Beispiel #1
0
def OSP2P1th(P2P1, th, k=1.4):
    '''
    Gasdynamics Module
    Location: GasDynamics\\CPG\\ObliqueShock
    Function: OSMP2P1(M,P2P1,k=1.4)
    Variables:
        T - Temperature[K]
        P - Pressure [Pa]
        P0 - Stagnation Pressure [Pa]
        T0 - Stagnation Temperature [K]
        rho - Density [kg/m^3]
        R - Gas constant [J/(kgK)], default value 287 J/(kgK) for air
        k - ratio of specific heats gamma=Cp/Cv, default value k=1.4 for diatomic gases
        a - speed of sound [m/s]
        V - local magnitude of gas velocity [m/s]
        M - Mach number
        A - Area of cross section
        m - mass flow rate
        B - beta the shock angle for a given flow deflection angle theta
        th - theta the flow defelection angle
    Numbers:
        1 - upstream of the shock
        2 - downstream of the shock
    Abbreviations:
        PG - Perfect Gas
        CPG - Calorically Perfect Gas
        TPG - Thermally Perfect Gas
    Inputs: M,P2P1,k
    Outputs: [M,M2,P2/P1,T2/T1,rho2/rho1,P02/P01,dS/R,th,B]
    Explanantion: Calculates the downstream shock properties of an attached oblique shock given M and P2P1
    Usage:
        B=OSMP2P1(M,P2P1,k=1.4)
    ###
    ver 0
    August 2020
    ###
    Credits:
    Srisha Rao M V
    '''
    M1n = InvNSP2P1(P2P1, k)
    M1max = InvOSthmax(th, k)
    Bmax = OSBmax(M1max[0], k)
    M2n = NSM1M2(M1n, k)
    T2T1n = NST2T1(M1n, k)
    b = M2n / M1n * math.sqrt(T2T1n)
    B1 = secant(residual_OSP2P1th, [0.99 * Bmax, 0.80 * Bmax], th, b, k)
    M = M1n / math.sin(B1[0])
    M2 = M2n / math.sin(B1[0] - th)
    out = [
        M, M2,
        NSP2P1(M1n, k),
        NST2T1(M1n, k),
        NSrho2rho1(M1n, k),
        NSP02P01(M1n, k),
        NSdSbyR(M1n, k), th, B1[0]
    ]
    return out
Beispiel #2
0
def InvF1(f1, k=1.4):
    '''
    Gasdynamics Module
    Location: GasDynamics\\CPG\\Isentropic
    Function: InvF1(f1,k)
    Variables:
        T - Temperature [K]
        R - Gas constant [J/(kgK)], default value 287 J/(kgK) for air
        k - ratio of specific heats gamma=Cp/Cv, default value k=1.4 for diatomic gases
        a - speed of sound [m/s]
        V - local magnitude of gas velocity [m/s]
        M - Mach number
        F1 - M*(1+(k-1)/2*M^2)^(-(k+1)/(2*(k-1)))
    Abbreviations:
        PG - Perfect Gas
        CPG - Calorically Perfect Gas
        TPG - Thermally Perfect Gas
    Inputs: f1,k
    Outputs: M [Msub,Msuper,f]
    Explanantion: Inverts the function F1=M*(1+(k-1)/2*M^2)^(-(k+1)/(2*(k-1))) which appears in isentropic area relations of perfect gas gasdynamics relations to give Mach number given f1 and k. For any given f1, there are two possible Mach numbers one subsonic and the other supersonic, accordingly the output is a list containing the two Mach numbers and a flag indicating the success of the operation.
    Usage:
        M=InvF1(f1) # calculates M for a perfect diatomic gas including air
        M=InvF1(f1,k) # calculates M for a general perfect gas given M,k
    ###
    ver 0
    August 2020
    ###
    Credits:
    Srisha Rao M V
    '''
    # The subsonic solution
    maxminsub = [0.1, 0.2]
    sol1 = secant(residualF1, maxminsub, f1, k)
    # The supersonic solution
    maxminsup = [1.1, 3.0]
    sol2 = secant(residualF1, maxminsup, f1, k)
    # Check for solutions
    if (sol1[1] > 0) and (sol2[1] > 0):
        return ([sol1[0], sol2[0], 1])
    else:
        print(
            'error: The function could not be solved, check the inputs given')
        return
Beispiel #3
0
def InvOSBmax(Bmax, k=1.4):
    '''
    Gasdynamics Module
    Location: GasDynamics\\CPG\\ObliqueShock
    Function: InvOSBmax(Bmax,k=1.4)
    Variables:
        T - Temperature[K]
        P - Pressure [Pa]
        P0 - Stagnation Pressure [Pa]
        T0 - Stagnation Temperature [K]
        rho - Density [kg/m^3]
        R - Gas constant [J/(kgK)], default value 287 J/(kgK) for air
        k - ratio of specific heats gamma=Cp/Cv, default value k=1.4 for diatomic gases
        a - speed of sound [m/s]
        V - local magnitude of gas velocity [m/s]
        M - Mach number
        A - Area of cross section
        m - mass flow rate
        B - beta the shock angle for a given flow deflection angle theta
        th - theta the flow defelection angle
    Numbers:
        1 - upstream of the shock
        2 - downstream of the shock
    Abbreviations:
        PG - Perfect Gas
        CPG - Calorically Perfect Gas
        TPG - Thermally Perfect Gas
    Inputs: Bmax,k
    Outputs: M
    Explanantion: Calculates the maximum shock angle for attached solutions given M and k
    Usage:
        M=InvOSBmax(Bmax,k=1.4)
    ###
    ver 0
    August 2020
    ###
    Credits:
    Srisha Rao M V
    '''
    M = np.arange(1.01, 20.01, 0.01)
    f = np.empty_like(M)
    for i in range(0, len(M)):
        f[i] = OSBmax(M[i], k)
        pass
    interpfn = interpolate.interp1d(f, M)
    M_in1 = 1.001 * interpfn(Bmax)
    M_in2 = 0.999 * interpfn(Bmax)
    return secant(residual_Bmax, [M_in1, M_in2], Bmax, k)
Beispiel #4
0
def InvNSP02P01(P02P01,k=1.4):
    '''
    Gasdynamics Module
    Location: GasDynamics\\CPG\\NormalShock
    Function: InvNSP02P01(P02P01,k)
    Variables:
        T - Temperature[K]
        P - Pressure [Pa]
        P0 - Stagnation Pressure [Pa]
        T0 - Stagnation Temperature [K]
        rho - Density [kg/m^3]
        R - Gas constant [J/(kgK)], default value 287 J/(kgK) for air
        k - ratio of specific heats gamma=Cp/Cv, default value k=1.4 for diatomic gases
        a - speed of sound [m/s]
        V - local magnitude of gas velocity [m/s]
        M - Mach number
        A - Area of cross section
        m - mass flow rate
    Numbers:
        1 - upstream of the shock
        2 - downstream of the shock
    Abbreviations:
        PG - Perfect Gas
        CPG - Calorically Perfect Gas
        TPG - Thermally Perfect Gas
    Inputs: P02P01,k
    Outputs: M1
    Explanantion: Calculates the upstream Mach number given P02/P01 across a shock
    Usage:
        M1=InvNSP02P01(P02P01,k)
    ###
    ver 0
    August 2020
    ###
    Credits:
    Srisha Rao M V
    '''
    return secant(residual_P02P01,[1.1,3.0],P02P01,k)
Beispiel #5
0
def OSMthB(M, th, k=1.4):
    '''
    Gasdynamics Module
    Location: GasDynamics\\CPG\\ObliqueShock
    Function: OSMthB(M,th,k=1.4)
    Variables:
        T - Temperature[K]
        P - Pressure [Pa]
        P0 - Stagnation Pressure [Pa]
        T0 - Stagnation Temperature [K]
        rho - Density [kg/m^3]
        R - Gas constant [J/(kgK)], default value 287 J/(kgK) for air
        k - ratio of specific heats gamma=Cp/Cv, default value k=1.4 for diatomic gases
        a - speed of sound [m/s]
        V - local magnitude of gas velocity [m/s]
        M - Mach number
        A - Area of cross section
        m - mass flow rate
        B - beta the shock angle for a given flow deflection angle theta
        th - theta the flow defelection angle
    Numbers:
        1 - upstream of the shock
        2 - downstream of the shock
    Abbreviations:
        PG - Perfect Gas
        CPG - Calorically Perfect Gas
        TPG - Thermally Perfect Gas
    Inputs: M1,k
    Outputs: Bmax
    Explanantion: Calculates the shock angle for attached solutions given M, th and k
    Usage:
        B=OSMthB(M,th,k=1.4)
    ###
    ver 0
    August 2020
    ###
    Credits:
    Srisha Rao M V
    '''
    thmax = OSthmax(M, k)
    Bmax = OSBmax(M, k)
    mu = machangle(M)
    if th == thmax:
        return ([Bmax, Bmax, 1])
    elif th > thmax:
        print(
            'error the angle is greater than the maximum flow deflection angle for attached shock solutions'
        )
        return ([0, 0, 0])
    elif th == 0:
        return ([mu, math.pi / 2, 1])
    else:
        Btemp1 = np.linspace(mu, Bmax, 100)
        Btemp2 = np.linspace(Bmax, math.pi / 2, 100)
        thtemp1 = np.empty_like(Btemp1)
        thtemp2 = np.empty_like(Btemp2)
        for i in range(0, len(Btemp1)):
            thtemp1[i] = OSMBth(M, Btemp1[i], k)
            thtemp2[i] = OSMBth(M, Btemp2[i], k)
            pass
        interpfn1 = interpolate.interp1d(thtemp1, Btemp1)
        Bestw1 = 0.999 * interpfn1(th)
        Bestw2 = 0.995 * interpfn1(th)
        interpfn2 = interpolate.interp1d(thtemp2, Btemp2)
        Bests1 = 0.999 * interpfn2(th)
        Bests2 = 0.995 * interpfn2(th)
        B1 = secant(residual_MthB, [Bestw1, Bestw2], M, th, k)
        B2 = secant(residual_MthB, [Bests1, Bests2], M, th, k)
        return ([B1[0], B2[0], 1])