Experimental and analytical studies on the shock wave length in convergent and convergent–divergent nozzle ejectors

•The shock wave structures are captured by the optical Schlieren measurements.•An analytical model is proposed to predict the shock wave length.•The model results agree well with the measurements with a maximum difference of 11%.•The ejector entrainment decreases with increasing wavelength at given primary flow pressure. The shock cell structure and the entrainment were investigated for convergent and convergent–divergent nozzle ejectors. The shock wave structures after the nozzle with over-expanded supersonic flow were captured by optical Schlieren measurements at different inlet pressures and temperatures. The first shock wave length was analyzed by using an image processing method. An analytical model was then proposed to predict the wavelength of the first shock wave in both convergent and convergent–divergent nozzle ejectors. The model results agree well with the measurements for the first shock wave length with a maximum difference of 11%. The influence of the first shock wave length on the ejector entrainment performance was analyzed to show that the ejector entrainment performance decreases as the shock wave wavelength is increased at a given primary flow inlet pressure.