8.18: Nomenclature DHLLDV Framework
- Page ID
- 32343
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ACv |
Coefficient homogeneous regime (1.3 by default) |
- |
|
Ap |
Cross section of the pipe |
m2 |
|
Ab |
Bed cross section |
m2 |
|
A1 |
Cross section restricted area above the bed |
m2 |
|
A2 |
Cross section of the bed |
m2 |
|
Cvb |
Bed volumetric concentration |
- |
|
Cvb,max |
Maximum bed volumetric concentration |
- |
|
CvB |
Concentration at the bottom of the pipe |
- |
|
CD |
Particle drag coefficient |
- |
|
Cvs |
Spatial volumetric concentration |
- |
|
Cvs,x |
Spatial volumetric concentration fines |
- |
|
Cvs,r |
Spatial volumetric concentration without fines |
- |
|
Cvr |
Relative concentration Cvs/Cvb |
- |
|
Cvr,ldv |
Relative concentration in bed at LDV |
- |
|
Cvt |
Transport or delivered volumetric concentration |
- |
|
Cx |
Durand & Condolios coefficient |
- |
|
CL |
Lift coefficient |
- |
|
d |
Particle diameter |
m |
|
d0 |
Particle diameter LDV transition region |
m |
|
dlim |
Limiting particle diameter pseudo liquid |
m |
|
DH |
Hydraulic diameter |
m |
|
DH,1 |
Hydraulic diameter restricted area above the bed |
m |
|
Dp |
Pipe diameter |
m |
|
Erhg |
Relative excess hydraulic gradient |
- |
|
Erhg,SB |
Relative excess hydraulic gradient in the sliding bed regime |
- |
|
Erhg,SF |
Relative excess hydraulic gradient in the sliding flow regime |
- |
|
Erhg,He |
Relative excess hydraulic gradient in the heterogeneous regime |
- |
|
Erhg,Ho |
Relative excess hydraulic gradient in the homogeneous regime |
- |
|
Erhg,HeHo |
Relative excess hydraulic gradient in the heterogeneous/ homogeneous flow regimes |
- |
|
Erhg,Cvt |
Relative excess hydraulic gradient with constant transport concentration |
- |
|
Erhg,Cvs=Cvt |
Relative excess hydraulic gradient with constant spatial concentration |
- |
|
f |
Factor determining sliding flow |
- |
|
fi |
Fraction of the ith fraction in PSD |
- |
|
F1,l |
Force due to shear stress between liquid and wall |
kN |
|
F12,l |
Force due to shear stress between liquid and bed |
kN |
|
F2,pr |
Force due to pressure gradient on the bed |
kN |
|
F2,sf |
Force due to sliding friction between bed and pipe wall |
kN |
|
F2,l |
Force due to shear stress of liquid in the pores with the pipe wall |
kN |
|
FL |
Durand limit deposit velocity Froude number |
- |
|
FL,s |
Durand limit deposit velocity Froude number, smooth bed |
- |
|
FL,ss |
Durand limit deposit velocity Froude number, small particles smooth bed |
- |
|
FL,vs |
Durand limit deposit velocity Froude number, smooth bed, very small particles |
- |
|
FL,r |
Durand limit deposit velocity Froude number, rough bed, large particles |
- |
|
FL,ul |
Durand limit deposit velocity Froude number, upper limit |
- |
|
FL,ll |
Durand limit deposit velocity Froude number, lower limit |
- |
|
FrDC |
Durand & Condolios Froude number |
- |
|
Frp |
Particle Froude number |
- |
|
g |
Gravitational constant (9.81) |
m/s2 |
|
h |
Thickness of bed at LDV |
m |
|
il, iw |
Hydraulic gradient of liquid (water) |
- |
|
im |
Hydraulic gradient of mixture |
- |
|
im,i |
Hydraulic gradient of ith fraction of PSD |
- |
|
im,ldv |
Hydraulic gradient mixture at LDV |
- |
|
im,SF |
Hydraulic gradient sliding flow |
- |
|
K |
Durand & Condolios constant (85) |
- |
|
ΔL |
Length of pipe segment considered |
m |
|
LR |
Lift ratio |
- |
|
m |
Mobilization factor homogeneous equation |
- |
|
mp |
Mass particle |
kg |
|
N |
Zandi & Govatos deposit criterion |
- |
|
Op |
Circumference pipe |
m |
|
O1 |
Circumference pipe in contact with liquid |
m |
|
O2 |
Circumference pipe in contact with bed |
m |
|
O12 |
Width of the bed |
m |
|
Δpl |
Pressure loss over pipeline length ΔL |
kPa |
|
Δpm |
Pressure loss mixture over pipeline length ΔL |
kPa |
|
r |
Position in pipe starting at the bottom |
- |
|
Re |
Reynolds number based on velocity difference liquid flow - bed |
- |
|
Rep |
Particle Reynolds number |
- |
|
Rsd |
Relative submerged density solids in carrier liquid |
- |
|
Rsd,x |
Relative submerged density solids in pseudo liquid |
- |
|
Shr |
Settling Velocity Hindered Relative |
- |
|
Srs |
Slip Velocity Relative Squared |
- |
|
Stk |
Stokes number |
- |
|
u* |
Friction velocity |
m/s |
|
u*,ldv |
Friction velocity at the LDV |
m/s |
|
v1 |
Average velocity above the bed |
m/s |
|
v2 |
Velocity of the bed |
m/s |
|
v12 |
Velocity difference bed interface (v1-v2) |
m/s |
|
vls |
Cross-section averaged line speed |
m/s |
|
vls,ldv |
Limit Deposit Velocity (LDV) |
m/s |
|
vls,t |
Line speed at tangent point slip ratio |
m/s |
|
vr |
Relative line speed vls/vls,ldv,max or vls/vsm |
m/s |
|
vsl |
Slip velocity (velocity difference between particle and liquid) |
m/s |
|
vsm |
Maximum LSDV according to Wilson |
m/s |
|
vt |
Particle terminal settling velocity |
m/s |
|
vth |
Hindered settling velocity |
m/s |
|
vthv |
Hindered settling velocity vehicle (Wasp model) |
|
|
vtv |
(Hindered) settling velocity in the vehicle (Wasp model) |
m/s |
|
vtv,ldv |
(Hindered) settling velocity in the vehicle (Wasp model) at LDV |
m/s |
|
X |
Fraction of fines |
- |
|
α |
Factor in left ratio |
- |
|
α |
Factor in concentration distribution | - |
|
αE |
Coefficient homogeneous equation |
- |
|
αp |
LDV factor |
- |
| αsm |
Factor concentration distribution |
- |
|
β |
Angle of bed with vertical |
rad |
|
β |
Power of Richardson & Zaki hindered settling factor |
- |
|
βsm |
Relation sediment diffusivity eddy momentum diffusivity |
- |
|
ε |
Critical particle diameter to pipe diameter ratio |
- |
|
ε |
Pipe wall roughness |
m |
|
φ |
Internal friction angle |
rad |
|
δ |
External friction angle |
rad |
|
δv |
Thickness viscous sub layer |
m |
|
λ1 |
Darcy Weisbach friction factor liquid to pipe wall |
- |
|
λ12 |
Darcy Weisbach friction factor bed interface |
- |
|
κ |
Von Karman constant (about 0.4) |
- |
|
κldv |
Slip ratio factor at the LDV |
- |
|
κC |
Concentration distribution constant |
- |
|
ρl, ρw |
Density of liquid (water) |
ton/m3 |
|
ρx |
Density of liquid including fines (pseudo liquid) |
ton/m3 |
|
ρm |
Mixture density |
ton/m3 |
|
ρs |
Density of solids |
ton/m3 |
| \(\ v_{\mathrm{l}}\) |
Kinematic viscosity carrier liquid |
m2/s |
| \(\ v_{\mathrm{x}}\) |
Kinematic viscosity pseudo liquid |
m2/s |
|
μl |
Dynamic viscosity liquid |
Pa·s |
|
μx |
Dynamic viscously liquid including fines (pseudo liquid) |
Pa·s |
|
μsf |
Sliding friction coefficient |
- |
| \(\ \tau_{1,\mathrm{l}}\) |
Shear stress liquid-pipe wall |
kPa |
| \(\ \tau_{2,\mathrm{sf}}\) |
Shear stress bed – pipe wall due to sliding friction |
kPa |
| \(\ \tau_{12,\mathrm{l}}\) |
Bed shear stress |
kPa |
|
ξ |
Slip ratio |
- |
|
ξ0 |
Slip ratio asymptotically for line speed zero |
- |
|
ξfb |
Slip ratio with fixed bed |
- |
|
ξldv |
Slip ratio at the LDV |
- |
|
ξHeHo |
Slip ratio in heterogeneous and homogeneous flow regimes |
- |
|
ξth |
Resulting slip ratio |
- |
|
ξt |
Tangent line slip ratio |
- |
|
ζ |
Bed fraction |
- |
|
ζ |
Smoothing factor lift ratio |
- |
|
FB |
Fixed bed regime |
- |
|
He |
Heterogeneous flow regime |
- |
|
Ho |
Homogeneous flow regime |
- |
|
LDV |
Limit Deposit Velocity |
- |
|
SB |
Sliding bed regime |
- |
|
SF |
Sliding flow regime |
- |