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The objective of this article is to perform detailed analysis of heat transfer in accelerated supersonic nozzle flows with cooled walls. Since most of the heat transfer occurs near the nozzle walls, correct prediction of the boundary layer under strong adverse pressure gradient is therefore required to achieve high fidelity numerical prediction. In this study, a two-equation SST-V turbulence model is used in conjunction with a second-order explicit-implicit method to solve axisymmetric compressible Navier-Stokes equations. First, the effect of the inlet pipe diameter and the associated contraction area on the heat transfer is studied in nozzles having 15 and 30 diverging half-angles. Then, a series of computations are conducted to examine the efficiency of the use of a constant wall temperature as a function of the stagnation temperature in heat transfer calculations. The computations are performed for nominal stagnation pressure of 208 N/cm 2 and stagnation temperature of 539 K. The computed heat-transfer coefficients are compared to experimental data and a good agreement is found. A pronounced increase in the throat heat transfer coefficient peak is observed accompanied with a reduction in the contraction area ratio. Also, the peak of the heat transfer coefficient for the pipe inlet diameter of 7.8 cm is found to be 70% higher than the one related to the pipe of 16.51 cm diameter.

Wall heat transfer coefficients and static wall pressures are determined over wide ranges of stagnation pressures and stagnation temperatures under large pressure gradients in a cooled convergent-divergent nozzle. The effects of specific heat ratio, turbulent Prandtl number and wall temperature value on the heat transfer and on the position of separation flow are not yet discussed accurately. Computing correct boundary-layer under adverse pressures gradients is of a particular importance to the accurate modeling of separated flow. This numerical investigation is conducted to assess the accuracy of the SST-V turbulence model when computing boundary-layer separation in supersonic nozzle with heat transfer. It is concluded that the wall heat transfer coefficients and the position of separation point are influenced by the variation of many parameters as heat specific ratio, wall temperature, and turbulent Prandtl number.

The difficulties associated with thrust-optimized contour nozzles have led to significant advances in our knowledge of the physical phenomena associated with flow separation. In this study, a fully implicit scheme is implemented using a combined weight function for splitting the flux to analyze the shock patterns in the optimized contour (TOC) that occur during the process of separation, leading to free (FSS) or restricted (RSS) shock separation. The switching FSS/RSS hysteresis at startup and shutdown is also investigated. To better understand and validate the findings and study the properties of the oscillating flow during the start-up procedure, an axisymmetric two-dimensional numerical simulation was performed for the TOC nozzle. A code was developed to solve the unsteady Navier-Stokes equations for compressible nozzle flow with boundary layer/shock wave interactions with the implementation of a full RSM-Omega turbulence model. These findings were used to analyze the separation structures, shock wave interactions, and hysteresis phenomena.

Due to the large number of correlations and relationships between variables and the physical phenomena involved, compressible flow simulations become very difficult or impossible if all the necessary scales and mechanisms are included and solved. Several research efforts have been made toward a more accurate flow field predictions and the current study aims to add to that knowledge base by exploring the capability of Delayed Detached Eddy Simulation employing the SST turbulence model to simulate the transonic region of over-expanded nozzle with small radius of curvature. An analysis was made of the transonic flow in axisymmetric nozzle, the paper shows the potential for using DES turbulence model to identify important internal radial flow downstream the throat region, where most RANS models fail to predict with high accuracy and in detail the structure of the flow. With small radius of curvature, the sonic line begins upstream of the throat and ends downstream due to turning flow near the wall transonic region. Comparison of the computational results with experimental data and some developed prediction methods are presented and good agreements are obtained.