Design and Analysis of a Multi-Window Aperture Structure

for a Small Particle Solar Receiver

Ioana D. Broome* and Fletcher Miller

†

San Diego State University, San Diego, CA 92182

This paper presents the design and analysis of a multi window toroispherical aperture

structure to be used on a Small Particle Heat Exchange Receiver (SPHER). SPHER consists

of a pressure vessel filled with a mixture of sub-micron particles and gas, with optical access

for concentrated sunlight on one end. Solar radiation is concentrated with a field of

heliostats and focused through the multi- window structure inside the vessel where the light

is absorbed volumetrically by the gas particle mixture. The spherical cap structure

presented in this paper serves as the head of the pressure vessel which comprises the

receiver. The interior walls of the receiver are under hydrostatic pressure of up to 5 bar and

the interior surface of the insulation protecting the metal will get as hot as 1000 Celsius. The

structure design has been continuously optimized in efforts to improve the physical and

mechanical properties of the receiver’s windows and increase the structural efficiency of the

solar receiver. Structural efficiency means minimizing the mass while maximizing the design

factor of safety. Subsequent to the studies and analyses ran on different geometries, a convex

stainless steel toroispherical cap under tension was designed, with six concave fused silica

windows mounted on it. The design choice is due to the cost and complexity of fabrication of

a larger, single fused quartz window, as well as maintenance and replacement of parts. The

final dimensions and geometry were established as a result of a series of static and thermal

analyses. It was found that for a minimum calculated factor of safety of 4, the pressure vessel

wall thickness must be at least 1.5 cm with thickened cylindrical section of 2 cm. The

windows minimum thickness was 1 cm.

Keywords: small particle solar receiver, pressure vessel, secondary concentrators, aperture structure

Nomenclature

���� = maximum Von Mises stress (Pa, MPa) H = height (m)

���� = maximum displacement (mm) SS = stainless steel

���� = maximum strain T = temperature (°C)

�� = principal stress 1 (Pa, MPa) FOS = factor of safety

� = principal stress 2 (Pa, MPa) P = pressure (Pa, MPa)

R = radius of circle / arc (m) V = volume (m3)

h = height (m) M = structural mass (kg)

t = thickness (m) = material density (kg/m3)

� = angle (°) Φ = diameter (m)

I. Introduction

ADIATION in the form of light and heat from the sun is what we call solar energy and it is an outstanding

source of renewable energy. Solar energy has been harnessed by people ever since the dawn of time. It is free,

renewable and only a minute percentage of solar heat is being used to help produce electricity. Solar power plants

are becoming more prevalent and they are being perfected all the time with the ultimate goal to produce cheap, non-

* Graduate Student, Aerospace Engineering, 1885 Diamond St, Apt. 320, San Diego, 92109, AIAA member

† Assistant Professor, Dept. of Mechanical engineering, MC 1323, San Diego, CA 92182

R

9th Annual International Energy Conversion Engineering Conference31 July - 03 August 2011, San Diego, California

AIAA 2011-5900

Copyright © 2011 by Ioana D. Broome. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

polluting and renewable energy. When developing such a facility there are many factors that have to be considered

regarding placement, weather and climate, structure and optics, cost and maintenance, and plant efficiency. All of

these affect the levelized cost of energy that is used as a metric for solar power plants.

Because of the rising levels of CO2 emissions and other energy concerns, the Solar Thermal Power Plants

(STPP) are becoming important candidates for producing clean, renewable energy4. The low flux density at Earth’s

surface makes it nearly impossible to heat up a Heat Transfer Fluid (HTF) such as air, steam or natural gas, to

temperatures adequate for industrial applications. In order to attain temperatures required to operate a

thermodynamic cycle, a STPP requires optical concentration. Solar radiation is converted to thermal energy inside

the receiver and later to electricity. Among the pioneers of solar energy technologies, the US developed tube

receivers in the late 90’s. Researching a cheaper, simpler and more efficient solution, Europe later developed the

volumetric receiver. The volumetric receiver is more flexible than the tube receivers due to its three-dimensional

configuration and its functionality.

From the structural point of view, the way to increase the plant efficiency is to design a capable and economical

structure that will maximize the intake of solar heat and minimize the thermal losses. Probably the most important

part of the receiver structure is the light and heat collector. The Small Particle Heat Exchange Receiver (SPHER)

that is currently being developed at San Diego State University will collect concentrated solar radiation through

several transparent quartz windows that can withstand the high pressure and high temperature located inside the

receiver. The windows are essential to this design to allow for volumetric absorption, and secondary concentrators

are proposed to minimize the size of the windows needed. The concept of volumetric absorption is explained in

Section II.

Figure 1. Small Particle Heat Exchanger Receiver (SPHER) Placement

In order to build the most efficient and cost-effective pressurized air-heating solar collector, a literature review

and study of similar structures was performed. The very few previous projects that have developed similar products

use windows shaped as shells of revolution that withstand the operating conditions of the receiver, including high

temperature and pressure. The first part of the study focused on these previously developed structures as a starting

point for improving this design and building the SPHER.

In this research, flat and curved profiles for the pressure vessel head were compared and a weight minimization

study was used to choose the depth of the head. Next, the profile of the pressure vessel head was analyzed and the

curvature reshaped as a result of the stress analysis performed on it. Finally, the vessel body was structurally

optimized and a series of stiffeners are evaluated. After determining the ideal thickness for both assembly parts:

head and body, respectively, a final design was presented. After the final design was confirmed, a material selection

step was carried out, choosing the material with the highest performance under the given operating conditions.

II. Literature Review and Research of Similar Products

A. The SPHER

The small particle solar receiver is a design introduced by A.J. Hunt in 1979.1 It is basically a volumetric

pressurized solar receiver that uses very small particle clusters of carbon to absorb the concentrated sunlight and

transfer it to a gas which flows into a turbine where the thermal energy is transformed into electricity. The choice of

carbon is due to its physical, chemical and optical properties.1

Heat and radiation from the sun is reflected from the

heliostats into the receiver where it is trapped. Very small carbon particles are injected into the receiver where they

capture the heat. The extremely hot mixture of air and carbon particles exits the receiver and enters a gas turbine

which powers a generator to generate electricity. The carbon particles actually burn up before they exit the receiver

so the hot mixture is mostly air.

The previously tested SPHER was limited to atmospheric operation and 30 kW of power. A variation of this

small particle solar receiver is currently being developed at San Diego State University (SDSU).10,14

Concentrated

sunlight will enter the pressurized vessel through a series of fused silica windows shaped so that they can withstand

a maximum hydrostatic pressure of 5-10 bar (0.5 – 1 MPa).2,10

The gas temperatures inside the receiver will reach

1000° Celsius. The pressure vessel’s inner walls are insulated as well as the head structure that contains the

windows. A conceptual schematic showing a single window is presented in Figure 2

Figure 2. SPHER schematic with a single window

The solar radiation (1) enters the receiver through the window or window assembly (2). Gas particle inlets (3)

inject a mixture of air from the turbine’s compressor (8) and small carbon clusters (4). The mixture circulates up to

the window area, where the gas temperature reaches the hottest point (5) and absorbs the heat. The hot mixture of air

and carbon clusters is transported through an outlet (6) and powers a gas turbine (7). The mechanical power is

transferred to a generator (9) which produces electricity.3

B. Volumetric Receiver

The basic operating principles of a volumetric receiver are: 4

• A cluster of porous shapes, foam, metal, ceramic or other

adequate materials with a specific porosity are placed in a

volume inside the solar receiver so that the solar radiation

is absorbed in the depth of the structure

• The porous material inside the receiver is heated by the

concentrated solar radiation. The working fluid passes

through the volume and is heated by forced convection

transforming the radiation into thermal energy.

The absorber can be ceramic or metallic. Ceramic absorbers can

reach higher temperatures than metallic ones, but are prone to

cracking.

Figure 3 Volumetric Receiver Schematic

Volumetric receivers have been studied in the past 30 years and classified in 4 subgroups: 4 Phoebus-TSA, SOLAIR,

REFOS and DIAPR. The classification above was made based on the air pressure and materials

• Phoebus – TSA type: open-loop volumetric receiver with metallic absorber

Projects of this type: MK-1, Sulzer 1 (MK-2), Sulzer 2, Catrec 1, TSA, Bechtel 1, Bechtel 2, Catrec 2,

SIREC

• SOLAIR type: open – loop volumetric receiver with ceramic absorber

Projects of this type: SANDIA foam, CeramTec, Conphoebus-Naples, Selective Receiver, HitRec 1,

HitRec 2, SOLAIR 200, SOLAIR 3000

• REFOS5and DIAPR

6 type: closed- loop volumetric receiver with metallic or ceramic absorber

Projects of this type: PLVCR-5, PLVCR-500, DIAPR 30-50, DIAPR multistage, REFOS, SOLGATE

C. REFOS (Solar-Hybrid Gas Turbine-based Power Tower Systems)

In 1996, the German Aerospace Center called Deutsches Zentrum für Luft-und Raumfahrt (DLR) developed a

pressurized volumetric solar receiver as part of the REFOS project, tested at Almeria, Spain. The receiver system

consisted of a module of 350 kW nominal power, which included a pressurized volumetric receiver and a secondary

concentrator. The system was operated for 90 hours and it reached a maximum power of over 400 kW. There was

only a minor mirror gluing issue; however the test was able to demonstrate the technical feasibility of the modular

receiver technology.5 The REFOS module operating conditions are: 350 kW of thermal power, 15 bar operating

pressure, up to 800° C air outlet temperature and a receiver efficiency of 80%. The schematic of the receiver as well

as an image of the secondary concentrator is shown in Figure 3.5

Figure 4. Schematic of the solar receiver with the secondary concentrator by DLR (left) and the DLR

secondary concentrator (right).5

The receiver window has a semi-elliptical profile with a 620 mm diameter at the open end and a 420 mm depth.

Its thickness is 8 mm and it has been certified up to a 19.5 bar pressure. The Compound Parabolic Concentrator

(CPC) has a hexagonal entry aperture with an inscribed circle of 1.2 m diameter. Its acceptance angle is 20° and its

length is 1m. The flat trapezoidal aluminum plates that form the structure are water-cooled and have backsilvered

glass mirrors glued onto the plates.5

D. DIAPR (Direct Irradiated Annular Pressurized Receiver)

This type of receiver is a volumetric (directly irradiated) cavity receiver. Its operating pressure is between 10 and

30 bar, the outlet gas temperature is up to 1300 °C and its aperture radiation flux is 10 MW/m2. The DIAPR receiver

can be used at a power of 100 kW to power a Brayton cycle. The three main innovative components of the DIAPR

receiver are: the high temperature ceramic Porcupine absorber, the fused silica Frustum-Like High–Pressure (FLHP)

window and the two stage secondary concentrator followed by the KohinOr light extractor.6

Figure 5. Schematic cross-section of the DIAPR receiver (left) and window (right).6

The Frustum-Like High-Pressure window’s purpose is to separate the receiver cavity from the outside medium

and allow operation at high pressure while minimizing the reflection losses of solar radiation which enter the

receiver. A closed- loop test using carbon dioxide (CO2) as the working fluid showed that the window survived a

pressure of up to 30 bar (3 MPa), contamination from dirt and large amounts of graphite from the CO2 deposited

onto its surface. Ray tracing calculations showed that the reflection losses of the window are about 1%. Window

dimensions (in millimeters) are shown in Figure 5. 6

E. Scope of the research (design and analysis of structure)

The work done in this research builds on the effort started over 30 years ago at the Lawrence Berkley Laboratory

and it supports a larger project with the purpose to help develop and test a prototype small particle solar receiver like

the one presented in Section II -A. Its relevance to the big project is to calculate the structure that will withstand the

workloads as well as show its structural capabilities as part of the whole power plant assembly.

The Small Particle Heat Exchange Receiver (SPHER) currently in development at SDSU proposes to use a

suspension of small carbon particles entrained in the gas as the absorber, in contrast to previous absorbers described

above that are fixed structures. The pressure vessel is much larger than anything developed before for this purpose,

and it has multiple large windows mounted on one end. The work of this research focuses on the structure of the

receiver, with special attention given to its head assembly that includes the windows and their mounting mechanism,

as well as the secondary concentrators. The secondary concentrators will reflect more of the light inside the vessel

and more solar radiation will be absorbed by the small carbon particle clusters. No optical analysis is performed on

the secondary concentrators.

Figure 6. SPHER assembly showing windows and secondary concentrators – artist’s rendition only

III. Conceptual Design

The receiver initial dimensions chosen for analysis were 3 meters in diameter and 5 meters tall. 3 The multiple

windows concept is investigated due to possible ease of manufacturing as well as lowering the costs compared to a

single large window. An array of 6 windows is proposed to be installed on the end oriented towards the heliostats.

They are about 1 meter in diameter, having the same profile as the head of the pressure vessel, but instead of being

in tension they will be compressed by the pressurized gas. 7

A. Pressure Vessel

Before the preliminary design phase started, the failure criteria were selectively analyzed. The failure criterion

was chosen to be Von Mises. This stress/failure theory is favorable for ductile materials. Although it is less

conservative than the Maximum Shear Stress Theory (Tresca yield criterion), it is more conservative than the

Maximum Normal Stress Theory (Rankine criterion). A comparison graph of all three theories is shown in the figure

below. 8

Legend

DE = Distortion Energy Stress Theory (Von Mises)

MN = Maximum Normal Stress Theory (Rankine)

MS = Maximum Shear Stress Theory (Tresca)

F

Figure 7. Projection of the Failure Criteria on

the σ1, σ2 plane. 8

1. Head Structure Profile

The first stage of the conceptual design phase was calculating and choosing the shape profile of the pressure

vessel head. The first step was to figure out whether the design should be a flat, convex‡ or concave

§ profile for the

spherical cap. Intuitively it can be said that the flat head would be very inefficient because of the large deformations

it would undergo or very costly because it would have to be very thick to withstand the constant pressure of 5 bar.

However, a flat head might provide some advantages for mounting the secondary mirrors so all three designs were

analyzed. The dimensions are listed in Table 1Table 1. For this analysis the rest of the pressure vessel did not need

to be modeled, the head shapes being enough to provide a good comparison. The caps (convex and concave) are

spherical caps cut at a 60° angle for reasons presented in the angle study section (III,A,2). The static analysis was

performed at room temperature and a pressure of 5 bar (0.5 MPa) was applied.

Table 1. Analysis results of the three head geometries

Analysis results Pressure only (5 bar) Pressure (5 bar) and temperature (100 °C) units

Flat Convex cap Concave cap Flat Convex cap Concave cap

� �� 738 30.501 30.584 920 459.7 420.9 MPa

� �� 46.87 0.1277 0.13 57.25 0.967 0.714 mm

� �� 2.671e-3 9.872e-5 9.935e-5 2.635e-3 1.138e-3 1.003e-3

The thickness chosen for this study was 1.54 cm (~1 in). The mass of the curved ones was 1887.17 kg, while the

mass of the flat head was, 23.89% lower (1436.34 kg)

‡ Convex spherical cap: has the pressure applied inside its curvature and it is in tension

§ Concave spherical cap: has the pressure applied on the outside surface and is under compression

Figure 8 Geometry of the three concepts from left to right: Flat, Convex, Concave

As it can be deducted from the results in Table 1, the convex head analysis returned better results (lower stress

and maximum deformation) and was therefore chosen to be the design solution for the pressure vessel head. The

pressure was applied on the inside curved surface.

2. Angle Study7

A weight minimization study (see Figure 9) was carried out next, meaning the least weight and therefore most

cost efficient profile of the spherical cap was calculated, which was represented by a shell of revolution of height H,

radius R, angle θ and thickness t (See Figure 10a). Using the thin shells of revolution theory9, the minimum

thickness t was calculated as described in Ref.7 for the optimum angle. Shells of revolutions are shells that have the

same exact cross-section at any plane that contains the axis of rotation we would use to intersect the shell (e.g. a

shape made from a profile sketch revolved around the axis of rotation)

Figure 9. Weight minimization study; θ=5° to 90°

As Figure 9 shows, the most efficient geometry for the head, corresponding to the minimum mass with the

maximum strength was the spherical cap cut at an angle � � 60°.

0

50

100

150

200

250

300

350

400

450

500

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

Mass

(k

g)

Angle (deg)

5 bar

10 bar

15 bar

20 bar

25 bar

Mimimum

Mass

Figure 10. Initial head profile (a. left) and optimized head profile (b. right). Dimensions in meters

3. Head curvature update

First, the calculated 60° profile was selected and a set of static analyses was performed on the head shaped as

seen in Figure 1010a. Stress concentrations were found around the joints (where the heads weld onto the cylindrical

body). As a result of these high stress concentrations, the ends are chosen to be filleted, thus creating a toroispherical

head. The toroispherical head simulates the ellipsoidal one by a compound curve made of a crown radius and a

knuckle radius (see Figure 10b). The knuckle radius has to be big enough to minimize the hoop stresses around this

region. According to the ASME Pressure Vessel Code, the knuckle radius (R1) has to be at least 6% of the crown

radius (R 1.73).11

In this case it is well over the minimum required in an effort to minimize the hoop stresses.

4. Pressure Vessel Bottom Profile

The design of a pressure vessel, especially one subjected to a thermal load, is far from simple and therefore a

series of steps need to be performed. According to the ASME Boiler and Pressure Vessel Code, section VIII, the

design factor of safety for a pressure vessel has to be a minimum of 2.5 – 4.11

Based on the head curvature study7

and the fact that the pressure vessel in question is not a storage tank, the flat bottom was eliminated in the

conceptual design phase. Two profiles were modified and analyzed. No thermal effects were considered at this stage

and the pressure applied was 5 bar (0.5 MPa). The material applied was stainless steel type 316, known for its high

temperature strength.

To make sure that the vessel will withstand the pressure inside without excessive deformation, a series of static

tests were performed. As a design outcome of this test, the geometry of the vessel was also improved, to

accommodate the pressurized gas inside the receiver. The design parameters, such as the bottom shape and the wall

thickness, were updated until the overall design was within the ASME constraints. The outcome and results are

presented in Table 2.

Table 2. Pressure Vessel Bottom Profile Selection

Profile 1 2 3

Thickness 2.5 cm 5 cm 2.5 cm

Shape Concave (compression) Concave (compression) Convex (in tension)

Min FOS 0.936 3.036 11.339

Stress

plot

Starting from a typical pressurized vessel, such as a soda can or a champagne bottle, the initial stage of the shape

selection is modeled accordingly. A bottom under compression (concave) is given to the pressure vessel and a

uniform thickness is applied. When the 2.5 cm initial selected thickness fails the static test, the thickness (and with it

the mass) is doubled. The factor of safety for the thicker vessel (5 cm) is still below the minimum accepted. In an

effort to minimize the mass, the convex (in tension) bottom is analyzed. A uniform thickness of 2.5 cm is given and

the minimum calculated factor of safety increased a great deal. Much more satisfying, the third profile was selected

for further analyses. During this design phase, the calculated factor of safety was brought from 0.936 to 11.339,

another proof that smart design can save unnecessary use of extra material.

5. Stiffeners

As a result of the pressure vessel bottom profile section, the convex bottom was selected as effective. The high

stress area for this design is around the cylindrical portion of the vessel. To help minimize or eliminate hoop stresses

on the cylindrical part without thickening the wall everywhere structural stiffeners are proposed. Three types of

stiffeners were analyzed.

Table 3. The three types of stiffeners tested

Stiffener One ring Three rings Thicken cylindrical part

Mass (kg) 392.96 1178.88 2416.8

Min FoS 11.36 11.388 17.148

Section

stress

plot

Assuming weight is not a factor but structure quality alone, the third proposed stiffener type was selected for

further studies. In Section IV an optimization of the wall thickness is performed and thus, the weight of this model

will be minimized.

6. Pressure vessel head with portholes analysis

A final shape was calculated for the pressure vessel but in order to install windows on one head, portholes need

to be created on the respective head. Holes will generally weaken the head which provides structural support for the

windows and the windows are desired to be as large as possible so a compromise needs to be made. The array was

established to be one central window port and five of the same size ports equally spaced around the middle one.

A static analysis was performed on the steel pressure vessel head with 6 portholes cut outs. This is called the

aperture structure. The inner pressure difference applied to the stainless steel 316 structure was 0.5 MPa (5 bar) and

the operating temperature was 25 °C. Circular loads corresponding to the windows were applied around each

porthole. Figure 11 illustrates the Von Mises stress field on the top (a) and the bottom (b) of the head. The stress

plot reveals stress concentrations around the window portholes which calls for some structural reinforcements

around the edges. Special flanges welded onto the edges could possibly solve this problem. Figure 12 is a

displacement plot of the head shown on the top (a) and bottom (b) of the same structure, the head of the pressure

vessel. The displacement plot exposes a radial deformation field around the center porthole. This type of

deformation cannot be avoided in the convex shell of revolution head geometry, so the solution proposed is to leave

enough clearance between the edges of the secondary concentrators that are to be installed on top of this structure.

The clearance is necessary to avoid surface interference and cracking of the secondary concentrators.

Figure 11. Stress plot on the: (a. left) top and (b. right) bottom of the head structure; Pressure = 0.5 MPa @

room temperature

Notice how the stress concentrations are seen only on the inside surface of the head structure due to the hydrostatic

pressure. The stresses are minimized and/or dissipated by welding of the mounting special flanges onto their edges.

Figure 12. Displacement plot on the: (a. left) top and (b. right) bottom of head structure; Pressure = 0.5 Mpa

@ room temperature

B. Window

The window is one of the most difficult parts of the assembly to fabricate in a custom shape and install on a

stainless steel structure. The selected material is fused silica due to its extremely low thermal expansion and very

good optical properties. It was showed by a weight minimization study10

that the optimum cut angle for the spherical

cap representing the window under compression is 60°. The portholes created on the head aperture structure exposed

to the concentrated solar radiation are no larger than 1 meter in diameter due to the need of structure for support as

well as to prevent intersection of the windows and/or flanges due to head curvature and thermal expansion (see

Figure 14a). Special flanges welded to the portholes are used for windows installation. Thus, the window outer

diameter must be less than or equal to 0.96 meters. A surface with a 0.96 meters diameter was revolved and a design

study was performed to calculate the optimum thickness. The tensile strength of fused silica is 50 MPa and a

minimum factor of safety of 5 was set for the window’s principal stresses. This means the maximum acceptable

principal stress can be no higher than 10 MPa. An optimization study was carried out following the constraints

mentioned earlier and thus the minimum allowable window thickness was found to be 1 cm. Because the edges are

especially problematic when it comes to principal stresses, a shape optimization step was performed changing the

curvature of the window from spherical cap to toroispherical.7

Table 4. Window curvature study; from the spherical cap with edges at an angle (profile 1) to the

toroispherical head with straight edges (profile 3)

Profile 1 Profile 2 Profile 3

Sketch

Max

principal

stress

(MPa) 7.053 3.78 1.445

Mass (kg) 20.86 24.36 28.98

All the results were within the principal stress limits established (max 10 MPa) and therefore they were all

feasible designs. As a result of this curvature study, the potential client is given the option to choose between cutting

fabrication costs by saving weight or maximizing performance where weight is less important than performance. For

future assemblies and analyses, the third profile is used. For more info on the window assembly and seal see Ref. 7

and Ref.10.

C. Secondary concentrators

The pressure vessel with windows is directly exposed to concentrated solar radiation coming from the heliostat

field. The addition of some secondary concentrators is necessary because they need to redirect radiation from

impinging on the solid portion of the head (see Figure 14a) into the windows. This will prevent overheating the

stainless steel head and allow all the light to be captured. The pattern is chosen to be a pentagonal aperture in the

center surrounded by hexagonal aperture concentrators. The “soccer ball” model (see Figure 14b) is chosen for best

fit. Their pentagonal aperture has an inscribed circle with the diameter Φ1.652 meters and the hexagonal apertures

have an inscribed circle with a Φ1.905 meters diameter.7 The acceptance angle is 132.12° at this stage in the design

but this could be changed once the heliostat field is chosen. This is shown in Figure 13 below.

Figure 13. Field concentration angle and secondary assembly acceptance angle

Figure 14. Solar receiver with windows exposed to concentrated radiation (a. left) and “soccer ball” pattern

secondary concentrators assembly without windows (b. right)

Backsilvered mirrors or a high temperature aluminum alloy are recommended for the fabrication of secondary

concentrators. A simple static analysis was run on the concentrators’ structure to assure its ability to withstand the

pressure from inside the vessel. A maximum displacement of 0.42 mm was exhibited by the edges around the center

concentrator and a maximum Von Mises stress of 41.174 MPa was calculated around the special flanges when the

concentrators were installed onto the aperture structure. This means a 66.54% decrease in maximum stress due to the

flanges and installed concentrators. The plots are shown in Figure 15.

Figure 15. Stress (left) and displacement (right) plots on the head assembly with concentrators and flanges.

IV. Design Optimization and Detailed Model Analysis

A. Material selection

Due to its high chromium content, very good corrosion and oxidation resistance and surface quality, the

austenitic class of stainless steels is selected for the high-pressure high-temperature pressure vessel head.12

A few

examples of steel belonging to this class are types: 201, 301, 304, 310,316, 316L, 321 steel, named by the SAE

standard. Four grades of austenitic stainless steel were selected for the pressure vessel design and analysis: SS310,

SS316, SS321 and SS347. Their mechanical and physical properties are listed in the Appendix. They are considered

high alloys due to their high chromium content. The high alloy steels typically exhibit excellent strength at elevated

temperatures along with creep deformation resistance and other environmental attacks such as oxidation and

corrosion.12

Figure 16 shows the effects of temperature on the yield strength of all four materials selected.

Because of all the challenges of fabricating such a complex structure, the actual design can help a great deal with

the structural workloads. A smart material selection is very important and can save future maintenance as well as

minimizes the weight of the structure.

Figure 16. Temperature Effect of Yield Strength of Stainless Steel **

B. Structural Optimization

In order to achieve the desired performance while designing the structure within the limits set by the ASME

standard, there is no need to over-design a bulky vessel, but rather optimize its design variables, such as the

thickness. After calculating the final geometry for the pressure vessel, a structural optimization step was performed,

in an effort to minimize the weight of the product. The optimization study was performed using SolidWorks® and

its optimization package, Design Study.

The design optimization study analyzed different thicknesses ranging between 1 cm and 3 cm for both parts of

the pressure vessel. The step chosen is 0.5 cm and therefore 16 design scenarios were described. The minimum

design factor of safety was set to 4, which limited the maximum Von Mises stress anywhere in the structure to less

than or equal to 77.5 MPa. The goal was to minimize the mass. It was found that for a steady hydrostatic pressure of

up to 5 bar and inside temperatures of up to 800 °C, the minimum required thicknesses of the pressure vessel with

the earlier mentioned dimensions are: 1.5 cm for the head and 2 cm for the middle section. It is desired that the wall

temperature be much lower than 800 °C, but this study was meant to show that the designed pressure vessel would

withstand the maximum operating temperature of stainless steel if it had to.

**

Data from http://www.sandmeyersteel.com/300-series-heat-resistant.html

0

50

100

150

200

250

300

350

0 200 400 600 800 1000

Yie

ld S

tren

gth

(M

Pa

)

Temperature (C)

310S

316

321

347

The optimization study was done for the targeted work conditions, but it was proven that the change in pressure

ratio of the cycle can lead to a greater expansion ratio through the turbine and increase the power output.13

To assure

the correct functioning during off-design operation, the margin of error established for the pressure will be 60%,

which means that the design factor of safety for an 8 bar pressure has to be higher than 4. A new study showed that

the structure could withstand a hydrostatic pressure up to 0.8 MPa (8 bar) but the temperature increase made the

structure fail.

In conclusion, it is advised that the steel inner walls not to reach temperatures higher than 800 °C at any given

time and the maximum allowed pressure at elevated temperatures should be no higher than 0.8 MPa (8 bar). There

are stainless steel types that could operate at temperatures up to 1000 °C, such as 310S, but when pressure comes in

play an insulation jacket is recommended to avoid thermal

cycling, fatigue and ultimately structural failure. For the

complete study see Ref.7.

C. Structural Characteristics

The stainless steel pressure vessel studied in this thesis will

be fabricated out of austenitic stainless steel of type 310S, 316,

321 or 347. Type 310S is preferred due to its higher maximum

service temperature. It is 4.76 meters tall, has an inner diameter

of 3 meters and non-uniform wall thickness of: 1.5 cm for the

toroispherical heads and 2 cm for the cylindrical section,

respectively. The design drawing with dimensions in meters is

shown in Figure 17. The structural capabilities of this structure

are: a constant hydrostatic pressure of 5 bar (0.5 MPa) with the

maximum no higher than 8 bar (0.8 MPa) and a maximum

continuous temperature of 800 °C.7 Cyclic loading, fatigue and

creep were not considered in this study. A future, final design

should include these considerations.

V. Conclusion

Considering factors like lawful constraints, such as the ASME Boiler and Pressure Vessel Code, service limits

and design boundaries, an optimum model for a SPHER receiver was calculated in an effort to minimize the weight

and cost of the material while maximizing performance. The material choice was an important step as it can save the

manufacturer extra work and the financer extra costs. The windows and the pressure vessel heads are loaded on

opposite surfaces and are made of very different materials, fused silica and stainless steel, respectively. Despite

these facts, it was found that the optimum shape profile for both components was toroispherical and the theory of

thin shells of revolutions was used in both cases to help calculate the weight minimization studies. Due to

continuous exposure to solar radiation as well as scattered light a mirrored secondary concentrator was attached to

each individual window. The structural capabilities of the SPHER assembly were calculated as well. Thus, the

maximum allowed continuous temperature inside the vessel was 800 °C and the maximum admissible pressure was

0.8 MPa (8 bar). Since the working gas inside the receiver is targeted to heat up to 1000 °C, the solar receiver

structure must be insulated effectively so that the inner walls will not overheat above 800 °C, to prevent structural

failure. A rendition of the complete exploded view of SPHER assembly is displayed in Figure 18.

Figure 17. Final Pressure Vessel Design;

dimensions in meters

Figure 18. Exploded view of solar receiver

VI. Appendix

Table 5. Material properties in SI units

Property Metric units 310S 316 321 347

Young's Modulus Pa (N/m2) 2.04E+11 2.05E+11 2.05E+11 2.04E+11

Shear Modulus Pa 8.1E+10 8.2E+10 8.2E+10 8.1E+10

Density kg/m3 8040 8070 8050 7970

Poisson's ratio - 0.275 0.275 0.275 0.275

Tensile strength Pa 6.2E+8 6.2E+8 6.6E+8 6E+8

Yield strength Pa 3.1E+8 3.1E+8 2.41E+8 2.8E+8

Specific heat J/kg/K 530 530 530 530

Max service Temperature K 1420 1200 1200 1200

Max service Temperature C 1146.85 926.85 926.85 926.85

Fatigue Strength (107 cycles) Pa 2.28E+8 2.52E+8 2.47E+8 2.52E+8

Thermal conductivity (100 C) W/(m*K) 13.8 14.6 16.3 16.3

Thermal conductivity (500 C) W/(m*K) 18.7 20.942 21.4 21.4

CTE (0-100 C) /K 1.440E-05 1.602E-05 1.674E-05 1.674E-05

CTE (0-200 C) /K 1.620E-05 1.620E-05 1.710E-05 1.710E-05

CTE (0-300 C) /K 1.692E-05 1.746E-05 1.854E-05 1.854E-05

CTE (0-400 C) /K 1.746E-05 1.854E-05 1.926E-05 1.908E-05

CTE (0-500 C) /K 1.908E-05 1.998E-05 2.016E-05 1.998E-05

Max temp w/o

excessive scaling K 1366.4833 1172.0389 1172.0389 1172.0389

Stress relieving temp K 1310-1422 1310-1422 1310-1423 1310-1424

VII. Acknowledgments

I would like to thank Dr. Fletcher Miller, my thesis adviser, for guiding me in the right direction and not letting

me get distracted.

Thanks to Dr. A.J. Hunt, the inventor of the SPHER, for his insight on different design matters.

Thanks to my lab peers for making the work environment pleasant.

Lastly, thanks to Google.org RE<C program for funding this project.

VIII. References 1Hunt, A. J., “A New Solar Thermal Receiver Utilizing Small Particles,” in Proc. Int. Solar Energy Society Conf.,

Atlanta, GA, 1979 2Kitzmiller, K., and Miller, F., “Thermodynamic cycles for a small particle heat exchange receiver used in

concentrating solar power plants”, Journal of Solar Energy Engineering, accepted for publication August, 2011. 3Ruther, S.J., Radiation heat transfer simulation of a small particle solar receiver using the Monte Carlo method,

M.S. Thesis, Mechanical Engineering, San Diego State University, CA, 2010 4Avila-Marin, A.L., Volumetric Receivers in Solar Thermal Power Plants with Central Receiver System Technology:

A Review, CIEMAT, Departamento de Energia, Avda Complutense 22, E-28040 Madrid, Spain††

5Buck, R., Abele, M., Kunberger, J., and Denk, T., “Receiver for Solar-Hybrid Gas Turbine and Combyned Cycle

Systems”, 9th

International Symposium ‘Solar Thermal Concentrating Technologies’ Font Romeu – Odeillo, France,

June 22-26, 1998 6Karni, J., Kribus, A., Doron, P., Rubin, R., Fiterman, A., Sagie, D., “The DIAPR: A High-Pressure High-

Temperature Solar Receiver”, ASME Journal of Solar Energy Engineering, vol. 119, Feb 1997 7Broome, I., “Design and Analysis of a Multi-Window Aperture Structure for a Small Particle Solar Receiver”, M.S.

Thesis, Department of Aerospace Engineering, San Diego State University, CA, December, 2011 (unpublished) 8Moss, D.R., Pressure Vessel Design Manual, 3

rd ed., Elsevier Inc., 2004

9Ugural, A.C., Stresses in Plates and Shells, 2

nd ed. McGraw-Hill, 1999

10Mande, O., “Window and Seal Design for a Small Particle Solar Receiver”, M.S. Thesis, Department of

Mechanical Engineering, San Diego State University, CA, August, 2011 (unpublished) 11

ASME Boiler & Pressure Vessel Code, Section VIII- Rules for construction of Pressure Vessels 12

Oberg, E., Jones, F.D., Horton, H.L., Ryffel, H.H. Machinery Handbook, 25th ed., Industrial Press Inc, New York,

1996 13

Kitzmiller, K. and Miller, F., Effect of Variable Guide Vanes and Natural Gas Hybridization for Accommodating

Fluctuations in Solar Input to a Gas Turbine, ASME 2011 Turbo Expo, June 6-10, 2011 Vancouver, Canada 14

SolidWorks Education Edition 2010-2011, Software Package, SP5.0, Dassault Systemes, Paris, France, 1995-2010 15

Microsoft Office, Software Package, Ver. 2003, Microsoft, Redmond, WA

††

Found at www.elsevier.com/locate/solener