Adiabatic nozzle

The ability to cool (and eventually liquefy) gases by adiabatic expansion underlies industrial gas liquefaction processes. Adiabatic cooling of gaseous nozzle-jet expansions is also an important technique in modem molecular beam and mass spectrometric research. Thermodynamicist John Fenn, winner of the 2002 Nobel Prize in Chemistry, pioneered many of the techniques of adiabatic nozzle-beam cooling. 

Air discliarges from an adiabatic nozzle at 288.15 K (15°C) with a velocity of 580 m s . Wliat is tile temperatureat tlie entrance of the nozzle if tlie entrance velocity is negUgible Assume air to be an ideal gas for which Cp = (7/2)/ . 

In the case of flow of a real gas through an adiabatic nozzle, the stagnation enthalpy between the entrance and the narrowest flow cross section, the nozzle throat, remains constant (ht = constant). The change in enthalpy corresponds to the change in kinetic energy and the irreversible frictional pressure loss is expressed by the resistance coefficient ... 

The hydrocarbon gas feedstock and Hquid sulfur are separately preheated in an externally fired tubular heater. When the gas reaches 480—650°C, it joins the vaporized sulfur. A special venturi nozzle can be used for mixing the two streams (81). The mixed stream flows through a radiantly-heated pipe cod, where some reaction takes place, before entering an adiabatic catalytic reactor. In the adiabatic reactor, the reaction goes to over 90% completion at a temperature of 580—635°C and a pressure of approximately 250—500 kPa (2.5—5.0 atm). Heater tubes are constmcted from high alloy stainless steel and reportedly must be replaced every 2—3 years (79,82—84). Furnaces are generally fired with natural gas or refinery gas, and heat transfer to the tube coil occurs primarily by radiation with no direct contact of the flames on the tubes. Design of the furnace is critical to achieve uniform heat around the tubes to avoid rapid corrosion at "hot spots."... 

The Dravo hydrate addition at low temperature process involves a two-step injection of water and dry sorbent in a rectangular 19.8-m duct having a cross section of 2 m. In one step water is injected through atomization nozzles to cool the flue gas from 150°C to approximately a 15°C approach to adiabatic saturation. The other step involves the dry injection of hydrated lime, either downstream or upstream of the humidifica tion nozzles. Typical SO2 removals were 50—60% at a Ca S ratio of 2. 

Adiabatic Frictionless Nozzle Flow In process plant pipelines, compressible flows are usually more nearly adiabatic than isothermal. Solutions for adiabatic flows through frictionless nozzles and in channels with constant cross section and constant friction factor are readily available. 

The equations for nozzle flow, Eqs. (6-114) through (6-118), remain valid for the nozzle section even in the presence of the discharge pipe. Equations (6-116) and (6-120), for the temperature variation, may also be used for the pipe, with Mo, po replacing Mi, pi since they are valid for adiabatic flow, with or without friction. 

Convergent/Divergent Nozzles (De Laval Nozzles) During frictionless adiabatic one-dimensional flow with changing cross-sectional area A the following relations are obeyed ... 

Equation (26-137) is recognized as the expression for aU-gas flow by adiabattc expansion across an orifice or nozzle. The factor k is the expansion coefficient for the adiabatic flow eqnahon of state ... 

The adiabatic flow of an ideal gas flowing through a frictionless conduit or a constriction (such as an orifice nozzle, or valve) can be analyzed as follows. The total energy balance is... 

The mass flow rate under adiabatic conditions is always somewhat greater than that under isothermal conditions, but the difference is normally <20%. In fact, for long piping systems (L/D > 1000), the difference is usually less than 5% (see, e.g., Holland, 1973). The flow of compressible (as well as incompressible) fluids through nozzles and orifices will be considered in the following chapter on flow-measuring devices. 

Air is fed from a reservoir through a converging nozzle into a 1 /2 in. ID drawn steel tube that is 15 ft long. The flow in the tube is adiabatic, and the reservoir temperature and pressure are 70°F and lOOpsia. 

A variation on this method, passing the vapors emitted from a heated source or sources through a nozzle, may cause clustering. The gas-phase species, which could be ions or neutral molecules, pass from a region of higher pressure to a region of lower pressure. This process has many collisions and then adiabatic expansion often produces cold clusters. If the clusters have not been ionized, they may be ionized in the low-vacuum region. 

Nitrogen contained in a large tank at a pressure P = 200000 Pa and a temperature of 300 K flows steadily under adiabatic conditions into a second tank through a converging nozzle with a throat diameter of 15 mm. The pressure in the second tank and at the throat of the nozzle is P, = 140000 Pa. Calculate the mass flow rate, M, of nitrogen assuming frictionless flow and ideal gas behaviour. Also calculate the gas speed at the nozzle and establish that the flow is subsonic. The relative molecular mass of nitrogen is 28.02 and the ratio of the specific heat capacities y is 1.39. 

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