Penetration Depth

Penetration Depth
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The penetration depth is calculated according to equation (2), which shows how it depends on the
dielectric properties of the material. The penetration depth is used to denote the depth at which
the power density has decreased to 37 % of its initial value at the surface.
Materials with higher loss factor ε r ’’ (imaginary part of the complex permittivity)
show faster microwave energy absorption. The power density will decrease exponentially from the surface to the core region.
Figure 1. Penetration depth (denoted with blue x) of the electric wave
decreases with increasing frequency. The left side represents air, the right side a material.
f = frequency, measured in Hz
ε O absolute dielectric constant (DC) = 8,85x10-12 As/Vm
с = 3x10 10 cm/s speed of light
Ε = electrical field strength, measured in V/m
ε = ε O * ( ε r ’ - j ε r ’’ ), complex dielectric constant
tan δ = ε r ’’/ε r ’
δ = dielectric loss angle, measured in degrees
λ 0 = wavelength, measured in, λ 0 =c / f
Table 1 shows the penetration depth values of various materials. It should be noted that the penetration
depth of the electric field strength is sometimes reported in the literature, with a value which is twice as high.
Table 1. Penetration depths of microwave energy of various materials at 2450MHz
Products with huge dimensions and high loss factor may occasionally overheat within a considerably thick layer on the outer surface. To prevent such a phenomenon the power density should be chosen so that enough time is provided for the essential heat exchange between boundary and core. If the thickness of the material is less than the penetration depth, only a fraction of the supplied energy will be absorbed.
Nevertheless, this only applies if the energy, which is not absorbed, spread away from the material after leaving it. The unabsorbed microwave radiation is, however, reflected from the metal walls of the application chamber and penetrates the material more than once.
Another consideration of the power density needed for microwave heating is that appropriate field strength values must be maintained inside the application chamber. Under atmospheric conditions, these are generally several orders of magnitude smaller than the breakdown strength for dry air (30 kV/cm). In the case of vacuum applications, or whenever the air inside the applicator is very moist, the electric field strength should be limited to an extent that prevents ionisation of the air, in order to avoid enormous damages that could be caused to both product and equipment.
By using microwave energy, heat is generated inside the product volume by directly transforming the electromagnetic energy into molecular kinetic energy.
Member of VDMA | AMPERE | ISPE | IEC | DIN / VDE Working Group 'Dielectric Heating' K362

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5 years, 8 months ago

thermodynamics acoustics terminology

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What is meant by thermal penetration depth ? I am doing a project on Thermoacoustics . while researching I came across about thermal penetration depth.I searched over the net but i didn't get a clear idea so please explain me about this and also give me an insight about what are the other applications of this.
As you understand from the term itself it has to do with the penetration of heat into a material.
Suppose you have a sufficiently thick material (size D ) of uniform temperature ( T 0 ), where you apply a constant (different) temperature ( T 1 ) at one side. Eventually, your whole material will be at this new temperature T 1 . But before this happens, that is, as long as the temperature of the other side of the block is still T 0 , we can talk about penetration.
The penetration depth is the depth to which the temperature has significantly changed, often, this is approximated with
In this context, also the Fourier number is relevant, as it relates the penetration depth with the domain length scale, i.e.
For penetration theory to be applicable (initial stage), F o < 1 .
In an unbound fluid it is sufficient to presume the adiabatic behavior (i.e. no heat transfer and "conservation of enthropy"). BUT! When we examine the flow in the nearby of walls and other real solid boundaries there is a significant energy dissipation due to viscosity, friction etc. etc. connected with thermoacoustical effects. E.g. if we have a duct wide enough, than along its axes the field will be (almost) adiabatic but the boundary layer (neighborhood of walls) will be more complicated. The penetration depth then tells what is the distance from a wall enough to presume the flow to be adiabatic.
I think the answer from Bernard seems correct, but I seem to remember a formula for penetration velocity. Pira appears to confuse boundary layer thickness with penetration depth, which to my memory is only for solid heat conduction.
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The penetration depth must be sufficient for the transfer of the ULS Moment, Shear, and Axial to the soil without: (1) without exceeding the soil (2) exceeding the allowable deflection
Allowable deflection limits: – Maximum deflection at pile toe : ≤ 0.02m – Maximum deflection at seabed: ~ 0.03·Dpile=0.19 m – Rotation at seabed : ≤ 0.1°
The check is done of the M, V, N as calculated at seabed level (section D). The required penetration depth for both factor sets (a) and (b) is calculated. The design load are: – Factor Set (A) : M=222 MNm, V=6.4 MN, N=15.7 MN – Factor Set (B) : M=300 MNm, V=8.6 MN, N=12.8 MN
First, we calculate the penetration depth to resist the Moment and Shear. Then we check if the depth is enough to resist the axial load and if need we further increase.
We used the tools below to calculate the nonlinear response of the pile for the design loads at seabed level. The input is the soil characteristics (su, γ, φ, ε). The results are the displacements of the pile. We evaluate them against the criteria shown in Table 23 and if the displacements are higher, we increase the penetration depth or the pile diameter. We assume that scour protection is used so the total pile length contributes to the bearing capacity. The required penetration depth was found to be 40 m.
Regarding the axial capacity, it is easy to show that the penetration depth of 40m is sufficient. Following the API (2000) Main Text Method for predicting the ultimately unit shaft resistance in sand we derive the result shown in Table 24. We assumed that the soil is uniform (silty-sand) with an ultimate unit shaft resistance equal to the average value obtained from the soil investigation. This assumption is logical and since the soil properties over the range of penetration depth considered here do not vary much.
From the soil investigation data, we can see that the site can be divided in three areas with regard to the ultimate unit shaft resistance of the soil.
Unplugged failure is assumed and considered only the shaft resistance of the pile
For the three soil types mentioned above the axial capacity of the pile is calculated.
Result: The external shaft resistance is in all cases higher than the vertical design load at the foundation. In area Β, although the capacity is sufficient, an increase in penetration depth might be desirable in order to increase the factor of safety.
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τ sf,ult , average of top 50 m [MPa]

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