23.3 Interaction of shocks of same family

Consider a supersonic flow over a double wedge as shown in Fig. 23.2. Lets understand the flowfield in the presence of this S/S interaction for same family shocks (left running) originating from the corners of the same wedge. This double wedge under consideration initially makes an angle θ₁ with freestream velocity vector and then θ₂ with the same. For this shock interaction studies, it is mandetory to have θ₁ < θ₂. However if θ₁ > θ₂ then there will not be any inward deflection of the flow after passing through the first shock originating from the first corner which intern avoids the apperance of the second shock originating from the second corner. Consider two streamlines viz. ABCD and PQ in the flow. Streamline ABCD initally gets deflected by and angel θ₁ in the presence of first left running shock which makes the flow parallel to the first wedge at region B. The same streamline gets further delfected by an angle equal to θ₂ - θ₁ due to the shock at the second corner which makes the flow parallel to the second wedge in the region C. Therfore after passing through two left running shocks, streamline ABC acquires a deflection equal to θ₂ in the region C. Now consider the streamline PQ which passes through only single left running shock which has been originated from the point of interaction of two left running shocks. Therefore the deflection incurred by the streamline PQ in the region Q may or may not be equal to θ₂ acquired by streamline ABCD in region C. In turn streamlines ABCD and PQ might not be parallel to each other downstream of the interaction point. Therefore to avoid this condition and streamline crossing, a wave (shock or expansion) originates from the interaction point through which the stream line ABCD passes and the onwards attains the same deflection as that of streamline PQ. Possibility of shock or expansion wave depends on the downstream pressures. However a slipline necessarily originates from the interaction point to seperate the two parts of flow of different entropies keeping their direction of velocity and pressure same.