Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, 70569, Stuttgart, Germany

Transcription

1 ICMAR 01 STATIC CALIBRATION OF WEDGE HOT-FILM PROBE AND DETERMINATION OF SENSITIVITIES FOR MODAL ANALYSIS IN T-35 SUPERSONIC WIND TUNNEL M. Krause 1, U. Gaisbauer 1, E. Krämer 1, Y.G. Yermolaev, A.D. Kosinov 1 Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, 70569, Stuttgart, Germany Khristianovich Institute of Theoretical and Applied Mechanics SB RAS, , Novosibirsk, Russia Introduction Supersonic and hypersonic vehicles recently moved again into the focus of research on reusable space flight systems. Vehicle design is greatly influenced by a profound understanding of phenomena occurring in supersonic flow such as e.g. compression shocks and the fluctuation of flow parameters. Experimental investigation on turbulent fluctuations is very often conducted by means of hot-wire anemometry. However in harsh environments such as in the vicinity of an oscillating shock wave mechanical loads cause this fragile device to break, which is why hot-films can be considered alternatively [1,, 3]. In order to be able to resolve the measured voltage fluctuations into the separate fluctuation modes of modal analysis according to Kovásznay and Morkovin, [, 5, 6], the sensitivities of the sensor to flow fluctuations (normally mass flux density (ρu) and stagnation Temperature T 0 ) need to be known as a function of overheat ratio. Sheplak, [1, ], designed, calibrated and tested his own wedge hot-film probe in hypersonic flow and found it to be an instrument for qualitative investigation. The sensitivities of his selfmade sensor to mass flux density and stagnation temperature are reported to be weak compared to hot-wires: the sensitivity to mass flux density was constant and close to zero and the one to stagnation temperature was also small and showed a shift in algebraic sign for high overheats. Seiner, [3], calibrated the commercial wedge hot-film probe DISA 55R31 in transonic and low supersonic flow and derived sensitivities. Since the sensitivity to velocity was much greater than the one to density, he suggested resolving for these three parameters (velocity, density and stagnation temperature) independently. However, the poor dependency of the sensitivities on overheat ratio made it actually impossible to solve the equations. He proposed to replace the variable density by pressure and to estimate the contribution of these pressure fluctuations to the voltage fluctuations by additional measurements or simply to neglect them. In the present study, a static free stream calibration of the commercial wedge hot-film probe DISA 55R31 was performed in T-35 Supersonic Wind Tunnel at Khristianovich Institute of Theoretical and Applied Mechanics in Novosibirsk, Russia. The constant-temperature probe was calibrated at four different Mach numbers (1.5,.0,.5 and.0) while the Unit Reynolds number was varied between /m and /m, depending on the Mach number. The sensitivities of the wedge hot-film probe were derived and compared to those of a hot-wire. Furthermore the standard procedure for deriving hot-wire sensitivities was modified and adapted to the wedge hot-film sensor. Wedge Hot-Film Probe, Hot-Film Anemometry and Modal Analysis In order to present the applied modifications of this study in a suitable way, it is necessary M. Krause, U. Gaisbauer, E. Krämer, Y.G. Yermolaev, A.D. Kosinov, 01

2 Section 1: Wind Tunnels and Gas-Dynamic Facilities, Methods of Flow Diagnostics to give more general information on hot-film anemometry, modal analysis and the procedures of how the sensitivities are derived. The wedge hot-film probe DISA 55R31 is shown in Fig. 1 and Fig.. The wedge shaped substrate is made of quartz glass and has a protective quartz coating on the 0.1 µm heated nickel Fig. 1. wedge hot-film probe DISA 55R31, [7] Fig.. cross section of wedge hot-film, dimensions in mm, [3] film at the sensor tip. The connectors at the side consist of a silver layer [3, 7]. The film diameter D is given in Fig.. At supersonic speed there is a detached shock in front of the sensor tip. At first the standard procedure of deriving the sensitivities and finally the fluctuation diagrams is outlined to allow for introducing the proposed modifications in a second step, [6]. The Nusselt number of a hot-wire or (cylindrical) hot-film is usually calculated as: 1 ( ) ( + + ) (1) E is the anemometer output voltage, q is a geometry factor (π for hot-wires and 1.3 for DISA 55R31), l is the film length and λ fl the thermal conductivity of the fluid. The temperatures T film and T rec refer to heated and recovery conditions and R film, R leads and R a represent electric resistances of the heated film, the connectors including cables and the active bridge arm. King s Law is normally given in one of the two forms: " + #$#%& ", ' (())+ ' *()) #$#%&, () + + (,) " #$#%& (3) Thermal conductivity λ and dynamic viscosity µ are calculated via power law, where Kovásznay, [9], used ab0.768, Morkovin, [5], proposed a0.885 and b0.765 and White, [10], suggested for air a0.81 and b Lenz, [11], provides a good summary. λ and µ are evaluated at static temperature T behind the shock, using T 0 or T rec is also possible. -. and - 3. () The overheat ratio τ and the recovery ratio η are commonly defined as follows with T 0 being the stagnation temperature: ) The overheat dependent functions f and g are introduced as: 5 (5) 5 (6)

3 ICMAR 01 (()) 1+( 6 ) (7) *()) 1+* 6 ) (8) Fig. 3. determination of n total Fig.. King s Law, Eq. (3) Fig. 5. King s Law, Eq. () King s Law exponent n total is determined as a function of overheat ratio according to Fig. 3: ;(ln) ;(ln(, )) (9) The perturbation equation for constant-temperature hot-film anemometry in basic nondimensional form is Eq. (10) with the overheat-dependent non-dimensional sensitivities S ρ for density, S u for velocity and S T0 for stagnation temperature, Morkovin, [5]: >?,, +> A B (10) According to [5] the sensitivities S ρ and S u of a hot-wire become approximately equal for supersonic flow. Horstman and Rose, [1], detected this approximation to be valid for an overheat ratio of τ 0.5 and a Reynolds number Re D 0 based on diameter. This is reported to be independent on Mach number. Therefore Eq. (10) can be simplified with the overheatdependent non-dimensional sensitivities of Eq. (1) and Eq. (13) resulting from logarithmic derivation, [6]: > (?@) (,) (, ) +> A B (11) ;Cln D > (?@) ;(ln(, )) E1 + F (1) > AB ;ClnD ;Cln D 1 GH 5 ) I ( +) E )+5 F- + (()) ;( +) ;) +( *()) ;*.J (13) ;) The vertical axes intercept L and the functions f and g originate from Eq. (3) and () respectively Fig. and Fig 5. According to Kosinov et al., [6], some approximations can be made for E >> L leading to (E L)/E 1. This allows for Eq. (1) and (15): > (?@) > AB 1 LH 5 ) > (?@)I ()+5) (1) 1 ;* *());) M (15)

4 Section 1: Wind Tunnels and Gas-Dynamic Facilities, Methods of Flow Diagnostics To identify the rms values of the measured fluctuations (ρu) and T 0 Eq. (11) is squared and time averaged leading to Eq. (16) that finally allows for drawing fluctuation diagrams according to Kovásznay, []. N O < (,) > O?@,AB < (,) >< > +< > (16) Eq. (16) introduces according to Lenz, [11], the rms values of the anemometer output voltage fluctuations, the mass flux density fluctuations and the total temperature fluctuations: with the ratios: < > R S T S, < (,) > R (?@) T, < (?@) > R A T B C A B D (17) N < > > AB, O > (?@) > AB (18) and the cross correlation coefficient:?@,ab (,) R(,) R. (19) By means of the separate modes of modal analysis these fluctuations can be further separated, compare e.g. Lenz, [11]. The special geometry of the wedge hot-film probe DISA 55R31 and thus its flow field require various modifications of this standard procedure which are proposed in the following paragraphs. Most of these modified approaches were developed within the present study. When modeling hot-wires and cylindrical hot-films it is assumed that except for heat conduction losses towards the prongs all generated electric heat is transferred directly to the fluid. For wedge hot-films this is far from being correct, since only the heat emitted on the front side of the film is transferred to the fluid via convective cooling, whereas the heat from the rear side of the film is conducted to the quartz glass substrate. Downstream, the substrate is again cooled by the flow. The percentage of heat being directly transmitted from the film to the fluid is defined by σ. Fig. 6 shows the upper half of the symmetrical sensor tip and the factor σ is determined from -dimensional CFD simulations of the wedge hot-film probe under flow conditions corresponding to the static calibration performed. The proportion σ is calculated and fitted as a polynomial function in different ways: The first fit gives σ as a function of velocity, density, film temperature and stagnation temperature and the second fit as a function of mass flux density, film temperature and stagnation temperature, σ 1 f(u,ρ,t film,t 0 ) and σ f((ρu),t film,t 0 ). The polynomial degree in ρ-, u- and (ρu)-direction is 3, whereas T film and T 0 are fitted with polynomials of nd degree. For simulating a hot-wire σ 1. Further information on the software is given in section Software and Experimental Setup. The percentage σ is used to modify the Nusselt number according to Eq. (0) in order to make sure that it refers only to the heated element of the sensor and not to the complete wedge:

5 ICMAR 01, 9 V ( 1 ) ( + + V ) (0) The recovery ratio η, Eq. (6), is assumed to be η const. for DISA 55R31, as suggested by Kosinov et al., [8]. Fig. 6. heat flux proportion σ: heat balance of hot-film Fig. 7. installation of wedge hot-film in T-35 test section Seiner, [3], suggests that the wedge hot-film probe shows a different sensitivity to changes in velocity and density and claims that the dependency of King s Law on Mach number can be reduced by using two different exponents. Consequently the simplifications of Eq. (11) are not justified and the separation of Eq. (10) is necessary for DISA 55R31. Starting from this approach the present study concludes that a different sensitivity to density and velocity will also require two separate exponents for King s Law, which can be derived in analogy to Eq. (9): ;(ln ;(ln ;(ln 7 ;(ln 7' ),) ) ) (1) () This leads to a modified King s Law with the correction term u1(n-n1): +, "W ( ') ("T X"W ) ++ ' (()) + C,' "W ' ' "T D *()), "W ( ') ("T X"W ) (3) () In Eq. (3) and Eq. () L and N represent the influence of T0, whereas the influence of density and velocity or mass flux density is located in the round brackets. However, when NuD,mod is used L and N also contain the factor σ in their denominator. This requires the derivation of new sensitivities since L and N become also functions of ρ and u respectively (ρu). The partial logarithmic derivatives of σ can be obtained from the polynomial fits. In Eq. (7) it is assumed that η η(t0). ;Cln D ;(ln(, )) ;Cln D >@ ;(ln( )) >? 1 ;(ln V) + L + 7' E1 FM ;(ln,) 1 ;(ln V) + L + 7 E1 FM ;(ln ) (5) (6)

6 Section 1: Wind Tunnels and Gas-Dynamic Facilities, Methods of Flow Diagnostics > AB ;ClnD ;Cln D 1 ;(lnv) GH ;(ln ) 5 ) I 7 'E1 + F E )+5 F- + ;( +) ;* (());) +( *()) ;).J (7) One of the problems coming up with this modified separation is that density and velocity change across the shock, whereas mass flux density and stagnation temperature stay constant. Therefore it is difficult to relate electrical parameters behind the shock via convective cooling to flow parameters in front of the detached bow shock. Alternatively a third form of King s Law can be used with the separation of Eq. (11) as well as with only one exponent. However, the information of the two exponents n 1 and n (for density and velocity) shall be preserved by constructing a new exponent out of these two. n * total can be used instead of n total Z7 ' 7 (8) The new exponent n * total allows to adapt the sensitivity S (ρu) from Eq. (1): > (?@) ;Cln D ;(ln(, )) 1 ;(lnv) L ;(ln(,)) E1 + FM (9) In this case n * total can also be used for calculating S T0. The exponents n 1 and n total are actually identical for a constant Mach number, since the velocity represents a constant factor. All three proposed forms of King s Law can be used either with a modified or a standard Nusselt number. The variables L, N, A, B and f, g originate from the related form of King s Law. Of course Eq. (9) can also be used in analogy for n total instead of n * total. Software and Experimental Setup The CFD software used to do the analysis on the heat flux proportion factor sigma is done with StarCCM+, a commercial nd order finite volume code (RANS). -dimensional simulations of the cross section of the wedge hot-film probe were conducted on a structured grid comprising the flow field as well as the solid body of the wedge. A grid convergence study based on the worst cooling case was performed varying grid fineness and length of the discretized area independently. Finally a grid with approximately 60,000 cells and a length of 1 mm discretized solid body measured from the sensor tip was chosen. Regarding the strong thermal gradients of the laminar boundary layer y+ varies between 0.01 and 0.3 while x+ is located in the range of The fitting of the data on σ was done with Matlab R013. The experiments were carried out in T-35 quiet wind tunnel of Khristianovich Institute of Theoretical and Applied Mechanics (ITAM SB RAS) in Novosibirsk, Russia. The supersonic blow-down wind tunnel provides a test section with a size of 0. x 0. x 0.6 m 3 and the turbulence intensity is decreased by honeycombs and damping screens. Furthermore measures are taken to suppress mechanical vibrations. The free stream Mach numbers can be adjusted in steps of M0.5 from 0.5 up to.0, while non-uniformity of Mach number in test sections is limited to 0.8%. The unit Reynolds number can be arranged between some /m and /m. The wind tunnel provides a maximum run time of approx. 85 minutes and a maximum adjustable total pressure of p 0 1 bar. A detailed description is given in [6, 11]. As constant-temperature measuring device for the wedge hot film probe the Cosytech CTA Scanner was used. The scanning system can quickly switch between up to 50 different 6

7 ICMAR 01 overheat ratios by using a resistance cascade and is suitable for short-time measurements. The AC and DC parts of the output voltage are separated by a 1 khz high-pass filter and a maximum frequency response of 100 khz is recorded for the Cosytech CTA Scanner. More information about the scanner can be found in e.g. [11]. The output voltage was recorded on PC with CAMAC standard equipment comprising a CC3 controller. A 1 bit analogue-digital converter (ADC) with a sampling rate of 750 khz was used for the mean as well as for the fluctuating part of the voltage signal. A square wave test was performed and the bridge was balanced. Fig. 7 shows the installation of the probe in T-35 test section. A free stream static calibration was performed for four Mach numbers: 1.5,.0,.5 and.0 with unit Reynolds number varying according to Table 1. Unit Reynolds number is enlarged by increasing density in some 0 steps while keeping velocity constant for a constant Mach number. At each setting 11 overheat ratios were measured ranging from approximately 0.9 to 0.5. Table 1. parameters of static calibration Mach number Unit Reynolds number (10 6 1/m) Results and Discussion Determining the exponents via Eq. (9), (1), () and (8) leads to n total 0.5 and n The density range of kg/m³ < ρ < kg/m³ could be realized for all four Mach numbers and at 11 interpolated density points within this range the coefficient n was derived. While n 1 is constant over velocity, n rises slightly with density and is fitted as a linear function of density and can be considered in average as n 0.5, while n * total0.33. These values seem to be fairly realistic compared to n total 0.57 used for hot-wires. Moreover, Kosinov et al., [8], found Fig. 8. L,N - τ plot of n total Fig. 9. L,N - τ plot of n * total Fig. 10. L,N - τ plot of n 1 & n

8 Section 1: Wind Tunnels and Gas-Dynamic Facilities, Methods of Flow Diagnostics n total 0.33 for several DISA 55R31 wedge hot-film probes, while Seiner, [3], still used n total 0.5. However, he indicated that the dependency of Nusselt number on Mach number was reduced when using two exponents with a greater exponent for velocity than for density. Using these exponents in Eq. (3) and () leads to the coefficients in Fig. 8, Fig. 9 and Fig. 10. Taking Fig. 8 with standard King s Law as reference value the modification with n * total reduces the dependency on Mach number moderately, while the modification with n 1 and n reduces this dependency radically for N, but not for L. Since L is the relevant parameter for deriving the sensitivities, the benefit of the latter modification seems to be limited at this point. Fig. 11. S ρu - τ plot of n total Fig. 1. S * ρu - τ plot of n * total Fig. 13. S ρ - τ plot of n 1 Fig. 1. S u - τ plot of n Using Eq. (1), (5), (6) and (9) finally leads to sensitivities plotted in Fig. 11, Fig. 1, Fig. 13 and Fig. 1. S ρu and S * ρu are very similar with S * ρu showing slightly less variation with Mach number. Like S ρ varies with velocity, S u varies with density and Fig. 1 gives S u for three out of the 11 defined density steps placed in the density range (0.095 kg/m³ < ρ < kg/m³) mentioned previously. Comparing S ρu and S * ρu to the results of Kosinov et al., [8], shows that if 8

9 ICMAR 01 the influence of σ is neglected, the data agrees quite well, especially since Kosinov et al., [8], also used the same exponent n * total In general the influence of the quartz substrate represented by σ reduces the sensitivities to ρ, u and to (ρu), as should have been expected. Sheplak, [1], found S (ρu) to be approximately 0.1 or smaller. However, his probe had a different design. Seiner, [3], obtained slightly higher values for S ρ and S u than the slopes presented in Fig. 13 and Fig. 1 that don t consider σ. Obviously S (ρu), S * (ρu), S ρ and S u are mostly constant for τ > 0.7. Up to now, there is no explanation for this behaviour. Compared to hot-wires, S ρu is smaller for DISA 55R31, especially if the influence of σ is taken into account, compare Fig. with S ρu F. Fig. 15. S ρu - τ plot of n total for several Reynolds numbers Fig. 16. S u - τ plot of n for several Reynolds numbers Fig. 15 shows the variation of S ρu with Reynolds number and this variation is much smaller than the one with Mach number. Therefore it can be neglected for S ρu based on n total. However, the dependence of S u with Reynolds number given in Fig. 16 is of the same size as the one on Mach number and is not negligible. While n 1 stays constant n varies with Reynolds number resulting in a variation of S u. Therefore n total doesn t show a variation with Reynolds number, but n * total does. This causes practically no variation of S ρ but a significant one of S * ρu. Fig. 17. f-, g- τ for standard Nusselt number Fig. 18. f-, g- τ for modified Nusselt number

10 Section 1: Wind Tunnels and Gas-Dynamic Facilities, Methods of Flow Diagnostics Sheplak, [1], claims that the highest proportion of the heat emitted by the film of his self-made probe will be conducted towards the substrate, whereas the simulations performed within the scope of this study showed σ to range approximately from This means that a percentage of only one third to one half of the heat is conducted through the body of DISA 55R31. In order to reduce the dependency of ST0 on Mach number, it is amongst others important to reduce the dependency of f(τ) and g(τ) on Mach. This is done by using the modified Nusselt number for King s Law according to Eq. (0), as shown exemplarily in Fig. 17 and Fig. 18 for King s Law with standard separation and ntotal. The effect is mostly similar for n*total and the combination of n1 and n. Here it should be kept in mind, that f(τ) and g(τ) represent calculated lines of best fit and that the symbols in Fig. 17 and 18 are no measured points but nodes intended to separate the different lines. The sensitivity ST0 is given in Fig. 19, Fig. 0 and Fig. 1 and is based on modified Nusselt numbers. According to common practice in literature ST0 is plotted versus overheat τ. Fig ST0 - τ plot of ntotal, with Numod Fig. 0. -S*T0 - τ plot of n*total, with Numod Fig. 1. -ST0 - τ plot of n1, with Numod Fig.. sensitivities of n0.57, hot-wire, [11] Due to an insufficient thermodynamic modeling the sensitivities based on non-modified Nusselt numbers show several poles and a huge scattering. All obtained sensitivities to T0 have 10

11 ICMAR 01 a shift in algebraic sign for high overheat ratios and S T0 based on n total has the smallest deviation with Mach number while S T0 based on n 1 and n deviates only slightly stronger. Both of them are quite similar to the plot of a hot-wire given in Fig. (G S T0 ). Compared to Fig. the curves show smaller absolute values for DISA 55R31, what may also be caused by the protective quartz coating having a damping and isolating effect towards the flow. The sensitivity S T0 based on n * total has this shift in algebraic sign already for smaller overheats and shows a rather linear trend. It is unknown, why S T0 for M.5 in Fig. 0 has a different slope. Fig. 3. S T0 - τ plot of n total for several Reynolds numbers Fig.. -k ϑ - τ plot of n total, with Nu mod The variation of S T0 for n total with Reynolds number is given in Fig 3 and can be neglected, since it is significantly smaller than the variation of S T0 with Mach number. Similar to the sensitivities for density, velocity and mass flux density S T0 based on the exponents n total as well as on n 1 shows no significant change with Reynolds number while it varies when n * total is used. The dimensional sensitivity for stagnation temperature k ϑ is given in Fig. for the exponent n total. k ϑ in [V/K] is calculated from the non-dimensional sensitivity S T0 according to Eq. (30). The variation with Mach number in Fig. is very similar to the one in Fig. 19. [ \ ;CD ;(]) > A B ] (30) The variation of S T0 with Mach number is usually reduced by computing the dynamic viscosity and the thermal conductivity of the fluid at stagnation Temperature T 0 or at recovery conditions T rec. However in this study the static temperature T behind the detached bow shock in front of the sensor was used since it is likely to represent the most physical modeling. Despite the significant change of T with Mach number no significant improvement could be noticed when using T 0 or T rec instead. This effect results from an obviously limited influence of the dynamic viscosity on the sensitivity to S T0. The approximation presented in Eq. (1) and (15) is not valid for the wedge hot-film probe DISA 55R31, since partly L/E² >>1%. Kosinov et al., [8], found S T0 to be very similar to Fig. 19 and Fig. 1. However it seems that a greater cold resistance of the probe moves the -S T0 graph in positive direction. Sheplak, [1], also recorded this change in algebraic sign for S T0 and stated S T0 to be very weak. Seiner, [3], reported S T0 of DISA 55R31 to have a similar trend like Fig., however he only plotted results for τ<0.5. Judging from all these diagrams a recommended procedure shall be proposed: S ρu as well as S T0 show a comparatively small dependence on Mach number and nearly no dependence

12 Section 1: Wind Tunnels and Gas-Dynamic Facilities, Methods of Flow Diagnostics on Reynolds number if the exponent n total is used in combination with a separation according to Eq. (11). This probably seems to be because of (ρu) and T 0 staying constant across a shock wave while ρ and u vary. However, a justification is needed to shift from Eq. (10) to Eq. (11). This can be done by Fig. 13 and Fig. 1. Deriving the sensitivity S u at conditions of ρ kg/m³ will cause S u to vary between 0.05 and 0.1. This is the range that S ρ moves in when varying the Mach number according to Fig. 13. So it is reasonable to assume S ρ S u S ρu. Therefore Eq. (11) and n total should be used for setting up S ρu and S T0. Finally it can be stated that detecting the best sensitivities means to set up fluctuation diagrams for all modifications and to compare the results for physical plausibility. Conclusions A static calibration of the wedge hot-film probe DISA 55R31 was performed for four different Mach numbers in supersonic flow of T-35 wind tunnel at Khristianovich Institute of Theoretical and Applied Mechanics in Novosibirsk, Russia. King s Law was set up, several modifications were proposed and the exponents of King s Law were derived from the experimental data. Sensitivities for density, velocity, mass flux density and stagnation temperature were determined as well as compared to those of hot-wires. It could be shown that the sensitivities to density and velocity are similar and that they should be summarized in a sensitivity to mass flux density. A procedure comprising a separation into fluctuations of mass flux density and stagnation temperature with corresponding sensitivities was suggested. The sensitivity to mass flux density is very small and constant versus overheat ratio, while the sensitivity to stagnation temperature shows a similar trend to the one of hot-wires except for an offset causing a shift in algebraic sign for high overheat ratios. Various modifications for modeling the wedge probe concerning heat balance, King s Law and sensitivities were proposed and their promising results compared. The sensitivities are intended to be used for modal analysis according to Kovásznay and Morkovin. REFERENCES 1. Sheplak M. Design, Validation and Testing of a Hot-Film Anemometer for Hypersonic Flow // Dissertation, Syracuse University, Sheplak M., Spina E.F., McGinley C.B. Characterization of a Hot-Film probe for Hypersonic Flow // AIAA Conference Paper, , Seiner J.M. The Wedge Hot-Film Anemometer in Supersonic Flow // Technical Paper 13, NASA, Langley Research Center Hampton, Virginia, Kovásznay L. Turbulence in Supersonic Flow // Journal of the Aeronautical Sciences, 0(10): , Morkovin M. Fluctuations and Hot-Wire Anemometry in Compressible Flow // AGARDograph,, Kosinov A.D., Semionov N.V., Yermolaev Yu.G. Disturbances in Test Section of T-35 Supersonic Wind Tunnel // Preprint No. 6-99, Dantec Dynamics. Probes for Hot-wire Anemometry // Nova Instruments, Publication No.: 38-v6. 8. Kosinov A.D., Yermolaev Yu.G. Calibration- and comparative measurements of hot-wire and hot-film probes for noise level detection in supersonic flow // Interim report on cooperative agreement with Institute for Aerodynamics and Gasdynamics (IAG), Kovásznay L. The Hot-Wire Anemometer in Supersonic Flow // Journal of the Aeronautical Sciences, 17: , White F.M. Viscous Fluid Flow // McGraw-Hill Book Company, New York, nd edition, Lenz B. Experimental Investigation of Fluctuations in Supersonic Boundary Layers via Hot-Wire Anemometry // dissertation, University of Stuttgart, Horstman C.C., Rose W.C. Hot-Wire Anemometry in Transonic Flow // NASA Technical Memorandum, TM X 6,95, Ames Research Center,