Università degli Studi della Basilicata

SCUOLA DI INGEGNERIA

CORSO DI LAUREA IN INGEGNERIA

MECCANICA

Tesi di Laurea

in Macchine e Sistemi Energetici

Titolo tesi

Development of LRE Cooling System Module in a

Concurrent Engineering Approach

Relatore:

Prof. Aldo Bonfiglioli

Correlatori:

Dott. Raffaele Votta

Ing. Gianpaolo Elia

Laureando:

Sabato Massimo

Matricola: 40943

ANNO ACCADEMICO 2013/14

I

Table of Contents

LIST OF FIGURES ............................................................................................................................. II

LIST OF TABLES .............................................................................................................................. IV

ACRONYMS, SYMBOLS AND ABBREVIATION .......................................................................... IV

INTRODUCTION ............................................................................................................................ - 1 -

CHAPTER 1 ..................................................................................................................................... - 3 -

LIQUID ROCKET ENGINE ........................................................................................................... - 3 -

1.1 OVERVIEW ............................................................................................................................... - 3 -

1.2 PROPULSION FUNDAMENTALS ................................................................................................. - 4 -

1.3 MAIN SYSTEMS OVERVIEW ....................................................................................................... - 8 -

1.3.1 Feed System ....................................................................................................................... - 9 -

1.3.2 Thrust chamber ................................................................................................................ - 14 -

1.3.3 Cooling System................................................................................................................. - 24 -

CHAPTER 2 ................................................................................................................................... - 27 -

THE HYPROB PROGRAM & CONCURRENT DESIGN FACILITY ....................................... - 27 -

2.1 THE HYPROB PROGRAM ..................................................................................................- 27 -

2.1.1 Introduction to National 2020 Vision .............................................................................. - 27 -

2.1.2 Industrial heritage and program road map ..................................................................... - 29 -

2.1.3 Propulsion Lines: 𝑳𝑶𝒙/𝑳𝑪𝑯𝟒 & Hybrid ......................................................................... - 31 -

2.1.4 Design and measurement methodologies ......................................................................... - 32 -

2.1.5 Experimental Facilities: CIRA & AVIO synergy ............................................................. - 33 -

2.2 CONCURRENT DESIGN FACILITY - CDF .......................................................................- 35 -

2.2.1 An innovative team working method ................................................................................ - 35 -

2.2.2 History and status of CDF ............................................................................................... - 36 -

2.2.3 Applications , Benefits and key elements of CDF ........................................................... - 37 -

CHAPTER 3 ................................................................................................................................... - 41 -

CIRA CONCURRENT DESIGN FACILITY ............................................................................... - 41 -

3.1 CIRA CDF FOR SPACE PROPULSION ..............................................................................- 41 -

3.2 ARCHITECTURE MODULE ...............................................................................................- 46 -

3.3 THRUST CHAMBER MODULE .........................................................................................- 53 -

CHAPTER 4 ................................................................................................................................... - 55 -

COOLING SYSTEM MODULE OF CIRA CDF.......................................................................... - 55 -

4.1 OVERVIEW..........................................................................................................................- 55 -

4.2 COOLING SYSTEM MODULE ...........................................................................................- 56 -

4.2.1 Heat flux analyses ............................................................................................................ - 56 -

4.2.2 Cooling Channels geometry ............................................................................................. - 60 -

4.2.3 Coolant flow analysis ....................................................................................................... - 63 -

CHAPTER 5 ................................................................................................................................... - 69 -

RESULTS ....................................................................................................................................... - 69 -

II

5.1 OVERVIEW ............................................................................................................................ - 69 -

5.2 VALIDATION OF THE COOLING SYSTEM DESIGN CYCLE .......................................................... - 70 -

5.3 CASE STUDY: 100 KN THRUST CLASS ENGINE ........................................................................ - 83 -

5.3.1 Models of friction factor ................................................................................................... - 85 -

5.3.2 Cooling channels diameter effect ..................................................................................... - 95 -

5.3.3 Heat flux evaluation model ............................................................................................ - 101 -

CHAPTER 6 ................................................................................................................................ - 109 -

CONCLUSIONS .......................................................................................................................... - 109 -

APPENDIX A – SUPERCRITICAL FLUIDA S COOLANT IN LRE ............................................................ - 113 -

REFERENCES ............................................................................................................................ - 115 -

List of Figures

FIGURE 1: GAS GENERATOR CYCLE, OPEN BLEED EXPANDER CYCLE & COMBUSTION TAP- OFF CYCLE .. - 11 -

FIGURE 2: STAGED-COMBUSTION CYCLE AND EXPANDER CYCLE ........................................................... - 12 -

FIGURE 3: PRESSURE-FED CYCLE ............................................................................................................ - 13 -

FIGURE 4: THRUST CHAMBER SKETCH .................................................................................................... - 15 -

FIGURE 5: COAXIAL ELEMENT AND SHOWER HEAD ................................................................................ - 17 -

FIGURE 6: UNLIKE DOUBLET AND UNLIKE TRIPLET ................................................................................ - 18 -

FIGURE 7: LIKE-IMPINGING DOUBLET ..................................................................................................... - 19 -

FIGURE 8: CONICAL NOZZLE ................................................................................................................... - 23 -

FIGURE 9: PARABOLIC APPROXIMATION OF BELL NOZZLE CONTOUR ...................................................... - 24 -

FIGURE 10: ESA CDF IN SESSION ........................................................................................................... - 37 -

FIGURE 11: LIQUID SPACE PROPULSION ENGINE - SCHEMATIC VIEW ....................................................... - 42 -

FIGURE 12: CIRA CONCURRENT DESIGN FACILITY FOR SPACE PROPULSION - SPECIALIST ..................... - 42 -

FIGURE 13: CIRA CONCURRENT DESIGN FACILITY FOR SPACE PROPULSION - DOMAINS ....................... - 42 -

FIGURE 14: CIRA CONCURRENT DESIGN FACILITY FOR SPACE PROPULSION - THE PROCESS .................. - 46 -

FIGURE 15:TYPICAL BASIC CONFIGURATION OF A THRUST CHAMBER ..................................................... - 47 -

FIGURE 16: CONICAL NOZZLE CONTOUR ................................................................................................. - 50 -

FIGURE 17: BELL NOZZLE CONTOUR ....................................................................................................... - 51 -

FIGURE 18: INITIAL AND FINAL PARABOLIC ANGLES VERSUS DESIRED NOZZLE EXPANSION RATIO FOR

DIFFERENT PERCENT BELL LENGTHS OF AN EQUIVALENT 15° CONICAL NOZZLE ............................. - 52 -

FIGURE 19: CONVERGENT NOZZLE CONTOURS FOR “STRAIGHT” AND “CUBIC” SOLUTIONS ..................... - 52 -

FIGURE 20: AN EXAMPLE OF THE THRUST CHAMBER GEOMETRY EVALUATED BY THE ARCH MODULE . - 53 -

FIGURE 21: REGENERATIVE COOLING ARCHITECTURE ............................................................................ - 56 -

FIGURE 22: HEAT TRANSFER FOR SCHEMATIC REGENERATIVE COOLING ................................................. - 57 -

FIGURE 23: VARIATION OF THERMAL CONDUCTIVITY WITH TEMPERATURE FOR TYPICAL METALLIC

ELEMENTS AND ALLOY ................................................................................................................... - 60 -

FIGURE 24: DETAIL VIEW COOLING CHANNEL GEOMETRY ...................................................................... - 61 -

FIGURE 25: CROSS-SECTIONAL VIEW OF A REGENERATIVE COOLING THRUST CHAMBER SHOWING THE

FLOWS DIRECTIONS ........................................................................................................................ - 61 -

FIGURE 26: TYPICAL CROSS-SECTIONAL SCALING OF A COOLING CHANNELS ALONG AXIAL DIRECTION . - 62 -

FIGURE 27: MOODY DIAGRAM ................................................................................................................ - 68 -

FIGURE 28: GEOMETRICAL PROFILE OF THRUST CHAMBER ..................................................................... - 70 -

III

FIGURE 29: ARCHITECTURE CONCEPT ..................................................................................................... - 71 -

FIGURE 30 COUNTER FLOW ARCHITECTURE FOR THE COOLING JACKET .................................................. - 71 -

FIGURE 31: GEOMETRIC PROFILE OF THRUST CHAMBER ......................................................................... - 72 -

FIGURE 32: COOLING SYSTEM CHANNEL AND BRAZING INTERFACE ........................................................ - 73 -

FIGURE 33: HEAT FLUXES GIVEN AS INPUT ............................................................................................. - 74 -

FIGURE 34: HYPROB-BREAD PRESSURE DISTRIBUTION VS CDF PRESSURE DISTRIBUTION ................ - 75 -

FIGURE 35: HYPROB-BREAD TEMPERATURE DISTRIBUTION VS CDF TEMPERATURE DISTRIBUTION .. - 76 -

FIGURE 36: HYPROB-BREAD HEAT SPECIFIC DISTRIBUTION VS CDF HEAT SPECIFIC DISTRIBUTION .. - 77 -

FIGURE 37: HYPROB-BREAD THERMAL CONDUCTIVITY DISTRIBUTION VS CDF THERMAL CONDUCTIVITY

DISTRIBUTION ................................................................................................................................ - 78 -

FIGURE 38: COOLING CHANNELS OF DEMONSTRATOR ............................................................................ - 79 -

FIGURE 39: HEAT FLUX – CFD ANALYSIS VS CDF ................................................................................. - 79 -

FIGURE 40: TEMPERATURE – CFD ANALYSIS VS CDF ............................................................................ - 80 -

FIGURE 41: TEMPERATURE – CFD ANALYSIS VS CDF ............................................................................ - 81 -

FIGURE 42: SPECIFIC HEAT – CFD ANALYSIS VS CDF ............................................................................ - 82 -

FIGURE 43: THERMAL CONDUCTIVITY – CFD ANALYSIS VS CDF ........................................................... - 83 -

FIGURE 44: GEOMETRICAL CONFIGURATION OF 100 KN CLASS THRUST CHAMBER................................. - 85 -

FIGURE 45: HEAT FLUX DISTRIBUTION ALONG THE COOLING CHANNELS ................................................ - 86 -

FIGURE 46: COOLANT DENSITY DISTRIBUTION ALONG THE COOLING CHANNELS .................................... - 87 -

FIGURE 47: COOLANT TEMPERATURE DISTRIBUTION ALONG THE COOLING CHANNELS .......................... - 88 -

FIGURE 48: COOLANT PRESSURE DROP DISTRIBUTION ALONG THE COOLING CHANNELS ........................ - 89 -

FIGURE 49: FRICTION FACTOR DISTRIBUTION ALONG THE COOLING CHANNELS...................................... - 90 -

FIGURE 50: SPECIFIC HEAT AT CONSTANT PRESSURE DISTRIBUTION ALONG THE COOLING CHANNELS ... - 90 -

FIGURE 51: COOLANT VELOCITY DISTRIBUTION ALONG THE COOLING CHANNELS.................................. - 91 -

FIGURE 52: REYNOLDS NUMBER DISTRIBUTION ALONG THE COOLING CHANNELS .................................. - 92 -

FIGURE 53: DYNAMIC VISCOSITY DISTRIBUTION ALONG THE COOLING CHANNELS ................................. - 93 -

FIGURE 54: THERMAL CONDUCTIVITY DISTRIBUTION ALONG THE COOLING CHANNELS ......................... - 93 -

FIGURE 55: COOLANT PRESSURE DISTRIBUTION ALONG THE CHANNELS ................................................. - 94 -

FIGURE 56: DIAMETER EFFECT ON THE COOLANT VELOCITY ALONG THE COOLING CHANNELS ............... - 95 -

FIGURE 57: DIAMETER EFFECT ON THE COOLANT PRESSURE DROP ALONG THE COOLING CHANNELS ...... - 96 -

FIGURE 58: REYNOLDS NUMBER DISTRIBUTION ALONG THE COOLING CHANNELS .................................. - 96 -

FIGURE 59: DIAMETER EFFECT ON THE HEAT FLUX DISTRIBUTION .......................................................... - 97 -

FIGURE 60: DIAMETER EFFECT ON THE CONVECTIVE HEAT FLUX COEFFICIENT OF COOLANT DISTRIBUTION .. -

98 -

FIGURE 61: DIAMETER EFFECT ON THE GLOBAL COEFFICIENT OF HEAT TRANSFER DISTRIBUTION .......... - 98 -

FIGURE 62: DIAMETER EFFECT ON THE TEMPERATURE DISTRIBUTION .................................................... - 99 -

FIGURE 63: DIAMETER EFFECT ON THE COOLANT DENSITY DISTRIBUTION ............................................ - 100 -

FIGURE 64: DIAMETER EFFECT ON THE COOLANT HEAT SPECIFIC DISTRIBUTION .................................. - 100 -

FIGURE 65: DIAMETER EFFECT ON THE COOLANT THERMAL CONDUCTIVITY DISTRIBUTION ................. - 101 -

FIGURE 66: HEAT FLUX DISTRIBUTION ALONG THE COOLING CHANNELS .............................................. - 102 -

FIGURE 67: COMPARISON BETWEEN HEAT FLUXES ............................................................................... - 103 -

FIGURE 68: COMPARISON BETWEEN TEMPERATURE TRENDS ................................................................ - 104 -

FIGURE 69: COMPARISON BETWEEN DENSITY TRENDS .......................................................................... - 104 -

FIGURE 70: COMPARISON BETWEEN VELOCITY TRENDS ....................................................................... - 105 -

FIGURE 71: COMPARISON BETWEEN REYNOLDS NUMBER TRENDS........................................................ - 106 -

FIGURE 72: COMPARISON BETWEEN SPECIFIC HEAT TRENDS ................................................................ - 106 -

FIGURE 73: COMPARISON BETWEEN THERMAL CONDUCTIVITY TRENDS ............................................... - 107 -

FIGURE 74: COMPARISON BETWEEN PRESSURE TRENDS ........................................................................ - 107 -

FIGURE 75: H2 AND CH4 COOLING CHANNEL OPERATIONAL CONDITION, ON A TYPICAL REDUCED

PRESSURE-TEMPERATURE STATE DIAGRAM. ................................................................................. - 113 -

FIGURE 76 SPECIFIC HEAT AND THERMAL CONDUCTIVITY AS FUNCTION OF TENMPERATURE; P=6.0 MPA .... -

114 -

IV

List of tables

TABLE 1: ENGINE CYCLE ADVANTAGES AND DISADVANTAGES ............................................................... - 14 -

TABLE 2: NUMBER OF CHARACTERISTIC LENGTHS OF TYPICAL PROPELLANT COMBINATIONS................ - 49 -

TABLE 3: MAIN GEOMETRIC PARAMETERS OF HYPROB-DEMONSTRATOR ............................................. - 72 -

TABLE 4: MAIN PERFORMANCE PARAMETERS OF HYPROB-DEMONSTRATOR ....................................... - 73 -

TABLE 5: MAIN PERFORMANCE PARAMETERS ......................................................................................... - 84 -

Acronyms, symbols and abbreviation

𝐴 Nozzle section

𝐴𝑐ℎ Channels section

𝐴𝑡 Throat section

𝐴2 Exit area of nozzle

𝐴𝑤 Wetted area

AR Aspect ratio

ARCH Architecture system

𝛼 Nozzle divergence angle

𝛥𝑉 Delta Velocity

CDF Concurrent Design Facility

CFD Computational Fluid Dynamic

COOL Cooling system

𝑐∗ Characteristic Velocity

𝐶𝐻4 Methane

𝐶𝑝 Heat Specific

𝑑 Diameter

𝑑𝑐ℎ Diameter of cooling channels in the throat region

𝐷𝑡 Throat diameter

𝐷𝑐 Combustion chamber diameter

V

𝐷𝐻 Hydraulic diameter

𝐷𝑒 Exit diameter

𝑒 Roughness

ԑ Theoretical nozzle expansion area ratio

FEED Feed system

𝐹 Thrust

𝑓 Friction factor

𝑓𝑠 Safety factor

𝜉 Joint coefficient

𝑔 Acceleration of gravity

𝑔0 Acceleration of gravity at sea level

𝛾 Specific heat ratio

𝜌 Density

ℎ𝑔 Convective Heat Flux Coefficient (gas)

ℎ𝑐 Convective Heat Flux Coefficient (coolant)

𝑯 Global coefficient of heat transfer

𝐼𝑠𝑝 Specific impulse

INJE Injection system

LRE Liquid Rocket Engine

𝐿∗ Characteristic Length

𝜆 Divergence angle correction factor for conical nozzle exit

𝑘 Thermal conductivity

�̇�𝑓𝑢 Mass flow rate (fuel)

�̇� 𝑓𝑢𝑐ℎ Mass flow rate (fuel) per unit channels

�̇�𝑔 Mass flow rate (gas)

𝐿𝑐ℎ𝑎𝑚 Chamber length

𝐿𝑐𝑜𝑛𝑣 Convergent nozzle length

𝐿𝑑𝑖𝑣 Divergent nozzle length

𝑀 Mach Number

VI

𝑀𝑥 Local Mach Number

𝜇 Viscosity

𝑛 Number of the channels

𝑁 Newton

𝑁𝑢 Nusselt number

𝑂𝑥 Oxygen

𝑂/𝐹 Mixture ratio

𝑃𝑎 Pascal

𝑝2 Rocket gas pressure at nozzle exit

𝑝3 Ambient or atmospheric pressure

𝑝𝑥 local gas pressure

𝑝𝑒 External pressure

𝑝𝑐 Chamber pressure

𝑃𝑟 Prandtl number

𝑞 Heat flux

𝑟 Local Recovery Factor

𝑟𝑒 Nozzle radius at the exit

𝑟𝑡 Nozzle radius at the throat

𝑟𝑥 Local nozzle radius

𝑅 Effective Recovery factor

R Gas constant per unit weight

𝑅′ Universal gas constant

𝑅𝑒 Reynolds number

𝑅𝑐 Combustion chamber radius

𝑅𝑡 Throat radius

𝑅𝑒 Exit radius

R&T Research and Technology

𝑠 Distance between the cooling channels

𝑡 Chamber Wall Thickness

VII

TCHA Thrust chamber system

𝑇𝑥 Gas temperature at the section x

𝑇𝑦 Gas temperature at the section y

𝑇𝑎𝑤 Adiabatic wall temperature

𝑇𝑐 Chamber temperature

(𝑇𝑐)𝑛𝑠 Nozzle stagnation temperature

𝑇𝑐𝑜 Coolant Bulk temperature

𝑇𝑤𝑐 Coolant side wall temperature

𝑇𝑤𝑔 Gas side wall temperature

𝜎 Bartz correction factor for property variation across the boundary layer

𝜎𝑦 Yield stress

v Specific volume;

vx Specific volume at section x

𝑣 Velocity

𝑣2 Exit gas velocity

𝑉 Volume

𝑉𝑐 Combustion chamber volume

𝑉𝑐𝑜𝑛𝑣 Convergent nozzle volume

𝑉𝑐𝑐 Volume 𝑉𝑐+ 𝑉𝑐𝑐

𝜃𝑐𝑜𝑛𝑣 Converging nozzle angle

𝜃𝑑𝑖𝑣 Divergent half-cone angle

𝜃𝑛 Nozzle bell starting angle

𝜃𝑒 Nozzle lip exit angle

- 1 -

INTRODUCTION

This work of thesis has been carried out after a trainee period spent at the Propulsion

department of the Italian Aerospace Research Center (CIRA), located in Capua,

Italy. CIRA was created in 1984 to manage PRORA, the Italian Aerospace Research

Program and uphold Italy’s leadership in Aeronautics and Space. Among others, one

of the most innovative research fields, in which CIRA is involved, is the aerospace

propulsion. In particular, the activities aim at technological development for the

modeling of rocket and ramjet/scramjet engines. The propulsion department is

currently managing and working within the HYPROB program. As defined by the

Italian Space Agency (ASI), this program will contribute to the implementation of

national strategies for space propulsion. The strategic goal is to evolve and

consolidate national technology and system development capabilities on rocket

propulsion for future space applications. A detailed description of the program will

be given in paragraph 2.1.

One of the main product under development in the frame of HYPROB program is the

CIRA Concurrent Design Facility (CDF) for Space Propulsion. The CDF exploits

concurrent engineering methodology to perform effective, fast and cheap space

mission preliminary studies. Concurrent Engineering Approach is the state-of-art

methodology for the preliminary design phase of an Aero-Space Project (Phase 0/A).

Equipped with a state-of-the-art network of computers, multimedia devices and

software tools, the CDF allows team of experts to perform design studies during

relatively short working sessions. The CDF design room has been designed and will

be equipped with relevant hardware and software tools, with the aim of creating an

effective communication and data interchange among team members.

Concurrent Engineering Approach, along with CIRA CDF for Space Propulsion will

be deeply described in paragraph 3.1.

The present work is focused on the development of the Cooling System Module for a

Liquid Rocket Engine. The cooling domain of the CDF will be equipped with this

- 2 -

module and thus this work will allow the specialist to preliminary design and

understand the feasible configurations of the cooling system.

Thermofluidynamic behavior of the coolant along the cooling channels has been

evaluated using engineering formulas and several approaches have been compared.

In particular, a numerical investigation has been performed to determine the effect of

the number of cooling channels on temperature, pressure drop and other

thermofluidynamic properties of the coolant.

Finally a validation of the performed work will be shown. This final result has been

obtained comparing the developed module simulation with the results achieved by a

3 ton class LOx/CH4 LRE developed at CIRA in the framework of HYPROB

Program.

- 3 -

Chapter 1

LIQUID ROCKET ENGINE

1.1 Overview

In this introductory chapter, the functioning of a LRE and its major components will

be presented in detail. This description follows the key points proposed in literature.

Rocket propulsion is a class of jet propulsion that produces thrust by ejecting stored

matter, called the propellant. The energy from a high-pressure combustion reaction

of propellant chemicals, usually a fuel and an oxidizing chemical, permits the heating

of reaction product gases to very high temperatures (2200 to 3800 K). These gases

are subsequently expanded in a nozzle and accelerated to high velocities (1800 to

4300 m/sec). Since these gas temperatures are about twice the melting point of steel,

it is necessary to cool or insulate all the surfaces that are exposed to the hot gases.

According to the physical state of the propellant, there are several different classes of

chemical rocket propulsion devices. Liquid propellant rocket engines use liquid

propellants that are fed under pressure from tanks into a thrust chamber. The liquid

bipropellant consists of a liquid oxidizer (e.g., liquid oxygen) and a liquid fuel

(hydrogen, kerosene, methane). A monopropellant is a single liquid that contains

both oxidizing and fuel species; it decomposes into hot gas when properly catalyzed.

Gas pressure feed systems are used mostly on low thrust, low total energy propulsion

systems, such as those used for attitude control of flying vehicles, often with more

than one thrust chamber per engine. Pump-fed liquid rocket systems are typically

used in applications with larger amounts of propellants and higher thrusts, such as in

space launch vehicles. In the thrust chamber the propellants react to form hot gases,

which in turn are accelerated and ejected at a high velocity through a supersonic

nozzle, thereby imparting momentum to the vehicle. A nozzle has a converging

section, a constriction or throat, and a conical or bell-shaped diverging section. A

liquid rocket propulsion system requires several precision valves and a complex feed

- 4 -

mechanism which includes propellant pumps, turbines, or a propellant-pressurizing

device, and a relatively intricate combustion or thrust chamber [1].

The present work is based on liquid bipropellant rocket engine. In particular, the

attention has been focused on liquid oxygen as oxidizer and liquid methane as fuel.

In order to better understand the functioning and the physics of rockets, next

paragraph will deal with the basic equations that describe the performance

parameters of a liquid rocket engine.

1.2 Propulsion Fundamentals

The total impulse 𝐼𝑡 is the thrust force F, which can vary with time, integrated over

the burning time t. 𝐼𝑡 is provided by Eq. (1.2 – 1).

𝑰𝒕 = ∫ 𝑭𝒅𝒕𝒕

𝟎 (1.2 – 1)

For constant thrust and negligible start and stop transients this reduces to Eq. (1.2 –

2).

𝑰𝒕 = 𝑭𝒕 (1.2 – 2)

The specific impulse 𝑰𝒔𝒑 is the total impulse per unit weight of propellant. It is an

important figure of merit of the performance of a rocket propulsion system. 𝑰𝒔𝒑 can

be expressed by Eq. (1.2 – 3).

𝑰𝒔𝒑 =∫ 𝑭𝒅𝒕𝒕

𝟎

𝒈𝟎 ∫ �̇�𝒅𝒕

(1.2 – 3)

This equation will give a time-averaged specific impulse value for any rocket

propulsion system, particularly where the thrust varies with time. During transient

conditions, for instance during start or the thrust buildup period, the shutdown

period, or during a change of flow or thrust levels, values of 𝐼𝑠𝑝 can be obtained by

integration or by determining average values for F and �̇� for short time intervals.

Considering constant thrust F and propellant flow �̇�, and negligible short start or

stop transients, this equation can be simplified as shown in the equation (1.2 – 4)

reported below.

- 5 -

𝑰𝒔𝒑 =𝑭

�̇�𝒈𝟎 =

𝑭

�̇�=

𝑰𝒕

𝒎𝒑𝒈𝟎 =

𝑰𝒕

𝒘

(1.2 – 4)

Where, 𝑚𝑝 is the total effective propellant mass, the product 𝑚𝑝𝑔0 is the total

effective propellant weight, and ẁ is the weight flow rate. The concept of weight

relates to the gravitational attraction at or near sea level, but in space or outer satellite

orbits, "weight" signifies the mass multiplied by an arbitrary constant, namely 𝑔0 . In

the Systeme International (SI) or metric system of units 𝐼𝑠𝑝can be expressed simply

in seconds. However, the units of 𝐼𝑠𝑝 do not represent a measure of elapsed time, but

a thrust force per unit “weight flow rate”.

In a rocket nozzle the actual exhaust velocity is not uniform over the entire exit

cross-section and does not represent the entire thrust magnitude. The velocity profile

is difficult to measure accurately. For convenience a uniform axial velocity “c” is

assumed which allows a one-dimensional description of the problem. This effective

exhaust velocity c is the average equivalent velocity at which propellant is ejected

from the vehicle. It is defined by Eq. (1.2 – 5).

𝒄 = 𝑰𝒔𝒑𝒈𝟎 (1.2 – 5)

It is given either in meters per second or feet per second. Since c and 𝐼𝑠𝑝 differ only

by an arbitrary constant, either one can be used as a measure of rocket performance.

It is worth to note that the thrust is the force produced by a rocket propulsion system

acting upon a vehicle. In a simplified way, it is the reaction experienced by its

structure due to the ejection of matter at high velocity. It represents the same

phenomenon that pushes a garden hose backwards or makes a gun recoil. The thrust

and the mass flow are constant and the gas exit velocity is uniform and axial. In

particular, this force is defined as:

𝑭 =𝒅𝒎

𝒅𝒕𝒗𝟐 = �̇�𝒗𝟐 =

�̇�

𝒈𝟎𝒗𝟐

(1.2 – 6)

This force represents the total propulsion force when the nozzle exit pressure equals

the ambient pressure. Because of fixed nozzle geometry and changes in ambient

- 6 -

pressure due to variations in altitude, there can be an imbalance of the external

environment or atmospheric pressure “𝑝3” and the local pressure “𝑝2” of the hot gas

jet at the exit plane of the nozzle. Thus, for a steadily operating rocket propulsion

system moving through a homogeneous atmosphere, the total thrust is expressed by

Eq. (1.2 – 7).

𝑭 = �̇�𝒗𝟐 + (𝒑𝟐 − 𝒑𝟑)𝑨𝟐 (1.2 – 7)

The first term is the momentum thrust represented by the product of the propellant

mass flow rate and its exhaust velocity relative to the vehicle. The second term

represents the pressure thrust consisting of the product of the cross-sectional area at

the nozzle exit “𝐴2” and the pressure difference evaluated at the same position.

When the ambient atmosphere pressure is equal to the exhaust pressure, the pressure

term is zero and the thrust is the same as in Eq. (1.2 – 6). In the vacuum of space 𝑝3

= 0 and the thrust becomes:

𝑭 = �̇�𝒗𝟐 + 𝒑𝟐𝑨𝟐 (1.2 – 8)

The pressure condition in which the exhaust pressure is exactly matched to the

surrounding fluid pressure (𝑝2 = 𝑝3) is referred to the rocket nozzle with optimum

expansion ratio. The effective exhaust velocity as defined by Eq. (1.2 – 5) applies to

all rockets that thermodynamically expand hot gas in a nozzle and, indeed, to all

mass-expulsion systems. From the previous equations its trivial to obtain that, for

constant propellant mass flow, the exhaust velocity can be written as:

𝒄 = 𝒗𝟐 + (𝒑𝟐 − 𝒑𝟑)

�̇�𝑨𝟐 (1.2 – 9)

Equation (1.2 – 10) shows that “c” can be determined from thrust and propellant

flow measurements. When 𝑝2 = 𝑝3 the effective exhaust velocity c is equal to the

average actual exhaust velocity of the propellant gases 𝑣2. When 𝑝2 ≠ 𝑝3 then c ≠

𝑣2. The second term of the right-hand side of Eq. (1.2 – 9) is usually small in

relation to 𝑣2, thus the effective exhaust velocity is usually close in value to the

actual exhaust velocity.

The characteristic velocity has been used frequently in rocket propulsion literature.

Its symbol 𝑐∗, is defined by Eq. (1.2 – 11).

c* = 𝒑𝒄𝑨𝒕

�̇� (1.2 – 11)

- 7 -

The characteristic velocity 𝑐∗, is used in comparing the relative performance of

different chemical rocket propulsion system designs and propellants; it is easily

determined from measured data of �̇�, 𝑝𝑐, and 𝐴𝑡. For ideal rocket, the hot gases

behavior is described by some fundamental principles such as:

Perfect gas law, defined by Eq. (1.2 – 12).

𝒑𝒙vx = R 𝑻𝒙 (1.2 – 12)

The principle of conservation of energy, defined as in Eq. (1.2 – 13).

𝟏

𝟐𝒈𝟎(𝒗𝒙

𝟐 − 𝒗𝒚𝟐) = 𝑪𝒑(𝑻𝒚 − 𝑻𝒙) (1.2 – 13)

Principle of conservation of matter is expresses by the Eq. (1.2 – 14).

𝒎𝒈̇ = 𝝔𝒙𝒗𝒙𝑨𝒙 = 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕 (1.2 – 14)

Finally, Eq. (1.2 – 15) that provides the Isentropic-Flow process.

𝒑𝒙vxγ = 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕 (1.2 – 15)

By an appropriate combination of these principles 𝐹, c* and other parameters can be

written in the way reported hereinafter. Of course, the demonstrations is widely

reported in literature[1] [5].

Area law can be expresses by Eq. (1.2 – 16)

𝑨𝒚

𝑨𝒙=

𝑴𝒙

𝑴𝒚 √{

𝟏+ (𝜸−𝟏)

𝟐𝑴𝒚𝟐

𝟏+ (𝜸−𝟏)

𝟐𝑴𝒙𝟐}

(𝜸+𝟏)

(𝜸−𝟏)

(1.2 – 16)

The exhaust velocity can be evaluated as :

𝒗𝟐 = √𝟐𝜸

𝜸−𝟏

𝑹′

𝑴𝑻𝒄 [𝟏 − (

𝒑𝟐

𝒑𝟏)

𝜸−𝟏

𝜸] (1.2 – 17)

It can be seen that the exhaust velocity of a nozzle is a function of the pressure ratio

𝑝2

𝑝1, the ratio of specific heats 𝛾, and the absolute temperature at the nozzle inlet 𝑇𝑐, as

well as the gas constant 𝑅′ . Because the gas constant for any particular gas is

inversely proportional to the molecular mass 𝔐, the exhaust velocity or the specific

impulse are a function of the ratio of the absolute nozzle entrance temperature

divided by the molecular mass. This ratio plays an important role in optimizing the

- 8 -

mixture ratio in chemical rockets. In the latter equation the combustion chamber

velocity has been considered negligible.

Finally, the thrust can be expressed as:

𝑭 = 𝑨𝒕𝒑𝒄√𝟐𝜸𝟐

𝜸−𝟏(𝟐

𝜸+𝟏)

(𝜸+𝟏)

(𝜸−𝟏)[𝟏 − (

𝒑𝟐

𝒑𝟏)

𝜸−𝟏

𝜸] + (𝒑𝟐 − 𝒑𝟑)𝑨𝟐 (1.2 – 18)

The thrust, moreover, can be expressed in function of thrust coefficient “𝐶𝐹” defined

as the thrust divided by the chamber pressure 𝑝𝑐 and the throat area 𝐴𝑡. After some

passages 𝐶𝐹 can be expresses by Eq. (1.2 – 19).

𝑪𝑭 = √𝟐𝜸𝟐

𝜸−𝟏(𝟐

𝜸+𝟏)

(𝜸+𝟏)

(𝜸−𝟏)[𝟏− (

𝒑𝟐𝒑𝟏)

𝜸−𝟏𝜸] +

(𝒑𝟐−𝒑𝟑)𝑨𝟐

𝒑𝒄𝑨𝒕

(1.2 – 19)

Therefore, the thrust becomes:

𝑭 = 𝑪𝑭𝑨𝒕𝒑𝒄 (1.2 – 20)

These equation provides an estimation of the performance of a liquid rocket engine.

Of course, some of these equations have been used in the present work. The

successive paragraphs deals with the main components of a LRE.

1.3 Main systems overview

The overall architecture of a liquid rocket engine (LRE) is composed by several main

systems, such as:

Feed system: provide propellants to the injectors at the design pressure. It

consists of: propellant tanks, pumps, turbines, valves and piping;

Thrust chamber: is the key subassembly of a rocket engine. Here the liquid

propellants are metered, injected, atomized, vaporized, mixed, and burned to

form hot reaction gas products, which in turn are accelerated and ejected at

high velocity[1]. A rocket thrust chamber is composed by injectors,

combustion chamber, supersonic nozzle and mounting provisions. The

injector has to introduce and meter the flow of liquid propellants to the

combustion chamber, which provides an area for proper mixing of propellants

and enough length to complete chemical combustion. The nozzle is

- 9 -

responsible for the enthalpy conversion into kinetic energy and, thus, of the

thrust generation[2];

Cooling system: this subsystem is mandatory due to the extremely high

temperature reached by the thrust chamber walls. Regenerative cooling is the

most commonly cooling technique used for LRE. It consists in let the coolant

running through passages formed either by constructing the chamber liner

from tubes or by milling channels in a solid liner[3]. This system is called

regenerative because the coolant is the fuel itself.

A deeper description is reported in the next sections of the paragraph.

1.3.1 Feed System

In liquid bipropellant rocket engine systems, propellants are stored in one or more

oxidizer tanks and one or more fuel tanks. A feed mechanism aims to move the

propellants from tanks into the thrust chamber and raise propellants pressure. The

energy for these functions comes either from a gas pressure feed system or

turbo-pump feed system, thus a description of those two systems is described

hereinafter. Finally, this paragraph will provide the main advantages and

disadvantages of these feed system.

Turbo-pump feed system and cycle engine:

The propellants are pressurized by means of pumps, which in turn are driven by

turbines. These turbines derive their power from the expansion of hot gases. Engines

with turbo-pumps are preferred for booster and sustainer stages of space launch

vehicles, long-range missiles, and in the past also for aircraft performance

augmentation. Those systems are usually lighter than other types for these high

thrust, long duration applications. The inert hardware mass of the rocket engine

(without tanks) is essentially independent of duration. An engine cycle for

turbo-pump fed engines describes the specific propellant flow paths through the

major engine components, the method of providing the hot gas to one or more

turbines, and the method of handling the turbine exhaust gases. There are open cycles

and closed cycles. Open denotes that the working fluid exhausting from the turbine is

discharged overboard, after having been expanded in a nozzle of its own, or

- 10 -

discharged into the nozzle of the thrust chamber at a point in the expanding section

far downstream of the nozzle throat. In closed cycles or topping cycles all the

working fluid from the turbine is injected into the engine combustion chamber to

make the most efficient use of its remaining energy. In closed cycles the turbine

exhaust gas is expanded through the full pressure ratio of the main thrust chamber

nozzle, thus giving a little more performance than the open cycles, where these

exhaust gases expand only through a relatively small pressure ratio[1]. Now a

discussion follows on several common open and closed engine cycles and their

characteristics:

Gas generator cycle. (see Figure 1)

Open cycle. Pumps increase the propellant pressure before they are injected

into the thrust chamber. The turbine that actuates the pumps is driven by a hot

gas generator which combusts propellant tapped off from the main feed lines

after the pumps. After it has passed the turbine, the gas is dumped into the

atmosphere, sometimes through smaller nozzles to generate additional thrust,

or alternatively injected back in the thrust chamber at the end of the nozzle.

The portion of the fuel which does not go to the gas generator, passes first the

nozzle where it is used for cooling before being injected in gaseous state into

the thrust chamber;

Bleed expander engine cycle. (see Figure 1)

Open cycle. Pumps increase the propellant pressure before they are injected

into the thrust chamber. The turbine that actuates the pumps is driven by hot

gaseous fuel after it has passed as a liquid the nozzle where it is used for

cooling. The gaseous fuel is dumped into the atmosphere after it has passed

the turbine. The thrust chamber uses the gaseous fuel which is not send to the

turbine.

Combustion tap-off cycle. (see Figure 1)

Open cycle. Pumps increase the propellant pressure before they are injected

into the thrust chamber. The turbine that actuates the pumps is driven by hot

combustion gas which is tapped of from the thrust chamber.

- 11 -

Figure 1: Gas generator cycle, Open bleed expander cycle & Combustion tap- off cycle

Staged combustion engine cycle. (see Figure 2)

Closed cycle. Pumps increase the propellant pressure before they are injected

into the thrust chamber. The turbine that actuates the pumps is driven by a

warm gas generator which combusts oxidizer tapped off from the main

oxidizer feed lines after the pump and gaseous fuel after the liquid fuel has

passed the pump and the nozzle where it is used for cooling. In the warm gas

generator the combustion is incomplete and the generated gas is injected in

the thrust chamber where it combusts, in the ideal case, completely.

Expander engine cycle. (see Figure 2)

Closed cycle. Pumps increase the propellant pressure before they are injected

into the thrust chamber. The turbine that actuates the pumps is driven by hot

gaseous fuel after it has passed as a liquid the nozzle where it is used for

cooling. After the gaseous fuel has passed the turbine it is injected into the

thrust chamber[4].

- 12 -

Figure 2: Staged-combustion cycle and Expander cycle

Gas pressure feed system:

One of the simplest and most common means of pressurizing the propellants is to

force them out of their respective tanks by displacing them with high-pressure gas.

This gas is fed into the propellant tanks at a controlled pressure, thereby giving a

controlled propellant discharge. Because of their relative simplicity, the rocket

engines with pressurized feed systems can be very reliable. It consists of a

high-pressure gas tank, a gas starting valve, a pressure regulator, propellant tanks,

propellant valves, and feed lines. Additional components, such as filling and draining

provisions, check valves, filters, flexible elastic bladders for separating the liquid

from the pressurizing gas, and pressure sensors or gauges, are also often

incorporated[1]. The functioning of a gas pressure feed system can be schematized as

already done for the engine cycles. A short description on the gas pressure feed

system is reported hereinafter:

Pressure fed engine cycle. (see Figure 3)

Closed cycle. No pumps are present, the oxidizer and fuel are injected

directly in the thrust chamber. Because of the absence of pumps to increase

the pressure after the tanks, the propellants have to be stored at high pressure

[4].

- 13 -

Figure 3: Pressure-fed cycle

Cycle advantages and disadvantages:

In this paragraph the engine cycles will be compared to each other. Each cycle has its

advantages and disadvantages in dry mass, wet mass, reliability, cost, specific

impulse, etc. Table 1 shows such comparison.

- 14 -

Cycle Advantages Disadvantages

Pressure fed • Simple reliable design

• No turbo-pump

• Limited to low burn times and

low thrust

• Limited throttling capabilities

• High pressure tanks

• Tank bladders can be required

Gas generator • Fairly simple

• Wide thrust operating range

• Turbine exhaust gas has low

specific impulse and leads to

effective loss in performance

• Gas generator required

Staged combustion

• High performance

• High chamber pressure and

thrust capability

• Very complex with lower

reliability

• Advanced turbine and pumps

required to cope with high

pressures

• Pre-burner (gas generator)

required

Expander

• Good performance

• Simple design with a low

weight

and wide thrust operating range

• No gas generator required

• Limited to low chamber

pressures

• Limited to cryogenic fluids

Bleed expander • No gas generator required

• Limited to cryogenic fluids

• Pressure and thrust limited by

fuel thermal properties

Table 1: Engine cycle advantages and disadvantages

The choice of a particular feed system depends on several parameters as propellants

properties, material properties, mission time, chamber pressure and operating

conditions.

The present work has been developed considering a LRE with turbo-pump feed

system and an regenerative expander cycle system.

1.3.2 Thrust chamber

The thrust chamber is the heart of a propulsion system as it is the component which

generates the thrust. As stated previously, this device is composed by an injection

system, a combustion chamber, a supersonic nozzle and mounting provisions. The

propellants are injected in the combustion chamber by injectors, here they react to

form hot gases and develop large amounts of energy. The supersonic nozzle

accelerates and ejects at high velocity the hot gases and it is responsible of the thrust

- 15 -

generation. The hot gases temperature can reach 3800 K and the chamber pressure is

supposed to be as high as possible to increase the performances. Hence, this situation

requires a careful design process. This section aims to describe in detail the

components and the functions of the thrust chamber. In Figure 4 an example of a

thrust chamber is reported.

Figure 4: Thrust chamber sketch

Injectors:

The functions of the injector are similar to those of a carburetor of an internal

combustion engine. The injector has to introduce and meter the flow of liquid

propellants to the combustion chamber, cause the liquids to be broken up into small

droplets (a process called atomization), and distribute and mix the propellants in such

a manner that a correctly proportioned mixture of fuel and oxidizer will result, with

uniform propellant mass flow and composition over the chamber cross section[1].

However, the injector, located directly over the high-pressure combustion, performs

many other functions related to the combustion and cooling processes and is much

more important to the function of the rocket engine than the carburetor is for an

- 16 -

automobile engine. No other component of a rocket engine has as great an impact

upon engine performance as the injector.

Injector design, like many engineering tasks, entails many compromises. The proper

design starting point considers the particular application, engine size, propellant

combination, and design priorities. Of course, the initial approach invokes complete

optimization of all features: light weight, high performance, low cost, reliability, etc.;

but that soon emphasizes priority for the main design parameters. One of most

common problems relevant the injectors design is linked at combustion instability.

All systems which release large amounts of energy have the potential for destructive

oscillations, particularly if there is regenerative feedback (gain) between the

combustion phenomena and the rate of energy release. This is particularly true of the

combustion process, because temperature and pressure variations can directly impact

the rates of vaporization and reaction. Stable operation can be achieved by either

damping or detuning these processes. Hence, high performance can become

secondary if the system can easily be triggered into a destructive instability, and

many of the injector parameters that provide high performance appear to reduce the

stability margin[5].

Now a discussion follows on the most common types of injection elements that are:

non-impinging, unlike-impinging and like-impinging.

Injection Elements: Nonimpinging elements

Coaxial. The coaxial, or concentric, injection element usually has a slow-moving

central stream of liquid oxidizer surrounded by a high-velocity concentric sheet of

gaseous fuel. The liquid oxidizer is deliberately injected at low velocity, with the

usual injection pressure-drop accomplished by an upstream metering orifice in each

element, and diffused to a reduced velocity in the tubular LOx post. On the other

hand, the fuel injection pressure is turned into high injection velocity in the annular

gap around the LOx post. Mixing, atomization of the liquid, and mass distribution

are provided by the shearing action of the high-velocity gaseous fuel on the surface

of the liquid. The fuel surrounding the oxidizer tends to shield the combustion

process, which enjoys a favorable combustor-wall heating environment, and also

appears to benefit combustion stability.

- 17 -

Showerhead. Directly axial, or near-axial, non-impinging streams of either liquid or

gaseous propellants are generally referred to as "shower-heads." This type of element

provides very little effective atomization or mixing, and is seldom used for primary

injection. It is most frequently used for fuel-film-cooling streams at the chamber

wall.

There are other types of injection elements, such as Fan formers and Slots and

sheets, but they have seldom been successful[5]. The injection elements which have

just been described, are represented in Figure 5.

Figure 5: Coaxial element and Shower head

Injection Elements: Unlike-impinging elements

Unlike doublets. A straightforward way of mixing two different fluid streams directs

one against the other; this in essence describes the basic unlike-impinging doublet.

The impact produces a fan-shaped spray made up of a mixture of the two impinging

fluids. With no combustion or other chemical reactions, the combined streams form a

largely two-dimensional spray in a plane basically at right angles to the plane which

includes the centerlines of the impinging streams. The width of the spray fan largely

reflects the included impingement angle of the two streams, the thickness to the

stream diameters, and the turbulence level. Mixing in the spray fan is not perfectly

distributed, being adversely affected by any momentum and/or stream-diameter

mismatch of the impinging fluids. Stream misimpingement, resulting from the fact

that the stream centerlines rarely intersect at the theoretical impingement point,

distorts the shape of the spray fan and produces mixing imperfections. Other effects

can be arise when combustion processes are superimposed upon impinging-stream

hydrodynamics.

- 18 -

Unlike triplets. A mismatch in stream size and momentum between the oxidizer and

the fuel in unlike doublet elements will force the spray away from the desired axial

direction and distort the fan, resulting in poorer mixing. This problem may be

avoided by use of a symmetrical, unlike-injection element consisting of an axial

central stream of one propellant and two symmetrically-impinging outer streams of

the other propellant. This unlike triplet may have either two fuel streams impinging

on a central oxidizer stream (fuel-oxidizer-fuel) or the reverse (oxidizer-fuel-

oxidizer). In most propellant combinations, the total oxidizer flow area will be the

greater, so the O-F-O system provides a closer match of stream sizes and

consequently better mixing. Unlike-triplet injectors have demonstrated high levels of

mixing and resultant combustion efficiency, but they also tend to be sensitive to

stability problems[5].

An example of Unlike doublets and Unlike triplets are represented in Figure 6.

Figure 6: Unlike doublet and Unlike triplet

Injection Elements: Like-impinging elements

Like doublets. Like-impinging elements impinge the injected streams (liquid or gas)

directly on other streams of the same propellant. The most common of these, a

doublet configuration, has two like-fluid streams angled together to an impact point,

producing in a fan-shaped spray of droplets similar to that of an unlike doublet.

There is no mixing within this fan, since only one reactant is present in each. Energy

dissipated by the impingement atomizes the liquids. Like-impinging elements are

frequently used for liquid/liquid propellant systems in which reaction or heat transfer

between unlike-impinging streams is undesirable. The like-impinging doublet avoids

most of the reactive-stream de-mixing of unlike-impinging designs and better

maintains combustion stability than unlike patterns[5].

- 19 -

In addition, a triplet configuration have been developed in which three streams of the

same propellants can be directed to a common impingement point. An example of a

like doublets is reported in Figure 7.

Figure 7: Like-impinging doublet

Combustion chamber:

A liquid-rocket combustion chamber converts propellants into high-temperature,

high-pressure gas through combustion, which releases the chemical energy of the

propellant, resulting in an increase in internal energy of the gas. The liquid

propellants are injected at the injection plane with a small axial velocity which is

assumed to be zero in gas-flow calculations. The combustion process proceeds

throughout the length of the chamber and is expected to be completed at the nozzle

entrance. Heat released between injection plane and nozzle inlet increases the

specific volume of the gas. To satisfy the conditions of constant mass flow, the gas

must be accelerated toward the nozzle inlet with some drop of pressure. The

combustion temperature is much higher than the melting points of most chamber

wall materials, therefore it is necessary either to cool these walls or to stop rocket

operation before the critical wall areas become too hot. If the heat transfer is too high

and thus the wall temperatures become locally too high, the thrust chamber will fail.

Nowadays the preferred solution is composed by a cylindrical chamber with a flat

injector and a converging-diverging nozzle. The chamber volume is defined as the

volume up to the nozzle throat section and it includes the cylindrical chamber and the

converging cone frustum of the nozzle.

The volume and shape are selected after evaluating some constraints:

The volume has to be large enough for adequate mixing, evaporation, and

complete combustion of propellants. Chamber volumes vary for different

propellants with the time delay necessary to vaporize and activate the

- 20 -

propellants and with the speed of reaction of the propellant combination.

When the chamber volume is too small, combustion is incomplete and the

performance is poor. With higher chamber pressures or with highly reactive

propellants, and with injectors that give improved mixing, a smaller chamber

volume is usually permissible.

The chamber diameter and volume can influence the cooling requirements. If

the chamber volume and the chamber diameter are large, the heat transfer

rates to the walls will be reduced, the area exposed to heat will be large, and

the walls are somewhat thicker. Conversely, if the volume and cross section

are small, the inner wall surface area and the inert mass will be smaller, but

the chamber gas velocities and the heat transfer rates will be increased. There

is an optimum chamber volume and diameter where the total heat absorbed

by the walls will be a minimum. This is important when the available cooling

capacity of the coolant is limited (for example oxygen-hydrocarbon at high

mixture ratios) or if the maximum permissive coolant temperature has to be

limited (for safety reasons with hydrazine cooling). The total heat transfer can

also be further reduced by going to a rich mixture ratio or by adding “film

cooling” (a technique discussed below).

All inert components should have minimum mass. The thrust chamber mass is

a function of the chamber dimensions, chamber pressure, and nozzle area

ratio, and the cooling method.

Manufacturing considerations favor a simple chamber geometry, such as a

cylinder with a double cone bow-tie-shaped nozzle, low cost materials, and

simple fabrication processes.

In some applications the length of the chamber and the nozzle relate directly

to the overall length of the vehicle. A large-diameter but short chamber can

allow a somewhat shorter vehicle with a lower structural inert vehicle mass.

The gas pressure drop for accelerating the combustion products within the

chamber should be a minimum; any pressure reduction at the nozzle inlet

reduces the exhaust velocity and the performance of the vehicle. These losses

become appreciable when the chamber area is less than three times the throat

area.

- 21 -

For the same thrust, the combustion volume and the nozzle throat area

become smaller as the operating chamber pressure is increased. This means

that the chamber length and the nozzle length (for the same area ratio) also

decrease with increasing chamber pressure. The performance also goes up

with chamber pressure[1].

The preceding chamber considerations conflict with each other. Depending on the

application, a compromise solution that will satisfy the majority of these

considerations is therefore usually selected and verified by experimental data.

Nozzle:

This paragraph will describe the functioning of nozzle and the hot gases behavior.

As already told, the combustion products are discharged through a

converging-diverging nozzle to achieve high gas velocities and thrust. This

phenomena will be described in condition of ideal rocket. Such hypothesis allows to

express the basic thermodynamic principles with simple mathematical relationships.

Besides, the flow in the nozzle will be considered quasi-one-dimensional.

Gas flow through rocket nozzles

The prime function of a rocket nozzle is to convert efficiently the enthalpy of the

combustion gases into kinetic energy and thus create high exhaust velocity of the

gas. The nozzle is the most efficient device for accelerating gases to supersonic

velocities. Rocket nozzles are conventionally of the converging-diverging De Laval

type, with the cross-sectional area decreasing to a minimum at the throat and then

increasing to the exit area. The flow velocity through a nozzle increases to sonic

velocity at the throat and then increases further supersonically in the diverging

section. In practice, for one-dimensional isentropic expansion, it is assumed that the

gas flow through the nozzle will be an isentropic expansion, and that both the total

temperature and the total pressure will remain constant throughout the nozzle. The

static pressure at a nozzle throat with sonic flow, where the maximum weight flow

per unit area occurs, is defined as critical pressure. The velocity of sound is equal to

the velocity of propagation of a pressure wave within a medium. It is therefore

impossible for a pressure disturbance downstream of the nozzle throat to influence

- 22 -

the flow at the throat or upstream of the throat, provided that this disturbance will not

create a higher throat pressure than the critical pressure. It is one of the characteristic

features of an attached diverging or De Laval nozzle, however, that sonic velocity in

the nozzle throat is maintained even if the back pressure (ambient pressure) at the

nozzle exit is greater than the pressure required at the throat for sonic velocity. As a

result, a pressure adjustment (recovery) must take place between the throat and the

nozzle exit (ambient pressure). This adjustment may take place through subsonic

deceleration (isentropic) or by way of non-isentropic discontinuities called shock

waves, or a combination of both. In short, pressures lower than ambient may be

present in a supersonic nozzle. The higher ambient pressure cannot advance

upstream within the nozzle, since the gases are flowing with supersonic velocity. An

exception to this is in the region of the flow along the nozzle walls, where, due to

friction, a boundary layer of slow-moving gases may exist. In this subsonic boundary

layer, ambient pressure may advance for a distance, forcing the low-pressure center

jet away from the walls. It might be expected that the point of separation will be at

the point of optimum expansion, but separation usually occurs further down-stream.

In fact, it rarely occurs at all in conventional rocket nozzles within the designed

region of operation, unless an extreme case of overexpansion exists or unless

excessive nozzle divergence angles are chosen[5].

Nozzle configuration

A number of different proven nozzle configurations are available nowadays. The

principal difference in the different nozzle configurations is found in the diverging

supersonic-flow section. The wall surface throughout the nozzle should be smooth

and shiny to minimize friction, radiation absorption, and convective heat transfer due

to surface roughness. Gaps, holes, sharp edges, or protrusions must be avoided. The

most common nozzle configurations are conical nozzle and bell-shaped nozzle.

Conical nozzle. In early rocket-engine applications, the conical nozzle, which proved

to be satisfactory in most respects, was used almost exclusively. A conical nozzle

allows ease of manufacture and flexibility in converting an existing design to higher

or lower expansion area ratio without major redesign. Since certain performance

losses occur in a conical nozzle as a result of the non-axial component of the exhaust

- 23 -

gas velocity, a correction factor, is applied in the calculation of the exit-gas

momentum[5]. This factor (thrust efficiency) is the ratio between the exit-gas

momentum of the conical nozzle and that of an ideal nozzle with uniform, parallel,

axial gas-flow. The value of this parameter can be expressed by the following

equation (1.3.2 – 1):

𝝀 =𝟏

𝟐(𝟏 + 𝐜𝐨𝐬𝜶)

( 1.3.2 - 1)

The configuration of a typical conical nozzle is shown in Figure 9: .

Figure 8: Conical nozzle

Bell nozzle. To gain higher performance and shorter length, engineers developed the

bell-shaped nozzle. It employs a fast-expansion (radial-flow) section in the initial

divergent region, which leads to a uniform, axially directed flow at the nozzle exit.

The wall contour is changed gradually enough to prevent oblique shocks. The

expansion in the supersonic bell nozzle is more efficient than in a simple straight

cone of similar area ratio and length, because the wall contour is designed to

minimize losses[5]. One convenient way of designing a near-optimum-thrust bell

nozzle contour uses the parabolic approximation procedures. The design

configuration of a parabolic approximation bell nozzle is shown in Figure 9 shows

the contour of a bell nozzle

- 24 -

Figure 9: Parabolic approximation of bell nozzle contour

1.3.3 Cooling System

All rocket engines show a common problem, high energy released by combusted

gases. This problem results in high combustion temperatures (2200 to 3600 K), high

heat transfer rates (0.8 to 160 𝑀𝑊/𝑚2) in thrust chamber and requires special

cooling techniques for the engine. Cooling techniques developed to cope with this

problem, either singly or in combination, include regenerative cooling, radiation

cooling, film or transpiration cooling, ablation, arid inert or endothermic heat sinks.

To choose the proper cooling technique mission requirements, environmental

requirements and operational requirements should be considered.

Regenerative cooling

Regenerative cooling is performed building cooling jackets around the thrust

chamber and circulating one of the liquid propellants, usually the fuel, through them

before the fuel is fed to the injector plate[1]. Regenerative cooling is one of the most

widely applied cooling techniques in liquid propellant rocket engines. It has been

effectively applied with high chamber pressure systems and for long durations with a

wide heat flux range, form 0.8 to 160 𝑀𝑊/𝑚2. Besides, this cooling technique is

used primarily with bipropellant chambers and medium/large thrust. The structure is

relatively light, however, regenerative cooling has also some disadvantages that

include limited throttling with most coolants, reduced reliability with some coolants,

high pressure drops required at high-heat-flux levels, and thrust levels, mixture

ratios, or nozzle area ratios possibly limited by maximum allowable

coolant-temperature.

- 25 -

It is possible to think about regenerative cooling of a liquid propellant rocket engine

as a balance between the energy rejected by the combusted gases and the heat energy

absorbed by the coolant. The energy absorbed by the coolant is not wasted but it

augments the initial energy content of the propellant prior to injection, slightly

increasing the exhaust velocity (0.1 up to 1.5%). Therefore thermal energy is

recovered in the system. However by this process the overall engine performance

gain is less than 1% [3]. In particular, the bulk temperature of the coolant increases

from the point of entry until it leaves the cooling passages, as a function of the heat

absorbed and of the coolant flowrate.

To maintain the chamber walls at temperatures below those at which failure might

occur because of melting or stress, a proper balance of these parameters becomes of

major importance for the design of a regeneratively cooled thrust chambers. For

metals commonly used in thrust-chamber walls, such as stainless steel, nickel,

NARLoy-Z, and nickel-base super-alloys, the limiting hot-gas-side wall temperature

ranges from 700 to 1300 K. The resultant differences between combustion-gas

temperature and wall temperature range from 1600 to 3600 K. Sometimes,

regenerative cooling, with attendant pressure losses requiring additional turbopump

power or higher gas-pressurization levels, imposes an overall performance penalty.

Design of a regeneratively cooled thrust chamber involves consideration of gas-side

heat flux, wall structural requirements, coolant-side heat transfer, and the effects of

temperature increases on coolant properties[5].

Dump cooling

Dump cooling. With this principle, a small percentage of the propellant, such as the

hydrogen in a LO2/LH2 engine, is fed through passages in the thrust chamber wall

for cooling and is subsequently dumped overboard through openings at the rear end

of the nozzle skirt. Because of inherent problems, such as performance losses, this

method has only limited application.

Film cooling

Here, exposed chamber-wall surfaces are protected from excessive heat by a thin

film of coolant or propellant introduced through orifices around the injector

- 26 -

periphery or through manifolded orifices in the chamber wall near the injector and

sometimes in several more planes toward the throat. The method has been used,

particularly for high heat fluxes, either alone or in combination with regenerative

cooling.

Traspiration Cooling

Transpiration cooling introduces a coolant (either gaseous or liquid propellant)

through porous chamber walls at a rate sufficient to maintain the desired temperature

of the combustion-gas-side chamber wall. This method is essentially a special type of

film cooling.

Ablative cooling

In this process, combustion-gas-side wall material is sacrificed by melting,

vaporization, and chemical changes to dissipate heat. As a result, relatively cool

gases flow over the wall surface, thus lowering the boundary-layer temperature and

assisting the cooling process. In addition, the ablative material is usually a good

thermal insulator, keeping to a minimum the heat transmitted to the outer structure.

Ablative cooling has been used in numerous designs, initially mainly for solid-

propellant systems, but later, equally successfully, for short-duration and/or low- 𝑝𝑐

liquid systems.

Radiation Cooling

With this method, heat is radiated away from the surface of the outer thrust-chamber

wall. It has been successfully applied to very small, high-temperature-material

combustion chambers and to low-heat-flux regions, such as nozzle extensions[5].

This work of thesis is focused on the development of a regenerative cooling system

module, thus chapter 4 will explain in detail the mathematic model describing the

regenerative cooling and the thermo-fluidynamics properties of the coolant.

- 27 -

Chapter 2

THE HYPROB PROGRAM &

CONCURRENT DESIGN FACILITY

2.1 THE HYPROB PROGRAM

One of the most important activity in which CIRA is involved is the HYPROB

Program. CIRA Concurrent Design Facility for Space Propulsion is one of the main

project of this program and this paragraph will provide a broad description of the

activities managed by the propulsion department.

The Italian program HYPROB, kicked-off in 2010, is carried out by CIRA under

contract by the Italian Ministry of University and Research (MIUR), as contribution

to the National Aerospace Research Program (PRORA), in coherence with the

long-term vision of the Italian Space Agency on Space Propulsion and the needs of

industrial national stakeholders. The program relies upon the national heritage

resulting from other development programs, supported by the Italian Space Agency

(ASI) at both national (LYRA) and European (FLPP) level, mainly focused on the

evolution of launchers, and represents a R&T effort to contribute to further develop

space propulsion assets at national level.

2.1.1 Introduction to National 2020 Vision Propulsion systems based on hydrocarbons, either liquid or hybrid, represent

nowadays a major technology challenge for future launchers and space transportation

systems, to be pursued through R&T demonstration programs addressing enabling

- 28 -

technologies. Methane is one of the most interesting solutions as propellant for liquid

rocket engines, in combination with Oxygen, due to good performances achievable in

terms of specific impulse (𝐼𝑠𝑝~ 380 s) combined with operation advantages, such as

storability, low toxicity, availability and production cost, as compared to hydrogen.

Additional features of methane regard its good cooling capability and well known

material compatibility, that makes it ideal for regenerative thrust chambers. In a long

term perspective, such a propulsion technology may encompass a wide range of propulsion

systems, from launcher main stages up to small thrusters, but present envisaged applications

regard mostly:

upper stages of small launchers

primary propulsion systems for interplanetary missions, such as ascent ad landing

modules

Hybrid technology also is of great interest for space propulsion, combining the best

features of both solid, namely storability, and liquid option, namely performances.

However, although the potential of such a technology has been proven, the level of

maturity toward real applications has not been completely achieved yet.

Possible architectures and features of future Space Transportation Systems are

strongly influenced by technologies that are already available and others that require

further or completely new developments. Furthermore, the actual scenario of

European launcher family and of the worldwide sector, dealing with the threats of a

highly competitive market, daily faces the challenge of increasing performances and

reliability, in parallel with cost reduction. Propulsion disciplines constitute an asset

of such space technology, especially in view of developing new skills leading to

define possible evolutions and future generation launch vehicles and space

transportation systems. Aiming to support and promote the consolidation and the

evolution of competences in the field by the national scientific and industrial

community, an integrated national program of research and development activities

has been structured taking the maximum results from Ministry of Research and

University initiatives and from ASI on going and future programs, then preparing for

the future technical challenges. As far as chemical propulsion is concerned, the

background gained by the Italian community is strongly based on solid rocket

motors, that have mainly contributed to the success of Vega qualification flight in

February 2012, which consolidation is one of the key elements of the future national

- 29 -

vision. In the Horizon 2020, strategic importance is given to the R&D (Research and

Development) programs in liquid and innovative propulsion. Several programs have

been started by years, mainly on LOx- Methane propulsion, with the development of

an engine demonstrator for the upper stage of Vega evolutions, and the setup of a

dedicated test facility. This activity is integrated by the HYPROB program, resulting

in the acquisition of base research competences and engineering design skills up to

the fully national development of the entire combustion chamber. Furthermore,

activities of research and experimental demonstration on Hybrid propulsion will be

pursued, in order to take the better results by the integration of competences in liquid

and solid rocket design, leading to promising alternative solutions. The synergy

among industry, research centers and university competences skills and

infrastructures, is a key element of such vision, as well as it is the international

cooperation with other space agencies, as actually are Roscosmos and JAXA.

2.1.2 Industrial heritage and program road map

The main heritage at industrial level on methane-based propulsion relies on AVIO

Group. Similarly to other worldwide industrial leaders in aerospace rocket design

and fabrication, in recent years AVIO Group has been carrying out R&D activities in

this field through either self-sponsored internal programs and projects sponsored by

both the Italian (ASI) and the European (ESA) space agency. More specifically,

investigations have regarded different aspects related to chemical rocket engines:

𝐿𝑂𝑥/𝐶𝐻4 - combustion phenomena, through small-scale engines combustion

chambers and torch, tested in FAST_2 facility;

Inducer super-cavitation phenomena, through a test article design based on

previous experience done by AVIO Group in the Ariane 5 Program (Vinci,

Vulcain , etc);

Characterization of hydrostatic bearings in a cryogenic environment (LN2);

Verification of the coupling between hot, high pressure gas from a Test

Burner working in a fuel rich environment and turbine stator vanes sample,

assessing the risk of sooting.

- 30 -

AVIO Group is also deeply involved in the national program LYRA, funded by the

Italian Space Agency with the goal of developing technologies for future cryogenic

upper stage propulsion. In this regard, a preliminary configuration, derived from

VEGA launch vehicle, and using a new LOx-LNG upper stage has been defined

aimed at improving the payload capabilities. A 100 kN demonstrator, representative

of an expander cycle engine, named LM10-MIRA, has been developed. The design

has been derived by the Russian KBKhA RD-0146 engine, combined with fuel

turbo-pump and injection head design developed by AVIO. The system has been

tested in Russian facilities with the aim of gaining additional experience on

Oxygen-Methane propulsion technology. AVIO is also carrying out the THESEUS

project, again supported by the Italian Space Agency, aimed at investigating thrusters

evolution for space exploration. The main focus is on hybrid technologies and

ablative cooling chambers.

In the above described national framework, the HYPROB Program strategic

objectives and the overall development plan have been set in a preliminary step,

based on interactions with the institutional, industrial and scientific stakeholders.

This step was completed in early 2011 with a Concept of Operation review. The

main outcome of this step was to maintain the focus on both liquid oxygen-methane

(𝐿𝑂𝑥 /𝐿𝐶𝐻4) and hybrid technology, in order to harmonise and consolidate the

national heritage from previous R&D activities. In this respect, the program Road

Map pursues a mid-term goal, in the time frame 2011-2015, related to the assessment

of system capabilities and technologies at demonstration level, based on a

technology-push approach, and a longer term goal, to be pursued in the time frame

2015-2017 and beyond, where those technologies will be devoted a specific space

application, based on a system-driven approach. In the mid-term perspective, for

both liquid and hybrid developments, the focus is pointed at:

development of technology demonstrators, including intermediate

breadboards;

development of R&D activities in relevant technology areas;

improvement of test capabilities.

- 31 -

At system level, the mid-term objective is to design, manufacture and test, in a

relevant facility, technology demonstrators of suitable class of thrust, with the main

scope of validating critical design and technology features and then to assess

technology readiness level of potential solutions for future engines. In the framework

of R&D activities, the focus is put on enabling technologies, such as combustion

modeling, thermo-mechanical modeling, materials and manufacturing processes at

both system and components level. Specifically in the methodology field, the main

scope is to enhance the capabilities of simulating the complex combustion and

thermo-mechanical processes, characteristic of both liquid and hybrid propulsion, as

a fundamental step to improve the design processes for future applications. The

models will be validated through extensive testing activities at small-scale level in

either newly designed or up-graded test benches.

2.1.3 Propulsion Lines: 𝑳𝑶𝒙 /𝑳𝑪𝑯𝟒 & Hybrid

The System line devoted to the 𝐿𝑂𝑥/𝐿𝐶𝐻4 technology aims at designing,

manufacturing and testing a LRE ground demonstrator, representative of a 30 kN of

thrust in flight conditions (vacuum). The architecture considered for the

demonstrator, in line with the project key level requirements, is a regenerative cooled

thrust chamber for ground testing. Regenerative cooling is one of the most widely

applied cooling techniques used in liquid propellant rocket engines. As stated in the

introductory chapter, it has been effective in applications with high chamber pressure

and for long durations with a heat flux ranging from 1.6 to 160 𝑀𝑊/𝑚2. In

particular, in expander engines, regenerative cooling enthalpy gain is used to move

turbines for pressurizing pumps. The study logic implemented in that project has

been based on the following drivers:

Exploit existing know-how and design solutions for critical items;

Design suitable intermediate breadboards to address the most critical design

solutions, such as injection and cooling.

- 32 -

This approach has been defined in order to proceed step by step, from the

understanding of the basic physical processes, i.e. combustion and heat transfer, to

the validation of design and analysis methodologies. The studies carried out in the

program will benefit the collaboration between ASI and JAXA (Japan Aerospace

Exploration Agency) agencies on methane technology. The System line devoted to

the Hybrid technology has again the objective of developing a demonstrator of

similar thrust class. The main interest is on the combination of paraffin with either

oxygen or nitrogen-based oxidants. The selection of paraffin as solid propellant has

been made due to the complementarities with other national developments where the

HTPB (Hydroxyl-terminated polybutadiene) polymer has been considered. The

activity is being carried out in collaboration with other national research institutions,

in order to benefit of a solid scientific and technology background for demonstration

purposes. The development plan has been set out in 2011 and approved after a

Concept of Operations review. A first slice of the project is devoted to the

development of R&D activities on both the oxidant and the propellant sides. This has

yield to the selection of the technologies to be integrated into the demonstrator, based

on suitable tests at sub-scale level.

2.1.4 Design and measurement methodologies

As clarified in previous sections, the final goal is to improve the capabilities in the

design of future rocket engines; to this aim, all the numerical tools developed or

tested within the project will be properly interfaced one each other and will be used

by following a concurrent design approach. The set-up of a small Concurrent Design

Facility, in which the experts of different disciplines will be allowed to meet and

work together to optimize the design phases, is also foreseen. The capability to

perform a detailed analysis of the processes occurring inside the combustion chamber

will be one of the fundamental aspects that will be taken into account; on one side an

advanced CFD code, named SPARK (Solver for Propulsion Applications including

Real Gas Kinetics), is being developed and validated, in order to be able to

numerically simulate the fluid dynamics inside the combustion chamber. On the

other hand, the code will be validated in representative conditions of a LRE

- 33 -

environment. The experimental data will be also made available from the testing

activities and thus used for code validation. State of the art models have been

implemented in the CFD code, in order to be able to take into account the most

important relevant phenomena, including high pressure real gas effects, turbulent

combustion, and sprays. A Large Eddy Simulation (LES) model will be implemented

as well. SPARK code will be applicable also for regenerative cooling system

simulation, that is one of the main goals of the system activities within the program.

As far as experimental activities are concerned, a preliminary design phase has been

carried out with the goal to identify the main diagnostic systems to be used in the test

bench, in order to obtain reliable and accurate data useful for code validation and for

a deep comprehension of the physical phenomena occurring in the combustion

chamber. Several optical techniques have been taken into account: High Speed

Camera (HSC) imaging, High-Speed Shadowgraphy/Schlieren, Time-Resolved High

Resolution Optical Emission Spectroscopy (OES), Planar Laser Induced

Fluorescence (PLIF), Particle Image Velocimetry (PIV), Coherent Anti-Stokes

Raman Spectroscopy (CARS). Obviously, in order to use optical diagnostics, the

designed combustion chambers will be provided with optical accesses. The attention

has being initially focused on the first four techniques, for which a significant

experience was already held by CIRA for several previous applications.

2.1.5 Experimental Facilities: CIRA & AVIO synergy

In the frame of HYPROB program, the realization of a combustion laboratory at

CIRA is foreseen, for assembly and integration of breadboards and basic testing of

combustion. This area will be useful to perform experimental research activities on

combustion chambers and several Fuels/Oxidizers combinations. Furthermore it will

be aimed at developing advanced diagnostic techniques and methodologies to

investigate specific aspect related to combustion and support the activities carried out

in the program itself. The test bench shall allow testing test articles representative of

small combustion chambers, provided with a limited number of injectors (up to

three), and able to withstand combustion chamber pressures up to 7 𝑀𝑃𝑎, both in

- 34 -

subcritical and supercritical conditions, for a maximum run-time of 30 seconds.

Oxygen and Methane, both gaseous and liquid, are the selected propellants to be

used. However, since the test bench has been designed to be quite flexible, other

fuels could be used, when needed. To improve facility productivity, two test stands,

using the same fluids storage tanks and piping, will be built, each one being able to

be used with a test setup different than the other one. The test bench shall be widely

used in the frame of basic R&D activities. Among them, the development of

advanced diagnostic techniques (such as PLIF, High Speed Cameras, High speed

Shadowgraphy/Schlieren, High speed Optical Emission Spectroscopy) is envisaged

to be performed using this small facility. With this aim, the facility layout is designed

in such a way to allow both the proper setup of the instrumentation, optics and lasers,

and a comfortable and easy use of the same ones. A diagnostic laboratory, hosting

the laser instrumentation, shall be located just close to the test fire area.

Furthermore, according to the synergic approach adopted in the program, FAST_2

facility running at Colleferro (Rome) within the AVIO plant, has been selected as the

main experimental facility to carry out tests on demonstrators and associated

combustion breadboards. The facility has been developed in the FAST_2 program,

funded by ASI some years ago in support to space transportation technologies and is

presently co-owned by ASI and AVIO Group.

The main characteristics of the actual configuration of the facility are hereinafter

reported:

𝐿𝑂𝑥 feeding line up to 10 kg/s at 200 bar (max pressure tank);

𝐺𝐶𝐻4 feeding line up to 2 kg/s at 200 bar (max pressure tank);

Cooling water feeding line up to 20 kg/s at 140 bar;

Test cell for combustor testing;

Command and control capability provided by two redundant units;

Data acquisition unit with 82 channels.

The facility has already been extensively used in recent programs to test thrust

chambers representative of 30 𝑘𝑁 thrust (vacuum) class. According to HYPROB

- 35 -

program requirements[6], a severe update of the facility will be carried out to enable

testing capability with liquid methane.

2.2 CONCURRENT DESIGN FACILITY - CDF

In recent years, the role of the CDF and the methodology adopted by this innovative

designing strategy has become increasingly important. In this regard, it is of utmost

importance to explain in detail the history of CDF and its key points.

2.2.1 An innovative team working method

System engineering has features of both art and science since requires creativity and

knowledge of systems engineers, but it also requires systems management and the

application of a systematic disciplined approach. The traditional or the most classical

design methodology is the sequential approach which means a sequence of

specialists working ‘in series’. The overall design passes from a technical domain

specialist, that works isolated from the other components of the design team, to

another, during various design steps in successive time intervals. Lack of

communication among the specialists can lead to wrong assumptions and obviously

the main system parameters are not monitored in real-time. This method reduces the

opportunity to find interdisciplinary solutions and to create system awareness in the

specialists. An improved method is the centralized design, where the various

technical domain specialists provide subsystem design information and data to a core

team of one or more system engineers, but even this approach is not sequential.

Concurrent Engineering is offered as an alternative to the classical approach and it

provides better performance by taking full advantage of modern Information

Technology (IT). Experts from various disciplines in the co-location could

communicate in real-time and face to face. Since many disciplines are involved in

the design process of complex systems, the concurrent approach has been proven

particularly effective. Hence, the Concurrent Design Facility is a workspace and

- 36 -

information system allowing multidisciplinary experts working in a focused

environment and conducting design collaboration.

2.2.2 History and status of CDF

Some attempts on CE (Concurrent Engineering) began from 1980's in the field of

aerospace and defense industry. A result of survey about CE was presented in 1993

by the Integrated Process Laboratory at the Concurrent Engineering Research Center

(CERC), which was established at West Virginia University in 1988 by Defense

Advanced Research Projects Agency (DARPA) to promote CE in United States

industry. The results showed several advantages such as the possibility to reduce the

design costs and to improve product quality at once. This survey clearly indicated

that the most pressing need was to foster a teamwork environment, and the greater

leverage exists in teamwork and process improvement. According to literature study,

the first CDF with full features, which named with the Project Design Center (PDC)

was opened by the Jet Propulsion Laboratory (JPL) in June of 1994[7]. The PDC

provides a facility with multiple rooms for design teams to be used to conduct

concurrent engineering sessions. Aerospace Corporation has developed the process

and the tools for CE almost at the same time and they had been successfully applied

to several programs. Based on the experience of the Aerospace Corporation, the JPL

contracted the Aerospace Corporation to develop CEM (Concurrent Engineering

Methodology) processes and tools for PDC. The Concept Design Center (CDC) was

developed by the Aerospace Corporation in 1997, to enhance the support to its

customers by providing a process for bringing together the conceptual design

capabilities and experts. In the European space industry, concurrent engineering was

also applied in the spacecraft design from the beginning of 1990'. The first example

is provided by the Satellite Design Office (SDO) at DASA/Astrium, with the

cooperation of the System Engineering (SE) group at the Technical University of

Munich. An experimental design facility, Concurrent Design Facility (CDF), was

created at the ESA Research and Technology Centre (ESTEC) at the end of 1998 and

used to perform the assessment of several missions. The CDF is an Integrated Design

Environment (IDE) based on the concurrent engineering methodology. Up to now,

- 37 -

more than 20 CDFs have been established around the world. These CDFs scatter in

United States, Germany, France, Italy, Switzerland, United Kingdom and Japan, and

are owned by governments, industries and universities.

2.2.3 Applications , Benefits and key elements of CDF

Concurrent design is primarily used at ESA to assess technical, programmatic and

financial feasibility of future space missions and new spacecraft concepts.

Additionally, the ESA CDF (see Figure 10) is also used for many other multi-

disciplinary applications, such as payload instrument preliminary design, System of

System (SoS) architectures and space exploration scenarios.

Figure 10: ESA CDF in session

Since 1994, two research teams, team-X and team-I, had conducted concurrent

engineering design for space mission and space instrument in PDC of JPL.

Applications of modern information systems enabled fundamental improvements to

the system engineering process through the use of real time concurrent engineering.

Many design teams have demonstrated dramatic savings in time and money

compared with the traditional process for space systems conceptual design. As

- 38 -

reported in literature[7], improvements in efficiency obtained by team-X and PDC

are significant and it should be noted that a dramatic reduction in average time to

prepare proposals and very significant decrease in cost per proposal is achieved.

The ESA/ESTEC summarizes the key elements on which the CDF implementation

has been based: process, multidisciplinary team, integrated design model, facility,

and infrastructure. These elements are detailed below:

Process

It is a fact that the space system has many interdependencies between

components. This implied that the definition and evolution of each

component has an impact on other components and that any change will

propagate through the system. Early assessment of the impact of changes is

essential to ensure that the design process converges on an optimized

solution. The process starts with a preparation phase in which some

representatives of the engineering team (team leader, system engineer, and

selected specialists) and of the customer meet to refine and formalize the

mission requirements, to define the constraints, to identify design drivers, and

to estimate the resources needed to achieve the study objectives. Then the

study kick-off takes place and the design process starts. It is conducted in a

number of sessions in which all specialists must participate. This is an

iterative process that addresses all aspects of the system design in a quick and

complete fashion. One key factor is the ability to conduct a process that is not

dependent on the path followed. At any stage it must be possible to take

advantage of alternative paths or use ‘professional estimates’ to ensure that

the process is not blocked by lack of data or lack of decisions;

A multi-disciplinary team

Human resources are the most important and crucial element. A fundamental

part of the CE approach is to create a highly motivated multi-disciplinary

team that performs the design work in real-time. The challenge, the novelty of

the method, the collective approach, the co-operative environment, the

intense and focused effort and a clear and short term goal are all essential

elements that contribute to personal motivation. To work effectively, the team

members had to accept to use a new method of working, co-operate, perform

- 39 -

design work and give answers in real-time, and contribute to team spirit. For

each discipline a position is created within the facility and assigned to an

expert in that particular technical domain. Each position is equipped with the

necessary tools for design modeling, calculations and data exchange. The

choice of disciplines involved depends on the level of detail required and on

the specialization of the available expertise. On the other hand, the number of

disciplines has to be limited, especially in the first experimental study, to

avoid extended debate and to allow a fast turn-around of design iterations;

An Integrated Data Model

The design process is model-driven using information derived from the

collection and integration of the tools used by each specialist for his or her

domain. A parametric model-based approach allows generic models of

various mission/technological scenarios to be characterized for the study to

perform. A parametric approach supports fast modification and analysis of

new scenarios, which is essential for the real-time process. It acts as means to

establish and fix the ground rules of the design and to formalize the

responsibility boundaries of each domain. Once a specific model is

established it is used to refine the design and to introduce further levels of

detail. Each model consists of an input, output, calculation and results area.

The input and output areas are used to exchange parameters with the rest of

the system (i.e. other internal and external tools and models). The calculation

area contains equations and specification data for different technologies in

order to perform the actual modeling process. The results area contains a

summary of the numeric results of the specific design to be used for

presentation during the design process and as part of the report at the end of

the study;

An Appropriate Facility

The team of specialists meets in the Concurrent Design Facility to conduct

design sessions. The accommodation generally comprises a design room, a

meeting room and project-support office space. The equipment location and

the layout of the CDF are design to facilitate the design process, the

interaction, the co-operation and the involvement of the specialists. The

- 40 -

facility is equipped with computer workstations dedicated to each technical

discipline. A multimedia wall, supporting two or three large projector

screens, is located in order to be visible from each working station. Each

screen can show the display of each workstation, so that the specialists can

present and compare design options or proposals and highlight any

implications imposed on, or by, other domains;

A Software Infrastructure

An infrastructure to implement the Concurrent Design Facility outlined above

requires tools for the generation of the model, integration of the domain

models with a means to propagate data between models in real time, a means

to incorporate domain-specific tools for modeling and/or complex

calculations, a documentation-support system, and storage capability. The

infrastructure must allow its users to work remotely from other facilities, and

exchange information easily between the normal office working environment

and the facility environment. Regarding the system model, Microsoft Excel

spreadsheets are usually chosen for their availability and flexibility. The

distribution of the model requires a mechanism to exchange relevant data

between domains. This can be solved preparing a shared workbook to

integrate the data to be exchanged, with macros to handle the propagation of

new data in a controlled way. In some specific cases it can be more

convenient not to use centralized data exchange, but rather to create a direct

interface between those applications, such as the transfer of geometrical 3-D

data of spacecraft-configuration to the simulation system[8].

- 41 -

Chapter 3

CIRA CONCURRENT DESIGN FACILITY

3.1 CIRA CDF FOR SPACE PROPULSION

A Concurrent Design Facility for Space Propulsion is under development at CIRA in

the frame of HYPROB program. The CDF will exploits concurrent engineering

methodology to perform effective, fast and cheap liquid rocket engine (LRE) design.

This discussion aims to describes the phases of design, the modules and their

interaction.

A liquid space propulsion system can be divided in the following main subsystems:

Feeding (Tanks & Turbo-pumps), Cooling System, Injection System and Thrust

Chamber (Combustion Chamber & Nozzle). Engineering Software shall be therefore

composed by different modules dedicated to each subsystem, and by an upper level

architecture module, that will compute the preliminary configuration of the LRE,

based on main requirements, and shall allow the correct data exchange between the

subsystem modules. Once a preliminary configuration is defined, more detailed

verification programs will be used to verify the fulfilment of the requirements,

including numerical tools for CFD computation and thermo-structural analysis. In

Figure 11 a schematic view of a liquid space propulsion engine is shown.

- 42 -

Figure 11: Liquid space propulsion engine - Schematic view

In order to apply the logic discussed above, the following specialists are foreseen:

Figure 12: CIRA Concurrent Design Facility for space propulsion - Specialist

For each specialist a proper domain is foreseen. In addition, the following domains

should be added: customer, team leader, CAD and schedule and planning. Figure 13

shows the total set of domains.

Figure 13: CIRA Concurrent Design Facility for space propulsion - Domains

Space propulsion architectural designer

Thrust Chamber analyst

Feeding/Turbopumps designer/analyst

Cooling system designer/analyst

Thermostructural analyst

Computational Fluid Dynamics (CFD)

Customer

Team Leader

Architecture (ARCH+ECOSIMPRO)

Thrust Chamber (TCHA+INJE+ROCCID)

Feeding System (FEED)

Cooling System (COOL)

Thermostructures (FEM)

CFD

Schedule and planning

CAD

- 43 -

The process definition is one of the key points in a concurrent engineering approach.

It is identified by three main phases:

Requirements definitions;

Subsystem preliminary design;

Verification of requirements.

For each module, the correct input/output parameters must be defined, along with the

local parameters that are not exchanged with the other modules but are used within a

single module for the subsystem sizing. Hereinafter the main steps of the overall

process are briefly described. It must be underlined that, in the first version of the

developed code, only pressure fed systems and expander cycle will be taken into

account. Future developments will take into account other kind of cycles such as gas

generator and staged combustion.

Step 1 – Requirements analysis

First of all the team leader will analyze the requirements, typically thrust T (in the

first version of the code) or 𝐼𝑠𝑝 or 𝛥𝑉 and external pressure/exit conditions 𝑝𝑒.

Additional requirements, like propellants, cycle, total mass, can also be provided by

the client; alternatively they are preliminarily defined within this step.

Step 2 – Preliminary architecture

Architecture module (ARCH) receives the inputs from step 1 and calculates the 𝑂/𝐹

that maximizes the 𝐼𝑠𝑝, mass flow rate of oxidizer and fuel, preliminary geometry

and the chamber pressure 𝑝𝑐 by using the engineering methods described in next

sections. Architecture module activates then the subsystem modules.

Step 3 – Thrust chamber parameters

TCHA receives the preliminary geometry, mass flow rates and chamber pressure as

input and evaluates the wall heat flux 𝑞 along the combustion chamber and nozzle,

that is provided to the COOL module. Moreover, this module calculates the chemical

1-D composition and thermo-fluidynamic properties along the thrust chamber axis.

Step 4 – Injector and spray parameters

- 44 -

INJE receives in input the preliminary geometry, mass flow rates and chamber

pressure and evaluates the pressure drop in the injection system, along with some

typical parameters of the spray, like the breaking length and spray angle.

Step 5 – Cooling system

Based on the inputs determined in the previous steps, COOL module calculates the

number and geometries of the cooling channels, wall chamber thickness and the

thermofluidynamic behavior of the coolant inside the channels. The necessary inputs

depend on the chosen cycle. For pressure fed, regenerative cycle, case the following

inputs are necessary:

ARCH Preliminary geometry, mass flow rates and chamber pressure;

TCHA Wall heat flux along the thrust chamber;

INJE Pressure drop at the injection system (pressure at the injector inlet);

For an expander cycle, the following inputs are required

ARCH Preliminary geometry, mass flow rates and chamber pressure;

TCHA Wall heat flux along the thrust chamber;

FEED Pressure at the turbine inlet.

FEM module will receive the same inputs and proceeds with the choice of the thrust

chamber materials.

Step 6 – Feeding system

FEED will receive from ARCH the general engine architecture; as previously

clarified, in the first version of the code only pressure fed systems and expander

cycle will be taken into account.

If the architecture is a pressure fed cycle, FEED module will calculate the tank size

and the feeding system layout based on the fuel conditions that must be realized at

the inlet of the cooling system (from COOL module) and on the oxidizer conditions

- 45 -

at the injectors inlet (from INJE module). For an expander cycle the module will

deal with the following subsystems:

Fuel Pump: FEED will calculate the main pump parameters with the goal to

obtain the required fuel conditions at the inlet of the cooling system,

according to the COOL module;

Oxidizer pump: FEED will calculate the main pump parameters with the

goal to obtain the required oxidizer conditions at the injectors inlet,

according to the INJE module;

Turbine: FEED will receive the conditions from COOL module and calculate

the turbine parameters.

Once the general architecture and the main parameters of the subsystems have been

defined, the detailed verification of the requirements can begin:

EcosimPro SW will be used to simulate simultaneously all subsystems

considering the transient phases;

CFD software will be used to verify the data calculated by TCHA module;

FEM software will perform detailed thermostructural calculations;

ROCCID will verify that no combustion instabilities occur, along with the

margins.

If some requirements are not verified, or an optimization is needed, a further design

iteration will be performed by ARCH module restarting from step 1, according to the

modifications indicated by the Verification phase. Figure 14 shows the process

implemented by CIRA Concurrent Design Facility for space propulsion[9].

- 46 -

Figure 14: CIRA Concurrent Design Facility for space propulsion - The process

As already reported, CIRA CDF for space propulsion has been developed for a

preliminary design of a liquid rocket engine. Therefore, in order to explain in detail

the Cooling system module, on which the present work of thesis has been focused, it

is of utmost importance to discuss the ARCH module and TCHA module. These

modules provide the inputs for COOL module which it is strongly conditioned by

ARCH and TCHA parameters. Thus, next sections are focused on the modules that

are logically before the cooling module.

3.2 ARCHITECTURE MODULE

The aim of the architecture module is to define a baseline for the sizing of the engine.

As stated in the previous section, the architecture module is an upper level module

that will use the input reported in step 1 to compute the first scheme of the

propulsion engine. Considering Figure 15, it can be noted that a thrust chamber is

constituted by three major elements: the combustion chamber, the exhaust nozzle and

the injector.

- 47 -

Figure 15:Typical basic configuration of a thrust chamber

The combustion chamber and the exhaust nozzle can be preliminary sized using

analytical and semi-empirical formulas. The first step is fixing the design point

starting from the required thrust, nozzle conditions and selected propellants. Thus,

the user has to decide which nozzle condition has to be adopted. In particular, three

cases have been implemented. The first is to consider the external pressure pe equal

to 1 atm and thus to consider the engine as it would be designed to ground

conditions; the second is to impose pe equal to 0.01 atm and so to consider the engine

as it would be designed for extra-atmospheric conditions; the last is to fix two

geometrical area ratios: the combustion chamber area over the throat area and the

exit nozzle area over the throat area (Ac/At and Ae/At). In particular, for the last case,

values of Ac/At=3 and Ae/At=70 have been firstly considered. It is important to note

that the software has been developed in order to cope with possible changes of those

two area ratios.

Considering the nozzle condition and the mixture chosen a large set of specific

impulse values (𝐼𝑠𝑝) is imported through a precompiled database. Those databases

are parameterized considering a wide range of operating conditions in terms of 𝑝𝑐

and 𝑂

𝐹. In particular, those databases are the outcomes of a nested analyses performed

using the RPA (Rocket Propulsion Analysis) software, which assume the chemical

equilibrium composition of the mixture. In general, this software utilizes a set of

input parameters: combustion chamber pressure, propellant combination, mixture

ratio or oxidizer excess coefficient or mass fractions of each component, list of

- 48 -

components at standard conditions or at assigned temperature, assigned enthalpy.

RPA calculates combustion equilibrium and the properties of the reaction products.

Additionally if the nozzle exit pressure, or alternatively the nozzle area ratio, is

defined together with a chamber contraction area or mass flux, then the conditions at

the nozzle throat, nozzle exit and the theoretical rocket engine performance are

determined as well. This tool hence only performs combustion calculations and

estimates the thruster performance.

The process continues with the user selection of the design point. This can be the

trivial maximization of the 𝐼𝑠𝑝 or the result of a different strategy. For instance if the

user has to take into account possible constraints like unfeasible values of 𝑝𝑐 and 𝑂

𝐹

ratio.

Once the design point has been chosen, and the 𝐼𝑠𝑝 is evaluated, the size of the thrust

chamber can be defined following the process reported hereinafter. From the

imposed thrust and the resulting specific impulse, it’s trivial to obtain the mass flow

rate of propellant, and hence the fuel and oxidizer mass flows are provide by Eq.

(3.2- 1), (3.2- 2) and (3.2- 3):

�̇� =𝑭

𝑰𝒔𝒑𝒈𝟎 (3.2- 1) ; �̇�𝒇𝒖 =

�̇�𝑶

𝑭+𝟏

(3.2- 2) ; �̇�𝒐𝒙 = �̇�𝑶

𝑭𝑶

𝑭+𝟏

(3.2- 3)

Knowing the values of chamber pressure, mass flow rate and characteristic velocity,

the throat area can be evaluated with the formula reported below (3.2- 4). The

characteristic velocity indeed is a result of the nested analysis directly linked to the

chosen 𝐼𝑠𝑝 value.

𝑨𝒕 =𝒄∗�̇�

𝒑𝒄

(3.2- 4)

The nozzle definition is completed by choosing the convergent-divergent geometry

that can be bell or conic shaped. From this choice it is possible to size the

combustion chamber. In an early design procedure phase, the chamber diameter has

been evaluated considering the ratio between the chamber area and the throat area

(Ac/At) equal to 3. However, if the user has decided to fix the pe as nozzle condition,

- 49 -

this choice, widely reported in literature and used to minimize chamber pressure

losses, has been upgraded by the following semi-empirical correlation (3.2- 5).

𝑨𝑪𝒉

𝑨𝒕= 𝟖𝑫𝒕

−𝟎.𝟔 + 𝟏. 𝟐𝟓 (3.2- 5)

The volume 𝑉𝐶𝐶, defined as the sum between the combustion chamber volume and

the nozzle convergent part, is evaluated through the simple relation (3.2- 6).

𝑽𝑪𝑪 = 𝑳∗𝑨𝒕 (3.2- 6)

Where the default value of the characteristic length is set equal to 1m, but can be

easily changed accordingly to experience and literature, see Table 2.

Table 2: Number of Characteristic Lengths of typical propellant combinations

The convergent nozzle length is then evaluated by Eq. (3.2- 7):

𝑳𝒄𝒐𝒏𝒗 = 𝑫𝑪−𝑫𝒕

𝟐 𝒕𝒂𝒏𝜽𝒄𝒐𝒏𝒗 (3.2- 7)

Where 𝜃𝑐𝑜𝑛𝑣 is an angle closely linked to the maximum slope of the nozzle. This

value is set in order to control the maximum slope of the converging part. Indeed, the

maximum slope is finally evaluated in order to be sure that is included between 20°

and 45°. The volume of the combustion chamber 𝑉𝐶 is then evaluated subtracting

from 𝑉𝐶𝐶 the volume of the converging nozzle. This quantity is estimated with the

formula (3.2- 8) reported below:

𝑽𝒄𝒐𝒏𝒗 = (𝝅𝟑⁄ )𝑳𝒄𝒐𝒏𝒗(𝑹𝑪

𝟐 + 𝑹𝒕𝟐 + 𝑹𝑪𝑹𝒕) (3.2- 8)

- 50 -

If we suppose the combustion chamber to be cylindrical, its length can be easily

obtained. Indeed, the chamber contraction ratio, defined as the ratio between the

chamber cross-sectional area and the throat area (Ac/At), gives us the chamber

diameter and, subsequently, its length. The last step is the sizing of the divergent part

of the nozzle. If the user has fixed the area ratios as nozzle condition, then the

evaluation of the nozzle exit area is trivial, on the contrary, if the user has imposed

the value of the exit pressure, then, the theoretical nozzle expansion ratio can be

obtained from the relation (3.2- 9) of an ideal gas flow through a rocket nozzle.

𝜺 =𝑨𝒆

𝑨𝒕=

(𝟐

𝜸+𝟏)

𝟏𝜸+𝟏

(𝒑𝒄𝒑𝒆)

𝟏𝜸

√𝜸+𝟏

𝜸−𝟏[𝟏−(

𝒑𝒆𝒑𝒄)

𝜸−𝟏𝜸 ]

(3.2- 9)

If the divergent part of the nozzle is supposed to be cone-shaped, the design will

follow the configuration sketched in Figure 16:

Figure 16: Conical nozzle contour

The nozzle throat section has the contour of a circular arc with a radius that can be

proportionally expressed in terms of throat radius 𝑅𝑡. Its default value is 0.5 Rt, but it

can range between 0.5 Rt and 1.5 Rt depending on engine size and experience

considerations. It’s worth to note that lower curvature values imply smaller

dimensions and can produce lower thermal loads but higher heat peaks.

The divergent half-cone angle 𝜃𝑑𝑖𝑣, instead, varies between 12° and 18° and has to

be set by the user. Thus, the length of the divergent part of the nozzle can be

evaluated by Eq. (3.2- 10).

𝑳𝒅𝒊𝒗 =𝑹𝒕(√𝜺−𝟏)+𝑹(𝒔𝒊𝒏 𝜽𝒅𝒊𝒗−𝟏)

𝒕𝒂𝒏𝜽𝒅𝒊𝒗

(3.2- 10)

- 51 -

The subsequent evaluation of the exit radius is trivial: 𝑅𝑒 = √𝜀𝑅𝑡.

If the parabolic design approximation for the bell nozzle is chosen, the design

process follows the guidelines summarized in Figure 17.

Figure 17: Bell nozzle contour

The upstream throat contour is circular with a default radius 0.5 times the throat

radius, terminating at the geometric throat. Even in this case its value can be changed

according to experience. The downstream throat radius is also circular with radius

0.382 Rt. It joins smoothly at the geometric throat with the upstream radius and

continues till the angle 𝜃𝑛 is reached. This procedure locates the final coordinates of

the bell nozzle and let the user complete the design by drawing a smooth, parabolic

curve using the parabola equation (3.2- 11):

𝒚 = 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 (3.2- 11)

This equation can be solved imposing three known conditions, that are: the starting

point; the value of the derivative in that point, that is equal to tan 𝜃𝑛 and the value of

the derivative in the ending point of the parabola, that is equal to tan 𝜃𝑒.

- 52 -

Figure 18: Initial and final parabolic angles versus desired nozzle expansion ratio for

different percent bell lengths of an equivalent 15° conical nozzle

The last remaining decision is the shape of the converging part of the nozzle. Two

possibilities have been considered and implemented. The first one, called ‘straight’

consists of two rounded joints and a straight segment connecting them. Obviously the

straight segment is tangent to the arcs. The second exploits a cubic function (Eq. 3.2-

12) to link the end of the CC to the throat.

𝒚 = 𝒂𝒙𝟑 + 𝒃𝒙𝟐 + 𝒄𝒙 + 𝒅 (3.2- 12)

The second case ensures continuous second derivative, this is of utmost importance

for the heat flux analysis and protection. In particular the solution can be achieved

imposing four known conditions, that are: the starting and ending points positions,

null first derivative at the throat section and the null second derivative in the

inflection point, located halfway between the starting and ending points[9]. The

Figure 19 shows the convergent nozzle contours for “straight” and “cubic” solutions

Figure 19: Convergent nozzle contours for “straight” and “cubic” solutions

- 53 -

A preliminary geometry of the thrust chamber is finally obtained and plotted.

Geometrical and fluid-dynamic parameters, such as chamber pressure, nozzle

expansion ratio, O/F ratio and the chosen propellants, are then considered as inputs

for lower level modules. To better understand the result obtained by this routine,

Figure 20 shows an example of the geometry obtained considering a conic shaped

nozzle with a cubic convergent part.

Figure 20: An example of the Thrust Chamber geometry evaluated by the ARCH

module

3.3 THRUST CHAMBER MODULE

Thrust chamber module is a point of connection among ARCH module and COOL

module. Starting from the architecture module’s output, such as the chamber

pressure, the nozzle expansion ratio, the O/F ratio and the chosen propellants, the

aim of the thrust chamber module is to perform an analysis of the combustion

process, providing temperature and chemical composition along the axis of the thrust

chamber. In order to accomplish this target, the simplifying assumption of chemical

- 54 -

equilibrium is considered valid. In particular the module uses the software named

CEA (Chemical Equilibrium Analysis). CEA is a tool developed by Gordon and

McBride at NASA Glenn/Lewis Research Center[4]. The name of this software

suggests that the chemical equilibrium has been assumed in the combustion chamber.

The chemical equilibrium of a reacting system permits to evaluate, in a simplified

way, the theoretical thermodynamic properties that are useful for the design of

several complex systems such as compressors, turbines, nozzles, engines. The

equilibrium is usually described by either of two equivalent formulations,

equilibrium or minimization of free energy. In particular, the minimization of free

energy formulation is used in the CEA program. In the thrust chamber the

propellants react to form hot gases. Hence, the thrust chamber module is focused on

the hot gas properties. The hot gas characteristics are obtained in three locations, that

are: combustion chamber, throat region and the nozzle exit. To obtain this result, a

MATLAB routine writes the input file for the software CEA, then it externally runs

the program and finally loads and saves the resulting data. The physical quantities

that are particularly interesting in this phases are: Mach number, characteristic

velocity, thrust coefficient, specific impulse, viscosity, thermal conductivity, Prandtl

number, velocity, sound velocity, specific heat ratio, heat specific, temperature,

pressure and Reynolds number.

Most of those parameters have been used in the first step of the cooling module.

- 55 -

Chapter 4

COOLING SYSTEM MODULE OF CIRA

CDF

4.1 OVERVIEW

The present chapter describes the main objective of the present work i.e., the cooling

system module for CIRA CDF. In particular, this chapters describes in detail all key

passages of numerical investigation. Obviously, this approach 1-D involves an

approximate description of the phenomena, but the obtained results (see Chapter 5),

are completely satisfactory for a phase 0/A of a space project.

The procedure design follows step by step the engineering formulas reported in the

literature. After the choice of the geometry of the thrust chamber and the operating

condition performed by architecture module, several models for the cooling system

design have been implemented. In particular, the coolant behavior changes with

different sizes and number of the cooling channels that surround the thrust chamber.

For the first development of the Cooling system module, the cross-sectional of the

channels has been assumed circular. In addition to the pressure drop, temperature and

other thermo-fluidynamics properties of the coolant may vary with a different

formulations of a friction factor. Several thermo-fluidynamics characteristics of the

coolant will be provided by a software tool, called CoolProp integrated with CDF

Software.

The primary objective of cooling is to preserve the chamber and nozzle walls from

the huge heat flux coming from hot gasses passage in the inner part of the thrust

chamber. The high temperatures may exceed 3600 K, the pressures may exceed 30

MPa and the heat fluxes can reach 100 MW/m2. This represents a very challenging

problem. Many cooling techniques have been developed in liquid rocket engine

- 56 -

manufacturing: regenerative cooling, radiation cooling, dump cooling, film cooling,

transpiration cooling and ablative cooling. The first version of the engineering

software will refer to a regenerative cooling architecture, therefore regenerative

cooling technique will be hereinafter discussed. The basic concept (see Figure 21) is

to use liquid propellant to cool the thrust chamber. The propellant flows inside the

cooling channels, increasing its energy and changing phase from liquid to gas.

Finally it is injected in the combustion chamber.

Figure 21: Regenerative cooling architecture

The cooling system module receives nozzle geometry by Architecure Module

(ARCH) and several thermo-fluidynamics properties of hot gases by Thrust Chamber

Module (TCHA).

4.2 COOLING SYSTEM MODULE

4.2.1 Heat flux analyses

The design of thrust-chamber cooling channels will start with the calculation of the

heat transfer from combustion gasses, through the solid walls, to cooling channels.

As a first step, a 1-D steady state condition is considered. The heat transfer from

combustion gases through the wall to the coolant region (see Figure 22) can be

expressed by the equation (4.2- 1):

- 57 -

𝒒 = 𝒉𝒈(𝑻𝒂𝒘 − 𝑻𝒘𝒈) = (𝑲

𝒕) (𝑻𝒘𝒈 − 𝑻𝒘𝒄) = 𝒉𝒄(𝐓𝐰𝐜 − 𝐓𝐜𝐨)

(4.2- 1)

Each part of this equation has to be modeled.

Figure 22: Heat transfer for schematic regenerative cooling

Let’s start with the gas side convective heat flux reported in eq. (4.2- 2)

𝒒 = 𝒉𝒈(𝑻𝒂𝒘 − 𝑻𝒘𝒈) (4.2- 2)

Obviously, the estimate of heat flux is preceded by some steps which provide some

parameters.

First of all, the designer must choose the value of 𝑇𝑤𝑔 at throat. Indeed, the user has

the possibility to set up the gas side wall temperature through a command menu.

According to literature, the default value is imposed equal to 700 K, but this value

can be easily changed to consider different throat conditions. Since the throat is the

critical point, the wall temperature is greater in that point than in other region of the

thrust chamber. Moreover, in along the nozzle, the hot gases temperature decreases

by isentropic expansion law, hence the gas side wall temperature decreases. In

preliminary design, the value of gas side wall temperature at the beginning of the

chamber has been set equal to 2

3⋅ 𝑇𝑤𝑔 while at exit of the nozzle this parameters has

- 58 -

been fixed at 1

3 ⋅𝑇𝑤𝑔 . In this way, the other parameters will be calculated in the same

points. The 𝑇𝑎𝑤 of the combustion gas may is obtained using eq. (4.2- 3)

𝑻𝒂𝒘 = (𝑻𝒄)𝒏𝒔 [

𝟏 + 𝒓 (𝜸 − 𝟏𝟐 )𝑴𝒙

𝟐

𝟏 + (𝜸 − 𝟏𝟐 )𝑴𝒙

𝟐] = (𝑻𝒄)𝒏𝒔𝑹

(4.2- 3)

Where 𝑟 is the “local recovery factor” and represents the ratio of the frictional

temperature increase to the increase caused by a adiabatic compression. Below, two

simplified correlations based on Prandtl number, are reported.

𝒓 = (𝑷𝒓)𝟎.𝟓 for laminar flow (4.2- 4)

𝒓 = (𝑷𝒓)𝟎.𝟑𝟑 for turbulent flow (4.2- 5)

Bartz proposed a semiempirical evaluation of the Nusselt numbers, and thus of the

gas-side heat transfer coefficient ℎ𝑔 [51] [5].

𝑵𝒖 = 𝟎. 𝟎𝟔𝟐𝑹𝒆𝟎.𝟖𝑷𝒓𝟎.𝟑 (4.2- 6)

where

𝑵𝒖=

𝒉𝒈⋅𝒅

𝒌

(4.2- 7)

Hereinafter, a modified Bartz equation is reported:

𝒉𝒈 = [

𝟎. 𝟎𝟐𝟔

𝑫𝒕𝟎.𝟐

(𝝁𝟎.𝟐𝑪𝒑

𝑷𝒓𝟎.𝟔 )𝒏𝒔

((𝒑𝒄)𝒏𝒔𝒈

𝒄∗)

𝟎.𝟖

(𝑫𝒕

𝒓𝒕)𝟎.𝟏

] × (𝑨𝒕𝑨)𝟎.𝟗

𝝈

(4.2- 8)

The correction factor for property variation across the boundary layer is evaluated as

specified in Eq. (4.2- 9)

𝝈 =𝟏

[𝟏𝟐𝑻𝒘𝒈(𝑻𝒄)𝒏𝒔

(𝟏 +𝜸 − 𝟏𝟐 𝑴𝟐) +

𝟏𝟐]

𝟎.𝟔𝟖

[𝟏 +𝜸 − 𝟏𝟐 𝑴𝟐]

𝟎.𝟏𝟐

(4.2- 9)

In this way, each of these magnitudes is known in three points, that are: in the

combustion chamber, at throat and at the exit of the nozzle. But, for some of these

- 59 -

magnitudes, the total distribution along the thrust chamber must be known.

Therefore, the variation of 𝑇𝑤𝑔 along the axis of thrust chamber has been

approximated by a logarithmic trend. The distribution of 𝑇𝑎𝑤 and ℎ𝑔 has been

similarly constructed. Successively, the equation (4.2- 2) has been used for calculate

the heat flux along the thrust chamber (see Chapter 5 for results).

This distribution has been utilized for a first evaluation of the phenomena, but it has

been corrected after some considerations. Because in combustion chamber the

chemical equilibrium has been assumed and the wetted area remains constant, the

heat flux distribution along the chamber can be reasonably assumed constant.

In the Typical axial heat transfer rate distribution for liquid propellant thrust

chambers, the peak is always at the nozzle throat and the lowest value is usually near

the nozzle exit.

The procedure design continues with the choice of the wall thickness. The default

value is fixed at 0.001 m, but the user, according its experience can choose a more

appropriate value. Of course, this choice will be the result of a compromise among

rocket weight, performance and manufacturing constrains. However, wall thickness

can be also evaluated by the relation (4.2- 10)[10]:

𝒕 = 𝒇𝒔𝒑𝒄𝑫𝒄

𝟐(𝝈𝒚𝝃−𝟎.𝟔𝒑𝒄)

(4.2- 10)

Where 𝒑𝒄 is the chamber pressure, 𝑫𝒕 is the throat diameter, 𝝈𝒚 is the yield stress

that depends by material and temperature, 𝝃 is the joint coefficient and 𝒇𝒔 is the

safety factor. Similarly, the user will impose the distance between channels at throat

section. The default value, according to literature studies, is fixed at 0.001 m.

Next step is dedicated to the evaluation of the thermal conductivity of the thrust

chamber walls. It depends on the selected material and it changes with temperature.

Hence, the designer must choose the walls material. CIRA CDF SW is already

provided by the following material database: CuCrZr alloy, copper , gold,

aluminium, iron, niobium. If the material desired it not yet schematized, the user can

- 60 -

set up a linear or constant law of thermal conductivity. The Figure 23 shows the

thermal conductivity distribution of these materials[11].

Figure 23: Variation of thermal conductivity with temperature for typical metallic

elements and alloy

At this point, exploiting the second part of the semplified Fourier equation (4.2- 11)

for 1D - linear assumption, 𝑇𝑤𝑐 can be evaluated :

𝑻𝒘𝒄 = 𝑻𝒘𝒈 −𝒕 ⋅ 𝒒

𝒌

(4.2- 11)

4.2.2 Cooling Channels geometry

The process design continues with the evaluation of the cooling channels geometry.

As already told, considering an early simplified approach, the cross-section area of

- 61 -

the cooling channels has been assumed circular. Figure 24 shows a sketch of the

channel.

Figure 24: Detail view cooling channel geometry

In regenerative cooling process, the coolant, generally the fuel enters passages at the

nozzle exit of the thrust chamber nozzle. Thus, the coolant passes through the throat

region and reaches the exit near the injection plane. This path is represented in the

Figure 25.

Figure 25: Cross-sectional view of a regenerative cooling thrust chamber showing the

flows directions

The nozzle throat region usually experiences the highest heat flux and therefore is the

most difficult to cool down. For this reason the first cooling passages section are

designed in such a way that the coolant velocity is highest at the critical regions. This

is achieved considering the minimum cross-section area of the coolant passage at

nozzle throat. As show in Figure 26, the cross-section area of cooling passages

scales according to the region of thrust chamber to uniformly cool the entire wetted

area.

- 62 -

Figure 26: Typical cross-sectional scaling of a cooling channels along axial direction

The geometrical sizing of channels starts with the imposition of the diameter at throat

and proceeds through the entire thrust chamber . The user can consider several

different values at throat, in order to understand the influence of the diameter and

finally choose the best solution. As already told, the diameter changes along the axial

direction according to the region of thrust chamber. Hence, in the throat region the

diameter will be the tiniest. For manufacturing reason, the diameter of channels can’t

be less than 0.8 mm. The user can therefore analyze several solution obtained

considering different values of the cooling channels diameter. The number of cooling

channels that surround the thrust chamber can be easily calculated when some

parameters have been considered. From Eq. (4.2- 12) it is possible to denote that the

number of channels depends by some factors such as: the geometry of the nozzle,

wall thickness 𝑡 and distance between coolant passages 𝑠.

- 63 -

𝒏 = 𝟐𝝅[(𝒕+𝒓𝒕)+(𝒅𝒄𝒉(

𝒓𝒆𝒓𝒕))]

[(𝒅𝒄𝒉+𝒔)(𝒓𝒆𝒓𝒕)]

(4.2- 12)

For every selected size of the channels diameter, a different number of cooling

channel is obtained. In this regard, a study has been performed to evaluate the

relationship between the size of the cooling channel and the variations in thermo-

fluidynamic properties of the coolant. Those effects will be widely reported in the

Chapter 5.

From 𝑛, using Eq. (4.2- 13) it is trivial to obtain the fuel flow rate of the single

channel:

�̇� 𝒇𝒖𝒄𝒉 =

�̇�𝒇𝒖

𝒏

(4.2- 13)

Before assessing the thermo-fluydinamic characteristics of the coolant, the wetted

area can be calculated from simple geometric considerations. Considering the thrust

chamber contour, the wetted area, useful for further calculations, can be easily

evaluated. This is the surface surrounding the hot gas flow and will be necessary to

obtain thermo-fluydinamic parameters of the coolant flow through the channels

4.2.3 Coolant flow analysis

This paragraph describes the coolant thermo-fluidynamic properties evaluation of the

coolant, once that the geometry of the channels has been designed as described in the

previous paragraph.

The developed routine is based on a software tool called CoolProp[12] hereinafter

described. For what concern pressure losses, different models of friction factor have

been implemented and will be described in this chapter.

Final results will be presented in Chapter 5.

- 64 -

CoolProp

The numerical procedure developed in the present thesis, is supported by

CoolProp[12] that allows the evaluation of the thermo-fluydinamics behavior of the

coolant. CoolProp is a C++ library that implements:

Pure and pseudo-pure fluid equations of state and transport properties for 114

components;

Mixture properties using high-accuracy Helmholtz energy formulations (or

cubic EOS);

Correlations of properties of incompressible fluids and brines;

Highest accuracy psychrometric routines

CoolProp is based on Helmholtz energy formulations and all thermodynamic

properties of interest can be obtained directly from partial derivatives of the

Helmholtz energy. It should be noted that the EOS are typically valid over the entire

range of the fluid, from subcooled liquid to superheated vapor, to supercritical fluid.

Cooling System tool numerical description

The first step of the developed procedure relies on the reading of input parameters

from the feeding module, therefore the thermofluidynamic state of the fluid at the

beginning of the channel is known.

Coolprop uses initial temperature and pressure. A series of magnitudes, reported

hereinafter, are calculated by CoolProp: thermal conductivity, density, specific heat

at constant pressure, sound velocity, viscosity and the phase.

During the numerical implementation, an issue occurs when the coolant temperature

approaches at one of the transition phase (as example form 190.41 K to 190.57 K for

methane). In particular, the temperature value has been set equal to a value

immediately greater than supercritical value in order to avoid the well-known strong

variation of thermodynamic coefficients. In the common range of pressure occurring

in an LRE liquid Hydrogen is in supercritical conditions, while Methane usually

works in transcritical conditions (see Appendix A for details).

- 65 -

The design procedure continues with the evaluation of other parameters such as

Reynolds number and Prandtl number as shown in the Eq. (4.2- 14) and Eq. (4.2-

15):

𝑹𝒆 =𝝔𝒗𝑫

𝝁

𝑷𝒓 =𝑪𝒑𝝁

𝒌

(4.2- 14)

(4.2- 15)

Moreover, by Eq. (4.2- 16) the coolant velocity in the channels can be calculated:

𝒗 =

�̇� 𝒇𝒖𝒄𝒉

𝑨𝒄𝒉 𝝆

(4.2- 16)

In supercritical/transcritical conditions the heat is transferred through a vapor-film

boundary layer and the coolant-side heat-transfer coefficient can be estimated from

one of the following equation (4.2- 17) [13] and (4.2- 18)[4]:

𝒉𝒄 = 𝟎. 𝟏𝟖𝟓 (𝒌

𝒅) (𝑹𝒆𝟎.𝟖𝑷𝒓𝟎.𝟒) (

𝐓𝐜𝐨𝑻𝒘𝒄

)𝟎.𝟏

𝒉𝒄 = 𝟎. 𝟎𝟐𝟓 (𝒌

𝒅) (𝑹𝒆𝟎.𝟖𝑷𝒓𝟎.𝟒) (

𝐓𝐜𝐨𝑻𝒘𝒄

)

(4.2- 17)

(4.2- 18)

Both the equation will be utilized in first evaluation, but the (4.2- 17) will be

considered in further verifications. Of course, each part (i.e., gas side fluidynamic,

wall thermal and coolant side fluidynamic analyses) shall be approached by means of

deeper methods, but the scope of the present paragraph is to underline the basic

approach in a phase A of design procedure.

The next step focuses on the evaluation of the global coefficient of heat transfer by

Eq. (4.2- 19) [12]:

𝑯 = (

𝟏

𝒉𝒈+𝒕

𝒌+𝟏

𝒉𝒄)

(4.2- 19)

This parameter is crucial in the evaluation of coolant temperature, it depends,

substantially, by hot gases properties, thrust chamber geometry, chamber wall

thickness, wall material and coolant properties.

- 66 -

In the first implementation of the SW, the global coefficient hasn’t been used for the

evaluation of the heat flux and thus of the coolant temperature. The heat flux has

been simply obtained using the hot gas side heat flux coefficient, resulting in a less

accurate estimation of temperature increase of the coolant

Indeed, the variation of the coolant temperature (𝑇2𝑐𝑜 − 𝑇1𝑐𝑜) along the channels can

be calculated by means following correlation:

𝑻𝟐𝒄𝒐 = 𝑻𝟏𝒄𝒐 +𝑨𝒘⋅𝒒

�̇�𝒇𝒖⋅𝑪𝒑 (4.2- 20)

It depends, substantially, by heat flux, wetted area, coolant mass flow rate and

coolant specific heat.

Successively, a new evolution of the coolant temperature, has been evaluated by

means of a deeper evaluation of the heat flux, using the global coefficient approach

(see equation 4.2- 21):

𝒒 = 𝑯(𝑻𝒂𝒘 − 𝑻𝒄𝒐) (4.2- 21)

Then, the coolant temperature is calculated by means of eq. (4.2- 20)

This step is one of most important because the coolant temperature is an input for

CoolProp software and the other thermos-fluidynamic properties will be strongly

affected by it. The coolant absorbs heat flux along the channels and its temperature

increases. In this way, the coolant will be injected in combustion chamber with a

greater level of enthalpy. However, this phenomena doesn’t improve significantly the

rocket engine performance in terms of efficiency.

The last step is focused on the coolant pressure along the channels. As already told,

the pressure is the other input for CoolProp. From the literature [1] [5] the pressure

drop can be calculated by the following equation:

𝜟𝒑 = 𝒇𝑳

𝑫𝑯

𝟏

𝟐 𝝆𝒗𝟐

(4.2- 22)

- 67 -

Pressure drop depends by density, velocity and geometric considerations. In

particular, the coolant behavior in terms of pressure drop is strongly conditioned by

the friction factor. In this work, several formulations of friction factor have been

considered and implemented:

For smooth pipes with 𝑅𝑒 < 106 Zandbergen proposes to use the following

relationships by Poisseuille and Blausius[4]:

𝑓 =

{

𝟔𝟒

𝑹𝒆 𝑹𝒆 < 𝟐𝟑𝟐𝟎

𝟎. 𝟑𝟏𝟔 (𝟏

𝑹𝒆)𝟎.𝟐𝟓

𝟐𝟑𝟐𝟎 < 𝑹𝒆 < 𝟐 × 𝟏𝟎𝟒

𝟎. 𝟏𝟖𝟒 (𝟏

𝑹𝒆)𝟎.𝟐 𝟐 × 𝟏𝟎𝟒 < 𝑹𝒆 < 𝟏 × 𝟏𝟎𝟔

(4.2-23)

For non-smooth pipes with Re > 106, Zandbergen proposes using the

following relation by Nikuradse[4]:

𝒇 = 𝟖 ⋅ (𝟐. 𝟒𝟓𝟕 ⋅ 𝐥𝐨𝐠 (𝟑. 𝟕𝟎𝟕 ⋅

𝒆

𝒅))

−𝟐

(4.2- 24)

The Moody diagram. To each diameter channel length, a given value of 𝑒

𝑑 is

provided by a particular curve on the diagram that is function of Reynolds

number (see Figure 27 ).

- 68 -

Figure 27: Moody Diagram

Colebrook relation[14]:

𝒇 = 𝟎.𝟐𝟓

[𝒍𝒐𝒈(𝒆

𝟑.𝟕𝑫 +

𝟓.𝟕𝟒

𝑹𝒆𝟎.𝟗 )]𝟐

(4.2- 25)

These models of a friction factor have been implemented, however, another

relationship has been considered for the pressure drop estimation[15]:

𝜟𝒑 = 𝒇

𝑳

𝑫𝑯

𝟏

𝟐 𝝆𝒗𝟐 + 𝝆𝟏𝒗𝟏(𝒗𝟐 − 𝒗𝟏)

(4.2- 26)

The only differences between Eq. (4.2- 22) and Eq. (4.2- 26) consists in the term

𝜌1𝑣1(𝑣2 − 𝑣1). In the next chapter its effect will be highlighted and plotted along the

channel direction.

The presented mathematical formulations has been used and compared to describe

the coolant behavior along the axis of the channels.

- 69 -

Chapter 5

RESULTS

5.1 Overview

The present chapter provides the description of the validation of the design cycle

focusing on the developed tool described in chapter 4.

The chosen test case is the CIRA demo LOX/CH4 described in [16] and [17].

Moreover a parametric analysis varying friction factor, cooling channel diameter size

and heat flux evaluation will be presented.

The first step is to run the architecture module and fix the design point starting from

the required thrust, nozzle conditions and selected propellants. Then, the user has to

decide which nozzle (bell conic, etc.) has to be adopted.

In the present work a conic-cubic nozzle has been chosen, the value of thrust has

been fixed equal to 23720 N, the chamber pressure has been set equal to 55 bar

(common value for this class of Rocket Engine), the convergence angle and

divergence angle have been imposed equal to 22.5° and 20° respectively. For the

nozzle conditions, the first strategy has been adopted, hence 𝑝𝑒 = 1 atm.

Liquid oxygen and liquid methane have been chosen as propellants and their mixture

ratio has been fixed at 3.4 maximizing specific Impulse (see [16] and [17]).

Finally the characteristics length has been fixed equal to 0.94 m, while the throat

radius ratio will be equal to 1.5. This procedure design provided a geometrical profile

of thrust chamber as shown in Figure 28:

- 70 -

Figure 28: Geometrical profile of thrust chamber

The inlet conditions for the cooling channels of the methane have been fixed for

temperature and pressure. In particular at inlet of channels 𝑇𝑐𝑜 has been imposed

equal to 110 K, while the pressure equal to 160 bar. A first evaluation has been

realized considering a only diameter of channels at throat.

5.2 Validation of the cooling system design cycle

In this paragraph a validation of the performed work will be shown. This final result

has been obtained comparing the simulation performed using the developed module

with the results obtained by the 3 ton class LOX/CH4 LRE developed at CIRA in the

framework of HYPROB Program.

The HPRB-BREAD project has been defined in order to develop and test a

LOX/LCH4 rocket engine regeneratively cooled ground demonstrator and related

Breadboards for technology and design validation.

The architecture considered for the demonstrator, in line with the project key level

requirements, is a regenerative cooled thrust chamber for ground testing. In the

HYPROB-demonstrator a counter-flow architecture will be considered for the

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

x [m]

y [

m]

- 71 -

chamber cooling system (see Figure 29 and Figure 30). In this type of architecture,

the coolant (LCH4) is injected liquid into the fuel manifold and enters the cooling

jacket counter flow with respect to the combustion gases. After being heated it is

injected directly in the fuel dome and then from the injector in the combustion

chamber where mixes, atomizes and burns with liquid oxygen.

Figure 29: Architecture concept

Figure 30 Counter flow architecture for the cooling jacket

The main CIRA demo parameters are shown in the following Table 3:

- 72 -

Parameter

𝐷𝑡 [m] Throat diameter 0.0598

𝐷𝑐 [m] Combustion chamber

diameter

0.1196

𝐷𝑒 [m] Exit diameter 0.1795

𝑉𝑐 [m3] Combustion chamber volume 2.693e-3

𝐿𝑐ℎ𝑎𝑚 [m] Combustion chamber length 0.192

𝐿𝑐𝑜𝑛𝑣 [m] Convergent nozzle length 0.0811

𝐿𝑑𝑖𝑣 [m] Divergent nozzle length 0.167

𝑛 Channels number 96

AR Aspect Ratio 1.4

Convergence angle 22.5°

Divergence angle 20°

Table 3: Main geometric parameters of HYPROB-demonstrator

With those parameters, the geometric configuration of the thrust chamber is

represented in Figure 31:

Figure 31: Geometric profile of thrust chamber

The geometric profile used for the performed work shows small differences with

respect to the thrust chamber configuration shown in Figure 31: 𝐿𝑑𝑖𝑣 is slighty

smaller than 𝐿𝑑𝑖𝑣 of the demonstrator (see Figure 28). Moreover, the channels of

- 73 -

HYPROB-demonstrator has been developed with a rectangular shape (see Figure

32), but in the present work the numerical simulations have been carried out

considering circular cooling channels (see Figure 26). This difference involves a

similar number of channels: 96 for the demonstrator and 94 for the numerically

simulated module. Of course, in this way the comparison between two models is

reasonable, because the differences are very small. For both models, CuCrZr alloy

has been chosen for inner wall material. Table 4 shows performance parameters of

HYPROB-demonstrator.

Figure 32: Cooling system channel and brazing interface

Performance parameters

𝑐∗ [m/s] Characteristic velocity 1827.16

𝑝𝑐 [Pa] Chamber pressure 5500000

𝑇𝑐 [K] Chamber temperature 3542

𝐼𝑠𝑝 [s] Specific Impulse 286.02

𝐶𝑓 Thrust coefficient 1.5351

𝐹 (sea level) [N] Thrust 23720

𝑇𝐶𝐻4 [K] Inlet coolant temperature 110

�̇�𝑓𝑢 [kg/s] Mass flow rate (fuel) 1.922

Mixture ratio 3.4

Table 4: Main performance parameters of HYPROB-demonstrator

- 74 -

Figure 33 shows the heat flux evaluation performed by means of CDF SW compared

with the one computed in the framework of HYPROB-BREAD project by means of

engineering approach. In particular, in the throat region a wall temperature equal to

750 K has been set, in the combustion chamber region the wall temperature has been

set equal to 600 K and 500 K in the nozzle region. The temperature in the throat

region is a common choice, i.e., just below the maximum allowable. The HYPROB-

BREAD result concerns a “step shaped” curve, while the CDF is based on

logarithmic interpolation between the set values. Good agreement has been reached

comparing the performed results with one computed within the HYPROB-BREAD

project.

Figure 33: Heat fluxes given as input

The HYPROB-BREAD heat flux is extended over the present nozzle contour

because is related to a geometric profile of thrust chamber shown in Figure 31 that is

longer than the nozzle contour performed by means of CDF SW (Figure 28). As

discussed previously, some factors will cause some differences between the models

and results, and they can be widely noted in terms of pressure distribution (see

Figure 34). This wide difference is particularly due at the different shape of cooling

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

7

x [m]

q [

W/m

2]

CDF nozzle contour

HYPROB-BREAD

CDF analysis (Twg = 750 K)

- 75 -

channels, in fact as shown in Eq. (4.2- 22) the geometrical parameters (𝑳

𝑫𝑯) affect

considerably the pressure drop. This term named Aspect Ratio don’t vary along the

channels for HPRB-demonstrator and it is equal to 1.4, while for the circular cooling

channels analyzed in the frame of CIRA CDF for Space Propulsion it is variable and

for some intervals it is less than 1. Moreover, the different shape of channels

involves a different friction factor that further justifies the differences among the

trends. The coolant transition phase occurs in throat region and it is highlighted by a

greater slope (red curve). In the future version of the CDF SW rectangular cooling

channels will be taken into account. The present work is focused on phase 0/A of a

space project on circular shaped channels, while the CFD is the actual DEMO

channel, therefore the present comparison has been performed with a similitude

focused on the number of cooling channels and the geometries differs in regions far

from the throat. This feature is the reason of the difference in pressure losses

prediction. Definitely, pressure distribution comparison differs from CFD caused by

the different simulated geometries, because CFD geometry is related to a deeper

phase project (i.e., phase B/C) not taken into account in the CDF 1-D approach.

Figure 34: HYPROB-BREAD pressure distribution vs CDF pressure distribution

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.451

1.1

1.2

1.3

1.4

1.5

1.6x 10

7

x [m]

P [

Pa

]

nozzle contour

HYPROB-BREAD

CDF

- 76 -

Figure 35 shows the temperature trends computed by CDF SW and HYPROB-

BREAD computations. The results are very close to each other, the differences are

function of the different heat flux and different geometry of cooling channels. Of

course, the coolant temperature increases along the channels because absorbs a huge

heat flux. For CDF analysis, the temperature distribution is almost linear, except at

throat, where the coolant phase change occurs and strong non-linearity phenomena

occur.

Figure 35: HYPROB-BREAD temperature distribution vs CDF temperature

distribution

Figure 36 shows the comparison between the two computed specifics heats. The

only small discrepancy consists in the horizontal displacements caused by the

different nozzle length. The peak of the 𝐶𝑝 is caused by the coolant supercritical

transition (see Appendix A).

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

50

100

150

200

250

300

350

400

450

x [m]

T [

K]

HYPROB-BREAD

nozzle contour

CDF

- 77 -

Figure 36: HYPROB-BREAD heat specific distribution vs CDF heat specific

distribution

Thermal conductivity comparison is shown in Figure 37. Also in this case the

distributions are very close each other, and the supercritical transition is predicted in

the throat region by both calculations

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

x [m]

Cp [

J/(

kg

K)]

HYPROB-BREAD

nozzle contour

CDF

- 78 -

Figure 37: HYPROB-BREAD thermal conductivity distribution vs CDF thermal

conductivity distribution

A preliminary CFD analysis on the demonstrator cooling channel has been carried

out (see [16] and [17] for details), it refers to a single channel, belonging to the

regenerative cooling system which covers the thrust chamber wall. Two different

configurations have been analyzed: an arrangement, considering constant the height

of the cooling channel, equal to 1.10 mm, has been proposed but it is identified in

order to have the best thermal performances in the throat zone but some critical

points could be encountered in other sections; a second arrangement, featured by a

channel height, with dimensions, changing at the inlet section, throat zone, chamber

and outlet section, has been studied in order to improve the thermal performances of

the whole cooling channel. In particular, the second configuration is more similar to

the geometry adopted in the numerical simulation described previously. Therefore,

the results of the developed CDF tool have been compared with the CFD analysis of

the latter configuration.

The Figure 38 shows the channels configuration with a variable height along the

thrust chamber.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

0.05

0.1

0.15

0.2

0.25

x [m]

k [

W/(

mK

)]

HYPROB-BRAED

nozzle contour

CDF

- 79 -

Figure 38: Cooling channels of demonstrator

The CFD analysis provides a better description of the phenomena, in fact as shown in

Figure 39, heat flux doesn’t remain constant along the combustion chamber and near

the injection plate the heat flux raises. In a preliminary design phase, using a 1-D

analysis approach, this phenomenon obviously neglected and difficult to describe.

Figure 39: Heat flux – CFD analysis vs CDF

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

7

x [m]

he

at

flu

x [

W/m

2]

CFD analysis - HYPROB-BREAD

CDF nozzle contour

CDF

- 80 -

A good agreement between the heat flux predicted by the developed tool and the

CFD results has been achieved.

Figure 40 and Figure 41 shows the comparison between the models in terms of

temperature and pressure respectively.

For CFD analysis, the temperature profile tends to increase along the channel, while

the pressure profile decreases. Furthermore, very sharp profiles are observed in the

throat region. The fluid thermo-physical properties are strictly linked to the fluid

temperature and pressure conditions. In fact, density decreases from the inlet section

towards the outlet of about one order of magnitude because the supercritical

transition occurs. Distribution is not uniform in the cross section and the fluid

behaves like a highly compressible fluid, i.e. a gas, near the hot walls of the channel,

and like a liquid near the cold ones. Just before the throat region, all the fluid is in

supercritical conditions, which are achieved in advance at the bottom surface of the

channel, since higher temperature values are reached. In the outlet section the fluid

is completely in vapor phase.

Figure 40: Temperature – CFD analysis vs CDF

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

50

100

150

200

250

300

350

400

450

500

x [m]

T [

K]

CDF nozzle contour

CFD analysis - HYPROB BREAD

CDF

- 81 -

Figure 41: Temperature – CFD analysis vs CDF

In terms of temperature, the greatest difference between models can be appreciated at

throat, where the CFD analyses describe in detail the transition phase. In other zones,

the trends are very similar. However, among the models a big difference occurs in

terms of pressure. As said before, the reason of this difference is related to the

different geometry of the channel in the combustion and nozzle region and to 1-D

assumption.

Finally Figure 42 and Figure 43 show the comparisons between coolant thermal

conductivity and specific heat.

In the CFD analysis, the highest value of specific heat is detected at about x = 0.26

m, a sections near the throat region, as depicted in Figure 42, while the minimum

value of thermal conductivity is observed at x = 0.18 m in accordance with the NIST

data. The temperature corresponding to the maximum values of specific heat is called

pseudo-critical temperature and, for example, for an operating pressure of 13.0 MPa

(the operating pressure in the throat region), it is equal to about 228 K. As a result,

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

2

4

6

8

10

12

14

16

18x 10

6

x [m]

P [

Pa

]

CFD analysis - HYPROB-BREAD

CDF nozzle contour

CDF

- 82 -

the fluid is very hot in the bottom part of the channel while it keeps cold near the

upper zone, because a kind of “thermal barrier” occurs inside the channel (see

Appendix A).

Figure 42: Specific heat – CFD analysis vs CDF

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

1000

2000

3000

4000

5000

6000

x [m]

Cp

[J/(

kg

K)]

CDF nozzle contour

CFD analysis - HYPROB-BREAD

CDF

- 83 -

Figure 43: Thermal conductivity – CFD analysis vs CDF

The analyses developed with numerical investigation is fairly good, indeed also the

specific heat trend and thermal conductivity trend is very near at the CFD analysis

reported above. In the case of thermal conductivity, the curves are completely

overlapped along the combustion chamber. In the specific heat distribution, the peaks

don’t occur at the same throat position because the demonstrator length of the nozzle

is higher than the nozzle profile considered in 1-D analysis. Pressure distribution

comparison differs from CFD because of different simulated geometries CFD

geometry is related to a deeper phase project (i.e., phase B/C) not taken into account

in the CDF approach.

5.3 Case study: 100 kN thrust class engine

In order to better understand the models reliability, another engine configuration has

been implemented. This paragraph focuses on the obtained results relevant to a

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

0.05

0.1

0.15

0.2

0.25

x [m]

k [

W/(

mK

)]

CDF nozzle contour

CFD analysis - HYPROB-BREAD

CDF

- 84 -

100kN class LRE simulated within the software developed for CIRA CDF for space

propulsion.

Considering a 100kN thrust engine and the assumption summarized in the table

below, some analysis can be performed varying some parameters, such as the cooling

channels diameter and the evaluation of the heat flux or changing the model for the

friction factor calculation.

Parameter

Thrust [kN] 100

Fuel CH4

Oxidizer O2

Mixture ratio 3.4

𝑝𝑐 [bar] 60

𝑝𝑒 [atm] 0.01

𝐿∗ [m] 1

Radius ratio 0.5

Nozzle shape Bell cubic

Convergence angle 25°

Wall temperature (at throat) [K] 750

Wall material CuCrZr

Table 5: Main performance parameters

Other parameters have been set as default values (see Chapter 4). Moreover, the

coolant inlet conditions in terms of pressure and temperature are kept equal to ones

considered in the previous paragraph.

As it can be noted, the engine is supposed to be designed for extra-atmosphere

environment. It’s easy to image that this type of engine can be associated with a 3rd

stage of middle thrust class launcher.

The geometrical configuration obtained for the thrust chamber is shown in Figure

44.

- 85 -

Figure 44: Geometrical configuration of 100 kN class thrust chamber

5.3.1Models of friction factor

The following results have been obtained considering a fixed cooling channel

diameter at throat equal to 3mm. As a matter of fact, as shown in Figure 26, the

cross-section area of cooling channels varies according to y-profile of the thrust

chamber.

The thermofluidynamic behavior of the coolant is strongly influenced by the heat

flux. Its evaluation is the main step of the cooling system module and it is shown

hereinafter.

0 0.5 1 1.5-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

x [m]

y [

m]

- 86 -

Figure 45: Heat flux distribution along the cooling channels

In Figure 45 the heat flux calculated by means of Eq. (4.2- 2) is shown. In particular,

two different fluxes are obtained, the first considering a conservative 𝑇𝑤𝑔 equal to

300 K and the second using a more realistic value of 750 K. Of course, for 𝑇𝑤𝑔 = 300

K the heat flux is greater than the one calculated with 𝑇𝑤𝑔 = 750 K. Following

results have to be considered related to the heat flux obtained considering the

realistic wall temperature at throat.

As known from literature, the peak of heat flux occurs near the throat region.

Indeed, in this zone the wetted area of hot gases reachs its minimum value.

Using a lower wall temperature value for the evaluation of heat flux is a conservative

method and is often used as a safety margin. Moreover, in order to save weight, the

design of a LRE is usually carried out considering 𝑇𝑤𝑔 just below the material

allowable temperature.

Hereinafter, the main thermofluidynamic properties will be shown. In particular, in

this section, the results obtained varying the friction factor models described in the

previous chapter, will be analyzed and discussed.

0 0.5 1 1.50

0.5

1

1.5

2

2.5

3

3.5

4x 10

7

x [m]

q [

W/m

2]

Twg = 750 K

Twg = 300 K

Nozzle Contour

- 87 -

Figure 46: Coolant density distribution along the cooling channels

Figure 46 provides coolant density trend along the cooling channels. As known from

the thermofluidynamic behavior of the coolant, the density decreases with the

absorbtion of heat flux. Moreover, it’s clearly visible the point at which the a

transition phase occurs. As already mentioned, at throat the fluid change phases from

liquid to supercritical conditions, accordingly the density decrease more rapdly. The

effect of friction factor can be negclected. This phenomenon occurs also in the

temperature distribution as it can be sees in Figure 47.

0 0.5 1 1.50

50

100

150

200

250

300

350

400

450

x [m]

de

nsity [

kg

/m3]

Poisseuille, Blausius

and Nikuradse

Moody

Colebrook

nozzle contour

- 88 -

Figure 47: Coolant temperature distribution along the cooling channels

Equation (4.2- 20) returns the temperature trend. The coolant absorbs the heat flux

along the channels, hence its temperature increases. Moreover, its trend is rather

linear along the combustion chamber. A slight irregularity is visible at throat, where

the coolant changes phase and the thermal conductivity, along with the slope of the

temperature curve, changes. In addition, Figure 47 shows that using different models

of friction factor have no effects on temperature trends. Indeed, the curves are almost

overlapped. This phenomenon can be understood looking at Eq. (4.2- 20), indeed 𝑞 is

slightly affected by 𝑓 as well as �̇�𝑓𝑢 and 𝐴𝑤 just depends on the geometry of the

thrust chamber. Moreover, 𝐶𝑝 slightly varies with friction factor as shown in Figure

50. This explains why coolant temperature evolution isn’t highly affected by friction

coefficient modeling.

0 0.5 1 1.50

50

100

150

200

250

300

x [m]

T [

K]

Poisseuille,Blausius

and Nikuradse

Moody

Colebrook

Nozzle Contour

- 89 -

Figure 48: Coolant pressure drop distribution along the cooling channels

Figure 48 shows the pressure along the cooling channels. The pressure drop is linked

to Eq. (4.2- 22). It is proportional to density, and 𝑣2. Therefore, the pressure drop is

greater at throat, where the channel section is small and the velocity increases, vice

versa, in the exhaust nozzle the drop is very small due to low coolant velocities. The

pressure loss is linked to friction between the fluid (coolant) and channel walls, and

this interaction is taken into account by means of friction factor 𝑓. A different

formulation of this parameter causes a dissimilar distribution of coolant pressure.

The trends related to the three different implemented models of friction coefficient

are shown in Figure 49. The curves are the results of Eq. (4.2-23), Moody diagram

and Eq. (4.2- 24).

0 0.5 1 1.51.575

1.58

1.585

1.59

1.595

1.6x 10

7

x [m]

P [

Pa

]

Poisseuille, Blausius

and Nikuradse

Moody

Colebrook

- 90 -

Figure 49: Friction factor distribution along the cooling channels

Figure 50: Specific heat at constant pressure distribution along the cooling channels

0 0.5 1 1.50

0.005

0.01

0.015

0.02

0.025

0.03

x [m]

f

Poisseuille, Blausius

and Nikuradse

Moody

Colebrook

Nozzle Contour

0 0.5 1 1.50

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

x [m]

Cp [

J/(

kg

K)]

Poissuille, Blausius and Nikuradse

Moody

Colebrook

nozzle contour

- 91 -

The variation of 𝐶𝑝 is strongly conditioned by the temperature. This condition

involves higher values of 𝐶𝑝 in throat region. As already explained, in this region the

coolant becomes supercritical and thus 𝐶𝑝 experience a peak. Approximately, in

other regions the 𝐶𝑝 distribution follows the heat flux trend. The effect of different

friction factor is very small.

The distribution of coolant velocity along the axis of the channels is very interesting.

It is shown in Figure 51, and its behavior is strongly affected by density and channel

area. This is due to the mass flow conservation that has to be respected.

Figure 51: Coolant velocity distribution along the cooling channels

It can be noted that the velocity shows a peak at throat section. Even if along the

combustion chamber the channels diameters remain constant, the velocity raises

because the density (see Figure 46) decreases. In the exhaust nozzle, the coolant

velocity increases also because the cross-section area of the cooling channels are

increases progressively till the throat section. In the converging-nozzle, the velocity

reduction is due to the opposite effect. Even in this case, the effect of considering

different friction factor models is not evident.

0 0.5 1 1.50

5

10

15

20

25

x [m]

v [

m/s

]

Poisseuille, Blausius

and Nikuradse

Moody

Colebrook

Nozzle Contour

- 92 -

Reynolds number is conditioned by the coolant density and velocity. It is provided

by Eq. (4.2- 14). From Figure 52 the great change that occurs along the channels can

be appreciated.

Figure 52: Reynolds number distribution along the cooling channels

Reynolds number increases along the cooling channels. This behavior is strongly

conditioned by dynamic viscosity (see Figure 53) which is strongly affected by the

phase change. The maximum value of 𝑅𝑒 occurs in combustion chamber, where the

velocity raises continuously. The different formulation of friction factor isn’t

perceived along the channels.

0 0.5 1 1.50

1

2

3

4

5

6

7

8

9

10x 10

5

x [m]

Re

Poisseuille, Blausius

and Nikuradse

Moody

Colebrook

Nozzle contour

- 93 -

Figure 53: Dynamic viscosity distribution along the cooling channels

Finally, the coolant thermal conductivity is reported in Figure 54.

Figure 54: Thermal conductivity distribution along the cooling channels

0 0.5 1 1.50

0.5

1

1.5x 10

-4

x [m]

Dyn

am

ic V

isco

sity [

Pa

*s]

Poisseuille, Moody

and Nikuradse

Moody

Colebrook

Nozzle Contour

0 0.5 1 1.50

0.05

0.1

0.15

0.2

0.25

x [m]

Th

erm

al co

nd

uctivity [

W/

(m K

)]

Poisseuille, Blausius

and Nikuradse

Moody

Colebrook

Nozzle contour

- 94 -

The thermal conductivity distribution of the fuel is strongly conditioned by transition

phase, which occurs at throat. Even in this case the effect of considering different

friction factor models isn’t appreciable.

It’s worth to emphasize that the evaluation of thermofluidynamic parameters has

been done exploiting the CoolProp software. An iterative process has been adopted

considering pressure and temperature updates through the evaluation, step by step, of

the heat flux. This procedure ensures good accuracy and faster computational times.

After this evaluation, the thermo-fluidynamic behavior of the coolant has been

determined considering a different pressure drop formulation expressed by Eq. (4.2-

26). The difference between Eq. (4.2- 22) and (4.2- 26) consists in the term

𝜌1𝑣1(𝑣2 − 𝑣1). As shown in Figure 55 in the converging part of the nozzle the

coolant pressure undergoes a growth. This phenomenon is due to coolant velocity

reduction in this region (see Figure 51). In the end, the total pressure drop is slightly

greater than the pressure drop shown in Figure 48.

Figure 55: Coolant pressure distribution along the channels

0 0.5 1 1.51.54

1.55

1.56

1.57

1.58

1.59

1.6x 10

7

x [m]

P [

Pa

]

Poisseuille, Blausius

and Nikuradse

Moody

Colebrook

- 95 -

5.3.2 Cooling channels diameter effect

In this paragraph, the obtained results will be shown considering different sizes of

cooling channels. Accordingly a different number of cooling channels are obtained.

The following analyses have been carried out setting five different sizes of diameters

at throat. In particular, the minimal diameter has been fixed equal to 3 mm, and the

maximal diameter is equal to 5 mm, those values have been considered feasible for

the resulting number of channels and velocity at throat. Other diameters have been

chosen equal to 3.5, 4 and 4.5 mm respectively. Obviously, also in this case, the

chosen heat flux is the one shown in Figure 45.

One of the magnitudes strongly conditioned by the diameter is the coolant velocity.

As shown by Eq. (4.2- 16) it is inversely proportional to the cross-sectional area of

channels, therefore is also inversely proportional to 𝑑𝑐ℎ2 . The arrow in Figure 56

shows the effect of increasing diameter on the coolant velocity.

Figure 56: Diameter effect on the coolant velocity along the cooling channels

This parameter influences the pressure drop of the coolant. Indeed, as shown by Eq.

(4.2- 22) the pressure drop varies with 𝑣2. Moreover, the effect of diameter is

reflected on the coolant pressure because the pressure drop is inversely proportional

to the hydraulic diameter. This behavior is clearly visible in Figure 57.

0 0.5 1 1.50

5

10

15

20

25

30

x [m]

v [

m/s

]

d = 3 mm

d = 3.5 mm

d = 4 mm

d = 4.5 mm

d = 5 mm

Nozzle contourgrowth d

- 96 -

Figure 57: Diameter effect on the coolant pressure drop along the cooling channels

As known from Eq. (4.2- 14) the channels diameter and the coolant velocity affect

directly the Reynolds number. Increasing the diameter, the velocity decreases, and

also 𝑅𝑒. Reynolds number distributions are shown in the Figure 58.

Other thermo-fluidynamic properties don’t vary significantly with diameter because

this models is 1-D. This situation represents a limit of the adopted model, although,

for preliminary design it provides fairly accurate results.

Figure 58: Reynolds number distribution along the cooling channels

0 0.5 1 1.51.57

1.575

1.58

1.585

1.59

1.595

1.6x 10

7

x [m]

P [

Pa

]

d = 3 mm

d = 3.5 mm

d = 4 mm

d = 4.5 mm

d = 5 mm

growth d

0 0.5 1 1.50

2

4

6

8

10

12x 10

5

x [m]

Re

d = 3 mm

d = 3.5 mm

d = 4 mm

d = 4.5 mm

d = 5 mm

Nozzle contour

growth d

- 97 -

Even if the coolant behavior doesn’t change with friction factor, a different evolution

occurs when the sizes of cooling channels vary. Starting again from heat flux

analysis, Figure 59 shows the distribution of heat flux along the cooling channels,

and it can be noted that the heat flux decrease when the diameter increases.

Figure 59: Diameter effect on the heat flux distribution

This result is due to the direct effect of global heat transfer coefficient on the heat

flux (see Figure 61). In particular, 𝐻 varies with the convective hot-gas heat flux

coefficient, with the thermal conductivity of thrust chamber walls material and with

the convective coolant heat flux coefficient. Since ℎ𝑔 depends just on hot gases and 𝑘

depends on the chosen material, they remain constant varying the size of channels.

Therefore, the only parameter that significantly varies with diameter is ℎ𝑐 as shown

in Eq. (4.2- 17). Indeed, the coolant convective heat flux coefficient is inversely

proportional to the diameter itself. The coolant convective heat flux coefficient

distributions are presented in Figure 60.

0 0.5 1 1.50

1

2

3

4x 10

7

x [m]

he

at

flu

x [

W/m

2]

d = 3 mm

d = 3.5 mm

d = 4 mm

d = 4.5 mm

d = 5 mm

Nozzle contourgrowth d

- 98 -

Figure 60: Diameter effect on the convective heat flux coefficient of coolant distribution

Hence, this distribution is reflected on the global heat transfer coefficient and on the

coolant temperature, as shown in Figure 61 and Figure 62.

Even if the coolant behavior doesn’t change with friction factor, a different evolution

occurs when the sizes of cooling channels vary. Starting again from heat flux

analysis, Figure 59 shows the distribution of heat flux along the cooling channels,

and it can be noted that the heat flux decrease when the diameter increases.

Figure 61: Diameter effect on the global coefficient of heat transfer distribution

0 0.5 1 1.50

0.5

1

1.5

2

2.5

3x 10

4

x [m]

hc [

W/(

m2 K

)]

d = 3 mm

d = 3.5 mm

d = 4 mm

d = 4.5 mm

d = 5 mm

Nozzle contour

growth d

0 0.5 1 1.50

2000

4000

6000

8000

10000

12000

x [m]

H [

W/(

m2 K

)]

d = 3 mm

d = 3.5 mm

d = 4 mm

d = 4.5 mm

d = 5 mm

Nozzle contour

growth d

- 99 -

Figure 62: Diameter effect on the temperature distribution

The thermo-fluydinamic behavior of coolant is strongly conditioned by different heat

flux evaluation model. In this case, all thermo-fluidynamic properties vary with

diameter. Indeed, as shown in Figure 63, Figure 64, and Figure 65 the effect of the

diameter on the density, specific heat and thermal conductivity is widely visible. This

behavior is a result of different input values of temperature (see Figure 62). For

velocity, pressure and Reynolds number the trend is analogous to distributions shown

in the Figure 56, Figure 57 and Figure 58.

0 0.5 1 1.50

50

100

150

200

250

300

x [m]

T [

K]

d =3 mm

d =3.5 mm

d =4 mm

d =4.5 mm

d =5 mm

Nozzle contour

- 100 -

Figure 63: Diameter effect on the coolant density distribution

Figure 64: Diameter effect on the coolant heat specific distribution

0 0.5 1 1.50

100

200

300

400

500

x [m]

De

nsity [

kg

/m3]

d = 3 mm

d = 3.5 mm

d = 4 mm

d = 4.5 mm

d = 5 mm

Nozzle contour

growth d

0 0.5 1 1.50

1000

2000

3000

4000

5000

x [m]

Cp

[J/(

kg

K)]

d = 3 mm

d = 3.5 mm

d = 4 mm

d = 4.5 mm

d = 5 mm

Nozzle contour

growth d

- 101 -

Figure 65: Diameter effect on the coolant thermal conductivity distribution

5.3.3 Heat flux evaluation model

In paragraphs 5.3.1 and 5.3.2 the results have been obtained considering a iterative

process for heat flux evaluation. This model consists in the evaluation, step by step,

of heat flux described by Eq. (4.2- 21). In this way, heat flux and other coolant

properties have been calculated iteratively. Considering a channel diameter at throat

equal to 3 mm, the Figure 66 shows the heat flux distribution along the channels.

The effect of friction factor can be neglected because, as already told, it doesn’t

affect the specific heat of the coolant (see Figure 66).

0 0.5 1 1.50

0.05

0.1

0.15

0.2

0.25

x [m]

k [

W/(

m K

)]

d = 3 mm

d = 3.5 mm

d = 4 mm

d = 4.5 mm

d = 5 mm

Nozzle contour

growth d

- 102 -

Figure 66: Heat flux distribution along the cooling channels

To speed up the calculation, as described in chapter 4 another model of heat flux has

been considered. This process involves a imposed distribution of heat flux along the

thrust chamber, except along the combustion chamber where heat flux remains

constant (see eq. 4.2- 2). The latter process is more conservative than the iterative

process adopted in previous paragraphs, but it is less reliable.

Many coolant thermo-fluidynamic properties show some changes if compared with

the results shown in the paragraph 5.3.1. The reason of this consideration can be

justified looking at Figure 67, that shows a comparison between the two models of

different heat flux evaluation. Indeed, the curves show some differences with each

other, especially in the heat flux peak and in the combustion chamber. In fact, for the

last model the peak exceed 50 MW/m2, while for the first model it is equal to 35

MW/m2. Of course, some differences are clearly visible along the combustion

chamber. In the exhaust nozzle, heat fluxes are very similar. Obviously, the

0 0.5 1 1.50

0.5

1

1.5

2

2.5

3

3.5

4x 10

7

x [m]

he

at

flu

x [

W/m

2]

Poisseuille,Blausius and Nikuradse

Moody

Colebrook

nozzle contour

- 103 -

discrepancies appreciated in the figure shown below affect other coolant thermo-

fluidynamic properties.

Figure 67: Comparison between heat fluxes

According to Figure 67, temperature trends (see Figure 68) are particularly different

along the combustion chamber. The values at the exit of channels clearly differs.

0 0.5 1 1.50

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

7

x [m]

q [

W/m

2]

q=hg(Taw-Twg)

q=H(Taw-Tco)

Nozzle contour

- 104 -

Figure 68: Comparison between temperature trends

Obviously, also the density distributions (see Figure 69) highlights some differences

more evident in the combustion chamber. Along the nozzle the trends are almost

overlapped. This behavior is easy to image once known the temperature evolution.

Figure 69: Comparison between density trends

0 0.5 1 1.50

50

100

150

200

250

300

350

x [m]

T [

K]

Iterative process

Imposed q process

Nozzle contour

0 0.5 1 1.50

100

200

300

400

500

x [m]

De

nsity [

kg

/m3]

Iterative process

Imposed q process

Nozzle contour

- 105 -

As already mentioned, coolant velocity is provided by mass flow conservation, hence

the differences between the two models in terms on density are reflected on velocity

trends (See Figure 70). For imposed heat flux process, the maximum value occurs at

the channels exit, while for iterative process it occurs at throat. Of course, this

situation involves some differences also in Reynolds number distributions.

Figure 70: Comparison between velocity trends

0 0.5 1 1.50

5

10

15

20

25

30

x [m]

v [

m/s

]

Iterative process

Imposed q process

Nozzle contour

- 106 -

Figure 71: Comparison between Reynolds number trends

Another parameter influenced by these evaluations is the specific heat (see Figure

72). In particular, for imposed heat flux profile, the peak occurs before as well as the

transition phase. Of course, this phenomenon is due to a greater value of heat flux for

the first method.

Figure 72: Comparison between specific heat trends

0 0.5 1 1.50

2

4

6

8

10

12x 10

5

x [m]

Re

Iterative process

Imposed q process

Nozzle contour

0 0.5 1 1.50

1000

2000

3000

4000

5000

x [m]

Cp

[J(k

g K

)]

Iterative process

Imposed q process

Nozzle Contour

- 107 -

In terms of thermal conductivity (see Figure 73) the disparity among the models are

very small. The different model do not affect the pressure drop (see Figure 74).

Figure 73: Comparison between thermal conductivity trends

Figure 74: Comparison between pressure trends

0 0.5 1 1.50

0.05

0.1

0.15

0.2

0.25

x [m]

k [

W/(

m K

)]

Iterative process

Imposed q process

Nozzle contour

0 0.5 1 1.51.57

1.575

1.58

1.585

1.59

1.595

1.6x 10

7

x [m]

P [

Pa

]

Iterative process

Imposed q process

- 109 -

Chapter 6

CONCLUSIONS

The HYPROB program is carried out by the Italian Aerospace Research Centre

(CIRA) to improve National system and technology capabilities on liquid rocket

engines (LRE) for future space applications, with specific regard to LOX/LCH4

technology. Within the HYPROB program, TECH project is focused on developing

key technologies, both numerical and experimental, to design and analyze such

generation of LRE.

One of the key product, currently under development, is the Concurrent Design

Facility for Space Propulsion.

The present work relies on the development and validation of an engineering module,

written using MATLAB, devoted to the design of a regenerative cooling system for a

Liquid Rocket Engine. It’s worth to remark that CDF is for preliminary design of

complex engineering systems, such as phase 0/A in space projects classification.

Since the module has been developed for a preliminary design phase, the 1-D

approach has been implemented for the thermodynamic properties prediction of the

coolant.

Common coolants used in LRE work in the supercritical region of the state diagram

and perform supercritical phase transition from liquid to gas along the cooling

channel. In order to simulate this feature, thermo-fluidynamic behavior of the coolant

has been calculated by means of NIST tables through CoolProp software.

In particular this work has been focused on numerical implementation of liquid

methane trans-critical conditions (i.e., very close to critical point), where strong

variation of thermofluidynamic parameters, such as thermal conductivity, specific

heat, density and viscosity occur.

- 110 -

Different formulation of friction factor have been modeled such as the Colebrook

equation, Poisseuille relation and the Moody diagram interpolation.

Moreover, hot gas side heat flux has been evaluated with Bartz semi-empirical

correlation and the heat passage at steady state from hot gases through the wall till

the coolant side has been implemented.

The heat flux has been modeled both, imposing a profile and evaluation it step by

step using the coolant temperature evaluation. The Validation of the implemented

methodology has been done using as test case CIRA HYPRO-BREAD LOX/CH4 30

kN demonstrator.

The comparison between the obtained results with ones performed in the framework

of HYPROB-BREAD Project (engineering methods and CFD) is fairly good.

In particular, pressure distribution comparison differs from HYPROB-BREAD

results because of different simulated geometries. The comparison between other

thermofluidynamic parameters are completely satisfactory.

In order to better understand the models reliability, further simulations by means of

the developed CDF software for space propulsion have been realized taking as case

study a 100 kN thrust class LRE.

The effect of friction factor on the coolant is clearly visible for the pressure drop

across the channels, although, this differences don’t affect other thermofluidynamic

properties.

In particular the pressure drop is small because the adopted diameter of channels is

quite wide.

The different diameter of channels affects the coolant properties, and in order to

avoid undesirable phenomena it has to be chosen appropriately. It has been possible

to understand the trend of the main parameters and the heat flux along the thrust

chamber. In particular, the heat flux decreases as the channel diameter increases and

thus the channel size has a great effect on the temperature profile along the cooling

- 111 -

channels. It’s worth to remark that the coolant exit temperature is one of the key

parameter for the design of a regenerative liquid rocket engine.

Finally two different method of considering the heat flux have been implemented and

compared. The first consists in imposing a temperature profile and thus an heat flux

profile. This results in a conservative approach and can be very useful for pre-design

calculations. During the final period of the thesis work, an iterative procedure for the

evaluation of the heat flux, has been implemented. This method considers the total

convective heat flux coefficient and the evaluated coolant temperature to calculate

the heat flux. This method is more accurate and reliable and can lead to better results.

The tool is still under development and further improvements, such as considering

different geometries for the cooling channels, will be implemented. The activity

undertaken and the results obtained will surely support future developments within

the CDF project.

- 113 -

Appendix A – Supercritical Fluida s Coolant in LRE

The design of regenerative cooled wall structures of cryogenic thrust chambers is

still a challenging problem for the rocket engineer. Moreover, the use of the methane

as coolant presents some difficulties since transcritical fluid dynamics operating

conditions occur in the cooling channels differently from the case of liquid hydrogen

for which the typical thermodynamic state is supercritical (see Figure 75). In

particular, methane enters in supercritical conditions into the cooling channels, as it

is heated temperature raises passing throught the critical value (Tc = 190.53 K),

while the pressure remains over the critical value (Pc=46 bar), therefore transicritical

conditions occurs.

Figure 75: H2 and CH4 cooling channel operational condition, on a typical reduced

pressure-temperature state diagram.

Transcritical conditions cause large fluid properties variation that strongly influences

the coolant performance.In particular, thermodynamic varialbles (specific heat,

thermal conductivity, viscosity, etc) strongly change with temperature. Figure 76

reports Specific heat and thermal conductivity as function of tenmperature for

- 114 -

pressure equal to 6.0 MPa, it is clear the strong variation arout the critical

temperature.

Figure 76 Specific heat and thermal conductivity as function of tenmperature; P=6.0 MPa

In particular, in transcritical conditions the heat flux from the lower part of a classic

rectangular high aspect ratio cooling channel cannot diffuse in the upper part causing

a sort of thermal barrier as a consequence of the strong variation of the specific heat.

- 115 -

References

[1] Sutton G., P., “Rocket Propulsion Elements”, John Wiley & Sons, Inc., 7th

Edition, 2001.

[2] CIRA., “Concurrent Design Facility Detailed Design Justification File”.

[3] Mustafa Emre Boysan., Abdullah ULAS., “Analysis of regenerative cooling

in liquid propellant rocket engine”, The Graduate School of Natural and

Applied Sciences of Middle East Technical University, 2008.

[4] R.R.L. Ernst., B.T.C. Zandbergen., “Liquid Rocket analysis (LiRA),

Development of a Liquid Bi-Propellant Rocket Engine Design, Analysis and

Optimization Tool”, Delft University of Technology, AE5810 Master of

Science Thesis, 2014.

[5] Huzel, D., K., Huang, D., H., “Modern Engineering for Design Liquid-

Propellant Rocket Engines”, AIAA,1992.

[6] S. Borrelli., P. De Matteis., F. Ferrigno., A. Schettino., E. D’Aversa., M.

Biagioni., IAC-12-C4.1.1 x14994, “The Hyprob program: mastering key

technologies, design and testing capabilities for space transportation rocket

propulsion evolution”, 63rd International Astronautical Congress, Naples,

Italy, 2012.

[7] Jeffrey L. Smith., “Concurrent Engineering in the Jet Propulsion Laboratory

Project Design Center”. 98AMTC-83.

[8] Dajun Xu., Cees Bil., Guobiao Cai., “Overview of the Development of

Concurrent Design Facility”, School of Astronautics, Beihang University,

Beijing, China School of Aerospace, Mechanical and Manufacturing

Engineering, RMIT University, Melbourne, Australia, 20th ISPE

International Conference on Concurrent Engineering, 2013.

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