Effect of bulk viscosity on a hypersonic boundary layer

Abstract

The bulk viscosity μb is generally set equal to zero (Stokes’ hypothesis). For certain gases, such as CO2, μb/μ exceeds 103, where μ is the shear viscosity. In this circumstance, the bulk viscosity may substantially alter a hypersonic boundary layer. A general, nonsimilar, laminar, boundary-layer formulation is provided in which the bulk viscosity terms are included as a correction. To obtain explicit results, flow over a flat plate is considered. In addition to the heat transfer, the transverse pressure gradient inside the boundary layer is not zero, whereas the skin friction is unaltered by the bulk viscosity. This analysis is relevant to aerogravity-assisted maneuvers in planetary atmospheres that largely consist of CO2.

Numerical estimates for the bulk viscosity of ideal gases

“…At 300 K, we find that our fit yields pτ v ≈ 0.72 kg/(m s) which is only about 5% higher than the value of pτ v used by Emanuel. 30 At 300 K, our estimates yield…”

“…II, → 0 near 257 K leading to the local maximum seen in Figure 6. We note that the magnitude of the slope of μ b of ethylene also becomes relatively small at 300 K. If we employ (30) to compute μ b for ethylene at temperatures slightly less than 300 K we find that ethylene also exhibits a non-monotone variation in μ b with T. We note that use of the data of Holmes and Stott 50 for ethylene also gives rise to a local maximum in μ b and μ b /μ. In each case the reason for the local maximum is the decrease in c v v and which overwhelms the increase in pτ v as T decreases.…”

“…Nevertheless, this extrapolated, but conservative, estimate suggests that μ b > 2200 μ at 300 K. The bulk viscosities for sulfur hexafluoride were computed using the data of Holmes and Stott 50 and the curve-fit provided by Breshears and Blair. 57 The latter authors concluded that their experimental data conformed to the Landau-Teller law and could be represented by (30) with…”

“…We assume that Shields' data for F 2 correspond to a pressure of 1 atm and obtain a result for pτ v which is approximately that plotted by Diebold, Santoro, and Goldsmith 55 in their Figure 3. In Figure 10 we have plotted the values of μ b /μ based on (32) and (30), but extended to 300 K along with values of μ b /μ based on Shields' data. Again, the newer data yield a lower value of μ b .…”

“…More recent computations based on (3) were given by Emanuel 30 who gave μ b ≈ 3000 μ for CO 2 at 303 K.…”