Expansion ratios

Within the limitations imposed by atmospheric operation, expansion to larger expansion ratios allows conversion of additional propellant enthalpy to kinetic energy and higher performance. The employment of high expansion ratio nozzles is a necessary adjunct to the development of higher pressure combustors. 

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Foams for firefighting appHcations are typically made from a concentrated foaming agent diluted with water and then mixed with air. Rather than consider the volume fraction of air in the foam, firefighting foams are characterized by their expansion ratio, which is the increase in volume of the Hquid after the foam is formed. Expansion ratios range from 5 1 to over 1000 1 ratios of 5 1 to 20 1 are called low expansion ratios of 21 1 to 200 1, medium expansion and ratios greater than 200 1, high expansion. 

The uniflow design reduces cyhnder condensation and also allows greater expansion ratios per cyhnder (see Figs. 29-9 and 29-10). Steam is admitted during the start of the power stroke and after cutoff... 

Size, rotating speed, and efficiency correlate well with the available isentropic head, the volumetric flow at discharge, and the expansion ratio across the turboexpander. The head and the volumetric flow and rotating speed are correlated by the specific speed. Figure 29-49 shows the efficiency at various specific speeds for various sizes of rotor. This figure presumes the expansion ratio to be less than 4 1. Above 4 1, certain supersonic losses come into the picture and there is an additional correction on efficiency, as shown in Fig. 29-50. 

Hydroearbon gas expanders range in the order of 100 hp to 8,000 and more hp. The majority of these maehines are usually designed for power reeovery duty, with a proeess eompressor direetly driven by the expander. The gas is usually expanded from an inlet pressure in the 100 bar to 50 bar range, down to outlet pressures in the 50 to 15 bar range. This results in an expansion ratio of 2 1 to 4 1, a very suitable expansion for a single-stage expander. Typieal effieieneies range from 84% to 86%. 

Pressures Turboexpanders ean be designed to operate at up to 3,000 psi and higher inlet pressures as required by eonditions. Expansion pressure ratios ean also be adjusted for eaeh proeess over a wide range. A majority of effieient expansion ratios are below 5 1, although pressure ratios up to 10 1 ean be aeeommodated with reasonable effieieney. Smaller, lower pressure units are popular for air separation and helium liquefaetion. Intermediate pressure (100-1,000 psi) and high pressure expanders (1,000-3,000 psi) are widely used in natural gas proeessing and industrial gas liquefaetion. 

Radial inflow turboexpanders are the best equipment for this application because they handle condensing streams, provide a high expansion ratio in a single stage, and are custom-built to accommodate the plant s process conditions. 

Tj = expander inlet temperature I p = expander expansion ratio Cp, k = gas constants determined by the gas equations... 

Turboexpander thermal effieieney (TTE isentropie) is defined as the ratio of aetual work produeed by the fluid, divided by the work produeed from the isentropie expansion proeess. Depending on gas eomposition, expansion ratio, and liquid formation, TTE varies between 80%-90%. These high effieieneies are the result of improvements to the thermodynamie and meehanieal design of turboexpanders sinee the early 1960s and their use in gas proeessing plant applieations. 

Rice [15] made a comprehensive study of the reheated gas turbine eombined plant. He first analysed the higher (gas turbine) plant with reheat, obtaining (t o)h> turbine exit temperature, and power turbine expansion ratio, all as funetions of plant overall pressure ratio and firing temperatures in the main and reheat burners. (The optimum power turbine expansion ratio is little different from the square root of the overall pressure ratio.) He then pre-seleeted the steam eyele eonditions rather than undertaking a full optimisation. 

Flame speed was observed to be nearly constant, but increased with the scale of the experiment. Because mixing with air was limited, a volumetric expansion ratio of approximately 3.5 was observed. The maximum pressure observed was found to be scale dependent (Figure 4.5). 

Mf = flame Mach number g = isobaric expansion ratio... 

H = visible flame height S = 2.3 X = flame speed = wind speed d = cloud depth g = gravitational acceleration po = fuel-air mixture density pj = density of air r = stoichiometric air-fuel mass ratio a = expansion ratio for stoichiometric combustion under constant pressure (typically 8 for hydrocarbons)... 

Calculate w from the actual mixture composition , the stoichiometric mixture composition <()s, and the expansion ratio for stoichiometric combustion a ... 

Takaoka, T., et al. (1998). A High-Expansion—Ratio Gasoline Engine for the Toyota Hybrid System. Toyota Review 47 2). 

TT( is nondimensionalized by the flame transit hme T( = 3/Sl. Here, 7 is the normalized gas expansion ratio. Because of the difference in density between the fresh and burnt gas, gravity will also influence the d5mamics of the flame front. The effect of gravity has been included through a Froude number, Fr = Sl/ Sg), positive for a flame propagating downward. Similar expressions have been derived by Matalon and Matkowski [13], and by Frankel and Sivashinsky [14]. 

Pu/Ph designates the volumetric expansion ratio of burnt to unburnt gases... 

After the establishment of a cylindrical flame, continuous reduction of the flame speed relative to an external frame of reference was observed. This reduction was linear in time and quenching occurred in the system when the flame speed was close to zero. The declining flame speed was attributed to heat losses to the walls (reducing the effective expansion ratio in the flame) and quenching was interpreted in terms of the following criterion ... 

Fig. 3 shows the emulsion phased expansion measured by the bed collapse method [10] under the reaction conditions. In this case, the value of a was 3.9. The expansion ratio when the bed was fluidized by only H2 shows that the emulsion phase slightly expanded, and that the ratio was not influenced by the temperature. On the other hand, when H2 and CO2 were supplied as fluidizing gases, the expansion ratio decreased with the reaction temperature when... 

The mesh expansion ratio, i.e. the size ratio of neighboring cells, should be kept small. Particularly in regions of large gradients, mesh size discontinuities should be avoided. 

Allen et al. (2007) produced puffed snack foods with com starch and pregelatinized waxy starch, WPC and instantized WPC, and protein concentrations of 16%, 32%, and 40% and showed that the air cell size, extru-date expansion ratio, and water solubility index decreased proportionally as protein and com starch levels increased. Protein concentration significantly affected total soluble protein, water absorption index, and water-soluble carbohydrate. A covalent complex between amylase and protein formed in the presence of cornstarch, but protein-protein interactions appeared with the presence of low levels of pregelatinized waxy starch. 

In some literature, there is a description that a bubble with linear resonance radius is active in sonoluminescence and sonochemical reactions. However, as already noted, bubble pulsation is intrinsically nonlinear for active bubbles. Thus, the concept of the linear resonance is not applicable to active bubbles (That is only applicable to a linearly pulsating bubble under very weak ultrasound such as 0.1 bar in pressure amplitude). Furthermore, a bubble with the linear resonance radius can be inactive in sonoluminescence and sonochemical reactions [39]. In Fig. 1.8, the calculated expansion ratio (/ max / Rq, where f max is the maximum radius and R0 is the ambient radius of a bubble) is shown as a function of the ambient radius (Ro) for various acoustic amplitudes at 300 kHz [39]. It is seen that the ambient radius for the peak in the expansion ratio decreases as the acoustic pressure amplitude increases. While the linear resonance radius is 11 pm at 300 kHz, the ambient radius for the peak at 3 bar in pressure amplitude is about 0.4 pm. Even at the pressure amplitude of 0.5 bar, it is about 5 pm, which is much smaller than the linear resonance radius. 

Passage of thionyl chloride through a flexible metal transfer hose which was contaminated with water or sodium hydroxide solution caused the hose to burst. Interaction with water violently decomposes the chloride to hydrogen chloride (2 mol) and sulfur dioxide (1 mol), the total expansion ratio from liquid to gas being 993 1 at 20° C, so very high pressures may be generated. 

Bedload was sampled during competent flows at the same vertical than suspended sediment. Bedload analysis has been based upon 215 samples, 145 during 2002-2003 and 70 during 2003-2004. At SMS we used a 29-kg cable-suspended Helley-Smith sampler with a 76-mm intake and an expansion ratio (i.e. ratio of nozzle exit area to entrance area) of 3.22 (Fig. 2c). Bedload was measured at... 

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