilizes on the grain surface. CONVERGE is able to capture these flame characteristics using the SAGE detailed chemistry solver or the Flamelet Generated Manifold (FGM) model with a diffusion flamelet. With these features, CONVERGE is able to accurately predict the chamber and throat pressure in hybrid rocket engines.

Rotating Detonation Engines

Rotating detonation engines (RDEs) operate using a form of pressure gain combustion, where one or more detonation waves continuously travel around an annular chamber. Conceptually, RDEs are well suited to rocket propulsion as they provide a steady source of thrust with more power and higher thermal efficiencies than traditional rocket engines. In addition, RDEs offer a compact, scalable design with no moving components.

The performance of an RDE is affected by many different factors, such as fuel and oxidizer composition and mass flow rates, global equivalence ratio, stagnation and back pressures, and the geometry of the injector and combustion chamber. CFD enables engineers to investigate these different factors to develop practical and high-performing RDEs.

CONVERGE offers a number of advantages for RDE simulations, including its fast detailed chemistry solver, high-fidelity turbulence models (e.g., URANS, LES), and AMR, which helps capture velocity, temperature, and density gradients. With these features, CONVERGE is able to predict a variety of key RDE performance parameters, such as detonation wave frequency, wave height, fill height, oblique shock angle, and pressure. Furthermore, CONVERGE is able to capture mode transition, a phenomenon that occurs when changes in inlet conditions lead to abrupt changes in the number of detonation waves. 

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