!calculating Aerodynamic Heating on Sounding Rocket Tangent Ogive Noses

A method is presented for calculating the aerodynamic heating and shear stresses at the wall for tangent ogive' noses that are slender enough to maintain an attached nose shock through that. portion of flight duringwhich heat transfer from' the botundary layer to the wall is significant. The lower entropy of the attached nose shock combined with the inclusion of the streamwise pressure gradient yields a reasonable estimate of the actual flow conditions. Both laminar and turbulent boundary layers are examined and an approximation of the effects of (up to) moderate angles-of-attack' is included in the analysis. The analytical method has been programmed in Fortran IV for an IBM 360/91 computer. Symbols Cf = friction coefficient local (-) Cp = specific heat of air (Btu/lbm °K) Idv/dx)(o0 = Newtonian velocity gradient at the stagnanation point on a circular nose (sec') (see Eq. 19) f') = velocity gradient parameter from Reference (6-) (see,Eqs. 27 and 28) = acelIeration of g;rnvityh (22. 174 ft/e2 ) 2 h = enthalpy (Btu/lbm) h* .= reference enthalpy (Btu/lbm)'H( ) = defined by Equation (18) (0)'. : Hx) = defined by Equation (17) ' k = coefficient of ther'mal conductivity (Btu/ft sec °K) . N = a constant; set = 0 for one-dimensional flow; set = 1 for axisymmetric flow (= 1 throughout this program) Nu,: = Nusselt Number (-) P (I) = pressure at stations 1. through 15 (atmospheres, except where otherwise noted) p = Prandtl Number (-) PXPO(I) = the local to stagnation point pressure ratio at each of the 15 station locations (-) | = heat transfer rate (Btu/ft2 see) QRATL = ratio of heat transfer with cross flow to tha' without cross flow for a laminar boundary layer' (see Eq. 29) (-) N]i iAE;RCDJY NAVILtC HATlN'11i UN N73-2601 3 Unclas /n1 172149 U tock spa et Division :e Flight Center QRATT = ratio of heat transfer,with cross flow to that without cross flow for a turbulent boundary layer (see Eq. 30) (-) R = tangent ogive radius of curvature '(see Figures 1 and 2) (ft) Re or R.: = local Reynolds number (Eq. 25) (-) -R = local momentum thickness Reynolds number .(9) (Eq. 26) (-) ' . N = spherical nose radius (for calculations of blunt bodylstagnation point heat transfer rate) (ft) r(I)or r(X) = the flow deflection distance defined by Eq. (11) and shown in Figures 1 and 2 (ft) V = velocity (ft/sec) X = tangent ogive longitudinal dimension (shown X (I) = surface coordinate distance along streamI line from nose tip to each station (ft) y = tangent ogive base radius, shown in Figures ~ 1 and 2 (ft) a = ALPHA = the vehicle angle-of-attack(deg. -or rad.) S or = the flow deflcet.inn inglQ (oonioal flow) at which the nose shock becomes detached for , '-a given free stream Mach number (deg. or 0 '= the local surface deflection angle; also, the central angle turned by the tangent ogive radius, R, to define the complete ogive (see i Figures 1 and 2):' (deg. or rad.) ! I 8 = cone half-angle (deg. or rad.) | -= viscosity coefficient-(lbf sec/ft2 ) p = density of air (Ibm see 2 /ft 4 = slugs/ft3 ) T = boundary layer shear stress at the wall (lbf/ft 2 ) L (I) = angle defined by Eq. (10) and shown in Figure 2 (deg. or rad.) Subscripts r I· e = local, external-to-the-boundary layer value Lam = considers a laminar boundary layer rec = evaluated at recovery conditions L----. -a I7 i IIN A 1 T T AS A7flt t-; l. I k_ -1 I I https://ntrs.nasa.gov/search.jsp?R=19730017274 2017-09-12T18:36:00+00:00Z ref = evaluated at reference conditions (see superscript) Tu rb = considers a turbulent boundary layer x = at a position X feet from nose tip along a surface streamline (same as e) w = evaluated at local pressure and wall temperature o = at stagnation point for a spherical nose of Radius, R N co = free streanim(ahead of nose shock) value Superscript * ='property evaluated at local reference enthalpy Introduction pressure and The generally favorable aerodynamic characteristics of the tangent ogive in supersonic and hypersonic flow result in the common use of this configuration for sounding rocket noses. Accordingly, an analytical method for calculating the aerodynamic heating on such configurations has been devised, combining basic analytical methods which are well known with some which are less common and with certain basic assumptions. These methods, while approximate in nature, yield results which have proved to be adequate for the design of both the structure of the rocket nose and the protection of payload items within. The entire analysis described here has been programmed in Fortran IV for an IBM 360/91 system I(Reference 1). The slenderness of the ogives of interest results in lan attached nose shock wave through periods of superIsonic and hypersonic flight during which significant aero!dynamic heating is experienced. The low entropy-jump across the oblique shock wave as opposed to the entropyjump across the normal shock wave associated with "blunt bodies" results in an increase of heat transfer to the ogive for a constant flight condition. This is similar to the case of the ~ cone heating as compared to that on a blunt,-axisymmetric body. However, unlike the cone case, the ogive body has a definite (first order) pressure gradient along the surface streamlines. A blunt body. analysis is treated in Reference (2) and a conical body analysis in Reference (3). 'The present analysis considers the in-between (tangent ogive) case in which the:' nose shock is oblique but there is a body pressure gradI ient. The effects of moderate angle-of-attack (local body| angle plus angle-of-attack of 30 to 35 degrees) are approximated. , Theory ',I The theory is derived from a combination of the analytical methods of References (2) and (3) with several new approximations and assumptions. The pertinent geometry along with the most important items of nomenclature are shown in Figures 1 and 2. The tangent ogive and flow geometry are completely defined by the parameters xmax Ymax anda (identified in Figure 1) in conjunretion with the geometric quations (7 throug 2). The !is , f 9 10 1.12 13' 14 15-STA. NUMBERS .,1 . Qs33zAi1 . YL-A Figure . Geometry of Tangent Ogive Nose Figure 1. Geometry of Tangent Ogive Nose effects of (up to) moderate angles-of-attack are accounted Ifor by assuming the local flow to -be similar to that on a cone of half-angle (equal to the ogive local surface angle) jat angle-of-attack. The applicable free st-ream conditions !are derived either from the vehicle altitude and an appropriate ARDC atmosphere or by electing-to define the |re-nose shock air properties by specifying two thermodynamic variables the pressure and the temperature Ithen obtaining all the other properties from the real gas (equilibrium) Mollier approximations of Hansen (Reference 4). For simplicity, a fixed number of body locations are specified for each problem. Either of two procedures can be adopted for defining the local flow conditions at these specified 15 body points. In the first case, the local pres sures at the calculation points are defined by Newtonian approximations or from experiment (if available). The entropy behind the attached nose shock (assumed to be conical) is then calculated and the local, external-toboundary layer properties are defined by isentropically expanding to the given local pressures. This assumes that