In gas turbine engines, secondary air is a bleed air taken from the compressor for the turbine blades cooling, combustion chamber liners cooling and for the prevention of hot gas ingestion at stator-rotor cavity region. In the secondary air flow path of a small gas turbine engine, labyrinth seals are used to prevent the hot gas ingestion from the main gas path region to the seal cavity. For the validation purpose, three teeth straight through labyrinth experimental seal data from the open literature is selected, the same geometry has been created in the present study, and the corresponding numerical results are validated. Both the straight through and stepped labyrinth seal geometries are modelled. The k-omega SST turbulence model is considered with 5% turbulence intensity to solve the mass, momentum, and energy equations with the steady-state two-dimensional axisymmetric flow. The numerical analysis has been carried out at both cold and hot flow conditions. From the numerical results, it is observed that, at a particular seal clearance, air flow function increases as pressure ratio increase up to some pressure ratio. At a constant pressure ratio, the leak flow is found to increase with the increase in seal tip clearance. The leak flow is found to be lower with the stepped labyrinth seals in comparison to the straight through seals. The leak flow is found to be lower at the cold temperature flow condition in comparison to the hot flow condition. And, the leak flow amount is found to be lower at the rotational condition in comparison to the stationary condition. This analysis will be useful for the optimization of the seal geometry for the effective utilization of secondary air, which will be useful for the enhancement of thrust and for the reduction of specific fuel consumption.