Daniel T. Banuti

The absence of a dense potential core in supercritical injection: A thermal break-up mechanism

Certain experiments in quasi-isobaric supercritical injection remain unexplained by the current state of theory: Without developing a constant value potential core as expected from the mechanical view of break-up, density is observed to drop immediately upon entering the chamber. Furthermore, this phenomenon has never been captured in computational fluid dynamics (CFD) despite having become a de facto standard case for real fluid CFD validation. In this paper, we present strong evidence for a thermal jet disintegration mechanism (in addition to classical mechanical break-up) which resolves both the theoretical and the computational discrepancies. A new interpretation of supercritical jet disintegration is introduced, based on pseudo-boiling, a nonlinear supercritical transition from gas-like to liquid-like states. We show that thermal disintegration may dominate classical mechanical break-up when heat transfer takes place in the injector and when the fluid state is sufficiently close to the pseudo-boiling...

Real Gas Library in Continuous Phase Propellant Injection Model for Liquid Rocket Engines

In this paper we introduce a novel model for liquid rocket engine (LRE) propellant injection. Most academic codes today use an Eulerian-Eulerian (EE) description, i.e. all involved propellants and reaction products are regarded as continuous uids instead of discrete droplets. These models have successfully been improved and are capable of high fidelity studies of single injectors and mixing layers, using LES or even DNS. While impressive, this is prohibitive with regard to the simulation of a full thrust chamber with fast turnaround times - as required in industrial applications. Focusing on a RANS model, we decided to take a different route in terms of enhancement: the equation of state (EOS). State of the art EE models perform a runtime evaluation of the EOS. Thus, its numerical efficiency becomes a constraint. By using a precalculated library for the EOS instead, we succeeded to decouple quality of the EOS and CFD runtime. A multi fluid mixing model is developed which allows for each species to be modeled individually. The approach is embed- ded in a Eulerian-Eulerian homogeneous two phase model, i.e. a thermal and mechanical equilibrium between surrounding gaseous flow and and injected cryogenic fluid is assumed in each numerical cell. Due to the general treatment of the oxygen thermodynamics, the oxidizer phase can assume any thermodynamic state, including gaseous, supercritical, liquid, as well as multiphase vapor liquid mixtures. The model is validated with 0D vaporization processes. As a first application, the supercritical pressure single injector Mascotte A60 test case is treated where cryogenic oxygen is injected. Excellent agreement is found with experimental OH emission data. Especially, maximum OH emission is correctly placed in the hydrogen oxygen shear layer

Effect of Injector Wall Heat Flux on Cryogenic Injection

This paper reports on numerical investigation and discussion of a cryogenic injection test case. This is a first step towards a numerical model for high pressure liquid rocket engine injection. Experiments with nitrogen injection at supercritical pressures are an accepted way of studying flow phenomena relevant for high pressure liquid rocket engines without introducing the complexities of mixing and combustion. CFD simulations of these cryogenic injection cases are found to typically agree on predicting a region of constant high density, extending some 10 injector diameters downstream into the chamber. This is in agreement with the traditional interpretation of liquid injection where instabilities on the phase boundary grow until the jet disintegrates. However, many experiments do not show this behavior: exceeding the critical pressure of the injected fluid, phase interfaces seize to exist, the jet tends to behave more like a dense gas jet with a rapid drop off of density starting at the injector exit. It is thus unclear whether the concept of a liquid core length is still true for thermodynamic states at temperatures near the critical point and supercritical pressures. To study this, experimental and numerical boundary conditions have been analyzed. Computations have been carried out using the DLR TAU code extended by a treatment for real gas thermodynamics. It has been found that the absence of a dense core, as found in experiments, can be reproduced numerically if numerical boundary conditions are chosen appropriately: taking into account heat transfer inside the injector leads to a preheating of the cryogenic stream and the development of a distinct radial density profile. This preheated jet then shows the more realistic immediate reduction of density instead of a dense core.

Flow Control by Energy Deposition in Hypersonic Flow - Some Fundamental Considerations

This paper discusses some general properties of energy deposition in hypersonics. Extending the flight envelope of passenger aircraft to high Mach numbers comes with problems unsolved before in civil flight, such as sonic boom, or excessive thermal and mechanical loads. Energy deposition is regarded as a possible remedy to a multitude of problems occurring in this flight regime and thus studied here. A new energy source term has been implemented into the DLR TAU CFD code which models a physical distributed heat addition. In a first step, energy deposition in free flow is investigated using this new term. Four flow topologies, dependent on the deposition energy, have been identified, ranging from negligible induced cross flow component, to a massive detached bow shock ahead of the deposition region. In a second step, ramp flow, as a precursor to flow about an airfoil, is studied under the influence of an upstream energy deposition region. An undesired low pressure region could be explained with a simplified model of wave refraction at thermally stratified ramp flow. Key of this model is a flow deflection above the ramp which is needed to balance pressure dierences. This model is discussed in detail to fully understand the physical nature of the flow structure. It predicts a way of increasing surface pressure compared to regular ramp flow at reduced total pressure loss. It furthermore predicts the occurrence of premature shock separation and oscillating shock patterns. Analyzing this model, a simple yet accurate functional formula is found for the additional deflection angle due to refraction which simplifies the calculation of the surface pressure distribution as no pressure balance iteration is needed anymore. These studies are currently carried out within the European ATLLAS project which is concerned with the development of hypersonic passenger aircraft. Computations are performed using the DLR TAU code, a finite volume, second order accuracy, compressible flow solver.

Thermodynamic Interpretation of Cryogenic Injection Experiments

This paper discusses a thermodynamic rather than mechanic discussion and interpretation of cryogenic injection of nitrogen in the vicinity of the critical point. There is no concensus in the literature on how to properly interpret and treat injection phenomena at supercritical pressures. While it is clear that the supercritical fluid loses many distinct liquid properties, such as heat of vaporization and surface tension, flows are being treated like they were liquid. Liquid core lengths are being determined in experiments, distinct droplets are tracked in computational fluid dynamic studies. And in fact, these approaches prove to be very successful. Nevertheless, a more appropriate treatment is desireable, taking into account the specifics of supercritical fluids. A contribution is attempted in this paper. The concept of pseudo-boiling, a maximum in heat capacity associated with a strong increase in specific volume, is discussed. It will be shown that the ensemble of supercritical maximum heat capacity states is in fact an extension to the saturation curve. A novel interpretation of the Clapeyron equation of thermodynamics in the limit of the critical point and beyond will be given. It will be shown that this generalization is able to characterize the pseudo-boiling line. Furthermore it will be shown that the slope (d log p/dT) is constant for supercritical conditions and equals the value at the critical point. The pseudo-boiling approach is then applied to characterize injection experiments. It can be shown that the power needed to reach the pseudo-boiling state correlates with the structure of the axial density distribution.

Interfacial Area Transport Equation in Statistical-Eulerian-Eulerian Simulations of Multiphase Flow

This paper discusses the ongoing extension of the DLR TAU Code with a multiphase flow model. The reasoning behind choosing a Statistical Eulerian Eulerian (SEE) model with Interfacial Area Transport Equation (IATE) is covered. Properties of the model are introduced, especially concerning the less known IATE concept which provides information about interphasic interfacial area (IA) available in a computational cell. This allows for a more elaborate sub grid scale modeling. An general IA convection velocity is derived which holds for the limiting cases of stratified flow and disperse flow. As an exemplary application, the development of a spray injection IATE is discussed. This includes interfacial growth due to velocity gradients and a new IA detection term which resolves ambiguities with boundary conditions.

Interfacial Area Modeling for Eulerian Spray Simulations in Liquid Rocket Engines

Contributions to Statistical Eulerian-Eulerian (SEE) flow models of two-phase flow are discussed in this article. Special attention is given to the Interfacial Area Transport Equation (IATE) which al-lows for sub grid scale modeling of exchange processes and a topological interpretation of continuous results. An interfacial area convection velocity is derived based on the assumption of strati-fied flow. This scheme will be shown to also hold in the limit of dilute spray. In the case of vanishing surface tension and heat of vaporization, disintegration of a supercritical jet can be described as a mixing rather than an atomization process. Following this assumption, growth of interfacial area due to stretching is dis-cussed and a new model term suggested. To resolve former diffi-culties with the interfacial area inflow boundary condition, an automatic interfacial area detection is proposed. This new term also allows for automatic creation of interfacial area in the case of unsteady injection or formation of a phase (e.g. condensation, cavitation, vaporization). The described model is implemented in the DLR finite volume TAU code.

Application of a Real-Gas-Library Multi-Fluid-Mixing Model to Supercritical Single Injector Flow

In this paper we report on supercritical single injector computations using a new type of real gas CFD model. This Euler-Euler model is an extension to the DLR TAU CFD code. By storing fluid data in a library, we were able to decouple equation of state (EOS) accuracy from runtime performance. The library covers all fluid states effciently and robust, including gaseous, liquid, supercritical, and multiphase states. In our new multifluid mixing model, an EOS is solved for each species. Computations were carried out using a modifed Benedict-Webb-Rubin high fidelity equation of state for cryogenic oxygen, with negligible penalty in performance compared to a pure ideal gas computation. Additional species (H, H2, O, OH, H2O, H2O2) were treated as perfect gases. The immediate goal is to create a flow solver for industrial application, i.e. to support design by enabling a fast turnaround. Thus, we focus on 2D RANS modeling in this first step. The baseline model is applied to the canonical Mascotte A60 test case. The chamber pressure is well met, the flame dimensions are within the spread found among other CFD results. In accordance with experimental results, the reaction zone is very thin. Maximum OH* occurrences are correctly predicted in the shear layer, reducing in magnitude towards shoulder and flame tip. The fluid library allows to pinpoint the extent of the liquid oxygen core, the length is determined to 20 LOX injector diameters. It is found to be embedded in a gaseous oxygen shell. Within this RANS context, H2 and O2 do not coexist in a premixed form. Finally, we show that numerical OH* concentration differs significantly from OH mass fraction distributions, the latter are thus no appropriate data to compare to experiments.

Flow Characteristics of Micro-Scale Planar Nozzles

Flow in micro chemical propulsion systems (µCPS) based on etched silicon deviates strongly from its conventional, macroscopic counterparts. This paper reports on peculiarities of small scale planar nozzles with a high aspect ratio, rectangular cross section. Design and analysis paradigms based on the assumption of rationally symmetric flow with a dominant isentropic core are shown to be no longer valid. We will point out insufficiencies of treating planar nozzles as two dimensional, inviscid, or assessing their performance with classical analytical isentropic 1D analysis. Instead, the resulting low Reynolds number flow is boundary layer dominated. Boundary layer build-up from the top and bottom walls threaten to choke the expansion. The geometrical expansion ratio is found to be essentially irrelevant, the length from throat to exit plane is found to be a much more important design parameter. The work has been carried out within the European PRECISE project which is focused on designing and testing a prototype using catalytically decomposed hydrazine as propellant.

Steady Shock Refraction in Hypersonic Ramp Flow

This paper discusses features of a supersonic flow with a transversal Mach number stratification when encountering a ramp. A flow of this nature can occur for a variety of reasons around a hypersonic vehicle. Formation of a heated wall boundary layer, external fuel injection on the compression ramp, energy deposition, and film or transpiration cooling are just some of the processes that will establish a flow where a wall near layer features a distinct difference in Mach number compared to the outer flow. This paper will introduce a flow topology framework that will help to understand phenomena associated with this stratification. Shock refraction is identified as the main mechanism which causes a redirection of the flow additional to the ramp deflection. It will be shown how, depending on the Mach number ratios between the layers, shocks or expansion fans will be created that will interact with the surface. This can be the cause for undesired or unexpected temperature and pressure distributions along the wall when shock refraction is not taken into account. As a possible application, it will be shown how shock refraction can act as a virtual external compression ramp. CFD computations are performed using the DLR TAU code, a finite volume, second order accuracy, compressible flow solver.