EXCEL Worksheet STAGPTCBL Page 1 04/17/2023 @ 20:34:44

Body Properties: Flow Properties: Gas Properties: Solution Properties:Geometry Sphere Minf 12.3597 Gamma 1.4 Etainf 6Rnose (ft) 0.020833 Pinf (lbf/ft²) 93.7255 Gas Con 1716 Delta Eta 0.005

Tinf (°R) 392.246 Thetav 5500 Conv Test 1.00E-10Twall (°R) 540 Pr 0.71 Max Iter 30

Solution: Converged Wall Type Temp Suther 2.27E-08 Print Eta 0.1Iterations: 22 RhoVbar 0 Tconstant 198.6

Axisymmetric Spherical Stagnation Point Profiles:Eta Y (ft) u/Uedge H/Hedge T/Tedge Gamma

0 0 0 0.0436373 0.0530336 1.3993748 Stagnation Conditions:0.1 3.646E-07 0.0235212 0.0597228 0.0725011 1.3948978 P0' (psf) T0' (°R) H0' (Btu/lbm)0.2 8.465E-07 0.0488697 0.0771441 0.0932924 1.38415 18802.76 10182.22 2968.8590.3 1.453E-06 0.0760114 0.0959163 0.1151529 1.36958470.4 2.188E-06 0.1048545 0.1160199 0.1378856 1.3548885 Qdot (Btu/ft²-sec)0.5 3.059E-06 0.135279 0.1374205 0.1613989 1.3420503 EVBSPBLC Fay-Riddell (Sphere)0.6 4.069E-06 0.1671526 0.1600781 0.18567 1.3315472 -2595.185 -2617.7450.7 5.222E-06 0.2003359 0.1839503 0.2107046 1.32318010.8 6.522E-06 0.234683 0.2089919 0.2365127 1.3165666 Profile Integral Parameters:0.9 7.976E-06 0.2700412 0.2351533 0.2630969 1.3113331 Delta* (ft) Theta (ft) Delta*/Theta

1 9.586E-06 0.3062493 0.2623785 0.2904477 1.30717 -8.93E-06 3.14E-05 -0.2845181.1 1.136E-05 0.3431365 0.2906032 0.3185408 1.30383511.2 1.33E-05 0.3805219 0.3197528 0.3473358 1.3011435 Reinf(Rnose) Stinf(H0'-Hwall)1.3 1.54E-05 0.4182147 0.3497406 0.376776 1.2989548 116613.9 0.0170041.4 1.768E-05 0.4560141 0.3804669 0.4067876 1.2971622 Stinf * Sqrt( Reinf / C* )1.5 2.014E-05 0.4937111 0.4118172 0.4372798 1.2956842 0.6769471.6 2.277E-05 0.5310901 0.4436627 0.4681449 1.2944581.7 2.559E-05 0.5679319 0.4758596 0.499259 1.29343511.8 2.858E-05 0.6040165 0.50825 0.5304829 1.29257731.9 3.176E-05 0.6391278 0.5406638 0.5616644 1.2918546

2 3.512E-05 0.6730572 0.5729202 0.5926397 1.29124332.1 3.866E-05 0.7056091 0.6048311 0.6232375 1.29072422.2 4.237E-05 0.7366053 0.6362047 0.6532816 1.29028212.3 4.626E-05 0.76589 0.6668495 0.6825959 1.28990462.4 5.032E-05 0.7933338 0.6965794 0.7110083 1.28958142.5 5.453E-05 0.8188371 0.7252178 0.7383558 1.28930422.6 5.891E-05 0.8423328 0.7526032 0.7644886 1.28906612.7 6.343E-05 0.8637878 0.7785929 0.7892749 1.28886152.8 6.809E-05 0.8832022 0.8030674 0.8126042 1.28868542.9 7.289E-05 0.9006089 0.8259329 0.8343903 1.288534

3 7.78E-05 0.9160703 0.8471238 0.8545731 1.28840383.1 8.283E-05 0.9296748 0.8666029 0.8731196 1.2882919

EVBSPBLC --- EXCEL VISUAL BASIC STAGNATION POINTBOUNDARY LAYER CALCULATOR

Hypersonic Cold Wall (Fig. 8-3, 12,000 ft/sec @ 70,000 ft, Hayes & Probstein Hypersonic Flow Theory, 1959)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.10

1

2

3

4

5

6

7

Velocity Profile

u / Uedge

Eta

EXCEL Worksheet STAGPTCBL Page 2 04/17/2023 @ 20:34:45

Axisymmetric Spherical Stagnation Point Profiles:Eta Y (ft) u/Uedge H/Hedge T/Tedge Gamma3.2 8.796E-05 0.9415326 0.8843618 0.8900235 1.28819583.3 9.319E-05 0.9517703 0.900419 0.9053039 1.28811353.4 9.849E-05 0.9605261 0.9148176 0.9190033 1.28804323.5 0.0001039 0.9679442 0.9276228 0.9311844 1.28798323.6 0.0001093 0.9741706 0.9389172 0.9419268 1.28793223.7 0.0001148 0.9793486 0.9487979 0.9513234 1.2878893.8 0.0001204 0.9836157 0.9573718 0.9594763 1.28785253.9 0.000126 0.9871006 0.9647521 0.9664935 1.2878218

4 0.0001316 0.9899217 0.9710543 0.9724853 1.28779614.1 0.0001373 0.9921855 0.9763937 0.9775613 1.28777474.2 0.000143 0.9939866 0.980882 0.9818281 1.2877574.3 0.0001487 0.9954077 0.984626 0.9853871 1.28774244.4 0.0001545 0.9965196 0.9877251 0.988333 1.28773044.5 0.0001603 0.9973826 0.9902712 0.9907531 1.28772064.6 0.000166 0.9980471 0.9923472 0.9927263 1.28771274.7 0.0001718 0.9985546 0.9940273 0.9943233 1.28770644.8 0.0001776 0.9989393 0.9953771 0.9956062 1.28770134.9 0.0001834 0.9992286 0.9964535 0.9966292 1.2876972

5 0.0001892 0.9994445 0.9973056 0.9974392 1.2876945.1 0.000195 0.9996044 0.9979754 0.9980757 1.28769155.2 0.0002008 0.9997219 0.9984979 0.9985724 1.28768965.3 0.0002066 0.9998076 0.9989028 0.9989571 1.28768815.4 0.0002124 0.9998695 0.9992141 0.9992531 1.28768695.5 0.0002183 0.9999138 0.9994519 0.999479 1.2876865.6 0.0002241 0.9999453 0.9996321 0.9996504 1.28768535.7 0.0002299 0.9999674 0.9997678 0.9997793 1.28768485.8 0.0002357 0.9999827 0.9998693 0.9998757 1.28768455.9 0.0002415 0.9999931 0.9999445 0.9999473 1.2876842

6 0.0002473 1 1 1 1.287684

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.10

1

2

3

4

5

6

7

Velocity Profile

u / Uedge

Eta

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.10

1

2

3

4

5

6

7Temperature Profile

T / Tedge

Eta

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

0

1

2

3

4

5

6

7Total Enthalpy Profile

H / Hedge

Eta

1.25 1.3 1.35 1.4 1.45

0

1

2

3

4

5

6

7Ratio of Specific Heats

Gamma

Eta

NOMENCLATURE

DefinitionBody Properties:Geometry Geometry Type

For Two-Dimensional Cylindrical Enter: CylinderFor Axisymmetric Spherical Enter: Sphere

Rnose (ft) Cylinder or Sphere Nose Radius

Flow Properties:Minf Free-Stream Mach NumberPinf (lbf/ft²) Free-Stream Static PressureTinf (°R) Free-Stream Static TemperatureTwall (°R) Wall Temperature

For Adiabatic Wall: Twall Will Be Automatically CalculatedWall Type Prescribed Wall Temperature or Adiabatic Wall

For Prescribed Wall Temperature Enter: TempFor Adiabatic Wall Enter: Adi

RhoVbar Wall Mass Transfer Parameter: RhowallVwall / RhoinfVinfFor Wall Mass Addition/Blowing/Injection Enter: (+) RhoVbarFor Wall Mass Removal/Suction Enter: (-) RhoVbar

Gas Properties:Gamma Ratio of Specific Heats (Cp / Cv)Gas Con Specific Gas ConstantThetav Characteristic Vibrational Temperature

For Perfect Gas Solution, Enter Thetav = 0.0Pr Prandtl NumberSuther Sutherland Viscosity Law ConstantTconstant Sutherland Viscosity Law Reference Temperature

Solution Properties:Etainf Maximum Eta Value ( 0 <= Eta <= Etainf)Delta Eta Eta Grid Increment in SolutionConv Test Solution Convergence TestMax Iter Maximum Number of Allowed Solution IterationsPrint Eta Eta Grid Increment in Profile Printout

Stagnation Conditons:P0' Stagnation Point Total PressureT0' Stagnation Point Total TemperatureH0' Stagnation Point Total Enthalpy

Qdot: Stagnation Point Heat Transfer

EVBSPBLC Computed From EVBSPBLC Boundary-Layer Profile SolutionFay-Riddell Computed From Fay-Riddell Correlation for a Sphere or Cylinder

Profile Integral Parameters:Delta* Boundary-Layer Displacement ThicknessTheta Boundary-Layer Momentum ThicknessDelta*/Theta Boundary-Layer Shape Factor (Delta* / Theta)

Reinf(Rnose) Free-Stream Reynolds Number Based on Nose RadiusReinf = Rhoinf * Vinf * Rnose / Muinf

Stinf(H0'-Hwall) Free-Stream Stanton Number Based on ( H0' - Hwall )Stinf = -Qdot / [Rhoinf * Vinf * ( H0' - Hwall )]

Correlation Parameter Stinf * Sqrt( Reinf / C* )C* = ((Rhoe * Mue) ^ 0.8) * ((Rhowall * Muwall) ^ 0.2) / (Rhoinf * Muinf)Rhoe = Rho( P0', T0' )Mue = Mu( T0' )Rhowall = Rho( P0', Twall )Muwall = Mu( Twall )Rhoinf = Rho( Pinf, Tinf )Muinf = Mu( Tinf )

Applicable Values:Units Air Nitrogen

Not Applicable

ft

Nondimensionallbf / ft² or psf°R°R

Not Applicable

Nondimensional

Nondimensional 1.4 1.4ft² / sec² - °R 1716 1774°R 5500 6102

Nondimensional 0.71 0.71lbf - sec / ft² - °R^0.5 2.27E-08 2.18E-08°R 198.6 192

NondimensionalNondimensionalNot ApplicableNot ApplicableNondimensional

lbf / ft² or psf°RBtu / lbm

Btu / ft² - sec

Btu / ft² - secBtu / ft² - sec

ftftNondimensional

Nondimensional

Nondimensional

Nondimensional

EXAMPLE INPUT

Body Properties: Flow Properties: Gas Properties: Solution Properties:

Geometry Sphere Minf 12.3597 Gamma 1.4 EtainfRnose (ft) 0.020833 Pinf (lbf/ft²) 93.7255 Gas Con 1716 Delta Eta

Tinf (°R) 392.246 Thetav 5500 Conv TestTwall (°R) 540 Pr 0.71 Max IterWall Type Temp Suther 2.27E-08 Print EtaRhoVbar 0 Tconstant 198.6

Cylinder With Prescribed Hot Wall Under Subsonic Flow Conditions (Note Overshoot in Velocity Profile)Geometry Cylinder Minf 0.25 Gamma 1.4 EtainfRnose (ft) 0.5 Pinf (lbf/ft²) 2200 Gas Con 1716 Delta Eta

Tinf (°R) 550 Thetav 0 Conv TestTwall (°R) 900 Pr 0.71 Max IterWall Type Temp Suther 2.27E-08 Print EtaRhoVbar 0 Tconstant 198.6

Cylinder With Adiabatic Wall (DO NOT INPUT Twall for Adiabatic Wall Cases)Geometry Cylinder Minf 3 Gamma 1.4 EtainfRnose (ft) 0.5 Pinf (lbf/ft²) 1000 Gas Con 1716 Delta Eta

Tinf (°R) 400 Thetav 0 Conv TestTwall (°R) Pr 0.71 Max IterWall Type Adi Suther 2.27E-08 Print EtaRhoVbar 0 Tconstant 198.6

Sphere With Massive Wall Injection @ Prescribed Wall Temp (Note Boundary Layer Effectively Blown Off)Geometry Sphere Minf 3 Gamma 1.4 EtainfRnose (ft) 0.1 Pinf (lbf/ft²) 1000 Gas Con 1716 Delta Eta

Tinf (°R) 400 Thetav 0 Conv TestTwall (°R) 540 Pr 0.71 Max IterWall Type Temp Suther 2.27E-08 Print EtaRhoVbar 0.01 Tconstant 198.6

Cylinder With Wall Suction Under Subsonic Flow Conditions and Adiabatic WallGeometry Cylinder Minf 0.25 Gamma 1.4 EtainfRnose (ft) 0.5 Pinf (lbf/ft²) 2000 Gas Con 1716 Delta Eta

Tinf (°R) 540 Thetav 0 Conv TestTwall (°R) Pr 0.71 Max IterWall Type Adi Suther 2.27E-08 Print EtaRhoVbar -0.001 Tconstant 198.6

Hypersonic Cold Wall (Fig. 8-3, 12,000 ft/sec @ 70,000 ft, Hayes & Probstein Hypersonic Flow Theory, 1959)

Reference Sphere (1 ft Radius) in Nitrogen @ Minf = 13.5 & Reinf/ft = 1.37E+06Geometry Sphere Minf 13.5 Gamma 1.4 EtainfRnose (ft) 1 Pinf (lbf/ft²) 2.4768 Gas Con 1774 Delta Eta

Tinf (°R) 91.2 Thetav 6102 Conv TestTwall (°R) 540 Pr 0.71 Max IterWall Type Temp Suther 2.18E-08 Print EtaRhoVbar 0 Tconstant 192

Solution Properties:

60.005

1.00E-1030

0.1

50.005

1.00E-1030

0.1

40.005

1.00E-1030

0.1

Sphere With Massive Wall Injection @ Prescribed Wall Temp (Note Boundary Layer Effectively Blown Off)15

0.11.00E-10

300.1

30.005

1.00E-1030

0.05

Hypersonic Flow Theory, 1959)

60.005

1.00E-1030

0.1