Optical Analysis of the Hydrogen Cooling Film in High Pressure Combustion Chambers

(1)

Film in High Pressure Combustion Chambers

Fabian Weber

Space Engineering, master's level (120 credits) 2019

Luleå University of Technology

Department of Computer Science, Electrical and Space Engineering

(2)

at Luleå University of Technology

Optical Analysis of the Hydrogen Cooling Film in High Pressure Combustion Chambers

Examiner: Dr. Victoria Barabash

Department of Computer Science, Electrical and Space Engineering

Luleå University of Technology

Supervisor: Dipl. Ing. Georg Kühlwein Department of Rocket Propulsion

Deutsches Zentrum für Luft- und Raumfahrt e. V.

Study Programme: M.Sc. Spacecraft Design

Author: Fabian Weber

Submitted: 1^stNovember 2019

(3)

Abstract

For performance optimisation of modern liquid cryogenic bipropellant rocket combustion chambers, one component which plays an important role in reducing the wall side heat flux, is the behaviour of the cooling film. At the Institute of Space Propulsion of the German Aerospace Center (DLR) in Lampoldshausen, hot test runs have been performed using the experimental combustion chamber BKM, to investigate the wall side heat flux which is – among other factors – dependent on cooling film properties. To gain more insight into the film behaviour under real rocket-like conditions, optical diagnostics have been applied. The chosen methods were shadowgraphy and OH* imaging producing optical data sets which are analysed in this study. In this context, a description of the necessary background information is given, concerning rocket combustion chambers, film cooling and optical diagnostics of O2/H2 combustion. The applied methodology for optical analysis is described, followed by a presentation of the results. During the test campaign, it became clear that the optical setup was not optimised for creating mean- ingful shadowgraphy recordings which is why the shadowgraphy data has to be treated as flame emission imaging.

The behaviour of the gas layer adjacent to the chamber wall could be characterised based on qualitative (luminosity, LOx shadow, reflection, recirculation zone and flame shape) and quantitative (layer thickness, layer length, pressure conditions) analysis. The thickness could be identified for each load step and an average length of the layer was found as well. OH* imaging has been used supplementary to support the observations from the flame emission images. An in depth frame by frame analysis was not possible due to time constraints. However, the time averaged images yielded results in accordance to the flame emission and could give a relative figure for the temperature distribution in the combustion volume. An artefact in the data was found, stemming presumably from the image intensifier. This artefact needs to be researched for a future error reduction in the data of this and other campaigns. Additionally, the thickness of the layer suggested a correlation to the models for film cooling efficiency. Such a correlation could not be established. Nevertheless, the film cooling models show the same behaviour as the data obtained from the flame emission imaging. Finally, suggestions are given how the data analysis and the optical setup could be improved for future, similar campaigns.

(4)

List of Figures

1.1 RD-180 Test Firing . . . . 1

2.1 Experimental Thrust Chamber . . . . 5

2.2 Phase Diagram of O₂ . . . . 7

2.3 Core Structure under Varying Chamber Pressures . . . . 8

2.4 Heat Flux in a Combustion Chamber . . . . 9

2.5 Tubular Cooling Jacket Diagram . . . . 10

2.6 Area of Application for Different Cooling Techniques . . . . 11

2.7 Tangential Cooling Film Injection . . . . 12

2.8 Velocity and Temperature Profiles for Cooling Film Injection and Mixing . . . . . 13

2.9 O₂/H₂Flame Spectrum . . . . 17

2.10 Chemically vs. Thermally Excited OH* . . . . 18

2.11 Blue Radiation of the SSME . . . . 19

2.12 Pressure Dependency of Blue Radiation . . . . 20

2.13 Ray Deflection through Inhomogeneous Medium . . . . 22

2.14 Typical OH* Image . . . . 22

2.15 Setup for Shadowgraphy . . . . 23

2.16 Example Shadowgraph of LOx . . . . 24

2.17 Imaginary Flame Emission Spectrum . . . . 24

3.1 Test Bench P8 . . . . 26

3.2 Brennkammer M Combustion Volume and Optical Access . . . . 27

3.3 Brennkammer M Combustion Volume Side View . . . . 27

3.4 Face Plate of Brennkammer M and E . . . . 28

3.5 Test Sequence . . . . 29

3.6 Optical Test Setup . . . . 30

3.7 Flame Emission Example Image . . . . 31

3.8 Flame Emission Image Characteristics . . . . 31

3.9 OH* Example Image . . . . 32

3.10 Recorded OH* Intensity Fluctuation . . . . 32

3.11 Histogram and Mean Image of Flame Emission Imaging Trigger 2 . . . . 34

3.12 Histogram and Mean Image of Flame Emission Imaging Trigger 9 . . . . 35

3.13 Visualisation of Workflow for Flame Emission Images . . . . 36

3.14 Visualisation of Workflow for OH* Images . . . . 38

3.15 Comparison of OH* Mean Images . . . . 40

3.16 Comparison of Colour Maps . . . . 40

4.1 Features of Flame Emission Mean Image Trigger 2 . . . . 42

4.2 Mean Flame Emission Images for all Triggers . . . . 43

4.3 Enlarged NIR with Reflections for all Triggers . . . . 44

4.4 CFD of Recirculation Zone . . . . 45

4.5 Thermally Weakened SSME . . . . 45

4.6 Comparison of Threshold Values . . . . 46

4.7 Pressure Dependency of WAL Thickness . . . . 47

(7)

4.8 Pressure Conditions in the NIR . . . . 49

4.9 WAL Thickness Variation with Mass Flow . . . . 50

4.10 Mean Images with Indicated WAL Thickness . . . . 51

4.11 WAL Length Distribution for Trigger 2 and 5 . . . . 52

4.12 Features of OH* Mean Image Trigger 1 . . . . 53

4.13 Mean OH* Images for all Triggers . . . . 55

4.14 Modelled Film Efficiency for all Load Steps . . . . 56

5.1 Preliminary Design of Experimental Combustion Chamber . . . . 59

6.1 Correction Factor for Intensity Correction . . . . 64

A.1 WAL Length per Frame for Triggers 2 and 3 . . . . 72

A.2 WAL Length per Frame for Triggers 4 to 6 . . . . 73

A.7 Modelled Film Efficiency with Extended x Axis for all Load Steps . . . . 78

(8)

List of Tables

2.1 Theoretical Performance of Liquid Fuels in Combination with LOx . . . . 6

2.2 Critical Conditions for O₂and H₂ . . . . 8

3.1 Combustion Conditions per Trigger . . . . 29

4.1 Pressure Condition in the NIR and Blowing Rates . . . . 48

4.2 Average WAL Length Values . . . . 51

(9)

Abbreviations

BKE Brennkammer E BKM Brennkammer M BPP Bits per Pixel

CCD Charged Coupled Device CFD Computational Fluid Dynamics

DLR Deutsches Zentrum für Luft- und Raumfahrt e. V.

FWHM Full Width Half Maximum GH₂ Gaseous Hydrogen

GLV Grey Level Value IR Infrared Radiation LH₂ Liquid Hydrogen LOx Liquid Oxygen NIR Near Injector Region OH* Excited Hydroxyl Radical SSME Space Shuttle Main Engine UV Ultraviolet

WAL Wall Adjacent Layer

(10)

Symbols

Sign Description Unit

A_e Area, exit m²

A_t Area, throat m²

C Correction factor –

E_ph Energy, photon eV

F Thrust N

I₀ Intensity, original –

I_R Intensity, recorded –

I_sp Specific impulse s

K Gladstone-Dale constant cm³g⁻¹

L Characteristic dimension m

M Blowing or injection rate –

Pr Prandtl number –

R Ideal gas constant, 8.314 462 618 J K⁻¹mol⁻¹

ROF Ratio of oxidiser to fuel –

Re Reynolds number –

T Temperature K

T Time, total s

T_ad Temperature, adiabatic K

T_cc Temperature, combustion chamber or hot gas K

T_crit Temperature, critical K

T_F Temperature, cooling film K

T_w Temperature, wall or without film cooling K

T_w,F Temperature, wall with film cooling K

Th Threshold value for binarisation %

V_m Volume, molar m³mol⁻¹

V_m,crit Volume, molar critical m³mol⁻¹

c Speed of light, 299 792 458 m s⁻¹

c_p Specific heat capacity J kg⁻¹K⁻¹

c_p,F Specific heat capacity, cooling film J kg⁻¹K⁻¹ c_p,cc Specific heat capacity, hot gas J kg⁻¹K⁻¹

d Thickness m

d_WAL Thickness, wall adjacent layer mm

g₀ Earth’s standard gravity, 9.81 m s⁻²

h Planck constant eV s

k Thermal conductivity W K⁻¹m⁻¹

l Distance m

˙

m Mass flow rate kg s⁻¹

˙

m_F Mass flow rate, cooling film kg s⁻¹

n_mol Amount of substance mol

n_{re f} Refractive index –

p Pressure bar

p_a Pressure, ambient bar

(11)

Sign Description Unit

p_cc Pressure, combustion chamber bar

p_crit Pressure, critical bar

p_dyn Pressure, dynamic bar

p_e Pressure, exit bar

p_stat Pressure, static bar

p_tot Pressure, total bar

˙

q Heat flux W m⁻²

s Light ray arc length m

s Injection slot height m

v Velocity m s⁻¹

v_F Velocity, cooling film m s⁻¹

v_cc Velocity, hot gas m s⁻¹

v_e Velocity, effective m s⁻¹

x Length of cooling film m

Θ Film cooling efficiency for thrust chambers –

α Heat transfer coefficient W m⁻²K⁻¹

β Deflection angle ^◦

η Film cooling efficiency –

κ Isentropic expansion factor –

λ Wavelength m

µcc Viscosity, hot gas Pa s

ν_kin Kinematic viscosity m²s⁻¹

ρ Density kg m⁻³

(12)

1 Introduction

As an introduction to the thesis’ topic a context is given for the reader in Section 1.1. The research goal and how it is tackled by the research questions is described in the next section (Sec. 1.2) followed by a thesis outline summarising the content of the document in Section 1.3.

1.1 Context

One of the most important and limiting factors in space mission design is the mass of the payload. The feasibility of a mission is therefore directly dependent on the launcher’s ability to carry this mass into space. On the other hand, the payload capacity of a rocket is relative to its engine’s performance, which therefore, is crucial to be optimised in any possible way. This means higher efficiency, higher thrust, sustainability, reusability and reliability whereas, at the same time, production costs need to be reduced.

Compared to the early stages of rocketry after World War II (e. g. Aggregat 4 with a chamber pressure of 15.5 bar), huge progress in engine development has been made until today. Steadily rising pressures of up to 257 bar, as featured by the Russian RD-180 (Fig. 1.1), and gas temperatures as high as 3600 K ensure increasing thrust but also create heat transfer rates of over 160 MW m⁻² [1, 9, 21]. Those conditions impose thermal and structural loads on the engines, pushing the limits of the incorporated materials in use. Therefore, the application of optimised high temperature resistant materials, novel manufacturing methods like additive engineering, and implementation of effective cooling techniques is necessary [37].

Figure 1.1: Test firing of the RD-180 after National Aeronautics and Space Administration [33].

Film cooling is one way to protect the materials from direct heat transfer. A thin cooling film, usually consistent of the fuel used for the combustion, injected and guided alongside the chamber walls, can create a temperature difference between hot gas and wall of about 2300 K [21, 46].

Since an implementation like this is always connected to a loss in engine efficiency, the cooling film needs to be accurately adjusted to maximise the engine’s performance [21]. In that sense,

(13)

the research about the efficiency of the cooling film is a key component in the optimisation of rocket combustion chambers, to design future-proof and competitive propulsion units.

1.2 Research Goal

One research goal of the work conducted on the experimental combustion chamber Brennkam- mer M (BKM), being the subject of this thesis project, is to optically investigate and characterise the behaviour and properties of the cooling film and how it impacts the wall side heat transfer from the hot combustion gases.

The research about cooling film efficiency and properties is a wide and complex area and the relevant aspects which are treated in this study are represented by several research questions which tackle facets of the research goal. The questions are broken down into sub-questions as this eases answering and shows relevant aspects of the research work.

1. Which qualitative and quantitative observations can be made by means of the optical setup in this study to characterise the cooling film?

• What are the dimensions of the cooling film or wall adjacent layer?

• How does the cooling film or wall adjacent layer behave under various chamber operation conditions?

2. In what way can the H₂cooling film in high pressure cryogenic liquid bipropellant rocket combustion chambers be studied most effectively by means of optical diagnostics?

• What are the benefits and drawbacks of the chosen optical setup?

• What are possible improvements to the setup?

• Are there more suitable optical investigation techniques for optical analysis of the cooling film?

• Are there any ’gaps’ which could be covered by other optical investigation techniques and which allow an unambiguous interpretation of the data possible?

• Is there a cooling film fluid which is more suitable for optical diagnostics?

3. Is there a correlation between the cooling film thickness as obtained from the optical data to the film cooling efficiency as theoretically proposed by models?

The goal of this study is to answer the research questions and their sub-questions. An as- sessment on how well and in which scale the obtained results are able to answer the research questions is presented in Chapter 5.

1.3 Thesis Outline

The content of the thesis and how it is structured follows the idea to introduce the reader to the topic and subsequent elaboration on the research which is conducted in this study. Therefore, Section 1.1 gives a context for the topic and helps to understand the aim of the study as stated in Section 1.2.

In the following, the background knowledge which is needed to tackle the research topic is pro- vided (Chap. 2). An introduction to liquid rocket combustion chambers, liquid propellants and

(14)

combustion conditions inside a combustion chamber is given. These conditions are more elaborated on (chamber pressure, critical point, thermal regime) to prepare the next section about cooling techniques for combustion chambers. Since the focus lies on film cooling, this method is subsequently explained in detail. This leads to the definition of film cooling efficiency and how the efficiency can be modelled with various existing approaches. For studiyng the cooling film, optical diagnostics are chosen in this study. For this reason, an overview is given about the optical properties of O₂/H₂combustion concerning the flame spectrum, Excited Hydroxyl Radical (OH*) radiation, blue radiation and refractive indices. It is necessary to discuss these properties to understand the investigation techniques of OH* imaging and shadowgraphy or flame emission imaging respectively. To conclude this chapter, the conducted optical research of recent years on O2/H2combustion is summarised.

Chapter 3 describes how the test, which was used for data generation, was conducted, how the combustion chamber is structured and under what kind of conditions it has been operated. The optical test setup and its settings are depicted as well. In the following, the raw flame emission and OH* test results are presented. The image processing procedure is then described for both data sets including a justification for the interpretation and a step by step description of the applied methods to process the optical data. The chapter closes with a description of how the film cooling efficiency models have been generated for this combustion chamber.

The results obtained from the data as treated by the aforementioned methodology, are presented in Chapter 4. Beginning with the results of the flame emission recordings presenting the obtained time averaged images and according identifiable characteristics. Subsequently, the wall adjacent layer and cooling film thickness and length is evaluated with respect to combustion conditions. The captured OH* images are analysed in the following. The time averaged mea- surements for all load steps are given with a feature depiction and interpretation. Film cooling efficiency models are presented, compared, analysed and discussed. The models are also put into relation to the film cooling thickness.

If the results of the study are able to answer the stated research questions from Section 1.2 is assessed and discussed in Chapter 5.

Chapter 6 closes the thesis and offers conclusions from the thesis project, focusing on a summary of the conducted research and pointing out how future work on a similar experimental setup could be improved. Subsequently, it is discussed in what ways the data analysis could be supplemented to maximise the research output from this topic.

(15)

2 Background

In order to give a general understanding about the working principles of rocket combustion chambers and the optical diagnostics of flames and combustion processes, these topics are ex- amined in detail within Section 2.1 and 2.3. Since the optical diagnostics are focused on the investigation of a cooling film in this thesis, it is described in section 2.2. To close this chapter, a summary about the conducted research by means of optical diagnostics for rocket combustion is given in Section 2.4.

2.1 Rocket Combustion Chambers

Within this section, a principal description of rocket combustion chambers is followed by a more detailed explanation of liquid bipropellants (Section 2.1.1), combustion conditions (Sec- tion 2.1.2) such as chamber pressures, behaviour of propellants at the critical point and thermal conditions in thrust chambers i. e. rocket combustion chambers. A general overview about state of the art cooling techniques is given in Section 2.1.3.

In general, different kinds of rocket propulsion systems exist which can be mainly subdivided into chemical, nuclear and electric propulsion [46]. In this study, the focus lies on chemical rocket propulsion by concentrating on a liquid bipropellant system which has been used to generate the scientific data.

In a propulsion system, the combustion or thrust chamber is the part of the rocket engine where oxidiser and fuel are injected, mixed and subsequently burnt, in order to accelerate and eject the resultant hot gas at supersonic velocities. Such a chamber consists of one or several injectors to inject the propellants, the chamber itself to provide a space for combustion processes and usually a converging-diverging nozzle. An ignition system needs to be included as well if non- hypergolic, i. e. non-spontaneously igniting, propellants are used. For the first stage of a launch system, bipropellant thrust chambers are usually preferred. A depiction of an experimental thrust chamber with its components can be found in Figure 2.1. [46]

2.1.1 Liquid Bipropellants

Within the combustion chamber, thrust is generated by conversing the energy inherent to the propellant. After the injection, the liquid propellants atomise into droplets which are subsequently vaporised by the heat transfer of the surrounding hot gas and mixed prior to taking part in the combustion process. Within the generated combustion flow, further mixing and heating steadily increases the gaseous mass flow rate towards the converging nozzle and throat section.

The molecular hot gas mixture then passes through the throat at sonic velocity and is accelerated to super sonic velocities in the diverging part of the nozzle and nozzle extension before being ejected. [21]

Generally, the bipropellant consists of an oxidiser and a fuel, mixed in a specific ratio which is appropriately chosen to optimise the engine’s thrust. The mass flow rate ˙m of oxidiser and fuel are put into relation (Eq. 2.1) and is given the name Ratio of Oxidiser to Fuel or ROF.

(16)

Figure 2.1: The experimental combustion chamber BKD used for research of high frequency (HF) in- stabilities after Gröning et al. [18].

Modern Liquid Oxygen (LOx)/Liquid Hydrogen (LH2) main engines, like the Space Shuttle Main Engine (SSME) or RS-68 (Delta IV) are designed for ROF of 6. [1]. For the Vulcain 2 of the Ariane 5 the ROF is between 6.8 to 7.3 [1]. The propellants are injected as a liquid or in a supercritical state (Sec. 2.1.2.1). Oxidisers may be LOx, liquid fluorine, nitric acid, etc. and fuels can be hydrazine, LH₂, methane, Rocket Propellant-1 (RP-1) etc. as presented in Table 2.1. A further categorisation can be done by introducing the term of cryogenic propellants which are liquefied gases with boiling points of 16.15 K to 127.15 K at 1 atm where LOx and LH₂are the most commonly used. [21]

ROF =m˙_oxidiser

˙

m_{f uel} (2.1)

Nowadays, there are several combinations of oxidisers and fuels in use, of which a selection is presented in Table 2.1. Among these, the cryogenic oxygen-hydrogen propellant system delivers the highest Specific Impulse I_sp achievable by non-toxic propellants and its theoretical values lie between 386 s and 390 s. I_sp is an expression to measure how effectively the rocket engine converts the propellant mass into thrust. It is defined by Equation 2.2.

I_sp= RT

0 Fdt

g₀^R₀^Tmdt˙ (2.2)

The specific impulse I_spputs the total impulse in relation to the total mass flow rate ˙mover the burn time T , considering Earth’s standard gravitation g₀. Assuming that both thrust and mass flow rate are constant, Equation 2.2 becomes

I_sp= F

g₀m˙ (2.3)

yielding the I_sp given in seconds. It is a useful figure to compare the efficiency of different engines to each other.

(17)

Table 2.1: Theoretical Performance of Liquid Fuels in Combination with LOx from Sutton and Biblarz [46]

Fuel ROF Tcc[K] vcc[m s⁻¹] Isp[s]

Hydrazine 0.74 3285 1871 301

Hydrogen 3.40 2959 2428 386

Methane 3.20 3526 1835 296

RP-1 2.24 3571 1774 285

Since both oxidiser and fuel are cryogenic and therefore liquid, they are referred to as LOx and LH₂ respectively. This propellant system is used in several present space launch vehicles in either their main and/or upper stage engines, like the Ariane 5 (Vulcain and Vulcain 2 engine) and upcoming Ariane 6 (Vulcain 2.1) [5] or the Delta IV (RS-68A) [48] and Centaur upper stage (RL-10) [34]. LOx/LH₂ also powers the new version of the SSME (RS-25), being the main engine of the Space Launch System [35].

Being one of the relevant propellant combinations in use for launch vehicles, experimental combustion chambers use the propellant combination of oxygen and hydrogen as well, in order to generate results transferable to a wide selection of engines which are nowadays in use.

2.1.2 Combustion Conditions

This section deals with the combustion conditions inside a rocket thrust chamber. Mathematical relations for the thrust force are given in connection with the chamber pressure in the beginning of Section 2.1.2.1. Furthermore, the influence of pressure on the propellants is explained by taking the critical conditions into account. The thermal conditions are elaborated on, relating the heat flux to the chamber pressure in Section 2.1.2.2.

2.1.2.1 Chamber Pressure and Critical Point

The thrust force acting on a rocket is dictated by the law of conservation of momentum which takes into account the mass flow ˙m of the combustion gas and its effective velocity ve. The thrust can be represented by

F = ˙mv_e+ A_e(p_e− p_a) (2.4)

where F denotes the thrust force as the sum of ˙mtimes v_eand the product of the difference in exit p_e and ambient pressure p_aand the nozzle exit area A_e. [46].

Expanding Equation 2.4 leads to Equation 2.5. [46]

F= A_tp_cc v u u t

2κ² κ − 1

2

κ + 1

(κ+1)/(κ−1)"

1 − p_e p_cc

(κ−1)/κ#

+ A_e(p_e− p_a) (2.5)

Equation 2.5 shows that F is dependent on the area of the throat At, the isentropic expansion factor κ, the pressure at the nozzle exit p_e, the chamber pressure p_ccand the nozzle exit area A_e. The throat area A_tregulates the mass flow ˙mof the hot gas and is directly connected to p_cc. This implies that an increase in the throat area A_t decreases the chamber pressure p_cc and raises the

(18)

mass flow ˙m. Thus, increasing the I_sp (Eq. 2.3) of an engine with a set propellant combination is only possible by raising the chamber pressure p_cc. [46].

This relation is responsible for the development of rocket engines featuring ever rising chamber pressures. Therefore, modern launch vehicles with LOx/LH2 propulsion systems, like the SSME, usually are operated with chamber pressures of up to 200 bar [46]. [19]

Pressures of this extent affect the behaviour of the propelling fluids which leads to the term of the critical point. At the critical point, which is dependent on the substance (i. e. molar volume, V_m), its temperature T and pressure p, the thermodynamic properties of this substance change significantly.

Below the critical point, an equilibrium between the gaseous and liquid phase is possible. If the substance is in thermodynamic equilibrium, a surface tension between both phases is present.

Increasing the temperature and pressure to the level of the critical point of a substance, the difference in density between the liquid and gaseous phase vanishes to approach zero, as well as the surface tension which is why the formation of droplets is not observable anymore. So, a differentiation between the phases for a fluid being above the critical point is not possible.

Additionally, in the vicinity of the critical point, the isobaric specific heat capacity c_p rises to very high values, compared to standard conditions. Moreover, the enthalpy of vapourisation becomes non-existent. This also implies that a heat input into the fluid results in a very small change of temperature but in a drastic change of density. Such a fluid is called supercritical. As an example, the specific heat capacity c_pand critical point for O₂, in dependence of T and p, is presented in Figure 2.2. [19, 25]

Figure 2.2: Phase diagram showing cpof O2depending on T and p with indication of the critical point and transcritical injection of LOx after Hardi [19].

The critical temperature T_crit and critical molar volume V_m,crit of a substance can be determined by putting the conditions in Equation 2.6 into relation with the van der Waals equation of state (Eq. 2.7), where p is the pressure of the fluid, T the temperature, n_mol the amount of substance, Rthe ideal gas constant and a and b being constants for the individual fluid [30]. The van der Waals equation needs to be solved for p, derived accordingly to the equations in 2.6, set to zero and then the set of equations needs to be solved for T_crit and Vm,crit respectively. Substi-

(19)

tuting T_crit and Vm,crit into the van der Waals equation of state, the critical pressure p_crit can be obtained.

∂ p

∂V_m

T

= 0

∂²p

∂V_m²

T

= 0

(2.6)

p+an²_mol V_m²

(V_m− n_molb) = n_molRT (2.7)

Table 2.2 lists the critical conditions for oxygen and hydrogen.

Table 2.2: Critical conditions for O₂and H2from Hardi [19]

Substance pcrit Tcrit

O₂ 50.43 bar 154.59 K H₂ 12.93 bar 32.97 K

The change in the thermodynamic properties of a substance influences its interaction with other substances. Since two fluids are always part of bipropellant rocket combustion, the behaviour and interaction of the oxidiser and fuel varies under sub-, near- and supercritical conditions which affects the combustion process concerning core disintegration, atomisation, droplet life- times and mixing, as for example investigated by Sirignano [42] and Kuo [23]. Mayer et al.

[27] studied the injection, mixing and combustion processes in a rocket combustor under various pressures with different fluids. A depiction of how the chamber pressure influences the shape and behaviour of an injected jet is exemplarily shown in Figure 2.3 where liquid N₂ at 105 K is injected into gaseous N2at 300 K and various pressures.

Figure 2.3: Core structure of liquid N2injected into gaseous N2under chamber pressures of 20 bar (left, subcritical), 30 bar (middle, 4 bar below the critical point) and 40 bar (right, supercritical) from Mayer et al. [27].

Since the thermodynamic properties of a fluid differ drastically above the critical point, it is important to keep the fluid regime in mind while conducting studies of combustion processes

(20)

[23, 27, 43]. For this study, BKM was fired under sub-, near- and supercritical conditions to cover a broad range of possible observations and apply conditions close to industrially used rocket engines.

2.1.2.2 Thermal Conditions

The development of new engines aims at maximising the thrust while keeping the engine as small as possible. The only way to reach this goal is to increase the chamber pressure, since it is directly connected to the performance (Sec. 2.1.2.1 and Eq. 2.4, 2.5). On the other hand, a steady increase in the chamber pressure pcc means that the thermal loads imposed by the hot gas rise almost linearly as well. This relation after Bartz [2] is shown in Equation 2.8 where ˙q, which is defined as well, describes the heat flux from the hot gas into the chamber wall, α is the heat transfer coefficient and T denotes the temperature. pccis the chamber pressure.

˙

q= α(T1− T₂)

˙

q ∝ p_cc^0.8 (2.8)

Thus, combustion processes within a thrust chamber create heat environments with hot gas temperatures of about 2500 K to above 3800 K and heat fluxes of 0.5 MW m⁻²to 160 MW m⁻², depending on size, measurement position and combustion conditions like chamber pressure etc.

The surfaces exposed to the hot gas are the injector face, the internal wall of the combustion chamber and the nozzle, whereby the region shortly before the throat always receives the highest heat input and the end of the diverging nozzle the lowest (Fig. 2.4). The fraction of heat, which is received by the chamber wall, is of about 0.5 % to 5 % of the total generated heat. A typical axial wall side heat flux distribution for an engine like the Vulcain 2 is presented in Figure 2.4.

Using p_cc= 115 bar and ROF = 7, ˙qreaches almost 100 MW m⁻². [1, 46]

Figure 2.4: Axial distribution of the wall side heat flux in a Vulcain 2-like combustion chamber after Arnold[1].

Most of this energy is transferred by convection [39] and an amount in the order of 5% to 35% can be accounted to radiation. This difference in the radiative contribution is accounted

(21)

to the relationship between chamber radius to volume and chamber radius to surface area. In applications where oxygen and hydrogen are used as propellants, the radiative contribution to the wall side heat flux can usually be neglected [1]. The influence of conduction can be neglected as well, due to the high velocity of the hot gas. [46]

2.1.3 Cooling Techniques

Since the occurring temperatures in rocket combustion processes lie well above the melting point of the structural elements of the thrust chamber (Sec. 2.1.2.2), it is necessary to introduce cooling techniques which minimise the heat loads to such a degree, that structural failure of the combustion chamber is prevented. The cooling technique needs to be chosen depending on the type of engine and performance requirements. There are several techniques which proved to be effective, being of either passive or active nature. A classification is done according to Huzel [21]. [21, 46]

• Regenerative cooling. This is the most commonly used solution, feeding a cooling liquid or coolant, usually the fuel, through cavities in the metallic rocket engine components which are in contact with the hot combustion gases. Those components are namely the injector faces, chamber wall and the wall of the nozzle. The accommodation of the coolant cavities can be realised in different ways, for example an inner and outer wall where the coolant flows between them or tubes which pervade the engine walls in a parallel manner and allow an axial flow of the cooling liquid with respect to the hot gas. Since the heat transfer profile from the hot gas to the walls changes axially, as schematically shown in Figure 2.4, the amount of coolant needed in specific areas of the engine varies. Those variations can be tackled by changing the cross sectional area of the cooling channels, increasing the speed of the coolant where a higher heat transfer is present, as for example in the throat area. This approach is presented in Figure 2.5 where the coolant enters at the inlet manifold into every second tube and passes axially through cooling jackets to the exit manifold, guiding it back into the injector through every other tube. It is also possible to inject fresh, cold fuel at the throat area. A variation of the regenerative cooling technique is dump cooling where a small percentage of the fuel mass flow can be used to be fed through cavities inside the chamber wall through the nozzle skirt to cool the structural elements. Yet, here the cooling fluid is subsequently dumped through openings in the nozzle extension and not reused as for purely regenerative cooling. Since this technique implies a loss in fuel mass flow, it has limited application.

Figure 2.5: Diagram of a tubular cooling jacket from Sutton and Biblarz [46].

• Film cooling. Another technique which works by means of a cooling liquid. The coolant is injected through orifices at the circumference of the injector face or in planes closer

(22)

to the throat area, to create a cool gas film that protects for example the chamber wall from the hot gas and decreases the heat transfer rates. Film cooling can be supplementary combined with other cooling techniques such as regenerative cooling – as implemented in Vulcain 2 or SSME [1] – to achieve higher cooling capacities. This technique is described in detail in Section 2.2.

• Transpiration cooling. Similar to film cooling, a gas or liquid is fed through the porous chamber walls into the chamber to keep the chamber walls at adequate temperatures.

• Ablative cooling. This technique makes use of the chemical changes of materials when exposed to thermal energy, such as melting, vaporisation or pyrolysis of organic materials to absorb heat. The ablative material, composed of resistant and oriented fibres (for example glass, Kevlar or carbon fibres) and organic binding matter (like plastics, epoxy resins or phenolic resins) forms a thin cooling layer upon heat induced decomposition due to outgassing of the consumed binder. The outgassed binder in return protects the wall of the thrust chamber against the thermal loads of the hot gas. An engine using this method is the Viking engine [1].

• Radiation cooling. It is usually utilised in low heat transfer applications and to small combustion chambers or thrusters. Here, the nozzle and chamber wall act as radiator.

High temperature materials have to be employed. It can be used in low heat flux regions, like the nozzle extension.

To coarsely categorise the application area of different cooling methods, the generated wall side heat flux ˙qof the rocket engine can be used. Figure 2.6 shows the application range of different cooling techniques and the proportional relation between ˙qand p_cc(Eq. 2.8).

Figure 2.6: Area of application for different cooling techniques dependent on chamber pressure pccand heat flux ˙qafter Arnold [1].

2.2 Film Cooling

Considering the high heat transfer rates in thrust chambers, it is sometimes necessary to improve the cooling capabilities of an engine. Usually, film cooling is implemented as a supplement for regeneratively cooled high pressure combustion chambers. To create a cooling film in the thrust chamber, a comparably cool fluid is injected along the walls of the chamber either through orifices or slots forming a cooler boundary layer. This boundary layer separates the hot gas flow spatially from the chamber wall and decreases the amount of energy which is transferred into the wall. Another benefit is that the gas layer protects the chamber wall from oxidation reactions

(23)

and increases its lifetime. The injection of the cooling fluid which usually is supercritical H₂ is realised via orifices or slots in an either tangential or slanted manner. Exemplarily, Figure 2.7 shows one method of how a boundary layer alongside a chamber wall can be created. The cooling film is injected tangentially, propagates in x direction and is non-uniformly distributed with respect to the z axis. In the following, only tangential injection is considered. Compared to a non-uniform injection, an uniform injection is preferred since it provides uniform cooling and heat transfer rates, thus increasing the lifetime of the engine. Yet, due to structural or technical limitations, an uniform implementation is not always possible. [1, 16, 46]

Figure 2.7: Tangential injection of a cooling film by means of several injection slots after Arnold [1].

Mostly, the fuel is used as cooling fluid. Since the fuel supply in space propulsion is limited, a trade off between cooling film efficiency and cooling film mass flow needs to be made in order to avoid a waste of fuel. Modern rocket engines use 0.5% to 5% of the total propellant mass flow for film cooling purposes, whereby the loss in performance is about 0.5% to 2%. For comparison, the first combustion chambers from the 1920s, built by Robert H. Goddard, were also film cooled but therefore forfeited I_spin the range of 5% to 17%. [1, 46]

In the following, an overview about the efficiency of film cooling and its definition, in general and for rocket applications, is given (Sec. 2.2.1). Subsequently, the two dimensional film layer efficiency modelling is described in Section 2.2.2.

2.2.1 Film cooling Efficiency

The film layer is able to provide maximum cooling to the chamber wall where it is injected.

Further downstream, the cooling ability decreases gradually until the film has completely mixed with the hot gas. Turbulent flow in the hot gas and ongoing chemical reactions, in combination with an acceleration of the flow due to steady energy input, are the fluid mechanical reasons for the gradual decrease in the cooling film’s efficiency. [1]

The gradual change in the temperature of the film T_F, the hot gas T_ccand their velocities v_F, v_cc is depicted in Figure 2.8. Typical profiles for temperature and velocity are shown, which can be subdivided into three zones:

• Core zone. The hot gas and cooling film are spatially separated and the cooling film has maximum efficiency.

• Mixing zone. The hot gas mixes with the cool fluid film and the efficiency of the cooling layer decreases with increasing film length.

• Boundary layer flow. The mixing between both fluids is complete. Together they form the boundary layer of the hot gas flow.

(24)

Figure 2.8: Velocity v and temperature T profiles for a tangentially injected cooling film after Arnold [1].

To quantify the efficiency of the cooling film and give a figure to ease the comparison between different film cooling methods, the adiabatic dimensionless film cooling efficiency η is used.

η sets the difference in the adiabatic wall temperature T_ad and the hot gas temperature T_cc into relation with the maximum temperature difference between film cooling fluid at injection T_F (temperature in the proximity of the injection slot) and the hot gas temperature T_cc. It is defined in Equation 2.9. [16]

η = T_ad− T_cc

T_F− T_cc (2.9)

Per definition, η = 1 at the point where the cooling film is injected which means that T_ad = T_F. Downstream, at the point where the cooling film got mixed with the hot gas and therefore T_ad = T_cc, the efficiency η is equal to 0.

In a high pressure combustion chamber, the adiabatic wall temperature is well above the melting point of the wall material (Sec. 2.1.2). Therefore, cooling techniques are applied to the thrust chamber (Sec. 2.1.3). Usually, film cooling by itself is not sufficient and combined with regenerative cooling. Since a cooling of the chamber wall implies a non-adiabatic situation, an enhanced definition of the cooling film efficiency for rocket combustion chambers needs to be done. For this reason, Arnold [1] proposed the dimensionless temperature relation Θ (Eq.

2.10) which is not related to the adiabatic wall temperature T_ad but to the local wall temperature without film cooling T_w, the local wall temperature with film cooling Tw,F and the injection temperature of the coolant T_F which can be understood as the temperature in the proximity of the injection slot. [1]

Θ = T_w(x) − T_w,F(x)

T_w(x) − T_F(x) (2.10)

The efficiency Θ equals 1 in case that Tw,F = T_F and Θ = 0 for Tw,F = T_w. If the chamber wall is cooled regeneratively or in a similar manner, the chamber wall can be assumed to be in a quasi-adiabatic condition. This is due to the fact that the absorbed heat by the cooling film is small compared to the heat absorbed by the cooling medium inside the chamber wall cavities.

Therefore,

η −→ Θ (2.11)

holds true for the models which are presented in the following. [1]

(25)

2.2.2 Modelling of Film Cooling Efficiency

Several mathematical models with different approaches have been proposed to quantify the film efficiency for a wide range of applications in two dimensions. Those models are based on em- pirically found correlations. The modelling goal is to express the downstream adiabatic wall temperature by means of the efficiency η according to Equation 2.9. In the case of rocket combustion chambers, Θ (Eq. 2.10) is needed to characterise the efficiency. However, as explained in Section 2.2.1, it is valid to put η = Θ.

The existing models can be categorised into heat sink models [6, 17, 24] and flow models. Heat sink models assume an instantaneous mixing of hot gas and cooling film fluids at the injection slot whereas flow models are based on the idea that no mixing between the hot gas and film takes place and both layers coexist downstream. Generally, both approaches are therefore faulty to a certain degree. The flow model provides an accurate description in the immediate vicinity of the injection slot i. e. the core zone in Figure 2.8 but due to the complete turbulent nature of the gas flow in thrust chambers, the flow model is not applicable to rocket engines [1]. This makes the heat sink model the preferred modelling method. Existing combined models as the one by Spalding[44] try to fuse the flow model approach with the heat sink model idea. [1]

In the next sections, the basic mathematical figures, which are used in the models, are explained, followed by a presentation of a few heat sink models and a combined model which are expected to show a satisfactory correlation between experimental and theoretical results. Those models were developed by Arnold [1], Goldstein and Haji-Sheikh [17], Kutateladze and Leontev [24]

and Spalding [44]. In a similar study by Arnold [1] it has been shown that these models deliver results which are comparable to data from rocket combustion film layer experiments. Since BKM and Brennkammer E (BKE) are similar in structure and combustion conditions the focus for modelling the efficiency lies on the models developed by Arnold [1] and Goldstein and Haji-Sheikh [17]. The models by Kutateladze and Leontev [24] and Spalding [44] serve as context.

2.2.2.1 Mathematical Figures

To quantify the heat transfer in rocket combustion chambers and set up representative and comparable models, basic mathematical figures and model related factors are used. An overview is given in the following.

• Reynolds number Re. The dimensionless Reynolds number is used to predict flow patterns using a relation between inertia to viscosity for a fluid. A high Reynolds number results in turbulent flow patterns whereas low numbers predict a laminar flow of a fluid.

Re= vL

ν_kin (2.12)

v is the fluid velocity with respect to the object and L the characteristic linear dimension, for example the diameter of the pipe where the fluid flows in. ν_kin is the kinematic viscosity. [53]

• Prandtl number Pr. The dimensionless Prandtl number is described as follows.

Pr= ν_kinρ cp

k (2.13)

It relates the fluid’s heat dissipation to the heat conduction and is an important figure to investigate and put heat convection processes into perspective. ρ is the density of the fluid, c_pits specific heat capacity and k the thermal conductivity. [53]

Optical Analysis of the Hydrogen Cooling Film in High Pressure Combustion Chambers

Film in High Pressure Combustion Chambers

Fabian Weber

Optical Analysis of the Hydrogen Cooling Film in High Pressure Combustion Chambers

Table of Contents

List of Figures

List of Tables

Abbreviations

Symbols

1 Introduction

2 Background