Traceable Numerical Screening of PV, CSP, Geothermal and Waste Heat Recovery Pathways for Hydrogen Production

1. Introduction

Hydrogen produced by electrolysis can connect variable or otherwise difficult-to-use energy resources with chemical storage and industrial demand. International assessments continue to identify renewable electricity and electrolyzer deployment as central elements of low-emissions hydrogen development [1,2]; system studies also emphasize the role of power-to-hydrogen when electricity supply and demand are mismatched over longer time scales [30,31]. The usefulness of hydrogen as a common end product, however, creates a methodological difficulty: identical hydrogen units can conceal very different upstream physics.

The PV pathway is fundamentally electrical. Irradiance and cell temperature modify the current-voltage response and therefore the DC power available to the downstream converter [3,4,5,17,18,19]. CSP instead concentrates solar radiation onto a receiver, so optical delivery, external heat loss and internal convection determine the thermal state available to a power cycle [6,7,20,21,22,23]. Geothermal conversion depends on the temperature and flow of the produced fluid, heat exchanger performance and the selected cycle, with scaling, corrosion and pumping becoming relevant when a simplified model is transferred to a real brine system [8,9,24,25]. WHR is still more site-dependent because the recoverable temperature level, flow and allowable disturbance of the host process constrain the useful heat source [10,11,26,27,28,29]. These are not interchangeable boundary-value problems.

A second difficulty appears at the turbomachinery interface. A pressure difference multiplied by volumetric flow has dimensions of power and is appropriate in specific hydraulic/head formulations, but a static pressure loss measured across a simplified CFD geometry is not automatically recoverable shaft work. Turbine work is normally established from rotor torque and angular velocity or from a thermodynamic change in stagnation enthalpy across a controlled expansion [12]. Conflating dissipative pressure loss with useful work can reverse the interpretation of a design comparison: a larger loss may indicate a greater penalty rather than a better turbine.

This study analyzes a four-pathway numerical dataset around this distinction. The objective is not to create a universal ranking of PV, CSP, geothermal energy and WHR, but to determine which comparisons remain defensible when the upstream models differ in physical meaning, prototype scale and verification status. The framework uses three rules: quantities are reported only when they are documented in the available simulation or post-processing data; derived quantities are recalculated only from documented source variables and assumptions; and unavailable numerical details are identified explicitly rather than reconstructed from typical CFD practice.

The resulting contribution is a traceable numerical screening framework with an explicit evidence hierarchy. It preserves the operating-point values generated by the pathway models, reclassifies the thermal pathway pressure-flow calculation as a comparative diagnostic, isolates the WHR high-flow stress case and separates numerical consistency from validation. Because the upstream thermal models and downstream turbine spreadsheets do not share a documented mass flow or thermodynamic state interface, the thermal downstream mapping is treated as a separate diagnostic rather than as a closed heat-to-shaft energy balance. This structure supports screening while identifying the additional evidence required before design-scale or technology-ranking claims are made.

2. Materials and Methods

2.1. Comparative Scope and Evidence Basis

Figure 1 summarizes the screening architecture. PV and the heat-driven pathways share scenario management and post-processing conventions but not the same upstream physics. The PV branch maps cell thermal states to the available DC power estimate. CSP, geothermal and WHR provide thermal-fluid fields and pressure/flow outputs, while the separate turbine stage spreadsheets provide a pressure-flow diagnostic. No documented mass flow or enthalpy state transfer links the thermal resource models quantitatively to that turbine stage calculation; the downstream thermal mapping is therefore not interpreted as a closed energy-conversion chain.

The numerical evidence is divided into three levels. Level 1 comprises direct exports and documented input parameters from the available spreadsheets, CSV files and launcher scripts. Level 2 comprises quantities recalculated algebraically from Level 1 values using explicitly documented assumptions. Level 3 covers information that cannot be recovered from the available project material, including grid refinement data and several Fluent solver settings. Level 3 quantities are not inferred from engineering defaults.

Table 1. Evidence hierarchy applied to the numerical screening framework.

Level	Content	Treatment in this paper
1	Scenario inputs; PV cell-average temperatures and final DC outputs; CSP heat transfer export; geothermal/WHR inlet/outlet states; static pressures; mass flow/density values; documented post-processing constants.	Reported directly, with units and scenario provenance.
2	$Q_v$, $|\Delta p|Q_v$, the efficiency-scaled electrical equivalent indicator, hydrogen equivalent mass and stoichiometric water minimum.	Recalculated from Level 1 values; interpretation is explicitly limited.
3	Mesh counts/quality, turbulence closure, wall treatment, detailed Fluent numerics, grid convergence, quantitative experimental validation, complete turbine thermodynamic states and common capacity/resource normalization.	Not reconstructed; treated as missing verification/reproducibility information.

Table 1. Evidence hierarchy applied to the numerical screening framework.

Level	Content	Treatment in this paper
1	Scenario inputs; PV cell-average temperatures and final DC outputs; CSP heat transfer export; geothermal/WHR inlet/outlet states; static pressures; mass flow/density values; documented post-processing constants.	Reported directly, with units and scenario provenance.
2	$Q_v$, $|\Delta p|Q_v$, the efficiency-scaled electrical equivalent indicator, hydrogen equivalent mass and stoichiometric water minimum.	Recalculated from Level 1 values; interpretation is explicitly limited.
3	Mesh counts/quality, turbulence closure, wall treatment, detailed Fluent numerics, grid convergence, quantitative experimental validation, complete turbine thermodynamic states and common capacity/resource normalization.	Not reconstructed; treated as missing verification/reproducibility information.

Table 2. Energy chain closure status. The table distinguishes physically connected calculations from separate diagnostic mappings.

Interface	Status	Interpretation in this paper
PV thermal state → PV DC estimate	Partially documented	Final DC values are available, but the exact final $V_{mp}$ temperature correction equation is not recoverable.
CSP imposed receiver flux → reported heat transfer	Documented within the reduced-order CSP model	Used as a thermal response only; no optical ray tracing is claimed.
Geothermal/WHR source conditions → outlet thermal states	Documented as operating-point states	Temperature responses are analyzed; archived direct heat transfer rate fields are zero and are not reinterpreted.
Thermal models → turbine diagnostic	Not closed	The turbine workbooks use a fixed $Q_v=1.8044$ ${\mathrm{m}}^3$ ${\mathrm{s}}^{-1}$ that is not derived from the upstream heat exchanger mass flow or enthalpy state.
Pressure-flow diagnostic → electrical equivalent	Algebraic mapping only	${\eta }_t{\eta }_g|\Delta p|Q_v$ is an illustrative electrical equivalent, not resolved shaft or generator power.
Electrical quantity → hydrogen metric	Algebraic mapping only	PV yields an energy-based hydrogen estimate; thermal branches yield hydrogen equivalents that inherit the diagnostic limitations above.

Table 2. Energy chain closure status. The table distinguishes physically connected calculations from separate diagnostic mappings.

Interface	Status	Interpretation in this paper
PV thermal state → PV DC estimate	Partially documented	Final DC values are available, but the exact final $V_{mp}$ temperature correction equation is not recoverable.
CSP imposed receiver flux → reported heat transfer	Documented within the reduced-order CSP model	Used as a thermal response only; no optical ray tracing is claimed.
Geothermal/WHR source conditions → outlet thermal states	Documented as operating-point states	Temperature responses are analyzed; archived direct heat transfer rate fields are zero and are not reinterpreted.
Thermal models → turbine diagnostic	Not closed	The turbine workbooks use a fixed $Q_v=1.8044$ ${\mathrm{m}}^3$ ${\mathrm{s}}^{-1}$ that is not derived from the upstream heat exchanger mass flow or enthalpy state.
Pressure-flow diagnostic → electrical equivalent	Algebraic mapping only	${\eta }_t{\eta }_g|\Delta p|Q_v$ is an illustrative electrical equivalent, not resolved shaft or generator power.
Electrical quantity → hydrogen metric	Algebraic mapping only	PV yields an energy-based hydrogen estimate; thermal branches yield hydrogen equivalents that inherit the diagnostic limitations above.

2.2. Numerical Workflow and Documented CFD Configuration

The available launch scripts call the ANSYS Workbench executable identified as v241. The project material documents ANSYS thermal/thermal-fluid calculations, MATLAB-based scenario launching and MATLAB/Python post-processing. Several boundary parameters can be recovered, but a complete Fluent setup cannot. Table 3 separates documented information from unresolved solver details.

Several turbine stage workbook rows contain generic fields corresponding to a 1 s time increment, a 10 s flow time field and 100 iterations. Because the associated Fluent journal, formulation and residual histories are unavailable, these fields are not treated as evidence of a particular transient scheme or of converged final iteration counts.

The absence of grid refinement evidence is material. Current CFD verification practice separates iterative convergence from discretization error assessment; grid convergence or an equivalent discretization study is required before quantitative claims of mesh independence are made [15,16,32,33]. The results below are therefore reported as prototype-scale numerical operating points, not validated design predictions.

A separate Supplementary Information document accompanies this manuscript and provides a verification evidence status table together with the processed scenario datasets and derivation notes used in the analysis. The available project material does not contain the cell/element counts and mesh quality statistics, a coarse/medium/fine refinement sequence, Grid Convergence Index (GCI) values, residual histories, mass or energy imbalance histories, or an experimental validation dataset. These quantities are therefore identified explicitly as unavailable rather than replaced by assumed values.

2.3. Scenario Definitions

The scenario sets perturb the dominant resource and ambient variables rather than imposing one nominal point on all pathways. Table 4, Table 5, Table 6 and Table 7 list the documented input values used in the present comparison.

2.4. PV Thermal–Electrical Post-Processing

The PV workbook contains 32 cell-average temperatures for each scenario, 32 corrected cell voltages, a series voltage, a series current and a final DC power value. The PV launcher table fixes surface emissivity at 0.85 and uses the scenario-specific irradiance/heat flux, ambient temperature and convection coefficient inputs reported in Table 4. It also contains a fixed field labelled “Heat Flow” with value 0.1, but the available files do not document its physical application sufficiently for interpretation. The final workbook states that the results were corrected using a “32-cell $V_{mp}$ temperature coefficient model” and were not produced by the preliminary Shockley-diode fit in the MATLAB development script. The exact final temperature coefficient equation and its reference parameters are unavailable, so the electrical model is not reconstructed from the preliminary script.

The reported PV electrical quantity is the final documented DC estimate,

$$P_{\mathrm{PV},\mathrm{DC}}=V_{\mathrm{series}}{I}_{\mathrm{series}},$$

(1)

with $V_{\mathrm{series}}$, $I_{\mathrm{series}}$ and $P_{\mathrm{PV},\mathrm{DC}}$ taken from the final workbook. This preserves the numerical results while avoiding a false claim of reproducibility for the missing correction law. Temperature dependence of PV output is well established in standard performance models, where irradiance and cell temperature modify the current–voltage characteristic [3,4,5,17,18,19].

2.5. CSP Reduced-Order Receiver Representation

The CSP model does not resolve the optical field by ray tracing. Instead, a receiver heat flux $q^{\prime \prime }$ is prescribed as a reduced-order representation of the optical stage. This is consistent with a thermal receiver study but cannot quantify intercept factor, tracking error, mirror slope error or nonuniform concentration from first principles. Detailed trough-receiver models show that optical delivery, receiver heat loss and internal convection are separate components of the collector problem [6,7,20,21,22,23].

The fixed CSP fluid, tube and thermal properties are summarized in Table 6. The parameter file documents a fluid inlet velocity of 0.5 m ${\mathrm{s}}^{-1}$, emissivity of 0.85 and a receiver temperature condition of 150 °C. Both tube_thickness and tube_thickness_geometry are 0.002 m for all nine scenarios; this value is therefore used as the documented geometry input. A separate legacy export field P92 is also labelled tube thickness and contains 0.010 m. Because its physical meaning is undefined, it is treated as ambiguous export metadata rather than as a second geometry specification. The reported CSP heat transfer output, $Q_{\mathrm{CSP}}$, is used directly rather than reconstructed.

2.6. Geothermal and WHR Thermal Resource Models

The geothermal branch is an operating-point heat recovery model, not a closed geothermal plant. Hot-side temperature and velocity, cold-side velocity and outlet temperatures are available. The direct “total heat transfer rate” field in the geothermal workbook is zero for all scenarios and is therefore not treated as a physical heat transfer result. A complete geothermal power model would additionally require a specified working fluid/cycle, pumping demand, brine chemistry and site constraints. Binary ORC systems are commonly used to exploit medium- and low-temperature geothermal resources, but cycle optimization requires thermodynamic states that are absent from the available dataset [8,24,25]. Corrosion and scaling are likewise material heat exchanger constraints in real geothermal fluids and are outside the present model [9].

The WHR branch uses hot gas temperature and velocity, cold-side conditions and outlet states. As with the geothermal workbook, the WHR “total heat transfer rate” field is zero and is not reinterpreted. WHR feasibility is inseparable from the host process: useful recovery must be compatible with the available heat source and with pressure and back pressure constraints imposed by the host process [10,11,26,27,28,29]. WHR-S5 doubles the baseline hot source velocity from 3 to 6 m ${\mathrm{s}}^{-1}$ and increases the documented hot source mass flow value from 185.4 to 370.8 kg ${\mathrm{s}}^{-1}$; it is treated as a stress/sensitivity point rather than a representative annual operating condition.

2.7. Energy Chain Closure and Pressure-Flow Diagnostic

The separate turbine stage workbooks calculate a static pressure difference and volumetric flow rate as

$$\Delta p_s=p_{in}-p_{out},Q_v=\left|{\displaystyle \frac{\dot{m}}{\rho }}\right|.$$

(2)

In all three turbine stage workbooks, the volumetric flow calculation uses $\dot{m}=1$ kg ${\mathrm{s}}^{-1}$ and $\rho =0.5542$ kg ${\mathrm{m}}^{-3}$, giving the same $Q_v=1.8044$ ${\mathrm{m}}^3$ ${\mathrm{s}}^{-1}$ for every scenario. The workbooks explicitly use this mass flow field because another available flow field was flagged as producing a nonphysical duct velocity. This fixed $Q_v$ is not derived from the upstream CSP, geothermal or WHR heat exchanger mass flow. Consequently, the upstream thermal resource models and this turbine stage calculation are not quantitatively coupled by a documented mass flow or thermodynamic state interface, and scenario-to-scenario variation in the pressure-flow diagnostic is driven by the static pressure difference rather than by an independently resolved turbine flow rate.

The CSP and geothermal post-processing assumption sheets also store a 0.18 m turbine diameter, a 0.20 m duct diameter, 24 blades and a tip-speed-ratio value of 1.5. Those values were used to generate algebraic RPM and torque estimates. The torque column is calculated from the assumed shaft power scale divided by an estimated angular velocity; it is not torque extracted from a rotating CFD domain. These geometry and kinematic assumptions are therefore documented but are not used as evidence of resolved turbomachinery performance.

The available pressure and flow values do not establish that the pressure change is a controlled expansion through an energy-extracting rotor. To prevent a dissipative loss from being misidentified as useful work, this study defines

$${\mathrm{\Pi }}_{\Delta pQ}=|\Delta p_s|Q_v,$$

(3)

which is termed the pressure-flow power-scale indicator. Its unit is watt, but its evidential meaning is limited to the product of the documented static pressure difference and the fixed workbook volumetric flow. A larger value is not, by itself, evidence of higher turbine efficiency or shaft power.

The turbine stage post-processing documents ${\eta }_t=0.35$ and ${\eta }_g=0.85$. Those factors are used only to reproduce an illustrative electrical equivalent mapping:

$$P_{\mathrm{eq}}={\eta }_t{\eta }_g{\mathrm{\Pi }}_{\Delta pQ}.$$

(4)

Equation (4) is a diagnostic mapping, not a validated generator output and not an energy balance closed to the upstream thermal resource model. A resolved turbine would normally require direct mechanical power,

$$P_{shaft}=\tau \omega ,$$

(5)

or, for a thermodynamic turboexpander under appropriate assumptions, a thermodynamic work relation based on mass flow and the change in stagnation enthalpy, for example

$$P_{shaft}\approx \dot{m}\left(h_{0,in}-h_{0,out}\right),$$

(6)

with efficiencies and losses defined consistently [12]. The available files contain neither resolved rotor torque from CFD nor the complete thermodynamic state set needed for Equation (6). The fixed 48 V DC bus in the post-processing is therefore kept only as a prototype reference for converting an electrical equivalent quantity to current; it is not proposed as an industrial bus voltage for systems operating from the kilowatt (kW) to megawatt (MW) scale.

2.8. Electrolyzer and Water Indicators

The downstream electrolyzer is an energy balance block rather than an electrochemical stack model. PEM electrolysis performance depends on stack voltage, load, operating pressure, temperature and balance-of-plant demand [13,14,30]. The specific electricity assumption used in the post-processing is

$$E_{sp}=50\mathrm{kWh}{\mathrm{kg}}_{{\mathrm{H}}_2}^{-1}.$$

(7)

A value of this order is compatible with stack-level PEM electricity requirements reported in authoritative technical targets, while a complete system can require additional balance-of-plant energy [13,14]. For PV, the hydrogen estimate is calculated from $P_{\mathrm{PV},\mathrm{DC}}$; for the thermal pathways, the same mapping is applied to $P_{\mathrm{eq}}$ and is therefore labelled a hydrogen equivalent indicator:

$${\dot{m}}_{H_2}={\displaystyle \frac{P}{E_{sp}}},$$

(8)

with consistent conversion between kW and kWh. The value is treated as an engineering assumption rather than fitted to a particular electrolyzer. The stoichiometric reaction $2H_{2}O\to 2H_2+O_2$ gives a theoretical minimum water mass of approximately

$${\dot{m}}_{H_{2}O,st}=9{\dot{m}}_{H_2}.$$

(9)

This quantity is the stoichiometric minimum and excludes purification, cooling, purges and other plant water uses [34]. No polarization curve, pressure dependence, dynamic response or degradation model is included [14].

2.9. Scale Compatibility, Normalization and Uncertainty Status

No common installed capacity, collector/module area, resource energy input or exergy denominator is documented consistently across all four pathways. The mean PV DC estimate is 0.05169 kW, whereas the thermal diagnostic electrical equivalents are 3.287 kW for CSP, 3.964 kW for geothermal energy and 4.245 kW for WHR when the deliberate stress case is excluded. Numerically, these thermal diagnostic values are approximately 64, 77 and 82 times the PV value, respectively. This difference primarily reflects incompatible prototype scales and different model definitions; it is not interpreted as a technology performance ratio. For this reason, the paper does not use the absolute PV and thermal values to rank the pathways, and their hydrogen metrics are reported separately by evidential class. Radar scoring and the earlier normalized heatmap across pathways are omitted because the available project material does not document a defensible weighting or common normalization basis.

The scenario ensemble provides deterministic sensitivity information but not probabilistic uncertainty quantification. Numerical verification is also incomplete because no multi-grid dataset was found. In the terminology of CFD verification and validation [15,16,32,33], the present work supports plausibility assessment and numerical consistency checks, not demonstrated grid convergence or experimental validation. This limitation is carried into the interpretation of every quantitative CFD-derived result.

3. Results

3.1. PV Operating-Point Response

The nine PV scenarios produce documented DC estimates from 33.31 to 65.44 W, with a mean of 51.69 W (Figure 2). The minimum occurs in PV-S1 at 500 W ${\mathrm{m}}^{-2}$, while the maximum occurs in PV-S3 at 1000 W ${\mathrm{m}}^{-2}$ and 25 °C ambient temperature. At the common 800 W ${\mathrm{m}}^{-2}$ solar input, the cold-ambient case PV-S4 gives 56.39 W whereas the hot-desert case PV-S5 gives 48.14 W, a 14.6% reduction. The cell-average temperature rises from 31.35 ^∘C in PV-S4 to 63.93 ^∘C in PV-S5, consistent with the expected negative temperature dependence of maximum PV power [3,4,19].

Wind-related convection also changes the thermal operating point. At 800 W ${\mathrm{m}}^{-2}$ and 25 ^∘C ambient, the weak-convection case ($h=5$ W ${\mathrm{m}}^{-2}$ ${\mathrm{K}}^{-1}$) gives a cell-average temperature of 54.70 ^∘C and 50.50 W, whereas the strong-convection case ($h=25$ W ${\mathrm{m}}^{-2}$ ${\mathrm{K}}^{-1}$) gives 35.14 ^∘C and 55.45 W. These values show the internal consistency of the documented thermal-to-electrical trend, although they do not substitute for validation of the final electrical correction law.

The raw PV-S3 thermal field contains a local plotted range of approximately 47.1–95.1 ^∘C, whereas the 32 extracted cell-average values for the same scenario cluster around 50 ^∘C. The distinction is important: a local field maximum and an area-averaged cell temperature are different observables and should not be used interchangeably in the electrical model.

3.2. CSP Heat Transfer Response

The CSP heat transfer export ranges from 2.333 to 6.421 kW. The maximum occurs in CSP-S3 under the 15,000 W ${\mathrm{m}}^{-2}$ imposed receiver heat flux. Figure 3 shows a positive relationship between imposed flux and the reported heat transfer result, but ambient and convection changes cause scenarios at the same imposed flux to separate. For the 10,000 W ${\mathrm{m}}^{-2}$ group, the heat transfer outputs span 3.702–4.805 kW. The reduced-order model with imposed flux therefore captures thermal sensitivity but cannot attribute these changes to optical concentration efficiency.

3.3. Geothermal and WHR Thermal States

At constant 0.5 m ${\mathrm{s}}^{-1}$ hot- and cold-side inlet velocities, increasing the geothermal source temperature from 363.15 K (GEO-S1) to 423.15 K (GEO-S3) raises the cold-outlet temperature from 340.51 to 386.37 K. At a fixed 393.15 K source temperature, increasing the hot-side velocity from 0.25 m ${\mathrm{s}}^{-1}$ (GEO-S4) to 1.0 m ${\mathrm{s}}^{-1}$ (GEO-S5) raises the cold-outlet temperature from 333.71 to 379.63 K. These operating-point trends are physically plausible for increased thermal capacity flow, but a direct geothermal heat transfer rate is not reported because the corresponding workbook field is zero.

The WHR thermal states show the same temperature-level sensitivity. At 3 m ${\mathrm{s}}^{-1}$ hot-side velocity, increasing the source temperature from 423.15 to 623.15 K raises the cold-outlet temperature from 349.88 to 432.38 K. The high-flow case WHR-S5 doubles the hot-side velocity to 6 m ${\mathrm{s}}^{-1}$ and contains a documented hot source mass flow of 370.8 kg ${\mathrm{s}}^{-1}$. This scenario is deliberately separated from representative operating-point averages below because its pressure-flow product is an outlier.

Figure 4 presents selected numerical fields. Each panel has its own legend and scale and is used only to document the numerical state corresponding to the scenarios; the images are not evidence of grid independence or experimental validation.

3.4. Indicators Derived from the Pressure-Flow Diagnostic

Table 8 summarizes the thermal pathway pressure-flow quantities. CSP gives ${\mathrm{\Pi }}_{\Delta pQ}=8.61$–13.85 kW and an efficiency-scaled $P_{\mathrm{eq}}=2.561$–4.121 kW. Geothermal scenarios give ${\mathrm{\Pi }}_{\Delta pQ}=9.62$–17.01 kW and $P_{\mathrm{eq}}=2.861$–5.061 kW. WHR spans a much wider interval because WHR-S5 reaches a static pressure difference of 34.62 kPa, producing ${\mathrm{\Pi }}_{\Delta pQ}=62.48$ kW and $P_{\mathrm{eq}}=18.586$ kW under the documented algebraic assumptions.

Figure 5 displays each pathway-specific scenario as an independent bar rather than connecting unlike scenario indices across technologies. The plot is a diagnostic of the pressure-flow post-processing rather than a turbine performance map. In particular, the geothermal pressure-flow indicator does not vary monotonically with the geothermal heat source flow labels, and all thermal scenarios use the same workbook value of $Q_v$. This decoupling is another reason not to interpret ${\mathrm{\Pi }}_{\Delta pQ}$ as recovered thermal work.

3.5. WHR Stress-Case Sensitivity

Including WHR-S5 gives a mean $P_{\mathrm{eq}}$ of 6.635 kW. Excluding that deliberate high-flow stress case gives 4.245 kW. The mean including the stress case is 56.3% higher than the mean obtained from the remaining scenarios (Figure 6). An unqualified arithmetic mean therefore overstates the central tendency of the representative WHR scenarios. This sensitivity is reported because it exposes the dependence of the downstream indicator on the pressure-flow formulation and on source flow selection.

3.6. Hydrogen and Stoichiometric Water Mapping

The downstream mapping uses 50 kWh ${\mathrm{kg}}^{-1}$ as an energy assumption. Because the PV and thermal branches have different scales and different evidential status, they are reported separately rather than combined into a single comparative technology table.

PV energy-based estimate.

The mean documented PV DC power of 51.69 W maps to an estimated hydrogen production of 0.0248 kg day${\mathrm{day}}^{-1}$ and a stoichiometric minimum water requirement of 0.223 kg ${\mathrm{day}}^{-1}$. This value belongs only to the small PV prototype represented in the workbook and is not normalized to the scale of the thermal models.

Table 9. PV prototype downstream estimate based on the documented mean DC power.

Basis	Mean DC power	${\mathrm{H}}_2$ estimate	Stoich. ${\mathrm{H}}_2$O minimum
		(kg ${\mathrm{day}}^{-1}$)	(kg ${\mathrm{day}}^{-1}$)
PV prototype	51.69 W	0.0248	0.223

Table 9. PV prototype downstream estimate based on the documented mean DC power.

Basis	Mean DC power	${\mathrm{H}}_2$ estimate	Stoich. ${\mathrm{H}}_2$O minimum
		(kg ${\mathrm{day}}^{-1}$)	(kg ${\mathrm{day}}^{-1}$)
PV prototype	51.69 W	0.0248	0.223

Thermal diagnostic hydrogen equivalents.

For CSP, geothermal and WHR, the same 50 kWh ${\mathrm{kg}}^{-1}$ mapping is applied to $P_{\mathrm{eq}}$. Because $P_{\mathrm{eq}}$ originates from the separate pressure-flow diagnostic rather than from a closed upstream heat-to-shaft balance, the resulting values are labelled hydrogen equivalents. They are not validated production forecasts and must not be compared directly with the PV estimate as a technology ranking.

Table 10. Hydrogen equivalents for the thermal pathways derived from the pressure-flow diagnostic. These values are not validated hydrogen production predictions.

Pathway	Diagnostic basis	${\mathrm{H}}_2$ equivalent	Stoich. ${\mathrm{H}}_2$O minimum
		(kg ${\mathrm{day}}^{-1}$)	(kg ${\mathrm{day}}^{-1}$)
CSP	Mean $P_{\mathrm{eq}}$ = 3.287 kW	1.578	14.20
Geothermal	Mean $P_{\mathrm{eq}}$ = 3.964 kW	1.903	17.13
WHR, all scenarios	Mean $P_{\mathrm{eq}}$ = 6.635 kW	3.185	28.67
WHR, S5 excluded	Mean $P_{\mathrm{eq}}$ = 4.245 kW	2.038	18.34

Table 10. Hydrogen equivalents for the thermal pathways derived from the pressure-flow diagnostic. These values are not validated hydrogen production predictions.

Pathway	Diagnostic basis	${\mathrm{H}}_2$ equivalent	Stoich. ${\mathrm{H}}_2$O minimum
		(kg ${\mathrm{day}}^{-1}$)	(kg ${\mathrm{day}}^{-1}$)
CSP	Mean $P_{\mathrm{eq}}$ = 3.287 kW	1.578	14.20
Geothermal	Mean $P_{\mathrm{eq}}$ = 3.964 kW	1.903	17.13
WHR, all scenarios	Mean $P_{\mathrm{eq}}$ = 6.635 kW	3.185	28.67
WHR, S5 excluded	Mean $P_{\mathrm{eq}}$ = 4.245 kW	2.038	18.34

The two tables intentionally separate the approximately 50 W PV prototype from kilowatt-scale thermal diagnostics. Without a common installed capacity, resource input, collector area, exergy basis or annual weighting, no quantitative superiority of one pathway over another can be inferred from these absolute values.

4. Discussion

4.1. Observed Numerical Behavior

The scenario set resolves several coherent sensitivities. PV power falls when cell temperature rises at fixed irradiance and increases when stronger convection suppresses the thermal operating point. CSP heat transfer rises with imposed receiver flux, while ambient and convection conditions shift the recovered heat at the same nominal flux. Geothermal and WHR outlet temperatures respond strongly to source temperature and source flow perturbations. These trends support physical plausibility of the scenario logic but do not establish quantitative accuracy.

The thermal pathway pressure-flow calculation behaves differently from a heat recovery metric. Its largest value occurs at WHR-S5 because the documented static pressure difference reaches 34.62 kPa while $Q_v$ remains 1.8044 ${\mathrm{m}}^3$ ${\mathrm{s}}^{-1}$. The same $Q_v$ is imposed by the turbine stage post-processing for every thermal scenario, so the apparent scenario variation in ${\mathrm{\Pi }}_{\Delta pQ}$ is mathematically proportional to the static pressure difference. The resulting outlier changes the WHR mean by more than half relative to the mean excluding the stress case. More importantly, this calculation is not quantitatively linked to the mass flow or enthalpy change on the source side from the CSP, geothermal or WHR thermal models. A larger static pressure loss may represent dissipation, a boundary condition artifact or an available head depending on where and how the pressure is defined; the available dataset does not contain the rotor or thermodynamic information required to distinguish those interpretations.

4.2. Coupling Limitation and Turbomachinery Interpretation

The central methodological limitation is the absence of a documented energy-conserving interface between the thermal resource models and the turbine stage spreadsheets. Replacing “fluid/turbine power” with a pressure-flow power-scale indicator prevents an algebraically correct unit conversion from becoming a physically unsupported energy-conversion claim, but it does not create the missing coupling. The downstream thermal hydrogen values are therefore not production forecasts; they are hydrogen equivalent mappings generated from a diagnostic pressure-flow quantity. A future turbine model supplied by the actual upstream working fluid mass flow and thermodynamic state, and providing $\tau \omega$ or a consistent stagnation enthalpy change, could replace ${\mathrm{\Pi }}_{\Delta pQ}$ while preserving the screening structure.

The modular structure remains useful because resource models, thermal outputs, pressure-flow diagnostics, electrical scaling and hydrogen mapping are kept as separate evidence stages. Improved physics can therefore replace one stage without changing scenario identifiers or the bookkeeping of downstream quantities. The value of the framework lies in traceability and explicit coupling status rather than in forcing every pathway into one nominal power number.

4.3. Comparison Across Pathways and Scale

The absolute numerical scales are intentionally not used for cross-technology ranking. The PV branch is a tens-of-watts prototype, whereas the thermal diagnostic mappings are in the kilowatt range. Placing these values on a single performance axis would therefore mix model scale with technology behavior. A defensible comparison would require at least one common denominator such as installed capacity, incident or recoverable resource energy, exergy input, collector area or cost, preferably combined with annual resource weighting and availability. None is documented consistently across all four pathways. The earlier radar and heatmap representations are therefore excluded rather than assigned arbitrary weights or normalization rules.

The environmental label also requires care. PV, CSP and geothermal energy can supply renewable electricity under appropriate deployment conditions. Recovered industrial heat does not automatically make the resulting hydrogen “green”; the carbon accounting depends on the host process, allocation method and whether the recovered heat would otherwise be rejected. The WHR branch is included because it is an energy recovery pathway to electrolysis, not because the numerical model establishes a lifecycle emissions classification.

4.4. Verification, Validation and Uncertainty

The available project material does not contain the cell/element counts and mesh quality metrics required to document the meshes quantitatively, nor does it contain a coarse/medium/fine refinement sequence. Discretization uncertainty therefore cannot be quantified using the Grid Convergence Index (GCI) or an equivalent procedure [16,32,33]. Residual histories, mass and energy imbalance histories, and complete Fluent solver settings are also unavailable. No experimental measurements are available for quantitative validation. Supplementary Table S1 records the availability status of these verification items so that missing evidence is explicit rather than implied. The present results consequently have a lower evidential status than a CFD study that reports formal verification under ASME V&V practice [15].

No experimental dataset is coupled to the models. Agreement with expected qualitative trends is therefore described as plausibility assessment, not validation. The scenario sweep is likewise a deterministic sensitivity study, not uncertainty propagation. Formal uncertainty quantification would require distributions or bounded uncertainties for boundary conditions, material properties, numerical discretization and empirical conversion assumptions, together with their propagation to hydrogen output.

4.5. Pathway-Specific Limitations and Next Numerical Steps

For PV, the highest-priority reproducibility gap is the exact final $V_{mp}$ temperature coefficient correction. The final workbook states which model family was used but does not contain the defining equation/reference values. For CSP, the imposed heat flux method is suitable for reduced-order receiver analysis, but ray tracing or an equivalent optical model is required to predict the incident flux distribution from mirror geometry and sun position. The scenario/geometry parameter file consistently documents a 0.002 m tube wall thickness; the separate legacy P92 field at 0.010 m remains ambiguous and should be traced to its original Workbench parameter definition before any wall thickness sensitivity analysis is attempted.

For geothermal energy, the present operating-point heat exchanger should be coupled to a closed Rankine/ORC model with explicit working fluid states, pumping and realistic brine properties. For WHR, a host process constraint on allowable back pressure is essential before any high-flow case is considered feasible. The duplicated cold-side input documented for the WHR-S6 “high cooling flow” label must be checked against the original simulation definition. Across all thermal branches, a resolved turbine/expander stage should replace the pressure-flow indicator before shaft power, generator output or realized hydrogen production are reported.

Finally, the electrolyzer block should progress from a fixed 50 kWh ${\mathrm{kg}}^{-1}$ mapping to a stack/system model that resolves load-dependent voltage, efficiency, operating pressure and balance-of-plant consumption. The 9:1 water-to-hydrogen factor should remain explicitly identified as stoichiometric minimum water rather than total plant water demand [34].

5. Conclusions

A four-pathway numerical dataset was analyzed through a traceable screening framework that distinguishes the direct PV electrical calculation from the thermal states calculated for CSP, geothermal and WHR. The PV workbook gives 33.31–65.44 W across nine small prototype scenarios, averaging 51.69 W. The thermal branches are treated separately because they are modeled at a different scale and do not share a closed energy interface with the turbine diagnostic. CSP provides a reported heat transfer output of 2.333–6.421 kW under the imposed receiver flux scenarios, while geothermal and WHR thermal states show coherent increases in cold-side outlet temperature as source temperature or flow increases. Their archived direct heat transfer rate fields are zero and are therefore not used as recovered energy quantities.

The principal methodological correction concerns the thermal pathway turbine stage. The available files support $|\Delta p_s|Q_v$ as a pressure-flow power-scale indicator, not as verified turbine shaft power, and the fixed turbine workbook $Q_v$ is not quantitatively coupled to the upstream thermal resource mass flow or thermodynamic state. Applying the documented efficiency factors therefore gives only an illustrative electrical equivalent mapping, averaging 3.287 kW for CSP, 3.964 kW for geothermal energy and 6.635 kW for WHR when all scenarios are included. Removing the WHR-S5 high-flow stress case lowers the WHR mean to 4.245 kW; the mean including all cases is 56.3% higher. The same qualification carries into the derived hydrogen equivalents.

No universal ordering of PV, CSP, geothermal and WHR follows from these numbers. The prototypes are not normalized to the same installed capacity, resource/exergy input, area, annual availability or cost, and the thermal electrical equivalent quantity is not a resolved turbine output. The strongest result is therefore the screening architecture itself: each metric remains linked to its source variables, assumptions, coupling status and evidential level.

Before design-scale conclusions are drawn, the numerical program requires documented Fluent settings, grid independence studies, quantitative validation where suitable reference data exist, a resolved turbine/thermodynamic cycle, confirmation of the final PV electrical correction, and a common normalization basis. Completing those steps would convert the present screening framework into a quantitatively coupled and reproducible comparative model suitable for stronger cross-technology inference.