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Thread: Software Estimates Bulk Solid Behaviour

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    Teus Tuinenburg

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    Mathematical description of State diagram.

    Is this derivation correct?

    Internal gas energy = function (m_gas * dp)

    Material loss energy = function (1/2 * K *m_mat * v^2 * L/D)

    SLR = (m_mat)/(m_gas)
    m_mat = SLR * m_gas

    Resulting in:

    Internal gas energy = function (m_gas * dp)

    Material loss energy = function (1/2 * K *= SLR * m_gas * v^2 * L/D)

    thus:
    (m_gas * dp) # (1/2 * K * SLR * m_gas * v^2 * L/D)

    Re = (rho_gas * v * D)/(eta_gas)

    v = (Re * eta_gas) / (rho_gas * D)

    Combined:

    (m_gas * dp) # (1/2 * K * SLR * m_gas * ((Re * eta_gas) / (rho_gas * D))^2 * L/D)

    Worked out:

    SQRT(SLR) = [SQRT(2)/(Re*SQRT(K))] * SQRT[(dp*D^3*rho_gas^2)/(eta_gas^2 * L)]

    or

    SQRT[(dp*D^3*rho_gas^2)/(eta_gas^2 * L)] = SQRT(SLR * K/2) * Re

    This formula is representing a line in the State Diagram for a specific material (K) and a specific SLR.

    Conclusion:
    - The state diagram accounts for material and SLR.
    - By calculating “SQRT[(dp*D^3*rho_gas^2)/(eta_gas^2 * L)]” and “Re” the installation parameter “SQRT(SLR * K/2) “ is determined, although SLR and K are not directly known.

    Note:
    In this derivation, only the pressure drop, caused by material losses, is used and the other pressure drops (Elevation, gas, suspension, acceleration, intake, filter, etc.) are ignored, although the total pressure drop is entered in the formula.
    Applying the principle of physical similarity, the factor K is acting as the similarity factor.
    Teus

  2. Hi, Teus!

    For this I can only confirm the following: When transferring the operating data, I could discover no subliminal functional dependencies of SLR or the type of bulk material. The bulk material throughput in Kg / h remained as the only parameter, quite independent of other influencing variables.

    Manfred Heyde

  3. Note:
    As far as my approach is concerned, it can be found at the following link, that leads to Google Drive. From there you can download as zip file all programs as well as documents in English and German together.
    https://drive.google.com/drive/folde...lRmVXlhR1dabFk

    Manfred Heyde

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