This document describes research on designing a solar air heater using feature-mapping methods. It involves numerically simulating the fluid flow through an absorber design using the Lattice Boltzmann method and solving the convection-diffusion equation to model heat transfer. Parameter studies are performed to optimize the absorber design for maximum heat output. Open questions remain around further validating the numerical model with experiments and improving the material property models. The overall goal is to provide optimized solar air heater designs to promote their sustainable and affordable use for heating applications.

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