EXPERIMENTAL INVESTIGATION OF A SUPERSONIC BACKWARD FACING STEP FLOW

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1 EXPERIMENTAL INVESTIGATION OF A SUPERSONIC BACKWARD FACING STEP FLOW Ferry F.J. Schrijer and Dario Modenini Delft University of Technology, Kluyverweg, 69 HS, Delft, The Netherlands University of Bologna, Italy ABSTRACT The flow over a backward facing step is investigated by means of infrared thermography. An inverse heat transfer procedure is used to calculate the surface heat flux from the measured surface temperature in time by taking into account multi-dimensional and unsteady conduction effects. Additionally schlieren visualization is used to get an overview of the flow field. The backward facing step flow is investigated for laminar, transitional and turbulent separating boundary layers. It is found that for the laminar and transitional cases the Stanton number and normalized length are influenced by the step height. For turbulent this is only marginally the case however the Stanton number downstream of reattachment increases with step height. For the transitional, large heat transfer peaks are measured at reattachment. Key words: Supersonic flow, Transition, Infrared Thermography.. INTRODUCTION In high speed aerodynamics backward facing step flows are often encountered. For high-speed vehicles typical examples are the gaps and steps occurring on a tile shaped thermal protection system and other type of irregularities on the vehicle body (control surfaces, junction of different materials). The presence of a step may trigger transition to turbulence causing increased aerodynamic heating which may have implications for the structural integrity of the vehicle. An example is the possible backward or forward facing step on the EXPERT vehicle, the nose of the vehicle is produced out of C/SiC while the afterbody is constructed from metallic parts (PM and Gamma-TiAl). Since both materials have different thermal expansion coefficients, a step may occur when the vehicle surface temperature increases during re-entry. This may cause boundary layer transition to be triggered early during reentry [5]. Figure. Occurrence of a backward facing step due to different thermal expansion Other examples of backward facing step flows are found in scramjets, where step geometries are added next to the injectors to enhance mixing between air and fuel, and plug nozzles where a base flow is created due to truncation of the terminal part of the plug. In both cases a proper knowledge of the fluid dynamics phenomena related to step flow geometry is of paramount importance for an accurate estimate of the engine performance. In literature al lot of information can be found on backward facing step flows [], [3], [], [4] and with this data enough confidence has been established in predicting the base pressure and to correlate the related data using scaling parameters, however this is not the case for the heat transfer. A similar conclusion is also valid for the numerical codes for which the accuracy of heat transfer rate prediction is always less than for the pressure. A particularly controversial point that still remains is the heat transfer overshoot at reattachment, and how this is influenced by the Mach number, Reynolds number and transition. Surface heat flux measurements are classically performed by means of heat flux gauges. In order to get an improved spatial resolution of the surface heat transfer distribution, techniques can be used such as infrared thermography, LCD crystals or TSP. These techniques return the surface temperature, quantitative heat transfer values can be obtained by using appropriate data reduction techniques. Of these thermometry techniques, infrared thermography is the most sensitive [8]. Infrared thermography, in combination with a heated thin skin technique, may lead to very accurate heat transfer values [6]. This technique requires a steady state situa-

2 tion where the surface temperature stays constant and the heat that is generated in the skin is dissipated to the flow. However the time it takes before thermal equilibrium is reached (approx minutes) prevents it to be used in supersonic blow down wind tunnels. A second approach which is often used is to compute the heat transfer from the surface temperature variation in time. In case when the time duration of the event is short (the model can be regarded as an infinite slab) and the gradients in surface temperature are not too large, the one-dimensional heat conduction equations may be used [7]. However in the current application, the assumptions are not adequate. Therefore the axisymmetric transient heat conduction equations are solved in order to obtain the surface heat flux.. INVERSE METHOD The surface temperature variation in time of the wind tunnel model is measured by means of an infrared camera. Before the wind tunnel is started, the model is heated by means of radiation ( kw lamp) to a uniform temperature of approximately 7 o C. When the wind tunnel is started, the model is cooled down by the flow. The amount of cooling (temperature decrease) is governed by the surface heat flux, the model geometry and model material. The objective is to measure the surface heat flux by using an inverse heat transfer technique. Normally when applying the heat transfer equations, a direct problem is solved where the temperature is calculated as a function of space and time by applying prescribed boundary conditions such as spatial temperature distribution, surface heat flux or surface heat transfer coefficient. In the application of Inverse Heat Transfer Problems (IHTP), for example surface temperature measurements are used for the determination of the surface heat transfer. The inverse heat transfer is essentially an optimization process. A surface heat flux variation in time and space is assumed and the surface temperature is calculated by means of a fully implicit finite volume solver, which is compared to the measured surface temperature. In the iterative process the heat flux is adjusted in such a way that the computed surface temperature approaches the measured temperature. In practise the presence of measurement noise may lead to instabilities hence the method is mathematically classified as ill-posed. For the solution to be stable, a regularization technique must be applied to the optimization process. In the current approach the iterative regularization principle is applied which uses a suitable choice of the stopping criteria for the iterations such that the final solution is stabilized with respect to the measurement errors. The iterative process uses a conjugate gradient method (CGM) that consists of the following parts [9]: Sensitivity problem; computation of step size in the direction of descent Direct problem; computation of the surface temperature to check for convergence In practise the following cost functional is minimized for the computed and measured temperature distribution: J [q(s, t)] = tf t= m= M [T m (t) Y m (t)] dt, () where Y m (t) is the measured temperature at location m and time t. T m (t) is the temperature computed from the boundary condition ˆq. The CGM consists of the following iterative procedure for the heat flux estimate: ˆq n+ (S, t) = ˆq n (S, t) β n d n (S, t) () where β n is the search step size obtained through the adjoint problem and d n (S, t) is the direction of descent from the sensitivity problem. For a schematic representation of the process, see figure. The iterative process is repeated until convergence is reached, in practise this means that the process is stopped when the following criterion is satisfied which relates the residual to the measurement error [9]: J n < σ Mt f (3) where σ is the standard deviation of the measurement technique, M is the number of spatial points included in the computation and t f are the number of time steps. Figure. caption 3. EXPERIMENTAL SETUP Adjoint problem; computation of direction of descent The model used in the experiments is an axisymmetric cone-cylinder, see figure 3. A backward facing step is

3 Table. Flow parameters Figure 3. Axis symmetric wind tunnel model θ L M M c Re/m Re L [deg] [mm] 6 [m ] obtained by applying a larger base radius to the cone compared to the cylinder. The model has a stainless steel core to ensure stiffness and is covered with a low conductive makrolon mantle which has an emissivity coefficient of approximately.9. The cone has a base diameter of 3 mm and step heights of h =, 4, 6, 8 mm are generated by applying the appropriate mantles. In addition to changing the total pressure, two cones were used in order to change the boundary layer Reynolds number at. recorded with a spatial resolution of mm/pixel. Since glass is nearly opaque in this wavelength range, optical access is provided by using a Germanium window which has a transmissivity of approximately.8. Although the data obtained from the IR camera are planar maps, a line parallel to the model centerline is selected since the inverse heat transfer process is based on an axisymmetric model; this is consistent with the flow under investigation which is also mostly axisymmetric. Finally schlieren visualization is used as additional measurement technique to visualize the overall flow field such as the leading edge shock, expansion wave at the step, possible lip shock, shear layer and reattachment shock. 4. RESULTS 4.. Overal flow visualization Figure 4. ST5 supersonic blowdown wind tunnel The flow facility used in the experiments is ST-5, see figure 4, a supersonic blow down wind tunnel having a 5 5 cm test section. The free stream Mach number can be set to either.5,, or 3, by using interchangeable sets of liners. In the current investigation, the free stream Mach number is 3. A total pressure of 4.7 or 7.4 bar was used to obtain different unit Reynolds numbers. Since the cone has a leading edge shock and the investigation focusses on the backward facing step, the free stream variables have to be corrected for the extra compression due to the leading edge shock. An overview of the flow parameters is given in table, it is apparent that the different shock angles do not have a significant influence on the unit Reynolds number. However due to the extra length of the 5 cone, the boundary layer Reynolds number at is increased with respect to the 5 cone, spanning complementary regions. A CEDIP Titanium 53L infrared camera was used to acquire the surface temperature. The camera has a 3 56 pixel Mercury Cadmium Telluride sensor which operates in a wavelength band between 7.7 and 9.5 µm. The measurement accuracy is ± o C and the sensitivity is 5 mk. The maximum full frame rate of the camera is 5 Hz, however for the current application the acquisition rate was set to 5 Hz. Thermograms were In figure 5 the raw thermograms are shows in combination with schlieren images. The leading edge shock is clearly visualized as well as the reattachment shock. The extent of the expansion fan at the location of the backward facing step is somewhat harder to discern. Except for the mm step, a lip shock was found in all cases. The separated shear layer was visualized as well, however it could not be inferred if it was laminar or turbulent. 4.. Transition detection In order to establish the state of the boundary layer at the location of (laminar, tubulent or transitional), experiments were performed aimed at detecting boundary layer transition on the cone. To establish the transition Reynolds number, measurements were performed at different unit Reynolds numbers and for two different cones. In figure 6 sample results of the measurements are given. When the boundary layer undergoes transition, the surface heat transfer increases and sharp decrease in surface temperature is measured. When transition is detected upstream of the step (bottom thermogram in figure 6) it is classified as turbulent, as transition occurs at the step (upper thermogram in figure 6) the is classified as transitional. In case transition is not detected the is laminar. Furthermore it was found that transition occurs at a constant Reynolds number of.75 6.

4 , M = 3, Re L = 6, M = 3, Re L = 6, M = 3, Re L = 4. 6, M = 3, Re L = 4. 6 Figure 5. Schlieren visualization and raw thermograms of the flow field (red means higher temperature) Table. State of the separating boundary layer Re/m [m ] 5 o cone 5 o cone laminar transitional transitional turbulent transition BFS Figure 6. Temperature maps indicating the transition location 4.3. Heat transfer profiles St [ ] x This section discusses the heat transfer profiles as obtained from the inverse heat transfer procedure. In the figures the Stanton numbers are given as a function of the streamwise position normalized by the step height (x/h). The origin is placed at the step location and is positive in streamwise position. In all figures the separated region features a low heat transfer region and at reattachment the Stanton number increases after which in downstream direction the Stanton numbers relax again, the turbulent reference level is indicated by the dotted line Figure 7. 5 o cone, Re/m = [m ], laminar In case of laminar the heat transfer is greatly affected by step height h in terms of length,

5 St [ ].5.5 x Figure 8. 5 o cone, Re/m = [m ], turbulent St [ ].5.5 x Figure 9. 5 o cone, Re/m = [m ], transitional expected since the step height influences the location of transition when is laminar (in the shear layer, during reattachment, or downstream of reattachment). In particular, a sharp peak in St is found for the highest step (8 mm), the magnitude is higher than the turbulent values. For turbulent, figure 8, the heat transfer values are only marginally affected by changing h. The nondimensional length is practically constant for h =, 4, 6 furthermore the St increase at reattachment is similar for all cases. A different behavior is found for the largest step height, currently this cannot be explained. It could be attributed to a measurement error. For a transitional separating boundary layer, measurements were done on both cones, figures 9 and. The corresponding heat transfer profiles show analogous behavior in terms of values and profile. Except for h = mm, sharp heat transfer peaks are found at reattachment. For, the highest values are found for all measurement conditions, in this case the heat transfer increases up to.5 to times the value for obtained for turbulent. For a step height of mm a low plateau heat transfer value is obtained. Currently this is cannot be explained, however it is measured for both cones and the measurement is repeatable, therefore the possibility of a measurement error is excluded Separation length A length of x sep /h = was found for all cases which agrees well with values found in literature. However it was found that on a local scale, boundary layer transition has an appreciable effect on the transition length, see figure. St [ ].5.5 x Figure. 5 o cone, Re/m = [m ], transitional steepness of the heat transfer increase in the reattachment region, and heat transfer peak, see figure 7. This is to be Figure. Effect of boundary layer transition on the length (red means higher temperature) It was found that when the transition location moves toward the step, the region becomes smaller Conclusions The inverse heat transfer technique was successfully applied to a backward facing step flow. The study focussed on the effect of the state of the boundary layer on the reattachment heat transfer profile. Boundary layer transition on the cone upstream of the step was detected by

6 means of infrared thermography. It was found that for the lowest unit Reynolds number and shortest cone the separating boundary layer was laminar. For the highest unit Reynolds number and shortest cone the boundary layer was transitional at, this was also the case for the lowest unit Reynolds number in combination with the longest cone. In case of the highest unit Reynolds number and the longest cone the boundary layer was found to be turbulent at. In general it was found that boundary layer transition occurs at a constant Reynolds number of In case of laminar the flow field downstream of the step was found to be largely influenced by the step height although no clear trend was found. For turbulent the step size has a limited effect on the heat transfer values, far downstream of the step the Stanton numbers were found to increase with step height. When the boundary layer is transitional at (short cone with high unit Reynolds number and long cone with low unit Reynolds number), high heat transfer peaks at reattachment were measured for all step heights except for. REFERENCES [] Chapman D.R., Kuehn D.M., Larson K.H., 957, Investigation of separated flows in supersonic and subsonic streams with emphasis on the effects of transition, Technical Report TN-56, NACA [] Roshko A., Thomke G.J, 966, Observation of turbulent reattachment behind an Axisymmetric BFS in supersonic flow, AIAA Journal, vol.4, nr.6 [3] Sfeir A., 967, Supersonic flow over a backward facing step, University of California, Berkeley, report nr. AS-66-8 [4] Smith H.E., 967, The flow field and heat transfer downstream of a BFS in supersonic flow, ARL report nr [5] Schrijer F.F.J., Scarano F., van Oudheusden B.W., Bannink W.J., 4, Experiments on hypersonic roughness induced transition by means of infrared thermography, 5th European Symposium on Aerothermodynamics for Space Vehicles Cologne, Germany [6] Carlomagno G.M., de Luca L., 989, Infrared thermography in heat transfer, in Handbook of flow visualization, chapter 3, editor Young W., Taylor & Francis [7] Cook W.J., Felderman E.J., 966, Reduction of data from thin-film heat transfer gages: A concise numerical technique, AIAA Journal, vol.4, nr.3 [8] Kowalewski T.A., Ligrani P., Dreizler A., et al, 7, Temperature and Heat Flux, in Handbook of Experimental Fluid Mechanics, chapter 7, editor Tropea C., Yarin A.L., and Foss J.F., Springer-Verlag [9] Özisik M.N., Orlande H.R.B.,, Inverse heat transfer. Fundamentals and applications, Taylor & Francis