1. 1
Group 4
Jun Dong (260442997)
Erbolat Riskulov (260483028)
Dillon Stanger (260411556)
BREE 501 – Simulation & Modeling
Assignment 2d
Dr. Grant Clark
April 14th
, 2014
Simulation of a Rocket Mass Heater Stove
Conceptual Model
Context
The Rocket Mass Heater Stove (RMHS) is a super-efficient hybrid masonry wood stove which,
anecdotally, uses between 75-90% less wood than conventional wood stoves, and emits no smoke
for the majority of the burn cycle. In summary, fire burns sideways and up a heat riser producing
turbulence and a clean burn. Then the exhaust snakes
through a system of piping within a thermal mass to store
excess heat and exits out building. To get the RMHS
authorized for permitted projects, the RMHS needs to be
tested by registered lab. Our team will simulate several heat
transfer characteristics of the RMHS to assure it will pass
the lab testing.
Figure 1. A 3d X-ray view of a fire-brick Rocket Mass
Heater Stove excluding the thermal bench exhaust piping.
From right to left, the wood feed to the firebox to the heat
riser on the left. The combustion chamber is included in the
cylindrical oil drum. Below is the pad which supports and
insulates the RMHS. Produced using AutoCADTM
.
Objective
The simulation will analyze for the correlation between high temperature and turbulence for clean
burning inside the RMHS system. The simulation will focus on locating the temperature
distribution and the airflow pattern. Our team anticipates that to successfully simulate the RMHS:
(1) the initial simulation must be simple (simulate the burning of wood within a cylinder) and (2)
our team must understand the heat transfer of combustion, fluid flow dynamics and how to
implement those physical models in COMSOL MultiphysicsTM
. This problem can be approached
as a direct analysis problem where the responses of the fluid flow and temperature profile are
simulated and analyzed (Karplus, 1983).

2. 2
Description
Refer to Figure 2 to the system and its component interactions. Wood fuel, the excitation, is
dropped into the wood feed and burns sideways (response) into and through the firebox. Smoke
produced from combustion, travels to the top of the heat riser, hits the bottom face of the
combustion chamber, and produces turbulent flow (response) within the combustion chamber.
Completely combusted exhaust drops from the combustion chamber to a manifold and exits the
exhaust as steam and carbon dioxide. Though not included in our team’s simulation, clean exhaust
travels through a system of piping (depositing excess exhaust heat to the masonry thermal mass)
and exits the building through an exit chimney.
Figure 2. RMHS profile with system components, interactions, excitations and responses.
To reduce the system to its simplest form, the system boundary will initially include just the region
within the combustion chamber (the cylindrical oil drum). As our team includes additional
components to the simulation, the system boundary will expand to include the region from the
wood feed to the combustion chamber exhaust. Depending on the effects of the stove material
(fire-brick and steel) our team might choose to or not to include the materials in the system
boundary. The system boundary conditions and the anticipated result are shown from Figure 3.

3. 3
Figure 3: RMH cross-section elevation with specified boundary conditions: temperature (specified
by point and by region), airflows, and aperture area. These temperature values were measured from
a physical prototype for validating the accuracy of the model later on. Specifically, these values
were chosen, as they were the only values empirically measured. Some of these temperature values
can be entered as boundary conditions in COMSOL.
Mathematical Model
Variables
The excitations of the system are the inlet airflow of 1.42 m s-1
at 300K and the heat flux from
wood combustion of 15 kW m-2
(Tran et al. 1992). The temperature for the bottom and the top heat
riser was respectively specified to be 1366K and 1255K. Moreover, the system parameters are
listed in the Table 1 below:
Table 1. System parameters
Parameters Definition
𝒓
𝒉
𝒕
A
µ 𝒂𝒊𝒓@𝟑𝟎𝟎𝑲
𝝆 𝒂𝒊𝒓@𝟐𝟓° 𝑪
barrel radius , 0.263545m
barrel height, 0.880m
barrel thickness, 0.001524m (16 gauge)
wood feed aperture area, 161cm2
1.983 ∗ 10−5
kg m−1
s (Engineering Toolbox, 2014a)
1.184kg m−3 (Engineering Toolbox, 2014b)

4. 4
The following Table 2 lists the variables for mathematical models described in the next
Mathematical Principles section.
Table 2: Equation variables
Variable Definition
𝑪 𝒑
𝑭
𝑰
𝒌
𝒑
𝝆
𝑻
𝒖
𝜵
𝜵𝒖
(𝜵𝒖) 𝑻
𝒈
Q
heat capacity (J K−1)
body force (N) (R. Hesketh, 2008)
velocity gradient tensor matrix
thermal conductivity (W m−1
K−1)
pressure (N m−2)
density (kg m−3)
temperature (K)
velocity field matrix (m s-1
)
gradient or "grad" of a scalar field (R. Hesketh, 2008)
velocity gradient (s−1) expressed as: 𝐢
∂u
∂x
+ 𝐣
∂u
∂y
+ 𝐤
∂u
∂z
, (R. Hesketh, 2008)
transpose of the gradient of the velocity matrix
acceleration due to the force of gravity (9.81 m s−2)
heating power per unit volume (W m−3
).
Mathematical Principles
Laminar Fluid Flow
As turbulence flow module was unavailable on the academic version of COMSOL, our team chose
the easier laminar flow module on COMSOL computing with the following set of Equation 1
(COMSOL, 2013). This is the Navier-Stokes equation governing the motion of a non-turbulent
Newtonian fluid, such as our working fluid, air. Fluid flow is important in understanding how the
hot air traverses our system and how the temperature is distributed.
𝜌(𝒖 ∙ 𝛻)𝒖 (1a)
𝛻 ∙ [−𝑝𝑰 + 𝜇(𝛻𝒖 + (𝛻𝒖) 𝑇) −
2
3
𝜇(𝛻 ∙ 𝒖)𝑰] + 𝑭 (1b)
𝛻 ∙ (𝜌𝒖) = 0 (1c)
Heat Transfer in Fluids
The physics module of heat transfer in fluids (Equation 2) in COMSOL (COMSOL, 2013)
described the relationship between the fluid flow and heat transfer because the majority of heat
transfer produced from the RMHS after combustion manifests in forced convection, a mode of
heat transfer integral with fluid flow. In the equation below, T2 is the initial temperature of the working
fluid (300K). During the simulation, we included additional boundary conditions from Figure 3.
𝜌𝐶 𝑝 𝒖 ∙ 𝛻𝑇2 = 𝛻 ∙ (𝑘𝛻𝑇2) + 𝑄 + 𝑄 𝑤ℎ + 𝑊𝑝 (2)

5. 5
Computational Model
Methodology
The physics, laminar fluid flow was chosen over turbulent because the turbulence module was not
available on the student version of COMSOL. Furthermore, the laminar flow allows simplifying
the simulation. Next, the heat transfer through fluids physics was added to simulate the
temperature profile. The implementation of the conceptual model followed several basic steps
illustrated in Table 3.
Table 3. Computational model building
Procedure Specification
Global variables Airflow velocity at the inlet and outlet
Temperature at the base and top of the heat riser
Create model geometry Oil drum shell Heat riser Air space
Assign material Steel AISI 4340 Fire brick Air
Physics Solid conductive heat transfer Fluid flow and
convective heat transfer
Mesh Coarse mesh
Computation Time dependent study for airflow velocity
Post-processing Check internal correctness and check applicability of model by
comparing it to empirical data from a prototype.
From Table 5, only the extra-coarse meshing was applied because the computer does not have
enough resource to perform the simulation within an hour. Finally, the meshed computational
model built in COMSOL is shown in Figure 4 below:
Figure 4. Top view (left) and bottom view (right) of the computational model built in COMSOL

6. 6
Preliminary Result
As shown in Figure 5, the air entering the heat riser at a speed of 0.7 m s-1
. The air cools down
through the heat riser and the barrel with a outside boundary temperature of 300K. As a result, the
airflow speed is decreased to a flow speed of about 0.2 m s-1
while the air is travelling through the
system. However, when air reaches the outlet, its flow speed increases to about 1.4 m s-1
.
Moreover, Figure 5 shows that the temperature is hotter (1300K) on the top part of the heat riser
and colder elsewhere (300K). In sum, the preliminary results do not seem to be reasonable and it
is not comparable to the anticipated values, as shown in Figure 3, measured from a prototype.
More details about the model are shown in the Appendix A.
Figure 5. The airflow velocity (left) is shown higher when air approaching the heat riser, but
slower as the air cools through the upper part of the barrel. The temperature distribution (right)
shows a hotter and lower part of the heat riser.
Problem & Challenge
The first simulation took no less than one hundred (100) minutes. Elimination of certain parameters
in future simulations reduced the solution time considerably. The simulation result showed the
flow velocity distribution in slices rather than a uniform distribution, but was corrected by using a
different viewing scheme in future models. The time dependent solver (set to calculate the
temperature and velocity one (1) second at ten (10) times steps) was unsuitable to address our
objectives to learn about the RMHS at steady state. Furthermore, the flow velocity and the
temperature distributions seem uncorrelated to the prototype values. For instance, the minimum
temperature within the system was actually the outside ambiance temperature of 300K. This means
that the upper part of the stove is not heated at all. Moreover, the simulation took more than one
hour to compute. Hence, these issues was resolved after some improvements that are discussed in
the upcoming Validation section.

7. 7
Validation
Simplifications and Improvements
The model was simplified that reduced the computation time. Firstly, the top cover attached to the
drum, which had a diameter slightly larger than the outer shell, is now reduced to fit the shell wall.
This lowered the number of unnecessary computation on the extra number of finite elements.
Furthermore, the stationary study provided more realistic results compared to the original time
dependency study. Velocity profile varied along the combustion chamber, indicating a possible
correlation to the prototype. Temperature profile change is gradual along heat riser, indicating a better
correlation to the prototype. Furthermore, the final steady state (stationary) simulation time was
reduced drastically down to five (5) seconds.
Conclusions
The final results from Figure 6 are different and more accurate compared to the preliminary results.
The flow velocity is relatively higher on the bottom (0.45-0.76 m s-1
) and the middle part (1.05 m
s-1
) of the system. High airflows, especially in the middle part, mostly occur in where the space is
large and the frictional effect is less. Furthermore, the temperature of about 1260K at the top and
about 1360K at the bottom of the heat riser seemed more reasonable. Thus, compared the airflow
to the simulated temperature distribution on the heat riser, high airflows occur in where the
temperature is hot. Therefore, the question from the objective is answered: there seemed to be a
correlation between high temperature and turbulence (high flow velocity) for a clean burning
inside the RMHS system. However, the turbulence flow module is unavailable for building this
model and the temperature distribution is not completely matching the measured temperature
values from the prototype system (Figure 3). Consequently, the accuracy of the result and the
answer remain invalid. For more information on the computational model, please consult the
Appendix B.
Figure 6. The isosurface plot of airflow velocity (left) shows higher velocities in the bottom and

8. 8
the middle parts of the system. The temperature distribution (right) shows higher temperature on
bottom of the heat riser.
Recommendations
For improvements, the physics of the conductive heat transfer in the barrel shell and the convective
heat transfer to the environment can be implemented so that the model will produce a more realistic
temperature profile of the entire system resembling to the prototype. Other parts of the RMHS,
such as the firebox and the exhaust outlet, can be introduced in continuing this project. Each part
of the RMHS will be simulated and the results can then be imputed on the boundary of the parts
adjoining it. In that way, the velocity and temperature profiles of the entire system can be simulated
without requiring much computational resources. Thus, the meshing size can be reduced to
improve the resolution of the results. Combustion of the wood could be simulated using an
additional module from COMSOL. By adding the extra turbulence flow module from COMSOL,
the model will be able to simulate the turbulence flow as stated in the objective. Moreover, the
RMHS system designed in AutoCAD with precise surface irregularities could be used as the
geometry if COMSOL was able to import it properly. Combining the CAD geometry with
turbulence flow and the time dependent particle collision and tracing physics, the airflow can be
simulated with higher degree of realism.
References
COMSOL. 2013. COMSOL: Multiphysics. Ver. 4.4. Burlington, MA.: COMSOL Inc.
COMSOL. 2013. Introduction to Multiphysics. Burlington, MA.: COMSOL Inc.
Engineering Toolbox. 2014a. Air - Absolute and Kinematic Viscosity. The Engineering Toolbox. The Engineering
Toolbox. Available at: http://www.engineeringtoolbox.com/air-absolute-kinematic-viscosity-d_601.html.
Accessed 17 March 2014.
Engineering Toolbox. 2014b. Air – Density and Specific Weight. The Engineering Toolbox. The Engineering
Toolbox. Available at: http://www.engineeringtoolbox.com/air-density-specific-weight-d_600.html. Accessed 17
March 2014.
Hesketh, R. 2008. Flow Between Parallel Plates – Modified from the COMSOL ChE Library module. Rowan
University Information Resources. Glassboro, NJ: Rowan University. Available at:
http://users.rowan.edu/~hesketh/0906-309/Lectures/Flow%20Between%20Parallel%20Plates%20-
%20Comsol2008.pdf. Accessed 27 March 2014.
Karplus, W. J. 1983. The Spectrum of Mathematical Models. L. A.: University of California.
Tran, H. C., R. H. White. 1992. Burning Rate of Solid Wood Measured in a Heat Release Rate Calorimeter. Fire
and Materials. 16(4): 197-206.

9. 9
Appendix
Section A – Preliminary Model Meshing Specifications
Table 4. Preliminary Model Meshing Specifications
Element Size Parameters Values
Maximum Element Size 0.605m
Minimum Element Size 0.0847m
Maximum Element Growth Rate 2
Resolution of Curvature 1
Resolution of Narrow Regions 0.1
Section B – Final Model Meshing Specifications
Table 5. Final Model Meshing Specifications
Parameters Values
Minimum element quality 1.167E-4
Average element quality 0.235
Tetrahedral elements 1342
Triangular elements 608
Edge elements 168
Vertex elements 36
Maximum element size 0.605
Minimum element size 0.0847
Resolution of narrow regions 0.1
Maximum element growth rate 2
Predefined size Extremely coarse