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|Title: ||Simulation of Supersonic Combustion Using Variable Turbulent Prandtl/Schmidt Numbers Formulation|
|Authors: ||Keistler, Patrick G.|
|Advisors: ||D. Scott McRae, Committee Member|
Hassan A. Hassan, Committee Chair
Jack R. Edwards, Committee Member
|Issue Date: ||21-Feb-2007|
|Discipline: ||Aerospace Engineering|
|Abstract: ||A turbulence model that allows for the calculation of the variable turbulent Prandtl (Prt) and Schmidt (Sct) numbers as part of the solution is presented. The model also accounts for the interactions between turbulence and chemistry by modeling the corresponding terms. Four equations are added to the baseline k-ζ turbulence model: two equations for enthalpy variance and its dissipation rate to calculate the turbulent diffusivity, and two equations for the concentrations variance and its dissipation rate to calculate the turbulent diffusion coefficient. The variable Prt⁄Sct turbulence model is used to simulate the SCHOLAR supersonic combustion experiments. The experiments include one model with normal hydrogen injection into a vitiated airstream at Mach 2.0, while the other injects hydrogen at Mach 2.5 and an angle of 30° to the vitiated airstream. Two sets of calculations are presented for each experiment, one where the turbulent Prandtl and Schmidt numbers are constant and one where they are allowed to vary. Two chemical kinetic models are employed for each calculation: a seven species/seven reaction model where the reaction rates are temperature dependent and a nine species/nineteen reaction model where the reaction rates are dependent on both pressure and temperature.
The simulation of the vectored injection experiment predicts an earlier ignition than what is suggested by the experimental data. Also, the downstream pressure is underpredicted. The temperature distribution in the downstream portion of the combustor is higher with the variable Prt⁄Sct model than with the constant model, which places it within the experimental scatter. When the computed temperature profiles are subjected to the same curve fit as the experimental scatter, very good agreement is observed. The simulation of the normal injection experiment showed similar results, with underprediction of downstream pressures and less overall combustion. However, the variable Prt⁄Sct model does show improved results over the constant model. The variable model shows a complex shock-boundary layer interaction that extends upstream of the backward facing step. The pressure distribution along the bottom wall is very closely matched in this region, but downstream, the pressures are still underpredicted. A pressure 'plateau' effect that is seen in the experimental data suggests that an area of large separation or intense combustion exists in the region immediately below the hydrogen injector. This is not reproduced in any of the simulations. In general the two chemical kinetic mechanisms provide nearly identical results. Finally, it is shown that the computed results are highly dependent on the compressibility correction for the turbulence model. When this term is neglected, unstart conditions result for both the vectored injection experiment and the normal injection experiment.|
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