Thermophysics and Aeromechanics, 2013, Vol. 20, No. 2 Flow field study in the T-313 wind-tunnel test section for М = 7 V.I. Zapryagaev, I.I. Mazhul, and A.I. Maksimov Khristianovich Institute of Theoretical and Applied Mechanics SB RAS, Novosibirsk, Russia E-mail: maksimov@itam.nsc.ru (Received January 19, 2012) Results of a numerical and experimental study of flow-field characteristics in the test section of the Т-313 supersonic blow-down wind tunnel of ITAM SB RAS at Mach number М = 7 are reported. The distributions of local Mach numbers, stagnation temperatures, static pressures, angles of flow deflection from the test-section axis were analyzed. For comparison, distributions of Mach numbers across the flow at several stations at М = 5 and 6 are reported as well. We show that, in the T-313 wind tunnel, two-dimensional nozzle inserts can be used to perform experiments at М = 7. Key words: wind tunnel, two-dimensional nozzle, test section, hypersonic Mach numbers, stream nonuniformity. Introduction The need in the development of high-speed aircraft and permanent improvement of their flight characteristics necessitates creation of new wind-tunnel facilities and extension of flow conditions in the already existing wind tunnels to hypersonic Mach numbers. As a rule, wind tunnels intended for high Mach numbers are equipped with axisymmertic conical or shaped nozzles. Although two-dimensional nozzles can be used under conditions up to Mach numbers М = 6 − 7 [1−4], very few wind tunnels equipped with Mach 7 two-dimensional nozzles are known. One of such facilities is the T-313 wind tunnel of ITAM SB RAS with cross-flow testsection dimensions 600×600 mm, provided with a set of two-dimensional replaceable nozzles and intended for operation in the range of Mach numbers М = 1.75 − 7. Yet, like in the majority of other similar facilities, including the wind-tunnel analogues, until recently the operation of Т-313 was restricted to the Mach-number range М = 2 − 6 [5]. Such state of things was due to the fact that, in using two-dimensional nozzles, on increasing the Mach number the problem of ensuring fixed values of throat dimensions and, correspondingly, fixed values of flow quantities in the test sections (Mach number М and related quantities, such as pressure, temperature, etc.) becomes a problem extremely difficult to solve. Even for precisely designed nozzle inserts their accurate fabrication for large wind tunnels proved to be a technologically difficult task since the largest acceptable inaccuracies in flow-path shaping proved to be as small as ± (0.02 − 0.05) mm [3, 4]. In addition, during long tests (~1 − 4 minutes) there exist no means for avoiding the effect on throat dimensions of the high air temperature required for preventing condensation of component gases in the wind tunnel [1]. Moreover, the necessity of frequent replacements of nozzle inserts leads to additional difficulties arising in connection with © V.I. Zapryagaev, I.I. Mazhul, and A.I. Maksimov, 2013 163 V.I. Zapryagaev, I.I. Mazhul, and A.I. Maksimov the accuracy of their installation and preservation of high quality of their working surfaces during the whole service life (several dozens of years) of the inserts. The situation becomes more and more complicated with increasing the Mach number, and at М = 7, it in fact becomes critical. Estimates made using the relations for isentropic air flow prove that an increase in Mach number from 5 to 7 should lead to a growth of nozzle expansion ratio F/Fcr from 25 to 104.1 [1, 4, 6]. For instance, for the 600-mm diameter exit of T-313 the calculated height of critical cross section h in the case of ideal-gas flow decreases from 24 to 5.76 mm. For real nozzles, on introducing correction for the boundary-layer displacement thickness, the above values become even smaller, reaching, respectively, 20 and 5 mm. In the Mach 7 regime, a ±0.1-mm deviation in the value of h results in a change of Mach number in the nozzle exit section respectively to 6.973 and 7.028, i.e., approximately by ±0.4 %. Similarly, for nozzle inserts of 600-mm width and 2470-mm total length, the same very small deviation of h in transverse direction leads to ±0.4-% nonuniformity of the flow over the test-section span. A detrimental influence on the flow quality in the test section can also be a result of possible local deviations of throat height h related with inaccuracies in the fabrication of nozzle inserts and also their thermal deformation arising as a result of nonuniformity of the metal structure and nonuniform distribution of temperature in this structure. Even rough estimates show that ensuring a high quality of Mach 7 flow with the help of two-dimensional nozzles presents a difficult problem; that is why investigations of the nonuniformity of flow quantities in the test section of particular wind tunnels present an important issue. The Т-313 wind tunnel of ITAM SB RAS was brought into service in 1965. The first precommissioning phase, which included measurement of the test-section flow field at М = 2, 3, and 4, was accomplished by the beginning of 1967. After a modernization performed in 1967−1969, the T-313 facility was put into regular service for conducting various tests in the field of aerogasdynamics. In 1967−1969, a new nozzle box with a pneumatic nozzle-insertfixation system, together with the doors, was designed and mounted on the wind tunnel (Fig. 1), and the so-called “hot” flow path, having allowed extension of the operating range of the facility to Mach numbers М = 5−7, and also a new measuring complex comprising a high-precision four-component aerodynamic balance of mechanical type, were put in service [4, 7]. During certification of the new aerodynamic facility, as early as in 1967−1968 a few series of multiple weighing tests of reference models in the range of Mach numbers М = 2−4 were performed; later, such series were regularly repeated during the whole operating period of T-313. At the beginning of 1969, pilot tests in the Mach 7 regime were carried out. Starting from 1970, systematic investigations of the flow field along the wind-tunnel test section were carried out in six characteristic cross sections with the help of a cross-shaped rake of Pitot and temperature sensors in the whole range of design Mach numbers [8]. Yet, attempts to put the T-313 wind Fig. 1. Nozzle inserts for Mach number М = 7. 164 Thermophysics and Aeromechanics, 2013, Vol. 20, No. 2 tunnel in regular operation in the Mach 7 regime, the most difficult-to-implement one, had for a long time remained unsuccessful. The latter was related to the fact that for air heating temperature Т0s ≈ 573 K, and also for higher air heating temperatures ensured by a 6-MW GP-6000 power supply and required for guaranteed prevention of air condensation in the wind tunnel, stabilization of height h inside the nozzle throat and preservation of constant parameters of the flow in the test section during experiments were found impossible. A second fundamental modernization of the Т-313 wind tunnel was undertaken in 1973; during this modernization, the settling chamber of 1400-mm inner diameter and 4000-mm length was replaced with a new settling chamber of 2600-mm inner diameter and 6000-mm length [4, 7]. The increase in stream contraction ratio from 4.3 to ~18.8 and application of honeycombs and a fabric filter as well as the use of an internal noise-absorbing shield, had enabled a considerable reduction of acoustic-noise and stream-turbulence levels; the measures applied had drastically improved the flow quality in the test section of the wind tunnel. Since 1973, due to permanent widening of the spectrum of conducted experiments and systematic modernization of measuring-computing system achieved through introduction of advanced equipment performed under guidance of Prof. A.M. Kharitonov, Dr. Tech. Sciences and, later, Prof. V.I. Zapryagaev, Dr. Tech. Sciences, the T-313 facility had become one of the most advanced aerodynamic facility of a kind engaged in many experiments. The purpose of the present experimental and numerical study performed at the stage of putting the Mach 7 regime into permanent service was determination of flow nonuniformity in the test section of the wind tunnel and development of a regular procedure for conducting routine experiments in the indicated operating regime of T-313. Preliminary results of this study were earlier reported in [9]. Testing conditions In compliance with the procedure adopted for Т-313 [10], the experimental study included the determination of local Mach numbers in the Mach 7 regime in six cross sections with coordinates х = 75, 225, 375, 525, 675, and 825 mm (Fig. 2) and in the cross section х = 675 mm at М = 5 and 6, test measurements of stagnation temperature Т0 at х = 75 and 675 mm, and also determination of boundary-layer thickness on the upper wall in the cross section х = 525 mm at М = 7. It should be noted here that the main focus in the present study was on a more detailed examination of flow characteristics in the cross section х = 675 mm since in the majority of cases models under tests in Т-313 are normally located in this cross section. The values of local Mach numbers were calculated from post-normal-shock (Pitot) pressures Р0′ measured with Pitot tubes (Fig. 3) and from the stagnation pressure Р0s in the hotflow-path settling chamber, i.e., from the ideal-gas isentropic ratios Р0′/Р0s. The stagnation temperatures Т0 in the test section were determined using a thermocouple array, and measurements in boundary layer were carried out with the help of a combined Pitot/static pressure probe. The Pitot rake was a cross-shaped welded structure that comprised two pylons, each about 410 mm long, with edges sharpened from the front and rear sides, and a cylindrical strut of length 1.42 m and outer diameter 38 mm. The pressure pipes of diameter 2.5×0.3 mm and total length ~3 m that connected the Pitot tubes with the sensors of the T-313 measuring system were led out through the strut and a cut made in the test-section bottom wall behind the fairing of the saber-shaped suspension of the mechanical balance (α-mechanism of the wind tunnel). The Pitot-rake strut was fixed in the saber-shaped suspension and, for making it more rigid, the strut was additionally supported by a saber-shaped pedestal with a clamping device at the end which could be displaced in a proper position along the slots provided in the test-section bottom wall. 165 V.I. Zapryagaev, I.I. Mazhul, and A.I. Maksimov Fig. 2. Location of coordinate axes and measurement stations in the test section of T-313. 1 ⎯ cold-flow-path settling chamber, 2 ⎯ air supply, 3 ⎯ heater, 4 ⎯ hot-flow-path settling chamber, 5 ⎯ nozzle insert, 6 ⎯ test section, 7 ⎯ aerodynamic balance, 8 ⎯ optical window, 9 ⎯ Pitot rake. The Pitot rake was equipped with 21 cylindrical Pitot tubes of outer diameter 2.5 mm, hole diameter 1.6 mm, and length 70 mm, in line with recommendations for no-wash measurements [11, 12]. The Pitot tubes were located equidistantly at 40-mm step in two mutually perpendicular planes. For ensuring required stiffness, the Pitot tubes were inserted in largerdiameter tubes at the distance of 45 mm from the leading face. The central Pitot tube was located at the point of intersection of the vertical and horizontal pylons, i.e., at the longitudinal axis of the test section. For enhancing rigidity, the rake pylons were reinforced with cross-plates wedged to the pylons at 45° angles (see Fig. 3). The post-normal-shock pressures Р0′ in the Pitot tubes were registered with the help of 0.3-accuracy-class TDM-A strain-gage absolute-pressure meters with 0 to 63 kPa range of measured pressures. The meters were located in a special heat-insulating foam-plastic box installed on the lower platform of the test-section pressure chamber. For measuring the settlingchamber pressure Р0s, an IPD meter (model 89008) with the largest measured pressure 1.57 MPa and accuracy class 0.06 was used. The relative measurement error for Mach number as determined from the relations for Р0′/Р0s was within ±0.0022, or 0.22 % [7]. Fig. 3. Location of the Pitot rake in the test section of T-313. 166 Thermophysics and Aeromechanics, 2013, Vol. 20, No. 2 The cross-shaped thermocouple array comprised 17 chromel-alumel thermocouples located uniformly at 50-mm step. The thermocouple junctions were contained in cylindrical stagnation chambers-tubes of outer diameter 5 mm and length 18 mm, which were provided with two lateral ventilation holes, each 1.5 mm in diameter, located near the insulator surface. The indications of the thermocouples were registered with an Agilent 34970A voltmeter. At the present stage of our study, measured temperature fields were considered just qualitative results. Normally, in measurements of Pitot pressure and temperature fields, the Pitot rake and the thermocouple array were installed at two positions: at zero angle (as shown in Fig. 3) and as rotated in the plane of the same cross section through the angle ϕ = 45° (i.e., at positions «+» and «×»). In some cases, for refining the flow field characteristics in a particular cross section, measurements at intermediate orientations of the Pitot rake and thermocouple array were performed. In connection with the possibility of variation of nozzle throat height h due to the thermal expansion of nozzle material, regular measurements of h at the beginning, in the course, and at the end of each test series were carried out. The average values of h, the coordinates of measured cross section, the value of stagnation temperature in the settling chamber, and the angle defining the Pitot-rake orientation are indicated in the pictures of Mach-number fields presented below. The experiments were carried out using the automated data acquisition and processing system of the T-313 facility [13, 14]. The mean values Мmean and Т0mean in measured cross sections and throughout the entire measured region in the wind-tunnel test section were determined using the procedure accepted in T-313 [10]; they present values integral-mean over an area or a volume. In plotting 2D flow patterns serving the function of providing an additional illustrative material, results of a preliminary treatment of gained data (local Mach numbers and stagnation temperatures) were interpolated with bicubic splines. At the initial stage of the study, an ohmic heater with resistance R = 0.105 Ohm and output power N ≈ 1 MW was used. At steady operation, with a stagnation pressure in the settling chamber Р0s ≈ 1.18 MPa (12 atm) in the Mach 7 regime, the heater could only ensure the heating of supplied air flow to temperature Т0s = 393 K. At the obtained static 2 parameters of the flow (Pst ~ 28.9 kg/m or 284 Pa and Тst ~ 36 K), this would not guarantee the absence of air condensation in the wind tunnel (Fig. 4) [15]. In this connection, for realization of an air temperature more suitable for preventing air condensation, Fig. 4. Air condensation in the test section of wind tunnels. 1 ⎯ averaged experimental data of [15], 2 ⎯ curve of air saturation; nozzles: 3 ⎯ conical, 4 ⎯ shaped, 5 ⎯ two-dimensional; Т-313: 6 ⎯ М = 5, Т = 370 K, 7 ⎯ М = 6, Т = 463 K, 8 ⎯ М = 7, Т = 413 K, 9 ⎯ М = 7, Т = 473 K. 167 V.I. Zapryagaev, I.I. Mazhul, and A.I. Maksimov experiments were conducted using the so-called preliminary overheating strategy. In the latter case, prior to attainment of normal operating regime of the wind tunnel the ohmic heater was heated to a maximum possible temperature at a low rate of air flow, and the indications of sensors were registered on raising the settling-chamber pressure to the nominal value of 1.18 MPa during a smooth reduction of temperature at Т0s ≈ 413 K, since the heater output power was obviously insufficient for stabilizing the temperature Т0s = const at the indicated level. In the course of the present experimental study, an improved ohmic heater with modified interconnections of the heating-element assembly was introduced. When used with the same GP-2300 dc supply, which was put in operation after breakdown of the previously used GP-6000 power supply, the new heater with electric resistance R = 0.177 Ohm was capable of ensuring an output power N ≈ 1.62 MW, and at typical operating regimes of T-313 it was capable of stabilizing the air heating temperature at М = 5, 6, and 7 at the level Т0s ≈ 373, 463, and 493 K for nominal values of stagnation pressure Р0s ≈ 0.79, 0.80, and 1.18 MPa, respectively. The values of stagnation temperature in the settling chamber implemented in each individual experiment, which, for safe operation of the heater, were set to a level somewhat lower than the above values, are shown in the upper right corner of the pictures of Mach-number fields presented below. In the regimes М = 5 and 6, the indicated values of stagnation temperatures proved to be quite sufficient for preventing air condensation in the wind-tunnel test section, and at М = 7, the temperature Т0s ≈ 473 K implemented in the ma2 jority of experiments (at this temperature, the static parameters were Pst ~ 28.9 kg/m and Тst ~ 45.7 K) was close to the temperature required for preventing condensation (see experimental data for T-313 in Fig. 4). Typical examples illustrating the variation of total pressure Р0s and stagnation temperature Т0s of the air in the settling chamber during typical experiments on examination of flow-field characteristics in the test section of T-313 at Mach 7 regime are shown in Fig. 5. From the graphs, it is seen that the total duration of each wind-tunnel run was approximately 2.5 to 4 minutes. The working regime with fixed values of pressure and temperature (with the improved heater used) lasted for 30 seconds; during this time, at least 3−4 readings were registered for improving the reliability of measured experimental data after equalization of pressures inside the Pitot tubes. The latter approach to registration of indications provided an additional check of equalization of pressures inside the Pitot pipes, and it allowed us to exclude random spikes in registered data. With the improved heater, the normal operating regime could be reached either with a preliminary overheating of the air in the settling chamber (curves 1, Fig. 5) or with a smooth growth of air temperature to its nominal level (curves 2) under the normal rate of air mass flow. The first variant, a typical one for running the T-313 facility at Mach numbers М∞ = 6 and 7 with the previous heater, was almost never used after heater Fig. 5. Measurements of pressure Р0s and temperature Т0s in the settling chamber of Т-313 during Mach 7 tests. 1 ⎯ with air preheating, 2 ⎯ with standard heating. 168 Thermophysics and Aeromechanics, 2013, Vol. 20, No. 2 modernization (i.e., after increasing the heater output power to N ≈ 1.62 MW) as it offered no advantages in comparison with the second variant both in terms of duration of performed experiments and in terms of total air consumption (because a predominant fraction of compressed air was spent for operation of two ejectors). Conditions adopted in the numerical simulations For analyzing the flow structure and for revealing possible flow-field perturbations, in addition to experiments, numerical calculations of flow characteristics inside the nozzle and in the test section of the Т-313 wind tunnel at Mach number М = 7 were carried out. The calculations were performed in 2D approximation with the help of the FLUENT software both for inviscid flow and under the assumption of a fully turbulent flow within the framework of averaged Navier−Stokes equations and the k−ω SST model of turbulence. In conducting numerical simulations, a coordinate system х′0у ′ was adopted whose axes were located at the initial point of nozzle channel (see Fig. 2) while the exit from the calculation domain, referring to х′ = 3442 mm, was at the location of the optical window for Toepler set-up. The calculation domain was bounded by the symmetry plane of the nozzle at у′ = 350 mm and by the channel surface. It included the hot-flow-path settling chamber (intermediate piece) of length L = 1200 mm, the nozzle proper (L = 2470 mm), a horizontal spacer (the so-called testsection threshold, L = 175 mm) and the initial length of the test section L = 800 mm. It should be noted here that, at the nozzle exit, the longitudinal flow path was assumed to be sloping at the angle θ = −1° and, hence, additional perturbations in the form of compression waves were generated at the point of junction with the horizontal insert. The wind-tunnel test section had a linear contour, which, for compensation of boundary-layer displacement thickness growth, had an angle of sloping to the longitudinal axis θ = −0.5°, so that at the point of junction with the horizontal insert perturbations in the form of rarefaction waves were also generated. In defining the contour of the real nozzle, we used an array of nozzle surface coordinates available in the database of the T-313 wind tunnel. In the whole calculation domain, the grid was generated with condensation of nodes towards the contour surface, and it comprised a total of 430 481 nodes. As the initial data at the inlet section of the calculation domain, the stream stagnation parameters were assumed to be Р0s = 1.18 MPa and Т0s = 433 K. In the outlet section, the static pressure Р = 284.3 Pa determined using the isentropic relations for М = 7, were adopted. Results of the investigation of the flow field As it was mentioned above, in constructing the 2D flow patterns, results of the preliminary treatment of experimental data (local Mach numbers and stagnation temperatures) were interpolated with bicubic splines. In each cross section, data gained in several wind-tunnel runs done with different positions of the rake over the roll angle ϕ (as a rule, in the positions «+» and «×») were used. Results of such a treatment of Mach-number fields for five cross sections along the test section are presented for М = 7 in Fig. 6. As it is seen from the data of Fig. 6, which were obtained at Т0s ≈ 473 K, along the entire test section local zones exhibiting large or small Mach-number values were observed. Within the experimentally examined region, which covered ~35 % of the cross-sectional area of the test section, the revealed zones with reduced Mach-number values were predominantly located in the vicinity of the flow core. As we moved farther downstream, a gradual shift of the zones to the left, their approaching each other, and merging in a single zone of reduced Mach-number values were observed. A similar flow pattern was also revealed in experiments performed at the first stage of the present study for stream temperature Т0s ≈ 413 K. For revealing possible effect due to the total number of measured points in the cross section х = 675 mm on the obtained distributions of Mach-number values, we performed measurements orientations ϕ = 15°, 30°, 60°, and 75°. Figures 6е and 6f show that a threefold increase 169 V.I. Zapryagaev, I.I. Mazhul, and A.I. Maksimov Fig. 6. The field of Mach numbers in the test section of T-313 in the regime М = 7. 6 Т0s ≈ 473 K, Re1 ≈ 7.58⋅10 . in the number of measured points has not substantially altered the flow patterns obtained, although the position and configuration of individual Mach-number zones showed some minor changes. Even threefold increase in the number of implemented orientations of the Pitot rake over the angle ϕ in each cross section did not ensure a sufficient density of measurement points in the peripheral zone covered by our measurements. Since the weighting coefficients for the points in the outer annular region (i.e. the test-section volume per the total number of readings 170 Thermophysics and Aeromechanics, 2013, Vol. 20, No. 2 taken from this region) were five times greater than the same coefficients for the points in the first inner annular region, the errors in the data taken from the former points made a greater contribution to the overall error in determining the Мmean–values and standard deviations. For avoiding such situations, further detailed experimental study employing Pitot rakes of other designs, namely, rakes with an equidistant arrangement of measurement points at 20−25-mm separation between the points throughout the whole cross section of interest (excluding regions affected by the wall-induced boundary layers) are necessary. We believe that this will help to substantially improve the accuracy in determining the mean flow quantities at the location of tested models. Also, we believe that this will allow identification of the sources of primary local variations of flow quantities and taking measures for their elimination or minimization to an acceptable level. According to experimental data, in the four upstream cross-sections (I−IV) of the test section, the values of Мmean amount, respectively, to 6.82, 6.86, 6.90, and the standard deviations of Mach-number values σМ fall in the range from 0.034 to 0.044, so that the relative standard deviations σМ = σМ/Мmean ∼ 0.5−0.6 %. Those values are quite comparable to the values of calculated flow nonuniformity that will be discussed later. Yet, in the two last cross sections (V and VI) the experimentally revealed standard deviations of Mach-number values increase to 0.060 and 0.134, although the values of Мmean themselves are retained at the same level (6.86 and 6.90, respectively). The maximum deviations of temperature in the examined cross-sections х = 75 and 675 mm at М = 7 amount to ±14 K (Fig. 7). The data presented show that the maximal spreads of Т0–values in the horizontal planes amount to ~ ±(0.8−1.2) %, and in the vertical planes, to ±(2.5−3) %. Here, in both cross sections, as we move towards the bottom wall of the test section, we observe a distinct reduction of temperature in the vertical plane, which starts somewhat over the wind-tunnel axis, to some minimum level; this observation is probably indicative of vertical stratification of the heated air stream over temperature. Another possible factor that could be the cause for such a distribution of temperature is an abrupt turn of the stream in the settling chamber of the hot flow path through 90º, which should necessarily induce flow separations and cause a profound modification of the flow structure in the upstream region of the entrance to the nozzle assembly. Also, it should be noted here that, in both indicated cross sections, both positive and negative deviations of stream temperature from its nominal (prescribed) value Т0s ≈ 478 K occur. For comparison, Fig. 8 shows the distributions of Mach numbers obtained in the cross section х = 675 mm in the regimes М = 5 and 6. The presented data show that at М = 5 and 6, the test-section flow nonuniformity exhibits a pattern resembling the above-discussed pattern for М = 7. It seems that the local zones with increased or decreased Mach-number values are formed not only under the influence of individual imperfections in the contour of a particular nozzle insert, but also because of design features of the hypersonic (hot) flow path of the T-313 wind tunnel proper, including those of the ohmic heater. Fig. 7. Distributions of stagnation temperature across the test section of T-313 at stations х = 75 (а) and 675 mm (b) in the horizontal (1) and vertical (2) planes of symmetry at М = 7. 171 V.I. Zapryagaev, I.I. Mazhul, and A.I. Maksimov 6 Fig. 8. The field of Mach numbers in the cross section х = 675 mm at М = 5 (Re1 ≈ 16.1⋅10 ) and 6 M = 6 (Re1 ≈ 7.65⋅10 ). Figure 9 illustrates the modification of the field of Mach numbers in the cross section х = 675 mm in the Mach 7 regime during a step-like reduction of stagnation temperature in the course of a single experiment. It is seen that, as the stagnation temperature Т0s decreases Fig. 9. Effect of stagnation temperature Т0s on the field of Mach numbers in the cross section х = 675 mm at М = 7. 172 Thermophysics and Aeromechanics, 2013, Vol. 20, No. 2 Table Re1⋅10 [1/m] Мaver Mmax Mmin 418 9.49 378 11.3 359 12.4 336 13.5 6.755 6.88 6.41 6.766 6.89 6.45 6.776 6.92 6.48 6.800 7.00 6.50 ⎯σ М, % 0.7 0.7 0.7 0.8 Т0s, K −6 from 419 to 336 K, the local Mach numbers exhibit some growth. Correspondingly, the mean Mach-number value in the cross section of interest increases as well. The table below shows that the increase in the mean Mach-number value resulting from a decrease of the temperature in the interval Т0s = 419−336 K amounts to 0.05, or ~ 0.7 %. Such an increase of Мmean can be 6 6 attributed, first of all, to the increase of unit Reynolds number Re1 from 9.49⋅10 to 13.5⋅10 [1/m], and also to the related reduction of boundary-layer displacement thickness at the walls of the nozzle inserts and wind-tunnel test section which occurs during the lowering of Т0s and additional expansion of the flow. In the cross section х = 675 mm, the relative standard deviation of Mach-number values⎯σМ amounts to ~ 0.7−0.8 % as well. The obtained data show that in performing experiments at one and the same Machnumber value yet at different air heating temperatures Т0s for avoiding systematic errors it is necessary to take into account the high probability of large variations of local and mean Machnumber values at the location of the particular model under study. Calculations performed for М = 7 show that intense perturbations are formed both in the nozzle proper and at the junction of the nozzle with the test section (Figs. 10 and 11). In the latter case, in the flow regions with coordinates х′ ≈ 210−230, 670−1230, and 1970−2100 mm we observe a distinct correlation of perturbations with the location of substantial nonuniformities in the nozzle contour. The generated perturbations, as they suffer successive reflections from the plane of symmetry and from the nozzle surface, finally enter the test section (Fig. 11). The obtained data show that the nozzle contour nonuniformities affect, first of all, the flow pattern in the vicinity of the walls. The latter is clearly seen from the distributions of relative static pressure⎯Рst = Рst /Р∞ (see Fig. 12). Fig. 10. Calculated pattern of nozzle throat flow at М = 7. Fig. 11. Calculated pattern of the flow inside the nozzle and in the test section of the wind tunnel at М = 7. 1 ⎯ nozzle, 2 ⎯ test section, 3 ⎯ plane of symmetry. 173 V.I. Zapryagaev, I.I. Mazhul, and A.I. Maksimov Fig. 12. The calculated distribution of static pressure along the nozzle: а ⎯ nozzle throat, b ⎯ nozzle, c ⎯ test section; 1 ⎯ nozzle surface, 2 ⎯ plane of symmetry, 3 ⎯ nozzle throat, 4 ⎯ horizontal insert. Also engaging attention is the fact that in the main part of the nozzle (x′ ~ 250−1750 mm), the staticpressure values in the plane of symmetry proved to be notably lower than the pressure values in the vicinity of the nozzle surface (Fig. 12b). In the flow region under consideration, a substantial nonuniformity in the distribution of Mach-number values over the nozzle height is observed; namely, here the local values of М show a substantial increase towards the plane of symmetry. For instance, already at x′ ~ 750 mm in the plane of symmetry values М ≈ 7 are attained while in the outside region of the boundary layer, in the vicinity of the wall, the Mach number turns out to be decreased to М ≈ 5.5. According to calculation data, the integral-mean value of the Mach number outside the boundary layer in the cross section х′ = 3442 (х ∼ 800) mm amounts to Мmean = 7, the relative standard deviation being σМ ≈ 0.7 %. The latter values are in a good agreement with the obtained experimental data discussed previously. For the inviscid flow, we have: Мmean= = 7.12 and⎯σ М ≈ 1.1 %; in other words, the predicted flow-field nonuniformities are well in excess of the predicted flow nonuniformities for viscous flow. Figures 13 and 14 exemplify distributions of dynamic pressure and stream deflection angles across the wind-tunnel channel in the cross section х′ = 3442 (х ∼ 800) mm. Here, the dynamic pressure is normalized by the value q = 9776 Pa obtained using the isentropic relations for the conditions adopted in the calculations. The integral-mean value of dynamic pressure in this cross section is qmean = 9982.2 Pa, and its relative standard deviation is⎯σq ≈ 2.9 %. Here, the mean value of static pressure is Рmean = 284.3 Pa, and⎯σр ≈ 0.5 %. The stream deflections show alternating signs, and they can reach values ±0.5° (Fig. 14). Figure 15 gives a comparison of calculated and experimental data on the thickness of boundary layer in the plane of symmetry of the test section (а), and Fig. 13. The calculated distribution of dynamic pressure in the cross section х ∼ 800 mm at М = 7. Flow: viscous (1), inviscid (2). 174 Thermophysics and Aeromechanics, 2013, Vol. 20, No. 2 Fig. 14. The calculated angles of stream deflection across the test section in the Mach 7 regime. Flow: viscous (1), inviscid (2). it also shows the distributions of Mach-number values along the test section (b) at М = 7. In the calculations performed using data measured with the help of the combined probe, the Mach-number values inside the boundary layer were determined from the Р/Р0′ ratios, and in the region outside the boundary layer (у > 80 mm), from the Р0′/Р0s ratios. A comparison of calculated and experimental boundary-layer profiles in the cross section х = 525 mm demon-strates a good agreement between the data. Here, the boundary-layer thickness is δbl ≈ 80−85 mm. The kink of the curve observed somewhat over the edge of boundary layer is due to the pertur-bations (compression and rarefaction waves) coming into this zone from the nozzle. The experimental data on the distribution of Mach-number values along the test section shown in Fig. 15b were obtained for stagnation temperatures Т0s ≈ 413 and ~ 473 K; here, each point represents a value Мmean averaged throughout a single cross section. We would like to emphasize here that the calculated data for viscous flow at the nozzle axis (curve 3) rather Fig. 15. A comparison of experimental and calculated data for boundary-layer thickness in the cross section х = 525 mm (а) and for Mach-number values along the test section of Т-313 (b) at М = 7. Data: experimental (1), calculated (2), calculated in the plane of symmetry (3); section-averaged experimental for Т0s ≈ 413 K (4) and 473 K (5). 175 V.I. Zapryagaev, I.I. Mazhul, and A.I. Maksimov closely approach the experimental values, in particular, in the region of Toepler set-up window, i.e., at the location of models under study. For instance, at х = 0.797 m, the calculated Machnumber value is Мс = 6.934, and the experimental Mach-number value at х = 0.825 m is Мexp = 6.904, the difference being within ~ 0.5 %. Conclusions An experimental and numerical study of the flow field inside the Mach 7 two-dimensional nozzle and in the test section of the T-313 wind tunnel of ITAM SB RAS was performed. Experimentally, it was established that at the location of a model in the test section (stations IV-VI) the mean Mach number at air heating temperature Т0s ≈ 473 K was Мmean ≈ 6.87 with standard deviation of Mach-number values σ М ≈ 0.08 (relative standard deviation σМ = 1.1 %). At station V (approximately the center of Toepler set-up window), the mean Mach number was Мmean = 6.865, and⎯σМ = 0.9 %. Within the experimentally examined region covering ~35 % of the cross-sectional area of the test section, the revealed zones with reduced Mach-number values were primarily located in the vicinity of the flow core; as the stream moved farther in the channel, those zones merged in a single zone. According to experimental data, at the first four stations (stations I−IV) inside the test section, the mean standard deviations of Mach-number values σ М were within 0.034−0.044, or ∼ 0.5−0.6 % of the mean Mach-number value Мmean. Yet, at the two last stations (stations V and VI), the experimentally estimated standard deviations of Mach-number values showed a pronounced growth, reaching, respectively, 0.060 and 0.134. The distributions of stagnation temperature measured in the horizontal and vertical planes at stations х = 75 and 675 mm have showed that, here, the maximum deviation of temperature was within ±14 K. Here, the largest spreads of Т0 –values in the horizontal planes were ±(0.8−1.2)%, and in the vertical planes, ±(2.5−3) %. In both cross sections х = const, measurements have revealed a gradual decrease of temperature in the vertical plane, which started somewhat over the channel axis and proceeded to some minimum value as we moved towards the test-section bottom wall; this observation can be an indication for vertical stratification of the heated air over temperature. Variations of stagnation temperature in the settling chamber and measurements made in the channel cross section at х = 675 mm are indicative of an increase of the mean Machnumber value from Мmean = 6.755 to 6.800 that occurred as the temperature decreased in the inter6 6 val Т0s = 419−336 K and of a related growth of Re1 from 9.49⋅10 to 13.5⋅10 , which amounted to ~ 0.7 %. Such increase of Мmean could be due to the reduction of boundary-layer displacement thickness at the nozzle insert walls and at the walls of the wind-tunnel test section proceeding during the decrease of Т0s and additional flow expansion. Numerical calculations performed in 2D approximation have showed that the mean value of Mach numbers outside the boundary layer in the cross section х′ = 3442 (х ∼ 800) mm inside the wind-tunnel test section was Мmean = 7, and the relative standard deviation was⎯σМ ≈ 0.7%, the latter values being in agreement with the experimental data obtained. The mean value of dynamic pressure in this cross section was qmean = 9982.2 Pa, the relative standard deviation for this pressure was⎯σq ≈ 2.9 %; the mean value of static pressure was Рmean = 284.3 Pa, and⎯σр ≈ 0.5 %. According to calculated data, the stream deflection angles show a signchanging behavior, and they can amount to ±0.5°. A comparison between the calculated and experimental velocity profiles in the boundary layer in the cross section х = 525 mm has revealed a good agreement between the profiles. In the latter case, the boundary-layer thickness was δbl ≈ 80−85 mm. 176 Thermophysics and Aeromechanics, 2013, Vol. 20, No. 2 The experience gained in putting the wind-tunnel into service and in conducting experiments on examination of the flow field in the regime М = 7 has showed that, for obtaining quasi-constant parameters of the wind-tunnel test section flow in each experimental series, prior to starting experiments a preliminary run of the wind tunnel should be made in order to ensure required heating and thermal expansion of nozzle inserts in the throat region until the level typical of normal operation of the wind tunnel is reached. For excluding systematic experimental errors, a thorough check of proper adjustment of installed nozzle inserts and precise measurements of the actual value of nozzle throat area are necessary. For identification of the actual sources of dominant perturbations responsible for the nonuniformity of Mach-number and temperature fields and for obtaining new metrological characteristics of the T-313 wind tunnel in the hypersonic range of speeds, an additional detailed experimental study with a uniform location of measurement points covering at least 60−70 % of the test-section cross-sectional area, is necessary. References 1. A. Pope and K. Goin, High-Speed Wind Tunnel Testing, John Wiley and Sons, New York−London−Sydney, Inc., 1966. 2. S.M. Gorlin, Experimental Aeromechanics, Vysshaya Shkola, Moscow, 1970. 3. S.M. Gorlin and I.I. Slezinger, Aeromechanical Measurements: Methods and Instrumentation, Nauka, Moscow, 1964. 4. A.M. 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