ES_Insu User Manual

1. Introduction

2. Basic Expressions

3. Major Screens

4. Test Results for Sample Problems of ASTM C680

5. Check of ES_Insu Results by Calculation

6. Test Results for 1997 ASHRAE Fundamental Handbook(SI)


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1.  Introduction

 The heat transfer calculation of thermal insulation does not represented by complicate equations.   The calculation consists of the calculations of conduction through insulation and the calculation of radiation/convection over the insulation surface, and is to find the insulation surface temperature at which the heat transfer rates of the two calculations are same.

However, as stated in Clause 5.4 of ASTM C680, computer programming is the best for the heat transfer calculation of thermal insulation because of its iterative nature of the method.

ES_Insu is the software to calculate the heat transfer of thermal insulation for plate(equipment) and cylinder(pipe) according to ASTM C680-89(Reapproved 1995).

ES_Insu calculates the followings for thermal insulation.

o Heat transfer calculation with conditions provided

o Thickness calculation satisfying target value(surface temperature or heat density)

o The most economic thickness calculation in view of installation and energy cost

o Thickness calculation satisfying both target value and economics

o Thickness calculation  satisfying both target value and economics for a range of temperature in steps

  (maximum 20 temperatures, from 1/2 inch to 26 inch pipes)

o Freezing hour or freezing flow calculation according to ASHRAE Fundamental Handbook

o Thickness calculation satisfying target freezing hour

 o Use of the nominal pipe insulation thickness specified in ASTM C585-90

 

2. Basic Expressions   (TOC)

2.1 Function Type of Thermal Conductivity

In the unit selection of ES_Insu software, there is not a unit of "Btu-in/hr-ft2-oF" used in the sample calculations of ASTM C680.   Instead, there is the unit of "Btu/hr-ft-oF" in ES_Insu Software.

In the types other than Type 2, the function with "Btu-in/hr-ft2-oF" unit can be converted into the function with "Btu/hr-ft-oF" unit by dividing the coefficient of temperature terms by 12.    However, in case of Type 2 function in natural logarithm, the function with "Btu-in/hr-ft2-oF" unit can be converted into the function with "Btu/hr-ft-oF" unit by adding the value of Ln(1/12) = -2.48491 to the exponent value.

For example, the thermal conductivity function of the Sample Problem 1 of ASTM C680 is "k = e^(-1.62 + 0.00213 * T)" and the unit of thermal conductivity is "Btu-in/hr-ft2-oF".    The function converted in the thermal unit of  "Btu/hr-ft-oF" is "k = e^(-2.48491 - 1.62 + 0.00213 * T) = e^(-4.10491 + 0.00213 * T)".

In ES_Insu software, there are five types of thermal conductivity functions the user can select.  The first three functions are the functions introduced in ASTM C680, while the others are the functions the insulation manufacturers normally use.    The five functions are as below.

< Type 1 >

k = a + b * T + c * T^2

< Type 2 >

k = e^(a + b * T)

< Type 3 >

k = a1 + b1 * T; T < TL

k = a2 + b2 * T; TL < T < TU

k = a3 + b3 * T; T > TU

< Type 4 >

k = a1 + b1 * T; T < TL

k = a2 + b2 * T + c2 * T^2; T > TL

< Type 5 >

k = a + b * T + c * T^2 * d * T^3

where,

k

: Thermal Conductivity of Insulation

 

T

: Temperature of Insulation

As in the source program of ASTM C680, ES_Insu stops the calculation when the thermal conductivity of a layer is less than 0.01 Btu-in/hr-ft2-oF.

2.2 Thermal Conductivity Calculation

When calculating the thermal conductivity from the function, someone calculates the arithmetic average of the inner and outer temperatures of a insulation and then gets the thermal conductivity of the insulation at the arithmetic average temperature.   The thermal conductivity calculated so is not the exact value of the thermal conductivity.

Exact thermal conductivity can be calculated by integration between the inner and outer temperatures of the insulation and then dividing by the temperature difference, which is the method used in the subroutine of KCURVE of ASTM C680.

The integrated average values of thermal conductivity for various terms are as below, where Ti is the inner temperature of insulation and To is the outer temperature.

1) Constant term

    k = Integral{a}dT / (Ti - To)

        = a * (Ti - To) / (Ti - To)

        = a

2) The first degree term

    k = Integral{b * T}dT / (Ti - To)

        = b / 2 * (Ti^2 - To^2) / (Ti - To)

        = b / 2 * (Ti + To)

3) The second degree term

    k = Integral{c * T^2}dT / (Ti - To)

        = c / 3 (Ti^3 - To^3) / (Ti - To)

4) The third degree term

    k = Integral(d * T^3)dT / (Ti - To)

        = d / 4 (Ti^4 - To^4) / (Ti - To)

5) Exponential term

     k = Integral{e^(a + b * T)}dT / (Ti - To)

        = {e^(a + b * Ti) - e^(a + b * To)} / b / (Ti - To)

 

ES_Insu software calculates the thermal conductivity of a insulation as the integrated average method used in ASTM C680 and the expressions for calculating the integrated average value are as below.

1) Type 1

        k =  a + b * (Ti + To) / 2 + c * (Ti ^ 3 - To ^ 3) / 3 / (Ti - To)

2) Type 2

        k = {e^(a + b * Ti) - e^(a + b * To)} / b / (Ti - To)

3) Type 3

Because Type 3 function uses different expression depending on the temperature, first the higher and lower temperature should be identified between the inner and outer insulation temperature.

If the higher temperature is named as "H" and the lower as "C", then the integrated average temperature is calculated as below.

        A) If C <= TL and H <= TL,

                k = a1 + b1 * (H + C) / 2

        B) If C <= TL and  H <= TU,

                k = {a1 * (TL - C) + b1 * (TL ^ 2 - C ^ 2) / 2 +

                    a2 * (H - TL) + b2 * (H ^ 2 - TL ^ 2) / 2} / (H - C)

        C) If C <= TL and TU <= H,

                k = {a1 * (TL - C) + b1 * (TL ^ 2 - C ^ 2) / 2 +

                     a2 * (TU - TL) + b2 * (TU ^ 2 - TL ^ 2) / 2 +

                    a3 * (H - TU) + b3 * (H ^ 2 - TU ^ 2) / 2} / (H - C)

        라) If C <= TU and H <= TU,

                k = a2 + b2 * (H + C) / 2

        마) If C <= TU and TU <= H,

                k = {a2 * (TU - C) + b2 * (TU ^ 2 - C ^ 2) / 2 +

                    a3 * (H - TU) + b3 * (H ^ 2 - TU ^ 2) / 2} / (H - C)

        바) If TU <= C and TU <= H,

                k = a3 + b3 * (H + C) / 2

4) Type 4

Because Type 4 function also uses different expression depending on the temperature, first the higher and lower temperature should be identified between the inner and outer insulation temperature.

If the higher temperature is named as "H" and the lower as "C", then the integrated average temperature is calculated as below.

        가) If C <= TL and H <= TL,

            k = a1 + b1 * (H + C) / 2

        나) If C <= TL and TL <= H,

            k = {a1 * (TL - C) + b1 * (TL ^ 2 - C ^ 2) / 2 +

                a2 * (H - TL) + b2 * (H ^ 2 - TL ^ 2) / 2 +

                c2 * (H ^ 3 - TL ^ 3) / 3} / (H - C)

        다) If TL <= C and TL <= H,

            k = a2 + b2 * (H + C) / 2 + c2 * (H ^ 3 - C ^ 3) / 3 / (H - C)

5) Type 5

            k = a + b * (Ti + To) / 2 + c * (Ti ^ 3 - To ^ 3) / 3 / (Ti - To) +

                d * (Ti ^ 4 - To ^ 4) / 4 / (Ti - To)

 

2.3 Surface Convection/Radiation Heat Transfer

1) Convection Heat Transfer

    hcv = C * (1/d)^(0.2) * (1/Tavg)^(0.181) * dT^(0.266) * Sqr(1 + 1.277 * Wind)

where,

hcv

: Convective surface coefficient, Btu/hr-ft2-oF

 

C

: Heat flow direction coefficient :

- Cylindrical, Horizontal heat flow (Vertical Surface) = 1.016

- Cylindrical, Vertical heat flow (Horizontal Surface) = 1.235

- Flat, Horizontal heat flow (Vertical Surface) = 1.394

- Flat, Heat flow down = 0.89

- Flat, Heat flow up = 1.79

 

d

: Diameter for cylinder, inch

(For flat surfaces and large cylinder d > 24, use d = 24)

 

Tavg

: Average temperature of air film, Tavg = (Ts + Tamb) / 2 , oR

Ts : Temperature of surface, oR

Tamb : Temperature of ambient, oR

 

(Note : In Equation (29) of ASTM C680 the unit of Tavg is expressed as "oF".   However in the subroutine SURCOF of ASTM C680 computer program source, the unit of Tavg is expressed as "oR".   Since the error is occurred for Tavg with "oF" unit when the Tavg value is negative value, the unit of Tavg must be "oR".)

 

dT

: Absolute value of surface-to-air temperature difference, dT = |Ts - Tamb|, oR

 

(Note : In Equation (29) of ASTM C680 the dT value is not expressed as an absolute value.   However in the subroutine SURCOF of ASTM C680 computer program source, the dT value is expressed as an absolute value.   Since the error is occurred for non-absolute dT value, the dT value must be an absolute value.)

 

Wind

Air movement speed, US mile per hour

 2) Radiation Heat Transfer

    hrad = Emiss * 0.1713 * 10^(-8) * {(Tamb + 459.6)^4 - (Ts + 459.6)^4} / (Tamb - Ts)

where,

hrad

: Radiative surface coefficient, Btu/hr-ft2-oF

 

Emiss

: Effective surface emittance (includes ambient emittance)

 

0.1713 * 10^(-8)

: Stefan-Boltzman constant, Btu/hr-ft2-oR^4

 3) Convective and radiative surface coefficient

    h = hcv + hrad, Btu/hr-ft2-oF

(As the computer program source of ASTM C680, ES_Insu software uses "h = 1.61 Btu/hr-ft2-oF" when the "h" value is zero or less than zero.)

 

2.4 Heat Resistance(Thermal Resistance) and Heat Density(Heat Flow per Unit Area)

When calculating heat transfer through insulation, especially through the insulation with different thermal conductivities, the use of heat resistance and heat density makes the calculation easy.

2.4.1 Plate(Equipment)

1) Heat Resistance by Thermal Conductivity of Insulation

    Ri = Thicki / ki

where,

Ri

: Heat resistance by thermal conductivity of i'th insulation layer, hr-m2-oC/kcal

 

Thicki

: Thickness of i'th insulation layer, m

 

ki

: Thermal conductivity of i'th insulation layer, kcal/hr-m-oC

2) Heat Resistance by Convective and Radiative Surface Coefficient

    Rs = 1 / h

where,

Rs

: Heat resistance by convective and radiative surface coefficient, hr-m2-oC/kcal

 

h

: Convective and radiative surface coefficient, kcal/hr-m2-oC

3) Total Heat Resistance of Insulation System

    Rt = Rs + R1 + R2 + ... + Rn

where,

Rt

: Total heat resistance of insulation system, hr-m2-oC/kcal

 

Rn

: Heat resistance by thermal conductivity of n'th insulation layer, hr-m2-oC/kcal

4) Heat Density

Since there is no energy loss or gain among insulation layers, the heat density of each insulation layer and entire insulation system is same.   That is, the heat density of the first insulation layer is same with that of the second insulation layer and same with that of entire insulation system.

The identical heat density can be expressed using various heat resistances as below.

    qn = (Ti - Ti_o) / Ri

    qn = (Ts - Tamb) / Rs

    qn = (T1 - Tamb) / Rt

where,

qn

: Heat density, kcal/hr-m2

 

Ti

: Inner temperature of i'th insulation layer, oC

 

Ti_o

: Outer temperature of i'th insulation layer, oC

 

Ri

: Heat resistance by thermal conductivity of i'th insulation layer, hr-m2-oC/kcal

 

Ts

: Temperature of surface, oC

 

Tamb

: Temperature of ambient, oC

 

Rs

: Heat resistance by convective and radiative surface coefficient, hr-m2-oC/kcal

 

Rt

: Total heat resistance of insulation system, hr-m2-oC/kcal

 

T1

: Inner temperature of the first insulation layer, same with the inside fluid temperature, oC

2.4.2 Cylinder(Pipe)

The calculation formulae of heat resistance and heat density for cylinder(pipe) is same with those of plate(equipment) except the formula for heat resistance by insulation thermal conductivity as below.

1) Heat Resistance by Insulation Thermal Conductivity

    Ri = rn * Ln(ri_o / ri) / ki

where,

Ri

: Heat resistance by thermal conductivity of i'th insulation layer, hr-m2-oC/kcal

 

rn

: Outer radius of outmost insulation layer, m

 

ri_o

: Outer radius of i'th insulation layer

 

ri

: Inner radius of i'th insulation layer

 

ki

: Thermal conductivity of i'th insulation layer, kcal/hr-m-oC

2) Heat Transfer Rate of Cylinder Unit Length

    ql = qn * 2 * 3.14 * rn

where,

ql

: Heat transfer rate of cylinder unit length, kcal/hr-m

 

2.5 Heat Transfer Calculation Procedure of Multi Layer Insulation System

The heat transfer calculation of multi layer insulation system is done with iterative nature of method as below.

1) First decide temporarily the temperature of each layer by dividing the temperature between T1 and Tamb in proportion to each insulation thickness.

2) Calculate convective and radiative surface coefficient and then calculate the heat resistance by the surface coefficient.

3) Calculate the thermal conductivity of each layer and then calculate the heat resistance by the thermal conductivity.

4) Calculate total heat resistance of insulation system and then calculate heat density using T1 and Tamb.

5) Using the head density calculated above and thermal conductivity of each layer, calculate the temperature of each layer.  Then compare with the temperature of each layer decided in Step 1) above.   If the temperatures of each layer compared are within a acceptable range, the calculation is complete.    If not, repeat calculation with the temperature calculated in this step from Step 2).   AS in the source program of ASTM C680, ES_Insu completes the calculation when the total sum of the temperature difference of each layer is less than 1 oF from the previous sum.

 

2.6 Economic Insulation Thickness Calculation

The method for economic insulation thickness calculation if ES_Insu software follows the method described in Korean Standard(KS) F2803.

KS F2803 uses the net present value method normally used in industry.   It finds thickness with the least cost sum of annual redemption value of installation cost and annual energy cost.  The calculation formulae are as below.

2.6.1 Redemption Rate(N)

Redemption rate is reverse of net pressure value rate which is used to calculates present value of future money.  For example, if we pay back 100 money per year with 10% annual compound interest for two years, the principal is calculated as below.

100 / 1.1 + 100 / 1.1^2 = 173.5 (money)

In other word, if we invest 173.5 money now, we have to make 100 money per year in order to be paid back with 10% compound interest, and then the redemption rate is 100 / 173.5537 = 0.57619.

The formula of redemption rate is as below.

N = {i * (1 + i)^m} / {(1 + i)^m -1)

where,

N

: Annual redemption rate

 

i

: Interest rate, discount rate or rate of return, not % unit

 

m

: Operating years, year

2.6.2 Installation Cost of Insulation(a)

The installation cost of insulation is the sum of the material and labor cost.  User may input the installation cost or may use the built-in cost estimation function which has been programmed according to the formula of KS F2803 as below.

a = 1.35 * {33000 * X^(-k) + C} * 1000

where,

a

: Installation cost of insulation, Korean Won/m3

 

X

: Insulation thickness, mm

 

k

: Correction factor for pipe OD(not insulation OD)

15A - 20A : k = 1.09

25A - 50A : k = 1.13

65A - 150A : k = 1.17

200A - 300A : k = 1.21

350A - 평면 : k = 1.28

 

C

: Coefficient for insulation material

For rock or glass wool : C = 150

For calcium silicate or perlite : C = 260

2.6.3 Annual Total Cost (F1, F2)

Annual total cost is calculated as below.

1) Cylinder(Pipe)

    F1 = 3.14 / 4 * (do^2 - di^2) * a * N + b * h * Q1

1) Plate(Equipment)

    F2 = X * a * N + b * h * Q2

where,

F1, F2

: Annual total cost, F1 = Currency/year/m : F2 = Currency/year/m2

 

do, di

: Insulation OD and ID, m

 

X

: Insulation thickness, m

 

b

: Energy cost, Currency/kcal

 

h

: Annual operating hour

 

Q1, Q2

: Heat loss through insulation, Q1 = kcal/m-hr : Q2 = kcal/m2-hr

To find out economic insulation thickness, ES_Insu increases the insulation thickness from the current thickness on the main screen by the [Adjustment step] thickness input on [Calculation Set] screen, and finishes the finding when the insulation thickness reaches the [Maximum thickness] of the last layer.

During the thickness increase, ES_Insu selects as an economic insulation thickness the thickness of one step before where the annual total cost changes from decrease to increase.   

If the annual total cost increase at one step thickness increase from the current thickness, ES_Insu selects the current thickness as the economic insulation thickness, even though there is possibility that a thickness thinner than the current thickness is more economic.   Therefore, it is recommended to input the current insulation thickness as thin as possible.

 

2.7 Freezing Calculation

 Freezing calculation is performed only for cylinder(pipe) in accordance with 1997 ASHRAE Fundamentals Handbook(SI).

The formulae in ASHRAE Handbook are for water.   However, the formulae are applicable for other liquid when the properties of liquid instead of water are used.

2.7.1 Freezing Hour

Freezing hour is the time for liquid temperature to drop down to freezing liquid temperature, but does not include the time for freezing to solid.    For example of water, the freezing hour is the time for water to drop down to 0 oC, but does not include the time to become ice.

The freezing hour calculation formula of ASHRAE Handbook is as below.

H = Ro * Cp * 3.14 * Di^2 / 4 / 3600 * Rt * ln{(ti - ta) / (tf - ta)}

where

H

: Freezing hour, hours

 

Ro

: Liquid density, kg/m3 (in case of waer, 1000 kg/m3)

 

Cp

: Specific heat of liquid at constant pressure, J/kg/K (in case of water 4200 J/kg/K)

 

Di

: Cylinder(Pipe) ID, m

 

Rt

: Total heat resistance of insulation system per cylinder(pipe) unit length, m-K/W

Rt = Rp + Ri + Ra

 

Rp

: Heat resistance of cylinder(pipe) itself, m-K/W

- In case the cylinder(pipe) material is metal, Rp = 0.

- ES_Insu uses Rp = 0, assuming that the cylinder(pipe) material is metal.

- If cylinder(pipe) material is not metal, then input the cylinder(pipe) material as one of the insulation layer.

 

Ri

: Heat resistance of insulation per cylinder(pipe) unit length, m-K/W

 

Ra

: Heat resistance by convective and radiative surface coefficient, m-K/W

 

ti

: Initial liquid temperature, oC

 

ta

: Ambient air temperature, oC

 

tf

: Liquid freezing temperature, oC

 

2.7.1 Freezing Flow

Freezing flow is the liquid flow rate at which the liquid temperature at the end of cylinder(pipe) drops down to freezing temperature.   It must not include the flow rate for icing because in icing condition the liquid does not flow.

The freezing flow calculation formula of ASHRAE Handbook is as below.

W/L = 1000 / Cp / (Rt + Rw) / ln{Rt / (Rt + Rw) * (ti - ta) / (tf - ta)}

where,

W

: Freezing flow, g/sec

 

L

: Cylinder(pipe) length, m

 

Rw

: Heat resistance between liquid and inner surface of cylinder(pipe) per meter of cylinder(pipe), m-K/W (in case of water, 0.13 m-K/W)

Rw = 1 / 3.14 / kw / Nu

 

kw

: Thermal conductivity of liquid near freezing, W/m-K (in case of water, 0.56 W/m-K)

 

Nu

: Nusselt number for fully developed laminar flow and constant heat density(in case of water, 4.36)

 

 2.8 Critical Diameter of Cylinder(Pipe) Insulation System

The thicker the insulation the less the heat transfer rate per unit area.   This is true for both plate(equipment) and cylinder(pipe).   However, the heat transfer rate(heat loss) per unit length of cylinder(pipe) is not always less for thicker insulation.   As the thickness of the insulation increases, the outer surface area of insulation increases and eventually the heat loss due to convection/radiation at the surface area also increases.   If the surface area increases more rapidly than the thermal resistance by the thermal conductivity of the insulation, the heat loss(heat transfer rate) per unit length of the cylinder(pipe) increases as the thickness of the insulation increases.

The diameter of cylinder(pipe) insulation system with the maximum heat loss per unit length is called as a critical diameter.

In order to prevent the increase of heat loss for thicker insulation, the critical diameter should be less than the cylinder(pipe) diameter and the critical diameter decreases as a insulation with lower thermal conductivity is used.

2.8.1 Critical Diameter for Constant Thermal Conductivity and Contant Convection/Radiation Heat Transfer Rate

The formula for calculation of a critical diameter is derived by solving the differential equation of heat loss and the formula has the assumption that the thermal conductivity of insulation and the convection/radiation heat transfer rate are constant.

The formula is as below.

Dc = k / h * 2

where,

Dc

: Critical diameter, m

 

k

: Thermal conductivity of insulation system, kcal/hr-m-oC

 

h

: Convection and radiation surface coefficient of insulation, kcal/hr-m2-oC

If insulation system consists of insulation materials with various thermal conductivity, ES_Insu uses the average value of the thermal conductivity calculated as below.

k_avg = rn * Ln(rn / r1) / Ri_total

where,

rn

: Outer radius of outmost insulation layer, m

 

r1

: Inner radius of the first insulation layer, m

 

Ri_total

: Total heat resistance due to thermal conductivity of insulation system, hr-m2-oC/kcal

2.8.2 Critical Diameter Calculation of ES_Insu

When the insulation thickness is varied, the outer surface temperature of insulation system varies and thereby the convection/radiation heat transfer rate varies, too.   Therefore, in actual insulation system the critical diameter calculated by the formula above varies as the insulation thickness varies.   The derivation of a formula for the varying critical diameter is not easy.

ES_Insu follows the variation of heat transfer rate per unit length of cylinder(pipe) insulation system(QLF) during [Conditional Calculation] and finds a approximate critical diameter.

ES_Insu calculates or finds the critical diameter as below.

1) User Input of Convection/Radiation Heat Transfer Rate

Even though the thermal conductivity changes depending on the insulation temperature, the change is negligible and the thermal conductivity can be assumed as constant for insulation thickness variation.

The convection/radiation heat transfer rate is also constant regardless of surface temperature because of user input.   Therefore, the critical diameter is constant for insulation thickness variation and calculated by the formula above.

In this case, ES_Insu calculates the critical diameter by the formula above and presents a definite critical diameter.

2) Not User Input of Convection/Radiation Heat Transfer Rate

In the calculations below the variation of QLF can not be followed because they are not [Conditional Calculation] and the [Thickness Adjustment] in the [Calculation Set] window is not performed.

The critical diameter is presented as "Not Calculated" in the calculations.

- Not [Conditional Calculation]

- [Freeze hour] or [Freeze flow] in [Freeze Calculation]

In case of [Conditional Calculation] or [Target minimum freeze hour] in [Freeze Calculation], the critical diameter is followed during thickness adjustment and presented as below.

- In case that the QLF value continues decreasing till the maximum thickness during thickness adjustment, the critical diameter must exist below the starting diameter.    In this case, the critical diameter is presented as located below the starting diameter. (< Starting Diameter)

- In case that the QLF value continues increasing till the maximum thickness during thickness adjustment, the critical diameter must exist above the maximum diameter.    In this case, the critical diameter is presented as located above the maximum diameter. (> The Maximum Diameter)

- In case that the QLF value has a turning point from increasing to decreasing within the maximum thickness during thickness adjustment, the critical diameter must exist at the turning point.   ES_Insu presents the critical diameter as the median value of the two diameters located before and after the turning point, but with "App.(Approximately) prefixed.   In some cases, there are two turning points and this means there are two critical diameters.   ENGSoft Inc. did not investigated the reason, but ES_Insu presents the two critical diameters in [Text Output] window.

ES_Insu does not present the critical diameter for [Range Calculation for Fluid Temperature].

The exact critical diameter within the maximum range may be obtained by running ES_Insu software by setting the [Adjustment step] of [Thickness Adjustment] at the accuracy the user wants.

 

 3. Major Screens   (TOC)

3.1 Main Screen of Plate(Equipment)

Main screen of plate(equipment) consists of three input frames, i.e.a temperature frame, an insulation frame and a convection/radiation heat transfer rate frame.

Temperature Frame

There are text boxes for fluid temperature inside of plate(equipment) and ambient temperature.   

Insulation Frame

There are a command button with insulation layer serial number, a combo box for insulation selection and a text box for insulation thickness input.   The [Thick input..] command button at the bottom is for cylinder(pipe) use only.

Clicking the command button with insulation layer serial number pops up the window for editing of the thermal conductivity of insulation used in the calculation.  Details about the editing is described below.

In the combo box for insulation selection, the user can select an insulation among the insulation list which has been saved in a file.   There are two ways for saving the thermal conductivity of insulation.   One is to save as a part of the calculation file itself and the other is to save in a common insulation file called as 'ES_InsuK.esd" and saved in a [common] sub-directory.   The thermal conductivity saved as a part of the calculation itself can be used only for the calculation and can not be used in other calculation.   On the other hand, the thermal conductivity saved in the common file can be used commonly in every calculation and be added or edited in a separate window which pops up by clicking the Menu [Set]-[Edit/Insert of Insulation List].   Details of the window is described below.

The insulation name can be edited in the combo box itself.  However this editing is not effective and meaningless.  The insulation name should be edited in the window poping up by clicking the command button of insulation layer number.

The layer number can be extended to seven in the Menu [Set]-[Calculation Set]

Convection/Radiation Heat Transfer Rate Frame

This frame is to input the data for convection/radiation heat transfer rate at insulation surface.    In the frame, by clicking the check boxes, the heat transfer rate or the emissivity can be input by user.  For details about the shape factor, please refer to ASTM C680.

3.2 Main Screen of Cylinder(Pipe)

Selection of calculation type, i.e.plate(equipment) or cyclinger(pipe), is done at the Menu [Set]-[Calculation Set].

The screen above is for calculation of 7 layer cylinder insulation system satisfying 60 oC target insulation surface temperature and economic thickness for the fluid temperature ranging from 100 oC to 600 oC by 50 oC step.

Temperature Frame

At the top of the frame the labels indicating the economic thickness and temperature range calculation is shown and the underneath frame shows the target surface temperature.   If the user selects heat density as the target value, the target heat density is shown in the frame.   These kinds of economic thickness and range calculation is available in plate(equipment), too.

Pipe Frame

In the Pipe Frame at the left side bottom of the window, a combo box is located for selecting the pipe ND from 1/2 inch to 26 inch.   The pipe OD is shown automatically in the left side text boxt when the user select the pipe ND.   The pipe ND is shown always in inch unit, whereas the pipe OD is shown in the unit the user selected that is shown underneath the frame title.

In temperature range calculation, the calculation is performed automatically from 1/2 inch to 26 inch pipe OD for the temperature range specified by the user.   Therefore, in case of temperature range calculation, the selection of pipe OD in the pipe ND combo box is meaningless.

Insulation Frame

The Insulation Frame of cylinder is same with that of plate.   Only difference is that the cylinder thickness can be input using the nominal insulation thickness specified in ASTM C585-90, in addition to the user direct input method.   The cylinder thickness method selection can be done in the Calculation Set Window by clicking the Menu [Set]-[Calculation Set] and the screen shown above is the thickness input according to ASTM C585-90.    If the user select the user direct input method, the command button of [Thick input..] is activated and the user can edit the cylinder insulation thickness in a window called [Cylinder(Pipe) Insulation Thickness Dimension Input] to be popped up by clicking the command button.   Details of the window is described below.

Convection/Radiation Heat Transfer Rate Frame

The frame is same with that of the plate(equipment) above.

 

3.3 Main Screen of Cylinder(Pipe) - Freezing Calculation

Freezing calculation is performed only for cylinder(pipe).

In the freezing calculation, the liquid quantity inside of the cylinder has an effect on the calculation.   Therefore, a command button with the name of [Sch/ID select..] is provided additionally on the Pipe Frame.   By clicking the command button, a pipe selection window pops up and the user can select a pipe there.  And then by closing the window using [OK] command, the pipe schedule and ID are automatically input on the relevant text boxes in the Pipe Frame.  The pipe schedule and ID can be edited only by clicking the [Sch/ID select..] command button.

One thing for the user to note is that the pipe schedule and ID selection is performed separately from the pipe ND and OD selection.   Therefore, the user should be careful in selecting the same ND pipe in both selections.   If the user selected different ND pipe, ES_Insu warns the same.

Other frames are just same with the frames described above for the main screen of cylinder(pipe).  

 The screen shown above is with the insulation thickness input by the user and shows the command button of [Thck input..] activated.

 

3.4 Calculation Set Screen

The Calculation Set screen is activated by clicking the Menu [Set]-[Calculation Set..] and the set content is self-explanatory.

Thickness Adjustment Frame

[Target Calculation] and [Economic Thick Calculation] require insulation thickness adjustment to find out the thickness satisfying the condition given.   ES_Insu adjusts the thickness only by increasing from the current thickness set in the main screen by the step to the maximum thickness/layer set in this screen.  The thickness adjustment starts from the layer set in this screen.   If the condition given was not satisfied at the maximum thickness of the last layer, ES_Insu flags a message with such contents.    In the case, the calculation results at the maximum thickness of the last layer are provided.

Range Calculation for Fluid Temperature Frame

In this frame the maximum and minimum temperatures with the step are set.   It is noted that the maximum number of temperatures to be calculated is limited to 20.

 If [Adjustment step] is too small, it takes time.

When [Range Calculation for Fluid Temperature] is selected in [Calculation Set] screen, every warning message is not flagged.   Instead, the finding of target thickness is flagged as "Yes" or "No" in [Text Output] screen.

In cylinder(pipe) insulation there is a insulation diameter at which the heat loss through insulation starts to increase as the insulation thickness increases.    The OD of cylinder(pipe) insulation where the heat loss starts to increase is called as a Critical Diameter.     In case of cylinder insulation, the critical diameter should be less than the OD of cylinder(pipe) so that the increase of insulation thickness decreases the heat loss.   ES_Insu finds out the Critical Diameter by that the insulation surface temperature increases by 0.1% from previous insulation temperature during the step increase of insulation thickness, and flags a critical warning message.

 

3.4.1 Economic Conditions Screen

This screen pops up when the user presses the [Economic conditions..] command button of [Calculation Set] screen and  is used to input the economic conditions to be used for [Economic Thickness Calculation].

The first radio button in [Insulation Installation Cost] frame is for input of the cost by the user and the second radio button is for the software to calculate the cost by the method of KS F2803 built in.    The currency used in this screen can be selected in the [Currency] screen below.   In the countries other than Korea, it is recommended to use the first radio button rather than the second.

 

 3.4.2 Freeze Condition Screen

This screen pops up when the user presses the [Freeze condition..] command button of [Calculation Set] screen and  is used to input the freeze conditions to be used for [Freeze Calculation].   The default values when the screen pops up first time are the values of water having described in ASHRAE handbook.

 

 3.5 Cylinder(Pipe) Insulation Thickness Dimension Input Screen

 

This input screen is for the user to edit the insulation thickness dimension when the [User input] radio button of [Cylinder(Pipe) Dimension] frame is selected in [Calculation Set] screen above.   This screen pops up when the user selects [Thick input..] command button of [Insulation] frame in the main screen. 

In the screen, the user can edit the nominal thickness [Nom. Thick], insulation ID [Insu ID] and OD [Insu OD].   [Thickness Calculation] command button is to calculate the thickness [Thick] by the insulation ID and OD the user inputs.   If there are any discrepancies in the user inputs, the software flags relevant error message.    The thickness calculation with error flagging is performed also by pressing the [OK] command button without pressing the [Thickness Calculation] command button.   The nominal thickness the user inputs is used as it is.   Therefore, the user may nominate the thickness as he want to.

 

3.6 Thermal Conductivity Edit Screen of a Insulation Layer

This screen is for the user to edit the thermal conductivity of a layer of insulation system and pops up when the user presses the layer number command button of [Insulation] frame of the main screen.

There are five formulae to be used in ES_Insu software.  The first three are those used in ASTM C680 and the second two are those used by insulation manufacturers.

One thing to be noted by the user is that the units of thermal conductivity are independent of those of main calculation.  The reason why ES_Insu uses a independent unit system is that the unit conversion of thermal conductivity is not simple.

 

3.7 Edit/Insert Screen of Insulation List(File)

This screen is for the user to edit or insert the insulation list(file) to be listed in the [Insulation] combo box of [Insulation] frame of the main screen.   This screen pops up when the user selects the Menu [Set]-[Edit/Insert Insulation List].

 

3.8 Currency Screen

 This screen pops up when the user selects the Menu [Set]-[Currency Set...] and  is used to select/add/edit/delete of the currencies to be used for [Economic Thickness Calculation].   Among the currencies, the "Korean Won" can not be deleted for its use in "Automatic Insulation Installation Cost according to KS F2803".

 

3.9 Calculation Result Screen

This screen shows the major calculation results automatically on completion of each calculation.   This screen has been prepared to avoid the inconvenience of popping up the [Text Output] screen for each calculation.   However, this screen does not pop up for [Range Calculation for Fluid Temperature] in [Calculation Set] screen.

 

3.10 Text Output Screen

[Text Output] screen shows the calculation result details and can be printed.

The screen shown above is for the [Range Calculation for Fluid Temperature] satisfying a target temperature(60 oC) and economics from 100 oC to 600 oC fluid temperature in 50 oC step.

 

4. Test Results for Sample Problems of ASTM C680 (TOC)

4.1 Thermal Conductivity Formulae in ASTM C680

The sample problems of ASTM C680 use three kinds of insulation with the following thermal conductivity and the unit of thermal conductivity is Btu-in./hr-ft^2-oF.

1) Formulae with Btu-in./hr-ft^2-oF unit

Type 1 Material

k = 0.4 + 0.105E-03 * T + 0.286E-06 * T^2

Type 2 Material

k = e^(-1.62 + 0.212E-02 * T)

Type 3 Material

k = 0.201 + 0.00039 * T; T < -25

k = 0.182 - 0.00038* T; -25 < T < 50

k = 0.141 + 0.00037 * T; T > 50

where,

k

: Thermal conductivity, Btu-in./hr-ft^2-oF

 

T

: Insulation temperature, oF

 Since ES_Insu does not have the Btu-in./hr-ft^2-oF unit, the formulae above have been converted into the formulae with Btu/hr-ft-oF unit as below.

1) Formulae with Btu/hr-ft-oF unit converted

Type 1 Material

k = 3.333333E-02 + 8.75E-06 * T + 2.38333E-08 * T^2

Type 2 Material

k = e^(-4.10491 + 0.212E-02 * T)

Type 3 Material

k = 0.01675 + 0.0000325 * T; T < -25

k = 0.0151667 - 0.0000317* T; -25 < T < 50

k = 0.01175 + 0.0000308 * T; T > 50

where,

k

: Thermal conductivity, Btu/hr-ft-oF

 

T

: Insulation temperature, oF

 

4.2 Sample Problem of Plate(Equipment)

1) Sample Problem 1

No. of insulation layer

: 1

Insulation

: Type 2 Material

Fluid temperature

: 450 oF

Ambient temperature

: 10 oF

Surface coefficient (Convection/radiation heat transfer rate)

: 6 Btu/hr-ft^2-oF

Insulation thickness

: 4 inch

Description

ASTM C680

ES_Insu

Total heat flux(density), Btu/hr-ft^2

36.5

36.4

Conductivity, Btu/hr-ft-oF

0.0281

0.028

Resistance, hr-ft^2-oF/Btu

11.88

11.91

Surface temperature, oF

16.09

16.07

 

4.3 Sample Problem of Cylinder(Pipe)

 1) Sample Problem 2

No. of insulation layer

: 1

Insulation

: Type 1 Material

Pipe ND/OD

: 3/3.5 inch

Fluid temperature

: 800 oF

Ambient temperature

: 80 oF

Surface coefficient (Convection/radiation heat transfer rate)

: 1.76 Btu/hr-ft^2-oF

Insulation thickness

: 2 inch (acc. to ASTM C585)

Description

ASTM C680

ES_Insu

.Total heat flux(loss) per unit length, Btu/hr-ft

230.5

232.8

Conductivity, Btu/hr-ft-oF

0.0437

0.0437

Resistance, hr-ft^2-oF/Btu

5.67

5.6

Surface temperature, oF

145.6

146.27

 

2) Sample Problem 3

No. of insulation layer

: 1

Insulation

: Type 1 Material

Pipe ND/OD

: 3/3.5 inch

Fluid temperature

: 800 oF

Ambient temperature

: 80 oF

Emittance (emissivity)

: 0.9

Wind speed/Shape factor

: 0.0 MPH/Horizontal

Insulation thickness

: 3 inch (acc. to ASTM C585)

Description

ASTM C680

ES_Insu

Surface coefficient, Btu/hr-ft^2-oF

1.76

1.76

Total heat flux(loss) per unit length, Btu/hr-ft

182.7

184.2

Conductivity, Btu/hr-ft-oF

0.0433

0.0433

Resistance, hr-ft^2-oF/Btu

9.36

9.28

Surface temperature, oF

121.24

121.52

 

3) Sample Problem 4

No. of insulation layer

: 3

Insulation

: Type 1 Material(Layer 1) / Type 2 Material(Layer 2) / Type 3 Material(Layer 3)

Pipe ND/OD

: 4/4.5 inch

Fluid temperature

: 600 oF

Ambient temperature

: -100 oF

Emittance (emissivity)

: 0.9

Wind speed/Shape factor

: 5 MPH/Horizontal

Insulation thickness

: 3 inch / 2 inch / 1.5 inch (acc. to ASTM C585)

Description

ASTM C680

ES_Insu

Surface coefficient, Btu/hr-ft^2-oF

1.57

1.58

Total heat flux(loss) per unit length, Btu/hr-ft

93.2

94.7

Conductivity, Btu/hr-ft-oF

0.0422/0.0252/0.0147

0.0422/0.025/0.0146

Resistance, hr-ft^2-oF/Btu

15.48/9.93/9.35

15.38/9.77/9.04

Surface temperature, oF

293.87/97.41/-87.42

290.93/94.47/-87.25

By the test results above, the results of ES_Insu is same with those of ASTM C680 within reasonable accuracy.   However, the results of pipe show a little bit larger difference than those of equipment.

When reviewing the conductivity and resistance values, we can find that the results of ES_Insu are more accurate than those of ASTM C680.

In the Sample Problem 4 above, we can calculate as below the resistance of the third layer from the conductivity using the formula (20) of ASTM C680.      According to ASTM C585, the ID and OD of the third insulation layer are 15.09 inch and 18 inch respectively.  The conductivity of the third layer of both results is same as 0.0147 Btu/hr-ft-oF which equals to 0.176 Btu-in./hr-ft^2-oF, the result value of ASTM C680.

    18 / 2 / 12 x Ln(18 / 15.09) / 0.0147 = 9.00

The resistance result of ASTM C680 is 9.35.   That is, ASTM C680 has its own discrepancy and rather the results of ES_Insu has consistency.

Consequently the calculation results of ES_Insu software are reliable.

 

5. Check of ES_Insu Results by Calculation  (TOC)

The results of ES_Insu software have been checked by calculation using Microsoft(R) Excel(R) software and the check results are as below.

No. of insulation layer

: 1

Insulation

: Rock wool cylinder

Pipe ND/OD

: 6 inch / 168.3 mm

Fluid temperature

: 600 oC

Ambient temperature

: 20 oC

Surface coefficient (Convection/radiation heat transfer rate)

: 12 W/m2-K

Insulation thickness

: 140 mm

Description

ES_Insu

Calculation

Surface temperature, oC

42.53

42.53

Conductivity, W/m-oK

0.10646

0.10667

Resistance by conductivity, m2-oK/W

2.0615

2.056

Resistance by surface coefficient, m2-oK/W

 

0.083

Total resistance, m2-oK/W

 

2.140

Heat density through insulation, W/m2

270.42

271.1

Heat density through surface, W/m2

 

270.4

Heat density of insulation system, W/m2

 

271.1

Heat loss per unit length, W/m

380.34

382.4

The check has been performed from the insulation surface temperature got from ES_Insu software run.

The picture of Excel(R) calculation results are as below.

In the Excel(R) sheet above, the cells from E1 through E13 and E16 are input cells and the expressions of other cells in "E" column are as below.

Conductivity(E15), W/m-K

    =(C6*(A6-E1)+E6*(A6^2-E1^2)/2+C7*(E2-A6)+E7*(E2^2-A6^2)/2+G7*(E2^3-A6^2)/3)/(E2-E1)

Resistance by conductivity(E18), m2-K/W

    =E13/2*LN(E13/E11)/E15/1000

Resistance by convection/radiation(E19), m2-K/W

    =1/E16

Total resistance(E20), m2-K/W

    =E18+E19

Heat density through insulation(E22), W/m2 :

    =(E2-E1)/E18

Heat density through surface(E23), W/m2 :

    =(E1-E3)/E19

Total heat density(E24), W/m2 :

    =(E2-E3)/E20

Heat transfer rate per unit length,  W/m :

    =E22*3.141592*E13/1000

Although ES_Insu software and the Excel(R) sheet above use identical formulae, the results show a little differences.  It is presumed that the differences resulted from the difference of precision levels used in the programs.   ES_Insu calculates in single precision, while Excel(R) calculates in double precision.

Anyway, the results of ES_Insu software have been verified as correct by the check above.

 

6. Test Results for 1997 ASHRAE Fundamental Handbook (S)  (TOC)

Below are the test results of ES_Insu for freezing calculation in comparison with the Table 1 of Page 23.16 of 1997 ASHRAE Fundamental Handbook(SI).

Since the design condition of Table 1 of the Handbook specifies that the air film at surface of insulation is ignored, a relatively large value(1000000) of surface coefficient has been used in order to make the surface temperature same with the ambient temperature.

The freezing conditions of the liquid(water) are same with those of the Handbook, which are default values of ES_Insu software.

Since there is no reference for the insulation thickness in the Handbook, the thickness according to ASTM C585-90 has been used in ES_Insu run.

No. of insulation layer

: 1

Conductivity

: k = 0.043 W/m/K

Surface coefficient

: 1000000 W/m2-K

Fluid temperature

: 5.5 oC

Ambient temperature

: -28 oC

Steel Pipe ND, mm

Insulation Thickness, mm

Insulation Thickness, mm

Freezing Hours

(ASHRAE/ES_Insu)

Freezing Flow, g/s/m

(ASHRAE/ES_Insu)

50

75

100

50

75

100

15

0.27/0.26

0.32/0.31

0.36/0.35

0.23/0.23

0.19/0.19

0.16/0.17

100

4.07/3.97

5.43/5.30

6.54/6.40

0.77/0.78

0.53/0.54

0.42/0.43

200

9.59/9.35

13.3/12.97

16.5/16.13

1.79/1.75

1.03/1.02

0.76/0.75

300

15.4/15.14

12.7/12.41

27.4/27.06

3.71/3.78

1.69/1.71

1.14/1.15

Consequently the results of ES_Insu software are in line with the results of ASHRAE Handbook.

 

References :  (TOC)

1. ASTM C680-89, Standard Practice for Determination of Heat Gain or Loss and the Surface Temperatures of Insulated Pipe and Equipment Systems by the Use of a Computer Program

2. ASTM C585-90, Standard Practice for Inner and Outer Diameters of Rigid Thermal Insulation for Nominal Sizes of Pipe and Tubing (NPS System)

3. 1997 ASHRAE Fundamental Handbook (SI)

4. KS F2803 - 1996, Standard Practice for Thermal Insulation Works


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