Merge pull request #5 from rydyb/90-degree-bends

adds pressure_drop for (90-degree) bend structures

Author: bodokaiser

Project.toml

@@ -1,7 +1,7 @@
 name = "HeatTransferFluids"
 uuid = "44505bb3-94ea-493c-a20c-f0ca548ab76b"
 authors = ["Bodo Kaiser"]
-version = "0.1.1"
+version = "0.2.0"
 
 [deps]
 DynamicQuantities = "06fc5a27-2a28-4c7c-a15d-362465fb6821"

src/HeatTransferFluids.jl

@@ -5,6 +5,7 @@ using DynamicQuantities
 include("fluid.jl")
 include("structure.jl")
 include("flow.jl")
+include("friction.jl")
 include("pressure_drop.jl")
 include("heat_transfer.jl")
 

src/flow.jl

@@ -1,4 +1,4 @@
-export reynolds_number, nusselt_number, prandtl_number
+export reynolds_number, nusselt_number, prandtl_number, dean_number
 
 """
     reynolds_number(f::Fluid, t::Tube)
@@ -21,6 +21,32 @@ function reynolds_number(f::Fluid, t::Tube)
     return ustrip(ϱ * v * D / μ)
 end
 
+function critical_reynolds_number(t::Tube)
+    return 2300
+end
+
+"""
+    pressure_drop(h::Helix)
+
+Computes the critical Reynolds number for a Helix.
+
+See VDI Heat Atlas, p. 1062 to 1063 for details.
+
+# Arguments
+- `h::Helix`: the coiled tube through which the fluid flows
+
+# Returns
+- `DynamicQuantity.AbstractQuantity`: the pressure drop of the fluid flowing through the tube
+"""
+function critical_reynolds_number(h::Helix)
+    Dw = h.diameter
+    H = h.pitch
+    D = Dw * (1 + (H / (π * Dw))^2)
+    d = h.tube.diameter
+
+    return ustrip(2300 * (1 + 8.6 * (d / D)^0.45))
+end
+
 """
     prandtl_number(f::Fluid)
 
@@ -86,3 +112,12 @@ function nusselt_number_turbulent(f::Fluid, t::Tube)
 
     return ((ξ / 8)Re * Pr) * (1 + λ^(2 / 3)) / (1 + 12.7(ξ / 8)^(1 / 2) * (Pr^(2 / 3) - 1))
 end
+
+function dean_number(f::Fluid, b::Bend)
+    Re = reynolds_number(f, b.tube)
+
+    d = b.tube.diameter
+    D = 2 * b.radius
+
+    return Re * √(d / D)
+end

src/friction.jl

@@ -0,0 +1,65 @@
+"""
+    pressure_drop(f::Fluid, t::Tube)
+
+Computes the friction coefficient of a `fluid` flowing through a `tube`.
+
+See VDI Heat Atlas, p. 1057 for details.
+
+# Arguments
+- `f::Fluid`: the fluid flowing through the tube
+- `t::Tube`: the tube through which the fluid flows
+
+# Keywords
+- `friction::Float`: the friction factor of the fluid flowing through the tube
+
+# Returns
+- `DynamicQuantities.AbstractQuantity`: the pressure drop of the fluid flowing through the tube
+"""
+function friction(f::Fluid, t::Tube)
+    Re = reynolds_number(f, t)
+    Re_c = critical_reynolds_number(t)
+
+    # laminar regime
+    if Re < Re_c
+        return 64 / Re
+    end
+    # turbulent regime
+    if Re > Re_c
+        # Blasius equation
+        if Re > 3000 && Re < 2e4
+            return 0.316 / Re^0.25
+        end
+        # Hermann equation
+        if Re > 2e4 && Re < 2e6
+            return 0.0054 + 0.3964 / Re^0.3
+        end
+    end
+
+    throw(DomainError(Re, "no analytical formula for flow regime"))
+end
+
+function friction(f::Fluid, b::Bend)
+    De = dean_number(f, b)
+    ξ = friction(f, b.tube)
+
+    # laminar flow as in straight tube
+    if De < 11.6
+        return ξ
+    end
+    # laminar flow with additional friction
+    if De >= 11.6 && De <= 2000
+        return ξ / (1 - (1 - (11.6 / De)^0.45)^(1 / 0.45))
+    end
+
+    r = b.tube.diameter / 2
+    R = b.radius
+
+    # turbulent flow
+    Re_c = critical_reynolds_number(b.tube) * 7.5 * (r / R)^0.25
+    Re = reynolds_number(f, b.tube)
+    if Re > Re_c
+        return (r / R)^0.5 * (0.003625 + 0.038 * (Re * (r / R)^2)^-0.25)
+    end
+
+    throw(DomainError(De, "no analytical formula for flow regime"))
+end

src/pressure_drop.jl

@@ -17,52 +17,36 @@ See VDI Heat Atlas, p. 1057 for details.
 # Returns
 - `DynamicQuantities.AbstractQuantity`: the pressure drop of the fluid flowing through the tube
 """
-function pressure_drop(f::Fluid, t::Tube; friction = nothing)
+function pressure_drop(f::Fluid, t::Tube; friction = friction(f,t))
     Re = reynolds_number(f, t)
     L = t.length
     d = t.diameter
     ρ = f.density
     u = f.velocity
-
-    if friction === nothing
-        ξ = 64 / Re
-    else
-        ξ = friction
-    end
+    ξ = friction
 
     return uconvert(us"bar", ξ * (L / d) * (ρ * u^2 / 2))
 end
 
 """
-    pressure_drop(f::Fluid, c::Coil)
-
-Computes the pressure drop of a `fluid` flowing through a coiled tube.
+    pressure_drop(f::Fluid, h::Helix)
 
-See VDI Heat Atlas, p. 1062 to 1063 for details.
+Computes the pressure drop of a `fluid` flowing through a `helix`.
 
 # Arguments
 - `f::Fluid`: the fluid flowing through the tube
-- `c::Coil`: the coiled tube through which the fluid flows
+- `h::Helix`: the helix through which the fluid flows
 
 # Returns
 - `DynamicQuantity.AbstractQuantity`: the pressure drop of the fluid flowing through the tube
 """
-function critical_reynolds_number(f::Fluid, h::Helix)
-    Dw = h.diameter
-    H = h.pitch
-    D = Dw * (1 + (H / (π * Dw))^2)
-    d = h.tube.diameter
-
-    return ustrip(2300 * (1 + 8.6 * (d / D)^0.45))
-end
-
 function pressure_drop(f::Fluid, h::Helix)
     Dw = h.diameter
     H = h.pitch
     D = Dw * (1 + (H / (π * Dw))^2)
     d = h.tube.diameter
     Re = reynolds_number(f, h.tube)
-    Re_crit = critical_reynolds_number(f, h)
+    Re_crit = critical_reynolds_number(h)
 
     if 1 < (Re * sqrt(d / D)) < (Re_crit * sqrt(d / D))
         ξ = (64 / Re) * (1 + 0.033(log10(Re * sqrt(d / D)))^4.0)
@@ -73,24 +57,6 @@ function pressure_drop(f::Fluid, h::Helix)
     return pressure_drop(f, h.tube, friction = ξ)
 end
 
-"""
-    function pressure_drop(f::Fluid, r::RectangularCoil; friction = nothing)
-        Re = reynolds_number(f, r)
-        L = r.length
-        d = r.diameter
-        ρ = r.density
-        u = r.velocity
-        ξb = r.friction
-        n = r.turns
-
-        ptube = pressure_drop(f, r.tube; friction = friction)
-        pbend = ξb*(ρ*u^2/2)
-        return ustrip(ptube + n*4*pbend)
-
-    end
-
-"""
-
 """
     pressure_drop(f::Fluid, v::Valve)
 
@@ -114,3 +80,23 @@ function pressure_drop(f::Fluid, v::Valve)
 
     return p₀ * (Q / Kv)^2 * ρ / ρ₀
 end
+
+"""
+    pressure_drop(f::Fluid, b::Bend)
+
+Computes the pressure drop of a `fluid` flowing through a `bend`.
+
+So far, we only support 90-degree bends, see Spedding, P.L., Bernard, E. and McNally, G.M., ‘Fluid flow through 90 degree bends’, Dev. Chem. Eng Mineral Process, 12: 107–128, 2004.
+
+# Arguments
+- `f::Fluid`: the fluid flowing through the tube
+- `b::Bend`: the valve through which the fluid flows
+
+# Returns
+- `DynamicQuantity.AbstractQuantity`: the pressure drop of the fluid flowing through the tube
+"""
+function pressure_drop(f::Fluid, b::Bend)
+    @assert b.angle == 90u"deg" "only 90-degree bends are supported at the moment"
+
+    return pressure_drop(f, b.tube; friction=friction(f, b))
+end

src/structure.jl

@@ -1,4 +1,4 @@
-export Structure, Tube, Helix, Valve
+export Structure, Tube, Helix, Valve, Bend, Elbow
 
 """
     Structure
@@ -75,18 +75,19 @@ struct Valve{T<:AbstractQuantity} <: Structure
     end
 end
 
-"""
-struct Rectangular_Coil{T<:Tube,V<:AbstractQuantity} <: Structure
-    tube::T
-    turns::V
-    friction::V
-
-    function Rectangular_Coil(t::T; turns::V, friction::V) where {T,V}
-        @assert dimension(turns) == dimension(u"") "turns must be dimensionless"
-        @assert dimension(friction) == dimension(u"") "friction must be dimensionless"
-        @assert ustrip(turns) > 0 "turns must be positive"
-        @assert ustrip(friction) > 0 "friction must be positive"
-        new{T,V}(t, turns, friction)
+struct Bend{T<:AbstractQuantity} <: Structure
+    tube::Tube
+    radius::T
+    angle::T
+
+    function Bend(tube::Tube; radius::T, angle::T) where {T}
+        @assert dimension(radius) == dimension(u"m") "radius must have units of length"
+        @assert dimension(angle) == dimension(u"rad") "angle must have units of angle"
+        @assert ustrip(radius) > 0 "radius must be positive"
+        @assert angle > 0u"deg" "angle must be positive"
+        @assert angle < 180u"deg" "angle must be less than 180 degrees"
+        new{T}(tube, radius, angle)
     end
+end
 
-"""
+Elbow(tube::Tube; radius::AbstractQuantity) = Bend(tube, radius = radius, angle = π / 2u"rad")

test/flow.jl

@@ -15,4 +15,8 @@
         @test nusselt_number(fluid, tube) ≈ 5 atol = 1
     end
 
+    @testset "dean_number" begin
+        @test dean_number(fluid, Elbow(tube, radius = 10u"mm")) ≈ 1561 * √(2.7 / 20) atol = 1
+    end
+
 end

test/pressure_drop.jl

@@ -7,7 +7,7 @@
         @test pressure_drop(fluid, tube) ≈ 0.25u"bar" atol = 0.01u"bar"
         @test pressure_drop(Water(velocity = 3u"m/s", temperature = 262.15u"K"), Tube(diameter = 5u"mm", length = 1u"m")) ≈ 0.25u"bar" atol = 0.3u"bar"
     end
-    
+
     @testset "coil" begin
         @test pressure_drop(fluid, Helix(tube, diameter = 63.1u"mm", pitch = 2.6u"mm")) ≈ 0.56u"bar" atol =
             0.01u"bar"
@@ -18,4 +18,8 @@
               0.0017u"bar" atol = 0.0001u"bar"
     end
 
+    @testset "bend" begin
+        @test pressure_drop(fluid, Elbow(tube, radius = 10u"mm")) ≈ 0.7u"bar" atol = 0.1u"bar"
+    end
+
 end

test/structure.jl

@@ -25,4 +25,16 @@
         @test_throws AssertionError Valve(flow_rate = 10u"L/hr", flow_factor = 1.5u"m^2/hr")
     end
 
+    @testset "Bend" begin
+        t = Elbow(tube, radius = 10u"mm")
+        @test t.tube == tube
+        @test t.radius == 10u"mm"
+        @test t.angle == 90u"deg"
+
+        @test_throws AssertionError Elbow(tube, radius = 0u"mm")
+        @test_throws AssertionError Elbow(tube, radius = -10u"mm")
+        @test_throws AssertionError Bend(tube, radius = 10u"m", angle = 0u"deg")
+        @test_throws AssertionError Bend(tube, radius = 10u"m", angle = 180u"deg")
+    end
+
 end