Skin Friction Reduction in Hypersonic Turbulent Flow by Boundary Layer Combustion

Skin Friction Reduction in Hypersonic Turbulent Flow by Boundary Layer Combustion M.V. Suraweera, D.J. Mee†, and R.J. Stalker‡ University of Queensland, Brisbane, Queensland 4072, Australia Results from an experimental and numerical study of skin friction levels obtained when hydrogen is injected into turbulent boundary layers are presented. Measurements are reported from experiments in the T4 free-piston reflected shock tunnel. Hydrogen was injected from a 3 mm high slot into the boundary layer on the flat surface of one of the walls of a duct 100 mm wide, 60 mm high, and 1745 mm long. The experiments were conducted at Mach numbers ranging from 4.2 to 4.7, flow stagnation enthalpies of 4.8 MJ/kg to 9.5 MJ/kg, static pressures of 59 kPa to 86 kPa, and Reynolds numbers of 8.9  106 m-1 to 17.2  106 m-1. Hydrogen fuel was injected 245 mm downstream of the inlet through a 3 mm slot. Mass flow rates of 0 kg/s/m and 0.36 kg/s/m, at a nozzle area ratio of 1.7, were used for test flows of air. Combustion occurred at all flow conditions with results indicating a maximum reduction in skin friction coefficient, of approximately 80% of the level measured with no injection. Skin friction reductions of approximately 60% were obtained at two other test flows. Measured heat transfer levels were found to be comparable with levels obtained without injection, for most of the experimental conditions. Hydrogen injection into a test flow of nitrogen was also trialed at all flow conditions to compare with the results obtained when fuel was injected into an air flow, in order to identify the effects of combustion. In general, the results showed that reductions in local skin friction coefficient were greater when combustion occurred than when fuel was injected and did not burn. Nomenclature B.L. cf ch H M P Pr QP Qcf Qch q r U u x   = = = = = = = = = = = = = = = = = boundary layer local skin friction coefficient local Stanton number enthalpy Mach number pressure Prandtl number net pressure increase (Eq. 1) net skin friction reduction parameter (Eq. 4) net Stanton number reduction parameter (Eq. 7) surface heat transfer rate recovery factor mainstream velocity local velocity distance downstream of injection location density shear stress  Post Doctoral Researcher, Centre for Hypersonics, Department of Mechanical Engineering, University of Queensland, QLD 4072, Australia. Member AIAA † Associate Professor, Centre for Hypersonics, Department of Mechanical Engineering, University of Queensland, QLD 4072, Australia. Senior Member AIAA ‡ Emeritus Professor, Centre for Hypersonics, Department of Mechanical Engineering, University of Queensland, QLD 4072, Australia. Fellow AIAA Subscripts aw e i n s o w = = = = = = = adiabatic wall condition at edge of boundary layer, exit flow condition injection condition, initial condition no injection condition stagnation condition, nozzle supply condition stagnation condition value at wall Introduction A vehicle in sustained hypersonic flight will be subject to high heat transfer rates and high levels of skin friction drag. Skin friction is expected to be a major component of drag for high-speed aircraft. For hypersonic vehicles, such as waveriders, calculations indicate that skin friction will constitute approximately half of the overall vehicle drag.1 For scramjet-powered vehicles, such ratios have been confirmed from results of model scramjet tests at The University of Queensland.2,3 Almost all viscous drag is due to the skin friction in turbulent boundary layers and, up to the present, there has been little prospect of greatly reducing the skin friction. A significant reduction in skin friction may be expected to have major effects on the design of hypersonic vehicles. For example, scramjet propelled vehicles will require intakes with very large capture areas and, consequently, the engine flow path is expected to dominate the design of the vehicle. A reduction in viscous drag would decrease the required capture area, leading to a reduction in engine size. Alternatively, flying at higher altitudes could reduce heat transfer levels without reducing engine size. It is known that injection of a low density gas into a boundary layer can be effective in reducing skin friction and heat transfer rates4. This process is often referred to as film cooling. In a previous study5 combustion of hydrogen in the boundary layer has been shown to result in an additional skin friction reduction, and to extend the length downstream of injection over which there is a substantial reduction in skin friction. The experimental study carried out in the T4 free-piston reflected shock tunnel at The University of Queensland indicated that a 70-80% reduction in viscous drag, for a given injectant mass flow, could be obtained by boundary layer combustion. In addition, a somewhat surprising experimental result was that heat transfer, rather than being increased, was slightly reduced by boundary layer combustion. The flow phenomena that reduce skin friction through combustion are still the source of some debate. However, most sources (e.g. Ref. 6 and Ref. 7) agree that the density reduction due to heat release at the surface results in local fluid dilatation which increases boundary layer displacement. The expansion of the boundary layer reduces mean velocity gradients, and hence lowers skin friction levels. In addition, Stalker’s analysis7 reasoned that the boundary layer density reduction due to combustion-induced temperature rise decreases turbulent viscosity and hence Reynolds (turbulent shear) stresses, thus reducing skin friction. A numerical study8 also found that heat release in hypersonic turbulent boundary layers suppresses pressure strain, ui  u j , which reduces wall normal velocity fluctuations and x j xi subsequently decreases momentum mass transfer. This paper presents the results of a shock tunnel investigation in which skin friction is reduced by slot injection and combustion of hydrogen in a hypervelocity turbulent boundary layer. The aim of the present study is to investigate whether this effect can be achieved at different flight speeds. Skin friction, heat transfer, and pressure measurements are made over a range of stagnation enthalpies. Numerical simulations of the flow have been carried out for general comparison with experimental results. Experiment Facility and Test Conditions The experiments were carried out in the T4 free piston reflected shock tunnel located at The University of Queensland. The facility has a 229 mm diameter driver that is 26 m in length, and a 75 mm diameter shock tube that is 10 m in length. A contoured axisymmetric nozzle with a throat diameter of 25 mm and an exit diameter of 135 mm, was attached to the downstream end of the shock tube. After expansion through the nozzle, the test flow was passed directly into the experimental duct. Due to a nozzle anomaly, expanded flow from outside the test core flow was ingested through the duct inlet, causing non-uniformities in the flow. An additional pitot survey of the nozzle established the characteristics of the exit flow, and a non-reacting 3D CFD simulation of the duct flow was carried out using the commercial software package FASTRAN TM. Significant computed 2 cross-flow disturbances were found to be present up to an axial distance of 0.15 m along the duct, as a result of pressure variations in this region. However, for most of the test surface downstream of this point, the axial velocity component of the flow was far greater than the transverse components. Within the injection region the maximum cross-flow component was less than 4% of the axial flow. Therefore it was assumed that there would be no break up of the hydrogen film, and that a fluid element would be convected downstream with very little transverse alteration. Four test conditions were used to explore the effect of stagnation enthalpy on the skin friction reduction technique. These are specified in Table 1. The stagnation enthalpy was calculated from the incident shock speed and the initial shock tube filling pressure. If required, an isentropic expansion of the air in the reflected region to the recorded mean nozzle supply pressure during the test time was also employed.9 An one-dimensional nonequilibrium nozzle expansion to the measured Pitot pressure in the test section yielded the nozzle exit conditions.10 All mainstream flow conditions at the point of hydrogen injection had a Reynolds number based on the distance from the leading edge, greater than 2.0 x 106. Based on evidence from previous experiments in the tunnel,11 all boundary layers were expected to be turbulent at the point of injection for the present tests. However, for some tests, a boundary layer trip 12 was attached 100 mm from the leading edge of the injection plate to ensure that the boundary layer was turbulent at the point of injection. Table 1. Shock tunnel flow conditions Units Expt.Error % 1 2 3 4 Stagnation enthalpy Nozzle supply pressure Mach no. Static Temperature Static Pressure MJ kg-1 MPa K kPa 8   1 9 4.8 33.7 4.7 865 59 5.6 35.1 4.6 1065 67 7.6 37.8 4.4 1525 80 9.5 38.2 4.2 1965 86 Static Density kg m-3 0.235 0.220 0.180 0.150 Quantity Velocity Unit length Reynolds no. -1 ms -1 m 1 5 Conditions 2695 - 1.72 x 10 2915 7 1.51 x 10 3315 7 1.13 x 10 3615 7 0.89 x 107 Experimental Duct Measurements of skin friction coefficient, Stanton number and static pressure are reported for injection of hydrogen into turbulent boundary layers, in a 1745 mm long experimental duct, as shown in Fig. 1a. The test surface comprises one wall of a duct consisting of an entry section and a test section. The entry section is 245 mm long and has a 57 mm x 100 mm cross section. It is terminated by a 3 mm rearward facing step where hydrogen can be ejected through an adjustable slot spanning the width of the duct. The 1500 mm long test section is downstream of this. At entry to the test section the duct is 60 mm high and 100 mm wide. The duct width increases downstream with the sidewalls diverging at 0.5º to account for boundary layer growth. The centreline of the test surface was instrumented with skin frictions gauges at 100 mm intervals. Thin film heat transfer gauges and PCBTM piezoelectric pressure transducers were located at 50 mm intervals on axes parallel to the test surface centreline at distances of 23, and 25 mm respectively. Hydrogen fuel was injected from a room temperature reservoir (Fig. 1b) through a fast-acting solenoid valve. The injection flow was initiated at least 5 ms prior to test flow arrival. Feeding the hydrogen from the base of the 3 mm step enabled the fuel to be injected into the boundary layer on the test surface, so that the effect of combustion within the boundary layer could be studied. The fuel injection Mach number could be varied by sliding the injector plate axially along the duct to change the throat area. For this study the area ratio was fixed to 1.7 to give a theoretical injection Mach number of 2.0. The reservoir pressure was recorded by three laterally located PCBTM piezoelectric pressure transducers. The supply pressure was always constant to within ±4% during the test time. The fuel system was calibrated prior to testing to determine the mass flow rate of hydrogen as a function of the reservoir pressure. The values for hydrogen mass flow rate per spanwise length for each of the test conditions are shown in Table 2. The calculated properties in the hydrogen layers formed as a result of recompression to the mainstream static pressures, within a few step heights downstream of the slot are also shown in Table 2. Note that the values were calculated by neglecting viscous effects. 3 Flow H2 a) b) Fig. 1. Cross-sectional layout of: a) experimental duct, b) duct entry section (dimensions in mm) Table 2. Injected hydrogen conditions -1 -1 Flow Mass flow, kg s m Condition 1 2 3 4 Measured 0.36 0.36 0.36 0.36 Error,% ±8 ±8 ±8 ±7 B.L. thickness on test surface m 0.0051 0.0051 0.0052 0.0052 Recompressed film properties Density Velocity Mach no. kg m-3 0.066 0.070 0.076 0.064 m s-1 1970 1920 1870 1940 2.02 1.93 1.85 1.96 Instrumentation Surface shear stress was measured using skin friction gauges that have a 10 mm diameter sensing disc that is mounted flush with the test surface. These gauges were designed and manufactured in-house and have been described in detail in previous publications.13,14,15 The gauges house an acceleration-compensated element and were individually calibrated for shear and pressure sensitivity. The test surface was also instrumented to measure heat transfer and pressure. Platinum thin-film gauges mounted on a quartz substrate were used to measure heat transfer, and PCBTM piezoelectric pressure transducers were used to measure the static pressure on the test surface. A measurement of static pressure was made adjacent to each skin friction gauge, and this was used with pressure sensitivity of the skin friction gauge to compensate the shear signal for pressure effects. 4 Data Recording A 12-bit transient digital data acquisition and storage unit with a sampling time of 1 s was used to gather data. The output of the skin friction, heat transfer, and pressure transducers were recorded through 4  multiplexers, resulting in a sampling time of 4 s per channel. The thin-film gauge signals were processed to calculate heat transfer rates using the technique of Schultz and Jones.16 Numerical Simulation Numerical simulations of the duct flow were carried out using the Supersonic Hypersonic Air-Reaction Calculator (SHARC) code.17 SHARC was developed for modelling scramjets with fuel injection along the wall. However, SHARC solves 2D planar and axisymmetric parabolic Navier-Stokes equations using a space marching technique. Due to the three-dimensional nature of the pressure field in the initial section of duct, including the fuel injection region, the SHARC simulations were included in this study to determine trends, and not to completely model the duct flow. Nonetheless, it should be noted that the 2D simulations are still practical as a benchmark for the modelling of experimental results. Analysis using the 2D simulations is useful, but is complicated by 3D perturbations. For these simulations the k turbulence model with compressibility corrections was used. The wall shear stress and heat fluxes were evaluated using wall functions in which it was assumed that the logarithmic law of the wall held for the fully turbulent region close to the wall. The combustion chamber was simulated as a twodimensional flow in a duct of 60 mm height. The length of the duct was 1500 mm. Hydrogen was injected as a parallel stream along one of the constraining surfaces of the duct through a 3 mm jet. Simulations were run for the four test conditions in Table 1. The conditions used for the hydrogen jet are shown in Table 2. The Reynolds numbers for all conditions were large enough that boundary layers were assumed to be turbulent upstream of the injection point. The simulation domain did not include the surface upstream of the injection. Therefore the turbulent boundary layer thickness on the injection plate (see Fig. 1b) was calculated by an implicit numerical method18. Boundary layer thicknesses between 5.1 and 5.2 mm were calculated at the point of injection for the various test flows (refer to Table 2). The velocity profile in the boundary layer was set using a one-seventh power law, and the temperature profile was calculated using the Crocco-Busemann law.19 Previous numerical studies5 indicate that the current duct height was large enough to ensure that the boundary layer on the test surface was not influenced by the boundary layer on the opposing wall. Therefore the lower wall was treated as inviscid. The basic 13 reaction NASP finite rate scheme20 involving species O2, H2, OH, HO2, H2O, O, H was used to model hydrogen combustion. The complete NASP mechanism, and the basic NASP hydrogen mechanism with nitrogen species supplements were also trialled. The results were very similar and the basic finite rate reaction scheme was chosen to minimize computational time. The computational grid used in all simulations comprised of 100 points normal to the model surface. The number of grid points was varied between 50 and 300 without affecting computational results. The space marching technique used automatically selects the step sizes in the downstream direction, as the computation progresses. In a previous study5 the number of downstream steps was manually altered, yielding unchanged results. Hence it was concluded that the computational results were independent of grid size Experimental Results and Discussion Pressure Measurements For all flow conditions, three cases were tested. Shots were made with air as the test gas and no hydrogen was injected, shots were made with air as the test gas and hydrogen was injected, and shots were made with nitrogen as the test gas and hydrogen was injected. Nitrogen was used as the test gas to suppress combustion so that “film cooling” effects alone could be studied. The differences between injection of hydrogen into air and nitrogen were used to detect if combustion was occurring and then, if so, to identify the influence of the combustion in the boundary layer on skin friction and heat transfer. In the figures the tests in which hydrogen was injected into air are indicated by "w/ combustion", those for hydrogen injection into nitrogen are indicated by "w/o combustion" and those in which no hydrogen was injected are indicated by "no injection". Based on evidence from previous experiments in the T4 shock11,12 all boundary layers were expected to be turbulent at the point of injection for the present tests. However, the test flow for condition 4 (refer to Table 1) was also initially tripped to ensure flow transition upstream of the injection location. A boundary layer trip8 was attached 100 mm downstream from the leading edge of the inlet to ensure that the boundary layer was turbulent. The boundary layer trip consisted of a 1.5 mm thick hacksaw blade placed flat along the width of the test surface. The teeth were bent by 90° so that the serrated edge was normal to the flow. Measurements were also obtained without a boundary layer trip. There was no difference to within experimental error in either of the data sets. Therefore it is assumed that the boundary layer was already turbulent prior to injection. The boundary layer trip was also in place for the tests at condition 1 (refer to Table 1). 5 Examples of typical distributions of static pressure along the test surface for injection with and without combustion, and for no injection are given in Fig. 2. These results are for flow condition 1 for a fuel injection rate of 0.36 kg/s/m. The measured static pressures are normalized by the measured nozzle-supply pressures for each shot. Results shown for each flow condition are an average of those from at least two shots at that condition. The static pressure along the test surface is higher for fuel injection into air than for fuel injection into nitrogen. The increased pressure beyond 0.5 m from the injector is attributed to combustion heat release within the boundary layer causing an increased displacement thickness of the layer. This is taken as evidence of combustion and it is inferred that combustion initiates at approximately 500 mm from the injector. Pressure distributions for injection of hydrogen into a nitrogen test flow and for no fuel injection with an air test flow are similar to a downstream distance of 1245 mm. A rise in pressure downstream of this point for the injection without combustion case is attributed to an increase in boundary layer displacement, as a result of the tangential fuel injection. 0.003 P / Ps 0.002 0.001 0.000 0.0 0.5 1.0 1.5 Distance from injection (m) w / combustion w /o combustion cf no injection Fig. 2. Typical static pressure distributions showing evidence of combustion Figure 3 shows distributions of static pressure along the test surface for the four flow conditions. The static pressure is normalized by the nozzle supply pressure measured for each shot. Results are shown for hydrogen injection into air and nitrogen test flows at a fuel injection rate of 0.36 kg/s/m. For each condition the difference between pressure measurements with combustion and without combustion are plotted on the right axis. Generally, results shown for each flow condition are the average of those from at least two shots. Distributions of static pressure along the duct from the 2D numerical simulations are shown in Fig. 4. Lateral pressure variations across the height of duct were suppressed in the numerical simulations. Due to the constant lateral pressure, the pressures from the numerical simulations increase monotonically with distance as a result of combustion. Thus the uneven pressure distributions apparent in the experiments that are attributed to waves in the duct are not obtained in these simulations. The general levels of pressure increase due to combustion are in reasonable agreement with the experimental results for flow conditions 2 and 3 for the first meter of the duct. For test condition 1, a measured peak pressure rise due to combustion of up to 40% above simulation values (see Fig. 3a) at 945 mm from injection was obtained. There are no distinct differences between the measured pressure distributions with and without injection for flow condition 4 (see Fig. 3d). This indicates that full combustion was not achieved. This is attributed to the energy release from combustion of hydrogen being absorbed by the dissociation of the water produced at this high stagnation enthalpy condition. Similar conclusions have been reached in numerical analyses of scramjet combustor experimental results at high stagnation enthalpies such as those by Krishnamurthy et al.21, Srinivasan et al. 22, and Bobskill et al. 23 6 0.003 0.003 0.002 s 0.001 0.000 0.0 0.001 0.5 1.0 0.000 0.0 1.5 Distance from injection (m) 1.5 P / Ps 0.003 Diff. in P / P s P / Ps 0.003 Diff. in P / P s 0.004 0.001 1.0 (b) Cond. 2 (5.6 MJ/kg) 0.004 0.002 0.5 Distance from injection (m) (a) Cond. 1 (4.8 MJ/kg) 0.000 0.0 Diff. in P / P 0.002 P / Ps 0.004 Diff. in P / P s P / Ps 0.004 0.002 0.001 0.5 1.0 0.000 0.0 1.5 0.5 1.0 Distance from injection (m) Distance from injection (m) (c) Cond. 3 (7.6 MJ/kg) (d) Cond. 4 (9.5 MJ/kg) w / combustion w /o combustion Diff. in P / Ps Fig. 3. Experimental static pressure distributions with and without combustion. 7 1.5 0.004 0.003 0.003 P / Ps P / Ps 0.004 0.002 0.001 0.000 0.0 0.002 0.001 0.5 1.0 0.000 0.0 1.5 Distance from injection (m) 1.5 (b) Cond. 2 (5.6 MJ/kg) 0.004 0.004 0.003 0.003 P / Ps P / Ps 1.0 Distance from injection (m) (a) Cond. 1 (4.8 MJ/kg) 0.002 0.001 0.000 0.0 0.5 0.002 0.001 0.5 1.0 0.000 0.0 1.5 0.5 1.0 Distance from injection (m) Distance from injection (m) (c) Cond. 3 (7.6 MJ/kg) (d) Cond. 4 (9.5 MJ/kg) w / combustion (SHARC) 1.5 w /o combustion (SHARC) Fig. 4. Numerical static pressure distributions with and without combustion. The net effect of fuel injection on the pressure distribution along the duct for each shot can be reduced to a single parameter by integrating the measured pressure distribution. The parameter used here is QP, referred to as the “net pressure increase.” It is defined as QP   P   P x2 x1   Pn    1dx Ps  s  , x 2  x1 (1) where P is the local static pressure measured for fuel injection, P n is the local static pressure measured when no fuel is injected, and x is the distance downstream of the injection location. The net pressure increase quantifies the total level of increase in measured static pressure along the test surface. When QP = 0.0, there is no change in measured static pressure over levels without injection and when QP = 1.0, there is a 100% increase in static pressure over measured levels without fuel injection. The net pressure increase is plotted in Fig. 5 for tests at a fuel injection rate of 0.36 kg/s/m. 8 Net pressure increase, Q P 1.0 0.8 0.6 0.4 0.2 0.0 0 2 4 6 8 10 12 Nozzle-supply enthalpy, H s (MJ/kg) w / combustion w /o combustion Fig. 5. Net pressure increase with and without combustion as stagnation enthalpy varies. The measured and numerical static pressure distributions shown in Fig. 3 and Fig 4 and the net pressure increase results in Fig. 5 indicate that the heat release due to combustion reduces with increasing stagnation enthalpy. This trend is a function of the change in velocity of the mainstream flow with the variation in enthalpy. The temperature at the combustor entrance increases as the stagnation enthalpy of the flow increases, leading to a lower heat release from combustion. This results in a reduced level of static pressure rise. For fuel injection without combustion, the experimentally measured and numerically calculated pressure rises also decrease with variation in stagnation enthalpy of the flow to within experimental uncertainty. The measured pressure distributions shown in Fig. 3 also indicated that the length taken to initiate combustion decreases as the stagnation enthalpy increases. This is important for scramjet design because a reduction in ignition length means that shorter combustors can be used. This leads to a decrease in vehicle structural weight and reduced skin friction drag, as a result of smaller surface area, thereby increasing the performance factors of payload and range. Figure 6 shows the measured ignition lengths as a function of pre-combustion temperature. The error bar for each measured value indicates the uncertainty in determining the occurrence of combustion. The first pressure rise due to combustion for the first two flow conditions occurs at approximately 445 mm from the injection point, whereas combustion may have already begun at the first pressure measurement location at 345 mm from the injector for flow condition 3. The numerical simulations of SHARC indicate that combustion starts within 50 mm of the injection location for all test flows. Also shown in Fig. 6 are locations of estimated combustion initiation based on the ignition time delay correlation by Pergament.24 That correlation predicts combustion initiation for condition 2 at 630 mm downstream of injection, approximately 200 mm further downstream than that observed in the T4 shock tunnel. For condition 3, the predicted ignition location is 30 mm from injection. The correlation of Pergament24 was developed for pre-ignition temperatures of 1000K – 2000K and therefore it is not applicable for flow condition 1. Although there was no distinct measured pressure rise due to combustion, an ignition length of 18 mm was predicted at test condition 4. For boundary layer combustion the correlation of Pergament,24 which was developed from mainstream combustion results, provides a relatively good indication of the ignition length. 9 Distance from Injection (m) 1.5 1.0 0.5 0.0 0 500 1000 1500 2000 Free-stream Temperature, T e (K) Experiment: Test Cond. 1 Test Cond. 2 Test Cond. 3 Pergament: Test Cond. 2 Test Cond. 3 Test Cond. 4 Fig. 6. Variation of pre-combustion temperature on measured and computed24 nominal ignition length, Hs = 4.8 – 9.5 MJ/kg. Skin Friction Measurements The conditions outside the boundary layer change as the flow passes along the test duct. This can be seen in the pressure distributions in Fig 3. The variations in conditions are due to compression and expansion waves caused by the step in the duct at the location of fuel injection and the fuel injection itself, viscous interaction caused by formation of boundary layers on the walls of the duct, non-uniformities in the inlet flow to the duct, and an increase in the displacement thickness of the fuel layer due to combustion.25 When presenting the measured skin friction coefficients and heat transfer values, it is appropriate to account for these variations in mainstream conditions along the duct. The streamwise variations in pressure seen in Fig. 3 are small enough to be modeled as isentropic compression or expansion from the oncoming flow conditions. All skin friction and heat transfer coefficients presented here are based on local free-stream conditions. These conditions have been determined using the local static pressure measurements. The local skin friction coefficient, cf, is defined as cf  2 w , 2  eue (2) where e and ue are local conditions at the edge of the boundary layer. Measured local skin friction coefficients are presented in the form of a proportional reduction in skin friction coefficient from the value measured with no injection as c fn  cf cfn 1 cf , c fn (3) where cf is the value measured for fuel injection and cfn is the value measured when no fuel is injected. Note that a value of zero corresponds to no change in skin friction coefficient and a value of 1 corresponds to a 100% reduction in cf. Measurements for this parameter at any location were obtained by averaging results from at least two similar shock tunnels tests. The exception was for the nitrogen test gas cases at condition 1 where only a single shot was made for the injection and no-injection cases. The values for the proportional reduction in local skin friction coefficient for the four test flow conditions are plotted in Fig 7 with results from the corresponding 2D numerical simulations in Fig. 8. Both experimental data for hydrogen injection into air, and for the film cooling case of hydrogen injection into a nitrogen test flow are displayed. The error bars included in Fig. 7 are based on the root-sum-square (RSS) of mean uncertainty in w computed from calibration constants and test flow uncertainties. 10 1.0 0.8 0.8 0.6 0.6 1 - c f / c fn 1 - c f / c fn 1.0 0.4 0.2 0.0 0.2 0.0 0.5 1.0 -0.2 0.0 1.5 1.0 Distance from injection (m) (a) Cond. 1 (4.8 MJ/kg) (b) Cond. 2 (5.6 MJ/kg) 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.2 0.0 -0.2 0.0 0.5 Distance from injection (m) 1 - c f / c fn 1 - c f / c fn -0.2 0.0 0.4 1.5 0.4 0.2 0.0 0.5 1.0 -0.2 0.0 1.5 0.5 1.0 Distance from injection (m) Distance from injection (m) (c) Cond. 3 (7.6 MJ/kg) (d) Cond. 4 (9.5 MJ/kg) w / combustion w /o combustion Fig. 7. Proportional reduction in measured skin friction with and without combustion. 11 1.5 1.0 0.8 0.8 0.6 0.6 1 - c f / c fn 1 - c f / c fn 1.0 0.4 0.2 0.4 0.2 0.0 0.5 1.0 -0.2 0.0 1.5 1.0 Distance from injection (m) (a) Cond. 1 (4.8 MJ/kg) (b) Cond. 2 (5.6 MJ/kg) 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.2 1.5 0.4 0.2 0.0 -0.2 0.0 0.5 Distance from injection (m) 1 - c f / c fn 1 - c f / c fn -0.2 0.0 0.0 0.0 0.5 1.0 -0.2 0.0 1.5 0.5 1.0 Distance from injection (m) Distance from injection (m) (c) Cond. 3 (7.6 MJ/kg) (d) Cond. 4 (9.5 MJ/kg) w / combustion (SHARC) 1.5 w /o combustion (SHARC) Fig. 8. Proportional reduction in numerical skin friction with and without combustion. Just as the net effect of pressure increase in the duct due to combustion is reduced to a single parameter, QP, it is useful to characterize the integrated reduction in local skin friction coefficient by a single parameter. The parameter used here is referred to as the “net skin friction reduction”, Qcf, and is defined in terms of the integral of the local skin friction coefficients measured along the test surface with and without combustion as 1 x2 Q cf  x1 x2  cf dx c fn ,  x1 (4) where x1 = 0.345 m and x2 = 1.345 m for most shots. The net skin friction reduction quantifies the total level of reduction in measured skin friction coefficient along the test surface due to tangential fuel injection and boundary layer combustion. When Qcf = 1.0, there is a 100% reduction in cf over measured levels without fuel injection, and when Qcf = 0.0, there is no change in measured cf over levels without injection. The net skin friction reduction for both the experimental and numerical results for a fuel injection rate of 0.36 kg/s/m are presented in Fig. 9. 12 Net skin friction reduction, Q cf 1.0 0.8 0.6 0.4 0.2 0.0 0 2 4 6 8 10 12 Nozzle-supply enthalpy, H s (MJ/kg) w / combustion w /o combustion w / combustion (SHARC) w /o combustion (SHARC) Fig. 9. Net skin friction reduction with and without combustion as stagnation enthalpy varies. The measured skin friction coefficients for flow condition 3 (see Fig. 7c) clearly illustrate the regions where film cooling and boundary layer combustion occur. The local skin friction coefficients at the first skin friction measurement location (345 mm downstream of injection) for both injection with combustion and injection without combustion agree to within experimental uncertainty. Pressure levels for cases with combustion and without fuel injection are also similar at this location (see Fig. 3c). There is also good agreement at this point with numerical results for the case of injection without combustion. All of these points indicate that there is little, if any, combustion at this location and that the reduction in skin friction coefficient is a result of a film cooling effect alone. For this test condition, the measurements for the case of injection of hydrogen into a nitrogen test flow (non-combustion condition) follow closely the results from the corresponding numerical simulation. The measured reduction in skin-friction coefficient at the second skin friction measurement location (545 mm from injection) in conjunction with pressure measurements in Fig. 3c show that the hydrogen injected into the boundary layer for the air test flow burns. Once combustion starts experimental values show a reduction in skin friction coefficient of approximately 70% to 80% at the three remaining downstream measurement locations. As shown in Fig. 9, the measured net skin friction reduction was higher at this condition than at the conditions tested for a fuel injection rate of 0.36 kg/s/m. The ignition time delay correlation by Pergament24 established that the combustion initiation period reduces exponentially with increasing pre-combustion static temperature. The large decrease in skin friction coefficient at condition 3 can be attributed to favorable conditions for combustion due to the high mainstream static temperature of the test flow. The higher mainstream temperature allows more heat to be transferred to the injected hydrogen, thereby decreasing the ignition time, and hence, reducing the length downstream of injection for combustion to initiate. The numerical simulations shown in Fig. 4 indicate that combustion starts upstream of the locations at which it was observed experimentally for all test conditions. Hence, the numerical curve for condition 3, plotted in Fig. 8c, reaches a peak in skin friction reduction 400 mm upstream of the location where the first large experimental reduction was recorded. The numerical results in Fig. 8c also indicate that the skin friction reduction due to combustion reduces from a maximum proportional reduction in cf of 77% at 120 mm from injection. However, the experimental values increase to a peak proportional reduction of approximately 80% at 1.3 m from the injector, well downstream on the test surface. The disparity may be due to a greater level of hydrogen mixing in air, and combustion, caused by pressure variations visible in Fig. 3c. As shown in Fig 7b, a peak proportional reduction in cf due to combustion of approximately 60% at 845 mm downstream of injection was recorded at condition 2. The measured reductions in skin friction coefficient upstream of the point of combustion initiation 445 mm from injection are attributed to the film cooling effect. This can be seen by the levels of reduction in skin friction coefficient recorded at the first two measurement locations. The values for the combustion case are similar in level to those measured for the film cooling case at x = 300 mm. The large reduction in skin friction is not maintained at the measurement locations at 1245 mm and 1345 mm from the injection point, although the skin friction coefficients are reduced for those without combustion in the same region. The pressure distribution in this region (see Fig. 3b) indicates that combustion is 13 still occurring. The level of skin friction reduction was expected to gradually diminish further downstream of the injection location due to decreasing local mass fractions of hydrogen. The local hydrogen mass fraction reduces with downstream distance as a result of additional air being entrained in the boundary layer, and due to the conversion of hydrogen into the combustion product water. The numerical simulations indicate that combustion starts approximately 400 mm further upstream than the location of combustion initiation inferred from the experimentally measured pressure distributions for condition 2. The experimental data shows partial agreement in reductions in skin friction coefficient with numerical levels at flow condition 2, for injection of hydrogen into both air and nitrogen test flows. For injection into air and injection into nitrogen, the measured levels of reduction of skin-friction coefficient are not as high as those from the numerical simulations. In particular, the reduction in cf for the case of injection into nitrogen shows a disparity approaching 20% between measured and computed levels. For the highest enthalpy tested, condition 4, the measured levels of reduction in cf at the first skin-friction measurement location (345 mm from injection) for both air and nitrogen test gases are similar. The amount of reduction in skin-friction coefficient then increases for the combustion case and decreases for the noncombustion case. The pressure measurements (see Fig. 3d) indicate only a small change in pressure for the combustion case and, as discussed earlier, this is attributed to dissociation of the combustion product (water) at the high post-combustion temperatures. This will absorb heat and reduce the effectiveness of boundary layer combustion for reducing skin friction. A peak reduction in cf of 35% over levels measured with no injection was observed 1.3 m downstream of the point of injection. The numerical simulations for the combustion case at this test condition overestimate the level of reduction in skin friction coefficient immediately downstream of injection, which also could be an indication that dissociation effects have not been modeled well. For condition 1, the results show a similar overall reduction in skin friction for the combustion case as was obtained for the combustion case at condition 2 (see Fig. 9). The net skin friction reduction for the noncombustion case at combustion 1 was more than double that measured for any of the other non-combustion cases. The large skin friction reduction for this non-combustion case persists to the most downstream measurement location. For all test cases except the non-combustion case at condition 1, at least two shots were made and results were averaged. In general, repeatability was very good. However, for condition 1 there was only one experimental run for injection of hydrogen into a nitrogen test flow. The measured skin friction levels for this shot were relatively low but no repeat shot was made to confirm these levels. For this reason, the results from this case are shown with dashed vertical error bars in Fig. 7a and Fig. 9. At condition 1 the reduction in skin friction coefficient with combustion is uneven (see Fig. 7a) although the pressure rise due to combustion is approximately constant beyond 445 mm from the injection location. A peak reduction of approximately 60% over levels measured with no fuel injection was obtained near the point of combustion initiation. The large skin friction reductions predicted by numerical simulations for this condition were not obtained experimentally. In fact the largest skin friction reduction for all test conditions (79%) was predicted by the numerical simulations for this low enthalpy condition, at which combustion would produce the highest heat release. The possibility that the combustion-induced pressure rise in the duct caused the boundary layer to separate was investigated. Korkegi’s analysis26 presents a correlation for the pressure rise needed to separate a turbulent boundary layer on a flat plate, as a result of shock wave boundary layer interaction. The correlation has also been found to give a good indication of the pressure rise due to combustion that could lead to boundary layer separation in a scramjet combustor.27 However, the largest measured relative pressure increase was approximately 40%, much less than the value of 630% indicated as the level required for boundary layer separation by the correlation of Korkegi26 at this test condition. Therefore boundary layer separation was discounted. The net skin friction reduction, Qcf, is also plotted as a function of mainstream temperature in Fig. 10. The measured pressure distributions seen in Fig. 3 indicated that the length taken to initiate combustion decreases as the stagnation enthalpy, and hence mainstream temperature increases. The decreasing combustion initiation length has a significant effect on increasing overall reduction in skin friction along the test surface. This trend of increasing skin friction reduction with increasing stagnation enthalpy can be seen in Fig. 9 for a fixed fuel injection rate of 0.36 kg/s/m. However, as discussed previously, the effectiveness of skin friction reduction due to combustion reduces with high stagnation enthalpies. This effect can be seen in Fig. 9 as the net skin friction reduction for a fixed fuel injection rate of 0.36 kg/s/m decreases from a peak at a stagnation enthalpy of 7.6 MJ/kg. 14 cf 1.0 Net skin friction reduction, Q 0.8 0.6 0.4 0.2 0.0 0 500 1000 1500 2000 2500 Free-stream temperature, T e (K) w / combustion w /o combustion Fig. 10. Net skin friction reduction with and without combustion as free-stream temperature varies. Heat Transfer Measurements The local heat transfer coefficient or Stanton number, ch, is defined as ch   eue h aw  h w  q . (5) 2 where haw = ho+ (r – 1) ue , ho is stagnation enthalpy and r is the recovery factor which for a turbulent boundary 2 layer is taken as Pr 1/3. Typical distributions of Stanton number at flow condition 1 for hydrogen injection into test flows of air and nitrogen, and for no injection in an air test flow are given in Fig. 11. 0.0010 0.0008 Ch 0.0006 0.0004 0.0002 Expt. error 0.0000 0.0 0.5 1.0 1.5 Distance from injection (m) w / combustion w /o combustion no injection Fig. 11. Typical Stanton number distributions at flow condition 1. The Stanton number along the test surface is higher for fuel injection into air than for fuel injection into nitrogen for this condition. This increase in Stanton number 500 mm downstream from the injector is due to combustion heat release in the boundary layer, causing an increased transfer of heat to the test surface. Close to the injector, the experimental results for fuel injection into air and nitrogen show a reduction in Stanton number. 15 After 500 mm downstream of injection, measured levels of Stanton number for hydrogen injection into nitrogen are unchanged from those for the no-injection case to within experimental uncertainty. The proportional reduction in local Stanton number due to injection of hydrogen is presented as c hn  c h c hn  1  ch . c hn (6) 1.0 1.0 0.5 0.5 1 - C h / C hn 1 - C h / C hn Again, measurements of this parameter at any location were obtained by averaging results from repeat shots where available. The values for the proportional reduction in Stanton number for the four test flow conditions are presented in Fig 12. Negative values in Fig 12 correspond to an increase in Stanton number over those for no injection. The error bars displayed in Fig. 12 are based on the root-sum-square (RSS) of mean uncertainty in q w computed from calibration constants, and test flow uncertainties. For the four flow conditions, the typical uncertainty in Stanton number is 15%. Results for the 2D numerical simulation are plotted in Fig. 13 for hydrogen injection into air, and hydrogen injection into nitrogen. 0.0 -0.5 0.0 -0.5 Expt. error 0.5 1.0 Expt. error -1.0 0.0 1.5 0.5 1.0 Distance from injection (m) (a) Cond. 1 (4.8 MJ/kg) (b) Cond. 2 (5.6 MJ/kg) 1.0 1.0 0.5 0.5 0.0 -0.5 0.0 -0.5 Expt. error -1.0 0.0 1.5 Distance from injection (m) 1 - C h / C hn 1 - C h / C hn -1.0 0.0 0.5 1.0 Expt. error -1.0 0.0 1.5 0.5 1.0 Distance from injection (m) Distance from injection (m) (c) Cond. 3 (7.6 MJ/kg) (d) Cond. 4 (9.5 MJ/kg) w / combustion w /o combustion Fig. 12. Proportional reduction in measured heat transfer with and without combustion. 16 1.5 1.0 0.5 0.5 1 - C h / C hn 1 - C h / C hn 1.0 0.0 0.0 -0.5 0.5 1.0 -1.0 0.0 1.5 1.0 Distance from injection (m) (a) Cond. 1 (4.8 MJ/kg) (b) Cond. 2 (5.6 MJ/kg) 1.0 1.0 0.5 0.5 0.0 -0.5 -1.0 0.0 0.5 Distance from injection (m) 1 - C h / C hn 1 - C h / C hn -1.0 0.0 -0.5 1.5 0.0 -0.5 0.5 1.0 -1.0 0.0 1.5 0.5 1.0 Distance from injection (m) Distance from injection (m) (c) Cond. 3 (7.6 MJ/kg) (d) Cond. 4 (9.5 MJ/kg) w / combustion (SHARC) 1.5 w /o combustion (SHARC) Fig. 13. Proportional reduction in numerical heat transfer with and without combustion. A summary of the distributions of Stanton number results shown in Fig 12 is presented in Fig. 14 in the form of a parameter called “net Stanton number reduction”, Qch, defined in terms of the integral of the heat transfer coefficients measured along the test surface with and without combustion as 1 x2 Q ch  x1 x2  ch dx c hn .  x1 (7) The net Stanton number reduction, Qch, quantifies the overall level of reduction in Stanton number along the test surface due to tangential fuel injection and boundary layer combustion. A positive value of Qch represents a reduction in ch over measured levels without fuel injection. A negative value of Qch represents an increase in ch over measured levels without injection. Close to the injector for all flow conditions, the experimental results show a reduction in Stanton number when hydrogen was injected into a test flow of nitrogen (see results labeled "w/o combustion" in Fig. 12). Further downstream, the levels approach those for no injection. For conditions 2 and 3, the levels of Stanton number for the cases where hydrogen was injected into an air test flow are similar to those for injection into nitrogen to within experimental uncertainty. However as shown in Fig. 14, for conditions 1 and 4, the Stanton number increased when hydrogen was injected into air. The high Stanton numbers for condition 1 are a result of the higher heat release due to combustion at the low enthalpy condition. Dissociation and recombination of water molecules may be responsible for these higher measured Stanton numbers for condition 4. As discussed earlier, the lack of a pressure increase along the duct for condition 4 can be explained by dissociation of water at the 17 high post-combustion temperatures. If there is a subsequent recombination to water molecules at the relatively cool temperature of the gas near the wall, there would be heat release near the wall, increasing the Stanton numbers. The experimental Stanton number distributions do not compare well with those from the computations. The magnitude of reduction in Stanton number is overestimated for both combustion and noncombustion cases. Net Stanton number reduction, Q ch 0.50 0.25 0.00 -0.25 -0.50 0 2 4 6 8 10 12 Nozzle-supply enthalpy, H s (MJ/kg) w / combustion w /o combustion Fig. 14. Net Stanton number reduction with and without combustion as stagnation enthalpy varies, Hs = 4.8 – 9.5 MJ/kg. For all conditions, the results from the computations suggest that the levels of Stanton number reduction obtained when combustion occurs are larger than those obtained without combustion. A study by Goyne et al. (2000) obtained results with a similar trend for a test flow with a stagnation enthalpy of 7.8 MJ/kg and fuel mass fluxes of 0.29 kg/s/m and 0.43 kg/s/m. This trend is not obtained in the results for a fuel injection rate of 0.36 kg/s/m at a similar condition in the present tests. Conclusion Shock tunnel experiments were conducted to establish the effects of boundary layer combustion of hydrogen on skin friction and heat transfer, through slot injection, over a range of stagnation enthalpies. Measurements were obtained for test flows with stagnation enthalpies of 4.8 MJ/kg to 9.5 MJ/kg, at fuel injection rates of 0.36 kg/s/m and 0 kg/s/m. Static pressure distributions indicated that for a fixed fuel mass flow rate there was a decrease in ignition length as stagnation enthalpy of the mainstream flow increased. Increases in stagnation enthalpy, and hence mainstream temperature, also lead to greater skin friction reduction for a fixed fuel mass flow rate. A maximum reduction in local skin friction coefficient of approximately 80% of the no-injection values was measured for the flow condition with a stagnation enthalpy of 7.6 MJ/kg, at a fuel injection rate of 0.36 kg/s/m. A maximum net skin friction reduction due to combustion of 0.62 was measured at this condition. Skin friction coefficient reductions approaching 60% of the no-injection values were also achieved for lower stagnation enthalpy flows. At higher stagnation enthalpies the heat release as a result of combustion decreases. Hence, the effectiveness of skin friction reduction due to combustion reverses in trend and decreases with increasing stagnation enthalpy. For a fuel injection rate of 0.36 kg/s/m, net skin friction reduction decreases from a peak at the 7.6 MJ/kg flow condition. Film cooling tended to be relatively ineffective in significantly reducing skin friction at distances greater than 0.5 m downstream of the injection location. Measured Stanton numbers for the combustion cases were generally either unchanged or higher than those measured for no injection. For the film cooling cases, heat transfer values for all flow conditions were lower or similar to the levels measured with no hydrogen injection. Numerical modeling of boundary layer combustion was also undertaken to make general comparisons with experimental results. The simulations indicated that boundary layer combustion causes a significant reduction in skin friction coefficient for most flow conditions. However, for all but condition 3, the computed levels of reduction in skin friction coefficient were larger than those measured. The simulations indicated that the 18 reduction in Stanton number due to hydrogen injection was relatively unchanged by combustion, but the levels of reduction in Stanton number calculated for the combustion and non-combustion cases were not observed experimentally. The analysis indicates that reductions in skin friction drag are achievable over a range of stagnation enthalpies. The effects of factors such as fuel injection rate, mainstream Mach number, injection Mach number, and static pressure are still to be reported. Nevertheless, the experimental and numerical results presented reiterate that boundary layer combustion of hydrogen to reduce skin friction can be developed into an enabling technology, for the realization of viable scramjet flight. Acknowledgement This project was supported by the Australian Research Council. References 1 Anderson J. D. Jr., Hypersonic and High Temperature Gas Dynamics, McGraw Hill, New York, 1989, p. 214. Paull A., Stalker R. J, Mee D. J, “Experiments on Supersonic Combustion Ramjet Propulsion in a Shock Tunnel,” Journal of Fluid Mechanics, Vol. 296, 1995, pp. 159-183. 3 Stalker, R., and Paull, A., “Experiments on Cruise Propulsion with a Hydrogen Scramjet”, Aeronautical Journal, Vol 102, 1998, pp. 37-43. 4 Cary, A. 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