Design Recommendations for Homebrewers Based on CFD Analysis of
Mash Tun Flow
by
Conor J. Walsh
An Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING
Major Subject: MECHANICAL ENGINEERING
Approved:
_________________________________________
Ernesto Gutierrez-Miravete, Project Adviser
Rensselaer Polytechnic Institute
Hartford, Connecticut
December, 2013
CONTENTS
LIST OF SYMBOLS ........................................................................................................ iii
LIST OF FIGURES .......................................................................................................... iv
LIST OF TABLES ............................................................................................................. v
KEYWORDS .................................................................................................................... vi
GLOSSARY .................................................................................................................... vii
ABSTRACT ................................................................................................................... viii
1. INTRODUCTION/BACKGROUND .......................................................................... 1
2. THEORY/METHODOLOGY ................................................................................... 11
3. RESULTS AND DISCUSSION ................................................................................ 24
REFERENCES ................................................................................................................ 40
APPENDIX A: HISTOGRAM PERCENTAGES........................................................... 42
APPENDIX B: COMSOL REPORTS............................................................................. 44
ii
LIST OF SYMBOLS
cwort
specific gravity of wort, unitless
mmalt
mass of malt, [kg]
Vwort
volume of wort, [L]
BG
boil gravity, in points of specific gravity
eextract
extraction efficiency, unitless
cmax
maximum theoretical specific gravity, unitless
q
Darcy flux, [m/s]
K
permeability, units of [m^2] or [darcy]

dynamic viscosity, [Pa*s]
p
pressure gradient vector, [Pa/m]
v
velocity, [m/s]
n
porosity, unitless

density, [kg/m^3]
T
stress deviator tensor, [Pa]
f
body force, [N]
n0
porosity at intial height, unitless
alpha
empirical constant, [1/ft]
d
depth below the surface, [ft]
Re
Reynold’s number, unitless
dg
representative grain diameter, used as characteristic length [m]
videal
ideal Narziss velocity, 0.18 [gal/min/ft^2] or 1.224e-4 [m/s]
%extraction
percent extraction, unitless
iii
LIST OF FIGURES
Figure 1.1: Mashing Process.............................................................................................. 3
Figure 1.2: Gravity-Driven Continuous Sparging Example Setup .................................... 5
Figure 1.3: Hydrometer Reading ....................................................................................... 5
Figure 1.4: Pipe Manifold .................................................................................................. 9
Figure 1.5: False Bottom ................................................................................................. 10
Figure 2.1: 3-Dimensional COMSOL Geometry Compared to Actual Cooler ............... 11
Figure 2.2: Planar Cuts of 3D Geometry for 2D Models (Left: x-y, Right: y-z)............. 12
Figure 2.3: 2D COMSOL Model (x-y plane type) .......................................................... 12
Figure 2.4: Example Mash Tun Parameter Variation - Number of Legs ........................ 13
Figure 2.5: 2D COMSOL Model (y-z plane type) .......................................................... 13
Figure 2.6: Material Properties for Liquid Regions......................................................... 17
Figure 2.7: Milled Grains for Use in Homebrewing........................................................ 18
Figure 2.8: Example Reynolds Number for x-y and y-z Type Models ........................... 20
Figure 2.9: Inlets and Outlets for Both Types of 2D Models .......................................... 21
Figure 3.1: Three-dimensional View of Initial Mash Tun Configuration ....................... 24
Figure 3.2: Velocity Plot for Initial Mash Tun Configuration ......................................... 25
Figure 3.3: Pressure Plot for Initial Mash Tun Configuration ......................................... 25
Figure 3.4: Example Histogram to Estimate Extraction Efficiency ................................ 26
Figure 3.5: Example Histogram to Estimate Wort Quality ............................................. 27
Figure 3.6: Example Histogram Showing Potential Higher Velocities ........................... 28
Figure 3.7: Manifolds with Different Number of Legs ................................................... 29
Figure 3.8: Improved Uniformity of Flow with Increasing Number of Manifold Legs .. 30
Figure 3.9: Baseline 4-Leg Manifold Design .................................................................. 31
Figure 3.10: Velocity Plot for Baseline y-z Type Mash Tun Model ............................... 32
Figure 3.11: Pressure Plot for Baseline y-z Type Mash Tun Model ............................... 32
Figure 3.12: Histograms for Baseline y-z Type Mash Tun Model .................................. 33
Figure 3.13: Even, Stretched, and Squeezed Spacing Between Manifold Legs .............. 37
iv
LIST OF TABLES
Table 1.1: Maximum Yield for Various Homebrewing Malts .......................................... 7
Table 3.1: Mash Tun Parameters Evaluated Through x-y Plane Models ........................ 28
Table 3.2: COMSOL Results from Varying Number of Manifold Legs ......................... 30
Table 3.3: Mash Tun Parameters Evaluated Through y-z Plane Models ........................ 31
Table 3.4: List of Mash Tun Parameters Considered and Impact on Performance ......... 35
v
KEYWORDS
Mash tun
Flow in porous media
Wort
Sparging
Homebrewing
Design
vi
GLOSSARY
body, 2: a qualitative measurement of the density of a beer
channeling, 30: the phenomenon where water runs along the walls of the mash tun
instead of through the grain bed, leading to lower extraction efficiencies
extraction efficiency, viii: the efficiency with which a sugar is extracted from malted
grains during the mashing process
hydrometer, 5: a measurement device for specific gravity used by floating in a liquid
mash tun, viii: a device in which grain is mashed and then sparged
mash/mashing, viii: a mixture of hot water and milled malted grains that are combined
in order to extract sugar from the grain into the water, which will eventually become
beer; also the act of performing this extraction
mouthfeel, 2: literally, how the beer feels in the mouth; a function of viscosity and
density
oversparged, 23: the condition where areas of the grain bed have been subjected to
flows in excess of the ideal Narziss velocity, leading to extraction of undesirable
compounds from the grain in addition to sugar
sparging, 2: the process of rinsing the grain in order to extract further sugar after letting
it sit in hot water
batch sparging, 3: sparge water is added and drained in batches
continuous sparging, 3: sparge water is added and drained continuously such that
the amount of water in the mash tun remains constant
no sparge, 3: no further water is added following the initial mashing step
specific gravity, 5: the ratio of the density of any liquid to the density of pure water
wort, 1: a beer brewing term for the sugar-rich water that leaves a mash tun and is then
boiled with hops in a brewing kettle
wort quality, viii: an assessment of the level of impurities and off flavors in wort
vii
ABSTRACT
A mash tun is the device used when brewing beer that allows fermentable sugars to be
extracted from malted grains (called mashing). The grain is crushed, then allowed to
soak in hot water in the tun for a prescribed period of time in order to activate enzymes
in the malt, which in turn convert starches in the malt into sugars. The water is drained
from the grains, and then more hot water is used to rinse the grains in order to extract
further sugars. The mash tun must include a filter of some kind to allow for hot water to
run through the grain and carry the sugar out while leaving the grain husks.
For
homebrewers, a popular design for filtering is the pipe manifold: a series of pipes with
small slots that allow water to enter, then exit the mash tun. This style of mash tun will
be modeled in COMSOL and the design will be optimized to provide flow through the
mash tun conducive for maximum extraction efficiency and wort quality, given some
parameters common to the average homebrewer.
The advantages and disadvantages of various design modifications are not
obvious or readily available to the average homebrewer and home mash tun designer.
There are a number of parameters that can be varied during the mash tun build, and it is
not at all clear how each factor affects the final device. When designing a set up that
maximizes extraction efficiency and wort quality, a homebrewer would be well served to
have an ideal design on which to base their own mash tun.
viii
1. INTRODUCTION/BACKGROUND
On May 9, 2013, Alabama's Governor Robert Bently signed into law House Bill 9,
making his state the 50th to pass legislation legalizing the production of beer within the
home. This event was considered by many to be long overdue, as Federal restrictions on
homebrewing were repealed with H.R. 1337, passed in October of 1978. This final legal
step also coincides with a recent increase in public interest in the United States in the
homebrewing hobby, and contributes to the passage of homebrewing from the
underground out into mainstream culture. This marks an ideal time for the homebrewing
community to take advantage of these developments and bolster the beer-making craft
with science and technology. This is not to say that no one in the community has yet
pursued the scientific side of brewing; obviously, commercial breweries in the U.S. have
been advancing in technical prowess since the end of Prohibition, and books such as
Charlie Papazian's The Complete Joy of Homebrewing (1984) are testament to the
existence of a technical approach to homebrewing for decades. To some extent,
however, homebrewing is very much still an art. This project aims to move in the
technical direction by utilizing the simulation capabilities of COMSOL Multiphysics, an
easily accessible and highly capable modeling program. In particular, this project will
evaluate a mash tun, and will attempt to produce reliable technical results that can be
used by any homebrewer.
At a high level, the recipe for beer is a simple one: water, malted grains, hops,
and yeast. Other ingredients can be and often are added, but only four ingredients are
required to make beer. The major steps in the beer process can also be outlined simply.
First, grain (usually barley) is wetted and allowed to partially germinate before dried in a
kiln. This is the malting process, and is done in order to convert starch reserves within
the grain into more easily fermentable sugars. Next, the malted grains are soaked in hot
water in order to extraction those fermentable sugars, and then rinsed to ensure as much
sugar is removed as possible. This step is the called “mashing,” and the device in which
it is conducted is called a “mash tun.” The water/sugar mixture (which is now referred
to as wort) that exits the mash tun is then boiled, at which point hops are added. It is
this step that determines the bitterness of the beer. Finally, the wort is cooled and
filtered to remove hop material, and then combined with beer yeast in a fermenter vessel.
1
In the fermenter the yeast will eat the sugars and produce alcohol and carbon dioxide,
forming beer.
The mashing process is critical to the final taste, aroma, color, and body of the
beer, and provides an excellent opportunity to use science and technology to improve the
homebrewing experience. The alcohol content in a beer is contributed by the yeast, and
the strain of yeast chosen by the brewer will often determine how much of the
fermentable sugar available in the wort will be converted and how much will remain.
However, the mash step determines exactly how much of the fermentable sugar is
available, and thus provides the upper limit for alcohol content. Further, most malts also
provide some level of nonfermentable sugars (highly caramelized and long-chain sugars
known as dextrins) and proteins to the wort. These compounds cannot be broken down
by the yeast, and will be present in the final beer. It is these compounds that contribute
most to the mouthfeel and body of the final product, which are both beer tasting terms
used to qualitatively assess the beer’s viscosity and density: literally, how the beer
“feels” in the mouth. Finally, the nonfermentable sugars also help to determine the
beer’s sweetness.
Mashing can be further broken down into the initial steeping step (where the
grains simply sit in hot water) and the subsequent rinsing step (called sparging). After
the malted grains are crushed in a mill in order to facilitate complete hydration and
expose the inner grain material, they are combined with hot water (usually at a
temperature of 160 to 165°F) in the mash tun and allowed to sit there for some period of
time, usually around 1 hour (see Figure 1.1). The mash temperature should settle at a
temperature between 150 and 155°F, and kept there for the entire steeping time. This is
why plastic coolers are the mash tun structure of choice for homebrewers: they are
relatively cheap and easily available options for creating moderate thermal insulation.
Any off-the-shelf plastic cooler will provide the thermal insulation sufficient for the
precision required of a beginner to intermediate homebrewer.
2
Figure 1.1: Mashing Process
After steeping, the newly-formed wort (water-sugar mixture) is then drained
from the mash, and the sparging process is initiated. At this point, there is still a
considerable amount of fermentable sugar left in the malted grains, and the goal of
sparging is to extraction as much of the sugar as possible without extracting other
undesirable compounds, particularly tannins. Tannins are astringent, bitter polyphenol
compounds that are produce some of the most common off-flavors in beer.
The
astringency of tannins creates a dry, mouth-puckering sensation that is much more
common and desirable in wine. The bitterness of tannins can also throw off a recipe’s
ratio of bitterness to sweetness, causing the sweet malt notes to be muted more than
intended. Other undesirable compounds can also be extracted from grain husks, and for
this reason sparging requires a delicate balance.
Different sparging techniques exist, but generally fall into three categories: no
sparge, batch sparging, and continuous sparging. The “no sparge” method is exactly
as it sounds: no further water is added to the grains, and whatever wort was drained off
after the initial steeping step is the only wort used for the final beer. This method is
highly inefficient, but is quick, simple, and often used by beginners. It also has the
added benefit of low risk of tannin extraction. Batch sparging is akin to a more rapid
version of the steeping step: water is added, the mash is stirred and allowed to settle, and
the wort is drained off. Continuous sparging is a more advanced process where sparge
3
water is slowly added while wort is slowly drained off such that the overall level of
water in the mash tun is not changing (Figure 1.2). This process can take some time,
anywhere between 30 minutes and 2 hours.
Continuous sparging is significantly more efficient than batch sparging and as a
result is used by all commercial breweries. Additionally, continuous sparging prevents
possible oxidation damage that occurs by exposing the grain periodically to oxygen as in
batch sparging. This is done by maintaining a small amount of water above the grain
bed at all times, usually about 1” high, that is kept constant by regulating flow into and
out of the mash tun. In fact, commercial breweries take the process one step further,
using closed piping systems to transport the hot wort after it leaves the tun. Oxidized
phenolic compounds can contribute to a darker wort color, harsher flavor, reduced
protein coagulation and reduced flavor stability in the packaged beer [1]. Wort quality
and flavor consistency is much more of a scientific process in commercial breweries,
and damage due to oxidation is unlikely to be a major problem for beginner and
intermediate homebrewers, if at all.
However, the increase in efficiency through continuous sparging is attainable for
homebrewers, and can be done with a simple setup. Using a container with the heated
sparge water elevated above the mash tun (which is in turn elevated above wherever the
wort will be collecting, see Figure 1.2), the flow of sparge water and wort into/out of the
tun can be gravity-driven but regulated with valves to ensure that the flow is slow and
equal.
However, with this increased efficiency there is an increased risk of over-
extraction of certain areas of the grain bed when using the continuous sparging process,
potentially causing extraction of unwanted compounds from the grain and leading to the
development of off-flavors. For this reason, one must also make sure to consider wort
quality factors along with extraction efficiency.
4
Figure 1.2: Gravity-Driven Continuous Sparging Example Setup
When calculating the extraction efficiency of a beer, the concept of specific
gravity must first be addressed. Specific gravity is the ratio of the density of any liquid
to the density of water, such that the specific gravity of pure water would equal exactly
1. Specific gravity is a direct measurement made by homebrewers using a hydrometer,
which is simply a device that is floated in a small amount of liquid and calibrated to
show the specific gravity based on the density of the fluid (see Figure 1.3). Specific
gravity of beer generally varies between 1.005 and 1.150, and as such is usually
expressed in “points,” where the leading 1 is dropped and the remainder is multiplied by
1000. For example, a specific gravity reading of 1.040 would be 40 points.
Figure 1.3: Hydrometer Reading
5
Using the specific gravity measurement, the volume of wort, and the amount of
malt added to the mash tun, the efficiency of extraction can be easily determined. First,
the concentration of sugar in the wort is calculated in ppg (specific gravity points per
pound per gallon), called cwort [2] :
c wort =
Vwort  BG
mmalt
[1]
In this equation, Vwort is the total volume of wort in gallons, BG represents the original
specific gravity of the boil in points (also the specific gravity of the wort after it leaves
the mash tun), and mmalt is the mass of the malt used in the mash tun in pounds. Once
this value is determined, it can be compared to the maximum potential yield from the
malt. The following equation defines the extraction efficiency of a beer:
eextract =
c wort
cmax
[2]
(where eextract is the extraction efficiency and cmax is the maximum yield for the given
malt in ppg). The maximum yield can vary for different malts used, but approximate
values are readily available for most common homebrewing malts, as shown in Table 1.1
[3].
6
Table 1.1: Maximum Yield for Various Homebrewing Malts
Potential Extract (points per
pound per gallon)
Type of Malt
Pale 2-row malt
37
Pale 6-row malt
35
Munich malt (Belgian/German)
37
Munich malt (US)
33
Wheat malt
39
Crystal malt
34
Special "B"
30
Chocolate Malt
30
Black Patent
29
Roasted Barley
29
Amber/Brown malt
32
Cara-pils (US)
33
Cara-pils (Belgian)
34
Aromatic
36
Biscuit
35
Homebrewer extraction efficiency values average around 75%.
As discussed
above, using the continuous sparging method can greatly increase the efficiency of a
given system. The methods for predicting extraction efficiency in this project using
computer simulation will be discussed in the next section.
7
Highly efficient setups are desirable for a number of reasons. High mash
extraction efficiency is an ideal goal of a homebrewer looking to save money or simply
minimize waste, as a highly efficient mash produces a higher sugar output per grain
input. For a specific beer recipe (for which the amount of sugar needed is a constant,
given a final beer volume), this equates to less grain to buy and less wasted grain overall.
As mentioned briefly above, the highly efficient setups achievable through
continuous sparging techniques bring with them an increased risk of over extraction and
poor wort quality due to the presence of undesirable flavor compounds. As a result, wort
quality should also be considered when optimizing a mash tun. Wort quality has been
found to correlate to the uniformity of flow of water through the mash tun [2], which
will be discussed further in the next section. This correlation is due to uneven flow
throughout the mash tun resulting in over-extraction of certain areas of the grain bed and
produce tannins and other compounds that negatively impact taste.
Homebrewers have a limited ability to affect wort quality compared to the
commercial brewer: for example, they do not have much control over the quality of
ingredients, and must select from those ingredients already available to them in their
area or, more recently, through a small number of internet retail providers. Further, they
have a limited range of heating and cooling techniques and equipment available to them.
Minimizing off-flavors during the mash is one of the few methods through which they
can improve the quality of the wort, and thus the final beer.
The initial inspiration for this Masters Project came from work done by John
Palmer, a homebrewing expert, writer and personality. Palmer, a chemical engineer by
education, often approaches homebrewing from a more technical position than most
when writing magazine articles and books. In particular, his book How to Brew and the
article “Fluid Dynamics -- A Simple Key to the Mastery of Efficient Lautering” in the
July/August 1995 edition of the magazine Brewing Techniques both address the concept
of extraction efficiency and how fluid dynamics analysis can be used to determine the
most efficient mash tun designs.
A mash tun must include a filter of some kind to allow for hot water to run
through the grain and carry the sugar out while leaving the grain husks. The differences
in how this filter is designed are the primary drivers of the efficiency of a mash tun. For
8
homebrewers, a popular design for filtering is the pipe manifold: a series of copper pipes
at the bottom of the tun with small slots cut into them, nearly halfway through the pipe
(Figure 1.4). The slots of a pipe manifold allow wort to enter while keeping grains in the
mash tun. The pipes are connected and run together to allow the wort to exit through a
hole in the tun wall.
Figure 1.4: Pipe Manifold
Palmer focuses on comparing different mash tun types than just the pipe
manifold, including the false bottom (Figure 1.5). He comes to the conclusion that the
false bottom is inherently more efficient than a manifold. This is due primarily to the
uniformity of flow that occurs in a mash tun with a false bottom, which is essentially a
perforated sheet filling the entire tun onto which the grain is placed. Small holes allow
wort to pass through an outlet but keeps the entire grain bed within the tun. This design
was not pursued in this Masters Project for several reasons. First, while false bottoms
are available commercially they are difficult to make, particularly with the holes spaced
uniformly enough to realize their inherent efficiency advantage over other filtering
styles. Additionally, false bottoms available commercially are designed only for round
coolers or buckets. False bottoms also have few parameters that can be modified and
optimized, and do not present a very interesting design opportunity. Pipe manifolds
provided a much more attractive topic for this project for these reasons.
9
Figure 1.5: False Bottom
In this project, a pipe manifold-type of mash tun will be examined and analyzed
using computational fluid dynamics (CFD). Design parameters will be optimized for
extraction efficiency, while also evaluating the impacts to wort quality. Above all, the
feasibility of a real-world mash tun build will be considered, and the final result of the
project will be a set of practical recommendations directed towards the average
homebrewer.
1
0
2. THEORY/METHODOLOGY
In order to analyze the extraction efficiency and wort quality of a mash tun,
computational fluid dynamics simulations were performed using the COMSOL
Multiphysics software. The program was used to model fluid flow through the grain bed
and pipe manifold. Ideally a single, accurate 3-dimensional model including all relevant
features would be used to evaluate different mash tun configurations (see Figure 2.1),
but due to computation limitations this was not feasible. In place of a single model were
substituted two types of 2-dimensional models, by taking various x-y plane or y-z plane
cuts (see Figure 2.2) and modifying individual features. These different planar cuts were
evaluated separately, but approximate the 3-dimensional parameter modification when
all results are viewed in aggregate.
In this way, no model considered all of the
applicable factors at once, but the results can be combined from the various models to
develop an ideal mash tun design.
In 3D, the geometry was contained within a rectangular impermeable boundary,
to represent the mash tun, with the dimensions of an average rectangular cooler often
used by homebrewers. This geometry (12” x 12” x 21”) was carried over into the 2dimensional models.
Figure 2.1: 3-Dimensional COMSOL Geometry Compared to Actual Cooler
11
Figure 2.2: Planar Cuts of 3D Geometry for 2D Models (Left: x-y, Right: y-z)
Figure 2.3: 2D COMSOL Model (x-y plane type)
As can be seen above in Figure 2.3, the x-y plane type of 2D model was made to
represent a plane of the manifold including all of the legs. The area within each pipe
was subtracted from the rest of the model, creating a negative space so that each leg of
the manifold could be made into an outlet for the CFD analysis in COMSOL (Figure
2.3). In this way, the 3-dimensional flow into/out of the 2D plane could be modeled.
The first parameter to be varied (as will be discussed further in the next section of the
12
report) was the number of legs, which was as simple as modifying the geometry as
shown below in Figure 2.4.
Figure 2.4: Example Mash Tun Parameter Variation - Number of Legs
In order to model the specific details (such as slot size and spacing) for the actual
filtering features of the pipe manifold and thus be able to determine the effects of their
variation, another type of 2-dimensional model was required. Cuts of the y-z plane were
used as shown in Figure 2.5 below.
Figure 2.5: 2D COMSOL Model (y-z plane type)
As can be seen from Figure 2.5, the y-z planar cuts allow examination of the slots
cut into the copper pipe manifold that actually performing the filtering, in practice
keeping the grain bed from flowing out through the manifold but allowing wort to pass
through. Another benefit of the y-z plane view is that flow within the manifold itself can
be calculated.
This provides further precision and confidence in the calculated
13
interactions around the manifold openings, and allows calculation of the Reynolds
number within the manifold itself (which will be discussed further later).
In a well-settled (stable) grain bed, the grain will be packed on all sides of the
manifold, including the area beneath the pipes, and as such this is also modeled in
COMSOL as a part of the porous medium. Understandably, there is a large region of
low flow underneath the manifold. Unfortunately, due to the manner in which the y-z
plane cuts are modeled, flow cannot occur in three dimensions around the manifold legs.
As a result, the COMSOL models predict even lower flows in the area underneath the
manifold in the y-z plane views.
Some critical assumptions were made for the fluid dynamic computer simulation
performed in COMSOL, and are outlined as follows. First, it was assumed that the flow
rate into and out of the mash tun would be constant and equal, as if it were regulated
with valves as described in the previous section of this report (continuous sparging).
This allows the analysis to be done in a steady state, without the overall volume of fluid
within the mash tun changing with time, and also provides the inlet boundary condition
necessary for solving the model. This assumption is considered reasonable as the valveregulated system is a common setup for homebrewers, and is ideal in that it requires the
least attention (since the flow is regulated, there is no need to periodically add water or
prevent overflowing).
A further assumption is that the ideal sparge velocity is 0.18 [gal/min/ft^2]. This
is a value Ludwig Narziss of Weihenstephan Brewery recommended for optimal starch
conversion based on empirical results [1] that is now used nearly universally by
homebrewers [2] [4]. However, the value is often simplified to the well-known 1
[qt/min] flow rate into the top of an cylindrical cooler with a diameter of approximately
16 inches, which is a common size cooler produced by brands like Igloo®.
The
methodology used to determine extraction efficiency and wort quality for this project
does not allow for reliable calculation of the effects of varying this velocity. However,
besides the widespread acceptance of this value in the homebrewing community, it also
has the added benefit of ensuring laminar flow throughout the mash tun (as will be
examined later in the report). In practice, 1 [qt/min] is a flow rate easily achievable and
manageable with a standard homebrewing setup.
14
One final important assumption is that the filter mechanism is assumed to be
perfect, which allows the porous media region to stop exactly at the filter features. This
is also reasonable, as most filtering setups are successful in keeping any major particles
from passing through with the wort. The smaller particles that do make it through are
often important components that factor in to the final beer taste and mouthfeel, such as
proteins and dextrins discussed in the previous section, and are accounted for in the
higher density and viscosity of the wort region as modeled in COMSOL. Additionally,
there is another common homebrewing step between steeping and rinsing the grains,
commonly called recirculating. This step involves draining wort from the mash tun and
adding it again carefully to the top of the mash tun, until there are no visible particles
making it through the filter. Recirculating allows the grain bed to compact further,
ensuring that large particles are pressed up against the filter features and minimizing the
amount of grain particles that pass through during the sparging process.
Wort quality and extraction efficiency will be analyzed using fluid dynamics as
follows. First, flow through the grain bed can be analyzed using Darcy’s law for flow
through porous media:
q= 
K

 p
[3]
In this equation, q is the Darcy flux, K is the permeability of the porous medium (in units
of “darcy” or square meters),  is the dynamic viscosity of the fluid, and p is the
pressure gradient vector [5] [6]. The negative sign is used to indicate that the Darcy flux
will be in the direction opposite the pressure gradient; i.e. that the fluid will flow from
high pressure to low pressure. Further, the flux is related to the average fluid velocity
through the porous medium by the porosity of the medium, as shown in the following
equation:
v=
q
n
[4]
(here, v is the fluid velocity and n is a unitless (percentage) measure of the porosity of
the porous medium). At a high level, it can be seen that the velocity is proportional to
the permeability of the grain bed and the pressure, and inversely proportional to the
15
porosity of the grain and the viscosity of the fluid. If there is no pressure gradient within
the tun, there is no flow.
In an attempt to incorporate the potentially significant effects of sugar
concentration within the wort and subsequent density and viscosity increase, two
separate materials were used for the fluid regions in the COMSOL models. The small
fluid region sitting on top of the grain bed, shown in blue in Figure 2.3 and Figure 2.4,
was given properties of pure water, using the built-in Water option from the COMSOL
material database. For the fluid through the remainder of the model, a custom material
called Wort was created and given average fluid property values for wort: specifically, a
viscosity of 1.5 mPa*s [7] and density of 1050 kg/m^3 (equal to a specific gravity of
approximately 1.050, which is an average pre-boil gravity). As a result, there are two
liquid material regions in the model, labeled “Water” and “Wort,” as shown in the
screenshots of Figure 2.6. All fluid regions of the model were held at 155 degrees
Fahrenheit, a common sparging temperature. While this temperature may decrease
slightly over the course of the continuous sparging procedure, modeling would require
use of a time-dependent solver and considerably increase complexity. The mash tun is
relatively well insulated (being made from a cooler) and the small drop in temperature is
not expected to significantly affect the flow through the tun.
For the y-z model a solid region of copper pipe was also created in COMSOL.
This region used the built-in copper material properties from the COMSOL material
database. No heat module used to couple the fluid and solid regions, for the reasons
described in the previous paragraph.
16
Figure 2.6: Material Properties for Liquid Regions
Flow anywhere outside of the grain bed (in the pipe manifold, as well as in the
water level above the grain bed) will be considered laminar flow and will be evaluated
using the Navier-Stokes equation. The validity of this assumption will be confirmed
later. The Navier-Stokes equation is as follows:
 v

+ v  v  = p +   T + f
 t


[5]
where v is the flow velocity,  is the fluid density, p is the pressure, T is the stress
deviator tensor, and f is a body force acting on the fluid. In this particular case, gravity
is the only body force that can be applied. However, because the inlet velocity is
regulated, this has no impact on the flow through the tun. This was confirmed by
running multiple COMSOL models with and without the gravity body force applied.
COMSOL conveniently includes a module called “Free and Porous Flow” that
easily combines these two flow regions, coupling Darcy’s Law with the Navier-Stokes
equation. The Free and Porous Flow module naturally requires properties of the porous
medium as inputs in order to evaluate Darcy's Law. Values for permeability (K) of the
grain bed vary significantly, and the estimated value of K = 9.87 e-11 m^2 [8], equal to
17
about 100 darcys was used in the model. For porosity (n) a value of 0.30 (30%) was
used, which is an average value used in soil analysis for a mix of gravel and sand
particles [9]. This seemed to reasonably approximate the grain after milling, which will
often consist of some large particles interspersed with fine, flour-like ground bits (Figure
2.7).
Figure 2.7: Milled Grains for Use in Homebrewing
For porous media composed of loose material (like the grain bed), porosity
depends on several factors such as grain packing, shape, arrangement, and size
distribution [10]. Media made up of poorly sorted particles (meaning that the grain size
varies) will have a lower porosity than well-sorted particles, all else equal. There is
some change in porosity with depth, as compacting forces increase with depth. Athy
[11] demonstrated that the change in porosity with depth could be calculated with the
following equation:
n = n0  e  alphad
[6]
where d is depth below the surface of the porous medium and alpha is a coefficient
dependent on the factors identified above. The largest value for alpha given in Bear’s
data [10] was for shale, where alpha = 3.84 e-4 [1/ft]. This example indicates that any
change in porosity through a height of less than 2 feet would be negligible.
For the y-z plane models, no physics module was applied to the copper region, as
there should be no flow through these boundaries. However, the filtering features of the
manifold could not be included in the x-y planar models. Instead, the Free and Porous
18
Flow module was also applied the copper region in the x-y models, which was given a
the same porosity as the grain bed but a lower permeability (1e-12 m^2, roughly 100
times smaller than the grain bed) in order to approximate the increased resistance to flow
into the manifold due to the small surface area of the filtering features.
In order to ensure that Darcy’s law is appropriate for this problem, it must be
shown that the flow is clearly laminar. For this reason the Reynolds number was
calculated throughout the model in order to ensure that this is the case for each variation
of the mash tun parameters. Any Reynolds number less than one is sufficient to show
that the flow is slow and viscous enough to apply Darcy’s law, although empirical data
has indicated that flow categorized by Reynolds numbers up to 10 may still be
considered Darcian [12]. The equation for Reynolds number in porous media is as
follows:
Re =
  v  dg

[7]
where ρ is the density of pure water, v is the outlet velocity, μ is the viscosity of the
fluid, and d g is a representative grain diameter for the porous media. The Reynolds
number was computed for every model, to ensure flow remained laminar (see Figure
2.8). The largest Reynolds number within the grain bed was below 1 for all models, and
even within the pipe manifold was never found to exceed 3. These values confirmed the
decision to assume flow throughout the model was laminar.
19
Figure 2.8: Example Reynolds Number for x-y and y-z Type Models
In order to provide the boundary conditions for the Free and Porous Flow
module, inlet and outlets were identified for each model (marked by blue lines in Figure
2.9). As discussed above, the inlet condition was to prescribe a normal velocity of 0.18
20
[gal/min/ft^2] into the top of the water region. This converts to approximately 1.2224 e4 [m/s]. The outlet was given a pressure condition of 0 Pa, with no viscous stress.
Figure 2.9: Inlets and Outlets for Both Types of 2D Models
The method through which extract efficiency and wort quality will be estimated
is fairly simple. When using a continuous sparging technique as discussed earlier, with
constant flow at the inlet and outlet, flow through the grain bed will be distributed about
the ideal velocity recommended by Narziss, about 1.224 e-4 [m/s]. After running a
21
simulation, a histogram plot can created showing frequency of velocities through the
grain bed. These plots can then be used to evaluate extraction efficiency and wort
quality.
Extraction efficiency is a measure of the efficiency of converting grain into
fermentable sugars, and is commonly measured while homebrewing using specific
gravity as discussed in the previous section. However, this value can also be calculated
using COMSOL analysis, by making the assumption that the ideal Narziss velocity
provides 100% extraction of sugars from the grain and into the wort. It follows that any
velocity in the grain bed that exceeds this value, such as 150% of the Narziss velocity, or
200% of the Narziss velocity, will also provide 100% extraction. Further, any velocity
below this value would provide less than 100% extraction. A linear correlation will be
assumed, such that the ratio of any velocity to the ideal Narziss velocity will be an
estimate of the percent extraction in that section of the bed. For example, if an area of
the grain bed sees a velocity of 0.5 e-4 [m/s], the percent extraction will be:
%extraction =
0.5e 4 [m / s]
0.5e 4 [m / s]

 40.8%
v ideal
1.224e  4 [m / s]
[8]
The histogram plot can be used to determine the overall efficiency of the grain
bed by calculating the percent area of the bed that sees various velocities.
For
simplicity, the histogram was broken up into quantized sections of 5% of ideal velocity
(see Figure 3.5 in the next section for an example). The percent occurrence of each of
these sections is then multiplied by that velocity and summed to give a direct
representation of the extraction efficiency.
Wort quality is more qualitative assessment. However, it has been documented
that highly uniform flow is well correlated with improved wort quality [2]. This is due
primarily to excessive flow through certain regions of the grain bed which result in
higher levels of tannins and other undesirable grain products in the wort. For the
purposes of this project, areas of the grain bed with velocities in excess of 100% are
considered oversparged. These oversparged regions are where the danger of poor wort
22
quality lies.
Exposed to high flow, these areas of grain will be subject to tannin
extraction.
The histogram plots generated by COMSOL will also be used to determine the
percent of the grain bed that is oversparged, and this will provide another performance
indicator for evaluating the various mash tun configurations.
23
3. RESULTS AND DISCUSSION
The COMSOL models developed for this project were first used to determine
velocities and pressures through the grain bed, in order to ensure that the simulations
were performing as intended, and to provide a level of reassurance in the results
ultimately calculated. For each mash tun configuration a velocity plot was created,
including streamlines, for visual confirmation of flow through the mash tun (Figure 3.2).
Pressures throughout the grain bed were also plotted for every model (Figure 3.3). The
two example plots for velocity and pressure through the grain bed shown here represent
the x-y plane cut of the initial mash tun configuration. This initial configuration, while
analyzed in two dimensions, is intended to represent a manifold made from a single pipe
running through the mash tun as shown below in three dimensions in Figure 3.1. The
results from all of the configurations examined in this Master’s Project are included in
Appendix B.
Figure 3.1: Three-dimensional View of Initial Mash Tun Configuration
24
Figure 3.2: Velocity Plot for Initial Mash Tun Configuration
Figure 3.3: Pressure Plot for Initial Mash Tun Configuration
Once the COMSOL model was developed and confirmed to run successfully,
different model parameters could be modified in order to determine their effect on
25
extract efficiency and wort quality. As discussed in the previous section, histogram plots
were used to evaluate these two performance measures. Using the 1D plot feature in
COMSOL, results from each new model were mapped to a histogram plot that quantified
the percentage of the grain bed experiencing specific velocity levels. The histogram plot
is used to determine the overall efficiency of the grain bed by calculating the percent
area of the bed that sees various velocities. For simplicity, the histogram was broken up
into 20 sections between 0 m/s and the ideal velocity (Figure 3.4). The relative area of
the bed that is subject to each particular velocity is then multiplied by the efficiency at
that velocity and summed to give a representation of the total extraction efficiency.
Although improvements in efficiency can be seen simply from looking at the histogram
plot, is difficult to determine the numerical values from a quick glance. Using the export
data function in COMSOL, a .csv file can be exported with the exact relative area
percentages for each of the 20 quantized velocity sections. It should be reiterated that all
areas of the bed with velocities in excess of the ideal value are considered to be 100%
efficient, and will be incorporated using the same histogram used for determining wort
quality (Figure 3.5). The efficiency for this example configuration was calculated to be
about 95%.
3.4:earlier,
Example
Histogram
to Estimate
Extraction
Efficiency
AsFigure
identified
wort
quality is correlated
with
uniformity
of flow.
26
Excessive flow through certain regions of the grain bed due to non-uniform flow
patterns can result in higher level of tannins and other undesirable grain products in the
wort. It is assumed that any value in excess of the ideal Narziss velocity is unecessarily
high, and creates the potential for overextraction of the grain.
These areas are
considered oversparged and are where the danger of poor wort quality lies. At high
flow, these areas of grain will be subject to extraction of tannins and other undesirable
grain products. In Figure 3.6 below, the percentage of the grain bed that is oversparged
can be evaluated by simply plotting the percentage of the bed experiencing a velocity
greater than the ideal velocity. It can be easily seen from the histogram that about 42%
of the bed is oversparged.
Figure 3.5: Example Histogram to Estimate Wort Quality
The values calculated for efficiency and oversparged percentage are not expected
to match real world data, primarily due to the oversimplification of the model geometry.
Other reasons include the inherent variability in real-world ingredients and other
measurements which needed to be estimated in order to minimize the scope of the
simulation. Additionally, for simplicity of calculation, the histogram shown in Figure
3.5 does not include higher velocity values which represent a very small portion of the
grain bed (see Figure 3.6 below). On the whole, the results of the simulation are an
27
approximation.
However, it is expected that this approximation can be useful in
determining trends of increased efficiency or wort quality. While the exact percentages
found through the simulations will not directly correlate to real-world testing,
predictions of significantly improved performance metrics due to certain design
variations are expected to transfer well to real-world mash tun builds.
Figure 3.6: Example Histogram Showing Potential Higher Velocities
The COMSOL analysis used simplified 2-dimensional geometries in order to
create a more easily solvable simulation, as discussed previously. The first type of
model, where x-y planar cuts (see Figure 2.3 of the previous section) were taken through
the mash tun, allowed for evaluation of a specific set of parameters (Table 3.1). These
models are intended to represent a plane cut perpendicular to the manifold legs..
Table 3.1: Mash Tun Parameters Evaluated Through x-y Plane Models
Parameter
Number of manifold legs
Interpipe spacing
Pipe diameter
Grain bed depth
Height of top water layer
Given Value/Range
1–8
even, stretched, squeezed
~3/8 – 2”
8 – 16”
0.1 – 6”
28
The baseline x-y type model included average or common values for the various
parameters to be evaluated. The initial model had a single copper pipe making up the
manifold, running right through the center of the mash tun. The pipe diameter was ½”, a
common size pipe used by homebrewers likely due to its wide availability. The grain
bed depth used was 12”, and the water level on top of the grain was 1”. The interpipe
spacing parameter has no meaning when there is only 1 manifold leg, but when the
number of legs was increased, they were initially evaluated with even spacing, such that
the legs divided the tun area into equal sections.
The first parameter to be evaluated was the number of manifold legs (shown in
three dimensions in Figure 3.7 below). Increasing the number of manifold legs adds
significant complexity to the mash tun build, but has a clear impact on performance.
The effects are shown in the data included in Table 3.2. Increasing the number of legs
was found to primarily improve wort quality. This follows, because as the number of
outlets for the grain bed increases, the outlets come closer and closer to encompassing
the entire lower area of the mash tun, which minimizes the regions to either side of the
tun that are subject to low flow (see Figure 3.8). Further, since the flow rate through the
outlets is constant, as the number and area of outlets increase the velocity at those outlets
decreases.
This results in improved wort quality.
Extraction efficiency is largely
unaffected, but decreases slightly with a very large number of legs. This is an interesting
phenomenon, likely due to the velocity dropping in some areas of the bed to values that
are lower than the ideal. This is a predictable result of the interplay between efficiency
and wort quality.
Figure 3.7: Manifolds with Different Number of Legs
29
Table 3.2: COMSOL Results from Varying Number of Manifold Legs
Percent of Grain
Configuration
Percent Efficiency
1 leg
89.9%
45.8%
2 legs
91.4%
46.9%
3 legs
91.4%
45.1%
4 legs
91.2%
42.4%
5 legs
91.0%
39.5%
8 legs
88.4%
28.5%
Bed Oversparged
Figure 3.8: Improved Uniformity of Flow with Increasing Number of Manifold Legs
These results indicate that, in terms of wort quality, the ideal mash tun design
would include as many manifold legs as can possibly be fit into the mash tun. First, the
difficult of constructing a manifold like this at home is significant. Additionally, there is
a slight drop in efficiency with high numbers of legs. There is also one further concern.
In practice, when manifold legs are placed to closely to the side walls of the mash tun,
flow along these walls is often prone to occur, a result called channeling [2]. The
interaction between the plastic walls of the cooler and the grain bed is not well modeled
in COMSOL, and thus is not predicted by the simulation. Despite this, channeling is
well known to lower efficiency due to an unexpectedly under-sparged grain bed. To
minimize these effects but also provide reasonable levels of efficiency and wort quality,
a 4-leg manifold was chosen for this project. This 4-leg configuration was used for the
30
remainder of the parameters varied in the x-y plane models (Figure 3.9). The results the
other parameters had on the performance of the mash tun can be seen in Appendix B and
are summarized later in this section in Table 3.4.
Figure 3.9: Baseline 4-Leg Manifold Design
The second type of model used y-z planar cuts as shown in Figure 2.5 of the
previous section. These cuts were taken along a single leg of the pipe manifold, and
allowed for evaluation of a different set of parameters from the x-y planar cuts, primarily
the individual features that provide the filtering for the manifold (Table 3.3).
Table 3.3: Mash Tun Parameters Evaluated Through y-z Plane Models
Parameter
Spacing between slots
Size of slots
Manifold location
Given Value/Range
1/2 – 2”
1/32 – 1/4”
1 – 5” from non-outlet side wall
The baseline y-z type model included some of the baseline values from the x-y
models, including a pipe diameter of ½”, a grain bed depth of 12”, and a water level on
top of the grain of 1”. Average values were also chosen for the new parameters. The
31
baseline spacing between the slots was chosen to be 1”, which is often used in
homebrewer mash tun builds. The initial size of the slots was 1/16”, intended to
represent the width of hacksaw blade that would be used to make these cuts. The initial
manifold location was chosen to end 3” from the non-outlet side of the mash tun, but as
with the other parameters will be varied in order to see what effect this measurement has
on tun performance.
Example velocity and pressure plots for y-z plane type models are shown below
in Figure 3.10 and Figure 3.11. Histogram examples are included in Figure 3.12.
Figure 3.10: Velocity Plot for Baseline y-z Type Mash Tun Model
Figure 3.11: Pressure Plot for Baseline
y-z Type Mash Tun Model
32
Figure 3.12: Histograms for Baseline y-z Type Mash Tun Model
At first glance, some significant differences are apparent between the two types
of models. For one, the efficiency appears significantly lower in the y-z type model than
in an x-y type. In fact, there is a large percentage of very low-velocity regions in this
baseline y-z type model: nearly 20%, in comparison to practically 0% in the x-y type
models. As discussed before, this is due to the lack of flow around the manifold legs in
the y-z type model that is captured in the x-y models. The result is that the low flow in
the region below the manifold is exaggerated in the y-z model.
However, the area below the manifold still experiences relatively low flow in the
x-y model, which meshes with actual experiences of homebrewers. In fact, one of the
primary sources of water lost when brewing comes from the percentage of water that
remains trapped in the mash tun below the manifold and cannot be drained, and is even
accounted for in specialized homebrewing software such as BeerSmith. This is an
indication of the lack of flow through this area. Logically, in order to improve efficiency
one could minimize this area and drop the manifold closer to the bottom of the mash tun.
However, the height from the bottom of the tun is determined by the height of the
existing spigot hole in the side of the rectangular cooler used to create the tun. For ease
of manufacturability for the average homebrewer, creating a new hole in the cooler or
33
alternatively installing a manifold that is not parallel to the bottom of the cooler is not
considered in this project.
Table 3.4 below shows the list of all parameters considered during analysis, and
what general effects they had on the mash tun performance. Some parameters were
taken to be constants and not varied at all during the analysis. This was mainly done in
order to keep the mash tun materials easily accessible. Any variation in these parameters
would have forced prospective mash tun builders to look elsewhere than their local
hardware store. For example, only one standard size cooler was considered for the mash
tun.
No significant variations were found in large rectangular coolers, except
occasionally that they were available in taller sizes. Further, only standard and widely
available copper piping sizes were used in the analysis: in particular, nominal diameters
of 3/8”, 1/2”, 3/4", 1”, and 1 ½”.
The exact dimensions for the diameters and
thicknesses of these pipes were determined by M-type copper piping, which is a light,
thin-walled pipe intended for above-ground residential and commercial uses.
The effects of all variables were isolated by varying those parameters in separate
COMSOL models. COMSOL reports are provided for every model in Appendix B. The
exported results from the histograms are included in Appendix A. All side-by-side
comparisons of the results contained in Appendix A should be done with the baseline
model for each type, which are marked bold in the tables: all x-y plane models should be
compared to the original 4-pipe model, and all y-z plane models should be compared to
the baseline of that type.
Obviously, not every parameter that goes in the design of a pipe manifold mash
tun could be considered in this project. However, an attempt was made to evaluate some
of the most common and most easily modified parameters for the average homebrewer.
In this way, the recommendations of this project can be easily and dependably translated
into a superior mash tun design.
To reiterate the methodology explained in the last section, an increase in the
percentage of the grain bed that was oversparged, or subjected to velocities that were too
high, was considered to lead to a decrease in wort quality.
34
Table 3.4: List of Mash Tun Parameters Considered and Impact on Performance
Parameter
Mash tun
dimensions
Height of
outlet hole
Thickness of
pipe
Type
Given
Value/Range
L = 21”
W = 12”
Constant
H = 12”
(modified with
grain bed depth)
1” from bottom
Constant
of tun
Dependent on
Constant
pipe diameter
Impact on
Extraction
Efficiency
Impact on Wort
Quality
-
-
-
-
-
Increased
quality with
more legs
Increased
quality with
increased
spacing
Slight increase
in quality with
increased
diameter
Increased
quality with
deeper bed
Slight increase
in quality with
higher water
level
Decreased wort
quality with
smaller spacing
No significant
effect
Number of
manifold legs
Variable
1, 2, 3, 4, 5, 8
Slight decrease in
efficiency with
more legs
Inter-pipe
spacing
Variable
Even, stretched,
squeezed
Peak efficiency
with even spacing
Pipe diameter
Variable
Nominal pipe
size of 3/8”, ½”,
¾”, 1”, 1 ½”
Grain bed
depth
Variable
8”, 10”, 12”,
14”, 16”
Height of top
water layer
Variable
0.1”, 1”, 2”, 6”
No significant
effect
Spacing
between slots
Variable
¼”, ½”, ¾”, 1”,
1½”, 2”
Size of slots
Variable
Manifold
location
Variable
Increased
efficiency with
smaller spacing
No significant
effect
Increased
efficiency closer
to wall
1/32”, 1/16”,
1/8”, 1/4”
1”, 3”, 5” from
non-outlet side
wall
35
Slight increase in
efficiency with
increased
diameter
Slight increase in
efficiency with
bed depth
Decreased wort
quality
As discussed earlier, there was a clear improvement in wort quality and a slight
decrease in extraction efficiency as the number of legs making up the manifold
increased. However, for several reasons it was concluded that a 4-leg manifold would
be sufficient for the purposes of this project, and would provide benefits over 1, 2, or 3leg manifolds, which have been observed to make up the majority of homebrewer mash
tun builds.
Interpipe spacing was a parameter intended to examine the effects of keeping the
same number of legs of the manifold and the same size pipes, but modifying the
locations of the legs. Figure 3.13 gives an indication of how this was accomplished.
The baseline model included an “even” configuration, where the 4 legs of the manifold
split the area of the tun into 5 equal sections, such that the spacing was roughly 2”
between each leg, and between the outer legs and the wall. A “stretched” spacing model
was also simulated, where the manifold legs were moved away from the center such that
the spacing between legs was about 3”, and the spacing between the outer legs and the
wall was less than 1”. Finally, a “squeezed” spacing model was simulated that included
all 4 legs of the manifold gathered together at the center of the tun, with only about 0.5”
spacing between legs and over 4” between the manifold and either wall of the tun. No
improvement was seen in extraction efficiency as interpipe spacing increased. However,
there was a massive improvement in wort quality with increased pipe spacing in the
“stretched” model, through a reduction in oversparged areas and thus an increase in flow
uniformity as seen in the velocity plots below (Figure 3.13). Unfortunately, the same
concern with channeling expressed earlier again comes into play, as the manifold legs
get too close to the walls of the mash tun. This significant improvement in quality is
considered valuable enough to take on the risk of channeling. While the exact
dimensions may be determined by the homebrewer, it is recommended that the spacing
of the manifold legs be more similar to the “stretched” spacing modeled here than the
“even” spacing, in order to achieve the benefits in wort quality. Attention should also be
kept to whether channeling seems to occur by comparing measured and expected
specific gravity.
36
Figure 3.13: Even, Stretched, and Squeezed Spacing Between Manifold Legs
The pipe diameter was varied significantly, but kept within the constraints of
widely-available M-type copper piping. A slight increase in efficiency was seen with
increase pipe diameter, along with a very slight increase in wort quality. One of the
reasons for the improvement is that the low-flow area beneath the manifold decreases in
size as the pipes extend further down, assuming they are centered on the plane 1” from
the bottom of the tun. These gains are not necessarily worth the trouble, however, as the
larger (and thus thicker) the pipe, the more difficult it is to work with, particularly to saw
slots into. Further, if the manifold is to pass through the existing hole in the cooler wall,
there is a maximum pipe diameter that can be used with available fittings to make this
connection watertight. Depending on the value the mash tun builder puts in the slightly
improved performance, larger diameters may be desired and used. It should also be
noted that there have been concerns expressed by homebrewing websites that smaller
piping may not be able to withstand the weight of the grain bed pressing down on it,
specifically anything less than ½” in diameter. For these reasons, it is recommended that
that a nominal pipe size of at least ½” be used.
The depth of grain bed was the next parameter evaluated in COMSOL.
There
was some correlation between increased depth and higher efficiencies, and there was a
significant increase in wort quality as the bed grew deeper and deeper. The issue here is
that the bed can only be as deep as the mash tun allows for, and deeper coolers are not
always readily available. However, given the COMSOL results it is recommended that a
cooler of at least 12” tall be used, and deeper ones considered if possible.
37
The height of the water level on top of the grain bed is normally not considered
critical to homebrewers. The requirement of at least 1” of water on top of the bed is
intended to provide some margin so that if the outlet flow rate exceeds the inlet flow rate
during continuous sparging, there is some time for the homebrewer to realize and correct
before air starts getting trapped in the grain bed. However, the simulation results
indicated that there may be a slight increase in wort quality with a higher water level.
The problem with increasing the water level is that it limits how much of the mash tun
can be used for the grain bed. For this reason, it is recommended to use the standard 1”
level of water on top of the grain bed. It is much more important to the sparging process
that there always be some level of water above the grain than the actual amount of water.
The spacing between slots in the pipe manifold was considered next.
The
baseline configuration used a 1” spacing between successive slots. Larger spacing and
smaller spacing was evaluated.
As was to be expected, the extraction efficiency
improved as the spacing decreased and the total number of slots increased. In this way,
the manifold resembled more and more the “false bottom” design discussed earlier.
However, wort quality also decreased at a similar rate as the spacing between slots
decreased.
It should also be noted that cutting slots into the copper piping when
producing the manifold can be quite an ordeal, and doubling the number of slots is
extremely difficult. It is therefore recommended that 1” spacing be used, which is
expected to provide a reasonably high efficiency and wort quality. A homebrewer
looking to build a mash tun can choose to add more slots if so desired.
The impact of varying the width of the slots in the manifold was also evaluated.
This parameter may be a difficult one to modify as a homebrewer, as the size of the slots
is usually dependent on the width of the saw blade used to cut the slots in the copper
pipe. Interestingly, there does not appear to a significant effect on either wort quality or
extraction efficiency with changing slot size, so a homebrewer should use whatever saw
blade they have on hand. One final note is that the larger slot size does increase the
possibility of grain pieces making it through the filtering mechanism, or simply
increasing the amount of time it would take to recirculate and successfully compact the
38
grain bed. With this in mind, if the homebrewer has multiple options when it comes to
saw blade thickness, it is recommended that the smallest blade width be used.
The final parameter that was evaluated was the distance between the manifold
and the non-outlet side wall of the mash tun. Initially, the manifold was kept 3” away
from the wall in order to moderate concerns with channeling occurring due to the
proximity of the pipe with the wall. However, the COMSOL analysis indicated that
moving the manifold closer to the wall would increase the efficiency substantially,
although this modification would also decrease the wort quality somewhat.
It is
recommended that the manifold be moved closer to the wall than 3”, but perhaps not
closer than 1” to minimize concerns with channeling.
In summary, based on personal experience and the CFD results, the ideal mash
tun design for a homebrewer looking for high efficiency and wort quality should feature
the following feasible characteristics:

4-pipe manifold

Manifold legs stretched out towards either side of the mash tun, with the
particular details to be determined by the homebrewer

½” copper pipe or larger

12” tall grain bed, or taller if possible (deeper cooler)

1” of water on top of grain

1” spacing between slots cut into manifold, although smaller spacing may
be desired

Any size slot is acceptable

Manifold should be roughly 1” from the non-outlet end of the mash tun
Any one of these design choices should help to keep high wort quality and
extraction efficiency, and incorporating all of these into one mash tun build will produce
the ideal mash tun design.
39
REFERENCES
[1] Narziss, Ludwig. The Technology of Brewing Beer. Ferdinand Enke Verlag,
Stuttgart, Germany, 1992.
[2] Palmer, John J. How to Brew. 3rd ed. Brewers Publications, 2006.
[3] Uchima, Mike. “Potential Extract Tables.” Mike’s Brew Page.
<http://hbd.org/uchima/tech/extract.html>
[4] Miller, David. Brew Like a Pro. Storey Publishing, 2012.
[5] de Lemos, Marcelo J.S.. Turbulence in Porous Media: Modeling and Applications,
Second Edition. Elsevier Science and Technology Books, Inc., © 2012. Books24x7.
Web. Sep. 17, 2013. <http://common.books24x7.com.colelibprxy.ewp.rpi.edu/toc.aspx?bookid=49256>
[6] Vafai, Kambiz. Handbook of Porous Media, Second Edition. CRC Press, 2005.
[7] Pahl, “Important Raw Materials Quality Parameters and Their Influence on Beer
Production,” Brewing Conference Bangkok 2011.
[8] Hirasaki, G. J. “Lecture Notes on Adsorption.” CENG 402, Chapter 3.
<http://www.owlnet.rice.edu/~ceng402/Hirasaki/CHAP3D.pdf>
[9] Fetter, C. W. Applied Hydrogeology, 3rd ed. Upper Saddle River, NJ: Prentice
Hall, Inc., 1994.
[10] Bear, Jacob. Dynamics of Fluids in Porous Media. Dover Publications, 1972.
<http://app.knovel.com/hotlink/toc/id:kpDFPM000I/dynamics-fluids-in-porous>
[11] Athy, L. F. Density, Porosity, and Compaction of Sedimentary Rocks. v. 14,
AAPG Bulletin, 1930.
[12] Wang, Herbert F. and Mary P. Anderson. Introduction to Groundwater Modeling:
Finite Difference and Finite Element Methods. Academic Press, Inc., 1982.
40
Additional References not Cited:
Fox, Robert W., Philip J. Pritchard, and Alan T. McDonald. Introduction to Fluid
Mechanics. 7th ed. John Wiley and Sons, Inc., 2009.
Spanos, T. J. T. The Thermophysics of Porous Media. Chapman and Hall/CRC, 2001.
Xie, Liquan, ed. Modeling and Computation In Engineering II. CRC Press, 2013.
41
APPENDIX A: HISTOGRAM PERCENTAGES
x-y Type Models
Model Number
Configuration
Percent Efficiency
Percent of Grain Bed
Oversparged
1.1
1 leg
89.9%
45.8%
1.2
2 legs
91.4%
46.9%
1.3
3 legs
91.4%
45.1%
1.4
4 legs
91.2%
42.4%
1.5
5 legs
91.0%
39.5%
1.6
8 legs
88.4%
28.5%
1.7
stretched spacing
90.7%
24.3%
1.8
squeezed spacing
90.6%
47.0%
1.9
large diameter (3/4”)
91.6%
42.3%
1.10
larger diameter (1”)
92.0%
42.2%
1.11
very large diameter
(1½”)
92.9%
41.3%
1.12
small diameter (3/8”)
89.2%
42.5%
1.13
short grain bed (10”)
90.4%
47.8%
1.14
shorter grain bed (8”)
88.9%
49.3%
1.15
deep grain bed (14”)
91.6%
35.3%
1.16
deeper grain bed (16”)
92.0%
31.3%
1.17
minimal water level
(0.1”)
91.6%
49.6%
1.18
high water level (2”)
91.1%
39.7%
1.19
higher water level (6”)
91.1%
39.7%
42
y-z Type Models
Model Number
Configuration
Percent Efficiency
Percent of Grain
Bed Oversparged
2.1
baseline yz
85.5%
62.7%
83.6%
60.2%
80.0%
55.9%
86.0%
63.5%
86.6%
64.3%
87.3%
65.3%
2.2
2.3
2.4
2.5
2.6
large spaced slots
(1½”)
larger spaced slots
(2”)
small slot spacing
(3/4”)
smaller slot spacing
(½”)
very small slot
spacing (1/4”)
2.7
1/8-inch wide slots
85.6%
63.0%
2.8
1/4-inch wide slots
85.3%
63.4%
2.9
1/32-inch wide slots
85.3%
62.3%
88.1%
63.3%
82.4%
59.3%
2.10
2.11
manifold closer to
wall
manifold further from
wall
43
APPENDIX B: COMSOL REPORTS
1-Leg Manifold
44
2-Leg Manifold
45
3-Leg Manifold
46
4-Leg Manifold
47
5-Leg Manifold
48
8-Leg Manifold
49
Stretched Spacing Between Legs
50
Squeezed Spacing Between Legs
51
Large Diameter (3/4”)
52
Larger Diameter (1”)
53
Very Large Diameter (1 ½”)
54
Small Diameter (3/8”)
55
Short Grain Bed (10”)
56
Shorter Grain Bed (8”)
57
Deep Grain Bed (14”)
58
Deeper Grain Bed (16”)
59
Minimal Water Level (0.1”)
60
High Water Level (2”)
61
Higher Water Level (6”)
62
Baseline y-z
63
Large Spacing Between Slots (1 ½”)
64
Larger Spacing Between Slots (2”)
65
Small Spacing Between Slots (3/4”)
66
Smaller Spacing Between Slots (1/2”)
67
Very Small Spacing Between Slots (1/4”)
68
1/8-inch Wide Slots
69
1/32-inch Wide Slots
70
1/4-inch Wide Slots
71
Manifold closer to wall (3”)
72
Manifold further from wall (5”)
73