On Inviscid Compressible Flows With Condensation

Condensation can be widely observed in numerous problems in technologies suchas gas turbines and wind tunnels and normally plays an important role. When con-densation takes place, gas is transformed into liquid and the latent heat of condensationreleases. Thisprocesshasastrongimpactontheflow, whichmayresultinadecreaseofthe efficiency in gas-turbine or a deviation of the design parameter in wind tunnel. Thepresent investigation contains the study of wave phenomena and relevant quantitativeestimate on condensation in compressible flows. Results and conclusions are brieflygiven as follows:Gas-liquid phase transition can be considered as heat influence and mass exchangeprocesses from gas dynamical aspect. In the present study, heat addition and mass con-sumptionarestudiedindetail. Foreachprocess,wefindthreewavepatternswhichhavebeenvalidatedbynumericalsimulationsusingthefinitevolumemethod. Bycombiningthe classical theory of gas dynamics, the states of zones in the entire flow for each wavepattern are iteratively solved. It is found that different materials show different per-formances in gas-liquid phase transition in compressible flows. Two typical materials,water and n-nonane, are adopted to discuss the strengths of the possible waves. Com-parison of the waves caused by the mass consumption with by the heat addition showsthat the mass effect cannot be always neglected. Furthermore, the coupling of the heatand mass effects are implemented to provide a reasonable evaluation of the waves incondensation. Results show that, for condensation of water at transonic flow, analysisbased on the heat effect can give a sound estimate. When condensation takes place ata higher Mach number flow, or a lower one, the mass effect should be included. Whencondensation of n-nonane is discussed, the wave generated is rather complex, relatingclosely withthevelocity atwhich massisexchanged. Competition mechanism betweenthe mass consumption and the heat addition processes is the main feature.Asdiscussedinthewaveanalysis, condensationofwatercanbeconsideredsimplyastheheatadditionprocess. Tovalidatethisconclusion,typicalcasesofcondensationinslender nozzle flow and condensation in shock tube flow are provided to show evidenceon the existence of unsteady wave patterns in the heat addition process.Furthermore, detailed investigation has been carried out for the homogeneous con-densation of water vapor in shock tube. Three stages can be defined in this process:the initial stage which contains the onset of the condensation and the formation of the condensation shock waves in both downstream and upstream directions, the oscillatingstagewhichischaracterizedastherepeatofquenchandonsetofcondensationintheex-pansion fan approximately in a logarithm time manner, and the asymptotic stage whichthe oscillating waves are damping out with time and no apparent condensation shockwave is formed. The repeated interaction of the condensation induced shocks with themain expansion wave leads to a distortion of the expansion wave towards its shape thatcan be expected on the basis of phase equilibrium, i.e. a self-similar wave structureconsisting of a dry part, a plateau of constant state and a wet part.Inspired by condensation in nozzle flow and shock tube flow, we further discussthe homogeneous condensation in Prandtl-Meyer flows. Two configurations are carriedout to study the formation of stationary waves and the movement of oscillatory shocksinduced by condensation. First a corner expansion model with bounded walls has beenstudied. Steady condensation shock intersecting with the characteristics of the wavescan be found at some supersaturations. If we increase the initial supersaturation, theupstream-moving shock motion appears and its frequency-supersaturation relationshipis similar with that in unsteady condensation cycle in nozzles. Second, condensation inone side unbounded corner expansion is studied. Steady state waves show strong two-dimensional effects. Condensation destroys the spatial self-similarity of Prandtl-Meyerflow, and oscillation along radial line and so-called'wavy shape'can be recognized.After discussion of condensation in typical flows, condensations in wind tunnelsare studied, including water condensation in combustion-heated wind tunnel and nitro-gen condensation in hypersonic wind tunnel.For water vapor condensation in combustion-heated wind tunnel, the flow is char-acterized by a large expansion ratio, a very high Mach number, a coexistence of high-and low-temperature gases, and a relatively high water vapor mass fraction. Firstly atypical case of exit Mach number 6 is studied. Different from the conventional super-sonic condensing nozzle flow, condensation in the hypersonic nozzle flow mainly takesplacefardownstreamofthenozzlethroat, wheretheflowMachnumberishighlysuper-sonic, and, therefore, the unsteadiness due to condensation shock has no importance. Itisfoundthatcondensationinhypersonicnozzleflowmayleadtoasignificantchangeofflowstateatthenozzleexitand, therefore, adeviationfromthedesignedstate. Thenon-uniform distribution of the liquid droplets and the possible existence of condensationshock greatly deteriorate the flow quality. Then, impacts of different inlet conditionson the outlet parameters are discussed. Results show that the extent of condensation inhypersonic nozzles varies greatly due to the change of initial conditions. The extent of condensation firstly increases with the initial water vapor mass fraction and decreasesafter a critical point, which is ascribed to the higher enthalpy of the inlet flow with ahigher vapor mass fraction for a given initial temperature. The high vapor mass fraction(after the critical value) leads to a very high static temperature at the nozzle exit (andinside the nozzle) and therefore weak condensation is found.For nitrogen condensation in hypersonic wind tunnel, physical model and numer-ical code for simulating homogeneous condensation of nitrogen in nozzle flows are es-tablished. Models similar with that of water condensation are evaluated and developed.Numerical code is developed based on finite volume method. Discussion of numericalresults shows the correctness but incompleteness of the physical model. For a more ex-actmodellingofnitrogencondensationinwindtunnel,heterogeneousnucleationshouldbe included.