Design, CFD validation, and process optimization of a cyclone integrated pilot scale vacuum spray dryer for functional food production

Abstract

This study presents the design, Computational Fluid Dynamics (CFD) validation, and Reynolds Stress Model (RSM) optimization of a cyclone separator integrated into a pilot-scale vacuum spray dryer for functional food production, comprising (Part A) cyclone design and validation, and (Part B) system-level process optimization. The cyclone was evaluated using Koch-Licht and Enliang-Yingmin theoretical models with gas properties corrected for vacuum operation (4 kPa, 90°C). CFD simulations employing the Reynolds Stress Model with Discrete Phase Model particle tracking characterized swirling flow and separation behavior. The Rosin-Rammler parameters for CFD inlet PSD (d̄ = 4.2 µm, n = 2.1) were estimated from nozzle specifications, while the collected powder PSD measured by laser diffraction yielded Dx(50) = 55.7 ± 0.87 µm (d̄ = 70.7 µm, R² = 0.984), indicating a ~17-fold size ratio between the collected coarse-powder fraction and the CFD inlet fine particle fraction. Experimental collection efficiency (97.8 ± 0.2%) agreed closely with the Koch-Licht prediction (98.38%). Using the correct vacuum gas density (0.039 kg/m³ at 4 kPa, 90°C), the CFD-predicted pressure drop (156 Pa) was consistent with the theoretical values (153–158 Pa); because pressure drop scales linearly with gas density, the close agreement among the three methods is preserved. For Part B, Central Composite Design optimized six quality responses with R² values of 0.756-0.987 and non-significant lack-of-fit. Optimal conditions (130 °C, 80 m³/h) produced powders with 3.9% moisture, 93% solid recovery, large particle size (~78 µm), and 89% solubility. Scanning Electron Microscopy (SEM) confirmed spherical morphology (16-56 µm). This integrated approach provides validated engineering data for cyclone design in vacuum spray drying of functional foods.

Keywords:
Cyclone separator; Collection efficiency; Particle size distribution; Rosin-Rammler model; Response Surface Methodology; Vacuum spray drying

Highlights

Experimental cyclone efficiency (97.8%) matched Koch-Licht prediction within 0.6 points

Neutral vane cut cyclone pressure drop by 53.1% (158 to 74 Pa) at 4 kPa vacuum

Optimal 130 °C and 80 m3/h gave 3.9% moisture, 93% recovery and 89% solubility

1 Introduction

Spray drying is one of the most widely used techniques for producing powdered foods, pharmaceuticals, and nutraceuticals because it rapidly transforms liquid feeds into free-flowing powders with controlled particle characteristics (Gharsallaoui et al., 2007; Masters, 1991; Vehring, 2008). In its sub-atmospheric variant vacuum spray drying, it can be noted that the reduced operating pressure lowers the boiling point of the continuous phase, enabling efficient drying at lower temperatures and preserving heat-sensitive bioactive compounds such as phenolics, flavonoids, and antioxidants that are abundant in functional food ingredients (Chegini & Ghobadian, 2005; Woo & Bhandari, 2013). This is particularly attractive for Thai agricultural ingredients including chrysanthemum (Chrysanthemum morifolium (Ramat.) Hemsl.), fingerroot (Boesenbergia rotunda (L.) Mansf.), ginger (Zingiber officinale Roscoe), and Indian gooseberry (Phyllanthus emblica L.), which contain valuable bioactive compounds (Jolad et al., 2004; Kaur & Kapoor, 2002; Liu et al., 2008; Thaipong et al., 2006); on the other hand, they are thermally labile under conventional atmospheric spray drying (Pinto et al., 2021; Sablani, 2006).

Cyclone separators are the primary device for capturing dried powders from the exhaust gas stream of a spray dryer (Cortés & Gil, 2007; Hoffmann & Stein, 2008; Nebra & Betta, 2000; Silva & Nebra, 1997); however, their turbulent vortex flow makes efficiency prediction challenging (Elsayed & Lacor, 2010; Zhao et al., 2006). Two classical semi-empirical (SE) frameworks, the Koch-Licht model (Koch & Licht, 1977) and the Enliang-Yingmin model (Enliang & Yingmin, 1989), have been extensively validated at atmospheric pressure but, to the best of our knowledge, these two models have not been systematically compared against Computational Fluid Dynamics (CFD) simulation and experimental data for a cyclone operating under vacuum conditions, thus being a representative of emerging spray drying technology. The extensibility of these half-century-old atmospheric correlations to operations at reduced pressure (4 kPa), where gas density falls approximately 25-fold, mean free path rises approximately 250-fold, and Cunningham slip corrections become significant for sub-10 µm particles, therefore it remains an open question that is directly relevant to cyclone design and to pilot-to-industrial scale-up of vacuum spray drying systems. Response Surface Methodology (RSM) with Central Composite Design is the standard tool for multifactor process optimisation in such systems (Bas & Boyaci, 2007; Bezerra et al., 2008), but its coupling with simultaneous cyclone validation has not previously been reported for vacuum operation.

The present study contributes four novel elements to address these gaps. First, it reports the first simultaneous theoretical (Koch-Licht and Enliang-Yingmin), CFD (Reynolds Stress / Discrete Phase Model) and experimental study of a cyclone separator operating at 4 kPa absolute pressure for food powder applications, in which the three methods agree within 0.6 percentage points on the global collection efficiency. Indeed, it is noted that the validation here is limited to global performance indicators (overall collection efficiency and pressure drop); however, the internal velocity fields, vortex structure and local particle concentrations predicted by CFD were not experimentally measured, so the CFD model is considered partially validated (Sections 2.6.3, 3.1 and 3.8). Second, a dimensional group analysis (Section 2.3) rigorously demonstrates that the classical atmospheric cyclone models remain predictive at subatmospheric pressure once gas density and Cunningham slip corrections are incorporated, thereby extending the applicability of these half-century-old correlations to the emerging vacuum spray drying technology. Third, a six response Central Composite Design RSM optimisation of the vacuum spray dryer for Thai functional food ingredients could be presented, yielding validated quadratic models for moisture content, product yield, particle size, bulk density, water solubility, and feed rate with adjusted R² in the range 0.79-0.99. Fourth, it could provide an internally consistent, pilot-scale engineering dataset geometry, operating window, regression models, and full GUM uncertainty budget for a single built pilot system, providing a reference baseline for technology transfer, subject to re-validation at different scales, without the reliability penalties associated with combining incompatible datasets from disparate sources. The two subsystems studied here (cyclone separation in Part A and drying optimisation in Part B) are physically coupled: the product yield maximised by Reynolds Stress Model (RSM) is arithmetically bounded by the cyclone collection efficiency validated in Part A, and the particle size distribution entering the cyclone is itself determined by the operating parameters optimised in Part B (Section 2.9). A study of either subsystem in isolation would, therefore, be incomplete for the technology-transfer objective of this work.

The specific objectives of this work were to: (1) design and construct a cyclone separator with geometric parameters suited to sub-atmospheric operation; (2) compare theoretical efficiency predictions from the Koch-Licht and Enliang-Yingmin models with CFD and gravimetric experiments at 4 kPa; (3) optimise six process quality responses using RSM with Three-dimensional surface and contour visualisation; and (4) validate overall system performance through encapsulation of Thai functional ingredients at the as-built optimal operating conditions.

2 Materials and methods

2.1 Vacuum spray dryer system design

A pilot scale vacuum spray dryer was designed and constructed in collaboration with Doi Kham Food Products Co., Ltd. (The third Royal Factory, Thailand). The system comprised: (a) a heat generation unit utilizing superheated steam combined with 50 kW; (b) a drying chamber fabricated from SUS 304 stainless steel with 4 mm wall thickness; (c) a high-pressure spray nozzle system (full cone type, 13.8 MPa) driven by a 5.6 kW motor; (d) a cyclone separator unit; and (e) a vacuum generation system using a liquid ring vacuum pump (11.2 kW, 300 m³/h capacity).

2.2 Cyclone separator design and specifications

The cyclone separator was designed with the geometric specifications shown in Table 1. All dimensions were converted to SI units for analysis. The cyclone was fabricated from 2 mm thick SUS 304 stainless steel. The complete design parameters, including gas operating conditions and particle data, are documented in Supplementary Table 1.

Table 1
Cyclone separator geometric parameters.

Parameter	Symbol	US Customary	SI Units
Barrel diameter	D	1.34 ft	0.408 m
Inlet height	A	0.375 in	9.53 mm
Inlet width	B	4.2 in	106.7 mm
Gas outlet length	S	1.5 ft	0.457 m
Gas outlet diameter	De	7.87 in	200 mm
Cylinder height	H	1.83 ft	0.558 m
Overall height	H	5.51 ft	1.68 m
Dust outlet diameter	B	4.5 in	114.3 mm
Natural vortex length	L	8.26 ft	2.52 m
Volumetric flow rate	Q	106 acfm	0.050 m3/s
Gas density	Ñg	0.0024 pcf	0.039 kg/m3
Temperature	T	194°F	90°C

Operating conditions were maintained at: volumetric gas flow rate (Q) = 0.050 m³/s (3.0 m³/min); gas density (ρ_g) = 0.039 kg/m³ (calculated from the ideal gas law at 4 kPa absolute and 90°C); gas viscosity (μ) = 0.021 mPa·s (2.1 × 10⁻⁵ Pa·s, from Sutherland’s equation at 90°C); operating temperature = 90°C. Particle characteristics included an input log-mean diameter of 80 µm with a calculated effective diameter of 11.9 µm after regression fitting to the particle size distribution.

2.3 Theoretical efficiency calculations

2.3.1 Koch-Licht Model (1977)

The collection efficiency was calculated using the semi-empirical correlation developed by Koch & Licht (1977). Calculated parameters included: inlet velocity = 49.2 m/s; vortex exponent (n+1) = 1.563; cyclone constant K_c = 0.541; saltation velocity ratio = 1.94; corrected vortex length = 1.22 m; and dimensionless parameter G = 116,697.

2.3.2 Enliang-Yingmin Model (1989)

This alternative approach incorporates a modified treatment of particle motion in the vortex field (Enliang & Yingmin, 1989). Calculated parameters included: inlet velocity = 48.6 m/s; vortex exponent (1-n) = 0.322; angular velocity parameter θ = 1929.2; wall radius r_w = 0.204 m; wall tangential velocity u_w = 3.60 m/s; and radial diffusion coefficient D_r = 9.76 × 10⁻⁴ m²/s.

2.3.3 Gas property corrections for vacuum conditions

Both theoretical models were originally developed for atmospheric conditions. In the present study, all gas properties were rigorously corrected for the actual operating conditions (4 kPa absolute, 90 °C inlet temperature). Gas density (ρ_g = 0.039 kg/m³) was calculated from the ideal gas law (Çengel & Boles, 2015) at the operating pressure, representing an approximately 25-fold reduction relative to the density of air at the same temperature under atmospheric pressure (~0.97 kg/m³ at 90 °C; ~1.21 kg/m³ at 20°C). This value is the thermophysical property used consistently throughout the present work and corresponds to the vacuum entry of Table 2; an earlier inconsistency in which a US customary value was mislabelled has been corrected in Table 1, Table 3 and Supplementary Tables 1 -3. Dynamic viscosity (µ = 2.1 × 10⁻⁵ Pa·s) was obtained from Sutherland's equation (Sutherland, 1893) at 90°C. At 4 kPa, the mean free path of air increases significantly to approximately 16.8 µm (compared to ~0.066 µm at atmospheric pressure), resulting in Knudsen numbers (Kn = 2λ/d_p) well above unity for all particles below ~30 µm (Kn ≈ 6.7 at d_p = 5 µm). Consequently, a Cunningham slip correction factor (C_c=1+ Kn[1.257 + 0.400exp(-1.10/Kn)]) was incorporated into particle drag calculations for the CFD simulations to account for non-continuum effects on submicron and fine particles. The Stokes number, characterizing particle inertia, also increases under vacuum due to extended particle relaxation time. Despite the original atmospheric development of both models, the fundamental separation mechanisms the balance between centrifugal force and aerodynamic drag force remain physically valid when these corrected gas properties are used as inputs. The close agreement between the corrected Koch-Licht prediction (98.38%) and experimental measurement (97.8%) validates this approach.

Table 2
Dimensionless group comparison between atmospheric and vacuum cyclone operation at 90 °C (dp = 5 µm reference particle).

Group / property	Atmospheric (101 kPa)	Vacuum (4 kPa)	Implication
Gas density 駁 (kg m−3)	0.972	0.039	~25× reduction
Gas viscosity ? (Pa穝)	2.1 × 10−5	2.1 × 10−5	Pressure-independent
Mean free path ? (祄)	0.066	16.8	~250× increase
Reynolds number Re	≈9.3 × 105	≈3.7 × 104	Both fully turbulent
Knudsen number Kn (dp = 5 µm)	0.026	6.7	Slip correction required
Cunningham factor Cc	1.03	≈11.0	Applied to Stokes drag
Particle relaxation 魀 (s)	≈4.0 × 10−5	≈4.2 × 10−4	~10× longer
Stokes number Stk (dp = 5 µm)	≈0.085	≈0.90	Inertia-dominated regime retained

Table 3
CFD Simulation parameters and boundary conditions.

Parameters	Value/Setting
Turbulence model	Reynolds Stress Model (RSM)
Mesh type	Hybrid (Hexahedral + Tetrahedral)
Number of cells	500,000
Inlet velocity	49.2 m/s
Inlet angle	45° (tangential)
Operating temperature	90°C (363 K)
Gas density	0.039 kg/m3
Gas viscosity	2.1 × 10−5 Pa·s
Particle density	550 kg/m3
Particle size range	0.1-20 µm (Rosin-Rammler)
Convergence criterion	Residuals < 10−5

2.3.4 Dimensional justification of atmospheric cyclone models under vacuum

To rigorously justify the applicability of the Koch-Licht and Enliang-Yingmin models at 4 kPa absolute pressure, a complete dimensionless-group analysis was performed comparing atmospheric and vacuum conditions. The results are summarised in Table 2. The analysis confirms that, when the Cunningham slip correction (Cc) is applied to the Stokes drag term, the fundamental separation mechanism, that is, the balance between centrifugal inertia and aerodynamic drag, is preserved under sub-atmospheric operation.

2.3.5 Four physical conclusions follow from this analysis

First, the Reynolds number remains an order of magnitude above the conventional turbulent transition threshold (Re ≈ 3.7 × 10⁴ at 4 kPa), indicating that the turbulent vortex flow regime assumed by both theoretical models is maintained under the sub-atmospheric operating condition. Second, rarefaction effects become important for the finer particles. Using Kn = 2λ/d_p, the Cunningham slip correction factor was calculated as Cc = 1 + Kn[1.257 + 0.400 exp(-1.10/Kn)] and incorporated into the Stokes-drag term of both theoretical models and the CFD Discrete Phase Model (Davies, 1945). Third, although the gas density decreases substantially under vacuum, the Cunningham correction reduces the effective drag and increases the particle relaxation time by approximately one order of magnitude, particularly for the smallest particles. Consequently, the calculated Stokes numbers remain above the model specific cut off value (Stk₅₀ ≈ 0.05), supporting inertia-dominated particle separation. This analysis qualitatively explains the slightly higher than expected separation efficiency observed experimentally under vacuum. Fourth, after incorporating the absolute pressure-dependent gas properties and slip correction, the Koch-Licht model predicted a collection efficiency of 98.38%, compared with the experimental value of 97.8 ± 0.2%, corresponding to a difference of only 0.58 percentage points. The pressure-dependent treatment adopted here is consistent with previous cyclone studies showing that operating pressure and the resulting gas properties govern the internal flow field and pressure profiles (Shi et al., 2006), and with recent computational work showing that dimensionless cyclone performance, pressure drop, cut size and separation slope scale systematically with the Reynolds number (Misiulia et al., 2024). The extension of the semi-empirical models to the present sub-atmospheric condition, including the combined gas-density and Cunningham slip corrections, was implemented in the present study.

2.4 Heat transfer mechanism in vacuum spray drying

In vacuum conditions, the reduction in ambient pressure modifies the balance among the heat transfer mechanisms compared to atmospheric operation. Forced convection from the heated carrier gas remains a significant pathway to the dispersed spray droplets, but the reduced gas density lowers the convective heat transfer coefficient and, for sub-micrometric to micrometric droplets, brings the heat transfer boundary layer toward the rarefied gas (Knudsen) regime, where the effective Nusselt number is further reduced. Under these conditions, the relative contribution of thermal radiation from the heated chamber walls and internal surfaces to the spray droplets becomes non-negligible and must be explicitly accounted for in the dryer energy balance. The radiative component is governed by the Stefan-Boltzmann law (Incropera et al., 2011):

$$Q=\epsilon \sigma A\left(T_1^4-T_2^4\right)$$ (1)

where Q is the heat transfer rate (W), ε is the emissivity of the surface (dimensionless), σ is the Stefan-Boltzmann constant (5.67 × 10⁻⁸ W/m²K⁴), A is the surface area (m²), and T₁ and T₂ are the absolute temperatures of the heat source and receiving surface, respectively (K).

A Stefan-Boltzmann analysis based on Equation 1, developed for representative droplet-scale conditions of the present system and detailed in the Supplementary Material (Section S2), indicates that the radiative contribution to the total droplet heat flux increases from approximately 12% to 17% under equivalent atmospheric pressure conditions to approximately 25% to 30% at the operating vacuum of 4 kPa, under near thermal equilibrium conditions characteristic of the downstream drying zone. This qualitative shift toward a greater relative radiative contribution at reduced pressures is consistent with experimental and theoretical studies of vacuum drying (Abdizhapparova et al., 2022; Perré et al., 2004). The enhanced radiative component enables more uniform heating of spray droplets while operating at lower bulk temperatures, which is advantageous for preserving heat-sensitive bioactive compounds (Mujumdar, 2014; Parikh, 2015). It could be noted that these radiative-fraction ranges are related to an order of magnitude engineering estimates obtained from a Stefan-Boltzmann analysis combined with standard convective correlations (Supplementary Material, Section S2), and were not measured directly in the present pilot system. The associated mechanistic statements should therefore be read as theoretically motivated rather than as experimentally established, and a full conjugate heat transfer characterisation is left to future work.

2.5 Particle size distribution and Rosin-Rammler Model

The particle size distribution (PSD) is central to understanding cyclone separator performance. Note on CFD inlet PSD: The Rosin-Rammler parameters used as the CFD boundary condition (d̄ = 4.2 µm, n = 2.1) represent an engineering estimate derived from nozzle specifications and literature correlations rather than a directly measured distribution. Direct in-situ measurement of the cyclone-inlet PSD under vacuum operation (4 kPa) was not technically feasible with the current pilot-scale setup. This assumption constitutes a recognised limitation of the CFD validation, and its implications for the generality of the simulation results are discussed in Sections 3.1 and 3.8. In cyclone operation, three distinct PSD domains must be distinguished: (i) the inlet PSD, representing the full spectrum of droplet/particle sizes entering the cyclone from the spray drying chamber (~1-200 µm); (ii) the collected PSD, consisting predominantly of coarse particles above the cut size (d₅₀, defined as the particle diameter at which the grade efficiency curve equals 50%, meaning that half of the particles of that size are collected and half escape) that are centrifugally separated into the dust bin; and (iii) the exhaust PSD, comprising fine particles below the cut size that escape through the vortex finder. CFD simulations and theoretical separation models target the fine-particle region around the cut size primarily, as this determines the grade efficiency curve, while the final product powder reflects the coarser fraction that is efficiently captured.

For CFD simulation of cyclone separator performance, the inlet particle size distribution representing the fine particle fraction entering the cyclone from the drying chamber was characterised using Rosin-Rammler parameters (the Rosin-Rammler distribution is a two-parameter cumulative mass fraction model widely used to characterise the spread of particle or droplet sizes in polydisperse populations) d̄ = 4.2 µm and n = 2.1 (corresponding to d50 ≈ 3.5 µm). It is important to distinguish between the primary atomised spray produced at the nozzle and the fine particle distribution that actually reaches the cyclone after traversing the drying chamber. The spray dryer employs a full cone pressure (hydraulic) nozzle (1.0 mm orifice diameter, 60° cone angle) atomising a pre-heated feed solution of 20% w/w maltodextrin (DE 10) at 50 °C at a feed pressure of 35 bar (3.5 MPa), for which the feed viscosity μ ≈ 6 mPa·s, surface tension σ ≈ 56 mN m⁻¹ and density ρL ≈ 1080 kg m⁻³ are representative values from the food-engineering literature (Lefebvre & McDonell, 2017). Under these pressure-atomisation conditions, Lefebvre's correlation for full-cone simplex nozzles predicts a primary spray Sauter mean diameter (d32) in the range of approximately 40-90 µm (Lefebvre & McDonell, 2017), consistent with the standard Lefebvre pressure swirl scaling (d32 ∝ ΔP-0.4) for the elevated feed pressure used in this study. This primary spray is considerably coarser than the cyclone inlet PSD used in the CFD simulation because the drying chamber performs a size classification function between the nozzle and the cyclone. Specifically, (i) drying shrinkage reduces droplet diameters by approximately 40% for the 20% w/w solids feed (characteristic volume reduction by a factor of ~5), yielding dried-particle diameters in the 24-53 µm range for the principal fraction of the spray, consistent with the 16-56 µm particle size range observed by scanning electron microscopy (SEM) of the collected powder; (ii) gravitational sedimentation and inertial wall impaction capture the majority of these coarse particles on the chamber walls and bottom outlet, where they constitute the primary product stream; and (iii) only the fine sub-population of particles (nominally below ~10 µm) that remains entrained in the exhaust gas reaches the cyclone through the chamber exit port, where it is separated by the centrifugal action characterised in this CFD analysis. The Rosin-Rammler parameters d̄ = 4.2 µm and n = 2.1 were therefore adopted as an engineering estimate of this fine fraction rather than as a prediction of the primary atomised spray. Direct in-situ measurement of this cyclone inlet PSD under vacuum operation was not technically feasible in the pilot system. The robustness of the Part A cyclone validation outcome to this estimate is nonetheless supported on theoretical grounds: the cyclone cut size (dc, defined as the Stokes diameter at which the grade efficiency curve reaches 50%) predicted by the Koch-Licht model for the present cyclone geometry and operating conditions is approximately 1.5 µm (Section 3.2), and the grade efficiency curve rises sharply through the cut size region and approaches the near unity collection plateau (i.e., the near 100% collection efficiency region reached for particles substantially larger than the cut size, where virtually all particles are captured regardless of further size increase) for particles above roughly 3 dc ≈ 4.5 µm. Because the Rosin-Rammler distribution with d̄ = 4.2 µm and n = 2.1 places approximately 85% of the mass above 3 dc and only 5-8% below the cut size, the total collection efficiency predicted by the Discrete Phase Model is dominated by the high-plateau region of the grade curve and is therefore only weakly sensitive to the precise form of the inlet distribution within the physical uncertainty of the engineering estimate. This theoretical argument is consistent with the agreement between the Koch-Licht prediction (98.38%) and the experimental measurement (97.8 ± 0.2%) within 0.6 percentage points, which would not be expected if the inlet PSD assumption dominated the predicted efficiency. The assumed distribution therefore serves as a physically reasonable seed population for the Discrete Phase Model rather than as an a priori prediction of the collected powder PSD, which is measured directly and reported separately (Section 2.5; Supplementary Table 4). The Rosin-Rammler functional form is appropriate for this fine fraction particulate population because it is the canonical mass distribution model for polydisperse sprays and powders and because its two-parameter form admits a smooth extrapolation into the sub-micrometre tail that governs cyclone slip (Crowe et al., 2011; Oakley, 2004). The model describes the cumulative mass fraction of particles larger than diameter d:

$$Y_{\text{d}}=\exp \left[-{(d/\overline{d})}^n\right]$$ (2)

where Yd is the mass fraction of particles with diameter greater than d, d̄ is the characteristic diameter (µm), and n is the spread parameter (dimensionless). The estimated parameters (d̄ = 4.2 µm, n = 2.1; corresponding to d50 ≈ 3.5 µm) obtained as described above, representing the estimated fine-particle fraction entering the cyclone from the drying chamber, were subsequently used in the Discrete Phase Model (DPM) simulations with OpenFOAM to predict grade efficiency curves for both theoretical models (Crowe et al., 2011; Chen et al., 2018; Yohana et al., 2018).

Collected Powder Particle Size Distribution. The PSD of the collected powder (from the cyclone dust bin) was measured by laser diffraction using a Malvern Mastersizer (Malvern Instruments Ltd., UK) in accordance with ISO 13320:2020 (International Organization for Standardization, 2020). Six replicate measurements were performed on maltodextrin-encapsulated powder samples. The results yielded: Dx(10) = 24.6 ± 0.32 µm, Dx(50) = 55.7 ± 0.87 µm, Dx(90) = 246 ± 28.9 µm, with relative standard deviations (RSD) of 1.30%, 1.57%, and 11.8%, respectively, indicating excellent measurement reproducibility. The span [(Dx(90) -Dx(10))/Dx(50)] was 3.97, indicating a broad distribution with a bimodal character a primary mode at ~50-55 µm and a secondary shoulder extending to ~400-800 µm attributed to post-collection agglomeration and residual moisture bridging. Rosin-Rammler fitting of the collected powder PSD yielded d̄ = 70.7 µm and n = 1.67 (R² = 0.984, nonlinear least-squares regression), with the fitted d₅₀ = 56.8 µm closely matching the measured Dx(50) = 55.7 µm. The collected powder Rosin-Rammler size parameter (d̄ = 70.7 µm) is approximately 17 times larger than the CFD inlet value (d̄ = 4.2 µm), which is physically consistent: the CFD simulation targets the fine-particle fraction around the cyclone cut size, while the collected powder represents the efficiently captured coarse fraction plus particles that have undergone agglomeration during collection. These measurements are summarized in Supplementary Table 4, and the corresponding probability density distribution is plotted in Supplementary Figure 1. Isopropanol was used as the dispersant medium, and samples were ultrasonicated for 60 seconds before measurement to ensure complete dispersion. The complete Rosin-Rammler parameter comparison between CFD inlet PSD and collected powder PSD is presented in Supplementary Table 5.

2.6 Computational Fluid Dynamics (CFD) simulation

Computational Fluid Dynamics (CFD) simulations were performed to analyze the flow field characteristics and particle separation mechanisms within the cyclone separator. The simulations were conducted using OpenFOAM with the Reynolds Stress Model (RSM) turbulence model, which is recommended for strongly swirling flows in cyclone separators (Chen et al., 2018; Yohana et al., 2018).

2.6.1 Geometry and mesh generation

The cyclone geometry was created based on the design specifications presented in Table 1. The computational domain was discretized using a hybrid mesh consisting of hexahedral elements in the cylindrical barrel section and tetrahedral elements in the conical section. A mesh independence study was conducted with three mesh densities: coarse (250,000 cells), medium (500,000 cells), and fine (1,000,000 cells). The medium mesh was selected as it provided grid independent results with less than 2% deviation in predicted pressure drop compared to the fine mesh. Near-wall refinement was applied with y⁺ < 5 to accurately resolve the boundary layer.

2.6.2 Boundary conditions

The following boundary conditions were applied to the CFD model:

Inlet: Velocity inlet with uniform velocity of 49.2 m/s normal to the inlet plane. The inlet angle was set at 45° tangential to the barrel wall to induce swirling flow. Turbulence intensity was specified as 5% with hydraulic diameter of 114.3 mm.

Gas outlet (Vortex finder): Pressure outlet with gauge pressure of 0 Pa and backflow turbulence intensity of 5%.

Particle outlet (Dust bin): Escape boundary condition allowing collected particles to exit the computational domain.

Walls: No-slip condition with standard wall functions. Particle-wall interaction was set as "trap" for the dust bin and "reflect" for other walls with coefficient of restitution of 0.9.

2.6.3 Solver settings and particle tracking

The pressure-based solver with SIMPLE algorithm was employed for pressure velocity coupling. Spatial discretization schemes included second-order upwind for momentum, turbulent kinetic energy, and Reynolds stresses. The simulation was considered converged when all residuals fell below 10⁻⁵ and monitored quantities (pressure drop, velocity at outlet) reached steady state.

Particle tracking was performed using the Discrete Phase Model (DPM) with one-way coupling, assuming dilute particle concentration (Crowe et al., 2011). The particle size distribution followed the Rosin-Rammler model with mean diameter d̄ = 4.2 µm and spread parameter n = 2.1 (Section 2.5). A total of 10,000 particles were injected from the inlet surface, and collection efficiency was calculated as the ratio of particles trapped at the dust bin to total injected particles. It should be noted that the present CFD analysis is validated against global performance metrics overall collection efficiency and pressure drop which constitute the primary engineering design parameters. Direct experimental validation of internal velocity fields, vortex structure, or local particle concentration distributions was not performed and remains a subject for future work using non-invasive optical diagnostics.

2.7 Response surface methodology optimization

A Central Composite Design (CCD) was employed to investigate the effects of two independent variables on product quality responses. The factors studied were: X₁ = hot air flow rate (100-240 m³/h) and X₂ = inlet air temperature (100-170°C). A total of 13 experimental runs including 5 center points were conducted. Response variables included: moisture content (%, wet basis); product yield (%); particle size (µm); bulk density (kg/m³); water solubility index (%); and liquid feed rate (L/h). The CCD consisted of 4 factorial points (±1 levels), 4 axial (star) points (±α = ±1.414), and 5 center point replicates for estimation of pure error and model curvature, totaling 13 experimental runs. All runs were performed in randomized order.

Data were analyzed using second-order polynomial regression to develop predictive models:

$$Y={\beta }_0+{\beta }_1{X}_1+{\beta }_2{X}_2+{\beta }_{11}{X}_1^2+{\beta }_{12}{X}_1{X}_2+{\beta }_{22}{X}_2^2$$ (3)

where Y is the predicted response, β₀ is the intercept coefficient, β₁ and β₂ are linear coefficients, β₁₁ and β₂₂ are quadratic coefficients, and β₁₂ is the interaction coefficient. Model adequacy was evaluated by coefficient of determination (R²), adjusted R², and lack-of-fit tests. Three-dimensional response surface plots and two-dimensional contour maps were generated to visualize the effects of process variables on each quality attribute and to identify optimal operating regions.

2.8 Cyclone collection efficiency measurement

Cyclone collection efficiency was determined gravimetrically following the rigorous four-step protocol described below. The protocol was specifically designed to account for the challenges of vacuum operation: (a) vacuum system leakage, (b) moisture related mass corrections, (c) quantification of fines escaping the cyclone, and (d) propagation of measurement uncertainty through the complete mass balance.

2.8.1 Vacuum system leakage testing

Prior to every experimental run, the complete drying chamber cyclone vacuum system was subjected to a pressure decay leak test. The system was evacuated to the target operating pressure (4 kPa absolute), isolated from the vacuum pump, and the rate of pressure rise was monitored for 10 min using an MKS Baratron 626B capacitance manometer (full scale 10 kPa, accuracy ± 0.15% of reading). A leak rate < 0.5 kPa min⁻¹ was required before proceeding; runs exceeding this criterion were aborted and flanged connections re-sealed with silicone vacuum service gaskets. During experimentation, the liquid-ring vacuum pump maintained 4.0 ± 0.2 kPa for the full duration of each run.

2.8.2 Moisture correction procedure

All gravimetric determinations were corrected to a dry basis. Moisture content of the feed slurry, the collected powder, and the HEPA filter retentate were measured by oven drying at 105 °C for 24 h (Association of Official Analytical Chemists, 2005, Method 925.10). Mass on a dry basis was computed as m_dry = m_wet × (1 - w), where w is the mass fraction moisture. Dry basis correction is essential under vacuum because the flash evaporation regime produces a significant solids mass flux to the cyclone while water vapour exits with the vent gas, such that wet and dry basis efficiencies can differ by 3-7 percentage points.

2.8.3 HEPA filter fines quantification

Fines escaping the cyclone vortex finder were captured on a downstream absolute HEPA cartridge (Pall Emflon HTPFR, rated 99.999% at 0.3 µm). The cartridge was conditioned in a silica-gel desiccator for ≥ 24 h before and after each run and weighed on a Sartorius CPA225D analytical balance (readability 0.1 mg). Measured retentate mass per run was 36-76 g (dry basis), corresponding to the fines fraction 1.9-3.8% of the feed solids. The collection efficiency was computed from the dry basis mass balance: η = m_collected / (m_collected + m_fines) × 100%. Triplicate runs yielded η = 97.8 ± 0.1% (mean ± SD, n = 3).

2.8.4 Uncertainty budget (GUM methodology)

A complete uncertainty budget was constructed following the Guide to the Expression of Uncertainty in Measurement (GUM; Joint Committee for Guides in Metrology, 2008). The dominant sources and their Type-B evaluations (assuming rectangular distributions with coverage factor divided by √3) were: balance calibration u(m) = ± 0.06 mg (negligible on ~30 g mass); repeatability of triplicate runs u_rep(η) = ± 0.10%; moisture determination u(w) = ± 0.05% mass fraction (propagated as ± 0.03% on η); vacuum-pressure variation u(P) = ± 0.12 kPa (propagated via gas-density correction as ± 0.04% on η); and HEPA retention correction u(η_HEPA) = ± 0.02%. Combining these contributions in quadrature yielded a combined standard uncertainty u_c(η) = ± 0.12%, and an expanded uncertainty U(η) = k × u_c = ± 0.24% at the 95% confidence level (k = 2). The final reported result is therefore η = 97.8 ± 0.2%.

2.8.5 Product yield calculation

Product yield for the RSM experiments (Part B) was calculated as: Y(%) = [m_powder,wet / (V_feed × C_solids)] × 100, where m_powder,wet is the mass of powder collected from the cyclone dust bin (weighed as-is, without dry basis correction), V_feed is the volume of feed solution processed (L), and C_solids is the feed solids concentration (g/L) determined once per batch by refractometry. It should be noted that, unlike the collection efficiency measurement (Section 2.8.2) which applied dry basis correction, the RSM yield determination did not correct the collected powder mass to dry basis prior to calculation. The weighed powder therefore included hygroscopic moisture re-absorbed during handling. Additionally, the peristaltic pump was calibrated gravimetrically before each experimental campaign by collecting and weighing the delivered feed over a timed 5-minute interval at each setpoint. Maximum deviation between gravimetric check and pump setpoint was ±3.2%.

A representative solids mass balance for the centre-point experiment (Run 9) is provided to demonstrate system closure: feed solids input = 2,800 g; cyclone dust bin collection = 2,742 g (wet basis); HEPA filter retentate = 58 g (dry basis); chamber wall deposits = not quantified (limitation). The mass balance closure on a wet-collected basis is (2,742 + 58)/2,800 = 100.0%, demonstrating that the system is materially closed when wall deposits are excluded. A schematic of the complete mass balance of the cyclone-integrated vacuum spray-drying system is given in Supplementary Figure 2.

2.9 Physical coupling between cyclone Validation (Part A) and RSM Optimisation (Part B)

Three physical couplings unify the two subsystems investigated in this study and justify their integrated treatment within a single manuscript: (i) product-yield coupling the overall system yield Y_system = Y_drying × η_cyclone, so the RSM-optimised yield is arithmetically bounded by the cyclone collection efficiency validated in Part A; (ii) PSD coupling the inlet PSD entering the cyclone is determined by the atomisation conditions (nozzle, pressure, feed rate) that constitute the RSM factors, so the cyclone grade efficiency and the RSM operating window are not independent; and (iii) residence-time coupling the vacuum level and airflow rate jointly set both the cyclone tangential velocity (Part A) and the drying-chamber residence time that governs moisture and bioactive retention (Part B). Consequently, Part A establishes the separation boundary condition, and Part B optimises the production conditions within that boundary. The results are organised accordingly: Sections 3.1-3.2 (Part A) present the cyclone separator validation; Sections 3.3-3.7 (Part B) address the RSM optimisation of the complete system; and Section 3.8 consolidates the limitations of the integrated approach.

2.10 Data reporting basis

All response variables are reported as directly measured in conventional engineering units; no scale normalisation was applied. The complete per-run measured values for all 13 runs are provided in Supplementary Table 6, and the quadratic regression models presented in Section 3.3 were obtained by direct least-squares regression on these measured values, so that the analysis can be reproduced independently.

3 Results and discussion

3.1 Cyclone separator efficiency: theoretical vs. experimental

Table 4 presents the comparison of cyclone separator efficiency predictions from the two theoretical models against experimentally measured values. The Koch-Licht model predicted an overall collection efficiency of 98.38%, while the Enliang-Yingmin model yielded a lower prediction of 88.95%. The experimental measurement demonstrated an overall efficiency of 97.8 ± 0.2%, agreeing closely with the Koch-Licht prediction (within 0.6 percentage points) while exceeding the Enliang-Yingmin prediction by 8.85 percentage points.

Table 4
Comparison of theoretical model parameters and predicted efficiency

Parameters	Koch-Licht (1977)	Enliang-Yingmin (1989)
Inlet velocity (m/s)	49.2	48.6
Vortex exponent	n + 1 = 1.563	1-n = 0.322
Cyclone constant Kc	0.541	-
Angular parameter è	-	1929.2
Radial diffusion Dr (m2/s)	-	9.76 × 10−4
Number of velocity heads Nh	3.33	3.33
Pressure drop, no NV (Pa)	158	153
Pressure drop, with NV (Pa)	74	72
Predicted efficiency (%)	98.38	88.95
Experimental efficiency (%)	97.8 ± 0.2	97.8 ± 0.2

The 0.58 percentage point gap between the Koch-Licht prediction (98.38%) and the experimental measurement (97.8% ± 0.2%) is within the combined modelling and experimental uncertainty, and is physically attributable to three non-idealities not captured by the theoretical framework: (i) minor re-entrainment of fines at the dust bin interface; (ii) partial particle wall rebound under the reduced gas film cushioning at low pressure; and (iii) small axial non-uniformity of gas density along the cyclone length. These losses are within the normal envelope reported for pilot-scale cyclones (Huang et al., 2018; Wasilewski & Brar, 2023).

The grade efficiency curves (Figure 1) show that the Koch-Licht model predicts substantially higher collection than the Enliang-Yingmin model for submicron particles, while both models converge to > 99.99% for particles larger than 7 µm. The experimental efficiency (97.8%, dashed line) exceeds both theoretical predictions in the fine-particle range, particularly that of the Enliang-Yingmin model. The deviation of each theoretical prediction from the experimental value is summarised in Figure 2, which shows that the Koch-Licht model departs from the measured efficiency by only 0.58 percentage points, whereas the Enliang-Yingmin model under-predicts it by 8.85 percentage points.

Figure 1
Grade efficiency curves comparing the Koch-Licht model, Enliang-Yingmin model, and experimental efficiency (97.8%) for the cyclone separator at 4 kPa absolute pressure and at 90 °C.

Figure 2
Deviation of the theoretical predictions from the experimental efficiency (97.8%).

Full pressure drop data across both models, with and without the neutral vane (Figure 3), are compiled in Supplementary Table 2.

Figure 3
Predicted pressure drop across cyclone separator with and without neutral vane for both theoretical models.

The CFD simulation results in Figure 4 visualise the flow field inside the cyclone at 4 kPa absolute pressure and 90 °C. The velocity field (Figure 4a) exhibits the characteristic Rankine vortex structure with a maximum magnitude of 32.1 m/s near the vortex finder and a low-velocity core surrounded by a high-velocity annular zone adjacent to the wall. The streamlines (Figure 4b) confirm the double vortex structure essential for particle separation, with an outer downward spiral along the wall conveying particles toward the dust bin and an inner upward spiral carrying cleaned gas through the vortex finder; the simulation resolves approximately 5.2 spiral turns before flow reversal, in good agreement with the Alexander correlation (Alexander, 1949) for this geometry. The static-pressure field (Figure 4c) shows a strong radial gradient from ~94 Pa at the centre line to ~237 Pa at the wall (corrected ρg = 0.039 kg/m³ basis), consistent with the centrifugal driving force for separation. The tangential velocity field (Figure 4d) reaches a maximum of 14.5 m/s in the annulus between the vortex finder and the wall, corresponding to the forced vortex zone of the Rankine model (Hoffmann & Stein, 2008).

Figure 4
CFD simulation of cyclone separator flow field at 4 kPa absolute pressure and at 90 °C: (a) velocity contour showing axial cross-section with velocity magnitude 0-32 m/s; (b) streamlines illustrating double-vortex flow pattern with inner upward and outer downward spiral motion; (c) static pressure distribution (94-237 Pa, on the corrected ρg = 0.039 kg/m³ basis) with radial gradient from center to wall; (d) top view of tangential velocity field showing inlet at 45° and Rankine vortex structure.

The particle separation behaviour predicted by the Discrete Phase Model (inlet PSD d̄ = 4.2 µm, n = 2.1) is summarised in Figure 5. Particle trajectories (Figure 5a) show that large particles (d > 10 µm) follow tight spiral paths with 2-3 turns before wall collection, while small particles (d < 3 µm) exhibit extended residence times with partial slip through the vortex finder consistent with their lower inertia and higher susceptibility to turbulent dispersion. The grade efficiency comparison (Figure 5b) shows cut size (d₅₀) values of 2.5, 3.5 and 2.8 µm for Koch-Licht, Enliang-Yingmin and CFD, respectively; the CFD predicted overall efficiency of 96.8% deviates from the experimental 97.8% by only 1.1 percentage points. The tangential velocity profiles at four axial heights (Figure 5c) display the characteristic Rankine structure with a peak of ~29 m/s at the forced/free vortex interface (r ≈ 10 cm) and moderate axial decay (~15% top-to-bottom), favourable for maintaining separation while limiting pressure drop. The pressure-drop decomposition (Figure 5d) shows that the neutral vane suppresses the core-vortex loss from 53 Pa to 9 Pa and the exit loss from 21 Pa to 11 Pa, reducing the total pressure drop from 158 Pa to 74 Pa, that is, a 53.1% saving. (These values are reported on the corrected vacuum gas density basis, ρg = 0.039 kg/m³; because the incompressible pressure field scales linearly with gas density at fixed inlet velocity, the relative 53.1% reduction is unchanged, and Figure 5d has been regenerated accordingly.)

Figure 5
CFD analysis of particle separation and flow characteristics at 4 kPa absolute pressure and at 90 °C: (a) particle trajectories by size (1-20 µm) showing size dependent spiral motion and collection paths; (b) grade efficiency curves comparing the Koch-Licht model, Enliang-Yingmin model, and experimental data with d₅₀ = 2.5-3.5 µm; (c) tangential velocity profiles at different heights showing Rankine vortex structure; (d) pressure drop analysis showing 53.1% reduction with neutral vane installation.

3.1.1 Sensitivity of CFD predicted efficiency to Inlet PSD parameters

Because the Rosin–Rammler parameters used as the CFD boundary condition were estimated rather than measured (Section 2.5), a parametric sensitivity analysis was performed in which d̄ was varied over 3.0-6.0 µm and n over 1.5-2.8, spanning the physically plausible range for the fine-particle fraction entering the cyclone. The results (Table 5) show that the predicted overall collection efficiency varies from 95.8% (d̄ = 3.0 µm, n = 1.5, worst case) to 98.9% (d̄ = 6.0 µm, n = 2.8, best case), with the baseline prediction (96.8%) falling near the centre of this range. All scenarios remain within 2 percentage points of the experimental value (97.8%), confirming that the global efficiency is only weakly sensitive to the assumed PSD parameters, as theoretically expected given that the cut size (~1.0-1.5 µm) is well below the mass-weighted mean of the inlet distribution.

Table 5
Sensitivity of CFD-predicted overall collection efficiency to Rosin-Rammler inlet PSD parameters.

d̄ (µm)	n	Predicted η (%)	Δη vs Expt. (pp)
3.0	1.5	95.8	-2.0
3.0	2.1	96.2	-1.6
4.2*	2.1 *	96.8*	-1.0
4.2	2.8	97.5	-0.3
6.0	1.5	97.4	-0.4
6.0	2.1	98.1	0.3
6.0	2.8	98.9	1.1

• ^*
  Baseline case used in the main CFD simulation. Expt. = 97.8 ± 0.2%. pp = percentage points. All scenarios remain within 2 pp of the experimental value.

3.2 Grade efficiency analysis

Two distinct cut size values appear in this study and correspond to different analytical contexts: (1) d₅₀ ≈ 1.01 µm is the theoretical Koch-Licht cut size calculated from the cyclone geometry and vacuum corrected gas properties (Supplementary Table 3), representing the intrinsic separation capability of the cyclone; (2) d₅₀ ≈ 2.5-3.5 µm are the apparent cut sizes read from the grade efficiency curves in Figure 5b, which reflect the intersection of the model specific grade efficiency functions with the particular inlet PSD used in the CFD simulation. The theoretical Koch-Licht cut size (1.01 µm) is geometry and gas property dependent and is independent of the inlet PSD; the apparent cut sizes (2.5-3.5 µm) are PSD dependent. Both values are internally consistent. Table 6 presents the detailed grade efficiency data for different particle size fractions. The most significant differences between models occur in the submicron range (0-3 µm), where the Koch-Licht model predicts substantially higher collection efficiency. This discrepancy arises from the different treatments of particle diffusion and re-entrainment mechanisms in each model.

Table 6
Grade efficiency for different particle size fractions.

Particle Size (µm)	Mass Fraction	Koch-Licht η (%)	Enliang-Yingmin η (%)
0-0.4	0.0020	30.14	0.01
0.4-0.6	0.0028	65.03	0.07
0.6-1.2	0.0168	77.14	0.97
1.2-1.8	0.0260	87.79	5.35
1.8-2.4	0.0309	92.80	17.18
2.4-3.0	0.0330	95.51	38.34
3.0-3.6	0.0336	97.09	64.32
3.6-4.2	0.0333	98.06	85.54
4.2-4.8	0.0324	98.68	96.37
4.8-7.0	0.1080	99.30	99.55
7-10	0.1197	99.81	100.00
>10	0.4615	≥99.95	100.00

The complete theoretical grade efficiency data for the Koch-Licht model, evaluated with the actual cyclone geometry (Table 1) and vacuum corrected gas and particle properties (ρ_p = 550 kg/m³, ρ_g = 0.039 kg/m³, µ = 2.1 × 10⁻⁵ Pa·s at 4 kPa), are reported in Supplementary Table 3. The theoretical cut size is d₅₀ ≈ 1.01 µm, reflecting the lower particle density of maltodextrin encapsulated powder relative to mineral dusts. When this grade efficiency curve is integrated over the fine-fraction inlet PSD (Rosin–Rammler, d̄ = 4.2 µm, n = 2.1) used as the CFD boundary condition, the overall Koch-Licht prediction of 98.38% is recovered in close agreement with the experimental measurement of 97.8 ± 0.2%.

3.3 RSM optimization of spray drying parameters

The Response Surface Methodology results revealed significant effects of both inlet air temperature (X₂) and air flow rate (X₁) on all six product quality attributes. Table 7 presents the developed regression equations with their corresponding coefficients of determination.

Table 7
Quadratic regression models for product quality responses.

Responses	Regression Equation	R2	R2_adj
Moisture (%)	Y = -0.05587 + 0.04926X1 + 0.04423X2 - 0.0002724X12 - 0.0003164X22 + 0.0001292X1X2	0.9227	0.8675
Solid recovery (%)	Y = 200.2 - 0.2636X1 - 1.044X2 - 0.0004863X12 + 0.001548X22 + 0.002573X1X2	0.9313	0.8822
Particle Size (µm)	Y = 528.1 + 0.4857X1 - 5.563X2 - 0.0002959X12 + 0.01594X22 - 0.003208X1X2	0.9870	0.9777
Bulk Density (kg/m3)	Y = 2202 - 5.031X1 - 21.96X2 + 0.009044X12 + 0.0744X22 + 0.02181X1X2	0.7563	0.5822
Water Solubility (%)	Y = 156.1 - 0.7039X1 - 0.3349X2 + 0.000533X12 - 0.0001603X22 + 0.003069X1X2	0.9089	0.8438
Feed Rate (L/h)	Y = 556.7 - 0.8543X1 - 6.134X2 + 0.002747X12 + 0.02047X22 + 0.0008958X1X2	0.9870	0.9777

The ANOVA (Table 8) confirms that inlet temperature is the dominant factor for moisture content (p = 0.004) and that air flow rate has no significant linear effect (p = 0.231), consistent with temperature governing evaporation kinetics.

Table 8
Analysis of Variance (ANOVA) for RSM Quadratic Models, with dual coefficient-of-variation reporting.

Responses	F-model (p)	Lack-of-fit (p)	Model CV (%)	Pure-error CV (%, n = 5)
Moisture Content	99.03 (< 0.0001)***	1.66 (0.312) ns	10.35	2.8
Product Yield	48.86 (< 0.0001)***	2.95 (0.161) ns	5.02	1.4
Particle Size	47.40 (< 0.0001)***	0.25 (0.861) ns	71.80	3.9
Bulk Density	10.02 (0.0043)**	0.76 (0.571) ns	5.11	2.1
Water Solubility	281.21 (< 0.0001)***	0.28 (0.838) ns	3.23	1.0
Feed Rate	77.59 (< 0.0001)***	0.32 (0.809) ns	100.71	4.3

• Note:^*** p < 0.001, ^** p < 0.01; ^ns = not significant. Model CV = RMSE / overall mean × 100%, reflecting the wide design-space range. Pure-error CV = σ_centre / mean_centre × 100%, computed from five centre-point replicates, reflecting experimental reproducibility. All pure-error CVs are below 5%, confirming excellent reproducibility. df_model = 5, df_residual = 7, df_LOF = 3, df_PE = 4.

The quadratic regression models reveal significant insights into the heat and mass transfer mechanisms governing product quality attributes. For the moisture content response, the fitted response surface describes a net decrease of moisture content with increasing inlet temperature, with the marginal effect diminishing toward the upper end of the experimental domain. At lower temperatures (100-135 °C), increasing temperature rapidly reduces moisture content by accelerating evaporation kinetics. Beyond ≈135 °C, the marginal benefit diminishes due to case hardening and the formation of a dried surface layer that impedes internal moisture migration, a phenomenon well documented in spray drying of sugar-rich functional food extracts. The positive curvature of the temperature response captured by β₂₂ is consistent with this mechanism, in which the surface layer resistance to internal diffusion causes the drying rate to approach an asymptote rather than continuing to increase linearly with temperature.

The particle size model exhibits a positive quadratic term for temperature (β₂₂ = +0.01594X₂²), suggesting that higher inlet temperatures promote particle expansion through rapid moisture evaporation and internal pressure buildup. This mechanism is particularly pronounced in vacuum spray drying, where the reduced external pressure facilitates bubble nucleation within droplets. The interaction term (β₁₂ = -0.003208X₁X₂) indicates that simultaneous increases in air flow rate and temperature produce smaller particles, likely due to enhanced atomization efficiency and reduced droplet coalescence in the drying chamber. The Analysis of Variance (ANOVA) (Table 8) confirms significant linear and quadratic temperature effects on particle size, with no significant effect of air flow rate.

Bulk density shows strong negative linear dependence on both air flow rate and temperature (β₁ = -5.031X₁, β₂ = -21.96X₂), which can be explained by the formation of more porous particle structures under rapid drying conditions. High temperatures and air flow rates create steep moisture gradients within droplets, leading to hollow or highly porous particles with lower bulk density. This structural characteristic is advantageous for instant dissolution properties but may require optimization for specific packaging and handling requirements. ANOVA (Table 8) confirms significant linear effects of both factors and a highly significant quadratic effect of air flow rate on bulk density. The bulk-density model showed the lowest coefficient of determination among the six responses (R² = 0.756, adjusted R² = 0.582); its predictions should therefore be regarded as indicative only.

The water solubility index (WSI) model achieved a good fit (R² = 0.909; Table 7), with optimal conditions favouring high temperature with moderate air flow. The enhanced solubility at elevated temperatures results from more complete surface amorphization of carbohydrate components and reduced crystallinity. The vacuum environment preserves heat-sensitive bioactive compounds while allowing higher processing temperatures, thus achieving both high solubility and bioactive retention, a critical advantage for functional food applications.

All six quadratic models exhibited R² values in the range 0.756-0.987 with adjusted R² values of 0.582-0.978 (Table 7), statistically significant regression (F-model p < 0.05) and non-significant lack-of-fit (all LOF p > 0.05), confirming that the polynomial forms adequately describe the process response relationships within the experimental domain.

3.4 Response surface analysis and contour plots

The three-dimensional response surface plots and corresponding two-dimensional contour maps for all six response variables are presented in Figures 6 and 7, respectively. These graphical representations provide comprehensive visualization of the interactive effects of air flow rate (X₁) and inlet temperature (X₂) on product quality attributes.

Figure 6
Response surface contour plots for vacuum spray drying optimization: (a) moisture content (R² = 0.923), (b) solid recovery (R² = 0.931), (c) particle size (R² = 0.987), (d) bulk density (R² = 0.756), (e) water solubility (R² = 0.909), (f) feed rate (R² = 0.987). ○ design points; ★ optimal conditions: air flow rate 80 m³/h, inlet temperature 130 °C.

Figure 7
Three-dimensional response surface plots for vacuum spray drying optimization: (a) moisture content, (b) solid recovery, (c) particle size, (d) bulk density, (e) water solubility, (f) liquid feed rate. X₁= air flow rate (m³/h), X₂ = inlet temperature (°C).

Moisture content (Figures 6a, 7a): The response surface exhibited a smooth monotonic decrease of moisture content with increasing inlet temperature, with predicted moisture content ranging from approximately 1% to 14% across the experimental domain. The contour plot revealed that low moisture content (2-4%) was achieved at high inlet temperatures (150-170 °C) combined with moderate to high air flow rates (160-200 m³/h). The positive but small coefficient for the quadratic term of temperature (β₂₂ = +0.000248) in combination with a strongly negative linear coefficient (β₂ = -0.2030) describes a drying response whose rate of moisture reduction diminishes as temperature increases, consistent with the development of case hardening resistance and indicating an optimal operating region near the upper end of the design range rather than an unbounded linear improvement.

Solid recovery and product yield (Figure 6b, 7b): On the dry basis solid-recovery scale now shown in Figures 6b and 7b, recovery was highest (≈95-100%) at low air flow rate combined with lower-to-moderate inlet temperature, and decreased as air flow rate increased; at the selected optimal conditions (80 m³/h, 130 °C) the predicted solid recovery was ≈93% (R² = 0.931). The selected optimum lies within this high-recovery region and simultaneously maximises particle size and water solubility (Section 3.5), at the cost of a modest increase in residual moisture and a lower drying throughput. The gravimetric product-yield model (wet basis) is described next and is retained only as a relative indicator of process direction, because its definition can give apparent values above 100% (see below). The response surface exhibited a convex profile, with predicted yield increasing monotonically with both inlet temperature (X₂) and air flow rate (X₁). A positive interaction between air flow rate and inlet temperature was observed for the gravimetric yield model (which is no longer tabulated; see Section 3.4 and Supplementary Table 7). Predicted yield values exceeded 100% in the high-temperature, high flow rate region of the design space and at the experimental design corner (X₁ = 240 m³/h, X₂ = 170 °C, observed yield 183.73%), It should be clarified that 183.73% is a model-predicted (RSM extrapolated) value at the axial-point corner of the design space, not a direct experimental observation. The maximum experimentally observed yield was 112.4% at Run 4 (factorial point: X₁= 240 m³/h, X₂ = 170 °C), which is physically explainable by moisture re-absorption (~5-8% of powder mass) combined with minor fines recirculation (~2-4%). RSM extrapolated values beyond the factorial range should be treated with caution. while yields above 95% were obtained across a broad operating window encompassing inlet temperatures ≥ 140 °C combined with air flow rates ≥ 160 m³/h. The apparent yield values above 100% do not represent a violation of mass conservation; rather, they reflect the specific gravimetric definition of yield used in this study, in which the mass of collected powder was referenced to the nominal solids content of the feed solution determined at a single moment in time prior to each run. Three factors contribute to the observed over unity ratios under the most intensive drying conditions. First, the functional food feed formulation is composed of highly hygroscopic sugars and maltodextrin type carbohydrates; after collection and prior to gravimetric determination, the dried powder re-adsorbed ambient moisture, so that the weighed mass included a water fraction that had not been present in the feed solids basis used as the denominator. Second, minor unavoidable contributions from recirculated fines and wall deposit re-entrainment at high gas velocity added to the collected mass without a corresponding increase in the feed-solids reference. Third, small run-to-run variability in the measured feed-solids content (performed once per batch) propagated as a systematic bias to the yield ratio. Accordingly, and consistent with the concern raised during peer review, the fitted regression model for yield should be interpreted as a tool for identifying the direction and relative magnitude of process effects i.e., the shape of the response surface and the location of favourable operating regions rather than as an absolute mass balance predictor. For subsequent work we recommend supplementing the gravimetric yield with online moisture correction of the collected powder, duplicate feed solids determinations, and explicit quantification of fines escaping through the HEPA filter, so that the raw yield data can be expressed on a consistent dry solids basis bounded above by 100%. To make this distinction explicit, the same runs expressed on a dry-solids basis (solid recovery, defined as dry collected powder mass divided by dry feed-solids input) all fall below 100%, in the range of approximately 76-95% across the design, which is the physically meaningful mass recovery efficiency; the apparent >100% values arise solely from the wet basis gravimetric definition described above and should not be read as mass recovery efficiencies. We therefore report the gravimetric yield only as a relative process indicator and direct the reader to the dry basis solid recovery (Supplementary Table 7) for the bounded, physically interpretable recovery.

Particle SIZE (Figure 6c, 7c): The response surface displayed an inclined planar profile, with particle size Primarily influenced by inlet temperature. The strong negative linear coefficient for temperature (β₂ = -5.244) indicated that increasing temperature significantly reduced particle size. Particles in the target d̄ range of 60-100 µm were obtained at temperatures between 130-170 °C across all flow rates studied. The relatively flat contour lines parallel to the X₁ axis confirmed that air flow rate had minimal effect on particle size.

Bulk density (Figure 6d, 7d): The saddle-shaped response surface indicated complex interactions between process variables. The contour plot revealed that bulk density in the range of approximately 600-900 kg/m³ could be achieved in a diagonal band across the experimental domain, with the low-flow/low-temperature and high-flow/high-temperature corners of the design space exhibiting the highest densities (≈ 950-1000 kg/m³) and the intermediate region showing values near the optimum target of ≈ 650 kg/m³. This bowl-shaped pattern is consistent with the formation of more porous particle structures under rapid drying conditions, where steep moisture gradients lead to hollow or highly porous particles of lower bulk density.

Water solubility (Figure 6e, 7e): The Three-dimensional surface exhibited a saddle-point topology, with the minimum solubility occurring in the central region of the experimental domain. The contour map showed that high solubility (> 85% to 90%) could be achieved at the high-temperature, high-air-flow corner of the design space. The quadratic coefficients of the fitted model (β₁₁ = +0.000533 and β₂₂ = -0.0001603; Table 7) describe opposing curvatures along the two axes (upward in air flow, slightly downward in temperature), consistent with the saddle-shaped surface.

Liquid Feed Rate (Figure 6f, 7f): Similar to water solubility, the feed rate response surface displayed a saddle-shaped profile with minimum values in the central region. The contour plot indicated that feed rates of 60-80 L/h (optimal range) were achievable across a broad operating window, while higher feed rates (>100 L/h) required operation at either extreme of the temperature range. This model exhibited one of the highest R² values (0.987), providing reliable predictions for process control.

3.5 Optimal operating conditions

Based on the response surface analysis and considering all quality constraints simultaneously, the optimal operating conditions for the vacuum spray dryer were identified as: inlet temperature 130 °C, air flow rate 80 m³/h, and feed rate 64 L/h. These conditions (marked with star symbols in Figures 6 and 7) produced powders with the following predicted characteristics: moisture content 3.9%; solid recovery 93%; particle size 78 µm; bulk density 490 kg/m³; and water solubility 89%.

The selection of these optimal conditions represents a compromise among multiple quality objectives. While higher temperatures could further reduce moisture content, they might also lead to thermal degradation of heat sensitive bioactive compounds. Similarly, while higher air flow rates improved product yield, they also increased energy consumption and might affect particle morphology. The solid-recovery surface (Figure 6b, 7b) shows that the highest dry basis solid recovery (≈95-100%) occurs at low air flow rate and lower inlet temperature; the selected optimum (80 m³/h, 130 °C) lies within this region, simultaneously delivering large particle size (≈78 µm), high water solubility (≈89%) and high solid recovery (≈93%). The principal trade-off of operating at this low-air-flow, low-temperature corner is a modest increase in residual moisture (≈3.9%) and a lower drying throughput, which is acceptable for the functional food quality objective of this work. These optimal conditions were identified for the specific pilot scale geometry studied; extrapolation to different scales or geometries would require re-validation with dimensional-similarity analysis.

3.6 Particle morphology analysis

Scanning electron microscopy (SEM) analysis revealed the morphological characteristics of spray dried functional food powders produced using the optimized vacuum spray dryer system (Figure 8). The particle morphology provides critical insights into the drying process and the structural properties of the encapsulated bioactive compounds. SEM imaging was performed using a field emission scanning electron microscope (JEOL JSM-7610F) after gold sputter coating.

Figure 8
Scanning electron micrographs (SEM) of spray dried functional food powders at 1,000× magnification: (a) Chrysanthemum (Chrysanthemum morifolium), (b) Ginger (Zingiber officinale), (c) Fingerroot (Boesenbergia rotunda), (d) Indian gooseberry (Phyllanthus emblica), (e) Chebulic myrobalan (Terminalia chebula), (f) Tomato (Solanum lycopersicum). Scale bar = 10 µm.

All six spray dried powders exhibited predominantly spherical morphology with smooth surfaces, confirming effective microencapsulation under vacuum conditions (Figure 8). Particle sizes spanned the range 16-56 µm: tomato (Solanum lycopersicum, Figure 8f) gave the smallest and most uniform particles (16.8-28.5 µm), consistent with the lower viscosity feed; chrysanthemum (C. morifolium, Figure 8a) and ginger (Z. officinale, Figure 8b) occupied the small to medium range (27-47 µm); while fingerroot (B. rotunda, Figure 8c), Indian gooseberry (P. emblica, Figure 8d) and chebulic myrobalan (Terminalia chebula Retz., Figure 8e) showed larger particles (32-56 µm) reflecting their higher total-solids content. Fingerroot particles exhibited a slightly textured surface attributable to essential-oil droplets; the other five powders showed uniformly smooth surfaces without cracks or surface indentations, indicating effective preservation of the encapsulated bioactive compounds. The 97.8% cyclone collection efficiency is therefore achieved without collision-induced damage during separation. The complete quality characteristics of the six powders, including moisture content, particle size, bulk density, total phenolic content and DPPH IC₅₀, are summarised in Table 9.

Table 9
Quality characteristics of spray-dried functional food powders.

Products	Moisture (%)	Particle Size (µm)	Density (kg/m3)	TPC (mg GAE/g)	IC50 (mg/mL)
Chrysanthemum	2.8 ± 0.2	27.0-33.9	620 ± 30	156.8 ± 5.2	2.45 ± 0.12
Ginger	3.1 ± 0.3	39.6-46.6	580 ± 20	189.5 ± 6.8	1.16 ± 0.01
Fingerroot	2.9 ± 0.2	44.9-54.5	650 ± 40	178.3 ± 4.5	1.89 ± 0.08
Indian gooseberry	3.2 ± 0.3	49.5-56.3	550 ± 20	248.7 ± 8.2	1.52 ± 0.05
Chebulic myrobalan	3.0 ± 0.2	31.9-49.1	610 ± 30	232.6 ± 6.9	1.35 ± 0.06
Tomato	2.5 ± 0.2	16.8-28.5	680 ± 30	134.2 ± 4.8	3.28 ± 0.15

• Note: TPC = Total Phenolic Content; IC₅₀ = half maximal inhibitory concentration (DPPH radical scavenging). Particle size ranges obtained from SEM analysis. Values represent mean ± standard deviation (n = 3).

The predominantly spherical particle morphology observed across all samples confirms successful microencapsulation under vacuum conditions. The smooth surfaces without cracks or surface indentations suggest effective preservation of the encapsulated bioactive compounds, as damaged particles would expose internal contents to degradation. The high cyclone collection efficiency (97.8%) ensures that these well-formed particles are efficiently recovered without collision-induced damage during the separation process.

3.7 Bioactive compound identification and retention mechanism

The preservation of bioactive compounds during vacuum spray drying is attributed to several synergistic mechanisms. Table 10 presents the major identified bioactive compounds in each functional food powder and their expected retention under vacuum conditions.

Table 10
Major bioactive compounds identified in functional food powders.

Products	Major Bioactive Compounds	Retention Mechanism
Chrysanthemum	Luteolin, Apigenin, Chlorogenic acid	Low-temperature encapsulation
Ginger	6-Gingerol, 8-Gingerol, 6-Shogaol	Rapid surface drying
Fingerroot	Pinostrobin, Panduratin A, Cardamonin	Vacuum protection from oxidation
Indian gooseberry	Gallic acid, Ellagic acid, Ascorbic acid	Reduced oxygen exposure
Chebulic myrobalan	Chebulinic acid, Corilagin, Tannic acid	Matrix encapsulation
Tomato	Lycopene, â-Carotene, Naringenin	Carotenoid stabilization

The vacuum spray drying environment (operating pressure ≈4 kPa) significantly reduces oxygen partial pressure, minimizing oxidative degradation of heat sensitive compounds such as ascorbic acid in Indian gooseberry and lycopene in tomato. The rapid surface drying facilitated by the optimized cyclone separator (residence time <2 seconds) further limits thermal exposure, preserving volatile bioactive compounds such as gingerols and essential oils.

Ginger powder exhibited the highest antioxidant activity (IC₅₀ = 1.16 mg/mL), attributed to the preservation of gingerols and shogaols under low-temperature vacuum conditions. Indian gooseberry demonstrated the highest total phenolic content (248.7 mg GAE/g), indicating excellent retention of its characteristic polyphenols including gallic acid and ellagic acid. Chebulic myrobalan also showed strong antioxidant properties (IC₅₀ = 1.35 mg/mL) due to effective preservation of chebulinic acid and corilagin.

These results suggest that the vacuum spray drying conditions are compatible with retention of measurable levels of bioactive compounds in the dried powders, while achieving high product recovery (>79.8%). However, quantitative retention rates (i.e., ratio of bioactive content in the dried powder to that in the original liquid feed) were not determined in the present study. Furthermore, no direct comparison with conventional atmospheric spray drying was performed. The reported TPC and IC₅₀ values therefore characterise the product quality of the vacuum dried powders but do not constitute evidence of superior retention relative to alternative drying methods. Here, “product recovery (>79.8%)” refers to the dry basis solid recovery defined in Section 3.4, not to bioactive retention. As an indication of product stability rather than feed relative retention, the total phenolic content, flavonoid content and DPPH radical-scavenging activity of all six powders were additionally monitored over 60 days of storage (Supplementary Table 8); the powders retained the large majority of their initial TPC and antioxidant activity over this period, which is consistent with effective matrix encapsulation but, again, does not by itself establish an advantage over atmospheric drying in the absence of a feed relative retention measurement and a side by side comparison. These two measurements are identified as priorities for future work in Section 3.8.

3.8 Limitations and future perspectives

Several limitations of the present study are acknowledged and indicate priorities for future work. (i) The inlet particle-size distribution used as the CFD boundary condition (Rosin-Rammler d̄ = 4.2 µm, n = 2.1) was estimated from atomiser specifications and literature correlations rather than measured in situ, because direct laser-diffraction of the spray plume inside the vacuum chamber was not technically feasible with the current setup. A parametric sensitivity analysis (varying ā over 3.0-6.0 µm and n over 1.5-2.8) showed that the predicted overall collection efficiency varies between 95.8% and 98.9%, confirming that the global efficiency is only weakly sensitive to the assumed PSD parameters because the cut size (~1.0-1.5 µm) is well below the mass-weighted mean of the inlet distribution. Nevertheless, the unvalidated inlet PSD limits the ability to draw conclusions about grade efficiency performance for individual size fractions near the cut size. (ii) The RSM design space covers one pilot scale geometry, so extrapolation to full industrial scale should be accompanied by dimensional-similarity analysis and re-validation. (iii) Bioactive compound retention was evaluated post-drying only; the full shelf-life stability of the encapsulated powders under accelerated storage conditions remains to be assessed. (iv) The product yield response locally exceeds 100% in the extrapolated high temperature, high flow rate corner of the RSM surface (Figures 6b, 7b); this is a known artefact of polynomial surfaces near design-space boundaries and of minor residual-moisture re-absorption during powder conditioning, not a physical impossibility. Future studies will employ non-invasive in-situ optical diagnostics (e.g. phase Doppler anemometry adapted for sub-atmospheric operation) to directly characterise the spray plume, and will extend the RSM framework to multi-response constrained optimisation with explicit physical bounds.

4 Conclusions

A cyclone separator integrated into a pilot scale vacuum spray dryer was successfully designed, constructed, and validated for functional food powder production. The key findings are:

1. The experimental cyclone collection efficiency (97.8% ± 0.2%) agreed closely with the Koch-Licht theoretical prediction (98.38%) within 0.6 percentage points, while exceeding the Enliang-Yingmin prediction (88.95%) by 8.85 percentage points, confirming the validity of the Koch-Licht semi-empirical framework for vacuum cyclone operation when gas-density and Cunningham slip corrections are applied.

2. Evaluated with the correct vacuum gas density (ρg = 0.039 kg/m³ at 4 kPa, 90°C), the cyclone design achieved low pressure drops of approximately 158 Pa (without neutral vane) and 74 Pa (with neutral vane), with the neutral vane providing a 53.1% reduction; these low absolute losses are consistent with sub-atmospheric operation and represent an energy efficient design for vacuum spray drying applications.

3. RSM optimization with Central Composite Design successfully developed quadratic models with high R² values (0.756-0.987) for all six response variables. The three-dimensional response surface plots and contour maps effectively visualized the interactive effects of air flow rate and inlet temperature on product quality.

4. Optimal operating conditions were identified as inlet temperature 130 °C, air flow rate 80 m³/h, and feed rate 64 L/h, producing powders with moisture content 3.9%, solid recovery 93%, particle size of approximately 78 µm, bulk density 490 kg/m³, and water solubility 89%.

5. The system successfully produced encapsulated functional food powders from Thai ingredients with measurable bioactive compound levels (IC₅₀ as low as 1.16 mg/mL for ginger) and product recovery (>79.89%). Quantitative retention relative to the original liquid feed was not determined in this study and remains a priority for future work.

This work provides practical engineering data and validated RSM models for the design and optimization of cyclone separators in vacuum spray drying systems. The response surface methodology approach demonstrated here offers a systematic framework for multi-objective optimization of spray drying processes for heat sensitive functional food applications. While the present results are specific to the pilot scale geometry investigated, the methodology combining theoretical models, CFD, and RSM within a single consistent framework is transferable to other cyclone geometries and scales, subject to re-validation with dimensional similarity analysis.

Supplementary Material

Supplementary material accompanies this paper.

Supplementary Section S1

Supplementary tables and figures.

Supplementary Table 1

Complete Cyclone Separator Design Parameters and Operating Conditions

Supplementary Table 2

Pressure Drop Analysis

Supplementary Table 3

Theoretical Grade Efficiency Koch-Licht Model with Corrected Parameters

Supplementary Table 4

Laser Diffraction PSD Data for Collected Powder (Malvern Mastersizer, ISO 13320:2020)

Supplementary Table 5

Rosin-Rammler Parameter Comparison: CFD Inlet vs. Collected Powder

Supplementary Table 6

Per-run measured response values for the central composite design (project data file).

Supplementary Table 7

Reconciliation of gravimetric product yield (wet basis) and dry-basis solid recovery.

Supplementary Table 8

Storage stability of total phenolic content (TPC) and DPPH antioxidant activity over 60 days.

Supplementary Figure 1

Particle size distribution (PSD) Plot of the probability density

Supplementary Figure 2

Mass-balance schematic of the cyclone-integrated vacuum spray-drying system.

Supplementary Section S2

Stefan-Boltzmann analysis of radiative heat transfer to spray droplets in a vacuum spray dryer (supporting calculation for Section 2.4).

This material is available as part of the online article from https://doi.org/10.1590/1981-6723.1552025

Acknowledgements

This research was funded by the Thailand Science Research and Innovation Fund (TSRI) and the Program Management Unit for Competitiveness (PMU-C), under Contract No. C10F630193.

Data Availability

The data that support the findings of this study are available from the corresponding author upon reasonable request. The experimental data including cyclone separator efficiency measurements, CFD simulation parameters (OpenFOAM), Response Surface Methodology optimization results, SEM micrographs, and spray dried powder characterization data (moisture content, particle size, bulk density, TPC, IC₅₀) can be provided for research purposes.

• Cite as:
  Rachpila, T., Pongthong, K., & Laohawiroje, T. (2026). Design, CFD validation, and process optimization of a cyclone integrated pilot scale vacuum spray dryer for functional food production. Brazilian Journal of Food Technology, 29, e2025155. https://doi.org/10.1590/1981-6723.1552025
• Funding:
  Thailand Science Research and Innovation Fund (TSRI) and the Program Management Unit for Competitiveness (PMU-C), under Contract No. C10F630193.

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Edited by

• Associate Editor:
  Rosinelson da Silva Pena.

Publication Dates

• Publication in this collection
  25 Sept 2026
• Date of issue
  2026

History

• Received
  11 Dec 2025
• Accepted
  09 July 2026