masters of engineering design project presentation
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Masters of Engineering Design Project Presentation. Jamison Hill Dr. Lou Albright, advisor. Dynamic Modeling of Tree Growth and Energy Use in a Nursery Greenhouse Using MATLAB and Simulink. Introduction. - PowerPoint PPT PresentationTRANSCRIPT
Masters of Engineering Design Project Presentation
Jamison HillDr. Lou Albright, advisor
Dynamic Modeling of Tree Growth and Energy Use in a Nursery Greenhouse Using MATLAB and Simulink
Introduction In the forestry industry,
there is a growing push towards the use of transplants for reforestation, as management becomes more intensive.
Planting transplants offer several advantages of the more traditional self-sowing approach:
Faster site establishment Year-round availability Larger size Better control over form
and genetics and species mix
Introduction cont… To meet demand for high quality seedlings, CEA
production techniques are used. Energy costs especially lighting often the determining
factor when deciding on production methods. Simulation provides a means of predicting the costs
and energy consumption statistics for different control strategies before carrying them out in the real-world.
Simulation Requirements
To make sense, results must be interpreted from the plant’s point of view.
For an accurate cost/benefit analysis, the model of the greenhouse must be coupled with a model of the plant.
Model Requirements To be useful, model should be
general: Apply to all situations in which it
would be used Help the user gain an
understanding of the process Be complex enough to capture all
the needed details and no more. More of an art than a science
Examples of Good Models Researchers have done this in the past
with a variety of horticultural crops ROSEGRO HORTSIM TOMGRO
Problem: most of them aren’t applicable to trees.
Same underlying process but different results
Special requirements for seedlings Landis: no current models exist for
greenhouse grown tree seedlings Trees growth is modeled differently: assumed
to be continuous as opposed to discrete basis Tree Growers have a different set of
objectives Total Biomass Height Caliper Root: Shoot ratio Cold hardiness And others (although these aren’t as easy to model)
GUESS Thus, for my design project I created a
new greenhouse-crop model: GREENHOUSE USE OF ENERGY GREENHOUSE USE OF ENERGY
& SEEDLING SIMULATION& SEEDLING SIMULATION or GUESS for short.
Goal of GUESS: To model the effects of greenhouse
climate upon the growth of the seedlings.
To predict the costs associated with controlling climate at a particular set point
The hope is this models could help growers rationally weigh projected productions decisions in terms of their energy cost and their benefit to the plant.
Other Goals
Create a general purpose mechanistic model adaptable for a variety of tree species.
Create a model that is easy for an end user to understand and modify
Goal of GUESS Project
Personal goals To understand the relative
importance of the different processes occur and how to explain them in a mechanistic manner
To learn about how mathematics can be used as a tool to model the natural world.
What does GUESS do? GUESS predicts the following:
The indoor climate characteristics or state (light, temperature, humidity, CO2)
The effect of state upon tree yield and development
The ability of the control system to maintain the indoor climate or state within a prescribed tolerance about pre-defined setpoints
The costs associated with control
What does GUESS do More specifically:
Given a raw weather data file, and a series of parameters
GUESS calculates and then produces graphs of costs, and environmental conditions (temp., CO2, rel H%, light), and growth rate (biomass, height, and diameter).
Show example
How does GUESS work
A two part answer The mathematical models The organization of the GUESS
software How the equations are expressed in
computer code
First lets describe GUESS
Technically speaking
GUESS is a dynamic lumped-parameter simulation coupling a heat/mass transfer model of the greenhouse climate and control processes with a process based model of tree seedlings.
0d A
CVdt r
Why Lumped?
The equations for heat and mass transfer are 2nd order PDE’s. Lumping(ignoring spatial variation) equations to 1st order ODE’s with respect to time. Simple mass/energy balances that can be solved with standard numerical methods. Good enough when gradients are small and average values are most important.
2
2C k
t x
Dynamic Model
In a dynamic model of greenhouse climate:
State variables represents the current conditions within the greenhouse.
At each time step: current outdoor conditions, external/internal fluxes and the previous state are used to calculate state derivatives.
Previous state derivatives are integrated to yield current state.
We are provided with a record of the states and the rates of change
Why Dynamic?
In the past, most energy modeling was done using the stepwise steady state method:
We would neglect storage, and calculate the steady state value for temp, etc.. (dT/dt = 0)
Relatively easy when time steps are large Problems:
Can’t be used with small time steps or to predict instantaneous values.
Won’t tell you how we get from one state to another? Most steady models were formulated years ago
when computers were slow. Now that processors have improved, why not build better models?
GUESS Structure GUESS is composed of three parts
Weather data preprocessor Interpolates needed weather: rel H, temp, wind,
and solar Calculates derived values humidity ratio, wind
pressure Core Simulink model Output Graph routine
Core GUESS Model In the core GUESS model we have: 3 lumped parameter balances for indoor
conditions Temperature Humidity CO2
1 lumped parameter balance for the plant
Carbon (biomass) And a cost calculator Represented using block diagrams
Greenhouse Energy Balance
An object’s temperature is equal to the amount of heat stored in a object divided by its heat capacity (ρCPV).
In the simplest models we consider everything inside the greenhouse to be at the same temperature: air temperature, and to figure this one out, we perform an energy balance:
Change in Energy Stored = Gain from internal sources + gain from solar – losses due to conduction through the cover – losses due to longwave radiation – latent losses (evaporation) – losses due to air exchange
:
:
:
:
1
inP in out r cover cover cover in cover
SHORTWAVECONDUCTION LONGWAVE COVER
r sky cover in sky P in outEVAPOTRANSPIRATION
VENTILALONGWAVE SKY
d TC V UA T T I h F T T
d t
h T T E HEAT nV C T T
TION INFILTRATION
Cover Conductance Sum of conductances
to/ from cover Includes longwave &
convection Strong functions of indoor
& outdoor temperatures, cloud cover, and wind speed
But can be treated as a constant over standard operating conditions since they partially cancel
Humidity in the Greenhouse Humidity is measured 3 ways
Vapor pressure Partial pressure of H2O in the air Used to calculate potential driven flows
Relative humidity Measure of potential to do work or humidity
difference VP/VPsat
Humidity ratio or absolute humidity Kg H2O/kg air Used in air mixing problems
Vapor Pressure VPD = driving force for most transfers
Difference between saturated and current air 2 basic kinds of transfers
Evaporation Condensation
VPsat: exponential func. of T Condensation
Occurs when T ≤ Tdewpoint Dewpoint: temp. at which VPsat = VP (current)
Evaporation requires energy Wet bulb: min. temp. one can cool to by evaporation
Humidity Balance
We need 3 types of units Humidity Ratio Vapor Pressure Deficit: VPsat-VP Rel H
Rate of Change of absolute humidity = Ventilation + Infiltration * (Humidity Difference with Outside) + Fogging + Cooling Pads + ET - Condensation ,
EVAPOTRAN-VENTILATION+INFILTRATION SPIRATION
inin out foggers in sat wetbulb conden sat
sation
dHnV H H k VP VP k VP VP E
dt
Condensation, Foggers, and Pads
All are driven by VPD Because of cooling, foggers take
VPsat at wet bulb Pads operate by changing Tout and
Hout usually within 80% of wet bulb
Evapotranspiration Modeled by Penman-Monteith EQ Sum of two terms
One driven by humidity gradient One driven by radiation
But since air resistance is so great in the greenhouse, we ignore the gradient term
* *
{ }P sat air airnet
a
C VP T VPs RE
s r
Plant Carbon Balance
View growth as mass balance Measured in dry units (g dry
weight) Change in dry weight = Conversion Factor *
(Net Photosynthesis – Respiration) Conversion factor: go from moles CO2 to g dry
weight
Photosynthesis Is catalyzed by Rubisco Farquhar et. al recognized: Rate governed by the limiting
substrate: RuBP CO2(inside the leaf)
Rate of RuBP production determined largely light reaction
Can be modeled as minimum of two saturation curves
Classical Michaelis-Menten: CO2 Light reaction curve
Take in account photorespiration and dark respiration
2 2RUBISCOCO RuBP PGA
2min 0.5CO
net O dlight
WA V R
W
Respiration 2 forms
Maintenance: CO2 released during maintenance of existing
biomass Temperature dependent Includes dark respiration
Growth: Temperature independent CO2 released during the synthesis of new tissue Usually constant * (Photo-Maintenance respiration)
Constant about 0.25
Allometry How do we go
from biomass to height and diameter, which are more interesting?
By using a series of simple power laws, see right panel
1.51
22
24
M K A
M K D H
A D
D
H
Structure of Model:Block Diagram Notation
The core model in GUESS was written in Simulink using block diagram notation:
Graphical programming language used by Simulink.
Allows modeler to focus primarily on equations, and ignore interface construction and numerical methods
Each block is viewed as a little black box where data is fed in at the output, and results leave at output
The type of model used by Simulink to characterize the block is the state-space or machine model, in a minute, we’ll see why its so useful
STATE
x
INPUT y OUTPUT
z
1,t tState f Input State
OUTPUT f State
In Out
Simulink Blockor
Subsystem
In Out
Simulink Blockor
Subsystem
Structure of Model:The State Machine
In Simulink, each block is viewed as a state machine, a black box whose output depends only upon its current conditions aka state variables
Parameters: Input (what we give the block) Output (what we want from the block) State (current conditions within the
block) Another property of the state machine
is that the rate of change of the state depends only two things: the inputs and the previous states.
Because of this we can use these state machines as mass balances, thus making Simulink a good choice for models where dynamics are more important than the spatial distribution.
STATE
x
INPUT y OUTPUT
z
1, t
dStatef Input State
dt
OUTPUT f State
In Out
Simulink Blockor
Subsystem
In Out
Simulink Blockor
Subsystem
Demonstration
Now that I discussed how GUESS works
Lets see what it can do
Model Verification Strategy
Due to budget, time, etc…, an actual validation with a real greenhouse and was infeasible
So, next best thing Phone interviews with various
growers See if my results at least qualitatively
support common growing practices.
Model Simulation A test case was set up to
validate the model. We experimented with
different lighting targets to see which one offered the most growth per unit energy cost
The model was parameterized for Douglas fir production in Corvallis, OR
Seedlings were started at 0.57g d.w and were harvested at 1.7 g dw
Temperature regulated to 68.5±6.3°F
Parameter Value
Unit
U-Value 6.2 Wm-2-K-1
Infiltration 1.1 A.C. hr-1
Floor Area 581 m2
Enclosed Volume
3711 m3
Cover Area 790 m2Lighting Parameters
Intensity Set pointBand-width
CO2 enrichment
No Lights -- -- Yes
25 50 15 Yes
75 88 40 Yes
75 88 40 No
100 100 55 No
250 250 130 Yes
Simulation Results Given the targets and parameters we
initially used: 3 growing seasons could be had only if
supplemental lighting is used. 100 molar required!
But Weyerhaeuser achieves 3 seasons/yr with only 10 molar photoperiodic lights!
Comparison: New conversion Factor
Tree GrowthNo supplemental lighting or CO2
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
0 50 100 150 200 250 300 350
Day
Am
ou
nt
Biomass(g) Height(cm) Diam.(mm)
Comparison: Old Conversion Factors
Tree GrowthNo CO2, No Lights
Old Conversion Factor
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
0 50 100 150 200 250 300 350Day
Am
ou
nt
Biomass(g) Height(cm) Diam.(mm)
Simulation Results Light levels required:
75 micromolar (with CO2 enrichment) 100 micromolar without
Values higher than recc’d Found to be highly dependent on W/m2 solar to
mol/m2 PAR Initial conversion factor of 2.2 changed to 2.34 to
reflect data from Langhans, now no supplemental lighting is required!
Problem: conversion factors are for 350-700 nm band only not for entire solar or artificial spectrum. PAR:NIR split approx 50:50 but can vary greatly
Results Continued
Growth rate highly sensitive to sunlight/PAR conversion factor.
A need for better data for unit conversion.
Growth rate could be highly sensitive to carbon content conversion as well.
Room for future improvements
Obtain better conversion factor data Separate model for shoot and root
temperature. In full sunlight, leaves and soil surface
approx 2-5K warmer than surrounding air.
Include dynamic storage effects of soil and cover on air temperature.
Wrapping It Up
Models can be very useful as simulation tools, but their utility depends highly upon the data used to parameterize them.
A mechanistically correct model may produce meaningless results when given inappropriate data and asked inappropriate questions.
THE END