The Inlet Passageway Optimization Research of Intermediate Heat Exchanger in HTGR

MASTER THESIS, DUAL DIPLOMA PROGRAM ADVANCED LEVEL, 30 ECTS

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STOCKHOLM BEIJING, 2018

The I nlet P assageway optimization research of I ntermediate Heat Ex changer in HTGR

Jingdan Cui

KTH School of Science

TSINGHUA UNIVERSITY KTH-ROYAL INSTITUTE OF TECHNOLOGY

The Inlet Passageway optimization research of Intermediate Heat Exchanger in HTGR

Jingdan Cui

Thesis Submitted to

Tsinghua University KTH Royal Institute of Technology In partial fulfilment of the requirement

for the degree of Master of Science

In

Nuclear Science and Technology

In partial fulfilment of the requirement for the degree of

Master of Science In

Engineering Physics

Co-supervisor: Associate Professor Yuan Kun

Co-supervisor: Lecturer Weimin Ma

Tsinghua University/Institute of Nuclear and New Energy Technology

KTH Royal Institute of technology/Nuclear Safety

UNDER THE COOPERATION AGREEMENT ON DUAL MASTER’S DEGREE PROGRAM IN NUCLEAR ENERGY RELATED DISCIPLINES

JUNE 2018

Sammanfattning

Sammanfattning

Mellanvärmeväxlaren är nyckelfunktionen för att realisera värmeutnyttjande och väteproduktion i en Gaskyld Reaktor med Väldigt Hög Temperatur. Det finns en 90-graders riktningsändring i inflödet av den mellanliggande värmeväxlaren. Denna struktur resulterar i ojämn fördelning av flödet och har ett negativt inflytande på den övergripande värmeväxlingseffektiviteten hos värmeväxlaren medan den bidrar till olika åldringsproblem. Det är därför nödvändigt att optimera inloppspassagen för den mellanliggande värmeväxlaren.

Eftersom spiralknippet i mellanvärmeväxlaren skulle ha kopplingseffekt på heliumflödet i passage, och att simulera den tredimensionella strukturen direkt kommer att ha svårigheter att modellera komplexa strukturer och hantera stor mängd beräkning, tillämpade detta papper ett snabbt tillvägagångssätt: behandla värmeväxlingsområdet som det porösa mediet, vilket kraftigt minskar beräkningsbeloppet. Beräkningsresultaten visar att denna förenklingsmetod är ett praktiskt och effektivt tillvägagångssätt. Denna metod kan fullständigt överväga kopplingseffekten av värmeöverföringsrörets mittvärmeutbytesområde på gasflödet i inloppsflödespassagen. På grund av kopplingseffekten blir fördelningen av heliumflödet i omkretsriktningen mer enhetlig, och ju större inloppsflödet är desto mer uppenbar blir kopplingseffekten.

Baserat på ovanstående beräkningsplan föreslås i detta dokument fem optimeringsmodeller av inloppspasseringen. De är installationen av luftdistributörer, styrskovlar, gallerplattor, respektive stympade konplattor och bågformad passage. Från beräkningsresultatet är det konstaterat att distributörens omfördelningsförmåga är bäst bland alla konstruktioner, och den har en hög potential till att ytterligare förbättra sin fluidfördelningsprestanda. Baserat på denna slutsats optimerades designen av distributören ytterligare genom att ändra parametrar så som flödesarea, distributörens höjd och installationsplatsen. Beräkningsresultatet visar att installationen av distributören i ett lägre läge inte kunde nå målet att omfördela helium jämnt. Medan konstruktionen att hålla luftdelarens nedre kant något högre än inloppspassagens nedre kant uppvisar en enastående omfördelningsförmåga, i vilket fall heliumflödet inte deltar i det ringformiga flödet, strömmar det annars direkt ut av luftfördelaren. Mekanismen bakom är att flöden som deltar i omkretsflödet och heliumet som strömmar ut direkt kan blandas bättre vid luftdistributörens utlopp, eliminera korsströmhastighetskomponenten och öka enhetligheten av fördelningen. Byte av flödesområde kan påverka flödet och styrkan i flödet som strömmar ut direkt. Beräkningsresultaten visar att flödesfördelningen med mindre flödesarea och installerad i den högre positionen bättre kan förbättra omfördelningsprestandan och minska hastighetsavvikelseindexet för utflödet med 68.6%.

Nyckelord: Gaskyld reaktor med hög temperatur; mellanvärmeväxlare; inloppspassage;

Sammanfattning

optimeringsdesign.

Abstract

Abstract

The intermediate heat exchanger is the key equipment to realize heat utilization and hydrogen production in Very High-Temperature Gas-Cooled Reactor (VHTR). There is a 90-degree direction change in the inlet flow of the intermediate heat exchanger. This structure results in the uneven distribution of the flow and has an adverse influence on the overall heat exchange efficiency of the intermediate heat exchanger meanwhile it contributes to the different aging problem. Therefore, it is necessary to optimize the inlet passageway of the intermediate heat exchanger.

As the spiral bundle of intermediate heat exchanger would have coupling effect on the helium flow in the passageway, and to simulate the three-dimensional structure directly will have difficulty in modeling complex structure and handling large amount of calculation, this paper applied a quick approach, treating the heat exchange area as the porous media, which greatly reduces the calculation amount. The calculation results show that the simplification method is a practical and effective approach. This method can fully consider the coupling effect of the middle heat exchange heat transfer tube area on the gas flow in the inlet flow passageway. Due to the coupling effect, the distribution of the helium flow in the circumferential direction becomes more uniform, and greater the inlet flow rate is, the more obvious coupling effect becomes.

Based on above calculation scheme, five inlet passageway optimization models are

proposed in this paper. They are the installation of air distributors, guide vanes, grid plates,

reversed truncated cone plates and arc-shaped passageway respectively. From the

calculation result, it is found that the distributor’s redistribution ability is best among all

designs, and it has a great high potential to further improve its fluid distribution

performance. Based on this conclusion, the design of the distributor was further optimized

by changing parameters such as the flow area, the height of the distributor and the

installation location. The calculation result shows that installing the distributor at a lower

position couldn’t reach the goal of redistributing helium evenly. While the design of

keeping the bottom edge of the air distributor slightly higher than the lower edge of the

inlet passageway presents an outstanding redistribution ability, in which case, part of the

helium flow does not participate in the annular flow, adversely it directly flow out of the

Abstract

air distributor. The mechanism behind is that flows participating in the circumference flow and the helium that flow out directly can be better mixed at the outlet of the air distributor, eliminating the cross-stream velocity component and enhancing the uniformity of the distribution. Changing flow area could influence the size and strength of the flow that flows out directly. The calculation results show that the flow distribution with smaller flow area and installed at the higher position, can better improve the redistribution performance and reduce the velocity deviation index of outflow by 68.6%.

Key words: HTGR; intermediate heat exchanger; inlet passageway;

optimization design

Table of Contents

Table of Contents

Chaper 1 Introduction ... 1

1.1 Background ... 1

1.2 Literature Review ... 8

1.2.1 Review on Inlet Passageway Optimization of IHX ... 8

1.2.2 Review on Inlet Passageway Optimization of Other Type of Heat Exchanger ... 10

1.3 Purpose and Objective... 11

1.4 Research Method ... 11

1.5 Contents of the Research ... 12

Chaper 2 Methodology ... 13

2.1 Computation Fluid dynamics ... 13

2.1.1 CFD Method ... 13

2.1.2 Governing Equations ... 15

2.1.3 Turbulence Modelling ... 15

2.1.4 Basic CFD procedure ... 16

2.2 Porous Media Theory... 17

2.2.1 Simplification of Spiral Bundle Area as Porous Media ... 17

2.2.2 Porous Media Theory ... 18

2.3 Conclusions ... 20

Chaper 3 Coupling Effect of Heat Transfer Area on Inlet Flow ... 21

3.1 Porous Parameters Calculation of Treating Heat Exchange Area as Porous Media ... 21

3.1.1 Calculation Model ... 21

3.1.2 Analysis Method ... 22

3.1.3 Calculation Condition ... 22

3.1.4 Result Analysis ... 23

3.2 The Coupling Effect of Heat Exchange Area on Inlet Flow ... 25

3.2.1 Physical Model ... 25

3.2.2 Computation Model ... 27

Table of Contents

3.2.3 Calculation Condition ... 28

3.2.4 Result and Analysis ... 29

3.3 Necessary of Coupling Effect ... 30

3.4 Conclusions ... 35

Chaper 4 Simulation of Passageway Optimization ... 37

4.1 Problem Description ... 37

4.2 Calculation Model ... 38

4.3 Optimization Model ... 38

4.3.1 Distributor Optimization Model ... 39

4.3.2 Guide Vane Model... 39

4.3.3 Grill Plate Model ... 40

4.3.4 Reverse Truncated Cone Model... 41

4.3.5 Arc-shaped Vane Model ... 42

4.4 Compare the Different Optimization Model ... 42

4.5 Grid independent test... 44

4.6 Conclusions ... 44

Chaper 5 Detail Optimization of Flow Distributor ... 46

5.1 Geometry Adjustment ... 46

5.2 Calculation Result ... 48

5.3 Result Analysis ... 51

5.3.1 Analysis for Long Distributor Design ... 51

5.3.2 Analysis for Original Size Distributor Design ... 53

5.3.3 Analysis for Shorter Distributor Design ... 55

5.3.4 Flow Area Influence ... 58

5.4 Conclusions ... 63

Chaper 6 Conclusions ... 64

6.1 Result and Conclusions ... 64

6.1.1 Simplification of Calculation Model ... 64

6.1.2 The Comparison of Optimization Designs ... 64

6.1.3 The Optimization of Flow Distrbutor ... 65

6.2 Future Research ... 65

References ... 67

Table of Contents

Acknowledgements ... 70

Resume ... 71

Abbreviation and nomenclature

Abbreviations and nomenclature

P pressure，Pa

T temperature，℃

K permeability，m

S flow are of distributor, mm

H flow distributor height, mm

Z flow distributor installation height，mm

c

specific heat，J/(kg·K)

u

Reynold time-averaged velocity，m/s

 dynamic viscosity，Pa·s

 density，kg/m

 porous media porosity

IHX intermediate heat exchanger

HTGR high-temperature gas-cooled reactor VHTR very high temperature reactor

Re Reynold number

Chapter 1 Introduction

Chaper 1 Introduction

1.1 Background

Nuclear power is an important pillar for solving future energy supply problems.

According to the relevant estimation, By 2030, the power need gap will reach 995 billion kilowatt, which needs to be replenished by installing capacity of 140 nuclear power plants on megawatt level.

At the same time, the nuclear power is an important way to reduce fossil energy consumption and carbon dioxide emission. According to the analysis of America Nuclear Energy Institute, the nuclear power plant in the United States reduce the 133 million tons carbon dioxide emission and 4.7 million ton sulfur dioxide and 2.2 million ton nitrogen oxide emission in 1993.

At present, commercial nuclear power stations in service in China use nuclear reactors in the stage of second-generation with second-generation technology, and commercial nuclear power plants under construction are mainly second-generation and third-generation reactors. The third-generation nuclear energy system is developing, which has gradually improved and entered the stage of engineering application process.

And a more advanced nuclear energy system is developing as well, already become a new direction for nuclear power technology research and development.

The safety accident at the Fukushima Daiichi nuclear power plant has caused widespread concern and deep thinking about the safety of nuclear power plants. With the purpose of developing safer and more efficient nuclear energy systems, the Fourth Generation Nuclear Energy Systems International Forum (GIF) proposed the concept of fourth-generation nuclear reactor, which is safer, more economical, produces less nuclear waste, and could effectively prevent nuclear proliferation. The research work on the fourth-generation reactor has become a hot spot for nuclear power technology research and development in various countries.

There are six recommended reactor types for the fourth-generation nuclear energy

system: gas-cooled fast reactor (GFR), molten salt reactor (MSR), lead alloy liquid metal

cooled fast reactor (LFR), and sodium-cooled fast reactor (SFR). Very high-temperature

gas-cooled reactor (VHTR) and supercritical water reactor (SCWR).

Chapter 1 Introduction

The high-temperature gas-cooled (HTGR) reactor, as a promising type of generation IV nuclear reactor, could generate power efficiently

with high economic efficiency, using the ceramic fuel element, helium as coolant and graphite as the moderator and structural material. At the same time, the high-temperature gas-cooled reactor could be used for hydrogen production

, process heat application

and combined cycle

. One of its advantages is its inherent safety

. The radioactive substance could possibly remain inside the reactor even the loss of cooling accident happens. It has large thermal inertia as well as negative reactivity feedback. In any type of accident, the core residual heat could be removed by means of convection heat transfer and thermal radiation in the reactor to avoid the danger of reactor meltdown accident

. This inherent safety allows for the possibility of arranging the reactor beside the user, which would further broaden the application field of nuclear energy.

The research about high-temperature gas-cooled reactor started from the 1950s last century, going through three stages: experimental reactor stage, demonstration plant stage and experimental modular HTR.

In the experimental reactor stage, British and France developed Magnox gas-cooled reactor, using the CO

as coolant. Later, the Dragon reactor in Europe, Peach Bottom in United States, AVR in Germany began to be developed and operated, with different form of fuel element, prismatic-shaped or pebble-shaped. The helium is used as coolant, and coated fuel particle is introduced. Beside Dragon reactor in Europe, reactors above all take advantages of steam cycle, lay a foundation for the later demonstration plant design process.

The stage two is demonstration plant stage: Based on the reactor experiment before, Germany and United States built HTR demonstration plant THTR and Fort. St. Vrain, respectively. The plant in this stage need core emergency cooling system to avoid the potential damage of fuel elements.

After Three Mile Island accident in the United States, the development of high-

temperature gas cooled reactor step into the modular HTR. The modular HTR reduces the

power of nuclear power plant, beneficial to heat loss in the reactor. The core emergency

cooling system becomes unnecessary, even in the accident event of losing all coolant in

the reactor, the highest temperature in the reactor will not exceed the designed

temperature limit of fuel elements. The radioactive residual could be safely remained in

the fuel element, reducing the possibility of radioactive material discharge.

Chapter 1 Introduction

Tsinghua University designed high-temperature gas cooled reactor HTR-10 in the 1990s and it reached critical state in 2000. Its structure is shown in Figure 1.1. HTR-10 realized power generation by steam turbine(ST) cycle and connected to the grid in 2003.

HTR-10 primary loop outlet and inlet temperature were 700℃ and 250℃ respectively。

This is the first step of design objective. The next step aims to raise the reactor core outlet temperature up to 900-950 ℃ by mean of further development and design improvement, which is the next leading research area. By now, the core outlet temperature of HTGR could be raised up to high-temperature level (900-1000 ℃). This temperature has already been realized by AVR Reactor in German and HTTR Reactor in Japan.

Figure 1.1 HTR-10

The higher temperature of VHTR would allow for broader applications than HTGR.

The very high-gas cooled reactor could further improve power generation efficiency and economy, realize hydrogen production taking advantage of nuclear energy and provide high-temperature heat for chemical technology design, i.e. realize process heat application due to its higher outlet helium temperature. At the same time, it could improve the nuclear power plant economy when widely application is realized. The possible operation of VHTR has been developed and validated by German AVR reactor and Japan HTTR reactor.

In VHTR , the core outlet temperature could be raised up to 900-1000 ℃, but in the

steam turbine cycle, the maximum helium temperature limitation is just about 550 ℃

which couldn’t take full advantage of the higher temperature potential. So when core

outlet temperature exceeds 900℃, the intermediate heat exchanger can be introduced. Li

Chapter 1 Introduction

R.Z

suggested series connection in reactor primary loop between intermediate heat exchanger and steam generator. The high-temperature helium firstly flow into the intermediate heat exchanger, transferring heat to gas in gas turbine cycle and helium reaching a lower temperature, then helium flows into steam generator transferring heat to steam turbine cycle, this process is called GT-ST combined cycle, its flow chart is shown in Figure 1.2.

Figure 1.2 GT-ST combined cycle of HTR-10

Li R Z proposed an integrated heat transfer device for HTR-10. The Figure 1.3(a) shows the component-based intermediate heat exchanger design, proposed by Li R Z. It was suggested to install intermediate heat exchanger inside steam generator, which could increase safety and economy. Figure 1.3(b) shows spiral-tube intermediate heat exchanger suggested by Li X T.

From the study of previous design, it could be found that the intermediate heat exchanger is the critical equipment for the combined cycle of VHTR. The intermediate heat exchanger works as the heat sink and the primary circuit pressure boundary.

As the intermediate heat exchanger needs to work in high-temperature environment

for a long time, which is near the metal material limitation, and it needs to defense the

threat on reactor as the primary loop pressure boundary

and prevent the tritium

contamination to heat application process, there are some requirements to design the

intermediate heat exchanger in VHTR:

Chapter 1 Introduction

(a) component-based IHX (b) spiral-tube IHX Figure 1.3 intermediate heat exchanger

Firstly, IHX should operate under the high temperature (900-1000℃) and high pressure (3-10MPa). Secondly, it should resist the oxidization or corrosion from impurity in helium flow. Finally, the design should extend the IHX service life as long as possible.

Therefore, all above all of which make the intermediate heat exchanger face challenges in material selection

, thermal design, structural design, and manufacturing process. Among them, the thermal hydraulic characteristics of the inlet flow of intermediate heat exchangers have significant influence on the performance of the intermediate heat exchanger in terms of IHX service life.

The inlet passageway of the intermediate heat exchanger is shown in the rectangular frame in Figure 1.4. The hot helium enters with a temperature of 950 º C at the bottom of the component and flows through the heat exchanger bundle upwards.

Intermediate heat exchanger is comprised of spiral tubes, central tube, inlet and

outlet tube-chambers, support plate, insulation layer. In the spiral bundle structure, the

spiral tube diameter is in the range of 15-30mm.

Chapter 1 Introduction

Figure 1.4 Inlet passageway of intermediate heat exchanger

The actual heat exchanger inlet passageway structure of HTR-10, HTR-PM and HTR-Module are shown in Figure 1.5. When helium passage through 90-degree elbow shape passageway, there exist asymmetry of the structure, transverse flow and vortex motion are intensified, even contributing to secondary vortex in the inlet passageway area.

So fluid in the original flow direction tends to be more and in the deviation direction flows tend to be less, contributing uneven flow distribution in the circumference direction in the heat transfer area.

HTR-10 HTR-PM HTR-Module Figure 1.5 Inlet Passageway Structure

This flow maldistribution contributes to an inefficient effect on the thermal and

hydraulic performance of heat exchange in the intermediate heat exchanger. The overall

thermal performance decrease and fluid pressure drop increase simultaneously as well

.

Chapter 1 Introduction

Some studies reveal that maldistribution of fluid in the heat exchanger would lead to 25%

decrease in thermal performance in a heat exchanger.

This maldistribution contributes to the temperature tilt in the heat transfer area which is revealed in the Advanced Gas-cooled Reactors built in the UK several decades ago.

When the reactor reaches its critical state, there is more than 80 ℃ temperature difference between inside line and outside line, for which the reactor had to decrease its power to prevent premature failure of steam generator.

Meanwhile, the uneven flow distribution leads to uneven heat transfer of the heat exchanger, resulting in the uneven distribution of the temperature and the uneven thermal stress of the heat exchange tube. The brought harm is that the heat transfer tubes age at a different rate, so there is a hidden danger of premature damage to the structure and adverse influence on the structure.

Moreover, it's obvious that there will be low pressure in specific position, contributing to vortex in the passageway, shown in Figure 1.6. Some tubes in specific region could be flushed by unsteady helium flow. This contributes to the vibration and even fatigue damage to the heat exchange tubes.

Figure 1.6 Vortex formed in the passageway

The flow misdistribution reduces the performance of heat exchanger from many

aspects. Therefore, it is significant to optimize inlet flow passageway of the intermediate

heat exchanger to reduce the adverse effect of misdistribution.

Chapter 1 Introduction

1.2 Literature Review

1.2.1 Review on Inlet Passageway Optimization of IHX

There are numerous tests and research about IHX designs, in which IHX is designed as tubular design or compact plate-type designs. The tests were in different stages: design, lab-scale, pilot-scale or engineering-scale type.

German conducted tubular IHX test in the KVK facility in the context of the PNP project, in which U-tube IHX and helical-tube IHX were studied during 1985-1988.

Helical-tube IHX, shown in Figure 1.7, was tested from October 1986 to June 1988, for 5200 hours during which 2200 hours reached the temperature of 950 º C.

(a) Helical Tube IHX (b) Inlet passageway structure Figure 1.7 Intermediate heat exchanger in KVK facility, German

The heated high-temperature fluid flows into the primary inlet situating at the bottom of IHX and then passed the mixing device and heats up the cold spiral tube bundle in the upward flow. Various tests were conducted, like startup, minimum power operation, maximum power operation, long-term testing at nominal load and at partial load, some cyclic operation and even accident testing (Quick change of primary inlet temperature).

In the bottom structure of German design, there is a special device to sample and

distribute the hot primary gas, before it enters the bottom part of the spiral tube bundle in

heat exchange area.

Chapter 1 Introduction

Japan also conducted the research about the intermediate heat exchanger. The HTTR (High Temperature Testing Reactor) reached high temperature of 950 º C in April 2004.

The heat transfer power of Japanese intermediate heat exchanger reached 10MW, and its structure was designed as vertical counter flow type, like IHX in German KVK facility.

The Japan intermediate heat exchanger is shown in Figure 1. 8.

Figure 1. 8 Intermediate Heat Exchanger of HTTR

Japan conducted several experiments about the IHX structural integrity. Five main tests were: tube creep collapse, tube creep fatigue under thermal stress, tube bundles seismic behavior, tube bundle thermal hydraulic behavior and tube in-service inspection.

As for Japan also introduced a special design to the inlet passageway of intermediate heat exchanger to contribute a more even flow distribution in heat transfer area.

However, there are only Germany and Japan had researched on intermediate heat

exchanger in VHGR.

Chapter 1 Introduction

1.2.2 Review on Inlet Passageway Optimization of Other Type of Heat Exchanger

About inlet configuration optimization design, there is some research in plate-fin heat exchangers. Wen et al.

proposed an improved configuration with punched baffle to improve the flow inside the entrance of plate-fin heat exchanger. Lsmail

modified headers in heat exchanger by providing suitable baffle plates with varying dimensions of holes arranged for improvement in flow distribution. Zhang et al.

introduced a two- stage distributing structure to reduce the flow nonuniformity, in which the fluid flows through first and second header configuration so that it can be distributed two times before entering heat exchange core. M.A Habib et al.

studied inlet flow velocity and nozzle geometry shapes’ influence on maldistribution in air-cooled heat exchangers by means of numerical analysis solution. The mass flow rate distribution in heat exchanger and their standard deviation are taken as the indexes in the analysis. The results indicated that inlet flow velocity had insignificant impact on flow distribution while the nozzle geometry had some influence on the flow distribution. It's also found that reducing the nozzle diameter results in an increase in the flow maldistribution.

For similar elbow inlet passageway structure, Sun Dongpo et al.

introduced internal diversion curve wall model to improve the maldistribution in an actual elbow- shaped channel. Jia X H et al.

introduced proportional distributed arc shape baffles in 90° elbow pipe to improve the flow in passageway. Cheng Y L et al.

introduced guide plates to the direct air-cooled condenser. Result shows that installing eight pieces of guide plates to the fan outlet could reach the goal of uniformly distributed flow and help to reduce local high temperature on tube bundle surface. Wu X H et al.

introduced a 16- hole deflector into the entrance of parallel-flow heat exchanger and found that distribution uniformity can be decreased by 76% to 87.8% compared to no deflector case.

The most research about inlet passageway optimization of intermediate heat exchanger by now mainly focus on entrance of specific heat exchangers, like plate-fin heat exchanger. In the plate-fin heat exchanger, fluid flows through inlet tube then entering header, in which the stream is separated and flows into alternating layers of heat exchanger. This structure is much different from actual passageway structure of intermediate heat exchanger in HGTR.

The research about elbow-shaped entrance passageway optimization in intermediate

heat exchanger is relatively sparse now.

Chapter 1 Introduction

1.3 Purpose and Objective

Helium maldistribution in the heat transfer area of intermediate heat exchanger, caused by one orientation of inlet, affects the exchanger performance. The research purpose is to propose an optimization design of inlet passageway to redistribute the flow on circumference direction to become more even so that the spiral heat exchange tube on circumference direction could age at the similar rate, prolonging the life of heat exchange tube overall, increasing the overall thermal efficiency as well. The intermediate heat exchanger with higher efficiency and reliability is more economic and safer, increasing the public acceptance to the HTGR.

1.4 Research Method

To optimize the inlet passageway of intermediate heat exchanger, experimental research approach and numerical simulation research approach are applicable. While the experimental research method has its disadvantages in high cost and time consuming in building experiment system. At the same time, it might be too tedious to fabricate many optimization equipment and install them in the inlet passageway. To analyze the optimization effect, the velocity distribution data on the entrance plane of spiral bundles area needs to be measured, which is hard to realize with the experiment approach.

Relatively, numerical simulations have the advantages of repeatability, less effort and the ability to view the flow field. To change the inlet passageway optimization design, i.e. to change the shape of distributor geometry shape, there is no need to fabricate new device like experiment method, in the numerical simulation, this can be done on computer, just adjusting the model, then meshing and compute again. At the same time, the visualized flow field can be easily got with the post process function on the computer.

The redistribution effect of specific optimization design can be quick and scientifically assessed with the numerical simulation approach.

Therefore, this study conducts inlet passageway optimization in intermediate heat

exchanger by computational fluid dynamic method. The flow distribution the passageway

under proposed different passageway optimization designs is calculated by CFD, and then

some specific important indexes which reveal the optimization effect are used for analysis.

Chapter 1 Introduction

1.5 Contents of the Research

As the spiral bundle in intermediate heat exchanger would have coupling effect on the helium flow in the passageway, the coupling effect is needed to be considered. To simulate the three-dimensional structure directly will have difficulty in modeling complex structure and handling large amount of calculation. So in the first part of study, a relative quick approach is adopted, the above spiral tube area is treated as porous media to simplify the complicated structure. Meanwhile the necessary of the coupling effect needs to be studied by means of contrasting simulation of treating heat transfer area as a hollow chamber or porous media.

Then, several different optimization structures need to be studied, modelled in ProEngineer and the flow field is numerically simulated by means of computational fluid dynamics approach, meanwhile taking into account of simulating heat transfer area as porous media, i.e. introducing a momentum source term to the standard fluid flow equations. Five inlet passageway optimization models are proposed in this paper. They are the installation of gas distributors, guide vanes, grid plates, reversed truncated cone plates and arc-shaped passageway respectively. Comparing the redistribution effect of proposed optimization designs and a better inlet passageway optimization design is determined.

Then analyzing the flow mechanism of redistribution effect and optimize the better design to further improve its redistribution ability. This was realized by changing the detail geometry characteristics of the better design and comparing the flow distribution effect of different designs.

Chaper 2 Methodology

Chaper 2 Methodology

In this chapter, the flow in passageway is depicted in mathematical method. Some basic method like CFD and models like Reynold time-averaged Navier-Stocks Model, standard k- model standard are introduced here. As there is necessary to simplify the complex spiral bundle as porous media, the basic concept of porous theory is explained as well.

2.1 Computation Fluid dynamics

2.1.1 CFD Method

At the beginning of the twentieth Century, fluid mechanics developed rapidly and Navier-Stocks equations were created. With the development of fluid dynamics, both experimental methods and theoretical studies have reached an unprecedented height. This research field flourished with the rapid development of computer science.

Computational fluid dynamics (CFD) is widely applied to many problems, and has many advantages. Firstly, the equations used to describe flow phenomena are nonlinear.

At the same time, the prototype of many devices and systems are complicated and the problems to be solved are complex and changeable as well, for which its governing equations can hardly be solved directly. Numerical analysis provides a useful way to meet the needs of the engineering.

Secondly, CFD method isn’t limited by some physical and experimental models. It could be used to simulate some extreme experiment conditions easily, like toxic condition, flammable condition, high-temperature condition, and some physical model with special dimensions. In the practical experiment ,these ideal conditions can only be approached but cannot be reached. At this time, the CFD method can be used to solve the problem on the computer. This method is economical and could quickly get the calculation result.

Based on fluid dynamics, computational fluid dynamics calculate the solution of

partial differential equations by means of numerical approach. Numerical discretization

is the basic thought of computational fluid dynamics. Software FLUENT is based on the

Finite Volume Method. Finite Volume Method is to discretize the flow domain into

limited non-overlapping control volumes and then discretized equations like RANS

Chaper 2 Methodology

equations are used to compute the control volume pressure, velocity and temperature in each mesh. Each mesh is closely related to the surrounding mesh to form the overall calculation scheme and some parameters like pressure, velocity of the analyzed domain could be computed. Moreover, the computed flow field results can be continuously visualized by the powerful computer.

When Reynolds number is larger than a critical value, there is a series of complex changes that eventually lead to the essential change of the flow characteristic, the flow becomes disordered and chaotic. In this case, the flow is unstable, some parameters like velocity change randomly, this kind of flow state is called turbulence flow. If the velocity of one point is monitored in the turbulence flow, it could be found that velocity value has an obvious pulsation characteristic. To analyze turbulent fluid flows, there are mainly three methods: Direct Numerical Solution (DNS)，Large Edie Simulation (LES) and Reynolds Averaged Navier-Stokes (RANS).

DNS method realizes numerical analysis by calculating instantaneous N-S equation directly, so this method doesn’t need any simplification or approximation, for which more accurate calculation results could be reached. Even though the result can be accurate, it has the disadvantage of computational complexity. It’s estimated that to calculate the flow in a 0.1 × 0.1m

small region, the number of grid mesh would reach to the 10

to 10

level. For such calculation requirements, existing computer capabilities are still difficult to meet. It requires the computer to have large memory space and high calculation speed, for which this method still isn’t widely available for practical engineering calculations.

LES method simulates large scale eddy directly, while for the small scale eddy, some approximations are introduced. LES method still requires the computer to have large memory space and high calculation speed. This method can be used in some workstations.

In the practical engineering situation, the average change in flow field caused by the

turbulence is more important, which concentrates on the overall effect, so Reynolds

Averaged Navier-Stokes method (RANS) was proposed. RANS avoids calculating the

instantaneous N-S equations directly, while this methods calculates a time-averaged

Reynolds equations. This method has been mostly widely used by now. To take the

turbulence flow pulsation characteristic into consideration, in the time average method,

the turbulence flow is considered as the composition of two part, one is time-averaged

flow, the other is fluctuating flow. All the flow parameters are written as the composition

of two part. Then the continuous equation and momentum equation could be written as

Chaper 2 Methodology

time-averaged equations.

2.1.2 Governing Equations

Fluid flow in the passageway obeys the conservation of mass, momentum and energy, shown as continuity equation, momentum equation and energy equation respectively. The governing equation reveals the relationship between temperature, pressure and density for a general moving flow, comprised of some partial differential equations with time- dependent.

Continuity equation is mathematical statement of mass conservation. In this thesis, only steady flow is studied, so Reynolds averaged continuity equation is shown as

( 

) 0

 

（2-1）

The momentum equation, also called Navier-Stokes equation, means that for a specific region, the time rate of momentum change equals to the total forces on that region, basically is Newton’s second law. The force includes body forces, surfaces forces.

Reynolds averaged momentum equation for steady flow is (  uu ) p (  u (  u u ' ')) S

        （2-2）

Energy equation is based on energy conservation law, i.e. the rate of energy change in material particle equals to rate that that energy is received by heat and work transfers in that particle. Reynolds averaged energy equation for steady flow is presented as,

[( ) ] ( ) =0

Pr

t

P E

t

T C uT S



 

       （2-3）

In which 𝑐

is specific heat capacity, T represents temperature, k is heat transfer coefficient. S

is heat internal heat source and the heat energy transferred from mechanical energy because of viscosity in fluid.

2.1.3 Turbulence Modelling

There is an additional term -  u u ' ' , which is called Reynolds Stress term, on the right side of the equation (2-2). To close the equations, the Reynolds stress term needs to be defined, which normally is approximated by turbulence models, comprised of Reynolds stress model and eddy viscosity model.

In eddy viscosity model, the Reynolds stress term is shown as a function of turbulent

viscosity. To determine the turbulent viscosity, some differential equations are needed.

Chaper 2 Methodology

According to the number of differential equations needed, viscosity model is comprised of zero-equation model, one-equation model and two-equation model.

In the viscosity model, two-equation model is widely applied, in which turbulent kinetic energy k and turbulence dissipation rate  are introduced. The turbulent viscosity μ

is a function of turbulent kinetic energy k and turbulence dissipation rate . In two- equation model, the standard k- model is mostly widely used. The standard k- model is applicable to the turbulence model with high Re number.

2.1.4 Basic CFD procedure

Basic CFD procedure is composed of three main steps:

First step is to model in 2 dimension or 3 dimension by means of modelling software like CAD, ProEngineer. This is to create computational domain which will later be analyzed. Then the model is exported in the form which could be imported to ICEM.

Next step is the discretization process, dividing the physical space into numerous geometric elements which is called grid cells. The grid cell can choose many types, like triangle, quadrilateral , tetrahedron, pyramid and so on. The meshing can be structured or unstructured. Structured grids have regular connectivity so this could reduce the storage space and its computation result is relative accurate. But to mesh the calculation region with structure grids could be very challenging. To mesh with unstructured mesh is comparatively much more automatic and flexible, which comprised of irregular connection with surrounding mesh. There isn’t particular order in the distribution of mesh, for which it requires much storage space. For the complex geometric model, the unstructured mesh can be a better choice to reduce the difficulty in meshing process. After mesh, grid mesh quality should be examined to ensure the numerical stability and accuracy later.

Thirdly, importing mesh file into computational fluid dynamics software FLUENT

and setup calculation condition, like boundary condition, computation model choice, cell

zone condition, solution control relaxation and so on. The computed result then go

through post process, including whole field flow visualization, computational report and

so on.

Chaper 2 Methodology

2.2 Porous Media Theory

2.2.1 Simplification of Spiral Bundle Area as Porous Media

In the research, the simplest optimization method is to simulate inlet passageway directly without considering spiral tube area. However, actual upper heat transfer part may compose resistance force on inlet passageway flow, i.e. there is a coupling effect of heat exchange tube area on inlet helium flow. If the coupling effect was neglected, the simulation result would be greatly different from actual flow situation. So to analysis the flow in the inlet passageway, the heat exchange area needs to be taken into consideration.

Figure 2. 1 displays actual spiral tubes bundle structure in intermediate heat exchanger.

Figure 2. 1 Spiral tube structure in intermediate heat exchanger

An ideal approach is to simulate spiral tube structure directly, but it could be found in the Figure 2. 1 that the actual spiral tubes structure is complex and hard to model. In the meshing process, to ensure the quality of mesh and later computation accuracy, the mesh number is estimated to be enormous. There is difficulty in handling too many meshes and calculation tends to become complicated, it is too costly for engineering design and optimization research process.

It’s estimated that to simulate a heat exchanger with 500 heat exchange tubes, 1500

million mesh elements are required, which already exceed the computers calculation

ability.

Therefore, for the simplification, a relative quick approach is adopted in present

study, with which method, the above spiral tube area is treated as porous medium to

simplify the complicated structure.

Chaper 2 Methodology

This kind of numerical analysis which is based on porous media, appeared from 1970s. As both nuclear reactor internal structure and heat exchanger structure are complex, this method is widely used in dealing with fluid flow and heat transfer problems in heat exchanger and nuclear reactor. Yao C H

simulated fluid flow in three-dimensional reactor core. Karayannis

simulated fluid flow and heat transfer in Shell-and-Tube heat exchanger by means of this approach. Deng B et al.

even developed a general program which could calculate porous media characteristic parameters automatically for shell-and- tube heat exchangers.

2.2.2 Porous Media Theory

The actual structure of a porous medium is complicated and hard to predict ， containing sponge like solid skeleton and void spaces. The fluid flow randomly thorough the void fraction in porous skeleton structure. It’s difficult to calculate its random flow in void spaces.

So in the analysis of porous media, its actual physical structure is normally neglected and disregarded, A methodology like time averaging a turbulence flow field for the purpose of reducing the flow complications. The influence of solid skeleton of porous media on fluid flow is neglected, simplifying that the whole flow field is composed of plenty of small feature unit, called Representative Elementary Volume (REV). The REV has a constant porosity in the whole flow field no matter where this small feature unit situates.

The porosity is defined as the fraction that void pore volume occupying in the total flow field volume. It is given as

V

  V （2-4）

In which 𝑉

is the pore space volume, V is the total flow field volume.

The average velocity of REV is usually used to describe the average seepage fluid velocity in porous media, this velocity is also called Darcy velocity. This method just focus on its overall capability of the porous system to transport fluid and energy.

The Darcy velocity is a continuous function of space. It is different from the actual fluid velocity in the pore structure of porous media. Their relation could be described as

u   v （2-5）

In which u is the average fluid seepage velocity in porous media, v is fluid actual

Chaper 2 Methodology

velocity in the void fraction. This equation is called Dupuit-Forchheimer equation.

When the inlet velocity of flow field is in the low range, viscous resistant prevails in the porous field fluid flow process. This porous media fluid mechanism is summarized by Darcy, through the experimental observations, revealing that the area-averaged velocity u through a column of porous media is proportional to the pressure gradient along the porous media.

The experiment also proved that the inlet velocity is inversely proportional to the fluid viscosity 𝜇.

( )

K dP

u ^  ^ dx （2-6）

Where K is an empirical constant called permeability, m

. P is pressure, Pa;  is viscosity,Pa.s; u is area-averaged velocity through the porous media column, m/s.

For a specific porous media, the equation could also be represented as

P u

L K



   （2-7）

Where L is the length of porous media, m.

It reveals that pressure loss per unit length along the flow direction, in a column of porous media, is approximately proportional to inlet velocity through the column when inlet velocity is relative low. Darcy law is applicable to the condition when Reynolds number is in the range of 1 to 10. As Reynolds number exceed O(10), the inertial effects came into dominant, the pressure difference and velocity come to deviate linear relationship.

In this case the fraction factor could be described as

f 1

Re C

  （2-8）

The more widely used modification of Darcy law is proposed by Forchheimer. In the equation (2-8) there is an added term, non-linear term. In this case, the pressure loss is comprised of two part, viscous loss term, which is linear term, and inertial loss term, square term

, represented as

3 3

1 1

1

i j ij

2

j ij j

S D  u C  u u

 

 

         （2-9）

Where S

is momentum source, i is x, y or z direction, D and C are viscous resistant matrix and inertial resistant matrix respectively.

For a simple and homogeneous porous media, the resistance could be simplyfied as

C2

2 P

L K

 

    u u

（2-10）

Chaper 2 Methodology

Where C

is intertial resistant coefficient, and it could be taken as the pressure loss coefficent per unit length along the flow direction.

As Reynold number increases to the range over 100, the flow turns into turbulence flow. Lage

pointed out that pressure gradient versus fluid speed relation will depart from the quadratic Forchheimer-extended Darcy flow model, and can be correlated by a cubic function of fluid speed for the velocity range when Reynold number is over 100.

The function is presented as

2 3

1/ 2

C

P u u cu

L K K





   

（2-11）

Where the cubic coefficient c is the cubic coefficient, Pa s

/m

.

In the flow field computation, porous media’s influence on fluid flow is achieved by adding source term in the momentum equation.

2.3 Conclusions

CFD has great advantages in terms of repeatability, less effort and flow field visualization compared to experiment approach. In numerical calculation, to depict the turbulence flow in the computation domain, there are DNS model, LES model and RANS model. The most commonly used one is RANS model. In this thesis, RANS model is used in the numerical calculation, in which there is an additional term called Reynolds stress term. To close the governing equations, the most widely used standard k- model is applied.

The spiral bundle in the heat exchange area may have influence on the inlet flow

distribution, so in the computation, the heat exchange area should be taken into

consideration. Whereas to simulate the actual structure of spiral bundle requires huge

amount of calculation. For the simplification, the spiral bundle is treated as porous media

according to the porous media theory. The actual simplification method will be introduced

in the chapter 3.

Chaper 3 Coupling Effect of Heat Transfer Area on Inlet flow

Chaper 3 Coupling Effect of Heat Transfer Area on Inlet Flow

The spiral bundle in the heat exchange area may have influence on the inlet flow distribution, so this influence is studied in this chapter. While, actual spiral bundle is complicated and difficult to be modelled. In this chapter, a simplification method, which treats the heat exchange area as porous media, is proposed. For this simplification method, a practical method is to analyze the relationship between heat transfer area pressure difference and average seepage velocity. Then according to the Darcy-Forchheimer law, the permeability and inertial coefficient of the heat transfer area could be calculated.

3.1 Porous Parameters Calculation of Treating Heat Exchange Area as Porous Media

In order to simplify the spiral bundle area as porous media, some key parameters describing the transport and geometry properties of porous media, like friction factor needs to be calculated. The friction factor describes the resistance of a porous media to the flow. To calculate the porous media friction factor, in this chapter, the pressure loss is analyzed as helium flowing through the heat exchange area, from which the friction factors of the porous media could be deduced further. The calculated friction factor is the key parameters revealing the characteristic of porous media and provides needed parameters for the later inlet passageway optimization analysis.

3.1.1 Calculation Model

The actual spiral tube structure in intermediate heat exchanger is shown in Figure 2.

1. The cross section of spiral tube bundles is shown in Figure 3.1.

The diameter of heat transfer tube is equal to 20mm, horizontal and longitudinal space is 30mm and 40mm respectively. The calculation model takes a section of whole passageway, which will not influence the viscosity resistant coefficient analysis process.

Tube layout of the calculation is set as 8 layers on horizontal direction and 7 layers on

longitudinal direction.

Chaper 3 Coupling Effect of Heat Transfer Area on Inlet flow

Figure 3.1 Cross section calculation model

3.1.2 Analysis Method

The pressure difference between inlet and outlet of the spiral tube cross section model with changing inlet velocity is used for analysis. Then fitting the pressure drop versus velocity to find the viscous loss coefficient and inertial coefficient which describes the overall characteristics of porous media.

3.1.3 Calculation Condition

Referring to the operating and design parameters, the helium flow condition in the heat transfer area is shown in Table 3.1.

Table 3.1 Helium flow condition

Condition Unit Value

fluid Helium

pressure MPa 3

temperature ℃ 900

density kg/m

1.2276

viscosity Pa ۰ s 5.17×10

flow rate kg/s 3.21

inlet velocity of heat transfer area m/s 2-4

The simulation was conducted using the CFD code ANSYS FLUENT 18.0. The simulation used the standard k- model. The Navier-Stokes equations were solved using the finite volume method on unstructured meshes.

The velocity and pressure coupling were given by the semi-implicit method for

pressure-linked equations (SIMPLE) algorithm. Second order upwind differences were

Chaper 3 Coupling Effect of Heat Transfer Area on Inlet flow

used for the diffusion and pressure terms in the momentum equation and the divergence terms in the mass continuity equation. The advection terms in the momentum, energy, mass transport, and turbulent kinetic energy were discretized using the second order upwind algorithm. The convergence criteria were 10

for velocity and other variables.

3.1.4 Result Analysis

The computed helium velocity and pressure distribution of spiral tube cross section model in heat transfer area is shown in Figure 3.2 and Figure 3.3 respectively. From the velocity distribution, it could be found that the helium is accelerated in the small interval of tubes. Meanwhile, there is an obvious pressure degradation in the flow field pressure distribution. The grid independent test was conducted and the grid number should exceed 45,000.

Figure 3.2 Helium velocity distribution contour

Figure 3.3 Helium pressure distribution contour

Chaper 3 Coupling Effect of Heat Transfer Area on Inlet flow

The Darcy-Forchheimer equation can be further deduced as C

2

P u

Lu K





       

  （3-1）

Where u is inlet velocity of spiral tube cross section model, changing in the range from 2 to 4 m/s with the step of 0.1m/s. 𝜇 is viscosity of helium, Pa.s; 𝜌 is helium density, kg/m

. K stands for permeability, m

. L is the distance from inlet to outlet, 0.24m.

Processing the pressure difference and velocity data as ∆𝑃 𝐿𝑢 ⁄ , and the relationship between ∆𝑃 𝐿𝑢 ⁄ and inlet velocity u is shown in . From the , it could be found that there is strong linear relationship between ∆𝑃 𝐿𝑢 ⁄ and inlet velocity u.

2 3 4

-220 -200 -180 -160 -140 -120

p/Lv

velocity (m/s)

Figure 3.4 The linear relationship between ∆𝑃 𝐿𝑢 ⁄ and inlet velocity u

Fitting the linear relationship between ∆𝑃 𝐿𝑢 ⁄ and inlet velocity u, then, there will be

 ^{41.49 44.03} 

P u

Lu

    (3-2)

So it could be calculated that equivalent permeability is K=1.24×10

，and inertial resistance factor is C

=71.73. Ward

used K

as characteristic length to calculate Re.

According to the Ward theory, in this case, Re is calculated to be in the range of 53~106

with changing velocity from 2~4m/s. So the majority of calculated Re lies in the

appropriate range of Darcy -Forchheimer law. In the later optimization calculation, spiral

tubes can be treated as porous media with the viscosity resistant coefficient 1/K=806168

and inertial resistant coefficient C

=71.73.

Chaper 3 Coupling Effect of Heat Transfer Area on Inlet flow

Actually, there is heat exchange on the spiral tubes, for which the helium property would change with it. The outlet helium temperature of intermediate heat exchanger is about 540 ℃. The linear relationship is researched with the helium property under 540 ℃, the fitting result is K=1.07×10

and C

=69.05. The fitting result of K and C2 changes 14% and 4% respectively, in permissible deviation. Moreover, this thesis mainly focuses on the inlet optimization of intermediate heat exchanger, so the porous media assumption is researched on qualitative analysis. So in the later calculation, the equivalent permeability is approximately set as K=1.24×10

，and inertial resistance factor as C

=71.73.

3.2 The Coupling Effect of Heat Exchange Area on Inlet Flow

In order to find whether the existence of heat exchange area would affect the inlet passageway flow distribution, a contrast approach is applied. In one case, the heat exchange area is treated as hollow chamber, defined as model A in this study, shown in Figure 3.6 (a). The other case is to consider the heat exchange area as porous media, defined as model B shown in Figure 3.6 (b). Comparing the inlet flow distribution of the two case to find whether heat exchange area has coupling effect on inlet passageway.

3.2.1 Physical Model

For a specific design of intermediate heat exchanger, the helium passageway geometrical dimensions in intermediate heat exchanger is shown in Figure 3.5.

Figure 3.6 displays inner region of two models used in the contrast calculations.

Figure 3.6(a) is the model of treating heat exchange area as hollow chamber. Figure 3.6

(b) is the model of treating heat exchange area as porous media, annulated column upper

section is where spiral tubes situate in the intermediate heat exchanger. The outer and

inner diameter of annulated column structure is 1380mm and 899mm, with the height of

2665mm.

Chaper 3 Coupling Effect of Heat Transfer Area on Inlet flow

Figure 3.5 Helium passageway geometrical structure in intermediate heat exchanger

(a) model A-—hollow chamber (b) model B—porous media Figure 3.6 Annulated column structure of heat exchange area

The physical passageway structure is modelled according to the actual structure of

intermediate heat exchanger by means of software ProEngineer, shown in Figure 3.7.

Chaper 3 Coupling Effect of Heat Transfer Area on Inlet flow

Figure 3.7 Whole passageway model

The unstructured tetra/mixed mesh is used to the whole domain and a refined surface mesh is used to specific region with small physical dimension to ensure good mesh quality.

The quantity of mesh elements is control to be over 0.4. The grid mesh model of two cases is shown in Figure 3.8. Figure 3.8(a) is the hollow chamber case and Figure 3.8 (b) is the porous media case.

(a) model A--hollow chamber model (b) model B-- porous media model Figure 3.8 Grid mesh model

3.2.2 Computation Model

The computation domain is divided into two regions, upper heat exchange region

and below inlet passageway region. The research is under the assumption of steady flow,

Chaper 3 Coupling Effect of Heat Transfer Area on Inlet flow

then governing equations are shown as following.

( u)  0

  (3-3)

2

(  uu ) p τ

 g S

        (3-4) u

(u( )) ( τ u)

p

2

c T p T S

  

         (3-5) In which,

2 2

τ ( )(2S uI) I

3 3

eff

 

 

   

k (3-6) Turbulence viscosity is,

2 t

C

k

  ^  (3-7)

u u

S 2

  



(3-8) In porous media region,

= ( F u )u S

K K

    ,

0 (3-9)

In other region,

=0

S

,  =1 (3-10)

3.2.3 Calculation Condition

According to the hot gas duct diameter and calculation condition shown in the Table 1, helium flow condition of inlet passageway is shown in Table 3.2. Inlet boundary is set as velocity inlet, normal to boundary, and the turbulence intensity is calculated by means of the equation,

0.16 Re

I u u



  (3-11) In which Re is the Reynold number calculated by means of hydraulic diameter.

The outlet boundary is set as outflow boundary. The walls of passageway are set as no-slip adiabatic wall.

Navier-Stokes equations were solved using the finite volume method. Refer to the

study by Zhou and Peng

the standard k-ε model was selected as the turbulence model

for the simulation in physical model. So in the calculation, the k-ε model is applied. The

heat exchange area is treated as hollow chamber or porous media for the contrast

computation.

Chaper 3 Coupling Effect of Heat Transfer Area on Inlet flow Table 3.2 Inlet helium flow condition

condition unit Value

helium velocity m/s 28.8

hydraulic diameter m 0.34

turbulence intensity 3.4%

temperature K 1173.15

pressure MPa 3

As helium flows through spiral tube area, it’s cooled by the heat exchange with the fluid in the second loop, thus helium physical character would change with it. Therefore, the heat exchange in this region should be considered. To make the model simple, it’s assumed that there is an even distributed heat source. When the inlet velocity in hot gas duct is 28.8 m/s, i.e. rated condition for the intermediate heat exchanger, the average heat exchange power is 6MW, then the even distributed heat source is calculated to be S

=- 2621110W/m

,in which, minus means that helium is cooled down in the heat exchange area.

In the calculation, the helium velocity is relative low, so the compressibility isn’t obvious. The helium is treated as incompressible ideal gas. Helium property is got by the fitted high order polynomials in reference temperature range by means of NIST Reference Fluid Thermodynamic and Transport Properties Database. The high order polynomials is fitted as following:

(3-12)  =0.05624 3.767 10  

T  8.735 10 

T

 1.664 10 

T

(3-13)

-6 -8 -11 2 -15 3

7.161 10 4.731 10

-1.016 10

1.88 10



(3-14)

Where C

is helium specific heat capacity, J/(kg·K). 𝜆 is thermal conductivity, W/(m·K). 𝜇 is helium viscosity, Pa·s .

3.2.4 Result and Analysis

Figure 3.9 represent the velocity contour of heat transfer area entrance cross section

plane. The velocity deviation of porous media model on this entrance plane is 0.5038,

while for the hollow chamber model velocity deviation is 1.7000.