Modeling fin efficiency considering transverse temperature gradients in rocket engine cooling channels

A complete set of equations describing the conservation of mass, momentum, and energy, and multicomponent transport and chemical reaction in a liquid propellant rocket (LPR) engine are given, along with appropriate boundary conditions. The formulation includes a detailed description of the two-phase (gas/liquid) flow in terms of a moving boundary problem, with droplets and vapor occupying time-dependent subdomains of the LPR chamber. Several sensor and actuator types are considered in detail, and their mathematical descriptions are incorporated into the differential equations and boundary conditions.

Blow forming technology has been used to produce glass and plastic components with easy and simple process. In order to apply this technology to metallic system, relatively high formability of material and elevated temperature are required. Since the blow forming temperature is quite high for metallic system, the main difficulty is to obtain adequate mold material which can sustain pressure difference between inside and outside of the tool. The present study demonstrates blow forming process with IN718 and steel can be applied to manufacturing of combustion chamber in liquid propellant rocket engine with complex shape. The result shows that the developed technology to process design of high temperature blow forming by the finite element method can be applied for near net shape forming of a combustion chamber of liquid rocket engine and a cone-shaped chamber extension part with cooling channels.

Non-stationary heat behaviour of liquid propellant rocket engines

Numerical study of combustion instability in liquid propellant rocket engine is presented in the paper. Time-depending two-dimensional Navier-Stokes equations were employed to describe the fluid flow in the combust chamber and solved by finite difference method with MacCormack scheme. Turbulent viscosity was taken into consideration by the subgrid scale turbulence model. Propellant spray was treated with a lagrangian tracking method and droplet source terms were incorporated into the gas phase calculation by PSIC method. Droplet initial conditions were determined by a stochastic spray model . Spray burning rate is calculated by the classic D2 vaporization law with Ranz-Marshall correlation. The coupling of pressure disturb and burning rate variation was described with Prime's twoparameter model. The actual axisymmetric combustor was transferred into equivalent annular geometry as the references do. Combustion instability analysis was performed by imposing a bomb pressure pulse on the computed steady flow field to trigger unstable combustion. By observing the pressure wave propagation , we can asses the damping capability of the engine.The computational analysis show that numerical schemes and physical models used to describe unstable combustion are the most important factors to the success of numerical study. d NOMENCLATURE a sound velocity b annular combustor width constant pressure spcific heat CP C,, drag coefficient d droplet diameter D mass diffusivity e total energy f frequency h enthalpy 1 L~ heat of evaporation f i transverse length of the annular combstor mass flux or evaporation rate M number of computational droplet NU Nusselt number pr Prantdl number Ice Reynolds number s source terms time T lempeerature X,Y coordinates p density h coductivity P I velocity components

Fault detection and diagnosis algorithms for an open-cycle liquid propellant rocket engine using the Kalman filter and fault factor methods

For low cost, high thrust, space missions with high specific impulse and high reliability, inert weight needs to be minimized and thereby increasing the delivered payload. Turbopump feed system for a liquid propellant rocket engine (LPRE) has the highest power to weight ratio. Turbopumps are primarily equipped with an axial flow inducer to achieve the high angular velocity and low suction pressure in combination with increased system reliability. Performance of the turbopump strongly depends on the performance of the inducer. Thus, for designing a LPRE turbopump, demands optimization of the inducer geometry based on the performance of different off-design operating regimes. In this paper, steady-state CFD analysis of the inducer of a liquid oxygen (LOX) axial pump used as a booster pump for an oxygen rich staged combustion cycle rocket engine has been presented using ANSYS® CFX. Attempts have been made to obtain the performance characteristic curves for the LOX pump inducer. The formalism has been used to predict the performance of the inducer for the throttling range varying from 80% to 113% of nominal thrust and for the different rotational velocities from 4500 to 7500 rpm. The results have been analysed to determine the region of cavitation inception for different inlet pressure.

A recent mathematical technique of homotopy perturbation method (HPM) for solving nonlinear differential equations has been applied in this paper for the analysis of steady-state heat transfer in an annular fin with temperature-dependent thermal conductivity and with the variation of thermogeometric fin parameters. Excellent benchmark agreement indicates that this method is a very simple but powerful technique and practical for solving nonlinear heat transfer equations and does not require large memory space that arises out of discretization of equations in numerical computations, particularly for multidimensional problems. Three conditions of heat transfer, namely, convection, radiation, and combined convection and radiation, are considered. Dimensionless parameters pertinent to design optimization are identified and their effects on fin heat transfer and efficiency are studied. Results indicate that the heat dissipation under combined mode from the fin surface is a convection-dominant phenomenon. However, it is also found that, at relatively high base temperature, radiation heat transfer becomes comparable to pure convection. It is worth noting that, for pure radiation condition, the dimensionless parameter of aspect ratio (AR) of a fin is a more desirable controlling parameter compared to other parameters in augmenting heat transfer rate without much compromise on fin efficiency.

Performance, weight, design, flexibility, engine cycles and reliability of liquid propellant rocket engines used in NASA and USAF vehicles

In the Republic of Korea, research on staged-combustion cycle liquid propellant rocket engines (LPRE) is proceeding to improve efficiency of rocket engines. Recently oxidizer-rich preburner using single triplex injector is developed in relation to the main injector development and combustion tests have been performed. This preburner is designed to operate in nominal conditions with the combustion pressure of 10 MPa, OF ratio of 60. For a stable ignition, LOx is fed in two steps. Triethylaluminum-Triethylborane (TEAB) is used as hypergolic fuel for ignition, supplied through a fuel injector. Despite the small amount of fuel flow rate and high pressure condition, the combustion pressure was stably maintained around 10 MPa as designed. As a result of Fast Fourier Transform (FFT) of the combustion chamber dynamic pressure, 1L mode frequencies related to the acoustic instability and hydraulic resistance exist in the combustion chamber. But their amplitudes are less than 1% of the combustion pressure and it does not affect the combustion. Therefore combustion test is stably completed. In the near future, coupled tests with uni-element triplex injector preburner and uni-element gas/liquid injector main combustion chamber will be carried out.

Liquid-propellant rocket propulsion systems of the first stages of launch vehicles of medium, heavy, and super-heavy class usually include POGO-suppressors, which are one of the most widely used methods to eliminate launch vehicle longitudinal structural vibrations (POGO phenomena). However, until now, the theoretical studies and analysis of the effect of the POGO-suppressors’ installation in the feedlines of main liquid rocket engines on transient processes in systems during rocket engine starting have not been carried out due to the complexity of such analysis and the lack, first of all, reliable nonlinear models of cavitation phenomena in rocket engine pumps. A mathematical model for the start-up of a clustered rocket propulsion of the Cyclone-4M launch vehicle has been developed that takes into account the low-frequency dynamics of the POGO-suppressors and the asynchronous start-up timeline sequences of the rocket engines. The first stage of the launch vehicle propulsion system includes four RD-870 rocket engines. A nonlinear mathematical model of low-frequency dynamic processes of the POGO-suppressor with bellows separation of liquid and gaseous media is presented. A significant effect of cavitation in the pumps of engines and the POGO-suppressor installation to the LOX feedline on the propulsion system dynamic gains is shown. Based on the developed mathematical model of the clustered rocket propulsion start-up, the studies of the Cyclone-4M main engines’ start-up transients were carried out. The asynchronous start-up timeline sequences of the rocket engine and the places of installation of the POGO-suppressors in the LOX feedline branches to the RD-870 rocket engine – near the general feedline collector as standard placement or directly at the entrance to the engines – were investigated. The analysis of start-up transients in the oxidizer feed system of the considered propulsion (the time dependences of the flowrate and pressure at the engine inlet) showed the following. Firstly, while the synchronous start-up of the engines, the installation of the POGO-suppressors near the feedline collector makes it possible to eliminate all engine inlet overpressures that exist in the rocket propulsion system in case of the absence of the POGO-suppressors. Secondly, the RD-870 engine asynchronous start-up operation affects negatively the time dependences of the propellant flowrate and pressure at the engine inlet if the POGO-suppressors are located near the feedline collector. So, in the propulsion system’s start-up timeline interval 0.95 s - 1.35 s, for some computational variants of the initial moments of the engine operation start, an abnormally large drop in the LOX flow rate and the overpressures at the engine inlet is observed. The asynchronous start-up of the RD-870 engines with the installation of the POGO-suppressors at the engine inlet does not significantly change the start-up transients compared to the synchronous starting of the engines. Thirdly, thus, it is shown that the installation of the POGO-suppressors both at the engine inlet and at the RD-870 branches near the collector has a significant positive effect on the quality of start-up transient processes for the main engines of the 1st stage of the Cyclone-4M launch vehicle. Placing the POGO-suppressors at the engine inlets is not standard and is considered without reference to the propulsion system layout. Nevertheless, the POGO-suppressors installed at the inlet to the engines are an effective means of preventing overshoots and dips in the parameters of the liquid-propellant rocket engine, including the conditions of asynchronous starting of the liquid rocket engines in the clustered propulsion system. The results obtained can be used in mathematical modeling of the start-up of the first stage propulsion system either for multistage sustainer rockets used in parallel with booster rockets or for the clustered multi-engine rocket propulsion system containing POGO-suppressors.

This paper presents the methodology for developing a diagnostic and control system for a current, operational jet engine. A description is given of each development stage, the system components and the technologies which could be transferred to liquid propellant rocket engines. Finally, the operational impact is described in terms of cost and maintenance based on actual jet engine experience. Efforts are continuing to develop new diagnostic techniques under IR D for application on the advanced technical fighter. Already improved techniques and application methods are becoming available. This technology is being evaluated and may also be transferred to rocket engine diagnostic and control system development.

Sensing and actuation in a liquid propellant rocket engine

We present a method that combines multiple sensory modalities in a rocket thrust chamber to predict impending thermoacoustic instabilities with uncertainties. This is accomplished by training an autoregressive Bayesian neural network model that forecasts the future amplitude of the dynamic pressure time series, using multiple sensor measurements (injector pressure/ temperature measurements, static chamber pressure, high-frequency dynamic pressure measurements, high-frequency OH* chemiluminescence measurements) and future flow rate control signals as input. The method is validated using experimental data from a representative cryogenic research thrust chamber. The Bayesian nature of our algorithms allows us to work with a dataset whose size is restricted by the expense of each experimental run, without making overconfident extrapolations. We find that the networks are able to accurately forecast the evolution of the pressure amplitude and anticipate instability events on unseen experimental runs 500 milliseconds in advance. We compare the predictive accuracy of multiple models using different combinations of sensor inputs. We find that the high-frequency dynamic pressure signal is particularly informative. We also use the technique of integrated gradients to interpret the influence of different sensor inputs on the model prediction. The negative log-likelihood of data points in the test dataset indicates that prediction uncertainties are well-characterized by our model and simulating a sensor failure event results in a dramatic increase in the epistemic component of the uncertainty, as would be expected when a Bayesian method encounters unfamiliar, out-of-distribution inputs.

The design of liquid propellant rocket engines (LPREs) necessitates the efficient cooling of the combustion chamber walls. Despite the prevalence of regenerative cooling, it frequently proves inadequate, necessitating supplementary techniques such as the injection of coolant into the combustion chamber to establish a thermal barrier. A critical deficiency in the prevailing methodologies pertains to the absence of dependable methodologies for the calculation of the parameters governing coolant flow as it transitions from the cooling path to the curtain belt. The objective of this study is to derive analytical formulas for determining the parameters of the coolant flow at the exit from the curtain belt of the cooling belt of an LPR combustion chamber. The coolant passes through tangential cylindrical channels into the annular slot, thereby forming a continuous swirling flow prior to entering the chamber. The analysis is conducted in two stages. First, a one-dimensional approximation is used to determine the temperature change in the cylindrical inlet channel. Then, the flow in the annular slot is considered using the laws of conservation of mass, momentum and energy. An analytical solution for the temperature distribution is obtained by means of simplification of the dependence for the Nusselt number. The model has been verified on the data of the RD-108 engine curtain belt with kerosene as a coolant. The results indicate that the coolant temperature at the outlet is nearly equal to the temperature of the chamber wall, thereby substantiating the practical applicability of the model. In this paper, analytical expressions for the coolant flow parameters at the outlet of the curtain belt are obtained for the first time, and an approximate method for evaluating the heat transfer in the annular slot is proposed. Despite its inability to account for alterations in fluid properties and variable wall temperature, the model functions as a framework for subsequent refinements.

Complete burning of liquid propellants droplets is very important to avoid combustion instability and to get higher specific impulse from liquid rocket engines. Combustion takes place in gaseous phase and reaction is fast. So, the time consumed by a droplet for complete burning is the time taken by a droplet to get evaporated. An analytical mono component fuel droplet evaporation model is developed and proposed for droplet evaporation in liquid rocket engine based on heat and mass transfer. Effect of the fuel droplet curvature on vapor pressure is incorporated in the model. The model is applied on a small-scale combustion chamber of bi-propellant liquid rocket engine where fuel concentration away from droplet is not zero. A code is generated and applied. The results of the model show that fuel droplet diameter, combustion chamber pressure, chamber diameter, mass flow rate and droplet relative velocity with hot gas has significant effects on the life of droplet and characteristic length. Effects of chamber pressure and diameter are more significant for larger droplet size.