Skin-friction measurements in high-enthalpy hypersonic boundary layers

Abstract

Skin-friction measurements are reported for high-enthalpy and high-Mach-number laminar, transitional and turbulent boundary layers. The measurements were performed in a free-piston shock tunnel with air-flow Mach number, stagnation enthalpy and Reynolds numbers in the ranges of 4.4–6.7, 3–13 MJ kg$^{-1}$ and $0.16\times 10^{6}$–$21\times 10^{6}$, respectively. Wall temperatures were near 300 K and this resulted in ratios of wall enthalpy to flow-stagnation enthalpy in the range of 0.1–0.02. The experiments were performed using rectangular ducts. The measurements were accomplished using a new skin-friction gauge that was developed for impulse facility testing. The gauge was an acceleration compensated piezoelectric transducer and had a lowest natural frequency near 40 kHz. Turbulent skin-friction levels were measured to within a typical uncertainty of ± 7%. The systematic uncertainty in measured skin-friction coefficient was high for the tested laminar conditions; however, to within experimental uncertainty, the skin-friction and heat-transfer measurements were in agreement with the laminar theory of van Driest (1952). For predicting turbulent skin-friction coefficient, it was established that, for the range of Mach numbers and Reynolds numbers of the experiments, with cold walls and boundary layers approaching the turbulent equilibrium state, the Spalding & Chi (1964) method was the most suitable of the theories tested. It was also established that if the heat transfer rate to the wall is to be predicted, then the Spalding & Chi (1964) method should be used in conjunction with a Reynolds analogy factor near unity. If more accurate results are required, then an experimentally observed relationship between the Reynolds analogy factor and the skin-friction coefficient may be applied.

Drag Reduction by Boundary-Layer Combustion: Effects of Flow Disturbances from Rectangular-to-Elliptical-Shape-Transition Inlets

“…For the present experiments, the wall temperature is very low in comparison with the adiabatic wall temperature, with T w ∕T aw ranging from 0.05 to 0.08. The finding that the theory of Spalding and Chi [51] outperforms the van Driest II theory [52] in the present experiments is thus unsurprising because it has been previously proven that the theory of Spalding and Chi [51] is more suited for flows over very cold walls (T w ∕T aw < 0.2) [54,55]. Despite this, the drag coefficients predicted by the theory of Spalding and Chi are still about 13-15% higher than the experimentally measured drag coefficients.…”

Thermal Management at Hypersonic Leading Edges

“…The heat flux of the boundary gas layer that impinges on the flat portion of the vehicle, ���� , can be evaluated by analyzing the simple case of a flat plate in a high enthalpy flow [99];…”

Skin-Friction Measurements and Flow Establishment Within a Long Duct at Superorbital Speeds

“…Although not strictly applicable to flows other than those over a constant-pressure flat plate, the Reynolds analogy factor is often presented for flows in scramjets [30] and ducts [29], to determine its applicability in combusting and noncombusting flows. Figure 12 shows the laminar Reynolds analogy factor for the present experiments, along with the theoretical flat-plate prediction [34] and CFD estimate.…”

“…During this comprehensive investigation, Goyne measured skin friction in laminar, transitional, and turbulent constant-pressure ducted flows [29], scramjet combustors [30], and within a combusting turbulent boundary layer [31]. The majority of Goyne's experiments provided simultaneous measurements of heat flux, pressure, and skin friction along one wall of a diverging rectangular duct.…”