For flights beyond Mach 6 ramjets are inefficient engines due to huge total pressure loss in the normal shock systems, combustion conditions that lose a large fraction of the available chemical energy due to dissociation and high structural loads. However if the flow remains supersonic inside the combustion chamber, the above problems could be alleviated and here the concept of SCRAMJET(supersonic combustion ramjet) comes into existence. The scramjets could reduce launching cost of satellites by carrying only fuel and ingesting oxygen from atmospheric air. Further applications could involve defense and transcontinental hypersonic transport. In the current study an effort is made to achieve supersonic combustion in a ground based short duration test facility(combustion driven shock-tunnel), which in addition to flight Mach number can simulate flight Reynolds number as well. In this study a simple method of injection i.e. wall injection of the fuel into the combustion chamber is used. The work starts with threedimensional numerical simulation of a non-reacting gas(air) injection into a hypersonic cross-flow of air to determine the conditions in which air penetrates reasonably well into the cross-flow. Care is taken so that the process does not induce huge pressure loss due to the bow shock which appears in front of the jet column. The code is developed in-house and parallelized using OpenMp model. This is followed by experiments on air injection into a hypersonic cross-flow of air in a conventional shock-tunnel HST2 existing in IISc. The most tricky part is synchronization of injection with start of test-flow in such a short duration(test time 1 millisecond) facility. Next part focuses on numerical simulations to determine the free-stream conditions, mainly the temperature and pressure of air, so that combustion takes place when hydrogen is injected into a supersonic cross-flow of air. The simulations are two-dimensional and includes species conservation equations and source terms due to chemical reactions in addition to the Navier-Stokes equations. This code is also built in-house and parallelized because of more number of operations with the inclusion of species conservation equations and chemical non-equilibrium. However, the predicted conditions were not achievable by HST2 due to low stagnation conditions of HST2. Therefore, a new shock-tunnel which could produce the required conditions is built. The new tunnel is a combustion driven shock-tunnel in which the driver gas is at higher temperature than conventional shock-tunnel. The driver gas is basically a mixture of hydrogen, oxygen and helium at a mole ratio of 2:1:10 initially. The mixture is ignited by spark plugs and the hydrogen and oxygen reacts releasing heat. The heat released raises the temperature of the mixture which is now predominantly helium and small fractions of water vapour and some radicals. The composition of the driver gas and initial pressure are determined through numerical simulations. Experiments follow in the new tunnel on hydrogen injection into a region of supersonic cross-flow between two parallel plates with a wedge attached to the bottom plate. The wedge reduces the hypersonic free-stream to Mach 2. A high-speed camera monitors the flow domain around injection point and sharp rise in luminosity is observed. To ascertain whether the luminosity is due to combustion or not, two more driven gases namely nitrogen and oxygen-rich air are used and the luminosity is compared. In the first case, the free-stream contains no oxygen and luminosity is not observed whereas in the second case higher luminosity than air driver case is visible. Additionally heat-transfer rates are measured at the downstream end of the model and at a height midway between the plates. Similar trend is observed in the relative heat-transfer rates. Wall static pressure at a location downstream of injection port is also measured and compared with numerical simulations. Results of numerical simulations which are carried out at the same conditions as of experiments confirm combustion at supersonic speed. Experiments and numerical simulations show presence of supersonic combustion in the setup. However, further study is necessary to optimize the parameters so that thrust force could be generated efficiently.