|
34 | 34 | 'Nicklin_Wilkes_Davidson', 'Gregory_Scott', 'Dix',
|
35 | 35 | 'Sun_Duffey_Peng', 'Xu_Fang_voidage', 'Woldesemayat_Ghajar',
|
36 | 36 | 'Lockhart_Martinelli_Xtt', 'two_phase_voidage_experimental',
|
37 |
| - 'density_two_phase'] |
| 37 | + 'density_two_phase', 'Beattie_Whalley', 'McAdams', 'Cicchitti', |
| 38 | + 'Lin_Kwok', 'Fourar_Bories'] |
38 | 39 |
|
39 | 40 | ### Models based on slip ratio
|
40 | 41 |
|
@@ -407,7 +408,7 @@ def homogeneous(x, rhol, rhog):
|
407 | 408 | Upward Inclined Pipes." International Journal of Multiphase Flow 33,
|
408 | 409 | no. 4 (April 2007): 347-370. doi:10.1016/j.ijmultiphaseflow.2006.09.004.
|
409 | 410 | '''
|
410 |
| - return 1./(1 + (1-x)/x*(rhog/rhol)) |
| 411 | + return 1./(1. + (1-x)/x*(rhog/rhol)) |
411 | 412 |
|
412 | 413 |
|
413 | 414 | def Chisholm_Armand(x, rhol, rhog):
|
@@ -1928,3 +1929,344 @@ def two_phase_voidage_experimental(rho_lg, rhol, rhog):
|
1928 | 1929 | no. 1 (October 1, 2008): 106-13.
|
1929 | 1930 | '''
|
1930 | 1931 | return (rho_lg - rhol)/(rhog - rhol)
|
| 1932 | + |
| 1933 | + |
| 1934 | +### two-phase viscosity models |
| 1935 | + |
| 1936 | + |
| 1937 | +def Beattie_Whalley(x, mul, mug, rhol, rhog): |
| 1938 | + r'''Calculates a suggested definition for liquid-gas two-phase flow |
| 1939 | + viscosity in internal pipe flow according to the form in [1]_ and shown |
| 1940 | + in [2]_ and [3]_. |
| 1941 | + |
| 1942 | + .. math:: |
| 1943 | + \mu_m = \mu_l(1-\alpha_m)(1 + 2.5\alpha_m) + \mu_g\alpha_m |
| 1944 | + |
| 1945 | + \alpha_m = \frac{1}{1 + \left(\frac{1-x}{x}\right)\frac{\rho_g}{\rho_l}} |
| 1946 | + \text{(homogeneous model)} |
| 1947 | +
|
| 1948 | + Parameters |
| 1949 | + ---------- |
| 1950 | + x : float |
| 1951 | + Quality of the gas-liquid flow, [-] |
| 1952 | + mul : float |
| 1953 | + Viscosity of liquid, [Pa*s] |
| 1954 | + mug : float |
| 1955 | + Viscosity of gas, [Pa*s] |
| 1956 | + rhol : float |
| 1957 | + Density of the liquid [kg/m^3] |
| 1958 | + rhog : float |
| 1959 | + Density of the gas [kg/m^3] |
| 1960 | +
|
| 1961 | + Returns |
| 1962 | + ------- |
| 1963 | + mu_lg : float |
| 1964 | + Liquid-gas viscosity (**a suggested definition, potentially useful |
| 1965 | + for empirical work only!**) [Pa*s] |
| 1966 | +
|
| 1967 | + Notes |
| 1968 | + ----- |
| 1969 | + This model converges to the liquid or gas viscosity as the quality |
| 1970 | + approaches either limits. |
| 1971 | + |
| 1972 | + Examples |
| 1973 | + -------- |
| 1974 | + >>> Beattie_Whalley(x=0.4, mul=1E-3, mug=1E-5, rhol=850, rhog=1.2) |
| 1975 | + 1.7363806909512365e-05 |
| 1976 | +
|
| 1977 | + References |
| 1978 | + ---------- |
| 1979 | + .. [1] Beattie, D. R. H., and P. B. Whalley. "A Simple Two-Phase Frictional |
| 1980 | + Pressure Drop Calculation Method." International Journal of Multiphase |
| 1981 | + Flow 8, no. 1 (February 1, 1982): 83-87. |
| 1982 | + doi:10.1016/0301-9322(82)90009-X. |
| 1983 | + .. [2] Awad, M. M., and Y. S. Muzychka. "Effective Property Models for |
| 1984 | + Homogeneous Two-Phase Flows." Experimental Thermal and Fluid Science 33, |
| 1985 | + no. 1 (October 1, 2008): 106-13. |
| 1986 | + .. [3] Kim, Sung-Min, and Issam Mudawar. "Review of Databases and |
| 1987 | + Predictive Methods for Pressure Drop in Adiabatic, Condensing and |
| 1988 | + Boiling Mini/Micro-Channel Flows." International Journal of Heat and |
| 1989 | + Mass Transfer 77 (October 2014): 74-97. |
| 1990 | + doi:10.1016/j.ijheatmasstransfer.2014.04.035. |
| 1991 | + ''' |
| 1992 | + alpha = homogeneous(x, rhol, rhog) |
| 1993 | + return mul*(1. - alpha)*(1. + 2.5*alpha) + mug*alpha |
| 1994 | + |
| 1995 | + |
| 1996 | +def McAdams(x, mul, mug): |
| 1997 | + r'''Calculates a suggested definition for liquid-gas two-phase flow |
| 1998 | + viscosity in internal pipe flow according to the form in [1]_ and shown |
| 1999 | + in [2]_ and [3]_. |
| 2000 | + |
| 2001 | + .. math:: |
| 2002 | + \mu_m = \left(\frac{x}{\mu_g} + \frac{1-x}{\mu_l}\right)^{-1} |
| 2003 | +
|
| 2004 | + Parameters |
| 2005 | + ---------- |
| 2006 | + x : float |
| 2007 | + Quality of the gas-liquid flow, [-] |
| 2008 | + mul : float |
| 2009 | + Viscosity of liquid, [Pa*s] |
| 2010 | + mug : float |
| 2011 | + Viscosity of gas, [Pa*s] |
| 2012 | +
|
| 2013 | + Returns |
| 2014 | + ------- |
| 2015 | + mu_lg : float |
| 2016 | + Liquid-gas viscosity (**a suggested definition, potentially useful |
| 2017 | + for empirical work only!**) [Pa*s] |
| 2018 | +
|
| 2019 | + Notes |
| 2020 | + ----- |
| 2021 | + This model converges to the liquid or gas viscosity as the quality |
| 2022 | + approaches either limits. |
| 2023 | + |
| 2024 | + [3]_ states this is the most common definition of two-phase liquid-gas |
| 2025 | + viscosity. |
| 2026 | + |
| 2027 | + Examples |
| 2028 | + -------- |
| 2029 | + >>> McAdams(x=0.4, mul=1E-3, mug=1E-5) |
| 2030 | + 2.4630541871921184e-05 |
| 2031 | +
|
| 2032 | + References |
| 2033 | + ---------- |
| 2034 | + .. [1] McAdams, W. H. "Vaporization inside Horizontal Tubes-II Benzene-Oil |
| 2035 | + Mixtures." Trans. ASME 39 (1949): 39-48. |
| 2036 | + .. [2] Awad, M. M., and Y. S. Muzychka. "Effective Property Models for |
| 2037 | + Homogeneous Two-Phase Flows." Experimental Thermal and Fluid Science 33, |
| 2038 | + no. 1 (October 1, 2008): 106-13. |
| 2039 | + .. [3] Kim, Sung-Min, and Issam Mudawar. "Review of Databases and |
| 2040 | + Predictive Methods for Pressure Drop in Adiabatic, Condensing and |
| 2041 | + Boiling Mini/Micro-Channel Flows." International Journal of Heat and |
| 2042 | + Mass Transfer 77 (October 2014): 74-97. |
| 2043 | + doi:10.1016/j.ijheatmasstransfer.2014.04.035. |
| 2044 | + ''' |
| 2045 | + return 1./(x/mug + (1. - x)/mul) |
| 2046 | + |
| 2047 | + |
| 2048 | +def Cicchitti(x, mul, mug): |
| 2049 | + r'''Calculates a suggested definition for liquid-gas two-phase flow |
| 2050 | + viscosity in internal pipe flow according to the form in [1]_ and shown |
| 2051 | + in [2]_ and [3]_. |
| 2052 | + |
| 2053 | + .. math:: |
| 2054 | + \mu_m = x\mu_g + (1-x)\mu_l |
| 2055 | + |
| 2056 | + Parameters |
| 2057 | + ---------- |
| 2058 | + x : float |
| 2059 | + Quality of the gas-liquid flow, [-] |
| 2060 | + mul : float |
| 2061 | + Viscosity of liquid, [Pa*s] |
| 2062 | + mug : float |
| 2063 | + Viscosity of gas, [Pa*s] |
| 2064 | +
|
| 2065 | + Returns |
| 2066 | + ------- |
| 2067 | + mu_lg : float |
| 2068 | + Liquid-gas viscosity (**a suggested definition, potentially useful |
| 2069 | + for empirical work only!**) [Pa*s] |
| 2070 | +
|
| 2071 | + Notes |
| 2072 | + ----- |
| 2073 | + This model converges to the liquid or gas viscosity as the quality |
| 2074 | + approaches either limits. |
| 2075 | + |
| 2076 | + Examples |
| 2077 | + -------- |
| 2078 | + >>> Cicchitti(x=0.4, mul=1E-3, mug=1E-5) |
| 2079 | + 0.0006039999999999999 |
| 2080 | +
|
| 2081 | + References |
| 2082 | + ---------- |
| 2083 | + .. [1] Cicchitti, A., C. Lombardi, M. Silvestri, G. Soldaini, and R. |
| 2084 | + Zavattarelli. "Two-Phase Cooling Experiments: Pressure Drop, Heat |
| 2085 | + Transfer and Burnout Measurements." Centro Informazioni Studi |
| 2086 | + Esperienze, Milan, January 1, 1959. |
| 2087 | + .. [2] Awad, M. M., and Y. S. Muzychka. "Effective Property Models for |
| 2088 | + Homogeneous Two-Phase Flows." Experimental Thermal and Fluid Science 33, |
| 2089 | + no. 1 (October 1, 2008): 106-13. |
| 2090 | + .. [3] Kim, Sung-Min, and Issam Mudawar. "Review of Databases and |
| 2091 | + Predictive Methods for Pressure Drop in Adiabatic, Condensing and |
| 2092 | + Boiling Mini/Micro-Channel Flows." International Journal of Heat and |
| 2093 | + Mass Transfer 77 (October 2014): 74-97. |
| 2094 | + doi:10.1016/j.ijheatmasstransfer.2014.04.035. |
| 2095 | + ''' |
| 2096 | + return x*mug + (1. - x)*mul |
| 2097 | + |
| 2098 | + |
| 2099 | +def Lin_Kwok(x, mul, mug): |
| 2100 | + r'''Calculates a suggested definition for liquid-gas two-phase flow |
| 2101 | + viscosity in internal pipe flow according to the form in [1]_ and shown |
| 2102 | + in [2]_ and [3]_. |
| 2103 | + |
| 2104 | + .. math:: |
| 2105 | + \mu_m = \frac{\mu_l \mu_g}{\mu_g + x^{1.4}(\mu_l - \mu_g)} |
| 2106 | + |
| 2107 | + Parameters |
| 2108 | + ---------- |
| 2109 | + x : float |
| 2110 | + Quality of the gas-liquid flow, [-] |
| 2111 | + mul : float |
| 2112 | + Viscosity of liquid, [Pa*s] |
| 2113 | + mug : float |
| 2114 | + Viscosity of gas, [Pa*s] |
| 2115 | +
|
| 2116 | + Returns |
| 2117 | + ------- |
| 2118 | + mu_lg : float |
| 2119 | + Liquid-gas viscosity (**a suggested definition, potentially useful |
| 2120 | + for empirical work only!**) [Pa*s] |
| 2121 | +
|
| 2122 | + Notes |
| 2123 | + ----- |
| 2124 | + This model converges to the liquid or gas viscosity as the quality |
| 2125 | + approaches either limits. |
| 2126 | + |
| 2127 | + Examples |
| 2128 | + -------- |
| 2129 | + >>> Lin_Kwok(x=0.4, mul=1E-3, mug=1E-5) |
| 2130 | + 3.515119398126066e-05 |
| 2131 | +
|
| 2132 | + References |
| 2133 | + ---------- |
| 2134 | + .. [1] Lin, S., C. C. K. Kwok, R. -Y. Li, Z. -H. Chen, and Z. -Y. Chen. |
| 2135 | + "Local Frictional Pressure Drop during Vaporization of R-12 through |
| 2136 | + Capillary Tubes." International Journal of Multiphase Flow 17, no. 1 |
| 2137 | + (January 1, 1991): 95-102. doi:10.1016/0301-9322(91)90072-B. |
| 2138 | + .. [2] Awad, M. M., and Y. S. Muzychka. "Effective Property Models for |
| 2139 | + Homogeneous Two-Phase Flows." Experimental Thermal and Fluid Science 33, |
| 2140 | + no. 1 (October 1, 2008): 106-13. |
| 2141 | + ''' |
| 2142 | + return mul*mug/(mug + x**1.4*(mul - mug)) |
| 2143 | + |
| 2144 | + |
| 2145 | +def Fourar_Bories(x, mul, mug, rhol, rhog): |
| 2146 | + r'''Calculates a suggested definition for liquid-gas two-phase flow |
| 2147 | + viscosity in internal pipe flow according to the form in [1]_ and shown |
| 2148 | + in [2]_ and [3]_. |
| 2149 | + |
| 2150 | + .. math:: |
| 2151 | + \mu_m = \rho_m\left(\sqrt{x\nu_g} + \sqrt{(1-x)\nu_l}\right)^2 |
| 2152 | + |
| 2153 | + Parameters |
| 2154 | + ---------- |
| 2155 | + x : float |
| 2156 | + Quality of the gas-liquid flow, [-] |
| 2157 | + mul : float |
| 2158 | + Viscosity of liquid, [Pa*s] |
| 2159 | + mug : float |
| 2160 | + Viscosity of gas, [Pa*s] |
| 2161 | + rhol : float |
| 2162 | + Density of the liquid, [kg/m^3] |
| 2163 | + rhog : float |
| 2164 | + Density of the gas, [kg/m^3] |
| 2165 | +
|
| 2166 | + Returns |
| 2167 | + ------- |
| 2168 | + mu_lg : float |
| 2169 | + Liquid-gas viscosity (**a suggested definition, potentially useful |
| 2170 | + for empirical work only!**) [Pa*s] |
| 2171 | +
|
| 2172 | + Notes |
| 2173 | + ----- |
| 2174 | + This model converges to the liquid or gas viscosity as the quality |
| 2175 | + approaches either limits. |
| 2176 | + |
| 2177 | + This was first expressed in the equalivalent form as follows: |
| 2178 | + |
| 2179 | + .. math:: |
| 2180 | + \mu_m = \rho_m\left(x\nu_g + (1-x)\nu_l + 2\sqrt{x(1-x)\nu_g\nu_l} |
| 2181 | + \right) |
| 2182 | + |
| 2183 | + Examples |
| 2184 | + -------- |
| 2185 | + >>> Fourar_Bories(x=0.4, mul=1E-3, mug=1E-5, rhol=850, rhog=1.2) |
| 2186 | + 2.127617150298565e-05 |
| 2187 | +
|
| 2188 | + References |
| 2189 | + ---------- |
| 2190 | + .. [1] Fourar, M., and S. Bories. "Experimental Study of Air-Water |
| 2191 | + Two-Phase Flow through a Fracture (Narrow Channel)." International |
| 2192 | + Journal of Multiphase Flow 21, no. 4 (August 1, 1995): 621-37. |
| 2193 | + doi:10.1016/0301-9322(95)00005-I. |
| 2194 | + .. [2] Awad, M. M., and Y. S. Muzychka. "Effective Property Models for |
| 2195 | + Homogeneous Two-Phase Flows." Experimental Thermal and Fluid Science 33, |
| 2196 | + no. 1 (October 1, 2008): 106-13. |
| 2197 | + .. [3] Aung, NZ, and T. Yuwono. "Evaluation of Mixture Viscosity Models in |
| 2198 | + the Prediction of Two-Phase Flow Pressure Drops." ASEAN Journal on |
| 2199 | + Science and Technology for Development 29, no. 2 (2012). |
| 2200 | + ''' |
| 2201 | + rhom = 1./(x/rhog + (1. - x)/rhol) |
| 2202 | + nul = mul/rhol # = nu_mu_converter(rho=rhol, mu=mul) |
| 2203 | + nug = mug/rhog # = nu_mu_converter(rho=rhog, mu=mug) |
| 2204 | + return rhom*((x*nug)**0.5 + ((1. - x)*nul)**0.5)**2 |
| 2205 | + |
| 2206 | + |
| 2207 | +def Duckler(x, mul, mug, rhol, rhog): |
| 2208 | + r'''Calculates a suggested definition for liquid-gas two-phase flow |
| 2209 | + viscosity in internal pipe flow according to the form in [1]_ and shown |
| 2210 | + in [2]_, [3]_, and [4]_. |
| 2211 | + |
| 2212 | + .. math:: |
| 2213 | + \mu_m = \frac{\frac{x\mu_g}{\rho_g} + \frac{(1-x)\mu_l}{\rho_l} } |
| 2214 | + {\frac{x}{\rho_g} + \frac{(1-x)}{\rho_l} } |
| 2215 | + |
| 2216 | + Parameters |
| 2217 | + ---------- |
| 2218 | + x : float |
| 2219 | + Quality of the gas-liquid flow, [-] |
| 2220 | + mul : float |
| 2221 | + Viscosity of liquid, [Pa*s] |
| 2222 | + mug : float |
| 2223 | + Viscosity of gas, [Pa*s] |
| 2224 | + rhol : float |
| 2225 | + Density of the liquid, [kg/m^3] |
| 2226 | + rhog : float |
| 2227 | + Density of the gas, [kg/m^3] |
| 2228 | +
|
| 2229 | + Returns |
| 2230 | + ------- |
| 2231 | + mu_lg : float |
| 2232 | + Liquid-gas viscosity (**a suggested definition, potentially useful |
| 2233 | + for empirical work only!**) [Pa*s] |
| 2234 | +
|
| 2235 | + Notes |
| 2236 | + ----- |
| 2237 | + This model converges to the liquid or gas viscosity as the quality |
| 2238 | + approaches either limits. |
| 2239 | + |
| 2240 | + This has also been expressed in the following form: |
| 2241 | + |
| 2242 | + .. math:: |
| 2243 | + \mu_m = \rho_m \left[x\left(\frac{\mu_g}{\rho_g}\right) |
| 2244 | + + (1 - x)\left(\frac{\mu_l}{\rho_l}\right)\right] |
| 2245 | + |
| 2246 | + According to the homogeneous definition of two-phase density. |
| 2247 | + |
| 2248 | + Examples |
| 2249 | + -------- |
| 2250 | + >>> Duckler(x=0.4, mul=1E-3, mug=1E-5, rhol=850, rhog=1.2) |
| 2251 | + 1.2092040385066917e-05 |
| 2252 | +
|
| 2253 | + References |
| 2254 | + ---------- |
| 2255 | + .. [1] Fourar, M., and S. Bories. "Experimental Study of Air-Water |
| 2256 | + Two-Phase Flow through a Fracture (Narrow Channel)." International |
| 2257 | + Journal of Multiphase Flow 21, no. 4 (August 1, 1995): 621-37. |
| 2258 | + doi:10.1016/0301-9322(95)00005-I. |
| 2259 | + .. [2] Awad, M. M., and Y. S. Muzychka. "Effective Property Models for |
| 2260 | + Homogeneous Two-Phase Flows." Experimental Thermal and Fluid Science 33, |
| 2261 | + no. 1 (October 1, 2008): 106-13. |
| 2262 | + .. [3] Kim, Sung-Min, and Issam Mudawar. "Review of Databases and |
| 2263 | + Predictive Methods for Pressure Drop in Adiabatic, Condensing and |
| 2264 | + Boiling Mini/Micro-Channel Flows." International Journal of Heat and |
| 2265 | + Mass Transfer 77 (October 2014): 74-97. |
| 2266 | + doi:10.1016/j.ijheatmasstransfer.2014.04.035. |
| 2267 | + .. [4] Aung, NZ, and T. Yuwono. "Evaluation of Mixture Viscosity Models in |
| 2268 | + the Prediction of Two-Phase Flow Pressure Drops." ASEAN Journal on |
| 2269 | + Science and Technology for Development 29, no. 2 (2012). |
| 2270 | + ''' |
| 2271 | + return (x*mug/rhog + (1. - x)*mul/rhol)/(x/rhog + (1. - x)/rhol) |
| 2272 | + |
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