TANKJKT spreadsheet template Heat for Tanks

TANKJKT spreadsheet template Heat Transfer Calculations for Jacketed Tanks Copyright 2001, 2015 by Stephen Hall, PE Introduction TANKJKT is an easy‐to‐use powerful spreadsheet template that calculates the rate of heating or cooling of tanks due to heat transfer from jackets and internal coils. Vessel heat transfer is complicated. It involves five resistances to heat flow each of which is dependent on specific conditions. Correlations have been developed for many different cases (e.g., half‐pipe coil jackets, turbine impellers, etc.). But other cases (dimple jackets, conventional jackets with nozzles) are either poorly researched or are proprietary and not available for use in this, or any, open product. Our challenge when designing TANKJKT was to keep the data entry as simple and intuitive as possible while maintaining a comprehensive feature set. We think you'll agree that this goal was met. Data Input is gathered onto a single worksheet, described in detail in these instructions. The results of the calculations are given on a "datasheet" that matches the look of all of chemengsoftware.com's spreadsheet templates. Fluid Data are included for most common heat transfer fluids. Because the data is regressed against temperature, jacket heat transfer calculations are very fast, accurate, and easily tested with alternative fluids.

UINS‐TJ‐02 February 2015

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TANKJKT Table of Contents Quick Start ........................................................................................................................................................................................ 3 Quick Results .................................................................................................................................................................................... 4 System Requirements ....................................................................................................................................................................... 5 Orientation and Initial Setup ............................................................................................................................................................ 6 Data Input Worksheet ...................................................................................................................................................................... 8 Vessel Data ................................................................................................................................................................................. 10 Jacket ......................................................................................................................................................................................... 12 Half‐Pipe Coil Jacket (Limpet Coil) .............................................................................................................................................. 12 Conventional Jacket ................................................................................................................................................................... 13 Dimple Jacket ............................................................................................................................................................................. 14 Bottom Head Jacket ................................................................................................................................................................... 14 Internal Coils .............................................................................................................................................................................. 15 Heat Transfer Fluid ..................................................................................................................................................................... 15 Flow Rate Data ........................................................................................................................................................................... 15 Vessel Fluid Data ........................................................................................................................................................................ 18 Agitator Data .............................................................................................................................................................................. 19 Environmental Conditions .......................................................................................................................................................... 20 Datasheet ........................................................................................................................................................................................ 21 Timeline .......................................................................................................................................................................................... 23 Flow Rate Calculations .................................................................................................................................................................... 25 Experimentally Determined Pressure Drop ............................................................................................................................... 26 Outside Heat Transfer Calculations ................................................................................................................................................ 27 Half‐Pipe Coil Jacket (Limpet Coil) .............................................................................................................................................. 27 Conventional Jacket ................................................................................................................................................................... 27 Dimple Jacket ............................................................................................................................................................................. 29 Internal Coil ................................................................................................................................................................................ 29 Inside Heat Transfer Calculations ................................................................................................................................................... 30 Agitator Power Calculations ........................................................................................................................................................... 34 Agitator Power Transferred to the Process Fluid ....................................................................................................................... 35 Depth of Vortex ......................................................................................................................................................................... 35 Fluid Data Worksheet ..................................................................................................................................................................... 36 Data Tables Worksheet ................................................................................................................................................................... 40 PictElements Worksheet (HIDDEN) ................................................................................................................................................. 40 Saved Calcs Worksheet ................................................................................................................................................................... 41 Result Details .................................................................................................................................................................................. 41 Nomenclature ................................................................................................................................................................................. 43 References ...................................................................................................................................................................................... 45

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TANKJKT Quick Start Perform your first heat transfer calculation by following these steps: 1. Ensure that Macros are enabled 2. Navigate to the Data Input worksheet 3. Use the dropdown boxes, radio buttons, check boxes and input fields to enter data about your tank and fluids. Input fields are displayed in RED text. 4. See the results!

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TANKJKT Quick Results Results are displayed on the Data Input worksheet. These can be printed, but the intent is to give immediate feedback so changes to the inputs can be made before finalizing the calculation and printing a datasheet. The heat transfer film coefficients are listed for the process and heat transfer fluid sides of each heat transfer surface. TANKJKT uses these, together with wall resistance and fouling, to calculate the overall heat transfer coefficient, U. Next, the flow rate, velocity and pressure drop for each of the surfaces are reiterated. The values are the same as those in the “Flow Rate in Side‐Wall Jacket” section described previously. The temperature and heat flow results are listed for each heat transfer surface and the top head. Inlet and outlet temperatures for the heat transfer fluid are given, along with the amount of heat transferred through each surface. A positive value for heat transfer indicates a heating effect; negative means cooling. When combined with power input from the agitator, the total heat transfer is computed. Based on the volume of process fluid that was input in the “Vessel Data” section, the instantaneous rate of heating or cooling is calculated and displayed. The picture of the tank provides visual confirmation that the jacket, coil, baffles, impeller and liquid level are configured as you intended. This picture is not to any scale except that the blue shading indicating fill level accurately indicates the percent of sidewall covered by liquid. You might see messages on screen, just to the right of the “Vessel Fluid Data” input area. When present they warn of unusual or unexpected parameters that you might want to correct.

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TANKJKT System Requirements 

Personal computer running Microsoft Excel with Visual Basic for Applications (VBA). This requirement means that Open Office and other programs capable of opening and editing basic Excel worksheets will not work – VBA is required. Excel 97 on the Mac lacks VBA and is therefore incompatible, however Office 2010 on the Mac is compatible



Excel must be configured to allow macros to run. This can be done through Security settings, or by enabling macros each time TANKJKT is opened

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TANKJKT Orientation and Initial Setup TANKJKT consists of six main worksheets. When you open the program you must enable macros, if your Excel security settings are set to Medium or High. The Data Input worksheet should then be displayed. The main worksheets are: Data Input

Enter tank, agitator and fluid (heat transfer fluid and process liquid) on this worksheet, and view the calculation results

Datasheet

Print a datasheet that documents the configuration of the tank system and presents the heat transfer calculation results

Timeline

Create and print a datasheet that shows the temperature change of the process fluid over time

Fluid Data

Add new heat transfer fluids to the database

Data Tables

See lookup values for various parameters. This worksheet contains intermediate calculations

Saved Calcs

Saved calculations are stored on this worksheet

Although TANKJKT is ready to use immediately, there are a few things you might want to adjust to improve your experience. Change the Logo

You can replace the chemengsoftware logo on the datasheets with your own logo. First, unprotect the datasheet. Then right‐click on the logo followed by left‐click on the logo. This selects it without opening the hyperlink. Hit the Delete key to get rid of it, then paste your own logo in its place. Please remember to protect the worksheet again so you don’t make inadvertent changes to it.

Enter company info

This is a good time to customize your copy by entering your basic company information into the “Project Data” section on the Data Input worksheet.

Set up the printer

Select all of the worksheets and then use the print settings dialog to establish your paper size. As shipped, TANKJKT is configured for U.S. 8½” x 11” paper. Outside of the U.S. you will probably want to choose A4 size.

Configure decimals

TANKJKT uses the function “=TEXT(value, format)” for many of the displayed numbers, especially on the datasheets. For example, the formula =TEXT(PI(), “0.00000”) displays the value of π to five decimal places, 3.14159. If you are in a country that uses a different convention than the U.S. for displaying thousand separators or decimals, then you’ll want to change this. 6

TANKJKT Your computer country setup does not affect the TEXT formulas as used in TANKJKT. We provided an easy‐to‐use tool to adjust the formatting in TANKJKT. Instead of hard‐coding the number formats in all those =TEXT formulas, we use a named cell value to get the format. These are found on the Data Tables worksheet, right at the top of the page. In the yellow field you can change any of the values in RED to a format of your choosing. The Name (e.g., N1Format) is what the format cell is named in the spreadsheet. So the TEXT formula for the π example would be: =TEXT(PI(), N5Format) To use a comma for the decimal separator, simply edit the cell next to N5Format to be: 0,00000. Name N1Format N2Format N3Format N4Format N5Format T1Format T2Format T3Format DateFormat

Format 0.0 0.00 0.000 0.0000 0.00000 #,### #,##0.0 #,##0.00 dd-mmm-yyyy

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TANKJKT Data Input Worksheet All of your project and calculation case data are entered on the “Data Input” worksheet. The worksheet is designed to simplify your task in assembling the large amount of information needed for a comprehensive calculation. Where your possible input is limited to a specific list of choices (such as materials of construction), TANKJKT presents the choices in the form of check boxes, radio buttons, or dropdown lists. Other data entry fields are checked as you enter data, with unexpected inputs (i.e., those outside “normal” ranges programmed into the spreadsheet) flagged with Warning messages. The complete Data Input worksheet is pictured on the next page. Your screen is probably too small to display the entire Data Input sheet at once. Use the vertical and horizontal scroll bars to reach all of its parts. You should notice right off the little red triangles that appear in some cells. These indicate that there are “comments” associated with the cell. By hovering your mouse pointer over the cell, the comment box appears, usually with guidance on how to fill in the cell. For example, the comment associated with surface roughness lists values in both Customary US and SI units for several common vessel materials. Here is a rundown of the Input sections, working from the top left of the screen, down the left side, followed by the middle column and then the right column. Project data is used in the header section of the datasheet output form. But the data are not involved in any calculations. It is recommended that the text strings be short to ensure they fit within the rather small boxes on the datasheet. Look at the datasheet to see how it fits.

Project Data Prepared by

SMH

Client

Hypo

Date

1/22/2015

W.O.

01-155

Unit

15

Area

B

Equip No

T-126

Customary US

SI

The radio buttons toggle between “Customary US” and “SI” units of measure. When you switch from one to the other all data input data are converted also, so you can freely toggle back‐and‐forth.

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TANKJKT

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TANKJKT Vessel Data Physical information about the vessel construction is entered here. When running multiple cases on the same vessel, this section will usually remain constant. The “Calc Title or Description” is used on the Datasheet. You can enter a lengthy description that covers an entire line of the printout. See the Datasheet, just above Line 1, for an example. TANKJKT always assumes the vessel is oriented vertically and is cylindrical. Changing this value has no effect. The “Total working volume” is used to calculate the rate of heating or cooling. TANKJKT uses this number to estimate the fill height, and if the jacket covers tank wall that isn’t wetted on the inside then that portion of the jacket is ignored. A warning is displayed if the input for working volume fills the tank higher than the top tangent (where the top head curvature begins), and the volume of the tank to the top tangent (including the bottom head) is displayed for reference. Inside diameter and tangent‐to‐tangent dimensions are used for many calculations and are critical input values. They are typically near a 1:1 ratio; very tall tanks (beyond about 3:1 height:diameter) and very squat tanks (1:2) are processed by all of the formulas, but use caution because the underlying heat transfer correlations, especially for the inside heat transfer coefficient, may not be very accurate under those conditions. Choose the type of head on the tank bottom using the dropdown list. The top head is immaterial to the calculations except for heat gain/loss to the environment (which is usually small compared with the total). The bottom head type is used for calculating the fill height and the surface area for the bottom. Material of construction for the tank wall is selected from the dropdown list. Wall thickness is important because it impacts the overall heat transfer coefficient. It is assumed that in internal coil is made of the same material as the tank wall. An inside lining may be selected from the dropdown list, or choose “None” from the list. Linings are typically glass, a polymer such as Teflon, or an exotic metal such as tantalum. Again, enter the thickness of the lining. Some suggestions are given in the pop‐up comment box for typical roughness values. Consider how the tank will be maintained, and the condition of the surface after a period of time. Similarly, fouling factors are entered. You should consider how the condition of the jacket might change over time (e.g., are there corrosion inhibitors in your water?), and cleaning practices for the inside of the vessel. For instance in 10

TANKJKT pharmaceutical, cosmetic or food processing where cleanliness is exceptionally important it is reasonable to set the “internal fouling factor” to zero. If you are uncertain what values to use for roughness or fouling, try running the calculation with alternatives to see the effect on your results; this will help you decide on an appropriate figure. The check box is used to signify the presence of internal baffles. Propeller and turbine agitators usually work much better with baffles, however if none are present TANKJKT uses appropriate correlations. Since baffles cannot be used with helical ribbon or anchor type impellers, the baffle checkbox is ignored in those cases. And glassed retreat curve impellers are normally accompanied by a “finger” style glassed baffle; the checkbox is ignored for the glassed retreat curve impeller case and it is assumed that there is a baffle.

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TANKJKT Jacket This part of Data Input has a general section, then additional sections for each of the three types of sidewall jackets. There’s another section for the bottom head. If you know for certain what type of jacket your tank will have then focus just on the corresponding input section. However, if you intend to compare one type with another, be sure to complete all relevant sections. Use the radio buttons to select what type of jacket is on the tank. The dropdown list of inlet/outlet nozzle sizes is only used for conventional annular jacket types. Sidewall jackets are often broken into separate “zones” for the purpose of decreasing the temperature change in the jacket fluid or to decrease pressure drop. The TANKJKT calculation procedures don’t differentiate between stacked and interleaved zones, so it doesn’t matter what type your tank uses. Enter the percentage of the sidewall covered by the jacket; it’s usually “1”, but can be any value from 0.1 to 1.0. For example, if the jacket only covers half the height of the sidewall, enter the value “0.5”. Half‐Pipe Coil Jacket (Limpet Coil) Half‐pipe coil jackets are normally constructed of 3‐inch pipe; TANKJKT permits 2, 3 or 4‐inch. Additional sizes may be added (see the section on Data Tables, page 40). The cross section angle is either 180 degrees (a true “half‐pipe”), or 120 degrees. Enter the appropriate value. This has a big impact on pressure drop, but not so much on the heat transfer coefficient. So when designing a new vessel, you want to compare the effect on temperature change of the jacket fluid (typically much higher with the 120 degree angle).

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TANKJKT The last data to enter is the spacing between adjacent coils. This is the actual distance between coils on the surface of the tank, not the distance between centerlines. It is typically in the range of ¾ to 1½ inches (20 to 40 millimeters).

180 deg 120 deg

Tank Wall

Conventional Jacket “Conventional” jackets are found on glass‐lined vessels and also often when the primary purpose for the jacket is heating with steam. The jacket consists of an outer shell separated from the vessel wall with an open space (the “annular” space). TANKJKT recognizes three mutually exclusive cases: 

A standard conventional jacket



A conventional jacket with internal baffles that direct the jacket fluid around the vessel, similar to a half‐pipe jacket



A standard conventional jacket with “agitating nozzles” that impart turbulence to the entering fluid.

The “annular space dimension” is the distance between the outside of the vessel wall to the inside of the jacket wall.

Jacket Wall

Tank Wall

Baffle

Baffle Spacing

If the “Baffled” checkbox is selected, a prompt appears for “baffle spacing.” This is the distance between adjacent baffles. If the “agitation nozzles” checkbox is selected, prompts appear for Annular Space entering the number of agitation nozzles and the throat diameter of each nozzle. Input the number of nozzles on the sidewall, ignoring the bottom head. TANKJKT makes a simplifying assumption that if there is a bottom head conventional jacket it will have the same nozzle configuration as the sidewall. By “same” is meant that there are the same number per unit area, rounded up to the next integer. Even if the conventional jacket is continuous around the bottom head and sidewall, as is usually the case, ignore the bottom head for the purpose of this entry. The throat diameter of the nozzles are assumed to be uniform for all nozzles. Refer to the pop‐up comment for typical values. The remaining checkbox in this section is “Aiding Flow.” Since standard conventional jackets have such a large cross‐sectional area, they typically operate in the laminar flow regime, at a velocity around 0.03 m/s (0.1 ft/s). When working in cooling service, if the coolant enters the bottom of the jacket and flows upward it will heat along its travel. This causes the fluid to expand slightly, giving it a buoyant force, and increasing its velocity. As a result the heat transfer coefficient from the jacket fluid to the tank wall is

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TANKJKT increased slightly. The opposite occurs when coolant flows from top to bottom, and heating applications work in reverse. Dimple Jacket Dimple jackets are often a good choice, combining low cost with excellent heat transfer. Unfortunately, the correlations published for dimple jackets are less reliable than for half‐pipe coils, perhaps only +/‐ 30% accurate. This is true for heat transfer coefficients and also for pressure drop. So, for critical applications always consult with the tank manufacturer. Enter the requested data. Annular space is the maximum distance between the tank wall and the jacket. Distances between dimples is measured as if a square grid were placed over the jacket wall (i.e., not the actual distance between dimples in the case of triangular pitch). And the mean dimple diameter is a measure of the space occupied by the dimple and surrounding depression. Thus, by manipulating the values for dimple diameter, spacing, and annular space, you affect the calculation for open area available for flow through the jacket. Bottom Head Jacket While normal practice is to match the bottom head jacket with the sidewall, TANKJKT supports a different type. Thus, you could specify a conventional jacket on the bottom head coexisting with a half‐ pipe coil on the sidewall. Use the radio buttons to select the type of bottom head jacket to model. Whichever type is chosen, the physical parameters are assumed to be the same as those specified for the sidewall jacket of like type. The only other decision to make is whether the bottom head will be piped in series or parallel. TANKJKT uses this flow information when it computes the flowrate through the jacket sections. In each case, the flow through the sidewall jacket (if any) is calculated first. Then, the bottom head jacket is calculated. In series flow, the flowrate through one of the sidewall zones is forced through the bottom jacket. This may result in a ridiculously high pressure drop in some cases, which means that you must make different design decisions with respect to series/parallel, jacket types, or how the flow is determined (see section on jacket fluid flow, on page 25). Series Flow

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TANKJKT Internal Coils Internal coils are helical when high heat transfer is required, or hairpin when the heat duty is low. Typically, the coil diameter is 1/30 of the vessel inside diameter, and the coils are spaced so that the distance between them equals their diameter. The flowrate through the coil is determined by criteria established in the Jacket Fluid Data section. Heat Transfer Fluid TANKJKT includes a database with physical properties of many heat transfer fluids correlated with temperature. This is a valuable feature because it makes comparison of different fluids at different temperatures so easy and fast. You might even find yourself turning to TANKJKT just to look up physical properties of an included fluid. All major heat transfer fluids sold in 2012 are in the database. For the glycol‐based low temperature fluids such as Therminol FS, properties are given for a range of concentrations. In addition, non‐proprietary chemicals such as water, steam, ammonia, alcohols, etc. are found in the database. See the complete list on the next page. You can add more compounds to the database. See the Fluid Data section (page Error! Bookmark not defined.) for instructions on how to add your own. On the Data Input screen simply choose a fluid from the dropdown list, then enter the bulk temperature of the fluid supply. Properties are automatically filled in. The only condensing vapor supported by TANKJKT is steam. Heat transfer fluids such as Dowtherm A that can be used in vapor/liquid service are not supported at this time. Flow Rate Data In the second part you provide your instruction on how to compute the fluid flowrate. For each heat transfer surface, you specify the flow rate, velocity, or pressure drop. TANKJKT calculates the other two 15

TANKJKT parameters. The value you enter is shown in RED and the two calculated values are in BLACK. You can enter a value into a black cell – it will turn RED and the other two values are calculated and displayed in BLACK. Try it! When there are multiple sidewall zones, the total flow entered is divided among the zones and pressure drop is calculated for each zone. TANKJKT assumes that sidewall zones are piped in parallel. If you want to pipe them in series, with flow leaving one zone then entering the next, you must specify ONE Sidewall Zone. Engineers commonly pipe the heat transfer surfaces in parallel and may, or may not, install control valves or orifices to manage the distribution of the flow. If you do not intend to install restricting devices, then specify the same pressure drop through each of the surfaces. TANKJKT then calculates the flow rates and velocity through each; this might help you decide if orifices or valves are needed.

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TANKJKT Table 1: List of Heat Transfer Fluids Included in TANKJKT (you can add more) Air

Dowtherm 4000, 20 vol%

Jarytherm AX320

Refrigerant R‐152a

Ammonia


Jarytherm BT06

Refrigerant R‐22

Argon


Jarytherm DBT

Steam

Butane, iso‐


Marlotherm LH

Syltherm 800

Butane, n‐


Marlotherm N

Syltherm HF

Calflo AF


Marlotherm P1

Syltherm XLT

Calflo FG


Marlotherm P2

Syntrel 350

Calflo HTF


Marlotherm SH

Thermalane 550

Calflo LT

Dowtherm A

Marlotherm X

Thermalane 600

Carbon Dioxide

Dowtherm G

Methane

Thermalane 800

Chemtherm 550

Dowtherm HT

Mobiltherm 603

Thermalane FG‐1

Dowfrost HD, 10 vol%

Dowtherm J

Multitherm IG‐2

Thermalane L


Dowtherm MX

Multitherm PG‐1

Thermia Oil B


Dowtherm Q

Nitrogen

Therminol 55


Dowtherm RP

Oxygen

Therminol 59


Dowtherm SR‐1, 10 vol%

Paratherm HE

Therminol 66



Paratherm NF

Therminol 75



Paratherm OR

Therminol D‐12

Dowfrost, 10 vol%


Propane

Therminol FS, 20 wt% pg

Dowfrost, 20 vol%


Propylene


Dowfrost, 30 vol%


Refrigerant R‐11


Dowfrost, 40 vol%


Refrigerant R‐113


Dowfrost, 50 vol%


Refrigerant R‐114


Dowfrost, 60 vol%


Refrigerant R‐12

Therminol LT

Dowfrost, 70 vol%

Ethane

Refrigerant R‐123

Therminol VP‐1

Dowfrost, 80 vol%

Ethylene

Refrigerant R‐124

Therminol XP

Dowfrost, 90 vol%

Hitec

Refrigerant R‐13

Water


Ilexan S

Refrigerant R‐134a

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TANKJKT Vessel Fluid Data The fluid inside the vessel is the process fluid. This is the material that you want to transfer heat to or from. Process data are not stored in the program, so unlike the heat transfer fluid you must enter data for the important physical properties. The values for thermal conductivity, specific heat and density are taken as constants over the range of temperatures considered by the program. Therefore, you should enter values that are appropriate for the temperature of interest. Viscosity, on the other hand, varies dramatically with temperature. There are two ways to enter viscosity. In the input box shown above, enter the viscosity at 20°C. TANKJKT estimates viscosity at other temperatures with the Lewis and Squires temperature correlation [Poling]. The formula for this chart is:

T 0.2661   20 0.2661 

T  20 233

The second way to enter viscosity is to provide the viscosity at three temperatures. TANKJKT constructs a formula, just as it does for heat transfer fluids, to predict the viscosity at other temperatures. These values must be entered using the units that are shown, and you must tick the checkbox for “Use this data”. You can test the validity of the formula by entering a “temperature of interest” and seeing the result. Finally, by ticking the “Use properties of water” checkbox, all other values are overridden; water properties are used. 18

TANKJKT Agitator Data Choose the type of impeller from the dropdown list. When you change impellers, input fields for the relevant data are presented; fill in the information that is requested. There are hundreds of types of impellers in industry; TANKJKT offers choices from the most common types. If your impeller isn’t listed, pick one that has similar characteristics for flow pattern (axial or radial) and category (turbine or close‐clearance). Impeller geometry is usually specified within standard ranges that are tied to the tank diameter. Some of the calculations take geometric values into account, but others ignore geometry because the effect is small. The most important parameter for calculating heat transfer and power is the Reynolds number which is computed from the impeller diameter, speed and properties of the process fluid (viscosity and density). Those are the four parameters that are most important and should be specified reasonably accurately. Table 2: Impeller Types in TANKJKT Alloy 3‐blade retreating. This is similar to a glass‐steel retreat‐blade impeller, but constructed of stainless steel or some other alloy. Radial flow. Anchor. Generally used for viscosities from 20,000 to 100,000 cP, anchors are lower cost than helical coils, and often provide better heat transfer. Close proximity.

Glass‐steel retreating. This is the workhorse impeller for glass‐lined reactors, although this is changing with the introduction of new impeller styles and materials. Heat transfer is worse than with the alloy retreating blade style (above) which is attributed to more slippage around its curved surfaces. Radial flow.

Helical Ribbon. This proximity type of agitator is generally used for higher viscosity fluids (100,000 to 1,000,000 cP, except highly non‐Newtonian liquids which tend to rotate with the impeller and are sheared near the vessel wall. Close proximity.

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TANKJKT

No Agitator. Inside heat transfer coefficients are low when there is no agitation. Paddle. Very similar to a turbine, but with only two or four blades. Generally with a diameter greater than 0.6 of the tank diameter, turning at a slow speed. Radial flow.

Propeller. Applicable when the viscosity is less than about 2000 cP, and for vessel volumes less than 6000 liters (1500 gallons) and vessel diameter < 1.5 m (5 ft) because they weigh much more (e.g., cost more) than turbines. Axial flow. Pumped Circulation (no agitator). TANKJKT does not model circulation with jets, but instead treats this as liquid flowing through the vessel as if it were a large pipe.

High‐Efficiency Hydrofoil. These are designed to provide more streamlined flow compared to pitched‐blade turbines or propellers. They have three or four tapering twisted blades, sometimes with rounded leading edges. Axial flow. Pitched‐Blade Turbine. The pitched blades are typically mounted at a 45°angle. Angles < 30° or > 60° are extremely rare. Axial flow. Pitched‐Blade Turbine (Rushton). The blades are sometimes mounted on a flat disk and typically have 4 or 6 blades (can range from 4 to 12). Radial flow. Impeller photos from [Dickey]

Environmental Conditions Enter the tank’s exterior environment in this section. If indoors, set wind speed to zero. Select insulation and the insulation covering from the dropdown lists. Uninsulated surfaces are also assumed to be unpainted. The surface treatment sets the value used for emissivity, which enters into the radiation heat loss/gain calculation. You can review and change the emissivity values on the Data Tables worksheet.

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TANKJKT Datasheet The datasheet organizes your pipe information on a form that has the same look as datasheets used throughout the chemengsoftware family. Information in the header section needs to be edited manually for your needs. If the cells are locked, simply Unprotect the sheet (there is no password needed) before editing the information. Notice that there are three triangles with numbers. These can be copied and pasted on top of the datasheet to indicate revisions

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TANKJKT

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TANKJKT Timeline The timeline datasheet is the same as the primary datasheet, except the heating/cooling curve is substituted for the calculated results. TANKJKT creates the curve by updating the temperature of the process fluid at time increments entered by the user. At the beginning of each time increment, TANKJKT evaluates the physical properties of the process fluid at the temperature and calculates the rate of heat gain or loss. Then, the temperature at the end of the increment is calculated using that rate and the time increment. The new temperature is substituted into the Data Input worksheet and the calculation is performed again. This repeats until 61 increments are computed. The results are charted. The results are also tabulated near the bottom of the Data Tables worksheet. Go to the named cell “interval_time” to quickly find the tabulated data. At the top of the Timeline worksheet, enter a value for the calculation interval in Cell B2. Then click the “NEW TIMELINE” button. The calculation takes several seconds – up to a minute on very slow machines – so be patient while the timeline data is generated. Typical results are pictured on the next page.

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TANKJKT

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TANKJKT Flow Rate Calculations The flow rates through each section of the jacket or inside the coils must be determined before the overall heat transfer is computed. TANKJKT support a limited number of permutations that are described here. We decided to favor a more simple user input at the expense of limiting the flexibility of specifying each jacket zone and coil flow individually. As seen in the screenshot below, you can enter the flow rate, velocity or desired pressure drop for each surface. The program calculates the other two. In this example, the flow for the sidewall and bottom head jackets are specified and the velocity through the internal coil is also specified. Flow Rate in Side-Wall Jacket Enter a value for each heat transfer surface. When one parameter is entered (flow , velocity, or pressure drop) the other tw o are calculated. Red value show s user entry. Total Flow

Velocity

Pressure Drop

Sidew all Jacket

80.0 liters/min

0.7 m/s

1.7 kPa

Bottom Jacket

60.0 liters/min

1.1 m/s

0.9 kPa

116.9 liters/min

0.9 m/s

3.2 kPa

Internal Coil

Here, the pressure drop for all three surfaces is specified. You can enter values in any of the nine fields (3 surfaces x 3 parameters). As soon as a new value is entered, the cell turns red while the other two values for that surface turn black and are calculated. Notice that in this example the flow rates for the sidewall and bottom jackets are approximately equal but the velocity for the sidewall is half that of the bottom jacket. The reason for this is that, for this example, the sidewall is specified to have two zones. The flow is divided equally between the zones, so the flow through each of the two sidewall zones is half of what is shown. Flow Rate in Side-Wall Jacket Enter a value for each heat transfer surface. When one parameter is entered (flow , velocity, or pressure drop) the other tw o are calculated. Red value show s user entry. Total Flow Sidew all Jacket

Velocity

549.9 liters/min

Pressure Drop

4.9 m/s

80.0 kPa

Bottom Jacket

552.5 liters/min

9.8 m/s

80.0 kPa

Internal Coil

586.1 liters/min

4.5 m/s

80.0 kPa

In the special case with one sidewall zone, if you check the “Series Flow” box under Bottom Head Jacket, then the flow rate in the sidewall and bottom jackets are equalized. For instance, if you enter a flow rate for the bottom jacket then the flow for the sidewall is immediately changed to equal it. If you enter a value for pressure drop through the sidewall, the sidewall jacket flow is calculated and displayed, then the bottom jacket flow rate is set equal to that calculated value.

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TANKJKT Bottom Head Jacket No Jacket

Conventional

Half-Pipe Coil

Dimple

Same type as Side-Wall Jacket Series Flow

The flow rates, velocities and pressure drops are all calculated using physical properties at the temperature of the HTF supply. Strictly speaking, the density and viscosity will change as the HTF cools or warms through the jacket, but these differences are not accounted for. We elected to make this simplification because the effect on the overall heat transfer calculations is insignificant. The flow rate, velocity and pressure drop calculations are contained in the “JacketFlow” subroutine (and supporting functions) found in the “FlowRate” VBA module. Experimentally Determined Pressure Drop

Use this section when you have experimental pressure drop data Input the know n conditions

If you have data for pressure drop through the jacket, then use it to possibly improve the reported flow and pressure drop results. The input box for experimental data is located in the center column at the bottom.

Flow rate liter/min Sidew all

Viscosity mPa-s

Density Press Drop Use Experimental g/cm³ kPa Pressure Drop Data

150.0

1

1.0

50.0

Sidewall

85.0

1

1.0

45.0

Bottom Head

(one zone) Bottom Head

See the instruction manual for further information about the use of this pressure drop technique

Enter the four pieces of data requested: flow rate, viscosity, density and pressure drop, all at the experimental conditions. Then select the checkbox. TANKJKT computes an “equivalent length” for the jacket flow path, using the hydraulic diameter and flow area that are calculated from the jacket dimensional data. It’s important to enter the jacket dimensional data (described previously) because this determines a Reynolds number which, in turn, is important for calculating the friction factor. If there are multiple zones, enter the flow rate and pressure drop for one zone. If there are multiple nozzles (conventional jacket), enter the flow rate for a single nozzle. For example, if you have a jacket with two agitating nozzles and you know the total flow rate is 200 liters/minute with a total pressure drop of 50 kPa, then enter 100 for the flow rate (200 divided by 2) and 50 for the pressure drop. Don’t divide the pressure drop in two.

26

TANKJKT Outside Heat Transfer Calculations The outside heat transfer coefficient refers to the heat transfer fluid side of the surface, whether it be outside the tank wall or the inside of an internal coil. This section gives the method used to calculate the outside coefficient for each type of surface. Half‐Pipe Coil Jacket (Limpet Coil) Turbulent flow is expected, and is modeled, for both sidewall and bottom head, with Gnielinski:

ho d e  f 8Re 1000Pr  0.5 k 112.7  f 8 Pr 2 3 1





[1]

Garvin’s presentation includes a correction factor for helical coils that accounts for improved heat transfer due to centrifugal forces on the outside of the coil. Since the outside of a jacket coil faces away from the tank we elected to ignore this factor. It is documented in the “HTFSideh” subroutine and may be restored by removing the comment apostrophes at Lines 10 and 20. ' 10 ' 20

CurvDiam = T / Cos(Atn(2 * H3 / cdPI / SidewallZones / NoCoils / T)) A = 1 + 0.059 * (Re * (HydDiamFlow / CurvDiam) ^ 2) ^ 0.34

If the flow is laminar (Re < 2100), then the following equation is used [Dream]:

ho d e d    1.86  Re Pr e  k L 

0.33

      w 

0.14

{2}

Conventional Jacket We follow [Garvin 1999] for the conventional jacket calculations. Conventional jackets may be strictly annular, fitted with internal baffles, or equipped with agitating nozzles. Annular jackets often operate in the laminar flow or transitional flow range, so the heat transfer algorithm is more complex than those seen for other jacket types. The internal baffle jacket is modeled like a half‐pipe coil, except that because the baffles don’t form full channels there is bypass flow that must be accounted for. Agitating nozzles provide turbulent flow and are considered to be the driving force for heat transfer. Conventional Annular Jacket The algorithm follows this path: 1. Calculate the equivalent diameter and curvature diameter of the jacket 2. Determine limits for Laminar, Transitional, and Turbulent regimes a. Lower limit for Turbulent regime is Re = 15000 b. If

de

dc

 0.307 then the Laminar regime extends all the way to Re = 15000 27

TANKJKT c. Otherwise the upper limit of the Laminar regime is calculated with

 d  2000 1  13.2  e   dc 

Re la min ar

  

0.6

   

d. The Transitional regime is between the upper limit of Laminar to 15000 3. Calculate Nu for the Laminar regime (if Re < 15000) using the value of Re or, if in the Transitional regime, at the Re at the upper limit of the Laminar regime a. Let X  Re

0.5

 d e Pr    d  c 

0.25

b. If X > 4.9 (high curvature) then

 1.48 23.2 120 212     Nu  0.984 X 1   2  3  4  X X X X    w  

0.14

c. If X <= 4.9 (low curvature) then, for aiding flow the sign is plus (+) and exponent m is 0.28, and for opposing flow the sign is negative (‐) and exponent m is 0.25

Nu fc

Gz  4.86  0.09525 1  0.0525 Gz 0.67

      w 

0.14

Iteratively calculate Nu using



  Nu    Gz 

0.888

  exp  0.4875  

   m

Nu nc   0.7287 



0.33

d    Gr Pr e  L 

Nu  Nu fc  Nu nc 3

3



1

3



4. Calculate Nu for the Turbulent regime (if Re > 15000) or at a Re = 15000 if in the Transitional regime

d a. Let X  Re  e  dc

2

  

28

TANKJKT b. If X > 4.72 (high curvature) then, if this is a cooling application (HTF temperature is less than the process temperature), set Ge = 1 and m = 0.18. For a heating application, set Ge = 1 and m = 0.3

 de  L

c. If X <= 4.72 calculate Ge  1  5.71

 L   1  exp  0.07 de  

  and m = 0.18 

d. Then

Nu  0.0192 Re

0.795

Pr

0.495



exp  0.0225 ln Pr 

2

m   d      1  0.059 Re  e Ge    d c  w   



  

2

  

0.34

   

5. For the Transitional regime, interpolate between the Nu calculated at the Laminar and Turbulent limits from above against the logarithm of Re. Conventional Jacket with Baffles This case uses the same formulas as the half‐pipe coil jacket [Garvin 1999]. Conventional Jacket with Agitating Nozzles TANKJKT follows the method given by [Garvin 2005] for conventional jackets with agitating nozzles. The method uses data for pressure drop and flow rate given by the tank manufacturer such as Pfaudler or De Dietrich. That data is given for the case of water, usually at 20°C, and TANKJKT uses it to calculate the effective nozzle outlet diameter. As Garvin states, this value is related to, but not equivalent to, the throat diameter of the nozzle. When nozzles are used you can either enter a value for throat diameter, which is taken to be the effective outlet diameter in the calculation, or enter pressure drop data with water (viscosity = 1 cP and density = 1 g/cc) in the “Experimental pressure drop” section of the Data Input worksheet. Dimple Jacket Using the mean dimple diameter as the characteristic length, applicable to sidewall and bottom head [Garvin 2001]:

ho d o  w  0.0845   k x

0.368

 Amin   Amax

  

0.383

Re 0.695 Pr 0.33

[3]

Internal Coil This case uses the same formulas as the half‐pipe coil jacket [Garvin 1999]. For a helical coil we applied the centrifugal force correction factor.

29

TANKJKT Inside Heat Transfer Calculations The inside heat transfer coefficient refers to the process side of the surface, whether it be the tank wall or the outside of an internal coil. The general form of the coefficient, for agitated vessels, is: c

   hi T   K Re a Pr b  k  w 

[4]

The coefficient, K, and exponents a, b, and c vary with the type of agitator impeller and which surface is under consideration Geometric corrections are made, depending on the impeller, for deviations from “standard” values for parameters such as blade width, blade height, impeller diameter, baffle width, etc. Typical values for K are 0.5 (baffled tank, axial‐flow impeller), 0.75 to 0.80 (baffled tank, radial‐flow impeller) and 0.35 to 0.4 (unbaffled tank regardless of impeller type). Typical values for a, b and c are 0.67, 0.33 and 0.14. The calculation utilizes physical properties of the liquid inside the tank, evaluated at the bulk temperature plus the viscosity evaluated at the wall temperature. The wall temperature varies with the amount of heat transfer, so the calculation is iterated. The first pass sets the wall temperature to the average of the process fluid bulk temperature and the heat transfer fluid supply temperature. After the inside and outside heat transfer coefficients are evaluated, the overall heat transfer coefficient is calculated and a new wall temperature determined. This is used for the second pass and the calculations are repeated until the algorithm converges, which takes only three or four iterations. For radial flow impellers, different coefficients for the sidewall and bottom head surfaces are reported. TANKJKT uses those different coefficients or uses identical coefficients if the literature doesn’t specify a difference. The coefficient for tanks without agitator use natural convection correlations for natural convection at vertical or horizontal surfaces (sidewall and bottom head respectively). These make use of the dimensionless Grashof number that relates buoyancy and viscous forces acting on the fluid. Instead of the bulk liquid temperature used for agitated vessels, the film temperature, defined as the average of bulk and wall temperatures, is used to evaluate the necessary physical properties: volumetric thermal expansion coefficient and kinematic viscosity. For the tank sidewall, setting L = wetted height of sidewall, we use the Churchill and Chu formulas which are [Welty]: For [Gr Pr} < 109,

0.25 hi L 0.67 Gr Pr   0.68  4 k 9   9   0.492 16  1   Pr



30



[5]

TANKJKT For [Gr Pr} > 109, 2

    1   hi L  0.387 Gr Pr  6   0.825  8    k 9 27  0.492  16     1   Pr  





{6}

For the bottom head, we use the simplifying assumption that it is a flat horizontal plate, with the characteristic dimension, L, equal to the ratio of tank bottom area divided by its perimeter. The formulas are [McAdams, Lloyd]: For tank cooling,

hi L 0.25  0.27 Gr Pr  k

[7]

hi L 0.25  0.54 Gr Pr  k

[8]

hi L 1   0.15 Gr Pr  3 k

[9]

For tank heating, with [Gr Pr} < 2 x 107

With [Gr Pr} >= 2 x 107

Pumped circulation is treated as a combination of natural and forced convection. The natural convection component is calculated as described above. For forced convection, we make an assumption that the vessel contents move as if flowing in a pipeline. This results in a laminar flow condition, and the film coefficient for laminar flow is computed with:

hi L  Re Pr T   1.86   k  L 

0.33

[10]

This result is combined with the natural convection result. In practice, the forced convection component makes no practical difference and might as well be ignored. For unbaffled tanks, if published data weren’t found we used a correction factor of 0.65 for the sidewall, and 1.0 for the bottom head.

31

TANKJKT Table 3: Parameters for Sidewall Inside Heat Transfer Coefficient Impeller Alloy 3‐blade retreating Anchor

Glass‐steel retreating Helical ribbon

Paddle Propeller

High‐Efficiency turbine Pitched‐blade turbine Disk turbine w/6 blades

K 0.37 0.69 0.32 0.33 0.55 0.54 0.94 0.248

a 0.67 0.5 0.67 0.67 0.67 0.67 0.33 0.5

b 0.33 0.33 0.33 0.33 0.25 0.33 0.33 0.33

c 0.24 0.14 0.14 0.18 0.14 0.14 0.14 0.14

0.238 0.67

0.33

0.14

0.415 0.67 0.36 0.67 0.5 0.67

0.33 0.33 0.33

0.24 0.14 0.14

0.313 0.67

0.33

0.14

0.31 0.45 0.74

0.67 0.67 0.67

0.33 0.33 0.33

0.14 0.14 0.14

0.85

0.66

0.33

0.14

0.54

0.66

0.33

0.14

Other [for 6‐blade, K‐0.37, c = 0.14] Re < 100 100 <= Re < 300 300 <= Re < 4000 4000 <= Re Re < 13 13 <= Re < 130 [(T‐D)/(2D)]‐.22(Pitch/D)‐.28 130 <= Re (Pitch/D)‐.25 Re <= 4000 4000 < Re Baffled tank (T/Z)0.15 [1.29 (Pitch/D)]/[0.29 (Pitch/D)] Un‐baffled tank (T/Z)0.15 [1.29 (Pitch/D)]/[0.29 (Pitch/D)] (W/0.17D)0.2 (T/Z)0.15 (W/0.17D)0.2 (T/Z)0.15 Re <= 400, Baffled tank (W/0.2D)0.2 (T/Z)0.15 [for 4‐blade, K = 0.66] 400 < Re, Baffled tank (T/Z)‐.56 (D/T)0.13 Un‐baffled tank (T/Z)‐.56 (D/T)0.13

Reference Dream Penny 2004 Penny 2004 Dream Dream Couper Penny 2004 Dream Dream Dream Dream Penny 2004

Penny 2004 Penny 2004

Dream Dream

Table 4: Parameters for Bottom Head Inside Heat Transfer Coefficient Impeller Alloy 3‐blade retreating Anchor

a 0.67 0.5 0.67 0.67 0.67 0.67 0.33 0.5

b 0.33 0.33 0.33 0.33 0.25 0.33 0.33 0.33

c 0.24 0.14 0.14 0.18 0.14 0.14 0.14 0.14

0.238 0.67

0.33

0.14

Propeller

0.415 0.67 0.36 0.67 0.5 0.67

0.33 0.33 0.33

0.24 0.14 0.14

High‐Efficiency turbine Pitched‐blade turbine Disk turbine w/6 blades

0.9 1.08 0.5

0.33 0.33 0.33

0.14 0.14 0.14

Glass‐steel retreating Helical ribbon

Paddle

K 0.37 0.69 0.32 0.33 0.55 0.54 0.94 0.248

0.67 0.67 0.67

Other [for 6‐blade, K‐0.37, c = 0.14] Re < 100 100 <= Re < 300 300 <= Re < 4000 4000 <= Re Re < 13 13 <= Re < 130 [(T‐D)/(2D)]‐.22(Pitch/D)‐.28 130 <= Re (Pitch/D)‐.25 Re <= 4000 4000 < Re Baffled and un‐baffled tank (T/Z)0.15 [1.29 (Pitch/D)]/[0.29 (Pitch/D)] (W/0.17D)0.2 (T/Z)0.15 (W/0.17D)0.2 (T/Z)0.15 Baffled tank and un‐baffled tank (W/0.2D)0.2 (T/Z)0.15 [for 4‐blade, K = 0.4]

32

Reference Dream Penny 2004 Penny 2004 Dream Dream Couper Penny 2004 Dream Dream Dream Dream Penny 2004

Penny 2004 Penny 2004 Penny 2004

TANKJKT Table 5: Parameters for Helical Coil and Hairpin Coil Process‐Side Heat Transfer Coefficient Impeller Alloy 3‐blade retreating

K 0.03

a 0.67

b 0.33

c 0.14

Other Reference No correlation found in literature; N/A using 6‐blade disk turbine parameters without geometric corrections Paddle 0.027 0.67 0.33 0.14 (W/0.2D)0.2 (T/Z)0.15(T/D)0.5 Penny and Fair Propeller 0.016 0.67 0.33 0.14 (3D/T)0.1(CoilD/T/0.04)0.5 Penny 2004 High‐Efficiency turbine 0.017 0.67 0.33 0.14 (W/0.17D)0.2 (T/Z)0.15(T/D)0.5 Penny and Fair Pitched‐blade turbine 0.023 0.67 0.33 0.14 (W/0.17D)0.2 (T/Z)0.15(T/D)0.5 Penny and Fair Disk turbine w/6 blades 0.03 0.67 0.33 0.14 (W/0.2D)0.2 (T/Z)0.15(3T/D)0.1 Penny 2004 (CoilD/T/0.04)0.5(2/#Blades)0.2 Proximity impellers are not compatible with helical coils, so anchor and helical ribbon impellers are excluded from the TANKJKT model. Internal coils are not generally used with glass‐lined vessels, and they are not modeled for glass‐steel retreating impellers.

Table 6: Parameters Baffle and Harp Coils Process‐Side Heat Transfer Coefficient Impeller Alloy 3‐blade retreating

K a 0.021 0.67

b 0.4

c 0.14

Other Reference No correlation found in literature; N/A using 6‐blade disk turbine parameters without geometric corrections Paddle 0.06 0.65 0.3 0.14 (W/0.2D)0.2 (T/Z)0.15(3T/D)0.33 Penny and Fair (CoilD/T/0.04)0.5 Propeller 0.016 0.67 0.33 0.14 (3D/T)0.1(CoilD/T/0.04)0.5 Penny 2004 High‐Efficiency turbine 0.017 0.67 0.33 0.14 (W/0.17D)0.2 (T/Z)0.15(T/D)0.5 Penny and Fair Pitched‐blade turbine 0.023 0.67 0.33 0.14 (W/0.17D)0.2 (T/Z)0.15(T/D)0.5 Penny and Fair Penny 2004 Disk turbine w/6 blades 0.021 0.67 0.4 0.14 (W/0.2D)0.2 (T/Z)0.15(3T/D)0.1 (CoilD/T/0.04)0.5(2/#Blades)0.2 Proximity impellers are not compatible with helical coils, so anchor and helical ribbon impellers are excluded from the TANKJKT model. Internal coils are not generally used with glass‐lined vessels, and they are not modeled for glass‐steel retreating impellers.

33

TANKJKT Agitator Power Calculations Agitator power (kW or hp) for turbine s is calculated from the general relationship:

P

N P  N 3 D5 gc

[11]

The power number, NP, is given in many sources and generally considered to be a constant for a specific impeller when operating in the turbulent region (Reynolds number > 20,000). At lower values of Reynolds number the same relationship applies, but the power number increases. However, the reason for a lower Reynolds number may be a decrease in speed or impeller diameter, both of which enter into the power relationship, so this is complicated. A generalized graph of power number as a function of Reynolds number is widely published and reproduced below. We fit fourth‐order polynomials to the curves and use those to estimate the power number after calculating the Reynolds number. The power numbers are adjusted for factors such as number of blades and blade width.

Figure 1: Power numbers for turbine impellers [Dickey]

34

TANKJKT Agitator Power Transferred to the Process Fluid You can configure the amount of the agitator power that is transferred to the process fluid as heat. On the Data Tables worksheet you’ll find a cell named AgitatorPowerCooling and another named AgitatorPowerHeating. These represent the percentage of the agitator power that is added to the process fluid as heat. A rule of thumb is that 50% of the motor power is transferred, but we suggest conservative values of 55% for a cooling application, and 35% when heating. Depth of Vortex For unbaffled tanks with turbine type impeller, TANKJKT estimates the depth of the vortex using the relationship from Rieger. This estimate is provided for information only and should not be taken as an absolute given. The result appears in the list of messages, just to the right of the Vessel Fluid Data on the Data Input worksheet. The correlation uses the Galileo and Freude numbers as follows. For high Ga,

T  Depth  D BH Ga 0.069   D

0.38

Fr 1.14 Ga

 0.008

T    D

0.008

T    D

0.24

[12]

For low Ga,

Depth  D BL Ga

0.33

T    D

1.18

Fr

3.38 Ga .0.074

[13]

The values for BH and BL depend on the impeller style as does the breaking point value between a high and low Ga number.

35

TANKJKT Fluid Data Worksheet Physical properties for heat transfer fluids are tabulated on the “Fluid Data” worksheet. These are regression parameters that TANKJKT uses to determine the properties at any temperature. You can add new fluids to this worksheet using the tool that described in this section. Properties are returned with the following units: Temperature ____________________________ °C Density ________________________________ lb/ft3 Specific Heat ____________________________ Btu/lb‐°F Thermal Conductivity _____________________ Btu/ft‐hr‐°F Viscosity _______________________________ cP Vapor Pressure __________________________ mm Hg Beginning with Version 2.1, all calculations are performed in SI units then converted to Customary US for display and reporting. Therefore, the function subroutines that utilize the properties on the “Fluid Data” worksheet return the results in SI units. We retained the Customary US units on “Fluid Data” to ensure backward compatibility; a user may safely copy‐and‐paste regression coefficients from a previous version of TANKJKT. The viscosity and vapor pressure are not actually regressed. Instead, three values are forced to fit a three‐parameter equation. Viscosity is divided into three temperature ranges so there are three sets of parameters. This isn’t actually necessary – excellent agreement between data and correlation are obtained with a force fit over a large temperature range – but to maintain backward compatibility the practice is continued in the program. Here are the equations used to fit the data, where t = temperature, °C: Density

  mt b

Specific Heat

cp  mt b

Thermal Conductivity

k  mt b

Viscosity

  exp A 

Vapor Pressure

P  A

 

 B  C  t  273.15 

B C t

36

TANKJKT Example Thermal physical properties for Paratherm HE® are published on the Paratherm web site (http://paracalc.paratherm.com) and reproduced below. For this example, we chose seven temperatures and the properties for viscosity, density, thermal conductivity and specific as highlighted. Notice that the vapor pressure data is listed only at high temperatures.

Screen shots showing this data entered onto the “Fluid Data” worksheet are shown and described on the next page.

37

The radio buttons are used to select units of measure consistent with those in the published data. Density is published in g/cc, but we selected kg/m3 instead and multiplied the density values by 1000 when entering them in the table.

Units that the original data are in: Temperature

degrees F

degrees C

Density

lb/cu.ft.

kg/cu.m.

Specific Heat

Btu/lb-F = cal/g-C

Kj/kg-K


Btu/ft-hr-F

W/m-K

Viscosity

cP

centi Stokes = mm2/s

Fluid Name: Manufacturer: Description: Operating range:

After entering all of the data, we clicked on the “Add Fluid to Database” button. This adds a new line to the properties table and enters the parameters for all of the properties.

Paratherm HE Paratherm Mineral oil 50 °C minimum 310 °C maximum

Liquid Thermal Temp. Density Sp. Heat Conduct. °C kg/cu.m. Btu/lb-°F Btu/ft-hr-°F 38 850 0.47 0.075 66 830 0.49 0.074 107 810 0.53 0.0724 149 780 0.56 0.071 191 750 0.6 0.0695 246 720 0.65 0.0675 316 670 0.71 0.065

Vapor Pressure

Visc. cSt

The four graphs confirm that the data is entered correctly since there are no obvious outlying data points. Notice, however, that the values entered for thermal conductivity at 107°, 191° and 246°are slightly higher than those in the published table. This was done to compensate for the lack of significant figures in the data and create a better match between data and regressed parameters.

mm Hg

45 16 5.5 2.9 1.8 1.1 0.7

0.07 19.50 422.00

Add Fluid to Database

Density

Specific Heat

900 800 700 600 500 400 300 200 100 0

Thermal Conductivity 0.076

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

100

200 Density

300

400

Predicted

UINS‐TJ‐02 February 2015

Viscosity 100

0.074 0.072

10

0.07 0.068

1

0.066

0

100

200 Specific H eat

300

400

Predic ted

0 0

100

200


38

100

200

300

400

0.064 300 Predicted

400

0.1 Vis cosity

Predicted

TANKJKT Vapor pressure data is entered separately in this example. The temperatures for three vapor pressure points are entered along with corresponding values for vapor pressure, as shown below. Fluid Name: Manufacturer: Description: Operating range:

Paratherm HE <-- Already in the database Paratherm Mineral oil 50 °C minimum 310 °C maximum

Liquid Density kg/cu.m.

Temp. °C

Thermal Sp. Heat Conduct. Btu/lb-°F Btu/ft-hr-°F

Visc. cSt

Vapor Pressure mm Hg

288

21.00

316

52.00

329

79.00

Take the following steps to get the results into the table: 1. Unprotect the worksheet if necessary. Review … Unprotect Sheet. There is no password. 2. Copy the three Antoine Coefficients to the clipboard. These are found on row 55, beginning in column G (unless you have inserted rows and/or columns to the worksheet). Antoine Coefficients A

B

C

88.65765 539906.1 5893.983

3. Use Paste Special … Values to paste the coefficients into the row for the fluid (in this example, Paratherm HE). This overwrites the values that were (incorrectly) placed there when the fluid was added initially. For this illustration the unneeded values for density, specific heat, etc. are erased from the input data table. In practice this isn’t necessary since only the vapor pressure (and corresponding temperatures) are actually used.

39

TANKJKT Data Tables Worksheet The Data Tables worksheet stores parameters for physical properties such as thermal conductivity of tank materials, emissivities, standard pipe sizes, and agitator geometries. You can edit some of these values, but be very careful that you don’t overwrite formulas that calculate the dimensions of tank heads, or values that save previous data entries for impellers. In general, don’t change values on this worksheet. The worksheet also stores the value of radio buttons, dropdown lists and check boxes. These are controlled by associated control on the Data Input worksheet and should not be edited. The timeline values are written to this worksheet with the results used to create the timeline chart. Again, these are programmatically determined and should not be manually edited. Refer to the Data Tables worksheet for additional information about the values that are stored there. PictElements Worksheet (HIDDEN) The PictElements worksheet is hidden from view and should not be changed. It contains the pictorial elements used to compose the tank picture on the Data Input screen. These elements are copied from this worksheet to the Data Input worksheet whenever needed to refresh the picture.

40

TANKJKT Saved Calcs Worksheet It takes time to enter all the data about a particular vessel. That’s why you have the option to save that data for reuse in the future. Data is stored on the worksheet called “Saved Data”. When you click on the “Save Calculation” button on the Data Input sheet, the current calculation is instantly copied to the Saved Data page. You must save the entire workbook to keep access to this data for the future!

TIP: Store information about commonly used classes of vessels. TANKJKT is shipped with physical dimensions of standard glass‐ lined vessels manufactured by Pfaudler and De Dietrich (USA). Similarly, you can add to this the types and sizes of vessels

Retrieving an old calculation is simple. Choose it from the dropdown list of saved data, then click the “Restore Saved Calculation” button. That’s it. To delete old calculations from the archive, go to the Saved Data worksheet. Unprotect the sheet (there is no password required). Then highlight the row(s) containing your unwanted data. Delete the row(s) by using Excel’s Edit…Delete… command. Result Details TANKJKT stores the results from calculations in an array. You can view the complete content of the array, displayed in the units that are currently selected, on the worksheet called “Result Details.” You can also write your own formulas to tap into the results. The syntax for the formula is: = Res(surface, parameter, units, chng) The arguments are: surface is the heat transfer surface, where 1 = sidewall, 2 = bottom, 3 = coil, 4 = tank roof parameter is the value (see list below) units is the units of measure for the result, where 1 = U.S., 2 = SI chng is a reference to a cell that updates whenever the calculations are run, which forces this formula to refresh

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TANKJKT Table 7: Parameters Stored in the Res() Array Parameter 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

16 17 18 19 20 21

Description HTF Film Coefficient, ho Process Film Coefficient, hi Overall Coefficient, U Heat Transferred, Q HTF Flow Rate HTF Pressure Drop HTF Velocity HTF Temperature In HTF Temperature Out HTF Temperature Average HTF Temperature Wall Process Temperature Process Temperature Wall Wall Coefficient, hw Agitator Power Surface 1 = total power Surface 2 = power as heat to fluid Environmental film coefficient, he Jacket‐to‐environment Ue Jacket‐to‐environment Qe Process‐to‐environment Ue Process‐to‐environment Qe Surface Temperature

U.S. Units Btu/hr‐ft2‐F Btu/hr‐ft2‐F Btu/hr‐ft2‐F Btu/hr lb/hr psi ft/s F F F F F F Btu/hr‐ft2‐F Btu/hr

SI Units W/m2‐C W/m2‐C W/m2‐C W kg/h kPa m/s C C C C C C W/m2‐C W

Btu/hr‐ft2‐F Btu/hr‐ft2‐F Btu/hr Btu/hr‐ft2‐F Btu/hr F

W/m2‐C W/m2‐C W W/m2‐C W C

The function EnergyResult returns the final results for the calculation. Its syntax is: = EnergyResult(parameter, units, chng) The arguments are: parameter is the result requested, where 1= total energy gained or lost from the process fluid in the tank, and 2= temperature change per minute units is the units of measure for the result, where 1 = U.S., 2 = SI chng is a reference to a cell that updates whenever the calculations are run, which forces this formula to refresh

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TANKJKT Nomenclature Note that the units associated with the variables are not entirely consistent. Formulas used in the TANKJKT calculations recognize this and apply the necessary conversions. In some cases, the units used on the Data Input sheet differ from those used in the VBA subroutines. For example, impeller diameter is input in millimeters, but converted to meters when transferred to the subroutine.

c p  specific heat, Joules/kg‐°C D  impeller diameter, m

g  acceleration of gravity, 9.81 m/s2 g c  conversion factor, 1 m/s2 hi  inside (process‐side) heat transfer coefficient, W/m²‐°C ho  outside (heat transfer fluid side) heat transfer coefficient, W/m²‐°C

k  thermal conductivity, W/m‐°C K  coefficient for heat transfer equation L  characteristic length, m N  agitator rotational speed, rps

P  agitator power, W T  inside diameter of vessel, m t  temperature, °C

U  overall heat transfer coefficient, W/m²‐°C

W  blade height, measured parallel to shaft, m Z  liquid depth in the tank, m For conventional jackets

d c  curvature diameter d e  equivalent diameter d h  hydraulic diameter = 2 x annulus L  length of the flow path from entrance nozzle to exit nozzle For dimple jackets

Amin  z w  d o  minimum flow area

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TANKJKT

Amax  z w maximum (unrestricted) flow area d o  mean dimple diameter, m w  center‐to‐center distance between adjacent dimples parallel to flow x  transverse center‐to‐center distance between adjacent dimples Greek variables

  coefficient of volumetric expansion, 1/°C

  density, g/ cm3

  dynamic viscosity, Pa‐s Dimensionless numbers

Fr 

N2 D

Ga 

Re 2 Fr

Gr 

Re 

Pr 

Froude number

Galileo number

g  L3 t  2

2

Gz  Re Pr Nu 



dh L

hi T k D2 N 

 cp  k

Grashof number

Graetz number

Nusselt number

Reynolds number

Prandtl number

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TANKJKT References Bolliger, Donald H., “Assessing heat transfer in process‐vessel jackets,” Chemical Engineering, September 20, 1982, page 95. Bondy, Frederick, and Lippa, Shepherd, "Heat transfer in agitated vessels", Chemical Engineering, April 4, 1983, page 62. Cau, Eduardo, Heat Transfer in Process Engineering, McGraw‐Hill, 2010. Couper, J.R., Penny, W.R., Fair, J.R., Walas, S.M., Chemical Process Equipment: Selection and Design, 3rd Edition, Butterworth‐Heinemann, Waltham, MA, 2012. Dickey, David S., “Mixing and Blending,” from the Kirk‐Othmer Encyclopedia of Chemical Technology, Wiley, published online 16 Apr 2010. Dream, Robert F., "Heat Transfer in Agitated Jacketed Vessels", Chemical Engineering, Vol 106, No 1, January 1999, pages 90‐96. Furukawa, H., Kato, Y., Inoue, Y., Kato, T., Tada, Y., Hashimoto, S., "Correlation of Power Consumption for Several Kinds of Mixing Impellers," International Journal of Chemical Engineering, Volume 2012 (2012), Article ID 106496. Downloaded from: http://www.hindawi.com/journals/ijce/2012/106496/ Garvin, John, "Understand the Thermal Design of Jacketed Vessels", Chemical Engineering Progress, Vol 95, No 6, June 1999, page 61. Garvin, John, "Estimate Heat Transfer and Friction in Dimple Jackets", Chemical Engineering Progress, Vol 97, No 4, April 2001, pages 73‐75. Garvin, John, “Evaluate Flow and Heat Transfer in Agitated Jackets,” Chemical Engineering Progress, August 2005, pages 39‐41. Hemrajani, Ramesh R., “Mixing and Blending,” from the Kirk‐Othmer Encyclopedia of Chemical Technology, Version 2, Wiley, published online 15 Apr 2005. Hemrajani, Ramesh R., and Tatterson, Gary B., "Mechanically Stirred Vessels," Chapter 6 in Handbook of Industrial Mixing, edited by Edward Paul, Victor Atiemo‐Obeng and Suzanne Kresta, John Wiley, 2004. Lloyd, J.R., Moran, W.R., Natural convection adjacent to horizontal surfaces of various platforms,” ASME Paper 74‐WA/HT‐66, 1974. McAdams, W.H., Heat Transmission, 3rd Edition, McGraw‐Hill, New York, 1954. Nienow, Alwin W., “Stirred Tank Reactors,” from Ullmann’s Encyclopedia of Industrial Chemistry, Wiley, published online 15 Jan 2010.

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TANKJKT Penny, W.R., "Heat transfer correlations", in Handbook of Heat Exchanger Technology, Hemisphere Publishing Corp., New York (1983). Penny, W.R., Atiemo‐Obeng, V.A., “Heat Transfer,” Chapter 14 in Handbook of Industrial Mixing, edited by Edward Paul, Victor Atiemo‐Obeng and Suzanne Kresta, John Wiley, 2004. Poling, B.E., Prausnitz, J.M., O'Connell, J.P., Properties of Gases and Liquids, Fifth Edition, McGraw‐Hill, 2001. Rieger, F., Ditl, P., Noval, V., “Vortex depth in mixed unbaffled vessels,” Chem Eng Sci, 34:397‐403 (1979). Uhl, Vincent W., "Mechanically Aided Heat Transfer," Chapter 5 in Mixing: Theory and Practice, Vol 1, edited by Vincent Uhl, Academic Press, 1966. Welty, J.R., Wicks, C.E., Wilson, R.E., Rorrer, G.L., Fundamentals of Momentum, Heat and Mass Transfer (5th Edition), John Wiley and Sons, 2007. Zlokarnik, Marko, Stirring: Theory and Practice, Wiley‐VCH, Weinheim, Germany, 2001. *** END OF DOCUMENT ***

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TANKJKT spreadsheet template Heat for Tanks

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