Cylinders composite

Consider radial, heat transfer through two concentric cylinders of length L, different thickness and different conductivity (Fig. 2.7). A typical example is the heat loss from an insulated pipe. Let the inside and outside fluid temperatures and the inside and outside heat transfer coefficients be 7, Tq and h-t, ho, respectively. 

Steam at 2 atm (saturation temperature Ts = 120 °C) is condensing in a 1-inch (ri = 1.33 cm and r2 = 1.67 cm) stainless steel pipe. The inside and outside heat transfer coefficients are hi — 100,000 W/m2-K and lie = 10 W/m2-K, respectively. The thermal conductivity of the pipe is k — 15 W/m-K. The pipe is suspended in a room at 20 °C. (a) We wish to evaluate the radial temperature drop inside, outside, and across the thickness of the pipe walls, (b) The pipe is insulated with a fiberglass (k = 0.04 W/m-K) layer of thickness 15 mm. Evaluate the reduction in the heat loss per unit length of pipe, 

2 The FORTRAN program EX2-2.F is Ested in the appendix of this chapter. 

The heat loss per unit length of pipe is then 

Note that the conductive and inside convective resistances are negligibly small compared with the outside convective resistance. Thus the temperature drop in the steam and that across the pipe walls, 

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Ballard Power Systems, in conjunction with the province of British Columbia and the government of Canada, have converted a diesel bus for Vancouver, B.C. Transit (43). This 9.1-m vehicle is powered by a 105-kW fuel cell. Gaseous hydrogen, stored on board the bus in DOT-approved glass-wound composite cylinders operating at 20.7 MPa (3000 psi), provides the necessary fuel requited for the 150-km projected vehicle range. 

A variation on the exact soiutions is the so-caiied seif-consistent modei that is explained in simpiest engineering terms by Whitney and Riiey [3-12]. Their modei has a singie hollow fiber embedded in a concentric cylinder of matrix material as in Figure 3-26. That is, only one inclusion is considered. The volume fraction of the inclusion in the composite cylinder is the same as that of the entire body of fibers in the composite material. Such an assumption is not entirely valid because the matrix material might tend to coat the fibers imperfectiy and hence ieave voids. Note that there is no association of this model with any particular array of fibers. Also recognize the similarity between this model and the concentric-cylinder model of Hashin and Rosen [3-8]. Other more complex self-consistent models include those by Hill [3-13] and Hermans [3-14] which are discussed by Chamis and Sendeckyj [3-5]. Whitney extended his model to transversely isotropic fibers [3-15] and to twisted fibers [3-16]. 

Figure 3-26 Self-Consistent Composite Cylinder Model...

The most established storage systems are high-pressure gas cylinders with a maximum pressure of 20 MPa. New lightweight composite cylinders have been developed that are able to withstand pressures up to 80 MPa and so the hydrogen can reach a volumetric density of 36 kg m, approximately half that in its liquid form at the normal boiling point. 

Figure 5.6 Dynetek composite cylinders consisting of an aluminum cylinderwrapped with carbon fibers (top and left) in an epoxy resin. Module with 10 cylinders (right) [6]. Companies that produce these tanks are Quantum Technologies, Lincoln Composites, Dynetek Industries and Advanced Lightweight Engineering (ALE).

Process models allow composite case manufacturers to determine the affects of process variable settings on final cylinder quality. Because the cost of a composite cylinder can be as great as 500,000, the ability to simulate filament winding can significantly reduce cost and improve quality. Several computer models of the filament-winding process for both thermoset and thermoplastic matrix materials have been developed. These models are based on engineering principles such as conservation of mass and energy. As such, numerous resin systems and fiber materials can be modeled. 

Flow charts with relevant inputs and outputs for each submodel are shown in Figures 13.7 and 13.8 for winding of thermosetting and thermoplastic composite cylinders, respectively. The primary differences between process models for thermosetting and thermoplastic cylinders arise in (1) the method of heating, and (2) the mechanics of consolidation/ fiber motion. 

In the following sections, the basic modeling approaches for thermosetting and thermoplastic matrix composite cylinders will be summarized. Differences between the thermosetting and thermoplastic model approaches are highlighted. 

In-Plane Shear Properties. The basic lamina in-plane shear stiffness and strength is characterized using a unidirectional hoop-wound (90°) 0.1 -m nominal internal diameter tube that is loaded in torsion. The test method has been standardized under the ASTM D5448 test method for in-plane shear properties of unidirectional fiber-resin composite cylinders. D5448 provides the specimen and hardware geometry necessary to conduct the test. The lamina in-plane shear curve is typically very nonlinear [51]. The test yields the lamina s in-plane shear strength, t12, in-plane shear strain at failure, y12, and in-plane chord shear modulus, G12. 

The explicit formulae given by Rosen55 are also of value. They are derived from a model consisting of a random assemblage of composite cylinders (Hashin and Rosen56 ) and expressed in terms of the axial Young modulus E, the Poisson ratio for uniaxial stress in the fibre direction v, the transverse plane strain bulk modulus k, the axial shear modulus G and the transverse shear modulus G. ... 

Figure 2. Gravimetric storage efficiency of composite cylinders (including peripherals)...

Steady heat transfer through multilayered cylindrical or spherical shells can be handled just like multUayered plane walls discussed earlier by simply add ing an additional resistance in series for each additional layer. For example, the steady heat transfer rale through the three-layered composite cylinder of length L shown in Fig. 3-26 with convection on both sides can be expressed as... 

The thermal resistance network for heal transfer through a three-layered composite cylinder subjected to convection on both sides. 

Figure 5.3 Composite cylinder storage of compressed hydrogen.

A novel method to improve the amount of hydrogen that can be stored in composite cylinders involves cryo-compression of the gas. This depends on the fact that gases are denser at cryogenic temperatures than at ambient temperature. Also, they adsorb more readily on to materials with high surface areas. A medium-pressure composite cylinder (20—40 MPa) is filled with activated carbon as an adsorbent and then enclosed in an insulated jacket of liquid nitrogen (77 K). Compressed hydrogen is introduced into the cylinder where it cools, densifies, and is adsorbed on the surface of the carbon. The resultant storage capacity is several times that of the same cylinder at ambient temperature. 

The composite cylinder is tested in compression. If the composite cylinder has a strength of 90% of that of a standard concrete cylinder, the epoxy compound is adequate for use with concrete. 

High pressure composite cylinders 13 33 25 100 Current choice for on-board storage in demo vehicles. 

Fig. 6.2 The six basic hydrogen storage methods and phenomena. The gravimetric density prr, the volumetric density pv, the working temperature T and pressure p are listed. RT stands for room temperature (25°C). From top to bottom compressed gas (molecular H2) in a lightweight composite cylinder (tensile strength of the material is 2000 MPa) liquid hydrogen (molecular H2), continuous loss of a few percent per day of hydrogen at RT physisorption...

Olson, B. D.. Lamontia. M. A., Gillespie, J. W.. and Bogetti, T. A. (1995). The elTects and non-destructive evaluation of defects in thermoplastic compression-loaded composite cylinders, 7. Thermoplastic Composite Materials. Jan. 1995,. 8. 109 136. 

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