1. Design of a solar air heater using
feature-mapping methods
WCSMO-15
Cork, 5. - 9. June 2023
Fabian Wein1
1
Friedrich-Alexander-Universität Erlangen-Nürnberg, Department Mathematik

2. Solar Air Heater I
FAU F. Wein Design of a solar air heater 2/17

3. Solar Air Heater II
Background
• solar air heaters are simple cheap sustainable devices (even DIY)
• to support heating (autumn and spring) and ventilation by warm fresh air
• industrial/agricultural usage (especially India) but rarely for private houses
Motivation
• main motivation: promote usage of solar air heaters as sustainable measure
• vision: provide open source blueprints (incl. control)
• technical approach: numerical framework and absorber design
FAU F. Wein Design of a solar air heater 3/17

4. State of the Art
www.builtisolar.com (unstructured professional DIY paradise)
screen soffit tubes baffles
• double construction and professional measurement/comparison
• the screen absorber design shows by far the best performance
• assumption: find balance of amount of absorber and pressure drop
→ almost no scientific publication covers the screen absorber
FAU F. Wein Design of a solar air heater 4/17

5. Feature-Mapping
• describe high level object absorber by P = (px, py), Q = (qx, qy), p, ai
• map as pseudo density (outside/partial/inside) to fixed mesh
• interpolate material properties air → (partial) absorber
• fully differentiable; allows gradient based optimization
• EFFICIENT SPLINE DESIGN VIA FEATURE-MAPPING FOR CFRS; 2023
• A REVIEW ON FEATURE-MAPPING METHODS FOR STRUCTURAL OPT.; 2020
FAU F. Wein Design of a solar air heater 5/17

6. Flow Simulation
• Lattice Boltzmann method for fluid simulation
• iterative procedure (collision and distribution of “particles”)
→ local element wise directional velocities
• porosity model by SPAID, PHELAN; 1997
• density based optimization by PINGEN ET AL; 2007
• model porosity of absorber (2-3 layers) via intermediate density
FAU F. Wein Design of a solar air heater 6/17

7. Flow Simulation II
density pressure
velocity velocity (streamlines)
• no realistic 2D model: doubled height, inlet and outlet not to be extruded
• solar air heaters usually have outlet fans; inlet fans are better scalable
FAU F. Wein Design of a solar air heater 7/17

8. Fan Characteristics
0
0.05
0.1
0.15
0.2
0.25
0.3
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
pressure
drop
/
static
pressure
velocity scaling / air flow
diagonal ρ=0.3
linearization
fan
• each system has own velocity / pressure drop characteristic
• fan’s flow rate depends on design dependent flow resistance
• determine working by LBM pressure drop → rescale velocity
FAU F. Wein Design of a solar air heater 8/17

9. Convection Diffusion
• stationary convective diffusion equation with scaled velocity v from LBM
∇ ·
k
cp ρ0
2
∇T
!
− ∇ · (v T) = R(T)
• temperature T, thermal conductivity k, specific heat capacity cp, density ρ0
• apply heat source on absorber center line: ρ 800 W/m2
scaled by absorber
FAU F. Wein Design of a solar air heater 9/17

10. Linear Heat Source
• nodal heat source at absorber center line
• general media is air (excellent isolator)
• velocity close to zero at boundary and in shadow zones
→ no heat transport → static heat equation with load in void
→ unrealistic hot temperature in shadowed absorber
diagonal: Tmax = 440◦
C horizontal: Tmax = 310◦
C
FAU F. Wein Design of a solar air heater 10/17

11. Nonlinear Heat Source
• model nonlinear heat source r(T) to
keep temperature ≤ 100◦
C
Rk(T) = (1 − δk)r(T) + δkRk−1
δk =
(
min{1.2 δk−1, 0.9}, if R oscillates
0.8 δk−1 else
• nodal damping parameters (≈ MMA)
1
2
3
4
0 20 40 60 80 100 120 140 160 180
25
50
75
100
heat
in
W
T
in
°C
position in cm
RHS
temperature
FAU F. Wein Design of a solar air heater 11/17

12. Parameter Study
• objective: heat flow
R
outlet
T vy dx
• diagonal not optimal, penalized flat design
• slight dependency on density
FAU F. Wein Design of a solar air heater 12/17

13. Parameter Study cont.
• left design is “reference design”
• right design has less heat source (due to nonlinearity)
• right design has 8% higher heat flow and 18% higher heat flux
FAU F. Wein Design of a solar air heater 13/17

14. Alternative Designs
heat flow ≈ full diagonal heat flow +68 %
FAU F. Wein Design of a solar air heater 14/17

15. Realistic Solar Heat Energy
400
600
800
1000
1200
1400
1600
1800
0 2 4 6 8 10 12
CO2
in
ppm
time in h
1
2
3
11.20 12.20 01.21 02.2103.21 04.21 05.21 06.21 07.21 08.21 09.21 10.21
kWh/d
total energy (230 kWh)
heating energy (130 kWh)
FAU F. Wein Design of a solar air heater 15/17

16. Open Questions
Feature-mapping
• few variables → do we need sensitivity analysis (not used yet)?
• density based feature-mapping or shape aligned mesh?
Material properties
• fan characteristic could include flow resistance in building
• not even linear material properties for carbon fiber absorber exist
• how to model (anisotropic) n-layer absorber for fluid and heat accurately?
Experiments
• does the numerical model match qualitatively?
• parametrize model/material properties based on experiments
FAU F. Wein Design of a solar air heater 16/17

17. Final Slide
Main final objectives
• provide model to improve solar air heater design
• promote solar air heaters as sustainable heating aid
• provide free blue prints for construction and control
Interest in collaborations?
• experimental validation
• determination of model parameters
• advanced numerical modelling and simulation
→ please contact fabian.wein@fau.de
FAU F. Wein Design of a solar air heater 17/17