It has earlier mentioned that commercial CFD code, ANSYS is used to simulate the flow. Pressure based coupled solver is used for the simulation where coupled algorithm solves a coupled system of equations comprising of the momentum and pressure equation. This is widely recommended by the different users of ANSYS. The governing equation for the conservation of mass, momentum and energy equations are discretized using a control volume-based technique. Based on earlier studies [10], RANS-based shear-stress transport (SST) k-ω model was applied in the steady-state runs. Simulations are carried out till the residuals falls to 10 − 3 order and the variation in the central line fluid parameter does not vary more than 1%. As the impingement flow itself is unsteady by its nature and we are interested in the mean flow quantities, convergence of 10− 3 is enough, no need to go for 10− 6 order which will unnecessarily increase of the computational cost.
3.1 Validation of the data
Before proceeding for the detailed simulations, CFD results are compared with the test data available in the literature [9]. In Figure the numerical schlieren is compared with the schlieren available in literature. Two different instants are shown in Fig. 4. It is noticed that the flow physics are nicely captured in CFD simulations.
Variation of mean pressure value (Cp) along the radial direction of the bottom plate is estimated from the present simulations and plotted along with the literature data [
9]. It is noticed that the pressure data so estimated also match well (Fig.
5). Here Cp is non-dimensional surface pressure coefficients where, Cp= (P – P
∞)/ (P0 – P
∞), similar as that was defined in literature [
9]. This gives the confidence on the data so generated.
3.2 Mach palette
Earlier it has been mentioned that the nozzle considered here is a sonic nozzle where M = 1.0 is expected at the exit plane irrespective of the nozzle inlet pressure (NPR). Mach number at the exit plane for all the simulated cases are checked for this consistence. Mach number variation along the radial direction is shown in Fig. 6. It is noticed that Mach number at the nozzle exit is identical except very close to the nozzle wall. This may be due to the non-identical grid distribution and differences in boundary layer thickness at the nozzle exit (which is not captured here). The area average Mach number at the nozzle exit is ~ 1.0 as expected.
After coming out of the nozzle, the jet will expand (as this is a convergent nozzle) before the jet flow faces the bottom impinging plate. Due to the expansion, the pressure drops and gets compressed by shock. Based on the NPR values, the strength of expansion and compression depend. The nozzle is designed for an NPR = 3.7. Hence, at NPR = 5.0, the jet will plume and its diameter will increase as soon as jet comes out of the nozzle. Due to this high expansion, there will be a Mach disc formation very close to the nozzle exit plane (Fig. 7). This is noticed for all the cases. It is noticed that the strength of the Mach disc is also similar across all the different cases studied. A normal shock (also called plate shock) is noticed near the bottom plate. Strength of this normal shock depends on the plate to nozzle distance(h/D). This is because, with the increase in distance, more amount of surrounding air gets mixed and reduces the strength of the main jet flow.
Numerical schlieren (density gradient) at different h/D are shown in Fig. 8. Mach disc, barrel shock, plate shock etc are clearly visible from it. Though Mach disc is formed for all the cases, for h/D = 2.0 and 4.0, no shock cell is noticed due to the close proximity of the bottom plate. At higher h/D (6.0 and 8.0), the shock cells are clearly visible. It is interesting to note that the length of shock cell does not depends on the h/D values. This is similar to the observation reported in literature [11]. All these gives confidence on the correctness of the results obtained. Another interesting point to note that the width of the Mach disc is highest for h/D = 2.0 and least for h/D = 6.0 and 8.0. This is due to the influence of the bottom plate and shock generated due to the presence of the plate. The shape of the plate shock is different for different h/D values because of the mutual interaction of the plate shock with the Mach disc formed.
3.3 Pressure palette
Earlier it has been mentioned that shocks are formed once the flow comes out of the nozzle as the jet is under expanded. Numerous shock cells are formed based on the distance of the impingement plate. Another shock is formed before the jet impinge on the bottom plate. Based on the distance of the impinging plate, the strength of the shock varies. This will lead to higher pressure on the plate. All these are clear from the pressure palette shown in Fig. 9.
Variation of pressure along the nozzle centre line is shown in Fig. 10. Pressure fluctuation due to the formation of shock cell is clearly visible here. Number of shock cells, its length etc all are clearly visible here. The sharp increase in pressure noticed at x/D = 5.3 is due to the formation of Mach disc. It is noticed that there will be a big separated flow for lower h/D values (2 and 4), which is absent in other two cases. This is in- line with the literature data [12].
3.4 Forces on the plates
Along with the jet flow, surrounding air gets entrained which will cause a reduction in the pressure at the bottom side of the plate located at the nozzle exit (top-plate). Whereas the top surface of the plate is unaltered. As a result, a downward force acts on the plate. The magnitude of this force varies depends on the distance between the impinging plate and nozzle. It is noticed that the amplitude of the force decreases exponentially with increasing the distance and with increase of NPR this value also increases.
Similar work is carried out to estimate the forces on the bottom plate. With the increase of the distance of the impinging plate, the pressure value decreases. This will cause a reduction in the force on the bottom plate.