## File: tankex.fe

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evolver 2.70+ds-4
 `123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101` ``````// tankex.fe // Equilibrium shape of liquid in flat-ended cylindrical tank. // Tank has axis along y-axis and flat bottom in x-z plane. This // is so gravity acting vertically draws liquid toward wall. // Straight edges cannot conform exactly to curved walls. // We need to give them an area so that area cannot shrink by straght edges // pulling away from the walls. The gaps are also accounted for // in volume and gravitational energy. SYMMETRIC_CONTENT // for volume calculations // Contact angles, initially for 45 degrees. PARAMETER ENDT = 0.707 /* surface tension of uncovered base */ PARAMETER WALLT = 0.707 /* surface tension of uncovered side wall */ // Gravity components PARAMETER GY = 0 PARAMETER GZ = -1 SPRING_CONSTANT 1 // for most accurate gap areas for constraint 2 #define TR 1.00 /* tank radius */ #define RHO 1.00 /* fuel density */ constraint 1 // flat base function: y = 0 energy: // for contact energy line integral e1: -ENDT*z e2: 0 e3: 0 #define wstuff (WALLT*TR*y/(x^2 + z^2)) // common wall area term #define vstuff (TR^2/3*y/(x^2 + z^2)) // common wall volume term #define gstuff (GY*TR^2*y^2/4/(x^2 + z^2) + GZ*TR^3*y*z/3/(x^2+z^2)**1.5) // common gap gravity term constraint 2 CONVEX // cylindrical wall function: x^2 + z^2 = TR^2 energy: // for contact energy and gravity e1: -wstuff*z + RHO*GY*y^2*z/4 + RHO*GZ*y*z^2/3 - RHO*gstuff*z e2: 0 e3: wstuff*x - RHO*GY*y^2*x/4 - RHO*GZ*y*z*x/3 + RHO*gstuff*x content: // so volumes calculated correctly c1: vstuff*z - z*y/6 + vstuff*z/2 c2: 0 c3: -vstuff*x + x*y/6 - vstuff*x/2 // named quantity for arbitrary direction gravity on facets quantity arb_grav energy method facet_vector_integral global vector_integrand: q1: 0 q2: -RHO*GY*y^2/2 - RHO*GZ*y*z q3: 0 // Now the specification of the initial shape vertices 1 0.5 0.0 0.5 constraint 1 2 0.5 0.0 -0.5 constraint 1 3 -0.5 0.0 -0.5 constraint 1 4 -0.5 0.0 0.5 constraint 1 5 1.0 0.5 0.0 constraint 2 6 0.0 0.5 -1.0 constraint 2 7 -1.0 0.5 0.0 constraint 2 8 0.0 0.5 1.0 constraint 2 edges 1 2 1 constraint 1 2 1 4 constraint 1 3 4 3 constraint 1 4 3 2 constraint 1 5 5 6 constraint 2 6 6 7 constraint 2 7 7 8 constraint 2 8 8 5 constraint 2 9 1 8 10 1 5 11 2 5 12 2 6 13 3 6 14 3 7 15 4 7 16 4 8 faces 1 13 6 -14 2 3 14 -15 3 15 7 -16 4 2 16 -9 5 9 8 -10 6 1 10 -11 7 11 5 -12 8 4 12 -13 bodies 1 1 2 3 4 5 6 7 8 volume 0.6 density 0 /* no default gravity */ ``````