# AVBP variable_gamma modeling¶

Get additional variables from AVBP conservative variables. The species_database.dat file is needed. The formulas are set for 3D solutions.

antares.eqmanager.formula.avbp.equations.Cp(DictMassFractions, T)

Mass Heat capacity of the mixture at constant pressure [J/K/kg].

$$C_p(T) = \sum_{k=1}^N Y_k C_{p,k}(T)$$

Computed with static temperature and AVBP’s species_database.dat.

antares.eqmanager.formula.avbp.equations.Cv(DictMassFractions, T)

Mass Heat capacity of the mixture at constant volume [J/K/kg].

$$C_v(T) = \sum_{k=1}^N Y_k C_{v,k}(T)$$

Computed with static temperature and AVBP’s species_database.dat.

antares.eqmanager.formula.avbp.equations.DictMassFractions(rho)

Get the dictionary of the species.

This dictionary is involved in the mixture and their mass fractions.

DictMassFractions is a specific keyword that might be called in functions’ arguments. It retrieves the following dictionary: $$DictMassFractions = \{'k': [Y_k], ...\}_{k \in \{Specie1, ...\}}$$ where SpecieX are the species involved in the mixture.

antares.eqmanager.formula.avbp.equations.Ec(u, v, w)

Mass mixture kinetic energy [J/kg].

$$E_c = \frac{1}{2}(u^2 + v^2 + w^2)$$

antares.eqmanager.formula.avbp.equations.Eint(Etotal, Ec)

Mass internal energy [J/kg].

$$E_{int} = E_{total} - E_c$$

antares.eqmanager.formula.avbp.equations.Etotal(rhoE, rho)

Mass mixture total energy [J/kg].

$$E_{total} = \rho E_{total}/\rho$$

antares.eqmanager.formula.avbp.equations.Htotal(hs, Ec)

Mixture total mass enthalpy [J/kg].

$$H_{total}=\sum_{k=1}^N Y_k h_{s,k}+e_c$$

antares.eqmanager.formula.avbp.equations.Htr(hs, W)

Relative total enthalpy (non-chemical).

antares.eqmanager.formula.avbp.equations.Mis(Ptris, P, gamma)

Isentropic mach number [-].

Need a reference total isentropic pressure $$P_{tris}$$.

$$M_{is}=\sqrt{2\frac{(P_{tris}/P)^{\frac{\gamma-1}{\gamma}}-1}{\gamma-1}}$$

antares.eqmanager.formula.avbp.equations.P(rho, T, rgas)

Static pressure [Pa].

$$P = \rho r_{gas} T$$

antares.eqmanager.formula.avbp.equations.P_KURT(P, P2, P3, P4)

Pressure kurtosis [Pa^4].

Requires an averaged AVBP solution with high stat.

antares.eqmanager.formula.avbp.equations.P_RMS(P, P2)

Pressure root mean square [Pa].

Requires an averaged AVBP solution.

antares.eqmanager.formula.avbp.equations.P_SKEW(P, P2, P3)

Pressure skewness [Pa^3].

Requires an averaged AVBP solution with high stat.

antares.eqmanager.formula.avbp.equations.Ptotal(DictMassFractions, rgas, P, T, Ttotal)

Absolute total pressure [Pa].

$$P_{total}=P_s\exp(\int^{T_{total}}_{T_s}\frac{C_p}{rT}dT)$$

antares.eqmanager.formula.avbp.equations.Ptotal_RMS(Ptotal, Ptotal2)

Total pressure root mean square [Pa].

Requires an averaged AVBP solution.

antares.eqmanager.formula.avbp.equations.Ptotal_gamma0D(P, coeff_gamma0D, exp_gamma0D)

Useful when computing under $$\gamma$$ constant assumption.

$$Ptotal_{\gamma_{0D}} = P (1 + \frac{\gamma_{0D} - 1}{2} M_{\gamma_{0D}}^2)^{\frac{\gamma_{0D}}{\gamma_{0D} - 1}}$$

antares.eqmanager.formula.avbp.equations.Ptr(DictMassFractions, rgas, P, T, Ttr)

Relative total pressure.

antares.eqmanager.formula.avbp.equations.R(z, y)

Compute the radius under the assumption x is the rotation-axis.

antares.eqmanager.formula.avbp.equations.T(DictMassFractions, Eint)

Static temperature [K].

Computed from the internal energy and the AVBP’s species_database.dat.

antares.eqmanager.formula.avbp.equations.T_KURT(T, T2, T3, T4)

Static temperature kurtosis [K^4].

Requires an averaged AVBP solution with high stats.

antares.eqmanager.formula.avbp.equations.T_RMS(T, T2)

Static temperature root mean square [K].

Requires an averaged AVBP solution.

antares.eqmanager.formula.avbp.equations.T_SKEW(T, T2, T3)

Static temperature skewness [K^3].

Requires an averaged AVBP solution with high stats.

antares.eqmanager.formula.avbp.equations.Theta(y, z)

Compute the cylindrical angle under the assumption x is the rotation-axis.

antares.eqmanager.formula.avbp.equations.Ttotal(DictMassFractions, Htotal)

Absolute total temperature [K].

Computed with the absolut total enthalpy and the AVBP’s species_database.dat.

antares.eqmanager.formula.avbp.equations.Ttotal_RMS(Ttotal, Ttotal2)

Total temperature root mean square [K].

Requires an averaged AVBP solution.

antares.eqmanager.formula.avbp.equations.Ttotal_gamma0D(T, coeff_gamma0D)

Useful when computing under $$\gamma$$ constant assumption.

$$Ttotal_{\gamma_{0D}} = T (1 + \frac{\gamma_{0D} - 1}{2} M_{\gamma_{0D}}^2)$$

antares.eqmanager.formula.avbp.equations.Ttr(DictMassFractions, Htr)

Relative total temperature.

antares.eqmanager.formula.avbp.equations.V(u, v, w)
antares.eqmanager.formula.avbp.equations.Vm(Wm)
antares.eqmanager.formula.avbp.equations.Vr(R, y, z, v, w)
antares.eqmanager.formula.avbp.equations.Vt(R, y, z, v, w)
antares.eqmanager.formula.avbp.equations.W(Wx, Wr, Wt)
antares.eqmanager.formula.avbp.equations.Wm(Wx, Wr)
antares.eqmanager.formula.avbp.equations.Wr(Vr)
antares.eqmanager.formula.avbp.equations.Wt(omega, R, Vt)
antares.eqmanager.formula.avbp.equations.Wx(u)
antares.eqmanager.formula.avbp.equations.Wy(Wt, Vr, Theta)
antares.eqmanager.formula.avbp.equations.Wz(Wt, Vr, Theta)
antares.eqmanager.formula.avbp.equations.alpha(Vt, Vm)

Sign is consistent with AVBP’s angle_alpha.

antares.eqmanager.formula.avbp.equations.beta(Wt, Vm)

Relative flow angle in degrees.

The sign is consistent with alpha, so it is the opposite of the convention used in elsA computations.

antares.eqmanager.formula.avbp.equations.c(P, rho, gamma)

Sound speed [m/s].

$$c = \sqrt{\gamma P / \rho}$$

antares.eqmanager.formula.avbp.equations.c_gamma0D(P, rho, gamma0D)

Useful when computing under $$\gamma$$ constant assumption.

$$c = \sqrt{\gamma_{0D} P / \rho}$$

antares.eqmanager.formula.avbp.equations.coeff_gamma0D(gamma0D, mach_gamma0D)

Useful when computing under $$\gamma$$ constant assumption.

$$coeff\_gamma0D = 1 + \frac{\gamma_{0D} - 1}{2} M^2$$

antares.eqmanager.formula.avbp.equations.exp_gamma0D(gamma0D)

Useful when computing under $$\gamma$$ constant assumption.

$$exp\_gamma0D = \frac{\gamma_{0D}}{\gamma_{0D} - 1}$$

antares.eqmanager.formula.avbp.equations.gamma(Cp, Cv)

Heat capacity ratio [-].

$$\gamma(T) = \frac{C_p(T)}{C_v(T)}$$

antares.eqmanager.formula.avbp.equations.h(DictMassFractions, T)

Mixture enthalpy [J/kg].

Sum of formation and sensible enthalpies $$h = \sum_{k=1}^N Y_k (h_{s,k} + \Delta h^{0}_{f,k})$$

antares.eqmanager.formula.avbp.equations.hs(Eint, P, rho)

Mass sensible enthalpy [J/kg].

$$h_s = E_{int} + P/\rho$$

antares.eqmanager.formula.avbp.equations.mach(V, c)

Absolute mach number.

antares.eqmanager.formula.avbp.equations.mach_gamma0D(V, c_gamma0D)

Useful when computing under $$\gamma$$ constant assumption.

antares.eqmanager.formula.avbp.equations.mach_rel(W, c)

Relative mach number.

antares.eqmanager.formula.avbp.equations.mixture_W(DictMassFractions)

Mean molecular weight of the mixture W [kg].

$$W ={ (\sum_{k=1}^N \frac{Y_k}{W_k}) }^{-1}$$ with $$Y_k$$ and $$W_k$$ respectively mass fraction and molecular weight of specie $$k$$. Computed with AVBP’s species_database.dat.

antares.eqmanager.formula.avbp.equations.mixture_sensible_enthalpy(DictMassFractions, T)

Mixture mass sensible enthalpy [J/kg].

$$h_s = \sum_{k=1}^N Y_k h_{s,k}$$

NOTE: Equal to $$h_s$$ but computed with species_database.dat

antares.eqmanager.formula.avbp.equations.phi(u, Vr)

Meridional flow angle in degrees.

antares.eqmanager.formula.avbp.equations.rgas(mixture_W)

Mixture specific gas constant [J/kg/K].

$$r_{gas} = R/W$$

with, respectively $$R$$ and $$W$$ associated to the perfect gas constant and the mean mixture molecular weight.

antares.eqmanager.formula.avbp.equations.s(DictMassFractions, T)

Mass mixture entropy [J/kg].

$$s = \sum_{k=1}^N Y_k s_k$$

antares.eqmanager.formula.avbp.equations.u(rhou, rho)
antares.eqmanager.formula.avbp.equations.v(rhov, rho)
antares.eqmanager.formula.avbp.equations.w(rhow, rho)