Criteria:
Every particle of milk shall be held for the
minimum legal hold time in both the forward and diverted flow positions.
Apparatus:
Tape Measure.
Method:
Determine the efficiency factor using the Reynolds
number for water and all products to be processed at the maximum flow rate.
Also determine flow rate ratio (product:water). Use the smallest efficiency
factor and the determined flow rate ratio to calculate the required holding
tube length.
Procedure:
Determine the inside diameter in meters of the
holding tube (Table 1).
Calculate the velocity of the product using the
following equation:
V = F/A
Where: V = Velocity (m/s).
F = Flow rate (liters/hr or liters/sec or m3/s).
A = Area (m2)
Table 1 - Holding Tube Dimensions
|
||||||||
Outside Diameter
|
Inside Diameter (d)Table
note 1
|
Area (a)
|
Volume (q)
|
|||||
in.
|
cm
|
in.
|
ft
|
cm
|
ft2
|
cm2
|
Imp. gal./ft Table
note 2
|
l/m
|
1
|
2.54
|
0.902
|
0.0752
|
2.291
|
0.0044
|
4.122
|
0.0277
|
0.4122
|
1.5
|
3.81
|
1.402
|
0.117
|
3.561
|
0.0107
|
9.959
|
0.0669
|
0.9959
|
2
|
5.08
|
1.87
|
0.156
|
4.749
|
0.0191
|
17.713
|
0.1190
|
1.7713
|
2.5
|
6.35
|
2.37
|
0.198
|
6.019
|
0.0306
|
28.454
|
0.1912
|
2.8454
|
3
|
7.62
|
2.87
|
0.239
|
7.289
|
0.0449
|
41.728
|
0.2803
|
4.1728
|
4
|
10.16
|
3.834
|
0.32
|
9.739
|
0.0802
|
74.494
|
0.5003
|
7.4 494
|
Table notes
Table note 1
"Fundamentals of Food Process Engineering – 3rd Edition",
Romeo T. Toledo, Department of Food Science and Technology, University of
Georgia, Athens, Georgia, 2007.
Return to
table note 1 referrer
Table note 2
1 imp. gal. = 0.16026 ft3
Return to
table note 2 referrer
Note: Holding tube dimensions:
1" & 1½" is 18 standard wire gauge (SWG), 2",
2½" & 3" is 16 SWG, 4" is 14 SWG.
Table 2 - Density and Viscosity Values
|
|||||
Product
|
Density (p)
|
Viscosity (μ)
|
|||
Type
|
Temp
|
g/l
|
lb/ft3
|
cP
|
lb/ft×s
|
Milk
|
72°C
|
1012
|
63.15
|
0.515
|
0.000346
|
Cream (40%)
|
75°C
|
982.6
|
61.3
|
3.4
|
0.00228
|
Ice Cream Mix
|
80°C
|
1100
|
68.64
|
150
|
0.1008
|
Note: These figures incorporate a safety
factor in recognition of the potential variances in product formulations and
batching procedures.
3. Determine the Reynolds number at the maximum
flow rate for water and all products to be processed using the following
formula:
Reynolds number (Re) = (p x V x d)/μ
Where: p = fluid density (kg/m3).
V = velocity (m/s)
d = tube inside diameter (m).
μ = viscosity (kg/ (sec x m)). (Table 2)
4. Convert the Reynolds number obtained into
logarithmic number.
5. Using the converted Reynolds number read the
efficiency factor from the provided chart (Figure 1).
6. Determine the flow rate ratio (r) using the
method outlined in Test 8, steps 11 and 12 and the following formula:
Flow rate ratio (r) = ((Mv)/Wv)
Where: Mv = average time required to deliver
a measured volume of product.
Wv = average time required to deliver an
equal volume of water.
For large pasteurizers this should be done by
using a magnetic flow meter instead of 36 litre can.
7. Calculate the minimum holding tube length using
the following formula:
L = (t x V)/(E x r)
Where: L = Length (m)
t = minimum holding time (s).
V = velocity (m/s).
E = efficiency factor.
r = flow rate ratio
8. Calculate the target salt test using the
following formula:
Target salt test in seconds = L/V
Where: L = Length (m).
V = velocity (m/s).
Description of image - Effect of
Reynolds number on the ratio of average to maximum velocity in smooth tubes
This graph is used to determine the efficiency
value by using the Reynolds number to calculate the time in smooth holding
tubes.
The x axis on the graph shows Efficiency Value for
the Ratio of Average to Maximum Velocity (V/V max). The values for the scale
range from 0.5 to 1.0.
The y axis shows Reynolds No. - Log
Chart. The values range from 102 to 107.
The graph also shows the points that the laminar
flow, transitional and turbulent flow occur.
Convert the flow rate from liters per hour to liters
per sec:
Flow rate = 25000/(3600) = 6.94 liters/sec
Convert the tube internal diameter from inches to meters:
Pipe diameter = 2"; therefore internal
diameter from Table 1 = 1.872" = 0.0475 m
Calculate the cross-sectional area of the tube
(internal):
Area = Ï€r2 = 3.14 × (0.0475)/4 =
0.00177 m2
Using the flow rate and cross-sectional area,
calculate the velocity:
Velocity = F/A; where F = flow rate and A =
cross-sectional area;
Velocity = (6.94 × 0.001(m3/s)) /(0.00177(m2))
= 3.90 m/s
Calculate the Reynolds number for water and milk:
Re water = (p x V x d)/μ; where p = density; V =
velocity; d = tube inside diameter; μ = viscosity of water;
Re water = (1000(kg/m3) × 3.90(m/s) × 0.0475(m))/0.0005(kg/sec×m)
= 370500 or 3.7 × 105
Using the calculated Reynolds number and Figure 1,
the efficiency factor of water = 0.86
Re milk = (p x V x d)/μ
= (1012(kg/m3) × 3.90(m/s) ×
0.0475(m))/0.000515(kg/sec×m)
= 364025 or 3.6 × 105
Using the calculated Reynolds number and Figure 1,
the efficiency factor of milk = 0.86
For holding tube length calculation use the lowest
efficiency factor of the two = 0.86
Calculating the tube length:
Tube length = L = (t x V)/(E x r); where t =
minimum holding time; V = velocity;
E = efficiency factor; r = flow rate ratio
Tube length = L = (16(s) × 3.90(m/s))/(0.86 ×
0.88)
= 83.42 metres
Calculating the target salt test:
Target salt test = L/V; where L = length; V =
velocity
= 83.42(m)/3.90(m/s)
= 21.39 seconds
References:
A Research Note, Prediction Of Holding Times For
Continuous Thermal Processing of Power-Law Fluids, Volume 41 (1976) Journal of
Food Science, J.A. Palmer and V.A. Jones. Department of Food Science, North
Carolina State University, Raleigh, NC 27607.
Effect of Process Variables on the Holding Time in
an Ultrahigh–Temperature Steam Injection System, Volume 53. No. 10
Journal of Dairy Science, E.R. Edgerton and V.A. Jones. Department of Food
Science and J. A. Warren Department of Experimental Statistics, North Carolina
State University, Raleigh 27607.
Test 9.1: Calculation of Holding Tube Length
(Under Review)
Application:
To all APPS and HHST systems
using direct and indirect heating.
Note: Because of the short holding times and
holding tube length, the required minimum holding times for
all APPS and HHST systems must be calculated from the pumping
rate rather than the salt conductivity test. Laminar flow may occur in
high viscosity products since the fastest particle can move at twice the speed
of the average particle. Therefore, the holding tube lengths must be calculated
as twice the length to compensate for laminar flow.
Frequency:
Upon installation and annually thereafter.
Whenever the seal on the speed setting is broken.
Whenever any alteration is made affecting the
holding time, the velocity of the flow (e.g. replacement of pump, motor,
belt, driver or driven pulley, decrease in number of heat exchange plates), or
the capacity of the holding tube.
Whenever a check of the capacity indicated a speed
up.
Criteria:
Every particle of product to be held for the
minimum holding time in both forward and diverted flow positions.
Apparatus:
None.
Method:
The holding tube length is determined by
calculation and is specified in the scheduled process. Fully developed laminar
flow is assumed. An experimental determination of pumping rate is required,
which is accomplished by determining the time required for the pasteurizer to
fill a vessel of known volume, converting this by division to obtain flow rate
in gallons per second and multiplying this by the applicable number from the
tables below to obtain the required length of the holding tube. The
resulting calculations will provide the required length of the holding tube for
the process. Holding tube lengths for pasteurizers with indirect
heating for a pumping rate of 1 gallon (4.546 L)/second are:
Table 1 - Holding Tube Lengths (Inches/cm) for
Indirect Heating Pasteurizers
|
|||||
Holding Time
|
1" (2.54 cm) Tube Diameter
|
1½" (3.81 cm) Tube Diameter
|
2" (5.08 cm) Tube diameter
|
2½" (6.35 cm) Tube diameter
|
3" (7.62 cm) Tube diameter
|
1
|
723.0 (1836.42)
|
300.0 (762)
|
168.0 (426.72)
|
105.0 (266.7)
|
71.4 (181.36)
|
0.5
|
362.0 (919.48)
|
150.0 (381)
|
84.0 (213.36)
|
52.4 (133.10)
|
35.7 (90.67)
|
0.1
|
72.3 (183.64)
|
30.0 (76.2)
|
16.8 (42.67)
|
10.5 (26.67)
|
7.14 (18.14)
|
0.05
|
36.2 (91.95)
|
15.0 (38.1)
|
8.4 (21.34)
|
5.24 (13.31)
|
3.57 (9.07)
|
0.01
|
7.23 (18.36)
|
3.0 (7.62)
|
1.68 (4.27)
|
1.05 (2.67)
|
0.714 (1.814)
|
Assumed Pumping rate =
1 US Gal/Sec (4.546 Litres/Sec) (1 US Gal =
3.785 Litres)
Note: These lengths assume fully developed
laminar flow
With steam injection processes, the holding tube
is adjusted since the product volume increases because of increased volumes in
the holding tube. With a 120°F (48.89°C) temperature increase by steam
injection, a volume increase of 12% will occur in the holding tube. The values
in the table below reflect this volume increase. This surplus water is
evaporated off as the pasteurized product is cooled in the vacuum chamber. The
temperature-time standard is chosen by the processor and the required holding
tube length is calculated from an experimental determination of the pumping
rate.
Table 2 - Holding Tube Lengths (inches /cm) for
Steam Injection Pasteurizers
|
|||||
Holding Time
|
1" (2.54 cm) tube diameter
|
1½" (3.81 cm) tube diameter
|
2" (5.08 cm) tube diameter
|
2½" (6.35 cm) tube diameter
|
3" (7.62 cm) tube diameter
|
1
|
810 (2057.4)
|
336 (853.44)
|
188 (477.52)
|
118 (299.72)
|
80.0 (203.2)
|
0.5
|
405 (1028.7)
|
168 (426.72)
|
94.0 (238.76)
|
59.0 (149.86)
|
40.0 (101.6)
|
0.1
|
81.0 (205.74)
|
33.6 (85.34)
|
18.8 (47.75)
|
11.8 (29.97)
|
8.00 (20.32)
|
0.05
|
40.5 (102.87)
|
16.6 (42.16)
|
9.40 (23.87)
|
5.90 (14.99)
|
4.00 (10.16)
|
0.01
|
8.10 (20.57)
|
3.36 (8.53)
|
1.88 (4.78)
|
1.18 (3.0)
|
.80 (2.03)
|
Assumed Pumping Rate = 1 US Gal/Sec (4.546 Litres/Sec)
(1 US Gal = 3.785 Litres)
Note: These lengths assume fully developed
laminar flow and temperature increase of 120°F (48.89°C) by steam
injection.
The calculations follow the
equation: A = B X C
Where:
A = holding tube length (inches)
B = measured pumping rate (gallons per second)
C = holding tube length from Table (inches per
gallon per second)
Example 1:
The health authority knows the time-temperature
standard and flow rate and wants to know the required length for the holding
tube. The pasteurizer has a nominal capacity of 10,000 pounds per hour.
The time required to fill a 10 gallon can with water from the pasteurizer
is 32.5 seconds. The temperature-time standard is 204°F (95.56°C) for
0.05 second, and the holding tube is 2 inches in diameter. The
pumping rate is 10 gallons divided by 32.5 seconds, which is
0.308 gallon per second.
The required holding tube length, A is calculated
from Equation 1 (A = B X C). The pumping rate, B, is
0.308 gallon per second, and from Table 1, the holding tube length,
C, required for a holding time of 0.05 second with a pumping rate of 1
gallon per second in 2 inch diameter tubing is 9.4 inches.
For this example,
A = 0.308 × 9.4
A = 2.9 inches
Therefore the holding tube must be at least 2.9 inches long.
Example 2:
The health authority knows the temperature-time
standard and the actual holding tube length and wants to know the maximum
permissible pumping rate.
The pasteurizer has a nominal capacity of 60,000
pounds per hour, and the temperature-time standard is 204°F (95.56°C) for
0.05 second. The holding tube is 3 inches in diameter and 6 inches long.
The pumping rate is calculated from
Equation 1 (A = B X C). The holding tube length, A, is
6 inches and from Table 1, the holding tube length, C, required for a
holding time of 0.05 second with a pumping rate of 1 gallon per
second in 3 inch diameter tubing is 4 inches. For this example:
6 = B × 4
B = 6/4
Therefore … B = 1.5 gallons per second.
The maximum permissible pumping rate is
1.5 gallons per second. At this pumping rate, the time required to fill a
100 gallon vat is 100 gallons divided by 1.5 gallons per second,
or 66.6 seconds.
Procedure:
Examine the entire system to insure that all flow
promoting equipment is operating at maximum capacity and all flow impeding
equipment is so adjusted or bypassed as to provide minimum resistance to the
flow. In-line filters must be removed, booster pumps must be in operation and
vacuum equipment in the system must be operating at a maximum vacuum.
Before beginning, the pasteurizer is to be
operated at maximum flow for a sufficient time to purge air from the system
(about 15 minutes) and tighten pipe connections on the suction side of the
metering pump enough to exclude the entrance of air. With the pasteurizer
operating on water, adjust the metering pump to its maximum capacity,
preferably with a new belt and full-size impellers.
Make sure no flow exists in the diverted line and
measure the time required to deliver a known volume of water at the discharge
line of the pasteurizer in forward flow. Repeat this at least once to determine
that the measurements are consistent.
Repeat the above steps 1 to 3 of this
procedure in diverted flow by collecting the water at the discharge of the
divert line.
Select the greatest flow rate (shortest delivery
time for the known volume) and calculate the flow rate in gallons per second by
dividing the known volume by the time required to collect the known volume.
Multiply this value by the appropriate number in the above tables (Table 1
for indirect heating and Table 2 for direct heating with steam injectors).
Determine the number and type of fittings in the
holding tube and convert these to equivalent lengths of straight pipe with the
use of Table 3. Determine the total length of the holding tube by adding
the equivalent lengths of the fittings to the measured lengths of straight
pipe. If the actual holding tube length is equivalent to or greater than the
required holding tube length, record the number and type of fittings, the number
and length of straight pipes and the holding tube configuration. Make sure the
holding tube slopes upward at least 6.35 mm (0.25 inch) per
foot. If the temperature sensor is located at the beginning of the holding
tube, the holding tube shall be protected against heat loss by material that is
impervious to water.
Re-seal regulatory controls as necessary.
Record results.
Table 3: Centerline Distances of 3-Fittings
|
|||||
3 A - Fitting Size Designation
|
1
|
1½
|
2
|
2½
|
3
|
2C 90° bend
|
3.4
|
4.8
|
6.2
|
8
|
9.7
|
2CG 90° bend
|
3.1
|
4.5
|
5.8
|
7.6
|
9.3
|
2F 90° bend
|
3.4
|
4.8
|
6.2
|
8
|
9.7
|
2FG 90° bend
|
3.1
|
4.5
|
5.8
|
7.6
|
9.3
|
2E 90° bend
|
3.4
|
4.8
|
6.2
|
8
|
9.7
|
2EG 90° bend
|
3.2
|
4.6
|
6
|
7.7
|
9.4
|