MODELING OF PROPELLANT TANK PRESSURIZATIONBy:Amr hassan ahmed darwish

LAYOUT

SELF PRESSURIZED SYSTEMS The advantages:

•Simple design with low parts count

•Inexpensive vehicle production

•Selectable tank pressures ranging up to 7Mpa

•Very few failure modes leading to superior reliability

INTRODUCTION

What is the major advantage of modeling the Propellant tank pressurization ?

Propellant tank pressurization is an essential element of the prediction of rocket performance. This is the case even more so for hybrid rockets that use a self-pressurizing oxidizer because the thrust produced by the motor is dependent on oxidizer tank pressure.

What is the Objective ?Developing a model of a propellant feed system that can be readily incorporated into a rocket design computer program. The model developed is general and should work well for propellant tanks that are pressure fed with an inert gas and also for self-pressurizing systems.

THE MODELING ANALYSISAssumptions• Open system• Real gas• Two-phase (liquid-vapor) homogenous

Nitrous oxide

• The saturation layer is a thin layer • Regular geometry shape of storage Tank

(cylinder shape)•   Frictionless flow in the tank• Tank is in vertical position• No chemical reactions• No mechanical work• Neglect change in potential energy

GOVERNING EQUATIONS

The first law of thermodynamics

FOR LIQUID CONTROL VOLUME

For gas control volume

Evaluation of Thermodynamic Properties

The Soave-Benedict-Webb Rubin Equation of State equation

Peng –Robinson Equation of state (PR EOS)

EVALUATION OF ENTHALPY AND INTERNAL ENERGY

EVALUATING THE RATE OF MASSESThe rate of condensed vapor

The rate of evaporated liquid

The rate of change of gas mass Equation

The mass flow rate through the propellant Feed system

The rate of change of Liquid mass Equation

EVALUATING THE RATE OF MASSES

EVALUATING THE RATE OF VOLUME CHANGE

The rate of change of bulk Liquid volume:-

The rate of change of gas volume

HEAT TRANSFERDuring the period of time when liquid is being expelled from the tank, vaporization takes place at the liquid -vapor mixture interface or possibly within the bulk liquid in the form of boiling

The free convection heat transfer between liquid and liquid surface layer is

THE SOLUTION METHODOLOGY

Initial condition: The capacity of the oxidizer tank is 0.0354 m^3

with Tmperature surround the tank and mass are well known. The injector area is 0.0001219352 m^2 in this model.

Calculate the saturation pressure from the surround temperature and use The Soave-Benedict-Webb Rubin Equation of State to get the density of gas and Liquid then evaluate the mass of liquid and vapor from mass balanced equation .

a) Integrate numerically with time using the modified Euler method 𝑇ሶ𝐿 , 𝑇ሶ𝑇𝐺 , 𝑉ሶ𝑇𝐺 , 𝑉ሶ𝐿 , 𝑚ሶ𝐿 and 𝑚ሶ𝑇𝐺 to obtain 𝑇𝐿, 𝑇𝑇𝐺,𝑃𝑇𝐺 ,𝑉𝑇𝐺, 𝑉𝐿, 𝑚𝑇𝐺, 𝑚𝐿

Assume initially 𝜌𝐿ሶ , 𝑃𝑇𝐺ሶ and 𝜌𝑇𝐺ሶ are all set to be zero.

RESULTS

TEST 1 ,

Comparison of measured and ullage pressure.

TEST 1 ,

Variation temperature time history.

TEST 1 ,

The variation of Propellant mass

TEST 2 , ,

Variation of tank pressure with time

,

TEST 2 , ,

The variation of Propellant mass

TEST 3 , , ,

Variation of tank pressure with time

TEST 3 , , ,

The variation of Propellant mass

TEST 4 , , , ,

Variation of tank pressure with time

TEST 4 , , , ,

The variation of Propellant mass

CONCLUSION •A computer program of a propellant tank pressurization system has been developed.• This model is used to predict the self-pressurizing oxidizer system of a moderate size hybrid rocket.• The model does not assume thermo or phase equilibrium (although the liquid surface is set equal to the saturated vapor temperature) and is applicable to propellants that exhibit real-fluid behavior.• The results obtained are in good agreement with the published and experimental data

REFERENCES•M. Arif Karabeyoglu ," Modeling of Propellant Tank Pressurization",AIAA 2005-3549, 41th AIAA/ASME/ASEE Joint Propulsion Conference, Tucson, Az, July 2005.•V.A. Zakirov, L. Li ," 1-D, Homogenous Liquefied Gas Self –Pressurization Model", Tsinghua University, Beijing, P.R. China, European conference Aerospace sciences (EUCASS).•.Claus K. Zéberg-Mikkelsen," Viscosity Study of Hydrocarbon Fluids at Reservoir Conditions Modeling and Measurements ", Department of Chemical Engineering, June 2001.•Alok Majumdar and Todd Steadman," Numerical Modeling of Pressurization of a Propellant Tank ", Sverdrup Technology, Huntsville, AI.•Don W.Green and Robert H.Perry ,Perry's Chemical Engineers' Handbook, 8thEd, McGraw-Hill , Inc.,New York ,NY,2008.•Rick Newlands," The physics of Nitrous Oxide", aspirespace, 2006.•http://www.tsinghua.edu.cn/docsn/lxx/mainpage/a/Web/index.htm•Margaret Mary Fernandez," Propellant Tank Pressurization Modeling for a Hybrid Rocket", Department of Mechanical Engineering,Kate Gleason College of Engineering,Rochester Institute of Technology,Rochester, NY 14623, August 2009.•Zakia Nasri and Housam Binous," Applications of the Peng-Robinson Equation of State using MATLAB", National Institute of Applied Sciences and Technology.•Matías A. Monsalvo," Phase Behavior and Viscosity Modeling of Refrigerant-Lubricant Mixtures", Ph. D. Thesis, Technical University of Denmark, Center for Phase Equilibrium and Separation Process.

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