Boundary Layer Development And Vapor Condensation In Sonic Nozzle

Sonic nozzles, which can be directly utilized to measure the mass flow-rate of natural gas, hydrogen, steam, air and many other gases as well as the gas flow transfer standard, are widely used in numerous fields including petrochemical, chemical engineering, energy conservation, environmental protection, aviation and aerospace. To meet the energy-saving and emission-reduction requirement, sonic nozzle ought to have a high accuracy and stability in wider range of Reynolds number and pressure. To improve the measurement level of sonic nozzle, the discharge coefficient Cd, which is the most significant performance parameter of sonic nozzle, was further studied in the two aspects of boundary layer development and vapor condensation. The main results and conclusions are as following:1. The critical flow factor of real gas was studied in detail. For hydrogen, an analytic model for Cr* based on the relationship of entropy-enthalpy and Helmholtz energy equation was presented. The Newton-Raphson iteration procedure was used to sovle the analytic model, and the values of Cr* over a wide range of temperature 150-600 K and pressure up to 100 MPa were obtained. An accurate empirical equation was determined by the nonlinear regression analysis based on evolutionary algorithm. Combining the multi-dimensional characteristic and boundary layer theory, a theoretical formula for the mass flow-rate of real hydrogen was obtained and verified by the experimental data of high-pressure hydrogen reported by Morioka. Thus, sonic nozzle was successfully applied to the domain of hydrogen energy.2. At high Reynolds number region, an approximate solution for discharge coefficient of the sonic nozzle with surface roughness was proposed. A CFD model based on k-ε turbulence model and wall function was built. Combining these two methods, the effect of surface roughness on discharge coefficient were analyzed. It was showed that, in transitional roughness region, discharge coefficient Cd increases with the increase of throat Reynolds number Red, while in full roughness region, Cd does not change with Red. In addition, it was indicated that the effect of surface roughness is positively correlative to the radius of curvature Rc and specific heat ratio y. At Last, real gas CFD model was bulit to analyze the effect of roughness on Cd at high pressure condition. It was found that the curves of real gas deviate obviously from that of ideal gas which can be explained by the variation of specific heat ratio y.3. At low Reynolds number region, based on the inviscid transonic flow model and laminar boundary layer theory, it was proved that the effect of divergent section depends on the interaction between boundary layer and core flow field. Meanwhile, the effect of divergent section of nozzle on flow field and discharge coefficient was analyzed. Combining the numerical results and the experimental data, it showed the divergent section will affect flow-rate of sonic nozzle at low Reynolds number. When the diffuser angle θ equals 1°,2.5° and 6°, the upper limit of Reynolds number Reg respectively are 2.0×104, 1.1×104 and 2.8×103. At last, a concept of effective critical flow was proposed to obtain the position and flow property of the real throat.4. At low Reynolds number region, the thermal effect of sonic nozzle was analyzed in detail. First, it was proved that the temperature drop of the nozzle wall really exists by measuring the dynamic temperature of nozzle with thermocouples. In experiment, the maximum temperature drop is up to 13℃. Then, a similarity solution of laminar thermal boundary layer for the nozzle flow was proposed and compared with the numerical result. It showed that discharge coefficientis related to the specific heat ratio y, the ratio between wall temperature and stagnation temperature Tw/T0 as well as Reynolds number Red. At last, the gradient of discharge coefficient Cd caused by the variation of wall temperature Tw was obtained when γ=1.4. Compared with the experimental data, it was indicated that the discharge coefficient increases by 0.2% with the wall temperature decreasing by 10 K which is necessary to pay more attention.5. Some analytical solutions for position and flow properties of Wilson point in nozzle flow with homogeneous nucleation at low and high pressures were presented. The position of Wilson point and the corresponding properties can be found efficiently and effectively by this method, only with the given values of the nozzle geometry, inlet stagnation pressure and temperature. The accuracy and reliability of this analytical method were validated by experiments. It is indicated that with the rise of throat diameter d and radius of curvature Rc, the absolute position X at Wilson point moves towards the exit, but the relative throat flow area A0 decreases. Thus, expansion rate coefficient kp, subcooling ΔT and Mach number M at Wilson point will also decrease. Bescides, with the increase of inlet superheat DT, the position of Wilson point will move downstream, both X and A0 at Wilson point increase.6. According to the theory of Rayleigh flow, thermal choking and unsteady self-excited oscillation phenomena were studied in detail. The Eulerian two-fluid models for both homogeneous and heterogeneous nucleations were constructed to investigate the effect of vapor condensation on mass flow-rate of sonic nozzle. It is found that the deviation of mass flow-rate reaches 0.275%when inlet relative humidity Φ0=95%, which coincides with the Lim’s experimental data. Besides, when Φ0 is small, CFD results utilizing heterogeneous model were in good agreement with the experimental data. Different modes of flow oscillation caused by homogeneous condensation were discussed. The results show that with the rise of inlet subcooling ΔT0, frequency f decreases first and then increases, while the variation of amplitude Ap was opposite. To improve tracking ability of measurement system for transient temperature, a prediction model for transient temperature was built and a compensator for temperature sensor was presented. A sensor for pressure distribution and oscillation monitoring was built, and the results of the experiment were discussed in detail.