1 !vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvC 2 ! C 3 ! Module: constant C 4 ! Purpose: Common block containing physical constants and constants C 5 ! used in the numerical technique C 6 ! C 7 ! Author: M. Syamlal Date: 5-FEB-92 C 8 ! Reviewer: Date: dd-mmm-yy C 9 ! C 10 ! Literature/Document References: C 11 ! Gera, D., Syamlal, M., and O'Brien, T. J., "Hydrodynamics of C 12 ! particle segregation in fluidized beds", Int. J. of Multiphase C 13 ! Flow, Vol 30, 2004, pp. 419-428. C 14 ! Johnson, P. C., and Jackson, R., "Frictional-collisional C 15 ! constitutive relations for granluar materials, with application C 16 ! to plane shearing", JFM, Vol. 176, 1987, pp. 67-93. C 17 ! Garzo, V., Tenneti, S., Subramaniam, S., and Hrenya, C. M., C 18 ! "Enskog kinetic theory for monodisperse gas-solid flows", JFM, C 19 ! Vol. 712, 2012, pp. 129-168 C 20 ! C 21 ! C 22 !^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^C 23 24 MODULE constant 25 26 !----------------------------------------------- 27 ! Modules 28 !----------------------------------------------- 29 Use param, only: dim_m, dimension_c 30 !----------------------------------------------- 31 32 ! Packed bed (close packed) void fraction 33 DOUBLE PRECISION :: EP_star 34 35 ! parameters used in the correlation to calculate the local maximum 36 ! solids volume fraction for a polydisperse powder: ep_s_max_ratio, 37 ! d_p_ratio and ep_s_max, m_max 38 DOUBLE PRECISION :: ep_s_max_ratio(DIM_M, DIM_M), & 39 d_p_ratio(DIM_M, DIM_M) 40 ! maximum packing volume fraction for indicate particulate phase 41 ! its value will default to 1-ep_star 42 DOUBLE PRECISION :: ep_s_max(DIM_M) 43 ! Index to rearrange particles from coarsest to finest for use in 44 ! function CALC_ep_star(IJK,IER) 45 INTEGER :: M_MAX(DIM_M) 46 47 48 ! SWITCH enables us to turn on/off modifications to certain kinetic 49 ! theory models for granular solids (i.e. no gas) that have been 50 ! adjusted to account for the presence of a fluid phase. If one wants 51 ! to simulate gas-particle flow then set SWITCH=1. As a result, the 52 ! effects of drag on particle viscosity/conductivity will be 53 ! incorporated. Additional gas-solids terms may also have been 54 ! introduced into the granular energy balance depending on the KT 55 ! model (see source_granular_energy for details). If we want to 56 ! simulate pure granular flow without the effects of an interstitial 57 ! gas, set SWITCH=0. 58 DOUBLE PRECISION, PARAMETER :: SWITCH=1.d0 59 60 ! ALPHA is a parameter introduced into the theory of Lun_1984 for 61 ! calculating solids viscosity. It also appears when invoking the 62 ! solids frictional model FRICTION, which uses the Lun et al. 63 ! theory. The factor (2+alpha)/3 was eliminated in the complete 64 ! analysis of Lun et al. but was introduced as an adjustable 65 ! parameter. To recover the original theory alpha should be set to 66 ! 1. For details see Johnson and Jackson, 1987. 67 DOUBLE PRECISION, PARAMETER :: ALPHA = 1.6d0 68 69 70 ! parameter used in the solids-solids drag model invoked in the 71 ! default KT (Lun_1984). For details see Gera et al., 2004 72 DOUBLE PRECISION :: SEGREGATION_SLOPE_COEFFICIENT 73 74 ! SWITCH_IA enforces consistency in the solids viscosity and 75 ! conductivity so that the results using 2 or more identical 76 ! solids phases are the same as an equivalent single solids 77 ! phase. Set to false to use original (published) theory of 78 ! Iddir-Arastoopour. 79 LOGICAL, PARAMETER :: SWITCH_IA = .TRUE. 80 81 ! parameter in the theory of GTSH that is related to length scale 82 ! of lubrication effects. For details see GTSH, 2012. 83 DOUBLE PRECISION, PARAMETER :: EpM = 0.01d0 84 85 ! PHIP = Specularity coefficient associated with particle wall 86 ! collisions 87 DOUBLE PRECISION :: PHIP 88 ! PHIP0 specularity coefficient for r->0 89 double precision :: phip0 90 ! k4phi k=7/2*mu*(1+e_w) 91 double precision :: k4phi 92 ! e_w = particle-wall coefficient of restitution 93 DOUBLE PRECISION :: e_w 94 95 ! Parameters used in the solids frictional model FRICTION: 96 ! - Fr, N_Pc, D_Pc, and EPS_F_min are all used in the equation for 97 ! Pc, the critical solids pressure: 98 ! Fr = Constant with dyne/cm2 units of pressure. It will be 99 ! automatically converted to Pa in calc_mu_s.f 100 ! N_Pc = exponent in numerator 101 ! D_Pc = exponent in denominator 102 ! EPS_f_min = minimum solids fraction above which friction 103 ! kicks in 104 ! - N_Pf appears as an exponent in the equation of state for Pf, the 105 ! frictional pressure: 106 ! - delta is a small deviation in void fraction near packing where 107 ! Pc and dPc/deps are calculated. 108 DOUBLE PRECISION :: EPS_f_min 109 DOUBLE PRECISION :: Fr, N_Pc, D_Pc, N_Pf, delta 110 PARAMETER(Fr = 0.5d0, N_Pc=2d0, D_Pc=5d0, N_Pf=1.03d0, delta=1d-2) 111 112 ! Coefficient of restitution 113 DOUBLE PRECISION C_e 114 115 ! (1+C_e)/2. 116 DOUBLE PRECISION eta 117 118 ! particle-type dependent rest. coef. for use in GHD theory 119 DOUBLE PRECISION r_p(DIM_M, DIM_M) 120 121 ! Coeficient of friction 122 DOUBLE PRECISION C_f 123 124 ! Angle of internal friction (degrees) 125 DOUBLE PRECISION Phi 126 127 ! Angle of wall-particle friction (degrees) 128 DOUBLE PRECISION Phi_w 129 130 ! (k=) Sin(PHI) in Plastic-flow stress formulation 131 DOUBLE PRECISION Sin_Phi 132 133 ! Sin^2(PHI) 134 DOUBLE PRECISION Sin2_Phi 135 136 ! (3-2k^2)/6k^2 in Plastic-flow stress formulation 137 DOUBLE PRECISION F_Phi 138 139 ! tan(PHI_w) 140 DOUBLE PRECISION tan_Phi_w 141 142 ! Default value for characteristic length for turbulence 143 DOUBLE PRECISION L_scale0 144 145 ! Maximum value of turbulent viscosity 146 DOUBLE PRECISION MU_gmax 147 148 ! Excluded volume (Boyle-Massoudi stress tensor) 149 DOUBLE PRECISION V_ex 150 151 ! Coefficients for calibrating Syamlal-O'Brien drag correlation with 152 ! Umf data 153 DOUBLE PRECISION drag_c1, drag_d1 154 155 ! success-factor for aggregation and breakage 156 DOUBLE PRECISION :: AGGREGATION_EFF 157 DOUBLE PRECISION :: BREAKAGE_EFF 158 159 ! Gravitational acceleration 160 DOUBLE PRECISION GRAVITY, to_SI, GRAVITY_X,GRAVITY_Y, GRAVITY_Z 161 162 ! Universal gas constant 163 DOUBLE PRECISION GAS_CONST 164 165 ! Universal gas constant in cal/mol.K 166 DOUBLE PRECISION, PARAMETER :: GAS_CONST_cal = 1.987207D0 167 168 ! Pi, the ubiquitous irrational number 169 DOUBLE PRECISION, PARAMETER :: Pi = 4.D0*ATAN(1.D0) 170 171 ! Square root of Pi 172 DOUBLE PRECISION, PARAMETER :: SQRT_Pi = 2.D0*SQRT(ATAN(1.D0)) 173 174 ! Maximum pressure correction allowed in one iteration 175 DOUBLE PRECISION MAX_DELP 176 177 ! User defined constants 178 DOUBLE PRECISION C (DIMENSION_C) 179 180 ! Names of user defined constants (for output file only) 181 CHARACTER(LEN=20) :: C_NAME (DIMENSION_C) 182 183 END MODULE constant 184