dryer-design

name	dryer-design
description	Dryer design — psychrometrics, drying rate (constant/falling rate periods), characteristic drying curve, spray dryer, fluidized bed, rotary drum, flash dryer, heat and mass balance, moisture content.
metadata	{"priority":7,"promptSignals":{"phrases":["dryer design","drying operation","spray dryer","fluidized bed dryer","drying rate","moisture content","psychrometrics"],"minScore":3}}

Dryer Design — Complete Skill

Psychrometrics (Moist Air Properties)

Humidity ratio (specific humidity): Y = m_water / m_dry_air = 0.622 × P_v / (P_total - P_v) [kg water/kg dry air]

Relative humidity: φ = P_v / P_v,sat(T) × 100%

Dew point temperature: T at which φ = 100% if air cooled at constant Y Wet-bulb temperature T_wb: equilibrium T of water surface evaporating into air Measured with psychrometer; used to determine drying capacity

Enthalpy of moist air: h = C_pa × T + Y × (h_fg,0 + C_pv × T) [kJ/kg dry air] C_pa = 1.006 kJ/kgK; C_pv = 1.805 kJ/kgK; h_fg,0 = 2501 kJ/kg at 0°C

Psychrometric chart: T_dry-bulb vs. Y; reads φ, T_wb, h, T_dew from any 2 known variables

Moisture Content Definitions

Wet-basis (wb): w_wb = m_water / m_wet_solid × 100%

Dry-basis (db): X = m_water / m_dry_solid [kg water / kg dry; dimensionless]

Conversion: X = w_wb / (1 - w_wb) w_wb = X / (1 + X)

Equilibrium moisture content X:* moisture in solid at equilibrium with drying air Critical moisture content X_c: marks end of constant rate period Residual moisture X_f: target final moisture content

Drying Rate Theory

Constant Rate Period (CRP)

Surface saturation: free moisture on surface; rate controlled by external heat/mass transfer Drying rate: N_c = h_c × (T_gas - T_wb) / h_fg [kg water / m² s] = k_g × (Y_wb - Y_gas) [mass transfer equivalent]

h_c = convective heat transfer coefficient [W/m²K] T_wb = wet bulb temperature of drying medium h_fg = latent heat of vaporization [kJ/kg] k_g = gas phase mass transfer coefficient [kg/m²s(unit Y)]

Duration of constant rate period: t_CRP = (X₀ - X_c) / N_c × (ρ_s × t_slab) [for thin slab; ρ_s = dry solid density]

Falling Rate Period (FRP)

Begins when X = X_c: surface becomes unsaturated; internal resistance controls Linear falling rate model: N = N_c × (X - X*) / (X_c - X*) [approximate; valid for many materials]

Drying time: t_FRP = [(X_c - X*) / N_c] × ln[(X_c - X*) / (X_f - X*)]

Diffusion-controlled (internal resistance): (X - X*) / (X₀ - X*) = (8/π²) × exp(-π² D_eff t / L²) [slab; first term approximation] D_eff = effective moisture diffusivity [m²/s]; typical 10⁻⁹ to 10⁻¹¹ m²/s for food/granules

Heat and Mass Balance

Water evaporation rate: ṁ_evap = ṁ_dry_solid × (X_in - X_out) [kg water/s]

Air flow rate required: ṁ_air = ṁ_evap / (Y_out - Y_in) [kg dry air/s] Y_in = humidity at inlet; Y_out = exit humidity (from energy balance)

Heat required: Q_dryer = ṁ_air × (h_air,out - h_air,in) + losses

Energy balance (adiabatic dryer): ṁ_air × (h_air,out - h_air,in) = ṁ_water × h_fg,T [water evaporated × latent heat at drying T]

Thermal efficiency: η_thermal = Q_evaporation / Q_total = ṁ_evap × h_fg / Q_heater

Dryer Types

Spray Dryer

Feed: liquid slurry or solution → atomized into droplet cloud → hot air dries droplets → powder Atomization: rotary atomizer (15,000–30,000 rpm disk; D_droplet = 50–200 μm) or pressure nozzle Residence time: 10–30 s (short → gentle; avoids heat damage) Applications: milk powder, pharmaceuticals, ceramics, detergents T_inlet: 150–300°C; T_outlet: 70–100°C; T_particle surface: approaches T_wb ≈ 40–70°C Outlet product: ρ_bulk = 100–500 g/L; D50 particle = 20–100 μm

Sizing: chamber diameter D from gas residence time τ = V_chamber / Q_gas; D ≈ √(4Q_gas τ / π L_chamber)

Fluidized Bed Dryer

Gas velocity: V_mf ≤ V_fluidization ≤ V_terminal [maintain bed in fluidized state]

Minimum fluidization velocity (Ergun at incipient fluidization): Ar = ρ_g (ρ_p - ρ_g) g d_p³ / μ² = Ar from chart → V_mf

Heat transfer in fluidized bed: h_bed ≈ 300–600 W/m²K (excellent)

Applications: granular products, crystals, food, pharmaceuticals; batch or continuous Advantage: uniform temperature; high h; gentle handling possible Disadvantage: gas needs to be filtered (entrainment); not suitable for sticky/agglomerating

Spouted bed: for larger particles (3–50 mm); central gas jet spouting

Rotary Drum Dryer

Horizontal rotating cylinder: solid material tumbles through hot gas stream Flight design: lifters lift and shower material through gas; maximize gas-solid contact L/D ratio: 4–10; slope: 2–5° (promotes material travel through) Rotation: 2–8 rpm; peripheral speed 0.3–0.5 m/s

Heat transfer: Q = U_vol × V_drum × LMTD [U_vol ≈ 30–100 W/m³K for direct-heated]

Applications: minerals, fertilizers, wood chips, sugar, coal; robust

Flash Dryer (Pneumatic)

Very short drying time: 1–10 s; dispersed solid in hot gas stream Applications: surface moisture only; heat-sensitive materials at moderate T V_gas: 15–30 m/s (suspends and transports material) Particle size: < 2 mm; dried then separated in cyclone/bagfilter

Freeze Dryer (Lyophilizer)

Sublimation: water frozen at -20 to -50°C; primary drying under vacuum (P < P_triple = 612 Pa) → ice → vapor Secondary drying: desorption of bound water at slightly higher T Applications: pharmaceuticals, biologics, coffee; preserves structure; expensive

Sublimation rate (primary drying): ṁ_ice = A_ice × k_m × (P_ice - P_chamber) / R_t [driven by partial pressure difference; R_t = thermal resistance]

Heat Recovery

Exhaust air energy: T_out = 70–100°C; φ = 70–90%; significant enthalpy Heat recovery options:

• Heat exchanger: preheat incoming air with exhaust (η_recovery = 40–60%)
• Heat pump dryer: condense water from exhaust; use heat pump to regenerate drying air; COP = 3–5
• Indirect heating + closed-loop: recirculate drying gas; add energy; condense moisture from bypass

Output

Provide: drying time [hr] (CRP + FRP durations), evaporation rate ṁ_evap [kg/hr], air flow rate ṁ_air [kg/hr], specific heat consumption (kJ/kg evaporated water), dryer type and size (volume or length × diameter [m]), inlet/outlet air conditions (T [°C], Y [kg/kg da], φ [%]), thermal efficiency η [%], and heat recovery recommendation.