where <r = maximum permissible stress /; = maximum internal pressure <1 = cylinder internal diameter I = wall thickness.

I he maximum stress to be used in the calculation depends on the material to be used for the cylinder wall. It should be some fraction, say O.N, of the yield or proof stress rather than the ultimate stress. The yield stress foi metals ranges typically from 138 to 1(134 MN/m2 (20 000 to 150 000 lbs per sq in) and varies widely with temperature. The sale stress declines markedly and progressively with elevated temperature. Therefore cylinder design should not be undertaken without a good knowledge and understanding of the materials to be used and the temperatures likely to be attained. Frequently, the superior strength characteristics of alloy steels are achieved by particular forms of heat treatment or mechanical processing and can be profoundly affected by operation al high or even moderately elevated temperatures.

A complete discussion of material properties is beyond this text. I lowever it should be clearly understood that selection of proper materials is the key to success and due regard should be paid at the design and development stage.

As a general rule the hot parts will likely be constructed from materials having superior strength characteristics at high temperatures. They will most likely be alloys containing an appreciable proportion of nickel and chromium. Stainless steels, typically an alloy of 18 per cent chromium and 8 per cent nickel, are readily available in a wide variety of sizes and forms and can be used for most early prototype development work.

In design of the engine care must be taken to avoid the creation Of 'stress raisers'. These are areas where sudden changes in section occur such as corners, kcyways. slots etc. where the local stress levels may be several times greater than the mean stress. This can lead to the formation and development «>f cracks that will eventually result in mechanical failure of the component. 'Stress raisers' can be avoided by careful attention to design to avoid sudden changes in section by the use of well rounded corners and fillets, large diameter holes, etc. There are many excellent texts on the design of mechanical machine elements which

Fig. 5.2. Application of domed cylinder heads and displacer to avoid local stress concentration.

The significance of local stress concentration is particularly important at high temperatures and for this reason many cylinders have curved or domed ends rather than a simple plane end. This is illustrated in f-ig. 5.2. The reciprocating element operating in the cylinder, the piston or displacer. should of course have a shape at the end corresponding to the internal form of the cylinder. This is necessary to reduce the 'clearance space', to a minimum— that is, the volume in the cylinder above the displacer at the top dead centre position.

Dome-ended metal forms for displacéis and cylinders may be acquired from many unlikely sources as ati alternative to 'one-off' manufacturing which tends to be expensive. Many model engines have been constructed with the cylinder and displacer made from aluminum cigar cases, one fitting inside the other. At a somewhat higher level, excellent stainless steel hemispherical forms in a reasonable range of sizes and wall thicknesses may be found among the soup ladles in the better class kitchen or commercial food equipment stores. These may be readily welded to stainless steel tubes to form the required shape.

Opportunities for such innovation abound and should not be overlooked by the designer anxious to minimize the tinte and cost of production.

thermai. ri-ff-cts

Thermal conduction

All materials conduct heat to a greater or lessei extcnl. Metals arc of heat conducted by a given material is characterized by the physical property called the thermal conductivity, k. The units of thermal conductivity are watts per square metre of cross section in the direction of heal flow per metre of thickness of the material per degree centigrade temperature dilTcrcnce across the thickness of the material, i.e. kW/m DC.

The amount of heat conducted along a cylinder from the hot end to the cold end may be estimated from the equation:

where Oc= rate of heat transfer (watts) by conduction along the cylinder walls k thermal conductivity of the material A = area of cross section for heat flow = tt<// A7 - temperature difference between the hot and cold ends of the cylinder I = length of cylinder.

I herefore

It will be recalled from the above discussion of the Heale number, that approximately.

where L - piston stroke. We know from the stress eqn (5.7) that p -(2ln)lil so that

Therefore, the ratio.

where K is a constant K = {arf2k). This illustrates the interesting lact that the ratio of power to heal transfer by conduction, is (1) Independent of cylinder diameter, wall thickness and temperature ratio, (2) strongly dependent on the length of the cylinder, the piston stroke and cyclic frequency.

The ratio P/Oc, which clearly, should be as high as possible, is increased by the use of a cylinder material having a high strength (high ir) •nwl *.i lr«»> <-<%rwliu'fivitv (Inw i I Fortiinnlflv 0:iinl<»<;<: sterl k ;t material which combines the characteristics of high strength at elevated temperatures with thermal conductivity. Furthermore, it is available at moderate cost and can be readily formed and joined by welding or brazing. It is therefore the preferred choice of material for most serious prototype engines. It is often replaced by more exotic materials in the 'second-round' sophisticated advanced designs of prototype engines.

Shuttle heat transfer

An important thermal effect found in Stirling engines called 'shuttle heal transfer' has the effect of increasing the apparent thermal conductance loss. 'I hc effect comes from the reciprocating action of the displacer in the cylinder. There is a temperature difference along the walls of the cylinder and the displacer, frotn the hot end to the cold end. With the displacer in the top dead centre position the temperature profile of the displacer along the length may be very similar to that of the adjacent cylinder wall as shown in Fig. 5.3. Then the displacer is moved to a region where the temperature of the cylinder wall is much less. Consequently heat will be transferred (by gaseous conduction and radiation) from the hot displacer wall to the cooler cylinder wall.

A similar process will occur if the cylinder wall temperature is above the displacer wall temperature when the displacer is returned to the top dead centre position. In this case of course the direction of energy flow would be from cylinder wall to displacer. I luis a progressive stepwise heat

Fig. 5.3. Dingram illustrating .shuttle heat trnnsfet in Stirling engines As the displarer moves from llie top to bottom dead ccntrc the hot parts of the displaeer nrc adjneent to the cooler cylinder walls. The ellect is to increase the heat transfer from Ihc diftplacci to the cvllnder walls, so increasinc the effective thermal conduction loss.

Fig. 5.3. Dingram illustrating .shuttle heat trnnsfet in Stirling engines As the displarer moves from llie top to bottom dead ccntrc the hot parts of the displaeer nrc adjneent to the cooler cylinder walls. The ellect is to increase the heat transfer from Ihc diftplacci to the cvllnder walls, so increasinc the effective thermal conduction loss.

transfer occurs, evocatively christened by Finkelstein as the 'bucket-brigade loss' but which has become known, more mundanely, as shuttle heat transfer.

The effect can be very important, particularly in small cryogenic cooling engines and most studies of the effect have been directed to that application (Zimmerman and Longsworth 1971). It corresponds to an effective increase in thermal conductance but is difficult to estimate until the design of the engine is complete.

It is self-evident that the shuttle heat transfer loss can be minimized by the use of a small stroke. However, given a particulai piston swcpl-voluinc, the use of a small stroke implies the use of a large diameter. This in turn requires a thick cylinder wall and large cylinder circumference which combine to give a large cross-section area for simple conduction heat transfer. This is true for both the cylinder and displacer wall conduction. Therefore, with use of a shorter stroke, the gain in reduced shuttle heal transfer may be largely offset by an increase in the conduction heat transfer. Martini (I978d) has summarized available data on shuttle heat transfer. Judicious generalization ol his recommendations lead 10 the following approximate equation which may be used, with caution, for estimation of the shuttle heat transfer:

Q,h-0.4/.2 •/<•/>( 7,, TC)/(.S- Z) where Q1h = shuttle heat transfer, walls I = displacer stroke, cm k = gaseous conductivity of working fluid W m 1 K D = displacer diameter, cm l'n = heater temperature, K. T, = cooler temperature, K, S = annular gap between displacer and cylinder, cm, Z = length of displacer, cm.

reciprocating lilhm i- n t

In Chapter (y different mechanical configurations that may be used for Stirling engines arc discussed. In all of these systems, various reciprocating members are included. In general, these may be divided into two categories: pistons or displacers. I he difference is illustrated in Fig. 5.4 which shows a diagrammatic representation of an engine arrangement known as the 'piston and displacer in same cylinder' engine.

The cylinder contains two reciprocating parts, a piston and. above it, a displacer. The uppci part of the cylinder above the displacer is the expansion space at high temperature. The space between the piston and displacer is the compression space and is at ambient temperature. The two spaces are in mutual communication through the heater, cooler, and

Fit}- 5.4. Stirling engine arrangement known as die 'piston and displaccr in same cylinder' illustrating the distinction between a piston and a displaccr.

The piston is the component used to convert the gaseous energy of the working fluid to mechanical work for driving the load. 1 his may be done directly, in the free-piston engine, or through a crank mechanism in the case of a 'kinematic1 engine. This energy transfer requires that the piston be a structural member sufficiently robust to withstand all the gaseous, mechanical, and inertia forces imposed on it.

There is likely to be a large pressure difference across lite piston between the working space and the crankcase. Therefore the piston also carries a seal to isolate the working space. The seal serves both to prevent the egress of working fluid and the ingress of lubricant. This latter is a very importanl function of the seal, to prevent contamination and blockage of the regenerator.

The temperature of the environmcnl above and below the piston is approximately the same, so the piston may be designed without regard to thermal effects apart from thermal expansion in the radial direction.

A piston may therefore be characterized briefly as a component having a high delta p and zero delta T. in other words, a high pressure difference and a zero temperature difference across the upper and lower transverse faces.

A displacer is quite the reverse and may be characterized as a component having a zero delta p and high delta T. in other words, no pressure difference but a large temperature difference between its ends. A small pressure difference does in fact exist, equal to the pressure drop across the regenerator and associated heat exchangers.

A displacer must therefore be constructed as a lightweight structural element required to sustain only low pressure and inertia forces but with minimum thermal conduction loss. This leads automatically to the classical displacer construction shown in Fig, 5.4 of a light, hollow, thin-wall envelope having a dome end and a length two or three times the diameter. I lie shell may be reinforced at intervals along the length by horizontal plates, spot welded, brazed or simply pushed into the displacer shell. These serve as radiation shields and, principally, to reduce internal convcctive heat transfer.

Engines of moderate to high specific output are pressurized to very high pressures of the working fluid. In Stirling engines used for automotive applications the pressure of the hydrogen working fluid may approach 200 MN/nr (30001b per sq in). In such cases an important decision must be made about the internal volume of the displacer. It may he either pressurized or unprcssurized. If unpressurized. the walls of the displacer will need to be sufficiently substantial to prevent crumpling of the shell. When exposed to the maximum cycle pressure this will increase the mass of the displacer and hence the ineitia loading and also the thermal conduction loss along the walls of the displacer shell. The alternative is to pressurize the displacer internally but if the unit is pressurized and scaled during construction then the walls must be sufficiently thick to contain the high internal pressure against zero external pressure when the engine is being constructed or maintained.

A better alternative is to provide a very small hole (less than 0.0254 cm or 0.010 in diameter) in the displacer so that some of the working fluid may pass into or out of the shell as the pressure of the working fluid changes. The hole must be made very small so that the rate of fluid flow in norma) operation will be small and the internal pressure will be approximately constant and equal to the mean pressure of the working fluid. It is vital that the flow to and from the displacer be restricted otherwise the internal volume of the displacer will become part of the internal void volume, the dead space, of the engine with consequent deleterious effects on both the power output and thermal

In every case il is likely to be advantageous to till the displacer void volume with thermal insulation to minimize convective heat transfer. Solid cellular or fibrous materials suitable for high temperatures may be used bul powder insulations are best avoided.

Double-acting engines

In Siemens double-acting engines a single reciprocating element per cycle is used. Successive cylinders are coupled through the regenerator and the associated heal exchangers so that the hot expansion space of one cylinder (above the reciprocating element) is connected to the cold compression space (below the. reciprocating element) of the adjacent cylinder. In this case the reciprocator serves both as a displacer and a piston for there is both a significant pressure and temperature difference between the ends and work is transmitted from the displaccr/piston to the load.

Piston side forces

A variety of kinematic mechanisms may be used to couple the reciprocating pistons or displacers to drive shafts. Many of these mechanisms result in side forces of variable magnitude acting to push the reciprocator against the sitie wall. Consider for example the simple crank connecting rod systems shown in l;ig. 5.5(a). The force C acting along the line of the

<l>) Ciosshead ciank slider mechanism

(«1 Simple crank slider mcchnnism

<l>) Ciosshead ciank slider mechanism

(c) Rhombic drive mechanism lria. 5.5. Kinematic mechanisms iot reciprocating «Irives. I tie simple crank slider inechan-

iciu iii /ct\ puicdc o c«rl#» ifimil t\i flu* rtitlmi tiitcimt:! fli». /'ullni"l/'r UHlll connecting rod A-li may be resolved at the small end bearing B into vertical and horizontal components V and II respectively.

The horizontal component II, the piston side-force, causes a vertical drag force between the piston and cylinder D = ¡xll where p. is the coefficient of friction and acts in a direction opposite to the direction of piston motion. The side force also results in increased wear of the rubbing surfaces.

And wear, whether due to side forces or not is particularly unwelcome where a very high pressure dilference has to be contained by seals in the piston. Elforts must be made therefore to separate the components responsible for sealing and for absorbing the side forces arising from Ihe kinematic mechanism. One possibility is to use the cross-head arrangement shown in Fig. 5.5(b). This type of arrangement is used in the MAN/MWM and United Stirling engines discussed in Chapters 14 and 15 respectively.

An alternative mechanism to eliminate piston or displaccr side thrust is the rhombic drive shown in Fig. 5.5(c). This type of arrangement is well-suited lor use on single-cylinder, single-cycle engines and is discussed in Chapter 12 in relation lo Philips engines.

Solar Stirling Engine Basics Explained

Solar Stirling Engine Basics Explained

The solar Stirling engine is progressively becoming a viable alternative to solar panels for its higher efficiency. Stirling engines might be the best way to harvest the power provided by the sun. This is an easy-to-understand explanation of how Stirling engines work, the different types, and why they are more efficient than steam engines.

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