Hypersonic Viscous Drag Effects on Blunt Slender Cones

Whitfield, Jack D.; Griffith, B. J.

doi:10.2514/6.1963-434

Cited by 2 publications

(3 citation statements)

References 5 publications

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“…[1][2][3]. The large viscousinduced drag increment at zero-lift observed in these studies encouraged Whitfield and Griffith (Ref.…”

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confidence: 69%

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Mass Transfer and First-Order Boundary -Layer Effects on Sharp Cone Drag

Lewis¹,

Marchand²,

Little³

1966

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A theoretical model is developed based on an iterated perfect gas inviscid-viscous flow field which includes first-order displacement {viscous interaction), transverse curvature, wall slip, and temperature jump in addition to mass transfer effects. The effects of inviscid (tangent cone) and viscous (nonsimilar laminar boundary layer) flow field matching conditions are also considered. Numerical results are compared with experimental and analytical results of King and Talbot (AI A A J., 1964) for a 5-deg half-angle cone at M" -3. 93 and 5. 64, The predicted viscous-induced pressure without mass transfer and the zero-lift drag with and without injection were in agreement with the experimental data within experimental uncertainty. The theoretical model was also used to predict zero-lift drag of a 9-deg half-angle cone at M^ = 9. 37 and 10 and Re M /in. -400 to 45, 000 for a range of wallto-stagnation temperature ratios. Again, in general, without mass transfer the predictions were within experimental uncertainty. The inability of the theoretical model to adequately treat nonuniform mass transfer distributions is discussed. At the lowest Reynolds number the effects of slip were most significant. At all conditions the effects of inviscid-viscous flow field matching were significant. Experimental zero injection equilibrium wall temperature distributions and cool-wall pressure data are given at M,,,, -10 and Re M /in. = 400 to 2600.in

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“…[1][2][3]. The large viscousinduced drag increment at zero-lift observed in these studies encouraged Whitfield and Griffith (Ref.…”

mentioning

confidence: 69%

“…Therefore for more direct comparison with King and Talbot, v e /u e = dSVdx (1)(2)(3) was used in most of the calculations. The inviscid flow field was computed from the approximate tangent cone theory.…”

Section: Aedc-tr-66-37mentioning

confidence: 99%

Mass Transfer and First-Order Boundary -Layer Effects on Sharp Cone Drag

Lewis¹,

Marchand²,

Little³

1966

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“…The axial force may be related to the drag coefficient by using the body axes as a reference : CA = CD cosa -CL sina (5) and for small a, CA = CD. Consideration must also be given to skin-friction drag; in general, the average skin friction in a laminar boundary layer maybe expressed as C F = CiRe L~1 12 .…”

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confidence: 99%

Proof tests of the terminal parachute-recovery system for the Biosatellite.

Cassanto

Eichel

Smrž

1968

Journal of Spacecraft and Rockets

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The total pressure drag obtained by integration along the body axial coordinate x is CD = CM^^/K*, or CD/M^P* = C/K* = /(M.0)The axial force may be related to the drag coefficient by using the body axes as a reference : CA = CD cosa -CL sina (5) and for small a, CA = CD. Consideration must also be given to skin-friction drag; in general, the average skin friction in a laminar boundary layer maybe expressed as C F = CiRe L~1 12 . The total drag at a 0 is then given byAt hypersonic speeds, interaction effects between the external flow and the boundary layer can strongly influence the boundary-layer development. A measure of this effect on the inviscid pressure and drag is 1^ M m */Re L 1/2 (7) X = Mn'Wy/n where C* = (MTOO/MOOT 7 *) is based on Eckert's reference temperature 6 and is near unity. Since values of the wall temperature corresponding to the test results are uncertain, we assume that (C*) 1/2 = 1. Therefore,To obtain a simple form for correlation purposes, it is postulated that this relationship can be modified by combining the first, third, and fourth parameters, so that plots of C A Re L 112 / M m n /3 3 vs Moo/3 may provide useful correlations. For finite values of /3, the parameter ft is replaced by sin/3. Correlation of Experimental ResultsTo establish the influence of M m , several exponents n were tried; n = 3 worked best. The results of the axial force correlation for short and long blunted elliptical cones are presented in Fig. 2. Data from three wind tunnels are correlated in "weak" (x < 1) and "strong" (% » 1, K*» 1) interaction regimes. The correlation for the long model with strong ' « Jo-O 1 TEST DATA FROM D >• VARIOUS FACILITIES A J REF 4 \O 36 > Moo > 14 X>4 M s,n 10 20 (.0 Fig. 4 Correlations for L/D and C N /C^ for long body, viscous interaction isThe correlations for CN, CD, and CL in Fig. 3 show that the test data fall into two groups, one for weak interaction with x < 6.5 and the other for strong interaction with x > 7. Most of the data for strong interaction can be represented by the relations C N = 6.761 (M m sin/5) 1 -205 Re L~L ' 2 (10) CD = 5.209 (M m sin/3) 1 -155 He L -^ (11) CL = 8.962 (M m sin/3) 0 -96 Re L -112The ratios L/D and C N /C A were correlated by means of the same parameters and are shown in Fig. 4. Concluding RemarksSignificant parameters for aerodynamic force coefficients for hypersonic regime with viscous interactions have been inferred from simple analysis and serve well to correlate experimental data for blunted elliptical cones. Since 1) 7 = 1.4 was assumed for all cases (but lower y's are typical for hypervelocity facilities), 2) no attempt was made to account for wall temperature T w (meager information) in the expression for x, and 3) there is greater uncertainty in the test flow conditions at high M m , it is not surprising that the results for very high Moo show a larger scatter than those for lower Moo's. Nomenclature

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Hypersonic Viscous Drag Effects on Blunt Slender Cones

Cited by 2 publications

References 5 publications

Mass Transfer and First-Order Boundary -Layer Effects on Sharp Cone Drag

Mass Transfer and First-Order Boundary -Layer Effects on Sharp Cone Drag

Proof tests of the terminal parachute-recovery system for the Biosatellite.

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